Maa-6.280 GIS and geodetic measurementsmvermeer/GIS-GPS_en.pdf · Maa-6.280 GIS and geodetic...

Maa-6.280 GIS and geodetic measurements

Martin Vermeer

8. marraskuuta 2010

Course Description

Workload 2 crTeaching Period I-IILearning Outcomes After completing the course, the student

• knows how to use geodetic tools, esp. GPS as differentional positioning or real-time kine-matic positioning, in practical mapping work for collecting data to process and put intogeographic information systems.• Can use and understands how to use both differential GPS and RTK in mapping work.• Knows about use of GNSS measurements in connection with geophysical measurements.

Content Use of GNSS in connection with GIS: GNSS in the production of spatial data, measure-ment methods, equipment and examples of applications.In the essay exercise, some fresh popular magazine articles on a GPS and GIS subject areanalyzed and presented, with the aim of learning something about the state of the art and atthe same time training for research and presentation collaboration.

Foreknowledge Maa-6.279 or Maa-6.2279 (obligatory for geomatics students, recommended forothers).

Equivalences Replaces course Maa-6.280.Target Group

Completion Completion in full consists of the exam, the outdoor exercises, and the essay exerci-se.

Workload by Component

• Lectures 10 × 2 h = 20 h• Independent study 22 h• Outdoor exercises 3×2 h = 6• Essay exercise 6 h• Total 54 h

Grading The grade of the exam becomes the grade of the course, 1-5Study Materials Lecture notesTeaching Language EnglishCourse Staff and Contact Info Martin Vermeer, room M309, name @tkk.fiReception times By agreementCEFR-taso

Lisätietoja

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Sisältö

1 Fundamentals of GIS and GPS 61.1 Geographic information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.1.1 Location data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.1.2 Property data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.1.2.1 Distinctive property information . . . . . . . . . . . . . . . . . . . . . . 61.1.2.2 Locational property information . . . . . . . . . . . . . . . . . . . . . . 71.1.2.3 Temporal property information . . . . . . . . . . . . . . . . . . . . . . . 71.1.2.4 Descriptive property information . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Geographic information systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.1 Geographical data base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.2 Spatial data standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.3 The Finnish situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Quality of spatial data, quality of co-ordinates . . . . . . . . . . . . . . . . . . . . . . . 81.4 Acronyms, concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5 The GPS system and measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5.1 Parts of the GPS system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5.2 GPS satellites and signal structure . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5.3 GPS receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.5.4 GPS observations in mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Technologies 162.1 Receiver technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.1 Geodetic recievers vs. inexpensive receivers . . . . . . . . . . . . . . . . . . . . . 162.1.2 Carrier phase measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1.3 Processor, firmware, programmability . . . . . . . . . . . . . . . . . . . . . . . . 172.1.4 Software receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Spatial data technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.1 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.2 Alternatives and applications for data collectors . . . . . . . . . . . . . . . . . . 182.2.3 Map background and spatial data base . . . . . . . . . . . . . . . . . . . . . . . 192.2.4 Various use modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Data communication technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.1 Between receiver and data collector . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.2 Between rover and base station . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.3 Obtaining information from the Internet . . . . . . . . . . . . . . . . . . . . . . 202.3.4 Mobile networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4.1 The RTCM SC-104 standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Carrier phase measurements and geospatial applications 233.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Error sources of GPS carrier phase measurements . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Satellite orbit error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.2 Satellite clock error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.3 The ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.4 The troposphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.5 Multipath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.6 Receiver noise level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Description and processing of observations . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.1 Phase measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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Sisältö

3.3.2 The RTCM protocol and carrier phases . . . . . . . . . . . . . . . . . . . . . . . 263.3.3 NTRIP protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.4 Resolving ambiguities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.5 Different ambiguity resolution methods . . . . . . . . . . . . . . . . . . . . . . . 273.3.6 Phase based pseudorange smoothing . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4 Measurement methods and geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.4.1 One base station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.4.2 The case of three base stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.4.4 Modelling the atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.5 Technical implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4.5.1 “Virtual base station” . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4.5.2 Network computations in the server . . . . . . . . . . . . . . . . . . . . 333.4.5.3 Network computation in the client . . . . . . . . . . . . . . . . . . . . . 33

3.5 Practical implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.5.1 The VRS-RTK solution by Geotrim . . . . . . . . . . . . . . . . . . . . . . . . . . 343.5.2 The tests by the Finnish Geodetic Institute . . . . . . . . . . . . . . . . . . . . . 343.5.3 Other use experiences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.5.4 Furthermore. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Code observations and spatial applications 364.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.1.1 Collection of geospatial data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.1.2 Maintenance of geospatial data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.1.3 Mobile geospatial data systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.1.4 Location based services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.1.5 The RTCM standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1.6 Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1.7 Satellite orbit error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1.8 Satellite clock error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.9 Ionosphere, troposphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.10 Multipath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.11 Noise level of device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.12 SBAS systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.13 Omnistar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.14 The service of the Finnish Maritime Administration . . . . . . . . . . . . . . . . 384.1.15 The Fokus service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Measurement methods and geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3 Practical implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3.1 GIS applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 New technology: GNSS systems 405.1 GPS modernization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1.1 Satellite types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.1.2 New codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.1.3 New frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2 GLONASS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2.1 Players . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2.2 System description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.3 Galileo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.3.1 Players . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.3.2 Satellites and orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.3.3 System description, components . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.3.4 Various services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.4 The Chinese Beidou system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.4.1 Beidou 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.4.2 Beidou 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6 New technology: SBAS systems 44

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Sisältö

6.1 Integrity and Safety-of-Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.2 WAAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6.2.1 LAAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.3 MSAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.4 EGNOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.4.1 EGNOS ground segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.5 QZSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.6 The SiSNET experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7 New technology: attitude determination 497.1 Inertial device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497.2 GNSS multi-antenna system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497.3 MEMS (Microelectronic Mechanical System) . . . . . . . . . . . . . . . . . . . . . . . . 51

7.3.1 Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517.3.2 Rotation sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.4 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

8 GNSS, GIS ja geofysiikka 53

5

1 Fundamentals of GIS and GPS

1.1 Geographic information

[6] defines geographic information as follows:“Map and register information in digital form, describing, e.g.:• natural resources• forms of the Earth’s surface• land use• habitation• economic activities• traffic networks• the state of the environment.”

The above things are visible in principle in the landscape. I would add to this the following, moreculture bound, things:• Land ownership rights and other objective rights (cadastre)• The planned purpose of use of land (zoning)• The names of places and objects in various languages, also traditional• Historical details connected to places

Geographic information consists of location data and property data.

1.1.1 Location data

Location data can be co-ordinates, geometry data and topology data.The location of a point object can be described by two or three co-ordinates of place, e.g., in Finlandkkj x,y and N60 H. For describing the location of a line or area shaped object one needs several co-ordinate sets describing its constituent points. Often the co-ordinates of a “representative point1”or centroid is given, and the shape and size are described in other ways.

1.1.2 Property data

. . . or technically, attribute data.Attributes may be distinctive, locational, temporal and descriptive. Attribute data is the whole ofthe data concerning a certain object. E.g.:• the identifying number, postal address, year of construction and intended use of a building• the road number, municipality identifier, year and type of paving and condition

1.1.2.1 Distinctive property information

Information which distinguishes or identifies the object uniquely: typically an identifying code, e.g.,the building number, cadastral number of a parcel, the road number of a road, the name of a lake(+ if needed, the name of the locality – there’s a lot of Pyhäjärvi-named lakes), etc.

1. . . like the front door of a building

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1.1.2.2 Locational property information

E.g., the street address, i.e., the data according an address system referring to the object; or infor-mation relating to an object located by co-ordinates.Also co-ordinates may be regarded as locational property data, although this is not customary;sometimes heights are registered as an attribute in a geographic data base, if the system acceptsonly two location co-ordinates.

1.1.2.3 Temporal property information

Information positioned on the time axis relating to the object or an event or observation relating tothe object.E.g., the construction or base renovation year of a building; construction or paving or base reno-vation year of a road; the day the ice breaks on a lake; the cleanliness of swimming water duringsummer; etc.

1.1.2.4 Descriptive property information

This may be data describing al other properties of the object. E.g., the intended use of a building;type of paving of a road; the colours announced in the building permit for a façade; the radoncontent of a well; etc. etc. etc.

1.2 Geographic information systems

A geographic information system is according to [6]:• An information processing system in which geographic data is being processed• An information processing system supporting

1. collection of data2. management and maintenance of data3. processing and analysis of data4. the output of data in various forms, e.g., graphically and textually, both digitally and in

analogue form

1.2.1 Geographical data base

Clearly, the central component of every geographic information system is a data base. This can bea simple flat file, even plain text, if the amount of data is small. In other cases, a “real” data baseis used, i.e., an SQL based relational data base.We may mention the “spatial SQL” developed by Oracle: “Oracle Spatial”, a plug-in for the data ba-se, which enables the efficient processing of spatial data. Cf. http://www.orafaq.com/faqsdo.htm.

1.2.2 Spatial data standards

Open Geospatial Consortium (http://www.opengeospatial.org/, earlier Open GIS Consor-tium) has been an active developer of geospatial standards.Among other things, GML, “geography mark-up language” (GML standard http://opengis.net/gml/), which is currently in drafting. Under the name ISO/TC 211/PT 19136 it is an ISO(International Standards Organization) candidate standard. GML is a variant of XML (ExtensibleMark-up Language) for spatial data use.

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http://www.orafaq.com/faqsdo.htm

http://www.orafaq.com/faqsdo.htm

http://www.opengeospatial.org/

http://opengis.net/gml/

http://opengis.net/gml/


1

1010

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1

0

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0

1

0

1

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= 100y

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Kuva 1.1: One way of constructing a spatial object. n is a number consisting of the bits in x, y. Iftwo objects n1, n2 are numerically close to each other, they are also close in the x, y plane,and conversely. The numbers n are used for indexing spatial objects

1.2.3 The Finnish situation

In Finland, spatial data systems are used in a great many organizations both in business and ingoverment administration. Spatial data systems may be, e.g.• Administrative registers; property registers, registers related to zoning• Planning systems, e.g., for infrastructural works• Control and optimization systems

As examples may be mentioned• The Finnish Land Administration System JAKO operated by the Finnish National Land Sur-

vey• The New (municipal) Real Estate Data System UKTJ• A system for the planning and monitoring of forest management, cutting and wood transport• A system for planning and monitoring construction (often CAD)

1.3 Quality of spatial data, quality of co-ordinates

The quality of spatial data is a broad field of study. It may be divided into the quality of locationdata and that of property (attribute) data.We will not discuss here the quality of property data. When location data is obtained throughgeodetic measurements, we must discuss the precision of the geodetic measurement process, butalso the precision of geodetic computation.One issue that is of central importance when studying the precision of location, is that of the datumof location data, or the used reference system.The ISO -standard 19111 “Spatial Referencing by Coordinates” defines:• Co-ordinate system (CS): a way to describe the location of points by means of co-ordinates

(abstractly).

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• Co-ordinate reference system (CRS): a way to connect co-ordinates with the Earth. Itsdefinition requires a co-ordinate system and a datum.

In international geodetic circles, especially IERS (International Earth Rotation and Reference Sys-tems Service) , also the following definitions are being used:• Co-ordinate system: a way to descibe points (abstractly). E.g., ITRS96, International Terre-

strial Reference System 1996.• Co-ordinate frame: here, the co-ordinates are connected to the Earth by way of geodetic mea-

surements. This process is called the realization of a CS. One CS may have several differentrealizations. E.g., ITRF96 (Int. Terrestrial Reference Frame 1996) is a realization of ITRS96.

We may say that the IERS term Coordinate System corresponds to the ISO concept of Coordina-te System and the ETRS concept of coordinate frame to the concept of Coordinate ReferenceSystem.In any case, co-ordinates obtained from real life are always relative to some datum, and that datummust be identified correctly.Between different datums (CRS, “frame”) we may perform a co-ordinate transformation. The pa-rameters of the transformation may be determined empirically, using a point set, the co-ordinatesof which are known in both systems. An often used transformation is the (seven-parameter) Hel-mert transformation. One should beware of using a transformation in an area for which it wasnot intended, e.g., an area where there are no points close by that were used in determining thetransformation.The OGC (Open Geospatial Consortium) has defined a standard “Coordinate Transformation Ser-vice Implementation Specification” (http://www.opengeospatial.org/standards/ct) for per-forming co-ordinate transformations in a way, that makes it possible for products from differentmanufacturers to work correctly together (interoperability). OGC also defines names for many geo-detic datums in use, so called WKT (Well Known Text). However, also other naming systems are inuse, e.g. the numbers used by the EPSG (European Petroleum Survey Group).At the address http://www.ncgia.ucsb.edu/globalgrids-book/specht/ one may find adescription of this standard and its possibilities for use. One possible use is setting up a trans-formation server; for this purpose there exists and Open GIS Web Map Server Interface Specifica-tion. Currently such an experimental server is in use at the Finnish Geodetic Institute: http://coordtrans.fgi.fi/.Exercise: Open Google Earth and find the streets view of the city of Vienna. Switch on the showing

of the street network.How much discrepancy is there between the background (aerial photography) street networkand the superimposed street network?

Exercise: repeat for different cities: choose a city the name of which starts with the first letter ofyour first name.

1.4 Acronyms, concepts

XML This mark-up language differs from HTML in this way, that it can be extended to describethe syntactic structures of documents from different professional fields in order to descri-be their content, rather than their graphical appearance. See http://herkules.oulu.fi/isbn951425242X/html/x1033.html. XML:ää kaavaillaan Internet-palvelujen ja -tiedon-siirron tehokkaaksi apuvälineeksi.

GML An XML variant for the spatial data profession.SQL “Structured Query Language”: A query language developed by IBM for interrogating relatio-

nal data bases.Relaatiotietokanta A data base into which data is stored in the form of “relations”, i.e., tables:

every table has a name, the rows of the table describe elements that are of the same type butnot identical, attributes of which describe the columns of the table.

As an example, we want to describe a municipal area where there are owners and parcels. If wewere to create two tables “Parcels” and “Owners”, they wouldn’t be neatly rectangular, because

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http://www.opengeospatial.org/standards/ct

http://www.ncgia.ucsb.edu/globalgrids-book/specht/

http://coordtrans.fgi.fi/

http://coordtrans.fgi.fi/

http://herkules.oulu.fi/isbn951425242X/html/x1033.html

http://herkules.oulu.fi/isbn951425242X/html/x1033.html


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Parcels

Ownership relationships

Owners

Kuva 1.2: An example of a relational data base

one person can own a variable number of parcels, and similarly, one parcel may be owned by avariable number of people. Also updating the data base would be complicated: we have to updatetwo non-rectangular tables. Direct access to the data isn’t possible in that case.In a relational data base, the situation would be described as follows:

1. We create a table “Ownership relationships”, containig two attribute fields: “Owners” and“Parcels”. Every ownership relationship, i.e., (owner, parcel) pair, can occur only once.

2. Additionally there may of course be (and always are) tables “Owners” and “parcels”, in whichthe other interesting properties of owners and parcels are registered as attributes.

Queries are done by SQL. E.g., “Output all parcels that have more than 3 owners”. One has totraverse the whole “Ownership relationships” table to compute, for every owner, how many parcelshe or she own, i.e., in how many “Ownership relationship” -records he or she occurs.However, these elementary operations can be implemented to be very fast, as the tables are rectan-gular. Also extending the tables with more columns is easy, and from the same material it is easyto produce different “views” for the user.Object-relational A relational data base, into which one may also store images, tables, multimedia

objects etc. Because these are of varying size, they are stored on the hard disc and the “coredata base” in memory only contains pointers to them.

JAKO is the SmallWorld based distributed real estate register application used by the FinnishNational Land Survey. The 30 gigabytes data base contains all Finnish real estate data, 10million real estate boundaries and 6 million boundary markers.

UKTJ The New Municipal Data System, the new spatial data project of Finland’s municipalities incollaboration with the National Land Survey.

CAD Computer Aided Design. Esim.If used for designing and mapping buildings, we may alsospeak of a spatial data system. E.g., AutoCAD, Bentley MicroStation.

1.5 The GPS system and measurements

1.5.1 Parts of the GPS system

The GPS system consists of three segments: the space, control and user segment. The space segmentconsists of at least 24, in practice 26-29 satellites, including “active spares”. Four orbital planes, ineach six satellites. The geometry, including satellite identities, repeats after 23h 56m (a siderealday, two GPS satellite orbital periods). The orbital inclination is 55◦.The satellites are of type Block I (original) and Block II (first one launched 1989). The newest typeis Block IIR.Due to the geometry, almost anywhere on Earth almost anytime we can see at least 4 satellitesabove the horizon, usually more.

10


Kuva 1.3: GPS constellation

Taulukko 1.1: Carrier waves of GPS signal

Carrier Frequency (MHz) Wavelength (cm) Multiple of basefrequency (10.23 MHz)

L1 1575.42 19.0 154×L2 1227.60 24.4 120×

More info: [5].The control segment consists of six tracking stations and four antenna stations, through whichnew orbital elements etc. are uploaded to the satellites’ memories, usually twice every 24 hours.The computing centre (MCS, Master Control Station) is Schriever Air Force Base, Colorado.

1.5.2 GPS satellites and signal structure

The radio signal transmitted by a GPS satellite consists of a carrier wave and so-called pseudorandom codes modulated on top of it. Both may be used for positioning.Carrier wave: wavelength ca. 20 cm, precision of positioning 1% of this, i.e., ca. 2 mm. Geodetic

GPS positioning is based on measuring the phase of the carrier wave. For this purpose, alwaysdual frequency receivers are used. See 1.1.Problem: all waves look the same, so we need ambiguity resolution.

Code: The “pseudo-wavelength” is 30 m (P code, the so-called “chip rate” or distance between bits):positioning precision is 1% of this, i.e., ca. 30 cm. The codes are modulated using so-calledphase modulation, see figure.More precisely: the chip rate or bit rate of the C/A code corresponds to a “wavelength” of300 m, the corresponding number for the P code gives 30 m. See table 1.2.

In practice the problem with both methods is the imprecision of the satellite orbits. In real time, byusing broadcast ephemeris, one can achieve at best ±10 m positioning precision.Solution: differential positioning, i.e., the use of a base station. If the distance from the base station

is sufficiently small, the greatest part of the orbit error will cancel out from the final result,see figure 1.5

The precision of differential positioning may be easily estimated using a geometric argument. Seefigure 1.6. If the geometric precision of the satellite orbit (broadcast ephemeris) is called ∆ andthe distance of the satellite from the observer s (in practice over 20 000 km), we obtain for thepositioning precision

δ ≈ d

s∆ ,

11


o

−1 = 0

+1 = 1+1 = 1

Principle:

...modulated

Carrier...

Phase flip(180 phase shift)

Modulation = code

Kuva 1.4: The principle of phase modulation

Taulukko 1.2: The different codes of the GPS signal (pseudo-random codes, PRC)

Abbrev. Name Modulationfrequency

Toisto-jakso Kanto-aalto

C/A Coarse/Acquisition 1.023 Mb/s 1 ms L1P Precise / Protected 10.23 Mb/s 1 week L1,L2Y Combination of P and the sec-

ret W code10.23 Mb/s L1,L2

Navigation message 50 bits/s continuous L1,L2

α

Sodankylä

Helsinki

Kuva 1.5: Differential positioning. The distance between two ground stations, in this case Helsin-ki and Sodankylä, is always small compared to the satellite orbital height, 20 000 km.Therefore the orbit error (like the satellite’s clock error) cancels for the most part out indifferential measurement.

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T

s

B A

δ

S∆

d

Kuva 1.6: The geometry of computing the precision of differential positioning.

Taulukko 1.3: The precision of positioning as a function of the length of the vector and the orbit er-ror. 2 m corresponds to the precision of broadcast ephemeris , 0.02 m to the precisionof today’s precise ephemeris.

Vector length Orbit error Positioning error1 km 2 m 0.1 mm

10 km 2 m 1 mm100 km 2 m 10 mm

1000 km 2 m 0.1 m1 km 0.02 m 0.001 mm

10 km 0.02 m 0.01 mm100 km 0.02 m 0.1 mm

1000 km 0.02 m 1 mm

where d is the length of the vector to be measured. Using this formula we form table 1.3.

1.5.3 GPS receivers

Today’s GPS receivers are able to do differential positioning using both carrier waves and codesstraight from the box. Nevertheless, the setting up of your own base station may require the purc-hase of a firmware “module”. And of course one also needs equipment for data communication (radiomodem, cell phone, . . . ) to establish a “link” between base station and observer, i.e., the “rover”.

1.5.4 GPS observations in mapping

GIS-GPS is defined as the collection of spatial data with the aid of GPS. In addition to locationdata, we collect also property data (attributes). For this purpose exist rapid, easy and inexpensiveGPS methods.• The demands for precision affect the choice of GPS method to be used• Often intended is a metre class (1-10 m) precision GPS measurement method, good enough

for general mapping• When we are dealing (for reasons of convenience of use) with real time positioning, we are

methodologically close to navigation• A popular and broadly used method is differential GPS (DGPS), which is based on code ob-

servations

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��

��

��

KnownKnown

equi-value surfaces

Movingreceiver

Base station

end point starting point

Double difference

Data link

Kuva 1.7: The principle of operation of the classical RTK method. Nowadays usually instead ofknow points we use so-called “on-the-fly ambiguity resolution”, and also partial inter-ruptions in the connection to the satellites are handled elegantly in software.

• If we demand greater precision from spatial data, we use methods of geodetic positioning, i.e.,in the case of GPS, carrier phase measurements. The differential technique used in that caseis referred to as RTK (Real Time Kinematic), cf. Figure 1.7

• Of course both techniques can be used also in a non- real time mode; in that case no datalink between base station and observer is needed. The results are then obtained throughpost-processing.

A GPS method used in spatial data measurement has to meet the following requirements (Mäen-pää, 1993, with modifications):• Data collection should be possible also on foot or from a moving vehicle• One base station should cover a large area of operation. The data communications solution

chosen is relevant for this. Today commonly a mobile phone• Today often also so-called virtual solutions based on many base stations are on offer. Opera-

tions area at the expense (somewhat) of precision• Real time measurement should be possible, although often post-processing is sufficient• Measurement possible under field conditions, especially in so-called “urban canyon” areas,

where high buildings cause many partial interruptions on the connection to satellites• Precision, depending on application, 0.05. . . 10 m• Post-processing should be easy and user friendly, also for large data volumes.

14


��

��

��

��

��

��

��

��

1a −> 1b 2a −> 2b

1a−2a

1a

1b 2a

2b

Common

Search area

solution

Kuva 1.8: “On-the-fly” ambiguity resolution. Principle

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2 Technologies

2.1 Receiver technologies

2.1.1 Geodetic recievers vs. inexpensive receivers

1. Consumer grade equipment

a) Inexpensive, mass producedb) Hand-held GPS receiversc) Card receivers (require integration)d) ”Modules” that can be connected straight to a hand-held micro, “GPS pockets”

2. Professional grade equipment

a) Significantly more expensiveb) Better precision; able to handle carrier phase etc.c) Ruggedized for field used) Versatile use, e.g., post-processing (storage of raw data format)

The division into consumer grade and professional grade equipment is not a hard one.

2.1.2 Carrier phase measurement

Measurement of the carrier phase is unusual in consumer grade devices. More common is codemeasurement. Code measurement is relatively easy to implement by using a correlator, whichcorrelated the signal in the reciever with self-generated signals.Typically, three synthetic signals are used for every satellite, i.e., every pseudo-random code: E(early), L (Late) and P (prompt). See figure.

L P E

+

−

Pseudo−

Comparison

”Early”

”Prompt”Signal

”Late” (Integration)

ClockCode generator

range

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2 Technologies

If the E-correlator gives a high value, then the clock of the code generator is fast and it must beslowed down. If, on the other hand, the L-correlator gives the higher value, then the clock of thecode generator must be speeded up.Observing the carrier phase is more difficult: for that, generally a so-called PLL (Phase LockedLoop) is used. The most commonly used type is a so-called Costas discriminator. It observes thephase difference of the carrier wave against that of the receiver’s reference oscillator and steers thereceiver’s reference frequency so, that the difference vanishes. The reference frequency is observedand integrated into the carrier phase observable.The Costas discriminator assumes that the code has already been removed from the carrier. Addi-tionally it is unable to distinguish between the carrier and minus the carrier, which means that itsunit of ambiguity resolution is half a wavelength, λ/2.

2.1.3 Processor, firmware, programmability

A lot of thinking in the design of a GNSS receiver goes into which methods are being used formeasuring and monitoring the codes and the carrier phase. Also the intended use is relevant: e.g.,a receiver intended to be used on board an aircraft (a “high dynamic” -environment) has to to havea lot “stiffer” PPL loops, so that one doesn’t get too many cycle slips. The sensitivity to signal thenbecomes accordingly weaker.Current development is going in the direction of software based GNSS receivers. A software recei-ver is one in which the program code is within reach of, and modifyable by, an ordinary user. Onsome level, already now most receivers are “software receivers”, as they contain firmware, whichhowever has been burned into read-only memories and can only be modified by the manufacturer.

2.1.4 Software receivers

As advantages of software receivers we may mention:• Easily updated• As there will be in the future several (2-4) different GNSS systems, the complexity needed is

more readily implemented in software than in hardware• All sorts of technical experimentation is easier if you can get your hands on the code• If the software in the receiver is of so-called Open Source type, then its operation is no longer

a so-called black box, and• then it is inexpensive, and• many more people can participate in its development.

As a drawback it may be mentioned that a software receiver requires a very fast processor. Currentpersonal computers just barely manage.Ks. http://www.gpscreations.com/NewFiles/GPS1A%20Brochure.pdf, http://gps.aau.dk/softgps/esa.pdf.

2.2 Spatial data technologies

2.2.1 Data collection

The collection of data may be divided into the collection of co-ordinates and that of attributes.Co-ordinate data is always collected in a certain co-ordinate frame. The information on the frameused must be available with the data as so-called metadata.The precision will depend on the intended application. High precision os not necessarily critical:however, information on the precision is, and belongs to the metadata. So, the metadata to becollected are:

1. The co-ordinate frame used2. The method of positioning (DGPS, RTK, . . . ) used

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http://www.gpscreations.com/NewFiles/GPS1A%20Brochure.pdf

http://gps.aau.dk/softgps/esa.pdf

http://gps.aau.dk/softgps/esa.pdf

2 Technologies

3. The estimated precision (point mean error, 2-D, 3-D, height, . . . ) in relation to what?4. Measurement conditions, i.e., DOP values, possible occlusion, multipath, . . .

In the computerized collection of attribute data we use a predefined form template (dictionary,catalog, . . . ) which defines, what attributes are being stored. It is ensured that• All necessary information will be collected• The collected data is logically consistent• The collected data is uniform.

On-screen, the attribute data may take the following forms:1. One chooses one alternative from a list, e.g., a pull-down menu (“rolling curtain”)2. One feeds a numeric value3. One writes into a text field.

A well designed form checks the data fed at least for formal correctness, as far as is feasible.The collected geometric objects may be

1. A point2. A line, curve or (open) polygon consisting of line segments3. An area, with as its (closed) border a polygon.

In the case of lines and areas, one can check the topological correctness or consistency, e.g.:• The areas may not overlap• Between the areas there may not be openings.

Note that consistency is only achieved when the spatial data base is being built. Data collected inthe field is not consistent, it requires topological cleaning up, which at least partly may be doneautomatically.

2.2.2 Alternatives and applications for data collectors

1. A portable micro (laptop)2. A hand-held micro3. A special device, ruggedized4. An intelligent mobile phone or the like.

There are available also ruggedized devices nevertheless based on a standard environment. Theadvantage then is, that one may use software developed for ordinary PC’s or handhelds also in thefield.Requirements for devices:

1. Portable, light2. Ruggedized, tolerant of field conditions and improper handling3. Display suitable for outdoor use in different lighting conditions; and remember, a touch screen

is no desk top.4. Battery capacity5. Wireless link possible6. Programming by the user possible: an operating system offering a development environment

(Windows, Linux, less so Symbian). Generally, a cross compiler is being used from the desktopof the host machine, as the computing power of the device is limited. The compiled programis “flashed” into the device over the USB port.

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2 Technologies

2.2.3 Map background and spatial data base

When moving in the field, it is useful to have access to a map background. It can be along insidethe device, or it may be dynamically downloaded from a map server. Similarly, if one is editing inreal time spatial data during GPS measurements and based on them, one may make the changeseither to the local copy of the spatial data base, or over the network to the central data base.When using the “remote” data base rich in detail, it requires careful design to keep the amount ofdata transferred reasonable, even when moving all the time in the field and changing details inthe data base. Only those geographic parts of the data base are transferred to the user, that arerelevant for him; the transfer of the user’s edits to the data base must be handled in such a way, thatno discrepancies (“conflicts”) are created, even though several users are editing it simultaneously.

2.2.4 Various use modes

The collection of spatial data may take place for different purposes, i.e., in different use modes:1. Data collection (original data, new data). In this case we generally operate off-line, i.e., data

will be transferred to the data base later on.2. Maintenance and update of existing data. In this case we operate in off-line or on-line mode.

In the latter case the data base is ubdated over the network.In this case, positioning may be helpful when searching for an object to be updated. A backgroundmap is useful. If no new data is being collected, then the positioning precision is less critical.

3. Mobile GIS. In this case one exploits pre-existing spatial information within an organizationon-line and in real time in the field. As a terminal device is commonly used a micro computercompatible with industry standards (hand-held, ruggedized laptop, “terrain micro”), in whichis running a tailor-made application atop a standard operating system. Often, GPS (DGPS,RTK) positioning is part of the application.

4. Location based services. Services aimed at the end user. The classic example “find the nearestpizzeria and its menu”. The terminal is a mobile phone. Its spread is still modest, but expecta-tions are great. Positioning method is often network or cell positioning (GSM, WLAN), use ofGPS is only starting, waiting for GPS positioning chips to become cheaper 1.

2.3 Data communication technologies

2.3.1 Between receiver and data collector

The following basic solutions exist:1. Receiver and data collector separately; cable2. Separately; wireless connection (Bluetooth)3. Receiver also serves as data collector.

If the receiver is already integrated with the antenna, this assembly is generally mounted atop apole way above the head of the user. In this case integration of receiver and data collector does notwork and one must use a cable or wireless connection.An advantage of a wireless connection is that mechanical parts are eliminated: cables and connec-tors have a way of breaking in use.A problem with Bluetooth may be the immaturity of the technology. Devices that are designed towork together generally do work together, in any other situation mystical problems may occur.

2.3.2 Between rover and base station

Here we have different solutions:

1In the mobile phone industry, the price of such an additional component becomes unsurmountable already if it exceeds afew cents!

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2 Technologies

1. One-on-many or broadcast -solution: one base station serves many moving users and sendsthem all exactly the same message. For this, e.g., FM radio transmissions may be used, usingthe RDS (Radio Data System), which, e.g., the FOKUS service uses.

2. One-on-one or singlecast -solution: e.g., the use of a mobile phone connection. Every user canreceive a message tailormade for him alone, e.g., a correction message which is valid for anearby, mathematically generated “virtual base station”. This also facilitates invoicing forservices rendered.

2.3.3 Obtaining information from the Internet

Not all data needed by a roving receiver user is provided by a base station. Part of it may come fromthe Internet, e.g., the map backgrounds that were already mentioned. Also data that the receivergets directly from the satellite, like orbital elements (ephemeris) may be obtained more practicallyand/or faster over the Internet (Assisted GPS). Connecting to the Internet from the field generallyrequires a connection to the mobile network.

2.3.4 Mobile networks

GSM Global System for Mobile Communications. Originally developed for voice transfer, but ne-vertheless digital. Possible frequencies 450, 750, 800, 850, 900, 1800 or 1900 MHz; mostcommon are 900 and 1800 MHz. With a “GSM modem” the standard transfer rate is 9600bits/second.

GPRS is GSMs data extension (General Packet Radio Service) which offers transfer speeds of 9600b/s – 115 kb/s.

EDGE (Enhanced Data for Global Evolution) offers again three times bigger data transfer capacitycompared to GPRS.

UMTS Universal Mobile Telecommunications System. See. WCDMA.WCDMA (Wideband Code Division Multiple Access), an important third generation (3G) mobile

communications technology. The capacity is 50 times that of the GSM network and 10 timesthat of the GPRS network. The transfer rate is typically 384 kb/s, but the technology enableseven 10 Mb/s.

WIMAX (Worldwide Interoperability for Microwave Access), popular name. The protocol is IEEE802.16, Wireless MAN (Metropolitan Area Network). Suitable for longer distances than WLAN(many kilometres). Frequencies in range 10 – 66 GHz (802.16a), i.e., one needs a line-of-sightconnection. Nevertheless it has also been developed for the frequencies 2 – 6 GHz (802.16e).in Finland 3.5 GHz. It is also suitable for sparsely populated areas as a broadband solution.The total capacity of a base station is 75 Mb/s, divided up among users.

WLAN (Wireless LAN). Also “WiFi”. Local wireless connection, protocol IEEE 802.11. Capacity va-riable. Distance max ca. 100 m in- or outdoors. Frequency 2.4 GHz. The protocol is a littleunreliable and in principle unsuited for real time applications (VoIP).

2.4 Standards

2.4.1 The RTCM SC-104 standard

Radio Technical Commission for Maritime Services (RTCM) is an independent organization createdin 1947. Member organizations are over 100, e.g., manufacturers of radio navigation equipment,state agencies responsible for radio positioning, shipbuilders, positioning service providers andinstitutes of learning.RTCM Special Commission 104 designed the standard for a GPS differential data service, carryingthe name RTCM SC-104 (or RTCM-104, or “RTCM”). The current version is 2.32.

2Additionally there exists a version 3.0, which however is not downward compatible with the versions 2.x. It is suitable forreal-time kinematic measurement and uses a more efficient data transfer mechanism than the 2.x protocol.

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2 Technologies

The RTCMmessage types are listed below.Message Type Message Title

1 DGPS corrections2 Delta DGPS corrections3 Reference station parameters4 Carrier surveying information5 Constellation health6 Null frame7 Marine radiobeacon almanacs8 Pseudolite almanacs9 High rate DGPS corrections10 P code DGPS corrections11 C/A code L1/L2 delta corrections12 Pseudolite station parameters13 Ground transmitter parameters14 Surveying auxiliary message15 Ionospheric/tropospheric message16 Special message17 Ephemeris almanac18 Uncorrected carrier phase measurements19 Uncorrected pseudorange measurements20 RTK Carrier phase corrections21 RTK pseudorange corrections

22-59 Undefined60-63 Differential Loran C messages

Data is transferred in packets of 30 bits, or words; of those, 24 bits are data an 6 bits a so-calledcheck sum (parity). Every message consists of at least two words. The first two words of a messageare called the header and it contains information common to all message types.About the parity bit still the remark, that understanding correctly the parity of every word requiresknowledge of the two alst parity bits of the previous word. . . this makes initialization of the wholeprocedure tricky.[2] gives software code for reading an RTCM message, as well as many technical details.Viestityyppi 1:

Header: consists of two words, as follows:Preamble Message type Station code (ID) Parity

8 bits 6 bits 10 bits 6 bitsModified Z counter Sequence

numberLength of“Frame”

Stationhealthstatus

Parity

13 bits 3 bits 5 bits 3 bits 6 bitsData records: word 3. . .n, as follows:

Scal-ing

UDRE Sat ID PRC Pari-tty

1 2 5 16 6RRC IOD Scal-

ingUDRE Sat ID Pari-

ty8 8 1 2 5 6

PRC RRC Pari-ty

16 8 6IOD Scal-

ingUDRE Sat ID PRC (msb) Pari-

ty8 1 2 5 8 6

etc. . .Explanation:

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2 Technologies

• The modified Z counter; this is the epoch of the correction, i.e., the moment when itwas determined. Unit: seconds within the hour (note that the time scale used is GPStime, not UTC!)

• Station’s health data: if different from zero, not wise to use the station. 6 (110) meansthat the transmission is not being monitored. 7 (111): station malfunctioning.

• Scaling0: The PRC’s unit is 0.02 m and the RRC’s unit 0.002 m/s1: The PRC’s unit is 0.32 m and the RRC’s unit 0.032 m/s

• UDRE: User Differential Range Error Index: 1σ error indicator:UDRE code 1σ error

11 > 8 m10 ≤ 8 m01 ≤ 4 m00 ≤ 1 m

• Sat ID: Satellite identification• PRC: Pseudo-range correction, msb = most significant byte, i.e., the leftmost 8 bits• RRC: correction to rate of change of pseudorange• IOD: Issue of Data. Which set of broadcast ephemeris the correction data refers to

Message type 2: Differences between corrections computed for two different IODs.Message type 3: Co-ordinates of base stationMessage type 5: State of satellite constellationMessage type 6: Empty message, for testing data communications linkMessage type 9: Correction data grouped in three-satellite groups. That way the corrections get

through fasterMessage type 15: Ionospheric correction

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3 Carrier phase measurements andgeospatial applications

3.1 General

As background reading, the following articles are useful: [7, 10] and textbooks: [9, 5].Carrier phase measurements and their ambiguity resolution problems have already been mentio-ned.When we can write code pseudo-ranges as follows:

p = ρ+ c (∆t−∆T ) + dion + dtrop, (3.1)

we can write carrier phase observables as follows:

P = λ

(φ

2π

)= ρ+ c (∆t−∆T ) +Dion +Dtrop + λN, (3.2)

where φ is the measured phase angle (including the counted full cycles after the last lock-on to thesignal), N ambiguity number, ∆t the satellite’s, ∆T the receiver’s clock error,

ρ =√

(x−X)2 + (y − Y )2 + (z − Z)2,

the geometric distance between satellite and receiver, and Dion and Dtrop the propagation delayscaused by iono- and troposphere. (In fact Dion = −dion and Dtrop = dtrop.) λ is the wavelength (orsemi-wavelength).

3.2 Error sources of GPS carrier phase measurements

As the most important error sources we may mention• Orbits• Satellite clock error• The ionosphere• The troposphere• Multipath reflections• The imprecision of phase measurement by the device

The following table gives their order of magnitude and nature.Error source Nature Size Size in diff. Elimination

measurementSatellite orbit Geometric ∼1 m ∼4 mm/100 km Precise ephemeridesSat. clock error Constant metres 0 Differencing between rec’versIonosphere Stoch. process ±10 m ∼1 cm/100 km Two freqs. L1, L2Troposphere Stoch. process ±10 cm ∼1 cm/100 km Estimated, 1/ cos ζMultipath Local ∼1 cm same ?Imprecision of device Local mm – cm same Technology

Additionally the following detailed explanations.

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3 Carrier phase measurements and geospatial applications

3.2.1 Satellite orbit error

If one uses the ephemeris broadcast by the satellites, one may compute the places of the satellitesin space to approx. ±1 m precision. This is already a considerable improvement over the previoussituation, when orbit errors were order of magnitude 10 m.In absolute positioning this orbit error propagates directly into the computed location, althoughof course the use of many satellites (more than the minimum of 4) will reduce the total errorby averaging. On the other hand, by differential positioning, i.e., using a base station, one mayeliminate most of this error. The base station determines the errors in pseudo-ranges caused bythe orbit errors and sends them to the moving user. If the moving user is close to the base station,then his pseudo-range error will be the same as that of the base station; when the distance fromthe base station grows, also the difference between the two pseudo-ranges will grow, which goesfully into the location of the moving receiver as positioning error.Nowadays there is available, in addition to precise ephemeris, so-called Rapid Orbits, within a fewhours or even under an hour. These are not good enough for real time positioning use, but they areuseful, e.g., in computing weather predictions (“GPS meteorology”).

3.2.2 Satellite clock error

This is eliminated in the difference between two receivers, i.e., in differential positioning it cancelsout completely.

3.2.3 The ionosphere

The effect of the ionosphere may be eliminated completely by using a dual frequency receiver.If one only has available a single frequency receiver (cheaper still today, but how long will thatlast?), one may model the ionosphere. In real time, this is challenging but possible. If the basestation is dual frequency, it may compute suitable ionospheric corrections, which are valid for aneighbourhood of a certain size around the base station.

3.2.4 The troposphere

The effect of the troposphere is the same on both frequencies, i.e, non-dispersive. It can not beeliminated by using two frequencies. However, it is eliminated approximately from differentialmeasurements, if the inter- base station distance is short.The refractive effect of the troposphere is inverely proportional to the cosine of the zenith angle ζ:

dtrop =dtrop,zenit

cos ζ

, where dtrop,zenit is the so-called zenith tropospheric delay, a property slowly changing with place.If we can use five or more satellites, we may estimate dtrop,zenit At least the difference

dtrop,zenit,base − dtrop,zenit,rover

would be estimable and thus eliminable. However, the extra unknown weakens the solution, es-pecially in the vertical direction.

3.2.5 Multipath

Multipath is a disturbance that is hard to eliminate. In carrier phase measurements it is substan-tially smaller than in code measurements, however it is still centimetres in the worst case.The GPS signal is polarized circularly. The plane of polarization rotates rightward. After reflection,the plane rotates leftward. One may consider circularly polarized light to consist of two linearlypolarized rays, that are oriented perpendicular to each other and between which there is a phaseoffset of λ/4.

24


GPS antennas are designed in such a way, that they only accept radio waves polarized rightward.E.g., a cross dipole antenna (where there are two dipole elements, both in the horizontal plane)receives two orthogonal components and “mixes” them with a λ/4 phase offset, so the two compo-nents of rightward polarized signal enforce each other, but those of a leftward polarized reflectedsignal cancel each other.This works well as long as the waves come in from near the zenith. From sources close to thehorizon, the antenna receives only one component, the one that is polarized in the direction of thehorizon. It is the same in the reflected as in the original signal.In order to minimize multipath disturbance, we must thus diminish the effect of low signals. Asfollows:• Physically, by designing an antenna, the sensitivity of which diminishes steeply close to the

horizon (and is close to zero for negative elevation angles)• On the software level, by rejecting or downweighting in the computation if the satellite has

1. a low elevation angle, or2. a low S/N (signal-to-noise) ratio, generally also due to low elevation.

Both techniques work. Unfortunately also satellites that are high in the sky may cause reflec-tions, which reach the antenna almost in the horizontal direction. That’s why both techniquesare needed. The first may be difficult, if the demand is also that the antenna must be compactand light, like is generally the case in GIS applications.

3.2.6 Receiver noise level

Important warning: here “noise” refers to the background radiation from the antenna, the receiverand the surroundings. We speak of the S/N, or signal-to-noise, ratio. Additionally we speakoften of the random uncertainty, or “noise”, of the measured quantity, i.e., the pseudo-range.

The noise level is partly a question of quality: better (more pricey) equipment performs better.This is not, however, the only issue. It is also a matter of software: the built-in software (firmware)makes certain assumptions, about the kind of environment in which the device is going to be used.E.g., a device meant to be used on board an aircraft has to consider, that the craft may manoeverand then the frequency of reception of the system may, because of the Doppler effect, suddenlychange. A device built for such an environment receives the signal in a broader frequency bandand its S/N ratio is therefore poorer. One also says that the CTR (Carrier Tracking Loop) of such a“high-dynamic” device is “looser” than that in a low-dynamics device.

3.3 Description and processing of observations

3.3.1 Phase measurement

In contrast to the pseudo-random noise codes modulated onto the GPS signal, that have “wave-lengths” of 30 m (P code) and 300 m (C/A code) the wavelengths of the GPS signal’s carrier wavesare 19 cm (L1) and 24 cm (L2). This means that a phase measurement which measures the phaseangle, e.g., with a precision of one degree, i.e., 1/360 of a cycle, measures actually a metric pseudo-range to a precision of 19 cm/360 = 0.5 mm tai 24 cm/360 = 0.7 mm.Also carrier phase measurement can be considered as measurement of pseudo-range, when wemultiply the phase angle φ with the quantity λ/2π or λ/360, depending on whether the phase angleis given in radians or in degrees. If, as is common, the phase angle is given in cycles, then thecoefficient is simply λ.Typical for phase measurement is, that the phase angle can be determined only modulo one wa-velength. However, as long as lock to the satellite signal is maintained, also this unknown integernumber of wavelengths will remain constant. If the lock-on is lost, we speak of a “cycle slip”.Some devices are built so, that they can determine the phase angle only module half a wavelength1.Then one must use λ/2 instead of λ in the ambiguity resolution.

1Namely, if the Carrier Tracker Loop uses a so-called Costas discriminator, which works in spite of all kinds of codingscontaining phase inversions of 180◦ (or π) being modulated on top of the carrier wave, e.g., the 50 Hz orbit data message.

25


3.3.2 The RTCM protocol and carrier phases

RTCM SC-104 (or RTCM-104, or “RTCM”), the current version 2.3, contains also message types forusing carrier phase measurements: the types 18-21.

Message Type Message Title18 Uncorrected carrier phase measurements19 Uncorrected pseudorange measurements20 RTK Carrier phase corrections21 RTK pseudorange corrections

We see that we can transfer both original phase measurements and correction data (i.e., differencesbetween observed phase angles and phase angles computed from orbit data and known base stationposition).

3.3.3 NTRIP protocol

NTRIP means “Networked Transport of RTCM via Internet Protocol”. It is a pretty young protocol,enabling the distribution of corrections also wirelessly, e.g., over the GPRS mobile network.NTRIP is based on the tcp/ip protocol, more precisely: http (hypertext transfer protocol), i.e., correc-tion data may be distributed in the same way as web pages. In fact, an NTRIP server is a “doctored”www server: this is real time “streaming” data, in the same way as broadcasting music over theInternet. See [1].In 2004 NTRIP became an RTCM standard. It is being used, e.g., in Geotrim’s VRS referencenetwork covering the whole of Finland.

3.3.4 Resolving ambiguities

This is a puzzle, the solution of which has many tricks on offer. The main requirement is sufficientredundancy. In the book [8], chapter 6.5, the situation is analyzed.If we have n satellites to solve the vector between two ground stations, we can form n − 1 doubledifferences, of which each contains one unknown, the integer valued ambiguity. We may write this,e.g., with the symbol

∇ij∆N,

where i and j are the satellite pair with repect to which the inter-satellite error is being computed.1. All possible real valued combinations ∇ij∆N form a n− 1 -dimensional linear vector space, of

which one element can be written in the form ∇∆N .2. Inside this space we may restrict the possible values of ∇∆N to a limited area: in addition to

carrier phase, we have available the pseudo-ranges for the same ground stations and satelli-tes, which do not contain any ambiguities. For sure their precision is much poorer. Based onthe equations 3.1, 3.2 (ignoring the atmosphere)

P ≈ p+ λN,

from which follows∇∆N ≈ (∇∆P −∇∆p) /λ.

The “search space” that has to be thus traversed is much smaller: only a certain-sized neigh-bourhood of this point. The size of the area depends on the quality of the code measurements,i.e., the uncertainty of the code pseudo-ranges.

3. In practice the unknowns in the double difference solution are only the three componentsof the inter-station vector in space; in other words, the solution has to be inside a certainthree-dimensional subspace of the n− 1 -dimensional space.

The most popular ambiguity resolution methods, like the famous LAMBDA method, are based onthis.

26


3.3.5 Different ambiguity resolution methods

A practical method for ambiguity resolution goes through three steps:1. We form a space of possible combinations of integer unknowns2. We search from this space the optimal (“best”) solution3. We make sure that the real solution is (with a high probability) just this one and not the

“second best” one (the contrast rule).For short vectors, we may resolve separatelyWidelane, i.e., φ1 − φ2, or in metric units

L5 =f1P1 − f2P2

f1 − f2=

λ

2π(φ1 − φ2) .

The effective wavelength of this is

λ5 =(λ−1

1 − λ−12

)−1= 86 cm.

Because the wavelength is this long, it is easier to find a unique integer: if the code basedpseudo-range tolerance (maximum error) is � 1

2λ5, it is sufficient to calculate the L5 ambi-guity N5 = N1 −N2.

For long vectors again we haveMelbourne-Wübbena observable:

LMW =1

f1 − f2(f1P1 − f2P2)− 1

f1 + f2(f1p1 + f2p2) .

Here we have used the same notation as earlier, i.e., p1, p2 are code pseudo-range observations, andP1, P2 phase pseudo-range observations, both in metric units. Using this presupposes the availabi-lity of pretty good code observations on both frequencies. The effective wavelength of LMW is also86 cm.Both widelane and MW observables can in principle be used for real time measurements. However,the latter is exclusively used for solving very long static vectors.

3.3.6 Phase based pseudorange smoothing

In this method (“pseudorange smoothing”) we take the absolute pseudorange from the code mea-surement, but its fractional wavelength from the phase measurement. Sounds easier than it is, cf.[9] page 161.Especially in kinematic GPS applications this is a recommendable measure: code measurementsdon’t contain ambiguities, when on the other hand phase measurements are much lower in noise.Let us assume that we have as observations the code observations p1 and p2 (metric units) and thecarrier phases φ1 and φ2 (angular units), at time t.First we construct a prediction equation for the (a priori) pseudorange for this moment, using thethe previous, i.e.

p− (ti) = p (ti−1) +λ

2π(φ (ti)− φ (ti−1)) . (3.3)

This equation applies for both frequencies 1 and 2, and as well for “widelane” observables, whichwe define as follows:

pWL =f1p1 − f2p2

f1 − f2, φWL = φ1 − φ2.

Note that the equation (3.3) may be interpreted as the dynamic equation of a Kalman filter: thestate is p (t) and the state variance matrix may be called P− (t). The phase correction term φ (ti)−φ (ti−1) may be considered known because it is precise in comparison to the code observations.Next, we add to this the Kalman filter’s observation equation: simply this moment’s p (ti) observa-tion, the precision of which we may write as Ri. Now the update equation is

p+ (ti) = p− (ti) +KH(p− (ti)− p (ti)

),

27


where H = [1] , K = −P−HT(HP−HT +R

)−1 = −P−/ (P− +R) , and thus

p+ (ti) =Ri

P− (ti) +Rip− (ti) +

P− (ti)P− (ti) +Ri

p (ti) .

So: the a posteriori pseudorange is a weighted linear combination of, on the one hand, the predictedand “carrier-smoothed”, on the other hand, a directly observed pseudorange.We find for propagation of variances

P+ (ti) = (I +KH)P− (ti) =Ri

P− (ti) +RiP− (ti) .

We see that, when the a priori state variance is poor, the improvement is remarkable; when thestate variance improves, also the improvements brought by observations diminish.(The propagation of variances in the dynamical model is simply: P− (ti) = P+ (ti−1).)It is possible to test for cycle slips in this method: the quantity to be tested is the difference(

p− (ti)− p (ti)),

the mean error of which is known:

σ =√HP−HT +R =

√P− +R.

This will work best when using the wide lane linear combination, due to its long effective wave-length, 86 cm.This Kalman filter can run as a continuous process inside the receiver (or inside the post-processingsoftware, without the real time property). The result of the Kalman filter p+ (ti) , i = 1, . . . is consi-derably smoother than the original measurements p (ti) .

3.4 Measurement methods and geometries

The RTK method may be used in two different ways or geometries:1. By using one base station2. By using a network of base stations.

In the following we use the notation {e1, e2, e3} for a triad of orthogonal unit vectors. Every vectorin space can be written as a linear combination of these base vectors. In a local horizon system, thevector e1 points South, e2 East and e3 up to the zenith.First we discuss, how the orbit and clock errors of GPS satellites propagate into the position solu-tion in the case of one base station; then in the case of three base stations.

3.4.1 One base station

In the case of one base station we may write the observable as follows, ignoring for a moment theatmosphere and other disturbances:

P =√

(x−X)2 + (y − Y )2 + (z − Z)2 + c (∆t−∆T ) + . . .

Here xe1 + ye2 + ze3 is the position vector of the satellite, Xe1 + Y e2 + Ze3 that of the receiver,while {e1, e2, e3} is an orthogonal triad of unit vectors. The expression

ρ =√

(x−X)2 + (y − Y )2 + (z − Z)2

is the geometric distance between satellite and receiver.Let the orbital errors (or their effect on the satellite’s position in space) be ∆x,∆y,∆z, and thesatellite’s clock error ∆t (which we already assume to be small). Their effect on the pseudo-range is

∆P =∂P

∂x∆x+

∂P

∂y∆y +

∂P

∂z∆z + c∆t. (3.4)

28


SE

NW

e′2

e′3

Satellite

e3

e2 Receivere1

e′1

Kuva 3.1: Geometry in the case of one base station

Let us now choose an alternative three-dimensional unit vector triad, in which e′1 points from thesatellite to the base station, and e′2 and e′3 are orthogonal with respect to each other and e′1

2. Let

ρ0 =√

(x−X0)2 + (y − Y0)2 + (z − Z0)2

be the distance between satellite and base station X0e′1 + Y0e′2 +Z0e′3; let furthermore the locationof the moving receiver (“rover”) be Xe′1 +Y e′2 +Ze′3 =(X0 + ξ) e′1 +(Y0 + η) e′2 +(Z0 + χ) e′3. Here ξ, ηand χ are now the co-ordinates of the rover relative to the base station in the co-ordinate systemagreed on above. The distance between base station and rover is

s =√ξ2 + η2 + χ2.

Let us write out Equation (3.4). We obtain

∆P =x−Xρ

∆x+y − Yρ

∆y +z − Zρ

∆z + c∆t,

in other words, we get separately for base station and rover

∆P0 =x−X0

ρ0∆x+

y − Y0

ρ0∆y +

z − Z0

ρ0∆z + c∆t

∆P =x−Xρ

∆x+y − Yρ

∆y +z − Zρ

∆z + c∆t.

The difference, i.e., the error in the rover’s position due to the distance from the base station, is

∆P −∆P0 =(x−Xρ− x−X0

ρ0

)∆x+

(y − Yρ− y − Y0

ρ0

)∆y +

(z − Zρ− z − Z0

ρ0

)∆z

2So: e′1 = − cosA sin z e1− sinA sin z e2− cos z e3, e′2 = sinA e1− cosA e2, e′3 = − cosA cos z e1 − sinA cos z e2 +sin z e3.Or [

e′1e′2e′3

]=

[− cosA sin z − sinA sin z − cos z

sinA cosA 0− cosA cos z − sinA cos z sin z

][e1

e2

e3

].

The matrix appearing here is orthogonal, in other words, RRT = RTR = I.

29


From here, the satellite’s clock error has disappeared.Let us look closer at the coefficient (

x−Xρ− x−X0

ρ0

).

If we define the functionf (X) ≡ x−X

ρ (x,X, y, Y, z, Z),

the above mentioned coefficient is

f (X)− f (X0) ≈ ∂f

∂X

∣∣∣∣X=X0

(X −X0) +12∂2f

∂X2

∣∣∣∣X=X0

(X −X0)2 + . . . =

=∂f

∂X

∣∣∣∣X=X0

ξ +12∂2f

∂X2

∣∣∣∣X=X0

ξ2 + . . .

(Taylor expansion). If we retain from this only the first term, we obtain

∂f

∂X

∣∣∣∣X=X0

= − 1ρ0

+(x−X0)2

ρ30

,

and

∆P −∆P0 =

(− 1ρ0

+(x−X0)2

ρ30

)ξ∆x+

(− 1ρ0

+(y − Y0)2

ρ30

)η∆y +

(− 1ρ0

+(z − Z0)2

ρ30

)χ∆z.

Because the co-ordinate axes are defined in the way described above, we have

x−X0 = −ρ0,

y − Y0 = 0,z − Z0 = 0,

and we obtain∆P −∆P0 = − 1

ρ0η∆y − 1

ρ0χ∆z. (3.5)

We see that the error is linearly proportional to the distance from the base station, and that onlythe distance sideways from the direction vector to the satellite has an effect.

3.4.2 The case of three base stations

Because generally, the case of a network of base stations can be reduced to the case of three basestations, we shall only study the latter.Let us start from the equations derived above. Equation 3.5 is linear in the parameters η andχ, onwhich we may interpret as the horizontal plane co-ordinates in two mutually orthogonal di-rections. Actually this is not quite correct: if a satellite’s azimuth is A, we may interpret η as ahorizontal co-ordinate in the direction A + 90◦, but the χ axis dives into the ground at an angle ζ,the zenith angle of the satellite. On the earth surface, we need the co-ordinate ω = χ/ cos ζ in thedirection A. Then, the error in the pseudo-range due to orbit error is

∆P −∆P0 = − 1ρ0η∆y − cos ζ

ρ0ω∆z,

where ω is the difference in horizontal co-ordinate with the base station in the direction of thesatellite, and η the difference in horizontal co-ordinate with the base station in the perpendiculardirection. ∆y is the position error of the satellite in the “left-right” direction, ∆z “upwards” on thecelestial dome.Because the above equation is bilinear in the co-ordinates (η, ω) and thus also more generally inmap co-ordinates, we may interpolate the correction linearly, when it has been determined at the

30


three base stations. If we assume the base stations A,B and C, and the measured corrections∆PA,∆PB ja ∆PC , we can compute the correction for an arbitrary point as follows:

∆P = pA∆PA + pB∆PB + pC∆PC , (3.6)

where pA, pB ja pC are the computation point’s barycentric co-ordinates within the triangle:

pA =

∣∣∣∣∣∣xB xC xyB yC y1 1 1

∣∣∣∣∣∣∣∣∣∣∣∣xA xB xCyA yB yC1 1 1

∣∣∣∣∣∣, pB =

∣∣∣∣∣∣xC xA xyC yA y1 1 1

∣∣∣∣∣∣∣∣∣∣∣∣xA xB xCyA yB yC1 1 1

∣∣∣∣∣∣, pC =

∣∣∣∣∣∣xA xB xyA yB y1 1 1

∣∣∣∣∣∣∣∣∣∣∣∣xA xB xCyA yB yC1 1 1

∣∣∣∣∣∣. (3.7)

Here we have used plane or map co-ordinates (x, y), but the formulas would work just as well inany plane co-ordinate system, also (η, ω).For barycentric co-ordinates it holds that pA+pB +pC = 1, and they are all three linear in both thex and the y co-ordinate. By simple substitution one may ascertain, that in the corner points, e.g.,point A, pA = 1 and pB = pC = 0 – the reproducing property.In reality, however, the pseudo-range correction is not precisely linear: one should use the quadraticequation

f (X)− f (X0) =∂f

∂X

∣∣∣∣X=X0

ξ +12∂2f

∂X2

∣∣∣∣X=X0

ξ2 + . . .

We already derived∂f

∂X

∣∣∣∣X=X0

= − 1ρ0

+(x−X0)2

ρ30

.

Furthermore we may derive, that

∂2f

∂X2

∣∣∣∣X=X0

= −x−X0

ρ30

− 2x−X0

ρ30

+ 3(x−X0)3

ρ50

=

= 3

((x−X0)3

ρ50

− x−X0

ρ30

).

Again

x−X0 = −ρ0,

y − Y0 = 0,z − Z0 = 0,

and∂2f

∂X2

∣∣∣∣X=X0

= 0,∂2f

∂Y 2

∣∣∣∣Y=Y0

= 0,∂2f

∂Z2

∣∣∣∣Z=Z0

= 0.

This is a surprising result, but not entirely surprising. Equation 3.5 applies in three-dimensionalspace, i.e., when the location difference vector between base station and rover is s = ξe1 +ηe2 +χe3;in the formula we only see η and χ, but don’t blame the formula for that.However, the interpolation between the three base stations should be done in three-dimensionalspace, taking into account the curvature of the Earth. Simple plane formulas like 3.6 are insufficient.However, formulas in the (η, χ) plane are good.

3.4.3 Summary

The procedure thus is the following:1. For every satellite separately, compute the base stations’ A,B,C and the rover’s special co-

ordinates η, χ in a plane that goes through the rover, which is perpendicular to the directionvector to the satellite (requires almanac data)3

3So: project the co-ordinate difference vector with the rover onto the e′2, e′3 plane. In other words, compute ηA =⟨

(rA − r) · e′2⟩

, χA =⟨(rA − r) · e′3

⟩, and do the same for base stations B and C.

31


��

��

��

��

��

��C

A

B

��

��

��

��

p = C = ω(∆ )ABP

ω(∆ )ABC

p = B ω(∆ )APC

ω(∆ )ABC=

p = A

= ω(∆ )PBC

ω(∆ )ABC

=

P

Kuva 3.2: Barycentric co-ordinates

2. Compute from those barycentric weights (equation 3.7) by substituting (η, χ) instead of (x, y),and

3. Do the interpolation of the ∆P values.For clarity we still present a picture.

3.4.4 Modelling the atmosphere

The effect of the satellite orbit and clock errors is by its nature functional, i.e., it may in principlebe calculated precisely for the roving receiver’s location, if we have been given the observations,or pseudo-range corrections, in three base stations, and the base stations are in a pretty trianglearound the measurement location. The effect of the atmosphere again is not functional but stoc-hastic.This is why precise prediction to the rover location will not work; the uncertainty grows withgrowing distance from the base station.How it grows, depends on the statistical properties of the atmosphere. The GPS signal delay causedby the atmosphere – both the ionosphere and the troposphere – (in case the satellite is in thezenith) forms a stochastic process, let’s say d (ϕ, λ), on the domain of geographical locations (ϕ, λ).One can define a signal covariance function for it. E.g., the covariance between two locations canbe described by a Gauss-Markov type covariance formula:

Cov (d (ϕ1, λ1) , d (ϕ2, λ2)) = C0e−‖ψ‖/ψ0 ,

where ψ is the angular distance between the points (ϕ1, λ1) and (ϕ2, λ2) on the Earth surface. Thequantity C0 is called the signal variance, the quantity ψ0 the correlation length. These quantitiesnay be chosen suitably, i.e., realistically for the tropo- and ionosphere of a certain time and place.Another approach is to model the atmosphere functionally, but with unknown parameters. E.g.,the global ionosphere may be well described by a spherical harmonic expansion4. Also a polyno-mial or Fourier expansion may be considered. The unknown coefficients are estimated from theobservations of the base stations.The “state of the art” of this moment is, that the RTK positioning using a network of base stationsis as precise as RTK positioning using one base station in the immediate vicinity, on condition thatthe distances between the base stations are at most approx. 80 km. The quality of positioning is

4In fact the GPS navigation message contains such a model with twelve parameters.

32


s

r

P ′

P

rs

A B

Kuva 3.3: The geometry of differential GPS. The radial satellite orbit error (r) does not stronglyaffect the difference measurements between different ground stations, the sideways orbiterror (s) on the other hand affects linearly in the distance between stations.We also depict the way the differential correction is computed: the location P of the rovermust be projected on the plane going through the base stations AB (projection point P ′)and after that, the correction must be linearly interpolated.

also preserved for some distance outside the coverage area of the network of base stations. Theatmosphere is the limiting factor.

3.4.5 Technical implementation

3.4.5.1 “Virtual base station”

In this solution (VRS, Virtual Reference Station) we generate a base station that is close to thelocation of the rover5. The solution requires that the rover announces its own approximate locationto the server of the base station network. The link with the server has to be one-to-one: “singlecas-ting”. ABroadcasting solution is not good enough, as the corrections are bound to a different loca-tion for every user, and are thus different. The Finnish (Geotrim) VRS solution uses the mobile(cell phone) internet. In this solution one pays only for the data actually transferred, the link is allthe time on.The format in which the corrections are sent to the rover is conformant to RTCM-104. Thus areceiver palnned for use with a single base station will also work with the virtual base station.

3.4.5.2 Network computations in the server

In this solution, the measurements at the rover are transmitted to the server, where it is beingprocessed together with the measurements from the base station network. Here, the availablecomputing power may limit the number of clients that can be handled.The advantage compared to the concept of virtual base station is, that in the processing, “tricks”may be used: e.g., the RTCM software assumes, that if the distance between rover and base stationis small, one may leave out the effect of the atmosphere may be neglected. If the base station isvirtual, this assumption may be inappropriate.

3.4.5.3 Network computation in the client

In this solution, the measurements from the base station network are sent in raw form to theclient or rover. This requires substantial bandwidth – because we’re talking about data from many

5So: we generate observational data that would be acquired, if there were a real base station at the location of the virtualstation.

33


stations – and processing power. On the other hand this scales better with increases in the numberof clients.

3.5 Practical implementations

3.5.1 The VRS-RTK solution by Geotrim

In 2003 an agreement was drawn up between the Finnish National Land Survey and GeotrimOy to build a network RTK system covering the Finnish territory. At this moment the network(GPSNet.fi) consists of over 80 stations, with inter-station distances of order 50–80 km.The measurements are made every second; this is why the system also supports the positioning ofmoving receivers (vehicles), e.g., aircraft doing aerial photography. The data comes via a GSM datacall in RTCM format for a virtual base station close to the user’s location.The number of simultaneous users may, during the National Land Survey’s field season, be severaldozens. There are also other users beside the NLS, e.g., municipalities. The servers of the networkare located on Geotrim’s premises in Vantaa. They form a cluster of six powerful PCs.Also the static measurements by the network of base stations is archived, for a limited time.

3.5.2 The tests by the Finnish Geodetic Institute

In tests by the FGI [4] it was shown, that both using the Geotrim network and the VRS basestation network of Tampere City one achieves results that are in practice nearly as good as moretraditional RTK measurements using a single base station. In 95% of cases, the error was less than5 cm. Initialization times (“on-the-fly ambiguity resolution”) lasted generally about half a minute.The distance between station had an effect on both the precision achievable and the initializationtimes. The effect is seen first in the height solution if the base station distance grows to exceed100 km.The good performance of the VRS system depends critically on the network software used, especial-ly its correct modelling of atmospheric (ionospheric and tropospheric) effects.The final phrase of the report is worth remembering:

“Finally we want to stress the responsibility of the surveyor. VRS demands from its userthe same aquaintance and experience as also traditional measurement methods.”

3.5.3 Other use experiences

Network RTK systems are being used currently in many countries. In Germany the SAPOS networkhttp://www.sapos.de/ is used.There are, also in Finland, cities that have their own RTK base station in the city centre. In thatcase, the precision will not be homogeneous: in the centre are of the city, within a distance of 10–20 km, precision is good, outside that it will deteriorate. This is not necessarily a bad thing, ashigh-value, measurement class 1, land is located in the central area of the city.

3.5.4 Furthermore. . .

• Details on various ambiguity resolution methods

34

GPSNet.fi

http://www.sapos.de/


Kuva 3.4: The GPSNet network. Figure c©Trimble Terrasat GmbH

35

4 Code observations and spatialapplications

4.1 General

Differential GPS measurements using “codes”, i.e., pseudo-random noise (PRN) codes are in verybroad use for measuring spatial data. The applications may be classified according to precisionclasses into the following categories (from most to less precise):• Data collection• Maintenance of geospatial data• Mobile geospatial data systems (“Mobile GIS”)• Location Based services, LBS

4.1.1 Collection of geospatial data

This is the collection of original data in the field. This includes always positioning, but also thedescription of measured objects according to a certain system (standard).The collection of spatial data, or mapping, can well be done off-line, i.e., data is collected into thefield device and is transferred later into the geospatial data base.Here the precision requirements are greatest, 0.2–10 m. Using code measurements one does notget better than 0.2 m, often less precision is good enough.

4.1.2 Maintenance of geospatial data

In this case we update pre-existing spatial data in the field. For this purpose the existing data(material on an area) is loaded into the mobile device (GPS device or a field computer or datacollector connected to it), either in advance (off-line) or during work wirelessly (on-line).Positioning is in this mode a means to finding objects. Precision isn’t critical any more, if one doesn’tmeasure new objects.

4.1.3 Mobile geospatial data systems

In this use mode the organization using spatial data enables the use and updating of its spatialdata base directly from the field (on-line). As terminal device a portable field micro containing ageneral purpose operating system (often Windows CE/Mobile/Pocket PC, more rarely MS-DOS).Often user made client softwares.

4.1.4 Location based services

Spatial data services aimed at the end user, i.e., the consumer. As terminal device one envisages awidely used consumer-grade device, i.e., an intelligent mobile phone.The classical example is “where is the nearest pizzeria?”. Haven’t however yet achieved a signi-ficant popularity.Technical solutions, beyond DGPS, also various mobile network positioning solutions (“AssistedGPS”, AGPS).Indoors various solution models: micromechanical motion sensors (MEMS) used like in inertialnavigation; WLAN supported positioning, etc. A rapidly developing field. Key is creating general,open standards.

36

4 Code observations and spatial applications

4.1.5 The RTCM standard

The already mentioned RTCM standard supports also (and primarily) DGPS positioning:Message Type Message Title

1 DGPS corrections2 Delta DGPS corrections3 Reference station parameters9 High rate DGPS corrections10 P code DGPS corrections11 C/A code L1/L2 delta corrections

In this table are listed only those message types directly related to DGPSAs one can see, besidesthe corrections are distributed also “delta-corrections”; therefore, that the transmitted correctionsare always out of data. I.e., the moment – the epoch – to which they refer and on which they arestrictly valid, is always in the past: the computation of corrections at a base station, their packagingaccording to the RTCM standard, their transmission, reception and use consume time.The delta correction tells what is the time derivative of the correction. With the aid of that –assuming that the correction behaves linearly – one can calculate, what the real correction is atthe moment of use.We speak of pseudorange (PR), pseudorange correction (PRC) and range-rate correction (RRC)which thus is the same as “delta”. The equation is

PRC (t) = PRC (t0) +RRC (t0) · (t− t0) .

The time difference t− t0 can well be as large as tens of seconds.

4.1.6 Precision

The precision of DGPSis in a small area considerably better than direct GPS measurement withoutusing a base station.As was the case for carrier phase measurement, the most important sources of error are:• Orbital elements• Satellite clock error• Ionosphere• Troposphere• Multipath reflections• The imprecision of the code measurement by the device.

Error source Nature Size Size in diff. Eliminationmeasurements

Satellite orbit Geometric ∼1 m ∼4 mm/100 km Not eliminatedSat. clock error Constant metrejä 0 DifferencingIonosphere Stoch. process ±10 m ∼1 cm/100 km Two freqs. L1, L2

Troposphere Stoch. process ±10 cm 1 cm/100 km DifferencingMultipath Local ∼1 m same ?Imprecision of device Local 0.2 - 2 m same Technology

Below more details:

4.1.7 Satellite orbit error

The orbital information transmitted by the satellites themselves (broadcast ephemeris) enablesdetermination of their location in space to about ±1 m precision.In absolute positioning, this orbital error enters straight into the computed position. In differentialpositioning, i.e., when using a base station, the greater part of the error is eliminated. The basestation determines pseuso-range errors caused by the orbit errors and sends them to the rovinguser. If the rover is close to the base station, then the error in his pseudo-range will be the same as

37


the base station’s; when the distance to the base station increases, also the difference between thetwo pseudo-ranges will grow, which enters fully into the position of the rover as positioning error.In practice in the most typical DGPS applications it is not necessary to use precise ephemeris.

4.1.8 Satellite clock error

This is eliminated in the difference between two receivers, i.e, in differential positioning it cancelscompletely.

4.1.9 Ionosphere, troposphere

The effect of the ionosphere may be totally eliminated with a dual-frequency receiver. If one doesn’thave on (cheaper), one used ionosphere modelling. The RTCM standard makes possible dissemina-tion of ionospheric corrections (message type 15).The effect of the troposphere is the same on both frequencies, i.e., non-dispersive, in contrast to theeffect of the ionosphere. It is approximately eliminated in differential measurement, if the distancefrom the base station is small.

4.1.10 Multipath

Multipath is a disturbance that is hard to eliminate. In code based measurements it may be subs-tantial, metre class.A good practical piece of advice is to avoid the proximity of reflective metal surfaces (like the roofof a car).

4.1.11 Noise level of device

Receivers are different, and so are antennas.

4.1.12 SBAS systems

More about these later on. These are distribution channels for corrections to code measurements,making use of geostationary satellites.

4.1.13 Omnistar

This is a commercial satellite correction service: www.omnistar.com. It distributes correctionsglobally. The corrections are computed using a rather large number of reference stations all aroundthe world. Precision is better than one metre on all land areas. Also a higher precision service levelis being offered.

4.1.14 The service of the Finnish Maritime Administration

This service, which is intended for use both on the eastern Baltic and the internal lake areas, useslong wave radio (frequencies 287.5 - 314.5 kHz) for distributing the corrections. The Finnish sta-tions are Porkkala, Mäntyluoto, Puumala, Outokumpu, Turku, Marjaniemi, Klamila ja Kokkola. Afree-of-charge public service.

4.1.15 The Fokus service

This is a service operated by Indagon Oy in collaboration with Digita Oy within Finland, using asdistribution channel a side band of the Radio Suomi FM transmission: RDS, Radio Data System,which is also used for station identification and automatic frequency switching etc. In order to usethe service, one needs in addition to a GPS device also a decoder (receiver for corrections) and avalid subscription.

38

www.omnistar.com


Station Frequency CoveragePorkkala 293.5 250 km

Mäntyluoto 287.5 250 kmPuumala 290.0 70 km

Outokumpu 304.5 70 kmTurku 301.5 200 km

Marjaniemi 314.5 250 kmKlamila 287.0 250 kmKokkola 290.5 250 km

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4.2 Measurement methods and geometries

Code based DGPS positioning is so modest in its precision, that compared to carrier phase measu-rements it is not worthwhile to try combine measuremets from multiple base stations. If one hasa network of base stations, only the correction from the nearest station is used. Also the use ofdual-frequency receivers is not worthwhile.

4.3 Practical implementations

4.3.1 GIS applications

GIS applications are primarily based on code measurements, because• the precision suffices• phase measurement has the ambiguity problem• requires sufficient satellites, and continuous visibility, not for “poor” locations.

However:• Mapping and setting out (e.g., pipe and line mapping, base network . . . )• Field surveys (NLS uses already)• Terrain control points measurements in photogrammetry, positioning of the photographing

plane• etc. . .

39

5 New technology: GNSS systems

GPS GLONASS GalileoOrbital planes; in-between angle 6; 60◦ 3; 120◦ 3; 120◦

Satellites / plane; in-between angle 4; 90◦ 8; 45◦ 9; 40◦

Satellites total (official) 24+4 21+3 27+3Orbit height (km) 20 000 19 100 23 222Period 11h58m 11h15m 14h05m”Resonance” (orbits/sidereal day) 2/1 17/8 17/10Inclination 55◦ 64◦.8 56◦

5.1 GPS modernization

In charge: GPS Joint Program Office http://gps.losangeles.af.mil/jpo/.

5.1.1 Satellite types

The different types of GPS satellites are called blocks.Block I consisted of test satellites used for testing the GPS concept.Block II was the first operational GPS satellite type. None are any longer in operation.Block IIA: A = “Advanced”. Still operating.Block IIR: First one launched in 1997.Block IIF: The first was launched in May 2010.Block III: Planned for 2012.

5.1.2 New codes

The first Block IIR-M satellite was launched September 25, 2005. It transmits the new civil codeL2C, modulated on the L2 carrier. It contains new pseudo-random codes, so-called CM (CivilianModerate) and CL (Civilian Long) codes, whose lengths is 10 230 and 767 250 bits. Together themodulation frequency (“chip rate”) is 1 023 000 bits per second. L2C contains also an improvednavigation message, to which belongs, among other things, the time scale offset of the GPS sys-tem (important in combined use with GLONASS and Galileo!) as well as an Alert-warning, whichannounces within six seconds, if one cannot rely on the satellite’s data (integrity).

5.1.3 New frequencies

The new frequency L5, 1176.45 MHz, is meant for Safety-of-Life type use especially in aviation.This frequency is internationally reserved for aviation. Block IIF satellites carry this frequency asthe first.Also SBAS systems use L5.

5.2 GLONASS

5.2.1 Players

See Information-Analytical Center http://www.glonass-ianc.rsa.ru/, press the “eng” flag.

40

http://gps.losangeles.af.mil/jpo/

http://www.glonass-ianc.rsa.ru/


Status: http://www.glonass-ianc.rsa.ru/pls/htmldb/f?p=202:3:392499057198675::NO:::.In October 2010 there were 24 satellites in orbit of which 21 operational and 3 undergoing mainte-nance. The number of satellites has grown slowly; after a long period of neglect, the system is backto full operationality again.

5.2.2 System description

The GLONASS system is described by the Interface Control Document ICD (50 pages) from 2002.The GLONASS system differs fromGPS and Galileo in that every satellite has its own carrierfrequency. However, like GPS, it uses two frequency bands L1, approx. 1.6 GHz, and L2, approx. 1.2GHz. Nowadays however the “antipodes” – satellites in the same orbital plane on opposite sides –can use the same frequencies.

fK1 = f01 +K∆f1,fK2 = f02 +K∆f2,

where K is the satellite’s channel number – can be found from the almanac – and

f01 = 1602 MHz ∆f1 = 562.5 kHz,f02 = 1246 MHz ∆f2 = 437.5 kHz.

The civil code – corresponding to C/A – has a bit frequency of 0.511 MHz, the encrypted militarycode 5.11 MHz. The modulation technique is the same as for GPS, phase modulation with a phaseshift of π = 180◦. The navigation message is only on L1; its bit frequency is 50 Hz.The satellites’ radiation is clockwise (“right-hand”) polarized, like GPS.GLONASS time scale: is the same as UTC/SU), i.e., the realization of UTC for the Russian Fede-

ration. This means that the leap seconds of UTC, which happen either at the end of Decemberor of June, enter into the GLONASS time scale. This is different from the GPS practice: GPStime does not have leaps.The differences between UTC and UTC(SU) as well as an announcement of upcoming leapseconds is contained in the navigation message.

Reference system: The system PZ90 is used, which is geocentric but slightly different from GRS89.The ephemeris give the location of the satellite in space in this system, however in rectangu-lar co-ordinates.

Orbits: The nominal orbits of the GLONASS satellites (in a full constellation) will be 21 in threeorbital planes, plus three spares. The inclination angle with the equator in 64◦.8, a high valueserving the area of the old Soviet Union better. Like also for GPS, the satellite geometry ofGLONASS repeats after a sidereal day. Differently from GPS, however, then there will be adifferent satellite in the same place. The orbital height is 19 100 km and the period 11h15m,shorter than a sidereal day. Only after eight days (17 orbits) the same geometry will repeatitself also with identical satellites in the same places. This solution reduces the resonantorbital perturbations, which for the GPS system consume a lot of rocket propellant.

5.3 Galileo

5.3.1 Players

The Galileo system is a joint undertaking of the EU Commission and ESA. The formed the “GalileoJoint Undertaking” (GJI), which again chooses a “concessionaire”, a private “Galileo OperatingCompany” responsible for Galileo’s daily operations and especially its commercialization.

5.3.2 Satellites and orbits

There will be 30 Galileo satellites, in three orbital planes, in each of which are nine satellites andone spare. The distance between satellites within the orbital plane is 40◦. The inclination of theorbits relative to the equator is 56◦.

41

http://www.glonass-ianc.rsa.ru/pls/htmldb/f?p=202:3:392499057198675::NO:::


E5

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Yellow: frequencies already in use

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Kuva 5.1: Galileos frequencies

The height of the Galileo satellites’ orbit is 23 222 km, higher than the GPS orbits.The geometry is repeated every sidereal day, like the GPS geometry; the difference is though, likealso for GLONASS, that after a day, the same places are taken by different satellites.Only after 10 days, or 17 revolutions, will the same satellites be again in the same places in theobserver’s sky.The first Galileo satellite, GIOVE-A, was launched on December 28, 2005. GIOVE-B followed onApril 27, 2008. Both are experimental satellites.

5.3.3 System description, components

The Galileo system is partially compatible with the GPS system. It is also intended to work seam-lessly with SBAS systems, like (in Europe) EGNOS.Galileo’s signal and frequency structure is complex, cf. http://www.esa.int/esaNA/SEM86CSMD6E_galileo_0.html. The carriers are L1, 1575.42 MHz like also for GPS; E5a (1176.45 MHz) and E5b(1207.14 MHz); and E6. E5a is also called L5.

5.3.4 Various services

The services offered by Galileomay be divided as follows:• Open service (OS). Useable by anyone. [L1, E5]• Safety-of-Life (SOL). [L1, E5b]• Commercial (CS). [L1, E5, E6]• Public Regulated Services (PRS). The latter also includes the police, border guards, defence

forces and peacekeeping forces as well. The fact that Galileo is called, “as opposed to the GPS,a civilian system”, is perhaps not quite accurate . . . [L1, E6]

New with Galileois the integrity service. It is part of the Safety-of-Life service.

5.4 The Chinese Beidou system

About the name: BeiDou is the constellation Big Dipper (Ursa Major), which is used to find theNorth Star (Polaris, αUMi). Thus the name is symbolic for navigation.

5.4.1 Beidou 1

This system is in early stage of construction. The Beidou-1 system is already in use. It consists atthis moment of three satellites in a geostationalry orbit. Originally it was believed that it works

42

http://www.esa.int/esaNA/SEM86CSMD6E_galileo_0.html

http://www.esa.int/esaNA/SEM86CSMD6E_galileo_0.html


like an SBAS system; however it was found out that it also functions independently: the groundstation sends a signal through two satellites to the roving receiver, which also answers throughtwo satellites (it is thus an active system). Thus the receiver location may be computed, at least onthe territory of China. The use of a terrain model improves precision (http://www.vectorsite.net/ttgps_2.html). The computed position is sent to the receiver encrypted for military use.

5.4.2 Beidou 2

For the future Beidou-2 system (English name “Compass”) also a civilian signal has been promised,with positioning precision of ±10 m. The Beidou-2 system will comprise of 35 satellites, of which 5will be geostationary.On April 14, 2007 China launched the satellite Beidou M-1, the first satellite to be in a GPS likeorbit, height 21500 km, inclination 55◦. It transmits on four frequencies: 1589.74 (E1), 1561.1 (E2),1268.52 (E6) and 1207.14 (E5b) MHz. The signal is modulated with pseudo-random codes a bit inthe same way as GPS or Galileo. Ks. [3].

43

http://www.vectorsite.net/ttgps_2.html

http://www.vectorsite.net/ttgps_2.html

6 New technology: SBAS systems

6.1 Integrity and Safety-of-Life

Integrity is, that the user is warned, in practice within six seconds, of the positioning signal of acertain GPS satellite appears to exceed certain tolerance values. In Safety-of-Life applications thisis mandatory. Safety-of-Life means that, if the system doesn’t function correctly, people may die.An example is approach and landing on an airport: if we descend in fog using GPS navigation, andthe height is wrong by many metres without any warning, an accident will happen. If in fog theheight is wrong by many metres and the pilot is warned, he doesn’t land. If, on the other hand, theprecision guaranteed by the integrity system is several metres and there is no fog but low cloud,the pilot may land on visual from 200 feet downward.

6.2 WAAS

WAAS (Wide Area Augmentation System)was declared operational in 2003. The system monitorsthe GPS system and computes differential corrections for the users, as well as providing a certi-fied integrity level. Precision after differential correction is order ±2 m. Other sources give 1 − 2 mhorizontally ans 2− 3 m vertically within the service area. Without WAAS, GPS positioning wouldonly be ±15 m using a single frequency GPS receiver, mostly due to the ionosphere.Integrity again enables operations in aviation that would be to risky only using GPS. GPS as suchhas already been used in RAIM mode (Receiver Autonomous Integrity Monitoring), but only in thestraight parts of route flights and not during descent. The requirement is, that at most six secondsafter a GPS signal goes unreliable, the user is informed of this. From 2007 on WAAS has beenapproved for guiding an aircraft safely to 200 feet height above an airport: ICAO Category I.WAAS is also cheaper, because traditional radio navigation support equipment in airport areas ismassive in size. Also fuel may be saved, as GPS/WAAS allows straight flights from field to fieldinstead of through a polygon over radio beacons.The American WAAS system uses 29 base stations (WRS, Wide-area Reference Stations) in NorthAmerica, including eight in Alaska, one in Hawaii and one in Puerto Rico. This is also the areawithin which the disseminated corrections are precise.The corrections are computed at three so-called WMS stations (Wide-area Master Stations). Thesecompute differential corrections in the form of a grid. The correction message is computed andtransmitted to a geostationary satellite, which sends the message on to the user on the samefrequencies used also by the GPS satellites, i.e., L1 and (in the newer satellites) L5.The data communication links between stations have been custom built. The open Internet is notreal time with acceptable reliability.The signal from a geostationary satellite is coded in the same way using pseudo-random codes likethe signals from the GPS satellites. The WAAS satellites have their own PRC codes separate from

Kategoria “Decision height” Visibility Visibility on runwayCat I ≥ 200 ft, and ≥ 800 m, or ≥ 550 mCat II 100 – 200 ft, and ≥ 350 m

Cat IIIA < 100 ft/ none; and ≥ 200 mCat III B < 50 ft /none; and 50 – 200 mCat III C none no limitations

Taulukko 6.1: The various approach categories according to ICAO. SBAS approach is possible onlyfor part of the categories.

44


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Kuva 6.1: WAAS ground segment. Red: WRS, yellow: WMS, blue: GUS. The system will soon beextended to Canada and Mexico.

Satellite Longitude Expires NoteInmarsat IIIs POR 178E Syys 2007Inmarsat AOR-W 142W Syys 2008Telesat Anik F1R 107,3W 2016 In test use

PanAmSat Galaxy 15 133W 2016

Taulukko 6.2: The WAAS satellites. These are communication satellites on which the WAAS trans-ponder is only a small part of the payload

each other and the codes of the GPS satellites, and the correlator in the receiver distinguishes themwith the aid of these.A WAAS capable GPS receiver receives corrections separately to the orbit and clock errors of thesatellites (the latter the same everywhere but different for each satellite, and the latter rapidlychanging in time) and the ionospheric effect (same for all satellites but location dependent, whichis why it is computed in the form of a grid). The ionospheric correction is valid only in the areawhere there are base stations.The system is being expanded to Mexico and Canada.WAAS is also being used outside aviation, e.g., in maritime navigation.

6.2.1 LAAS

LAAS (Local Area Augmentation System) is intended to enable the automatic landing of aircraft onbusy airports: ICAO Category III. In the LAAS system, GPS receivers are used in the airport area,from the observations of which corrctions are computed locally and transmitted to the aircraft byradio (VHF). In contrast to WAAS kuten, it does require special equipment on the airport. However,one such set of equipment would replace many traditional installations, like VOR beacons, for everyrunway.LAAS can also be used to guide ground vehicles within the airport area.

45


Satellite Longitude Expires RemarksInmarsat IOR-W 25.1EArtemis 21.5E 2015 ionic engineInmarsat III AOR-E 15.5W

Taulukko 6.3: EGNOS satellites. These are general communications satellites and the SBAS trans-ponder is only a small part of the payload.

LAAS is a so-called Ground Based Augmentation System (GBAS). Its use is not yet generallyapproved, because the GPS system constitutes a risk factor, a so-called single point of failure.

6.3 MSAS

MSAS (MTSAT Satellite-based Augmentation System) is a Japanese SBAS. It is compatible withWAAS and EGNOS.

6.4 EGNOS

EGNOS is a joint project by the European Commission, ESA and Eurocontrolin (the joint Europeanaviation safety organization). It is sometimes called GNSS-1, to distinguish it from Galileo, whichis thus GNSS-2.EGNOS is in principle compatible, or “interoperable”, with WAAS. There have however been prac-tical problems with this related to the way transmissions are flagged as “test transmissions”.EGNOS started operations in July 2005.EGNOS consists of four functional parts: the ground segment, support segment, space segmentand user segment.

6.4.1 EGNOS ground segment

The ground segment of EGNOS consists of the following components:1. RIMS (Ranging and Integrity Monitoring Stations): 34. Receive the signal and send it forward

to the MCC centres.2. MCC (Master Control Centres): 4. Receive data from the RIMS and compute from it correc-

tions and integrity data, which is sent forward.3. NLES (Navigation Land Earth Stations) Send data forward to the geostationary satellites.

Like also in the case of WAAS, also the EGNOS ground stations have dedicated data connectionsbetween them.In the framework of the EGNOS Transafrica project, after 2002 were 10 EGNOS-RIMS establishedin Africa, in addition to Hartebeesthoek.

6.5 QZSS

Japan is designing a system named QZSS, Quasi-Zenith Satellite System. It is planned as anaugmentation system for GPS using the GPS signal structure.The satellite orbits are 24-hour orbits, the inclination of which is high, approx. 45◦ − 53◦, and veryelongated, i.e., the orbital eccentricity is high. The intention is that at any time there would be onesatellite hanging over Japan at a reasonably high elevation angle. From this originates the label“quasi-zenith” originates. It would require three satellites in orbit. The satellites are also suited,and especially so, as communication satellites, like in its day the Soviet Molnya satellites, that hada similar operational concept.

46


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Kuva 6.2: EGNOS ground segment Red: RIMS, yellow: MCC, blue: NLES. In addition to this, thereare ground stations in South Africa, Canada, Singapore, French Guyana.

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Kuva 6.3: QZSS-radan toiminta-idea

47


QZSS is at the time of writing in the design phase, the launch is planned for 2008. Differentlyfrom other (geostationary) SBAS systems, this system offers useable measurables pseudo-rangeand carrier phase.

6.6 The SiSNET experiment

SiSNet (Signal in Space over the Internet) enables the download of EGNOS corrections in (near)real time over the Internet. Thus we may use the EGNOS satellites’ corrections also in places (likeon high latitudes) where geostationary satellites are poorly visible.See http://www.egnos-pro.esa.int/sisnet/index.html. SiSNet is a technology sponsoredby ESA, developed in the years 2001-2006. The client application is freely available for the Pocket-PC hand-held micro.

48

http://www.egnos-pro.esa.int/sisnet/index.html

7 New technology: attitude determination

When using positioning technology in the field, it is often also reasonable to determine one’s ownattitude. In this way one may relate the map visible in the device to the surrounding world.In a way all devices that are able to show the user a map, already perform an attitude measu-rement, but very “informally”: it works in this way, that the device assumes that the user moves(drives, walks) straight ahead, and orients the map on the screen according to that assumption.This is an intuitive behaviour, of which users are often not even aware. Nevertheless, if one standsstill or changes direction, the device doesn’t follow along.There exists also real attitude measurement equipment. Its use in field measurement devices ishowever still at the start.

7.1 Inertial device

This device contains three accelerometers and three (laser) gyroscopes. With their aid it can fol-low its own (i.e., the equipment into which it is integrated) rotational movements as well as linearmovements. As time elapses, the positioning solution, obtained by integrating the measured acce-lerations twice, first into velocities, and then once more into locations will deteriorate.The deterioration may be controlled, if one at certain intervals performs a “real” positioning, e.g.,using GNSS. Thus one may build a system that preserves its positioning precision even though theGNSS signal is patchy (tunnels, bridges, indoor space). At the same time we also obtain a preciseorientation for the equipment.An example of such an integrated equipment is the Novatel SPAN (Synchronized Position AttitudeNavigation), http://www.imar-navigation.de/download/novatel_imar_gyrosymposium2005paper.pdf.The measurement precisions of these devices are impressive: the stability of rotation is (for a highquality mechanical gyroscope) 0.0001◦/h.

7.2 GNSS multi-antenna system

Also with a GNSS system we may measure attitudes, by using several (at least three) differentantennas. The method is real time kinematic positioning over very short vectors.As can be seen from the figure, the same satellite is being observed from two different antennas.The observable is the difference between two measurements of carrier phase:

∆P s = P s2 − P s1 = 〈v · es〉+ kλ,

where v is the inter-antenna vector, es is the direction vector to used satellite s (unit vector, ‖e‖ =1) and k kokonaisluku.is an integer describing the ambiguities (potential for many alternativevalues).We re-write this by reducing the observable to the interval [0, λ):

∆P smodλ = 〈v · es〉+ k′λ.

Here, we have to solve simultaneously for the vector v and the integer unknown (ambiguity) k′.Solving for the vector requires observations from at least three different satellites, and then thevalues k′ remain still undetermined:

∆P 1modλ =⟨v · e1

⟩+ k′1λ,


⟩+ k′2λ,


⟩+ k′3λ.

49

http://www.imar-navigation.de/download/novatel_imar_gyrosymposium2005paper.pdf

http://www.imar-navigation.de/download/novatel_imar_gyrosymposium2005paper.pdf


1

2

v

Kuva 7.1: Attitude determination by GNSS

About the values k′1, k′2, k′3 we know at least that they cannot be very large if the vector v is short;as ∆P smodλ lies in the interval [0, λ) and 〈v · es〉 in the interval [−‖v‖ , ‖v‖], then k′s can only liein the interval

[−‖v‖λ , ‖v‖λ + 1

]. If the vector is, e.g., 2 m long, and the wavelength is 24 cm, then the

only possible values for k′s are: -8, -7, . . . , +8, +9.The solution is obtained as follows:

1. Try out all possible values k′s for three satellites 1,2 and 3, and compute for every combinationa vector solution v. The total number of solutions to be computed is in the example case183 = 5832.

2. If the vector is, e.g., 20 m long, then the total number of solutions to be computed is already1803 = 5.8 million. This requires already processing capacity. On the other hand, if we havethe use of a dual-frequency device, we may use widelaning, the effective wavelength of whichis 86 cm. Then we need only 483 = 110592 different solutions.

3. If we can see more than three satellites, we choose three of them, which together producethe best possible geometry. This is easy: traverse all triplets and compute their determinante1 ·

⟨e2 × e3

⟩. The maximum value wins. If we can see, e.g., 10 satellites, we have to compute

10 · 9 · 8 = 720 determinants.4. After this, we compute for every provisional solution thus found, vk′1,k′2,k′3 , whether ‖v‖ is

close enough to the known distance between the antennas. Solutions that are not, can bediscarded immediately.

5. After this we compute again the observables of the other satellites:


⟩+ k′4λ,∆P 5modλ =

⟨v · e5

⟩+ k′5λ,

. . .∆Pnmodλ = 〈v · en〉+ k′nλ.

All the values on the left hand side should agree, within their measurement uncertainties,with the measured carrier phases for one value k′4, k′5, . . . . Generally, this only happens forall values k′s, s = 4, . . . , n only in the case of one solution.

6. Using the set of values thus found, k′s, s = 1, . . . , n, the final adjustment is executed in orderto compute v from all observations.

7. When the device (vehicle) moves, and no cycle slips occur, the values k′s stay the same. Thenone can continuously solve for v in real time from the observations collected.

50


7.3 MEMS (Microelectronic Mechanical System)

These devices are small and inexpensive acceleration and rotation sensors. The manufacturingprocess is similar to that of computer micro circuits: photolithography.

7.3.1 Accelerometers

These circuits measure accelerations by measuring, e.g., capacitively, the movement of a small testmass under the influence of acceleration (a pseudo-force). One model is capable of measuring downto 1.7 g (17ms−2) with stability 0.2% ,i.e., 340 mGal. In order to get an idea what this means, let ussay that an acceleration of 340 mGal during a minute moves over a distance of 6 m. The sensitivityof the device is even better than that, several mGal. It also survives dropping, e.g., onto a concretefloor (acceleration 3500g!). They have also been fired from cannon.See http://www.scharfphoto.com/stockphotos/archives/000504.php for a picture.Prices are nowadays (2007) around a few dollars, even below one dollar. They are a few mm in size.Applications: e.g., triggering sensors for automotive airbags, and drop protection triggering sensorsfor laptop hard drives.

7.3.2 Rotation sensors

Rotation sensors commonly are based on measuring the frequency of oscillation of a tunign fork,cf. [11]. Like a rotating object, also a vibrating object tries to stay within the same plane. Thetorque required for this, the so-called Coriolis force, is measured, e.g., capacitively; the measure-ment value is proportional to the rotation rate. Cf. figure. A three-axis or degrees-of-freedom deviceis manufactured from three one-axis components.These devices are capable of a precision of 0.1◦/s which is six orders of magnitude poorer than a“real” inertial device, see above.Fields of application: stabilizing the image of video cameras, robotics, unmanned aerial devices(UAD), . . .

7.4 Integration

In practical devices the above described hardware solutions are integrated into a working system.To that must be added also always processing power; the processing algorithm typically is a Kal-man filter, which takes in the measurements by all the sensors and estimates in real time theparameters describing the state of the system, the state vector. This contains at least location andattitude.

51

http://www.scharfphoto.com/stockphotos/archives/000504.php


Rotaatio−liike

VibraatioliikeCoriolis−voiman värähtely

Kuva 7.2: The principle of a rotation sensor. When the substrate rotates, the vibration of the testmass (in the picture up and down) will cause a Coriolis force (left-right, also periodic),which is measured capacitively.

52

8 GNSS, GIS ja geofysiikka

• General: geolocation of measurements• Airborne measurements; gravimetry, magnetometry. . . [see Methods of Navigation course]• Airborne photogrammetry, remote sensing• Shipborne measurements; sonar, side-scanning sonar, . . .• Measurements on land

– Example: ground penetrating radar– Example: archaeological excavation

http://www.google.fi/search?hl=fi&client=firefox-a&rls=com.ubuntu%3Aen-US%3Aofficial&hs=0JW&q=GPS+GIS+geophysics&btnG=Hae&meta=

53



Kirjallisuutta

[1] Frankfurt am Main BKG. NTRIP. URL: http://igs.ifag.de/ntrip/ntrip_toc.htm. Luettu3.10.2005. 3.3.3

[2] Kai Borre. RTCM2ASC rel 1.0. URL: http://kom.aau.dk/ borre/masters/receiver/rtcm2asc.htm.Luettu 3.10.2005. 2.4.1

[3] Grace XingXin Gao, Alan Chen, Sherman Lo, David de Lorenzo, and Per Enge. GNSS overChina – The Compass MEO Satellite Codes. Inside GNSS, 2(5):36–43, 2007. 5.4.2

[4] Pasi Häkli and Hannu Koivula. Virtuaali-RTK (VRS TM ) tutkimus. Tiedote 27, Finnish Geo-detic Institute, Masala, 2004. 3.5.2

[5] B. Hofmann-Wellenhof, H. Lichtenegger, and J. Collins. GPS Theory and Practice. Springer-Verlag, fourth, revised edition, 1997. ISBN 3-211-82839-7. 1.5.1, 3.1

[6] Jaana Järvinen. Luentomoniste 2003:n GIS-GPS-kurssi. 2003. 1.1, 1.2[7] Herbert Landau, Ulrich Vollath, and Xiaoming Chen. Virtual Reference Station Systems.

Journal of Global Positioning Systems, 1(2):137–143, 2002. 3.1[8] Patrap Misra and Per Enge. Global Positioning System – Signals, Measurements, and Perfor-

mance. Ganga-Jamuna Press, 2001. ISBN 0-9709544-0-9. 3.3.4[9] Markku Poutanen. GPS-paikanmääritys. Ursa, Helsinki, 1998. Ursan julkaisuja 64. 3.1,

3.3.6[10] Lambert Wanninger. Introduction to Network RTK. URL: http://www.network-

rtk.info/intro/introduction.html, 2004. Luettu 27.09.2005. 3.1[11] Wikipedia. Vibrating structure gyroscope — wikipedia, the free encyclopedia, 2007. [Online;

accessed 10-September-2007]. 7.3.2

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