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GEOG 425/525 GPS Concepts and Techniques John Benhart, Ph.D. Indiana University of PA Dept. of Geography & Regional Planning
GEOG 425/525GPS Concepts and
Techniques
John Benhart, Ph.D.
Indiana University of PA
Dept. of Geography & Regional Planning
What Are Global Positioning Systems
(GPS)?
What is GPS Used For?
The Historical Context of the Global Positioning System (GPS)
• The origins of surveying:– Efforts to measure distance on the earth’s
surface– Efforts to specify location on the earth’s
surface– Efforts to determine property/land boundaries
• How?
How Eratosthenes Estimated the Earth’s Size
Early Estimates of the the Earth’s Size
1753 French Survey Establishes that the Earth Bulges at the Equator
The Basics of Surveying
• Definition: The science of measuring and mapping relative positions above, on, or below the surface of the earth; or establishing such positions from a technical plan or title description
• Types: – Plane surveying: Does not take into account the
curvature of the earth– Geodetic surveying: measurements covering larger
distances where the curvature of the earth must be taken into account
Surveying: History
• Evidence of surveying has been recorded as early as 5,000 years ago
• Ancient Egyptian surveyors called harpedonapata (“rope stretcher”– Ropes and knots were tied at pre-determined
intervals to measure distances– The 3-4-5 triangle (later formalized by Pythgoras) was
discovered to derive a right angle easily by using a rope knotted at 3,4, and 5 units
– Early Egyptian levels that were essentially plumb lines were derived
• Surveying inventions– Lodestone used to identify magnetic north– Thomas Diggs invents an instrument used to
measure angles called the theodolite in the mid-1500s
– Jean Praetorius invents the plane table in 1610
– W.J. Young invents the transit based on the theodolite, which “flips” to allow back sighting in 1831
Surveying: History
Theodolite
How a Theodolite Works
Plane Table and Alidade
Surveyor’s Transit
Total Station
The Basics of Surveying
• Starting from a position with a known location and elevation, known as a “benchmark,” the distance and angles to the unknown point are measured– Using a leveled theodolite or total station– Distance: previously chains, now lasers– Horizontal angle: from compass on theodolite– Vertical Angle: sighted in on a measuring or
leveling rod at the location in question
The Historical Context of the Global Positioning System (GPS)
• 1978 – launch of first GPS satellite• 1982 – macrometer prototype tested at MIT• 1984 – geodetic network densification in
Montgomery, Co. PA• 1989 – Launch of first Block II satellite; Wide Area
GPS concept tested• 1990 – GEOID90 for NAD83 datum established• 1993 – Real-time kinematic GPS implemented• 1996 – First US GPS policy expressed in
presidential directive• 1999 – US GPS modernization initiative• 2000 – Selective availability (SA) deactivated
Overview of GPS - Logic
• A continuous coverage of satellites exists within view of virtually every location on the earth’s surface (NAVSTAR)
• These satellites launch signals at recorded times on specific frequencies that can be “received” by units on the earth’s surface
• By calculating the amount of time it takes the signals from 4 satellites to reach a receiver on the earth surface, it is possible to determine the distance between the receiver and any satellite (pseudoranges)
• By using the intersection of the radii from 4 satellites, it is possible to determine exactly where a GPS receiver is located on the earth’s surface (trilateration)
** A huge amount of science and technology has to be applied for any of these conditions above to exist…
Overview of GPS - Objectives• The GPS was “conceived as a ranging system
from known positions in space to unknown positions on land, at sea, in air and space.” (p.11)
• The original objectives of GPS were “instantaneous determination of position and velocity (i.e. navigation), and the precise coordination of time (i.e. time transfer).”
• “The global NAVSTAR Global Positioning System (GPS) is an all-weather space-based navigation system under development by the DoD to satisfy the requirements of the military forces to accurately determine their position, velocity and time in a common reference system, anywhere on or near Earth on a continuous basis.”
Overview of GPS
• GPS can be conceptually be divided into 3 segments:– Space Segment: the constellation of satellites– Control Segment: tracking and monitoring of
the satellites– User Segment: varying user applications and
receiver types
Overview of GPS
• Space Segment– The NAVSTAR constellation: 24 evenly-spaced
satellites in 12-hour orbits inclined 55 degrees to the equatorial plane…each is assigned a pseudorandom noise code # (PRN code)
• Types: Block I, Block II, Block IIA, IIR, IIF, and Block III
– Continuous signal coverage of every location on the earth’s surface
– Satellite signals: launched at extremely-precisely recorded times (atomic clocks), and travel at the speed of light (through earth atmosphere) to receivers on the earth’s surface
• L1: 1575.42 MHz, L2: 1227.60 MHz
Overview of GPS
• Control Segment– Master control station: located at the
Consolidated Space Operations Center at Shriver Air Force Base, Colorado Springs, CO
• Collects monitoring data from global stations• Calculates satellite orbits and clock parameters for
each satellite…passed to ground control stations• Responsibility for satellite control
Overview of GPS
• Control Segment– Monitoring Stations: Five located at Colorado Springs,
Hawaii, Ascension Island (South Atlantic), Diego Garcia (Indian Ocean), Kwajalein (North Pacific)
• Precise atomic time standard• Continuous calculation of satellite pseudoranges• Official network for determining broadcast ephemerides
– Ground Control Stations• Also located at Ascension, Diego Garcia, and Kwajalein• Communication links to upload ephemeris, and clock
information to NAVSTAR satellites
GPS Monitoring Locations
Overview of GPS• User Segment
– Military Users• Original envisioned users; have access to precise
P-code satellite signals
– Civilian Users• Range from recreational to GIS and survey grade
applications – all made possible by federal infrastructure
– Receiver Types• C/A code pseudorange; C/A code carrier phase; P-
code carrier phase; Y-code carrier phase
GPS Summary
• The system is predicated on:– A constantly monitored constellation of
satellites– Very accurate time measurement– The ability to determine satellite location– The use of unique radio signals on specified
wavelengths launched from satellites and received by receivers on the earth’s surface
– The ability to translate pseudoranges into recognized coordinates through trilateration
Reference Systems
• GPS satellites are orbiting earth and launching signals with time stamps…we are usually trying to determine locations on earth…to do this we have to define suitable coordinate and time systems
• 3 Types of reference systems that are relevant in the context of GPS– Earth-fixed reference: the international terrestrial
reference system– Space-fixed reference: the international conventional
celestial reference system– Geodetic reference system
The Earth and Its Axis of Rotation• The Earth’s axis of rotation changes over time• Why? 1) Mainly caused by the gravitational forces of
the moon and the sun…as well as other celestial bodies 2) changes in the mass of earth-based phenomena – Precession – a slight change in the direction of the axis of
the rotating earth – Nutation - a slight irregular motion in the axis of rotation of
an axially symetrical body (planet)– Polar Motion - the movement of the earth’s axis across its
surface (~ 20 m westward since 1900)…due to motions in the earth’s core and mantle, and redistribution of water mass
• Who Cares? These factors cause the position of the earth in its orbit (revolution) around the sun to change over time (equinoxes and solstices)
• Precession• Nutation• Polar Motion
Precession: Cause
The gravitational pull of the sun on the closest part of the oblate spheroid is stronger…
Nutation
Reference Systems and Reference Frames
• Reference Systems: the complete specification of a coordinate system, such as the origin, coordinate axes, coordinate units, etc.
• Reference Frames: consist of a set of identifiable points along with their coordinates, which serve as a realization of the reference system
International (Conventional) Celestial (Space) Reference
System• The celestial reference system adopted by the
International Astronomical Union (IAU) for high-precision positional astronomy
• Characteristics: Origin at the solar system barycenter (center of mass) and “space fixed” axis directions
• Has been chosen by the IAU as the “most appropriate coordinate system for expressing reference data on the positions and motions of celestial objects.”
• A set of specifications based on space-fixed axes defining the location of bodies in space
• For example, the base plane of the system is the extension of the earth’s equatorial plane at J2000.0 (Jan. 1, 2000)
• Locations (of planets and stars) are specified based on declination (north-south) and right ascension (east)
International (Conventional) Celestial (Space) Reference
System
Earth-Centered Earth-fixed Reference
• The mass center of the earth is used as a reference
• Conventional Terrestrial Reference System: X axis is identical to the mean Prime (Greenwich) Meridian; Z axis is identical to the earth’s mean rotational axis (also called the Conventional International Origin (CIO)); Y axis points to the mean equatorial parallel
• See www.iers.org (the International Earth Rotation and Reference Systems Service)
International Union of Geodesy and Geophysics (1991) Resolution on the Conventional Terrestrial Reference
System
The International Union of Geodesy and Geophysics, Considering the need to define a Conventional Terrestrial Reference System (CTRS) which would be unambiguous at the millimeter level at the Earth's surface and that this level of accuracy must take account of relativity and of Earth deformation, and noting the resolutions on Reference Systems adopted by the XXIst General Assembly of the International Astronomical Union (IAU) at Buenos Aires, 1991, endorses the Reference System as defined by IAU at the XXIst General Assembly at Buenos Aires, 1991 and recommends the following definitions of the CTRS:
1) CTRS to be defined from a geocentric non-rotating system by a spatial rotation leading to a quasi-Cartesian system, 2) the geocentric non-rotating system to be identical to the Geocentric Reference System (GRS) as defined in the IAU resolutions, 3) the coordinate-time of the CTRS as well as the GRS to be the Geocentric Coordinate Time (TCG), 4) the origin of the system to be the geocenter of the Earth's masses including oceans and atmosphere, and, 5) the system to have no global residual rotation with respect to horizontal motions at the earth's surface.
International (Conventional) Terrestrial (Earth)Reference System
The International Terrestrial Reference Frame
• The Earth is constantly changing shape, because of plate tectonics and regional subsidence and/or used to represent the Earth when measuring its rotation in space.
• To be understood in context, when the motion of the Earth's crust is observed, it must be referenced. A Terrestrial Reference frame provides a set of coordinates of some points located on the Earth's surface. It can be used to measure plate tectonics, regional subsidence or loading and/or used to represent the Earth when measuring its rotation in space.
The International Terrestrial Reference Frame
• This rotation is measured with respect to a frame tied to the celestial reference frame. The International Earth Rotation and Reference Systems Service (IERS) was created in 1988 to establish and maintain a Celestial Reference Frame, the ICRF, a Terrestrial Reference Frame, the ITRF.
• The Earth Orientation Parameters (EOPs) connect these two frames together. These frames provide a common reference to compare observations and results from different locations
• Reference locations are periodically evaluated for position change to re-define the reference frame
• The ITRF is regularly updated by the IERS…the latest frame is ITRF 2005
• World Geodetic System of 1984 (WGS84)– The reference system utilized in GPS– Provides the basic reference frame and
geometric figure for the earth, based on the USDMA (Defense Mapping Agency’s) measurements and modeling of the earth from a geometric, geodetic, and gravitational standpoint, using techniques and technology available in 1984
Earth-Centered Earth-fixed Reference
Earth-Centered Earth-fixed Reference
• World Geodetic System of 1984– WGS84: a = 6,378137 m, f = 1/298.2572236 – Geocentric coordinate system originally
realized from the coordinates of approx. 1500 reference stations derived from TRANSIT observations
– Uniform specification of the earth’s size, shape, geoid surface characteristics, and reference station coordinates (unlike ITRF)
WGS84
Reference Systems• Time – 3 major systems are used in GPS
– Sidereal time: a measure of the earth’s rotation…defined as the hour angle of the vernal equinox (ie.
– Dynamical time: a uniformly-scaled time used to describe the motion of bodies in a gravitational field
• Terrestrial dynamic time may be used to describe satellite motion without taking into account the gravitational field of the sun
– Atomic time: time systems kept and defined by atomic clocks such as International Atomic Time (IAT)
• Uniformly-scaled time used in earth-centered coordinate systems
• Because of the slowing of the earth’s rotation with respect to the sun, “leap seconds” are used to create the Coordinated Universal Time System (UTC)
• In most cases UTC and GPS time are synonymous….it is the basis of GPS time calculations
Reference Systems – Time Systems
• GPS Calendar references– Julian Date (JD): defines the number of mean solar
days elapsed since January 1, 4713 BC– Modified Julian Date (MJD): obtained by subtracting
2,400,000.5 days from JD• Saves digits and has MJD start at midnight instead of noon
– GPS standard epoch (time, calendar): the atomic time scale implemented by the atomic clocks in GPS ground control stations and satellites
• GPS standard epoch was initiated on Jan. 6th, 1980• Current GPS reference to January 1, 2000 (J2000.0)
Inertial Frame of Reference
• A reference frame in which…– Newton’s first and second laws of motion are
valid: inertia; acceleration
• Newton’s laws are valid in an environment that is nether rotating nor accelerating relative to other bodies
• By contrast, bodies may be subject to forces that result from the acceleration of the reference frame itself….
Earth-Fixed (Non-Inertial)Frame of Reference
• One in which a body violates Newton’s law of Motion….that is, it is rotating or accelerating– An example of an non-inertial frame is an
earth-fixed coordinate reference, as the earth is rotating and body (satellite) motion is measured with respect to it
Inertial vs. Earth-fixed Reference
• The inertial frame of reference is theoretical….
• Therefore, a satellite’s orbit, and it relational location to the earth, must be translated into an earth-fixed reference
• One that takes into account the movement of the earth, including rotation, gravity impacts, etc.
Johannes Kepler – 1571-1630Scientist and Astronomer
Developed important theories (laws) regarding planetary orbits…
Terms Relating to Keplerian Motion
• Perigee: closest approach of a satellite with respect to the earth’s center of mass
• Apogee: most distant position (in an orbit) ” “
• Nodes: intersections between the equatorial and orbital planes
• Anomaly: instantaneous position of a satellite within its orbit
What are we Saying?
• The orbits of satellites around the earth can be described by an ellipse…that has the following characteristics (parameters):– Right ascension of the ascending node– Inclination of the orbital plane– Argument of the perigree– Semimajor axis of the orbital ellipse– Numerical eccentricity of the ellipse– Epoch of the perigree passage
• Orbits do not occur in an inertial environment
Keplerian Motion and Perturbed Motion
• Perturbed motion is “characterized by the temporal variations of orbital parameters.”– Caused by: gravitational forces (sun, moon),
solar radiational pressure, eclipse periods, etc.
• Perturbed motion also causes the Keplerian orbit model specification to be modified
Almanac
• A data file that contains the approximate orbit information of all satellites, which is transmitted by each satellite within its Navigation Message. It is transmitted by a GPS satellite to a GPS receiver, where it facilitates rapid satellite signal acquisition within GPS receivers.
Broadcast Ephemeris
• The "Broadcast Ephemeris (or Ephemerides)" for a satellite are the predictions of the current satellite position and velocity determined by the Master Control Station, uploaded by the Control Segment to the GPS satellites, and transmitted to the user receiver in the Data Message.
Sources of Error
• Satellite Atomic Clock Errors (corrected periodically)
• Satellite Orbit (Position) Errors (corrected periodically)
• Earth’s ionosphere (charged particles)
• Earth’s troposphere (moisture)
• Receiver Noise (local conditions, radio interference)
• Multipath Errors (bounce off buildings, etc.)
• Local Weather (moisture in air, lightning)
• Poor Satellite Geometry (GDOP)
• Receiver Clock Errors (corrected by 4th + Satellites)
1.5 m
2.5 m
5.0 m
0.5 m
0.3 m
0.6+ m
Typical amount of Error (per Satellite)
• Satellite Atomic Clock Errors (corrected periodically)
• Satellite Orbit (Position) Errors (corrected periodically)
• Earth’s ionosphere (charged particles)
• Earth’s troposphere (moisture)
• Receiver Noise (local conditions, radio interference)
• Multipath Errors (bounce off buildings, etc.)
• Local Weather (moisture in air, lightning)
• Poor Satellite Geometry (GDOP)
• Receiver Clock Errors (corrected by 4th + Satellites)
Beyond quality of equipment/size of antennea, etc.
GPS Masks: PDOP, Elevation, SNR
Allow the user to control the quality of the data accepted at the time of data collection (unacceptable readings are filtered out)
Elevation Mask: Sets minimum elevation above horizon for satellites to be used. The lower on the horizon a satellite is the more atmosphere the signal must pass through, thus the greater the potential for signal diffraction (inaccurate estimations of time/distance), as well as greater chance of multi-path errors.Also, with Differential Correction, insures that all satellites usedare visible to base station as well as the field receiver.
SNR (Signal to Noise Ratio) Mask: (higher is better, stronger signal)Filters out signals with excessive noise, using only those satellites with low noise (more accurate). SNR ranges from 0-35; 10-15 is typical, less than 5 is generally considered unusable.
PDOP Mask: Allows the recording of positions only when there isacceptable satellite geometry. Typically considers both quantityand quality of satellites (e.g., 4 satellites with good precision, or 6 with reasonable precision, or 8 with average precision)
Differential Correction
• Requires local Base Station (w/in 100 miles)
• No effect on multi-path and/or receiver errors
• Requires “post-processing” (back in the lab) OR can be done on-the-fly using Real-Time DGPS
• Can improve accuracy by up to 20 m. (50-90%)
• Need better data – longer recording period, better GDOP
• More Base Stations near coasts (navigation)
Differential Correction
Compare GPS data file from Rover file (handheld unit) with a data file from a Base Station (at a known coordinate) for the exact same time period. Relies on the fact that receivers located relatively close together, will record similar errors from the same constellation of satellites.
Uses the apparent “error” of the base station file to correct the corresponding error of the Rover file.
Differential Correction 2
10m
10m
Base Station(w/known coordinates)
Receiver(unknown Location)
GPS ReceiverEstimated Location
Differentially Corrected Estimated Position
GPSEstimated Location
Actual (Known) Position
GPS Data Collection Procedure Using Trimble TerraSync
• Once you start the unit up and check status (navigation screen)
• You will open a new data collection file– .SSF file (default DDMMYYHH.SSF)
• A .DDF file is required data collection in an .SSF file (data dictionary)– A default is provided if one is not selected
• The .DDF file becomes the template for the positional definition of features
THE GPS SIGNALS
Each Satellite transmits two carrier waves
L1 - frequency of 1575.42 MHz and a wavelength of approx 19cm
L2 - frequency of 1227.60 MHz and a wavelength of approx 24cm
The following satellite-specific signals, called the pseudo random noise (PRN) codes are modulated on the carrier waves:
On L1: C/A (Coarse/Acquisition) code λ = approx 300m - Accessible to civilian users
- Consists of a series of 1023 binary digits (called chips) that are unique to each satellite.- The chip pattern is repeated every millisecond
P (precise) code λ = approx. 30m- Accessible only to military equipment
On L2: P code only
SVs transmit two microwave carrier (carry information) signalsL1 (1575.42 MHz): carries navigation message; SPS code
(SPS: standard positioning service)L2 (1227.60 MHz): measures ionospheric delay
C/A code (coarse acquisition) modulates L1 carrier phase …repeating 1 MHz pseudo random noise (PRN) code
…pseudo-random because repeats every 1023 bits or every millisecond…each SV has its own C/A code
…basis for civilian SPSP-code (precise) modulates both L1 and L2 …long (7 days) pseudo random 10 MHz noise code …basis for PPS (precise positioning service) …AS (anti-spoofing) encrypts P-code into Y-code
(need classified module for receiver)navigation message modulates L1-C/A; 50 Mhz signal ….describes satellite orbits, clock corrections, etc.
3 binary codes shift L1 and/or L2 carrier phases
GPS receiver produces replicas of C/A and/or P (Y) code receiver produces C/A code sequence for specific SV
C/A code generator repeats same 1023 chip PRN code sequence every millisecond
PRN codes defined for 32 satellite ID numbers
modern receivers usually store complete set of precomputed C/A code chips in memory
GPS Satellite Signals
• (Coarse Acquisition or C/A) Code Phase– Based on each satellite’s unique pseudo Random Noise Code
(PRN)– Each satellite’s PRN code is totally unique, and can be
replicated by GPS receivers– The receiver “slides” its code later and later in time until it
matches up with the satellite’s code (code correlation)– This is called “code phase lock”…however, even if this is
achieved, there can be significant error• Because the PRN codes are not that complicated (large cycle width
~ microsecond ~ 300 m. of error)• Even with highly accurate code phase lock, error can be 5-10
meters (with the signal traveling at 180,000 miles per second)
Receiver Signal
Delayed Satellite Signal
Time Delay
Subframe of message
Matching Subframe
The ‘mis-match’ between the code patterns is a measure of the time the signal has taken to travel from satellite to receiver.
Code Signal Positioning
GPS Observables – Code Phase
• The Pseudorange: The GPS receiver measures the distance between the satellite and antenna by measuring the time the signal takes to propagate from the satellite to the receiver…the pseudorange is the time offset multiplied by the speed of light
Code Pseudorange
• Based on travel time between when signal is sent and when it is received
• Time data also includes errors in both satellite and receiver clocks– Δt = tr – ts = [tr(GPS)-δr] – [ts(GPS) – δs]
• Pseudorange given by R = c Δt = ρ + cΔδ– Pseudo because of cΔδ (where Δδ = δs – δr)
factor
Code Phase Acquisition• Code phase estimation
• PRN code characteristics– Maximum autocorrelation at lag 0– Minimum auto-correlation in all other cases– Minimum cross-correlation in all cases
• Generate local PRN code
• Perform circular correlation to obtain code phase
• Code phase is the circular shift of the local code that gives maximum correlation
receiver slides replica of code in time until finds correlation with SV signal
(codes are series of digital numbers)
if receiver applies different PRN code to SV signal …no correlation
when receiver uses same code as SV and codes begin to align …some signal power detected
when receiver and SV codes align completely …full signal power detected
usually a late version of code is compared with early version to insure that correlation peak is tracked
0 1 2 3 4 5 6 7
AcquisitionIncoming
code
Generatedcode
Correlation
Code tracking• Enhance the accuracy of code phase obtained
by acquisition• Generate three local PRN codes 0.5 chips apart
– Early– Prompt– Late
• Correlate the local codes with incoming code• Adjust code phase according to result of
correlation
Code tracking
Early
Prompt
Late
Incoming code
-1 -0.5 0 0.5 10
0.5
1
Correlation
Delay in chips
GPS Satellite Signals
• Carrier Phase– The carrier signal has a much higher frequency than
the PRN code, and therefore if “matched” has a much higher level of accuracy
– The carrier signal is ambiguous…that is it is much less differentiated than the PRN code
– The code correlation is used to “narrow down” the time frame of signal travel…then the carrier signal is used to very accurately determine signal travel time
– Used for high end mapping grade and survey grade GPS
Carrier Phase
• Based on the number of cycles (wavelengths) between satellite and receiver
• Phase data will include errors in both the satellite and receiver as well as an initial integer number, N
Nc
NcR
Combinations of Code and Carrier Phase
• “Smoothing” of the code pseudorange using carrier phase correlation
• Several different algorithms
Carrier Phase Acquisition
• Acquisition purpose– Estimate coarse value of PRN code phase– Estimate coarse value of carrier frequency
• Operates on 1ms blocks of data– Corresponds to the length of a complete PRN
code
Acquisition
• Carrier frequency estimation
• Generate local carrier
• Adjust frequency until highest correlation is obtained
Acquisition
1 2 3 4 5 6 7 8Correlation
Acquisition
• Correct value for code phase and carrier frequency provides a peak correlation
Carrier Tracking• Enhance the accuracy of the carrier frequency
obtained by acquisition• Generate local carrier signal• Measure the phase error between incoming
carrier and local carrier signal• Adjust frequency until phase and frequency
becomes stable
Incomingsignal
NCO carrier
generator
Phasediscrimina
tor
Loopfilter
PRN code
GPS signalCarrierwave
Navigationdata
Carrierand data
20ms1ms
1 data bit
GPS signalCarrierand data
Resultingsignal
PRN code
GPS Navigation Message • The GPS navigation message consists of time-
stamped data bits marking the time of transmission of each data bit frame– A data (bit) frame is transmitted every 30 seconds
and is comprised of 1500 bits, subdivided into 5 300-bit subframes
• Subframe 1 – Clock correction (6 seconds)• Subframes 2 and 3 – Ephemeris data for short segments of a
satellite’s orbit• Subframe 4 – Ionospheric corrections (GPS-UTC time offset)• Subframe 5 – Almanac information
– An entire navigation message (25 data frames made up of 125 subframes) is sent over a 12.5 minute period
GPS Navigation Message
Important tasks of a GPS receiver
• Prepare received signals for signal processing• Find satellites visible to the receiver• For each satellite
– Find coarse values for C/A code phase and carrier frequency– Find fine values for C/A code phase and carrier frequency– Keep track of the C/A code phase and carrier frequency as they
change over time– Obtain navigation data bits– Decode navigation data bits– Calculate satellite position– Calculate pseudorange
• Calculate position
Surveying with GPS
• Terminology– Code range: less complex, unambiguous
signal…lower level of accuracy– Carrier range: more complex, ambiguous
signal…higher level of accuracy– Real-time processing: position results must be
available in the field immediately– Post-processing: positional data are
processed later
Surveying with GPS
• Terminology continued– Point positioning: a single receiver measures
pseudoranges– Differential positioning: an improved point positioning
technique where corrections are applied to pseudoranges
– Relative positioning: two receivers are used, and simultaneously receive signals from the same satellites
– In general…point = navigation; relative = surveying, carrier phase; differential = code phase
Surveying with GPS
• Terminology continued– Static point positioning: derivation of point
positions without correction; 10 m accuracy– Static relative positioning (static surveying,
carrier): most accurate; surveying technique; determination of the vector between two stationary receivers; cms. accuracy
– Kinematic relative positioning: two receivers perform observations simultaneously; one is stationary and one is moving
Surveying with GPS – Observation Techniques
• Point Positioning– Standard Positioning Service is standard for
civilian users– Precise Positioning Service for military
• Differential GPS: Two or more receivers are used…one as a stationary “base”, and the other as a mobile “rover”– Position correction; and pseudorange
correction
Differential GPS
• Real-Time– Wide Area Augmentation System (WAAS)– Originated for commercial air flights
• Post-Processing– National Oceanic and Atmospheric
Administration (NOAA) National Geodetic Survey (NGS) Continuously Operating Reference Station (CORS) network
Real-Time DGPS: The WAAS Network
• Wide Area Augmentation System –– Wide area ground reference stations (WRS) have been
linked to form a U.S. WAAS network. • Signals from GPS satellites are received by these precisely
surveyed ground reference stations and any errors in the signals are identified.
– Each station in the network relays the data to one of two wide area master stations (WMS) where correction information for specific geographical areas is computed.
– A correction message is prepared and uplinked to a geostationary communications satellite (GEO) via a ground uplink station (GUS).
– This message is broadcast on the same frequency as GPS (L1, 1575.42 MHz) to GPS/WAAS receivers within the broadcast coverage area
Wide Area Augmentation System (WAAS)
Base Station Data: Where Does it Come From?
• In many cases, base station data in the United States is obtained from the National Oceanic and Atmospheric Administration (NOAA) National Geodetic Survey (NGS)
•USNGS administers a program called CORS – Continuously Operating Reference Stations
•Data from a network of base stations across the US is available…including customized data sets
Surveying with GPS – Relative Positioning
• “…the highest accuracies are achieved in the relative positioning mode with observed carrier phases.”– Processing of baseline vectors – Static relative positioning– Kinematic relative positioning– Pseudokinematic relative positioning
Surveying with GPS – Planning a GPS Survey
• The Federal Geodetic Control Subcommittee (FGCS) has classified GPS surveys based on the levels of accuracy necessary– A & B – very high accuracy geodetic control– 1st, 2nd , 3rd – surveying, engineering,
topographic mapping• The higher the accuracy requirements, the more
planning required
Planning a GPS Survey
• GPS Survey Planning Parameters:– Site characteristics (obstructions, cover, etc.)– Satellite configurations (number, constellation
dispersion, data quality)– Number and type of receivers
• Primitives– Where, When, How Long, Quality
Planning a GPS Survey
• When – determination of the optimum daily observation period(s)– The period when the maximum number of
satellites can be observed simultaneously– The period when the most advantageous
constellation of SV azimuth/elevation combinations is “in view”
– Use of Plan modules available on receivers and/or lab software
What have We Covered• Context of the GPS• Structure of the GPS• Reference Systems
– Earth-fixed, Space-fixed, Geodetic– Time systems
• Satellite orbits– Specification and characteristics– Keplerian motion; perturbed motion
• Characteristics of Trimble GeoXH and GeoXT GPS receivers
• GPS Satellite Signals– Code phase; pseudoranges– Carrier phase; ambiguity
What have We Covered• Combination of Code and Carrier phases
(smoothing)• GPS Navigation message explanation• Explanation of PathFinder Office and TerraSync
softwares• Hands-on use of PathFinder Office and TerraSync
softwares• Data Dictionary expanation/development• Field Data Collection• High Accuracy (survey-grade) GPS
What You Should Have Obtained
• Project experience– Needs assessment– Database design– Data development
• Final Project documents (portfolio)
• References
• Other?
TRANSFORMATION PARAMETERS AND THEIR RATES FROM ITRF94 TO OTHER FRAMES
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SOLUTION T1 T2 T3 D R1 R2 R3 EPOCH Ref.
cm cm cm 10-8 .001" .001" .001" IERS Tech.
. . . . . . . Note #, page
RATES T1 T2 T3 D R1 R2 R3
cm/y cm/y cm/y 10-8/y .001"/y .001"/y .001"/y
----------------------------------------------------------------------------------------------
ITRF93 0.6 -0.5 -1.5 0.04 -0.39 0.80 -0.96 88.0
RATES -0.29 0.04 0.08 0.00 -0.11 -0.19 0.05 18 82
ITRF92 0.8 0.2 -0.8 -0.08 0.0 0.0 0.0 88.0 18 80
ITRF91 2.0 1.6 -1.4 0.06 0.0 0.0 0.0 88.0 15 44
ITRF90 1.8 1.2 -3.0 0.09 0.0 0.0 0.0 88.0 12 32
ITRF89 2.3 3.6 -6.8 0.43 0.0 0.0 0.0 88.0 9 29
ITRF88 1.8 0.0 -9.2 0.74 0.1 0.0 0.0 88.0 6 34
X,Y,Z (Lat, Lon, h) based on the definition of WGS84 ellipsoid
• The original WGS 84 reference frame established in 1987 was realized through a set of Navy Navigation Satellite System (NNSS) or TRANSIT (Doppler) station coordinates
• Significant improvements in the realization of the WGS 84 reference frame have been achieved through the use of the NAVSTAR Global Positioning System (GPS).
• Currently WGS 84 is realized by the coordinates assigned to the GPS tracking stations used in the calculation of precise GPS orbits at NIMA (former DMA).
• NIMA currently utilizes the five globally dispersed Air Force operational GPS tracking stations augmented by seven tracking stations operated by NIMA. The coordinates of these tracking stations have been determined to an absolute accuracy of ±5 cm (s).
World Geodetic System 1984 (WGS 84)
Using GPS data from the Air Force and NIMA permanent GPS tracking stations along with data from a number of selected core stations from the International GPS Service for Geodynamics (IGS), NIMA estimated refined coordinates for the permanent Air Force and DMA stations. In this geodetic solution, a subset of selected IGS station coordinates was held fixed to their IERS Terrestrial Reference Frame (ITRF) coordinates.
World Geodetic System 1984 (WGS 84)
Within the past years, the coordinates for the NIMA GPS reference stations have been refined two times, once in 1994, and again in 1996. The two sets of self-consistent GPS-realized coordinates (Terrestrial Reference Frames) derived to date have been designated:
• WGS 84 (G730 or 1994)
• WGS 84 (G873 OR 1997) , where the ’G’ indicates these coordinates were obtained through GPS techniques and the number following the ’G’ indicates the GPS week number when these coordinates were implemented in the NIMA precise GPS ephemeris estimation process.
These reference frame enhancements are negligible (less than 30 centimeters) in the context of mapping, charting and enroute navigation. Therefore, users should consider the WGS 84 reference frame unchanged for applications involving mapping, charting and enroute navigation.
World Geodetic System 1984 (WGS 84)
Differences between WGS 84 (G873) Coordinates and WGS 84 (G730), compared at 1994.0
Station Location NIMA Station Number East (cm) North (cm) Ellipsoid Height (cm)
Air Force Stations
Colorado Springs 85128 0.1 1.3 3.3
Ascension 85129 2.0 4.0 -1.1
Diego Garcia(<2 Mar 97) 85130 -3.3 -8.5 5.2
Kwajalein 85131 4.7 0.3 4.1
Hawaii 85132 0.6 2.6 2.7
NIMA Stations
Australia 85402 -6.2 -2.7 7.5
Argentina 85403 -1.0 4.1 6.7
England 85404 8.8 7.1 1.1
Bahrain 85405 -4.3 -4.8 -8.1
Ecuador 85406 -2.0 2.5 10.7
US Naval Observatory 85407 39.1 7.8 -3.7
China 85409 31.0 -8.1 -1.5
*Coordinates are at the antenna electrical center.
• The WGS 84 (G730) reference frame was shown to be in agreement, after the adjustment of a best fitting 7-parameter transformation, with the ITRF92 at a level approaching 10 cm.
• While similar comparisons of WGS 84 (G873) and ITRF94 reveal systematic differences no larger than 2 cm (thus WGS 84 and ITRF94 (epoch 1997.0) practically coincide).
• In summary, the refinements which have been made to WGS 84 have reduced the uncertainty in the coordinates of the reference frame, the uncertainty of the gravitational model and the uncertainty of the geoid undulations. They have not changed WGS 84. As a result, the refinements are most important to the users requiring increased accuracies over capabilities provided by the previous editions of WGS 84.
World Geodetic System 1984 (WGS 84)
• The global geocentric reference frame and collection of models known as the World Geodetic System 1984 (WGS 84) has evolved significantly since its creation in the mid-1980s primarily due to use of GPS.
• The WGS 84 continues to provide a single, common, accessible 3-dimensional coordinate system for geospatial data collected from a broad spectrum of sources.
• Some of this geospatial data exhibits a high degree of ’metric’ fidelity and requires a global reference frame which is free of any significant distortions or biases. For this reason, a series of improvements to WGS 84 were developed in the past several years which served to refine the original version.
World Geodetic System 1984 (WGS 84)World Geodetic System 1984 (WGS 84)
Other commonly used spatial reference systemsOther commonly used spatial reference systems
• North American Datum 1983 (NAD83)
• State Plane Coordinate System (SPCS) based on NAD83
• Universal Transverse Mercator (UTM)
North American Datum (NAD)North American Datum (NAD)
NAD27 established in 1927NAD27 established in 1927
defined by ellipsoid that best fit the North American continent, fixed at Meades Ranch in Kansas
over the years errors and distortions reaching several meters were revealed
In 1970’s and 1980’s NGS carried out massive readjustment In 1970’s and 1980’s NGS carried out massive readjustment of the horizontal datum, and redefined the ellipsoidof the horizontal datum, and redefined the ellipsoid
The results is NAD83 (1986)The results is NAD83 (1986)
based on earth-centered ellipsoid that best fits the globe and is more compatible with GPS surveying
in 1990’s state-based networks readjustment and densification, accuracy improvement with GPS (HARN and CORS networks)
Parameter Notation Magnitude
Semi-major Axis a 6378137.0 meters
Reciprocal of Flattening 1/f 298.2572221
Datum point – none
Longitude origin – Greenwich meridian
Azimuth orientation – from north
Best fitting – worldwide
NAD 83 Defining Parameters
X,Y,Z (Lat, Lon, h) based on the definition of GRS80 ellipsoid
State Plane Coordinate SystemState Plane Coordinate System
Based on Lambert and Transverse Mercator projections
Developed in 1930’s and redefined in 1980’s and 90’s
NAD ellipsoid was projected to the conical (Lambert) and cylindrical (Transverse Mercator) flat surfaces
Allowed the entire USA to be mapped on a set of flat surfaces with no more than one foot distortion in every 10,000 feet (maximum scale distortion 1 in 10,000)
Coordinates used are called easting and northing; derived from NAD latitude, longitude and ellipsoidal parameters
Lambert projectionLambert projection
Lambert projectionLambert projection
Transverse Mercator ProjectionTransverse Mercator Projection
State Plane Coordinate SystemState Plane Coordinate System
The scale of the Lambert projection varies from north to south, thus, it is used in areas mostly extended in the east-west direction
Conversely, the Transverse Mercator projection varies in scale in the east-west direction, making it most suitable for areas extending north and south
Both projections retain the shape of the mapped surface
Each state is usually covered by more than one zone, which have their own origins – thus, passing the zone boundary would cause the coordinate jump!
Universal Transverse Mercator, UTMUniversal Transverse Mercator, UTM
Developed by the Department of Defense for military purpose
It is a global coordinate system
Has 60 north-south zones numbered from west to east beginning at the 180th meridian
The coordinate origin for each zone is at its central meridian and the equator
Universal Transverse MercatorUniversal Transverse Mercator
• UTM zone numbers designate 6-degree longitudinal strips extending from 80 degrees south latitude to 84 degrees north latitude
• UTM zone characters designate 8-degree zones extending north and south from the equator
• There are special UTM zones between 0 degrees and 36 degrees longitude above 72 degrees latitude, and a special zone 32 between 56 degrees and 64 degrees north latitude
UTM ZonesUTM Zones
• Each zone has a central meridia. Zone 14, for example, has a central meridial of 99 degrees west longitude. The zone extends from 96 to 102 degrees west longitude
• Easting are measured from the central meridian, with a 500 km false easting to insure positive coordinates
• Northing are measured from the equator, with a 10,000 km false northing for positions south of the equator
Ohio State Plane (Lambert projection, two zones) Ohio State Plane (Lambert projection, two zones) and UTM Coordinate Zoneand UTM Coordinate Zone
Universal Transverse Mercator, UTMUniversal Transverse Mercator, UTM
Vertical Datum Definition 1/2Vertical Datum Definition 1/2
Horizontal control networksHorizontal control networks provide positional information (latitude and longitude) with reference to a mathematical surface called sphere or spheroid (ellipsoid)
By contrast, vertical control networksvertical control networks provide elevation with reference to a surface of constant gravitational potential, called geoid (approximately mean see level)
• this type of elevation information is called orthometric height orthometric height (height above the geoid or mean sea level(height above the geoid or mean sea level) determined by spirit leveling (including gravity measurements and reduction formulas).
Height information referenced to the ellipsoidal surface is called ellipsoidal heightellipsoidal height. This kind of height information is provided by GPS
Height Systems Used in the USAHeight Systems Used in the USA
Orthometric
Normal (orthometric normal)
Dynamic
Ellipsoidal
Variety of height systems (datums) used requires careful definition of differences and transformation among the systems
Vertical datumVertical datum is defined by the surface of reference – geoid or ellipsoid
An access to the vertical datum is provided by a vertical control vertical control networknetwork (similar to the network of reference points furnishing the access to the horizontal datums)
Vertical control network is defined as an interconnected system of bench marks
Why do we need vertical control network?
• to reduce amount of leveling required for surveying job
• to provide backup for destroyed bench marks
• to assist in monitoring local changes
• to provide a common framework
Vertical Datum Definition 2/2Vertical Datum Definition 2/2
The height reference that is mostly used in surveying job is orthometric
Orthometric height is also commonly provided on topographic maps
Thus, even though ellipsoidal heights are much simpler to determine (eg. GPS) we still need to determine orthometric heights
- angle between the normal to the ellipsoid and the vertical direction (normal
to the geoid), so-called deflection of the vertical
H – orthometric height
h – ellipsoidal height h = H + N
N – geoid undulation (computed from geoid model provided by NGS)
terrain
geoid
ellipsoid
P
Normal to the geoid (plumb line or vertical)
Normal to the ellipsoid
H
N
h
Orthometric vs Ellipsoidal HeightOrthometric vs Ellipsoidal Height
(Orthometric height)(computed from a geoid model)
So, how do we determine orthometric height?So, how do we determine orthometric height?
By spirit leveling
And gravity observations along the leveling path, or
Recently -- GPS combined with geoid models (easy!!!) but not as accurate as spirit leveling + gravity observations
H = h-N
But why do we need gravity observations with spirit leveling? But why do we need gravity observations with spirit leveling?
Because the sum of the measured height differences along the leveling path between points A and B is not equal to the difference in orthometric height between points A and B
Why?Why?
Level Surfaces and Plumb Lines 1/2Level Surfaces and Plumb Lines 1/2
Equipotential surfaces are not parallel to each other
The level surfaces are, so to speak, horizontal everywherehorizontal everywhere, they share the geodetic importance of the plumb line, because they are normal to it
Plumb lines (line of forces, vertical lines) are curved
OrthometricOrthometric heights are measured along the curved plumb linesheights are measured along the curved plumb lines
Equipotential surfaces are rather complicated mathematically and they are not parallel to each othernot parallel to each other
Consequently:
Orthometric heights are not constant on the equipotential Orthometric heights are not constant on the equipotential surface !surface !
Thus, points on the same level surface would have different Thus, points on the same level surface would have different orthometric height !orthometric height !
Level Surfaces and Plumb Lines 2/2Level Surfaces and Plumb Lines 2/2
Spirit levelingSpirit leveling
Height differences between the consecutive locations of backward and forward rodscorrespond to the local separation between the level surfaces through the bottom of the rods, measured along the plumb line direction
Orthometric Height vs. Spirit LevelingOrthometric Height vs. Spirit Leveling
dh1
dh3
dh2
dh4
C1
C3
C2
C4
C1, C2, C3, C4 – geopotential numbers corresponding to level (equipotential) surfaces
dh1, dh2, dh3, dh4 – height difference between the level surfaces (determined by spirit leveling, path-dependent); their sum is not equal to H !
dhi H
Because equipotential surfaces are not parallel to each othernot parallel to each other
Geopotential Numbers 1/3Geopotential Numbers 1/3
The difference in heightdifference in height, dh, measured during each set up of leveling can be converted to a difference in potentialconverted to a difference in potential by multiplying dh by the mean value of gravity, gm, for the set up (along dh).
geopotential difference = gm*dh
Geopotential number CGeopotential number C, or potential difference between the geoid level W0 and the geopotential surface WP through point P on the Earth surface (see Figure 2-8), is defined as
Where g is the gravity value along the leveling path. This formula is used to compute C when g is measured, and is independent on the path of integration!
P
P
WWCgdh 0
0
Geopotential Numbers 2/3Geopotential Numbers 2/3
Since the computation of C is not path-dependentcomputation of C is not path-dependent, the geopotential number can be also expressed as
C = gm*H,
where H is the height above the geoid (mean sea level) and gm represents the mean value of gravity along H (along the plumb line at point P on Figure 2-8; see “orthometric height vs. spirit leveling)
the last relationship justifies the units for C being kgal*meter; it is not used to determine C!
Finally:
Geopotential number is constant for the geopotential (level) surfaceGeopotential number is constant for the geopotential (level) surface
Consequently, geopotential numbers can be used to define height Consequently, geopotential numbers can be used to define height and are considered a natural measure for heightand are considered a natural measure for height
REMEMBER: Orthometric heights are not constant on the equipotential REMEMBER: Orthometric heights are not constant on the equipotential surface !surface !
Observed difference in height depends on leveling route
Points on the same level surface have different orthometric heights
Local normal (plumb line direction) to equipotential (level) surfaces
H1
Orthometric height measured along the plumb line direction
S1
S2
Reference surface (geoid)H2
dhdown
dhup
H = H1-H2 dhup + dhdown 0
P2P1
No direct geometrical relation between the results of leveling and orthometric heights
S3
What then, if not orthometric height, is directly obtained What then, if not orthometric height, is directly obtained by leveling?by leveling?
If gravity is also measured, then geopotential numbers, C (defined by the integral formula shown earlier), result from leveling
Thus, leveling combined with gravity measurements furnishes potential difference, that is, physical quantities
Consequently, orthometric height are considered as Consequently, orthometric height are considered as quantities derived from potential differencesquantities derived from potential differences
Thus, leveling without gravity measurements introduces error (for short lines might be neglected) to orthometric height
Geopotential Numbers 3/3Geopotential Numbers 3/3
Let’s summarize:Let’s summarize:
The sum of leveled height differences between two pints, A and B, on the Earth surface will not equal to the difference in the orthometric heights HA and HB
The difference in height, dh, measured during each set up of leveling depends on the route taken, as level (equipotential) surfaces are not parallel to each other
Consequently, based on the leveling and gravity measurements
the geopotential numbers are initially estimated (using the integral formula introduced earlier), based on the leveling and gravity measurements along the leveling path
geopotential numbers can then be converted to heights (orthometric, normal or dynamic – see definitions below) if gravity value along the plumb line through surface point P is known
Height = C/gravityHeight = C/gravity
Height Systems 1/5Height Systems 1/5 In order to convert the results of leveling to orthometric heights we need In order to convert the results of leveling to orthometric heights we need gravity inside the earth (along the plumb line) gravity inside the earth (along the plumb line)
since we cannot measure it directly, as the reference surface lies within the Earth, beneath the point, we use special formulas to compute the mean value of gravity, along the plumb line, based on the surface gravity measured at point P
reduction formulas used to compute the mean gravity, gm, based on gravity measured at point P on the Earth surface lead to:
Orthometric height, (H = C/gH = C/gmm) or
The reduction formula used to compute mean gravity, based on normal The reduction formula used to compute mean gravity, based on normal gravity at point P on the Earth surface leads togravity at point P on the Earth surface leads to:
Normal (also called normal orthometric) height, (H* = C/ H* = C/ m m )
Where is so-called normal gravity (model) corresponding to the gravity field of an ellipsoid of reference (Earth best fitting ellipsoid), and subscript “m” stands for “mean”
Height Systems 2/5Height Systems 2/5
We can also define dynamic heights
use normal gravity, 45, defined on the ellipsoid at 45 degree latitude, (HHDD = C/ = C/ 4545))
Note:Note: term “normal gravity” always refers to the gravity defined for the reference ellipsoid, while “gravity” relates to geoid or Earth itself
Height Systems 3/5Height Systems 3/5
Sometimes, instead of formulas provided above (involving C), it is Sometimes, instead of formulas provided above (involving C), it is convenient to use correction terms and apply them to the sum of convenient to use correction terms and apply them to the sum of leveled height differences:leveled height differences:
Consequently, the measured elevation difference has to be corrected using so-called orthometric correction to obtain orthometric height (height above the geoid)
Max orthometric correction is about 15 cm per 1 km of measured height difference
Or, the measured elevation difference has to be corrected using so-called dynamic correction to obtain dynamic height (no geometric meaning and factual reference surface; defined mathematically)
Or, normal correction is used to derive normal heights
All corrections need gravity information along the leveling path (equivalent to computation of C based on gravity observations!)
Height Systems 4/5Height Systems 4/5
Dynamic heights are constant for the level surface, and have no geometric meaning
Orthometric height
differs for points on the same level surface because the level surfaces are not parallel. This gives rise to the well-known paradoxes of “water flowing uphill”
measured along the curved plumb line with respect to geoid level
Normal height of point P on earth surface is a geometric height above the reference ellipsoid of the point Q on the plumb line of P such as normal gravity potential and Q is the same as actual gravity potential at P.
measured along the normal plumb line (“normal” refers to the line of force direction in the gravity field of the reference ellipsoid (model))
All above types of heights are derived from geopotential numbers
Height Systems 5/5Height Systems 5/5
A disadvantage of orthometric and normal heights is that neither indicates the direction of flow of water. Only dynamic heights possess this property.
That is, two points with identical dynamic heights are on the same equipotential surface of the actual gravity field, and water will not flow from one to the other point.
Two points with identical orthometric heights lie on different equipotential surfaces and water will flow from one point to the other, even though they have the same orthometric height
The last statement holds for normal heights, although due to the smoothness of the normal gravity field, the effect is not as severe
Vertical Datums: NGVD 29 and NAVD 88 Vertical Datums: NGVD 29 and NAVD 88
NGVD 29 – National Geodetic Vertical Datum of 1929NGVD 29 – National Geodetic Vertical Datum of 1929
• defined by heights of 26 tidal stations in US and Canada
• uses normal orthometric height (based on normal gravity formula)
NAVD 88 – North American Vertical Datum of 1988NAVD 88 – North American Vertical Datum of 1988
• defined by one height (Father Point/Rimouski, Quebec, Canada)
• 585,000 permanent bench marks
• uses Helmert orthometric height (based on Helmert gravity formula)
• removed systematic errors and blunders present in the earlier datum
• orthometric height compatible with GPS-derived height using geoid model
• improved set of heights on single vertical datum for North America
Vertical Datums: NGVD 29 and NAVD 88Vertical Datums: NGVD 29 and NAVD 88
Difference between NGVD 29 and NAVD 88Difference between NGVD 29 and NAVD 88
• ranges between – 40 cm to 150 cm
• in Alaska between 94 and 240 cm
• in most stable areas the difference stays around 1 cm
• accuracy of datum conversion is 1-2 cm, may exceed 2.5 cm
• transformation procedures and software provided by NGS (
www.ngs.noaa.gov)
International Great Lake Datum (IGLD) International Great Lake Datum (IGLD) 19851985
IGLD 85IGLD 85
• replaced earlier IGLD 1955
• defined by one height (Father Point/Rimouski, Quebec, Canada)
• uses dynamic height (based on normal gravity at 45 degrees latitude)
• virtually identical to NAVD 88 but published in dynamic heights!
Use of proper vertical datum (reference surface) is very important
Never mix vertical datums as ellipsoid – geoid separation can reach 100 m!
Geoid undulation, N, is provided by models (high accuracy, few centimeters in the most recent model) developed by the National Geodetic Survey (NGS) and published on their web page
www.ngs.noaa.gov
So, in order to derive the height above the see level (H) with GPS observations – determine the ellipsoidal height (h) with GPS and apply the geoid undulation (N) according to the formula H = h - N
Vertical DatumsVertical Datums
Space-fixed Reference• The Conventional Celestial Reference System
– Based on a kinematical definition, making the axis directions defining the coordinate system fixed with respect to distant matter of the universe
– A celestial reference frame defined by the precise coordinates of extragalactic objects (mostly quasars)
– Based on IAU recommendations, the coordinate origin is to be at the barycenter of the solar system, and the axes should be fixed with respect to the quasars
– Principal coordinate plane to be as close as possible to the mean earth equator at J2000.0
Satellite Orbits
• Implementation of GPS depends heavily on being able to quantify satellite orbits
• Keplerian Motion – a satellite is supposed to move in a central force field– Equation of satellite motion is described by
Newton’s second law of motion: where f is the attracting force; m is the mass of the satellite
The fundamental frequency of GPS signal
• 10.23 MHz
• two signals, L1 and L2, are coherently derived from the basic frequency by multiplying it by 154 and 120, respectively, yielding:
L1 = 1575.42 MHz (~ 19.05 cm)
L2 = 1227.60 MHz (~ 24.45 cm)
The adaptation of signals from two frequencies is a fundamental issue in the reduction of the errors due to the propagation media, mainly, ionospheric refraction and SA
GPS SignalsGPS Signals
• Two carrier frequencies (to remove ionospheric effects)
– L1: 1575.42 MHz (154 10.23 MHz) wavelength - 19.05 cm
– L2: 1227.60 MHz (120 10.23 MHz) wavelength - 24.45 cm
New GPS Signal FOR Civilian UsersNew GPS Signal FOR Civilian Users
• Planned for Block IIF satellites (2005)
– L5: 1176.45 MHz (115 10.23 MHz) wavelength – 25.5 cm
• Signal L2 will remain a civilian signal as well
• Carrier L1 and L2
• Codes superimposed on carrier
• P-code (precise/protected code, under AS it’s replaced by a Y-code) on L1 and L2
• C/A – code (clear/coarse acquisition) on L1
• The fourth type of signal transmitted by GPS satellites is the broadcast message (navigation message) on L1 and L2 (identical)
GPS SignalsGPS Signals
GPS Signal StructureGPS Signal Structure
• Code modulation (sequence of binary values: +1 or –1)
– L1: P1 & C/A code, navigation message– L2: P2 code, navigation message
– P-code frequency - 10.23 MHz (i. e., 10.23 million binary digits or chips per second)
– P-code repetition rate: 266.4 days, 7-day long portion of the code are assigned to every satellite; codes are restarted every week at midnight from Saturday to Sunday.
– P-code “wavelength” - 29.31 m
– C/A-code frequency - 1.023 MHz (i.e., 1.023 million binary digits or chips per second; codes are repeated every millisecond)
– C/A-code “wavelength” - 293.1 m
• Assuming 1.023 MHz frequency for C/A-code, and repetition rate of 1 millisecond:
• 1,023,000 Hz * 10-3 sec = 1023 bits (or chips); this is the length of the C/A code
• For 1023 chips in 1 millisecond we get separation between two chips equal to (roughly) 1 microsecond
• 1 microsecond separation between the chips corresponds to ~300 m chip length (for 300,000 km/sec speed of light)
• Check it out the same way for the P-code!!!
How do we get the numbers right?How do we get the numbers right?
GPS Signal StructureGPS Signal Structure
• The epochs of both codes are synchronized
• In civilian receivers, the short C/A code is acquired first to allow access to the P-code
• Carrying two codes on L1 is achieved by phase quadrature
• unmodulated L1 carrier is split off and shifted in phase by 90º, then mixed with C-code and then added to the
P-modulated signal – see Figure 7.8 below
APD(t)P(t)sin(1t)
GPS Signal Summary TableGPS Signal Summary Table
GPS MessageGPS Message• Data File - carrier phase, pseudorange, and range rate (Doppler)
• Navigation Message (broadcast ephemeris) - provides information about satellite orbits, time, clock errors and ionospheric model to remove the ionospheric delay (error) from the observations)
• Provided in binary-receiver dependent format
• Usually converted to RINEX - Receiver Independent Exchange format (ASCII file)
GPS Navigation Message
TLM = Telemetry Word HOW = Handover Word (contains Z-count)
1500 BITS 30 SEC.
SUBFRAME NUMBER
TLM HOW CLOCK CORRECTION
TLM HOW EPHEMERIS
TLM HOW EPHEMERIS
TLM HOW IONOSPHERE, ETC.
TLM HOW ALMANAC
EACH FRAME: -10 30-BIT WORDS, 6 SEC.
1 2 3 4 5
TLM, telemetry word – contains a synchronization pattern which facilitates the access to the navigation data
HOW, handover word allows direct access to the P code; but first the C/A code must be acquired to allow for time synchronization; this allows an access to HOW from the navigation message, and then the P-code can be acquired
• P-code can be accessed only after the C/A code-supported receiver time synchronization with GPS time through the Z-count
• HOW contains so-called Z-count
Z-count is defined as integer number of 1.5-second periods since the beginning of the GPS week, and thus identifies the epoch of a data record in GPS time
• If one knows the Z-count, one can acquire the P-code within the next six seconds
• We already discussed how a GPS receiver measures the range (or pseudorange) to the satellite by measuring the time delay between the incoming signal and its replica generated by the receiver
• Signal synchronization (correlation) provides the signal travel time measure
• The PRN code (P-code) carried by the signal allows to achieve that (if its known; currently, civilians know only C/A code)
• But how do we get an access to the precise code under AS policy, if the Y-code (replacing the P-code) is not known, and thus, the time synchronization scheme will not work?
But we don’t know the actual P-code (under AS)
Techniques to recover L2 signal under AS
GPS Navigation Message (RINEX)GPS Navigation Message (RINEX) 2 NAVIGATION DATA RINEX VERSION / TYPE
DAT2RIN 1.00e The Boss 29JUN98 17:59:25 GMT PGM / RUN BY / DATE
COMMENT
.1118D-07 .0000D+00 -.5960D-07 .0000D+00 ION ALPHA
.9011D+05 .0000D+00 -.1966D+06 .0000D+00 ION BETA
-.142108547152D-13 -.372529029846D-08 61440 159 DELTA-UTC: A0,A1,T,W
12 LEAP SECONDS
END OF HEADER
3 97 10 10 18 0 0.0 .605774112046D-04 .352429196937D-11 .000000000000D+00
.760000000000D+02 .494687500000D+02 .448018661776D-08 .220198356145D+00
.264309346676D-05 .244920048863D-02 .842288136482D-05 .515366117668D+04
.496800000000D+06 .335276126862D-07 -.790250226717D+00 -.372529029846D-07
.951777921211D+00 .211531250000D+03 .259765541557D+01 -.819891294621D-08
.160720980388D-10 .100000000000D+01 .926000000000D+03 .000000000000D+00
.700000000000D+01 .000000000000D+00 .139698386192D-08 .588000000000D+03
.490320000000D+06
6 97 10 10 15 59 44.0 -.358093529940D-06 .000000000000D+00 .000000000000D+00
.220000000000D+02 .526250000000D+02 .438268255632D-08 -.281081720890D+00
…………………….
GPS Observation File Header (RINEX)GPS Observation File Header (RINEX) 2 OBSERVATION DATA RINEX VERSION / TYPE
DAT2RIN 1.00e The Boss 29JUN98 17:59:19 GMT PGM / RUN BY / DATE
Mickey Mouse CFM OBSERVER / AGENCY
5137 TRIMBLE 4000SSI Nav 7.25 Sig 3. 7 REC # / TYPE / VERS
0 4000ST L1/L2 GEOD ANT # / TYPE
____0001 MARKER NAME
____0001 MARKER NUMBER
557180.9687 -4865886.9211 4072508.3413 APPROX POSITION XYZ
0.0000 0.0000 0.0000 ANTENNA: DELTA H/E/N
1 1 0 WAVELENGTH FACT L1/2
4 L1 C1 L2 P2 # / TYPES OF OBSERV
1 INTERVAL
1997 10 10 15 13 5.000000 TIME OF FIRST OBS
1997 10 10 16 38 8.000000 TIME OF LAST OBS
8 # OF SATELLITES
3 1598 1603 1504 1504 PRN / # OF OBS
6 4051 4051 4051 4051 PRN / # OF OBS
9 4208 4212 4150 4150 PRN / # OF OBS
……………………… (rest of the SV is given here)………………………………… PRN / # OF OBS
END OF HEADER
GPS Observation File (RINEX)GPS Observation File (RINEX)97 10 10 15 13 6.000 0 5 6 10 17 23 26 0.000215178
-331628.90610 21627234.69600 -258412.19950 21627239.86440
-330564.59210 23839375.76600 -264155.63150 23839382.29440
-344922.28510 20838559.61800 -268770.84150 20838564.48140
-344734.12710 22476960.02400 -268624.54850 22476965.59140
-338016.17810 20319996.64100 -263389.71350 20320000.46240
97 10 10 15 13 7.000 0 5 6 10 17 23 26 0.000215197
-329205.73500 21627695.91400 -256524.01640 21627700.98840
-327788.16700 23839904.12500 -261992.18640 23839909.89140
-346924.68000 20838178.43000 -270331.14940 20838183.24640
-346674.25800 22476590.73400 -270136.33740 22476596.25440
-337719.08000 20320053.10100 -263158.20940 20320056.88740
97 10 10 15 13 8.000 0 5 6 10 17 23 26 0.000215216
-326782.19000 21628157.18700 -254635.54040 21628162.34340
-325011.83600 23840432.60100 -259828.81640 23840438.14440
-348926.80400 20837797.46000 -271891.24440 20837802.31240
-348614.34600 22476221.42900 -271648.09340 22476226.99540
-337421.42500 20320109.74100 -262926.27040 20320113.51540
………………………………………………………………………………. continues
RINEX 2 description:
http://www.ngs.noaa.gov/CORS/Rinex2.html
http://lox.ucsd.edu/GPSProcessing/Pythagoras/rinex.html
GPS Observables
Data
• Code Pseudorange
• Carrier Phase Pseudorange
• Doppler
• Combinations of data
• Biases and Noise terms
Doppler
• Doppler shift depends on radial velocity– More useful for determining velocities than for
determining positions
• To get positions, need to integrate Doppler shifts (phase differences)
cdt
d
dt
dD
Data Combinations
• Theoretically, data can be obtained from– Code ranges – RL1, RL2
– Carrier phases – ΦL1, ΦL2
– Doppler shifts – DL1, DL2
• Combinations of these data could be used as well
Data Combinations
• In general, linear combinations of phase will look like– φ = n1φ1 + n2φ2
– Where n1 and n2 can be any integer
• Noise level increases for combined data– Assuming noise levels are equal for both, the
increase is by a factor of √2
Data Combinations
• If n1 = n2 = 1, then
– ΦL1+L2 = ΦL1 + ΦL2
• Denoted narrow-lane
• λL1+L2 = 10.7cm
• If n1 = 1 and n2 = -1, then
– ΦL1-L2 = ΦL1 – ΦL2
• Denoted wide-lane
• λL1-L2 = 86.2cm
• Used for integer ambiguity resolution
Data Combinations
• If n1 = 1 and n2 = –fL2/fL1, then
– ΦL3 = ΦL1 – fL2/fL1 ΦL2
– Called L3 (sometimes denoted ionosphere-free)
• Used to reduce ionospheric effects
What to do with Errors?
• There are essentially 4 options:– Ignore them
• Works if the errors are small (negligible)
– Model them• Need good models• Not all effects can be modeled
– Solve for them• Increases complexity of solution
– Make them go away
GPS Ephemeris Errors
• 3 types of ephemerides– Almanac – very crude (~100m), used only for
planning purposes– Broadcast – reasonably accurate (~1m), used
for real-time work– Precise – very accurate (~10cm), used for
high precision work• Available after the fact
Selective Availability (SA)
• Way to degrade the navigation accuracy of the code pseudorange
• Comprised of two parts:– Dithering the satellite clock (δ-process)– Manipulating the ephemerides (ε-process)
Selective Availability
• Dithering the satellite clock– Changing the fundamental frequency– Changes over the course of minutes– Can be eliminated by differencing between
receivers
• Manipulating the ephemerides– Truncating the navigational information– Changes over the course of hours
Clock Errors
• Both satellites and receivers will have clock errors– There’s no such thing as a perfect clock
• Any error in a clock will propagate directly into a positioning error– Remember distance = velocity*time
• Satellite clock errors can be reduced by applying the corrections contained in the broadcast
Ionospheric Delay
• Caused by the electrically charged upper atmosphere, which is a dispersive medium– Ionosphere extends from 40 to 1100 km– Effects carrier phase and code ranges differently– Effect on the phase and group velocity
• nph = 1 + c2/f2 …• ngr = 1 – c2/f2
– Note that this will effect frequencies differently• Higher frequency is affected less
Ionospheric Delay
• Measured range given by s = ∫n ds– n is the refractive index– ds is the path that the signal takes
• The path delay is given by– Δph
iono = –(40.3/f2) ∫Ne ds0 = –40.3/f2 TEC
– Δgriono = (40.3/f2) ∫Ne ds0 = 40.3/f2 TEC
• Where TEC = ∫Ne ds0 is the total electron content
Ionospheric Delay
• Still need to know TEC
• Can either– Measure using observations– Estimate using models
• Note that with data on 2 frequencies, estimates of the unknowns can be made
Tropospheric Delay
• Caused by the neutral atmosphere, which is a nondispersive medium (as far as GPS is concerned)– Troposphere extends up to 40 km– Effects carrier phase and code ranges the same
• Typically separate the effect into– Dry component– Wet component
• ΔTrop = 10-6∫NdTrop ds + 10-6∫Nw
Trop ds– Where N is the refractivity– ds is the path length
Tropospheric Delay
• Dry component contributes 90% of the error– Easily modeled
• Wet component contributes 10% of the error– Difficult to model because you need to know
the amount of water vapor along the entire path
Tropospheric Delay
• There are many models which estimate the wet component of the tropospheric delay– Hopfield Model– Modified Hopfield Model– Saastamoinen Model– Lanyi Model– NMF (Niell)– Many, many more
Special Relativistic Considerations
• Time dilation– Moving clock runs slow
• Lorentz contraction– Moving object seems contracted
• Second order Doppler effect– Frequency is modified like time
• Mass relation
General Relativistic Considerations
• Perturbations in the satellite orbit• Curvature of the path of the signal
– Longer than expected in Euclidian space
• Effects on the satellite clock– Clocks run fast further out of the potential well
• Effects on the receiver clock (Sagnac effect)
Phase Center Errors
• Phase center is the ‘point’ from which the GPS location is measured
• Difficult to measure precisely• Changes with different factors:
– Elevation– Azimuth– Frequency
• Either model the error or reduce the effect of the error by always orienting antenna the same direction
Receiver Noise
• All electronic devices will have a certain amount of noise
• Because of the characteristics of the noise modeling is not an option
• The best that can be done is average the data to reduce the effects of the noise
Multipath Errors
• GPS assumes that the signal travels directly from the satellite to the receiver
• Multipath results from signal reflecting off of surface before entering the receiver– Adds additional (erroneous) path length to the
signal
• Difficult to remove; best to avoid
Multipath Illustration
From http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap6/6212.htm
Geometric Factors
• The strength of figure of the satellites is taken into consideration by the dilution of precision (DOP) factor– Depends on number of satellites– Depends on location of satellites
Geometric Factors
From http://www.romdas.com/surveys/sur-gps.htm
Geometric Factors
• Different kinds of DOPs– HDOP (horizontal)– VDOP (vertical)– PDOP (position) (3-D component)– TDOP (time)– GDOP (geometric) (PDOP and TDOP)
User Equivalent Range Error(UERE)
• Crude estimate of the expected error• Consists of contributions from
– Measurement noise– Satellite biases– Wave propagation errors
• Transmitted through the Navigation message
• Combined with DOP information
GPS signals
• Navigation data
• Pseudo-random noise sequences
• Carrier wave
Navigation data
• Satellite orbit information (ephemerides)
• Satellite clock information
• Satellite health and accuracy
• Satellite orbit information (almanac)
• Bit-rate of 50bps
• Repeated every 12.5 minutes
Pseudo-random noise sequences
• Spreading sequences (C/A)
• Length of 1023 chips
• Chipping rate of 1.023Mcps
• 1 sequence lasts 1ms
• 32 sequences to GPS satellites
• Satellite identification
• Separate signals from different satellites
Carrier wave
• Signal transmission
• Two frequencies: L1=1575.42MHz L2=1227.60MHz
• C/A code on L1
• Bipolar phase-shift keying (BPSK) modulation
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiver overview
RF front-end
A/Dconverter
Acquisition
Receiverchannel
Positioncalculatio
n
• Prepare received signals for signal processing
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiver overview
RF front-end
A/Dconverter
Acquisition
Receiverchannel
Positioncalculatio
n
• Find satellites visible to the receiver– Find coarse values for C/A code phase and
carrier frequency for each satellite
Receiver overview
• Find fine value for C/A code phase
• Find fine value for carrier frequency
• Keep track of the C/A code phase and carrier frequency as they change over time
Code tracking
CarrierTracking
Bit syn-chronizati
on
Decodenav. data
Calculatesatellite position
Calculatepseudo-range
Receiver channel
Receiver overview
• Obtain navigation data bits
Code tracking
CarrierTracking
Bit syn-chronizati
on
Decodenav. data
Calculatesatellite position
Calculatepseudo-range
Receiver channel
Receiver overview
• Decode navigation data bits
Code tracking
CarrierTracking
Bit syn-chronizati
on
Decodenav. data
Calculatesatellite position
Calculatepseudo-range
Receiver channel
Receiver overview
• Calculate satellite position
Code tracking
CarrierTracking
Bit syn-chronizati
on
Decodenav. data
Calculatesatellite position
Calculatepseudo-range
Receiver channel
Receiver overview
• Calculate pseudorange
Code tracking
CarrierTracking
Bit syn-chronizati
on
Decodenav. data
Calculatesatellite position
Calculatepseudo-range
Receiver channel
Receiver overview
• Calculate position
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
Receiverchannel
RF front-end
A/Dconverter
Acquisition
Receiverchannel
Positioncalculatio
n
Implemented parts
Prepare received signals for signal processing
Acquisition
Code tracking
Carrier tracking
Bit synchronization
Decode navigation messages
Calculate satellite positions
Calculate pseudoranges
Calculate receiver position
Signal conditioning
• Purpose of signal conditioning– Remove possible disturbing signals by
filtering– Amplify signal to an acceptable amplitude– Down-sample signal to an intermediate
frequencyAntennasignal
Intermediatefrequency
signal
Filter
Amplifier
Localoscillator
Mixer
Filter
receiver PRN code start position at time of full correlation is time of arrival of the SV PRN at receiverthe time of arrival is a measure of range to SV offset by amount to which receiver clock is offset from GPS time
…the time of arrival is pseudo-range
position of receiver is where pseudo-ranges from set of SVs intersect
• position determined from multiple pseudo-range measurements from a single measurement epoch (i.e. time)• psuedo-range measurements used together with SV position
estimates based on precise orbital elements(ephemeris data) sent by each SV
GPS navigation datafrom
navigation message
each SV sends amount to which GPS time is offset from UTC (universal time) time…correction used by receiver to set UTC to within 100 nanoseconds
THE GPS MEASUREMENT PRINCIPLE
Based on the basic physical relationship:
distance = velocity * time Observations (pseudo-ranges) from 4 satellites provide 3 dimensional position (3 positional and 1 time unknown)
Coordinate system realized by the satellite orbits (ephemerides) and by the coordinates and physical locations of the control and tracking stations
A
Trilateration
The Geocentric Cartesian Coordinate System
A
Z
X
Y
XP
YP
ZP
N
SEquator
Greenwich Meridian
Satellite P
AP = √(XP-XA)2 + (YP-YA)2 + (ZP-ZA)2
Geometric Dilution of Precision - Measures the effect of geometry on the precision of the observations - Multiply GDOP by the Std Error to get actual uncertainty - Also HDOP, VDOP
Position Dilution of Precision (PDOP) - This is positional part of GDOP
Post-processing vs Real Time Correction
Base station over known point Base station over free point
Real Time Kinematic (RTK)
Differential corrections are broadcast via radio
“Site Calibration/Local Transformation”
THIRD PARTY DIFFERENTIAL CORRECTION SERVICE
Geostationary Communication SatelliteDifferential Base
Station
Rover
GPS satellites
Footprint of CommunicationSatellite coverage
Service available commercially (e.g. Omnistar) Sub-meter accuracies possible when used in combination with L1 User needs only one receiver
See http://www.omnistar.com/
Eccentric Points
Useful when Canopy prevents direct occupation of point or when Communication Satellite is blocked
Geostationary Communication Satellite
1 m
mm
5 m
10 m
0.5 m
cm
100 m
20 m
RELATIVEPOSITIONING
POINT (ABSOLUTE)POSITIONING
A B C D E
A: Geodetic (carrier phase with resolved ambiguities), real-time/post-processedB: Carrier smoothed C/A Code Phase, post-processedC: Real-time (RTCM SC104), post-processed C/A CodeD: Real time P-Code (Precise Positioning Service [PPS])E: Real time C/A-Code (Standard Positioning Service [SPS])
AP
PR
OX
IMA
TE
A
CC
UR
AC
Y
geodeticgrade
mappinggrade
navigation/recreationalgrade
dm
civilian (S
PS)
Selective Availability switched off – see http://geography.about.com/library/weekly/aa050400a.htm
civilian (S
PS) – post 05/02/00
(prior to
05/02/00)
military (P
PS)
GPS TECHNOLOGY CLASSIFICATION
