Surveying, GPS and GNSS Geomatics lectures

transcript

APG3016C

SURVEYING II

≈ 30 Lectures , 4 Assignments

Recommended Texts:

Surveying : H Kahmen & W Faig

GPS Theory & Practice : B Hofmann-Wellenhof, H Lichtenegger & J

Collins

+ many other texts

Monday to Friday: 10h00 to 10h45

Venue: GTL

Practical assignments: Wednesday afternoons,

see Vula calendar

Tests: see Vula calendar

Surveying 2 lecture times

Surveying 2 outline of modules

Module 1. History of surveying in southern Africa

Module 2. Advanced instrumentation

Module 3. GNSS basic principles and the Global

Positioning System (GPS)

Module 4. GNSS Differential data processing

techniques

Module 5. GNSS Carrier Phase data processing

techniques

Module 6: Other GNSS systems

1. Referencing Workshop

2. Essay: History of surveying / Walk up

Table Mountain

3. Assignment: Robotic Total Stations

4. Ntrip VRS RTK GPS

See Vula calendar

Assignments4

International: essays

National: readings on Vula

Module 1: History of Surveying5

Laser instrumentation

Robotic total stations

Inertial positioning systems and gyroscopy

Module 2: Advanced instrumentation6

Basic Concepts of GNSS ( GPS, Glonass,

other systems

Satellite Positioning

GPS space and control segments

GPS products and policy

GPS signals

Module 3: Principles of Global Navigation

Satellite Systems and GPS7

Mathematical principles

Biases and Errors

Differential Solutions (DGPS) Principles

Virtual reference stations

Data transmission media and formats

Space/satellite-Based Augmentation Systems (SBAS)

Ground-Based Augmentation Systems (GBAS)

Module 4: Differential Data Processing

Techniques8

Mathematical principles and differencing carrier phase

observation equations

Carrier phase data errors/biases and mitigation

Surveying methods:

integer ambiguity resolution

recovering L2

static GPS

kinematic positioning

network RTK/virtual reference stations

Practical aspects of GPS surveying

Module 5: Carrier Phase Data

Processing Techniques9

GLONASS

Galileo

Compass

Others proposed

Module 6: Other GNSS10

International: essays

National: readings on Vula

Module 1: History of Surveying11

La Caille and

Cassini de Thury

observing zenithal

stars for latitude

determination

National History of Surveying12

La Caille measuring

a baseline in France

La Caille’sArc at the Cape

Maclear

Triangulation end point at

Klypfontein

Cannon base station in

Golden Acre in Cape

Teastern pyramid marker

of the Baseline

Baseline measurement16

National History of Surveying

H S Williams ( 1982), South African national report to the International Association of Geodesy

Laser instrumentation

Robotic total stations• Including your seminars

Inertial positioning systems and gyroscopy

Module 2: Advanced instrumentation22

Laser Ranging: distance meters

Pulsed IR laser

Short range – up to 100m

Precision: 1mm to 3mm

Hand or tripod mounted

Some units have tilt sensors

Can be linked to GPS

Application in sectional title

surveys

from: www.leica-geosystems.com

Laser Ranging: EDM/electronic

tacheometers

Pulsed or Continuous Wave laser

Reflectorless or with prism

Medium range –

up to 1km reflectorless

up to 5km with prism(older CW models up to 25km)

Precision:

1mm to 3mm ± 1 to 2ppm

Integrated distance & angle measurement

Can be linked to GPS

from: www.agageo.com

Visible IR laser

Rotating beam, with tilt sensor

Can be set to specified gradient

Precision: 10" to 60"

Range: up to 200m

from: www.spectraprecision.com

Laser levelling

Construction sites:

Rotating laser beam 360 deg

inside/ outside constructions – transfer line of constant height

some can be tilted –transcribe a tilted plane

from: www.afgen.co.za

Laser alignment

Visible IR laser

Used to align drilling and boring machines

Range up to 1km, typically 200m

Spot size at 200m: 15mm

from: www.leica-geosystems.com

Laser alignment

Plumbing/centring of Theodolite

“vertical” laser beam

Position to middle of ground target

Relies on instrument to be correctly adjusted and axes and bubbles checked

Airborne laser mapping (LIDAR)

Read the excerpt in

the notes

Combination of

sensors

Integrated airborne

system

from: www.southernmapping.com

INS/IMU to get attitude (pitch, roll, yaw)

Differential GPS to get position

Can penetrate forest canopy

Can get multiple returns (e.g. powerline plus ground)

Applications:

Corridor mapping (powerlines, railway lines, etc)

Forestry, coastal mapping

Airborne laser mapping (LIDAR)

Laser scanning

tS c + refraction and calibration corrections

Pulsed laser beam

Rotating mirror creates a swath along flight path

Return pulse(s) detected with photodiode

Distance:

Thousands of points per second

Swath width – up to 45° from vertical

Elevation accuracy: 10cm to 20cm

Robotic Total Stations

See Seminar Presentations!

Motorised with automatic target tracking only

Motorised with automatic target finding and tracking

Fully robotic total station

from: www.topcon-positioning.eu

IMU: inertial measurement unit : basic unit in:

IPS: Inertial Positioning Systems

ISS: Inertial Surveying Systems

INS: Inertial Navigation Systems

Inertial Positioning Systems

(IPS, ISS, INS, IMU)32

Consists of:

Three orthogonal accelerometers

Three orthogonal gyroscopes

Initially developed (and still used) for aircraft navigation

Vehicle-based units developed for military (passive)

Adapted for civilian use – low relative accuracy (±0.5m) surveying

Inertial Positioning Systems

(IPS, ISS, INS, IMU)33

Accelerometer

Double integration of acceleration over time yields distance travelled

Integration errors cause drift, and accumulation of error over time

Vertical accelerometer cannot distinguish acceleration from gravity – need to stop periodically to measure gravity - ZUPT

Gyroscope

MECHANICAL:

Spinning mass, maintains orientation with respect to inertial reference frame

Gimbal-mounted, senses change in orientation, servo-motors used to restore platform to null position

Local level system – V, N, E

Mechanically complicated, calculations simple

from: AD King: Inertial Navigation – Forty years of evolution

RING LASER:

Laser beam sent through glass tubes in opposite directions

Rotation of assembly causes small frequency difference between the two beams (Sagnaceffect)

Change of frequency is a measure of change of orientation

Strap-down system – fixed to vehicle

Mechanically simple, robust, but need high update rate and complex data processing

from: AD King: Inertial Navigation – Forty years of evolution

Gyroscope37

Applications in surveying

Inertial Surveying Systems (ISS, IPS) are no longer used (expensive, low accuracy)

INS/IMU used in conjunction with GPS for land navigation in areas of poor signal reception – IMU interpolates gaps in GPS coverage, GPS calibrates INS

GPS/IMU used for direct georeferencing of airborne sensors (e.g. cameras) – providing position and attitude

Basic Concepts of GNSS ( GPS, Glonass,

other systems

GPS space and control segments

GPS products and policy

GPS signals

Module 3: Principles of Global Navigation

Satellite Systems and GPS39

Satellite positioning

Greenwich

M eridian

Geocentre

Position

vector

M ean rotation

Point Positioning

Relative Positioning

Greenwich

M eridian

Geocentre

rotation

interstation

vector

satellite

geocentre

R i R j

Satellite observations

Directions:

Photograph satellite against a star background.

Interpolate direction to satellite from known co-ordinates (right ascension, declination) of stars. No longer used.

Ranges:

Pulsed laser (SLR), or time codes superimposed upon microwave radio carrier signals (GPS)

Range Rate:

Doppler shift in frequency of received radio signal can be integrated to obtain change in range –related to relative position of transmitter and receiver (DORIS, Argos, SARSAT)

Basic concepts of GPS

Originally developed for the US military

Joint Use Policy since 2004 (Defence,

Transportation)

Position, Navigation & Timing (http://pnt.gov)

Fully operational since 1995

Four GPS satellites

Four Ranges

3D Position & Time

Basic concepts of GPS45

from: www.punaridge.org/doc/factoids/GPS

Observation Equation:

i i P i P i P Pc t x x y y z z - c t

Four unknowns – solve for xP, yP, zP, tP

GPS time

GPS Week:

# of weeks since

6 January 1980

GPS Epoch:

# of seconds in

the week

(adapted from IERS graphic)

GPS Space segment – orbits revision

Geostationary orbits – fixed in relation to the earth

Geosynchronous – move within a defined range in relation to the earth

comms sats

37 000 km above the earth

Crowded orbits above the equator

Launch sites close to Equator

Orbital elements: e, a, i, W, w, Mo

(wikipaedia)

GPS Space segment - orbits

31 satellites in six orbital planes

55° orbit inclination

20 200km altitude

Period of 11h 58m

L1 and L2 carrier signalsC/A-code and P(Y)-code modulation

GPS Space segment – orbital

planes51

to receive and store information concerning their positions, health, and clock offsets and drifts

to maintain accurate time, within the GPS time system

to transmit time codes, ephemerides and other information to the users

GPS Space segment – satellite

functions52

GPS Control Segment:

Vandenberg

Colorado Springs

Cape Canaveral

Hawaii

AscensionDiego Garcia Kwajalein

Tahiti

New Zealand

Alaska

South Korea

South Africa Australia

USNO Wash, DC

England

Bahrain

Ecuador

Argentina

Master/Backup Control Station

Uplink Station

USAF Monitor Station

NGA Monitor Station

GPS Control Segment:

Monitor

station -

Pretoria

Tracking of all satellites by monitor stations

Processing at master control station to predict orbits (ephemerides) of all satellites at least 26 hours into the future

Uploading of ephemerides and satellite clock corrections twice daily

Improvement in prediction to achieve 1m accuracy in signal-in-space

GPS Control Segment:55

GPS Signal structure - old

GPS Signal structure -

modernized

L2C – currently only 8 Block IIRM satellites – allows civilian dual frequency code phase measurements, and better L2 carrier phase measurements

L5 – will be on new IIF satellites, with new civilian code

IIF satellites will have 3 carriers, with C/A code on L1, P(Y) code on L1 and L2, L2C on L2 and L5C on L5

New navigation message (CNAV) on L2C – more flexible, faster updates

Dual (and triple) frequencies provides greater redundancy and removal of ionospheric refraction effect

GPS Signal structure -

modernized

Amplitude Modulation

Frequency Modulation

Phase Modulation

GPS Signal modulation codes

C/A and L2C code: binary, chipping rate of 1.023MHz

P(Y) and L5C code: chipping rate of 10.23MHz

from: www.leicageosystems.com

GPS Signal modulation codes

generated code

received code

GPS Signal code correlation

Satellite clock time and satellite clock correction coefficients

Time offset between GPST and UTC

Satellite ephemeris (orbital parameters and their rates of change with respect to time)

Ionospheric refraction correction model coefficients

Almanac and health data for all the satellites

TLM and HOW – containing Z-count

GPS Signal navigation message

Standard Positioning Service (SPS):C/A-code observations on L1 only. Guaranteed accuracy of 3m horizontally (2σ level) and 5m vertically (2 σ); 40nanoseconds timing accuracy (2 σ). Globally, PDOP not to exceed 6

(actual horizontal accuracy (1 σ) better than 1m)

Precise Positioning service (PPS):C/A-code on L1, P(Y)-code observations on L1 and L2. Only available to US and NATO military. Accuracy specifications are cryptic – see www.gps.gove/technical/ps.

GPS Policy

Mathematical principles

Biases and Errors

Differential Solutions (DGPS) Principles

Data transmission media and formats

Space/satellite-Based Augmentation Systems (SBAS)

Ground-Based Augmentation Systems (GBAS)

Module 4: Differential Data Processing

Techniques64

MATHEMATICS of pseudo-range

positioning

tc. - z - z y - y x- x d - d - c.dt - t.c2

iptropionii

or:i i i ion trop iR c. t - c.dt - d - d - c. t r

R i = r i

o . d x p +

o . d y p +

o . d z p - c . t

Linearised:

There are at least four such equations, and in matrix form:

A.x = ℓ

where:

positioning

Where there are more than four observations,

the least squares solution is:

T Tx A PA A P

positioning

Dilution of Precision (DOP)

Measures geometric strength of a single point position:

TGDOP Tr A PA

Also: PDOP, HDOP, VDOP, TDOP

Dilution of Precision (DOP) 69

Dilution of Precision (DOP)

Satellite visibility

Satellite sky plot

Satellite ground tracks

Cape Town 2014 10:00-16:00

Antarctica

Equator76

55 degrees latitude77

Satellite dependent:

Orbit bias

Clock bias

Propagation medium dependent:

Tropospheric refraction

Ionospheric refraction

Receiver dependent

Receiver resolution

Clock error

Multipath

Antenna phase centre error

BIASES AND ERRORS

Orbit Bias

ddB B.

For dr = 2m,

dB 0.1ppm of B

After application of the satellite clock correction (transmitted as part of the navigation message), the error in the clock is less than 5 nanoseconds. The effect on the pseudo-range is less than 2m

Satellite clock bias

1255d 2.27 10 P 0.05 e tan sec

zenith

satellite

Reduced by:

Modelling (residual effect < 20cm)

Differencing (common errors eliminated)

Tropospheric refraction

zenith

satelliteion 2

40.3d TEC sec

16.2 sec

Reduced by:

Modelling (removes about 70%)

Differencing (common effect eliminated)

Eliminated by:

Use of dual-frequency receivers (frequency-dependent)

Ionospheric refraction

Sunspot

Activity

Sunspot activity

40.3d TEC sec

Eliminated by use of dual-frequency receivers (frequency

dependent):

2ion 1 1 2 2 2

fd L L L .

f fr r r

2 1 1ion 1 1 2 1 22 2

2 1 2 2

f f fd L L L . N L N L .

f f f f

Modelling and reduction of

ionospheric refraction

Not an issue – better than 0.5% of effective wavelength:

1.5m for standard C/A-code handheld receivers10-20cm for C/A-code receivers using narrow correlators

1mm for carrier phase receivers

Receiver resolution

Determined as part of the solution for stand-alone pseudo-range positioning

Eliminated by differencing in differential positioning

Receiver clock error

Mitigation:

Siting

Antenna design

Narrow correlator

Choke ring

Averaging

Effect < 5cm

for carrier

Multipath

Choke Ring Antennas

Variation in azimuth: use same type of antenna, oriented in same direction

Variation in zenith angle:

use same type of antenna

calibrate and use PCV correction tables

Carrier frequency:

use different phase centres for L1 and L2

Antenna phase centre

GoodPoor

Position accuracy ≈ UERE · PDOP (UERE approximately 1-2m)

Influence of satellite constellation

geometry

Error Source Stand-Alone GPS Differential GPS

Orbit < 2m < 0.1ppm

Satellite clock < 2m eliminated

Troposphere refraction < 20cm, after modelling < 1ppm

Ionospheric refraction 3-10m, after modelling < 1ppm

(dual frequency) eliminated eliminated

Receiver resolution 15cm - 1m 20cm - 2m

(carrier phase) 1mm 1-2mm

Receiver clock eliminated eliminated

Multipath < 10m < 10m

(carrier phase) < 5cm < 5cm

Antenna phase centre < 20cm < 10cm

(carrier phase) < 2cm < 1cm

Error and bias summary

Most errors are spatially correlated and can be reduced or removed by differencing:

DIFFERENTIAL GPS SOLUTIONS (DGPS)

222 )()()( i

R zzyyxx r

tcdddtctcR tropionii

i RR r

Ranges are computed at the reference station using the broadcast

ephemeris and the known reference station co-ordinates:

Measured ranges (corrected for receiver clock bias) at the reference

station:

Range corrections applied at rover unit, before computing

position:

Range corrections

With no multipath, single base:

2m - 3m (function of baseline length)

With multiple base stations:

sub-metre

(see also WAAS and VRS later)

DGPS accuracy95

Resolution: NOT reduced - limits the

solution

Satellite Orbits : Reduced to less than 0.1ppm(1cm on 100km)

Satellite Clocks : Eliminated

Ionosphere : Reduced to less than 1ppm

Troposphere : Reduced to less than 1ppm

Multipath : NOT reduced: 1-5m

DGPS effect on errors96

Range corrections are computed at reference station and transmitted to rover unit

reference

stationmobile

usercorrection signal

Realtime DGPS97

DGPS corrections computed by a network of fixed

and continuously operating reference stations

Corrections interpolated to a point in the area of

work – point called the Virtual Reference Station

VRS concept99

VRS advantages

No user-operated base station is required

Reduced cost; increased productivity

More accurate corrections than owner-base station

More base station data is included

Sophisticated modelling of systematic errors sources can

be undertaken: refraction, orbits and multipath

VRS disadvantages

User may have to pay

Modernization of the GPS system may reduce the

advantages of DGPS in many cases

UHF/VHF

Satellite Communication links

Cell phones (GPRS)

Bluetooth

DGPS data transmission media

These are (more on the following slides):

RTCM SC-104 – Format for transmission of DGPS correction data from reference station to rover unit

RINEX – Format for GNSS data storage and processing

NMEA - Protocol/format for real-time communication of position from GPS to other devices

Realtime DGPS data transmission

formats

Radio Technical Commission Maritime, Special Commission 104

Message type 1: Differential GPS corrections

Message type 3: GPS reference station parameters

Also (version 3) capable of providing RTK data(code and carrier phase observations)

RTCM SC-104

Two main types:

Observation (file name: ssssdddf.yyo)

Navigation message (file name: ssssdddf.yyn)

(also compressed observation file: ssssdddf.yyd)

RINEX (Receiver Independent

Exchange) format

2.10 OBSERVATION DATA G (GPS) RINEX VERSION / TYPE

teqc 2007Feb5 20080702 00:35:07UTCPGM / RUN BY / DATE

HERM MARKER NAME

HERM MARKER NUMBER

CDSM CDSM TrigNet OBSERVER / AGENCY

Unknown TRIMBLE NETR5 Nav 3.50 / Boot 3 REC # / TYPE / VERS

0 RCV CLOCK OFFS APPL

ASH701941.B ANT # / TYPE

4973168.8045 1734085.3905 -3585434.1455 APPROX POSITION XYZ

0.0000 0.0000 0.0000 ANTENNA: DELTA H/E/N

1 1 WAVELENGTH FACT L1/2

9 C1 P1 P2 L1 L2 S1 S2 D1 D2# / TYPES OF OBSERV

30.0000 INTERVAL

MSXP|IAx86-PII|bcc32 5.0|MSWin95->XP|486/DX+ COMMENT

teqc 2007Feb5 20080702 00:34:02UTCCOMMENT

teqc edited: all GLONASS satellites excluded COMMENT

Forced Modulo Decimation to 30 seconds COMMENT

2008 7 1 0 0 0.0000000 GPS TIME OF FIRST OBS

2008 7 1 23 59 30.000000 GPS TIME OF LAST OBS

2.10 OBSERVATION DATA M (MIXED) COMMENT

teqc 2007Feb5 20080702 00:31:45UTCCOMMENT

GPSNet 2.51 2653 01-Jul-08 00:00:00 COMMENT

Cartesian values are base on the ITRF 2005 reference frame COMMENT

Station Position values are final COMMENT

END OF HEADER

RINEX sample

08 7 1 0 0 0.0000000 0 10G 5G30G22G14G16G12G31G32G29G20

24244117.102 24244115.152 -4907159.038 4 -3709921.24346

39.000 24.000

22318647.578 22318645.961 -14108663.616 7 -10866901.02347

48.000 36.000

23163277.086 23163274.066 -9810912.005 6 -7626200.02947

45.000 32.000

21058755.297 21058753.051 -21643392.083 7 -15891024.63547

49.000 41.000

23170436.898 23170434.449 -10175134.522 6 -7667313.47846

43.000 30.000

25266425.992 25266423.746 -601615.489 3 -449767.67745

37.000 20.000

20597668.336 20597665.492 -24949999.741 7 -19416354.05548

52.000 46.000

21413778.000 21413776.645 -18068659.996 6 -14038897.14847

47.000 38.000

24157775.781 24157775.074 -6390958.425 5 -4948960.63346

40.000 25.000

23966539.055 23966536.605 -7385208.568 6 -5419453.03446

43.000 25.000

08 7 1 0 0 30.0000000 0 9G 5G30G22G14G16G31G32G29G20

24261702.344 24261701.332 -4814742.678 5 -3637908.48546

40.000 24.000

RINEX sample

RS232 protocol, 4800bps, 8 data bits, no parity, one stop bit

Most common message: GGA:

$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47

NMEA (National Marine Electronics

Association)

Space-based (SBAS): Correction data are transmitted via geostationary satellites, using the L-band

Ground-based (GBAS): Correction data are transmitted via:

300MHz MF transmissions ("over-the-horizon") –Beacon DGPS (range of up to 500km)

Combination of internet and cellphone GPRS data transmission –NTRIP (restricted to cell network GPRS coverage)

SPACE/SATELLITE-BASED

AUGMENTATION SYSTEMS (SBAS)

Primary purpose is to provide GPS system integrity monitoring for safe aviation

Multiple reference stations (Ranging and integrity monitoring stations (RIMS)) over a region

Data processed at master station to produce satellite orbit and clock corrections, integrity data and ionospheric refraction correction grid

Data uploaded to geostationary satellites, which re-transmit data in the L-band

Accuracy improvement to around 1m, integrity warning latency of less than 6sec

SBAS key features

These are (pictures to follow):

WAAS: Wide Area Augmentation System, operated by the Federal Aviation Authority of the USA

Omnistar/FUGRO – private, paid, international

EGNOS: European Geostationary Overlay System, operated by the European Space Agency

QZSS: Japanese Quasi Zenith Satellite System

Starfix/NAVCOM

(also GAGAN and MSAS: Multifunction Satellite Augmentation

System, operated by the Japan Civil Aviation Bureau)

from: http://gps.faa.gov

Wide Area Augmentation Systems (WAAS)

Commercial SBAS

Fugro Omnistar VBS (sub-metre):

from: http://www.egnos-pro.esa.int

Quasi Zenith Satellite System

Navcom Starfire

40 GNSS reference stations

JPL Real Time GYPSY (RTG)

Commercial SBAS

Beacon:

Network of single reference stations, with range corrections in RTCM-104 format

Distribution via MF (300KHz) marine radio navigation beacons, range of up to 500km

Generally provided as a free service by marine navigation authorities (coastguard, lighthouse service, harbour service)

GROUND-BASED AUGMENTATION

SYSTEMS (GBAS)

US NDGPS

from: www.navcen.uscg.gov

from: www.trignet.co.za

TRIGNET

Dual-frequency receivers with choke ring antennas

Network DGPS – sub-metre accuracy

Network RTK (VRS) – 2cm accuracy

Single base RTK – 5cm accuracy

Real time delivery in RTCM-104 format via NTRIP and GPRS (restricted to cell phone network data coverage)

Post-processed data available in RINEX format

TRIGNET

Network Transport of RTCM via Internet Protocol

Used for provision of RTCM-104 data via the internet(data are stored at an IP address for access by multiple users, over the internet or via GPRS)

accuracy of 3m –5m

from: Portnet brochure

PortNet DGPS

NGDGPS

NASA Global GPS Network (GGN) – JPL owned

70 reference stations

Internet or satellite comms

Mathematical principles and differencing carrier phase

Carrier phase data errors/biases and mitigation

Surveying methods:

integer ambiguity resolution

recovering L2

static GPS

kinematic positioning

network RTK/virtual reference stations

Practical aspects of GPS surveying

Module 5: Carrier Phase Data

Processing Techniques125

Carrier phase GPS

With DGPS, best accuracy obtainable is 30-50cm

This is inadequate for surveying, geodesy, etc

Problem is mainly one of resolution – effective

“wavelength” of C/A-code is 300m. L1 carrier has

wavelength of 19cm

ij = i(T) - j(t)

signal transmitted

at time t

signal generated

at time T

Mathematical principles of carrier

phase GPS127

f.(dtj- t i) +

c.(-d ion + d trop)

i i j i j i jx x y y z zr

phase GPS128

integer cycle ambiguity

fractional phase

whole number of

cycles since lock-on

fractional phase

= m + N i

phase GPS

Integer Ambiguity

m i i trop ion i

f ff dt t d d N

m ion trop i i id d c dt t N r

Multiplying by the wavelength, and re-arranging:

phase GPS

21 ion trop 21 21 21d d c. t N r

Eliminates satellite clock error; effects of refraction and orbit bias

reduced

phase GPS

Differencing

between stations

Differencing carrier phase

21 21 21 21

i ion trop i id d c. dt N r

Eliminates receiver clock error

Differencing

between satellites

d ion - 2

d trop = r21

- .N21

Eliminates clock errors; reduces orbit and refraction errors

Double

differencing

ri(t )2

ri(t )1

Between epochs

differencing

(t 2- t 1) + d ion - d t r op = r i

(t 2- t 1) + c.dtj(t 2- t 1) - c.t i(t 2- t 1)

Eliminates Integer Ambiguities

Triple Differencing

Eliminates all nuisance unknowns

(t 2- t 1) + 3

d ion - 3

d t r op = r21

(t 2- t 1)

Satellite Orbits : 1-2m

Satellite Clocks : 1-2m

Ionosphere : 10-50m (model 2m)

Troposphere : 2-5m (model 20cm)

Multipath : < 5cm

Carrier phase data errors/biases and

mitigation136

Satellite Orbits : Reduced to less than 0.1ppm

(1cm on 100km)

Satellite Clocks : Eliminated

Ionosphere : Reduced to less than 1ppm

(eliminated using dual

frequency)

Troposphere : Reduced to less than 1ppm

Multipath : NOT reduced: < 5cm

Carrier phase data errors/biases and

mitigation137

A single double difference contains four unknowns:

three co-ordinates of the new point, one double-

differenced integer ambiguity

Adding another satellite just adds another integer

ambiguity

Need to observe several satellites over several

epochs, while maintaining lock (no fresh ambiguities)

Minimum configuration:

three satellites, three epochs

four satellites, two epochs

All differencing done with respect to a single reference

satellite

CARRIER PHASE GPS – receiver-

satellite configuration138

Minimum configuration of four satellites and

two epochs139

The double-differenced integer ambiguities in the

equation are resolved as real numbers ("floating

point") in the least squares solution

For greater accuracy they should be resolved as

integers, and the solution repeated, treating them as

known quantities.

The integer resolution ("initialization") makes use of

statistical testing:

Minimizing Sv2

Identifying integers within confidence intervals

Solving the integer ambiguity -

Initialization

If the observations are affected by errors ("noisy" data),

then it becomes difficult, if not impossible, to resolve the

correct integers.

More data helps - i.e. observing over a longer time span.

Residual ionospheric refraction makes the data appear

noisy – this effect can be eliminated by using dual-

frequency receivers:

Some form of iteration required, to solve for ionospheric

refraction correction and for integer ambiguities

2 1 1ion 1 1 2 1 22 2

2 1 2 2

f f fd L L L . N L N L .

f f f f

Solving the integer ambiguity -

Initialization

Want to use L2 as well as L1:

Calculate ionospheric correction and eliminate it

Better ambiguity resolution over longer baseline distances

L2 is encrypted by the Y-code (P-code)

Do not know this so cannot strip it off as in L1 code

Only newer satellites broadcast the L2C signal

which is available.

Using the L2 carrier for dual –

frequency GPS

Need to strip the code off the carrier before it can

be used. There is not a problem with the L1

carrier, as the C/A code is known and can be

removed.

For L2C-capable receivers the L2 carrier can be

recovered for the Block IIR-M-F satellites in a

similar fashion.

For the other satellites

and for older receivers the

technique of code-aided

cross-correlation must be

used to recover L2

Using the L2 carrier for dual–

frequency GPS

A number of different Surveying modes exist

Static GPS surveying

Kinematic GPS surveying

Initialisation

Continuous

Real time kinematic

Ambiguity resolution on the fly

GPS and GLONASS

Network RTK/VRS

Carrier Phase GPS Surveying Methods

Data collected over a time period of ten minutes

to several hours

Data stored, downloaded and post-processed

Single-frequency integer ambiguity resolution

possible, for baselines up to 20km in length

Dual-frequency integer ambiguity resolution

possible for baselines of 100's of km, using many

hours of data

(rule-of-thumb: 10min + 1min per kilometre)

Accuracy of 3mm + 0.5ppm

(with scientific software: 1mm + 0.01ppm)

Static GPS Surveying

Dual-frequency receivers – one at base station, the other

roving

Initialisation (resolution of integers) carried out over 1-2

minutes:

Rover at known point

"Antenna swapping" (obsolete)

Dual freq+wide laning (comb L1 and L2) +stat testing

Ambiguity resolution on the fly (AROF), with Kalman

filtering

Kinematic GPS Surveying

Need to maintain lock on at least four satellites, otherwise

re-initialisation required

Post-processed or Real Time

Cannot easily resolve integers over baselines longer than

Accuracy of 1-2cm + 1ppm

Kinematic GPS Surveying

Continuous Kinematic

Rover moves in continuous trajectory – mounted

on vehicle or aircraft

Issues:

Initialisation carried out prior to vehicle/aircraft

moving

Range restricted: baseline lengths generally

under 100km

Synchronisation with other sensors

Orientation differences due to non-colocation

Loss of lock “in-flight”

Continuous Kinematic

Generally post-processed, with AROF (PPK)

Integrated with other sensors: ALS, INS, digital

camera

Accuracy of 5-10cm + 1ppm (multipath)

Real Time Kinematic (RTK) for

surveying

Required for searching and setting out; coords needed on

ALL data from base station transmitted to rover unit (code

and carrier phase observations)

Baseline data processing carried out at rover

Dual-frequency, with AROF, minimum of five satellites

Baselines restricted by communication link:

UHF/VHF need line of sight communication

NTRIP/GPRS needs cell phone link

On site statistical feedback

As in non-real time: 1-2cm + 1ppm

As in non-real time: Baselines < 20km

ambiguities resolved

loss of lock

ambiguities resolved again

forward processing

backward

processing

backward

processing

forward processing

Ambiguity resolution on the fly

No need to stop survey if re-

initialisation is required

rapid static approach

(combination of dual

frequency, wide-laning and

statistical testing) as well as

antenna trajectory are used

to resolve the integer

ambiguities

Ambiguities are back

substituted to obtain track

coordinates

Assists AROF by increasing constellation

Need at least 6 satellites as there is an additional unknown – the time offset between GPS and GLONASS (min 5 for non-AROF)

Recommended minimum is 6 satellites for GPS only and 7-8 for combined GPS/GLONASS for initialisation

Integer ambiguity resolution is faster with more satellites

Integer ambiguity resolution is more certain with more satellites – need FIXED solutions for cadastral work

Single frequency receiver performs better with GLONASS added (GNSS)

Number of satellites should be enough - NB in urban canyon, trees, obstructed sky view

GPS and GLONASS in surveying

All the time:

Data processed between multiple base stations (fixed

solution) yielding:

Local ionospheric errors

Local tropospheric errors

Orbit errors for

observed constellation

control centre

base station

Network RTK / VRS153

When client surveying:

Sends pseudo-range

solution to the control

centre

Requires two-way

communication –

cellphone link to web

This position becomes

the Virtual Reference

Station

Error models for refraction

and satellite orbits are

interpolated to the position

approx. position

control centre

base station

Observation data from

the nearest reference

station is artificially

displaced to the VRS

position

artificial (virtual)

base station data

created (quasi-

carrier phase data)

like eccentric set-up

approx. position

virtual data

control centre

base station

Client surveys with

virtual base station data

baselines

determined are now

between the VRS

and the rover

Advantages of network RTK/VRS

baseline lengths are shorter

higher accuracies are claimed

Initialization (ambiguity resolution) times reduced by as

much as 2/3rd’s

fixed-point solutions more easily achievable

position determined by the roving GPS receiver is

automatically integrated into the national control system as

defined by the Reference Stations included in the system.

temporal disturbances to the ionosphere are automatically

modeled in real time yielding better accuracy that those

predicted in the navigation message.

TrigNet and VRS

from: www.trignet.co.za

3 VRS networks in SA

TrigNet and VRS

Provides a set of continuously operating reference

stations (CORS)

User only requires a single receiver to get position

Post-processing using downloaded RINEX data

RTK using single base stations and network RTK

(needs NTRIP/GPRS capable receiver)

Reference station heights are ellipsoidal,

not orthometric

Reference Frame:

Co-ordinates of all TrigNet stations are in the

ITRF2008 reference frame, updated to 2012.01

All real time results will be in this frame (DGPS,

RTK, VRS)

User can choose to use Hart94 co-ordinates for

TrigNet station, for post-processed static GPS

The official datum is Hartebeesthoek 1994

ITRF2008(2012.01) to Hart94 shifts are variable –

average of 19cm (y) and 41cm (x), but ranges from

4cm to 32cm (y) and from 28cm to 58cm (x)

TrigNet and VRS

PRACTICAL ASPECTS OF GPS

FOR SURVEYING

Reconnaissance and Design

Observations

Data processing

Datum transformation

Reconnaissance & Design

Select suitable sites – no multipath, no

electromagnetic interference, good overhead

visibility

Choose best time of day – most satellites, low

Select independent baselines

( # baselines = # receivers – 1 )

Ensure redundancy – baselines form closed figures

– at least two, preferably three, connections to each

Ensure direct connections between close points –

20% rule

Connect to at least three higher order control points

Network Geometry

double polars

Contro l Network

Practical aspects of static observations

Select suitable observation period:

10 minutes plus 1minute per kilometre

Allow sufficient time to access points; plan

observation sequence; Ensure simultaneity

Check batteries

Double-check measurement of antenna heights

Static data processing

Data transfer – cable, memory card

Pre-processing, if required:

- download & import CORS (TrigNet) data

- download and convert precise ephemeris

Process independent baselines, solving for integer

ambiguities

(may require removal of satellites; editing of cutoff

elevation angle; use of precise ephemeris)

Combination of baselines in network adjustment:

- minimum constraint

- constrained to fixed points

- solve for datum transformation parameters

GPS for cadastral surveys:

RTK most common approach, often using TrigNet

Initialization is the process to determine (or re-

determining) integer ambiguities

Calibration is the process of tying (transforming) the

survey to the national datum (Hart94)

Checks are essential for cadastral surveys

Many (most) surveyors fail to take sufficient

redundant measurements to ensure that checks are

independent of calibration

Calibration for RTK

Calibration essential to

ensure transformation

from base station co-

ordinate frame (e.g.

ITRF2005) to official

datum (Hart94)

visit at least two

(preferably three) control

points after initialization

(on-board software

determines local

transformation parameters

and applies them to all

subsequent positions)

Checks for RTK

Poor design of checks

Single visit to surveyed

points

Although multiple base

stations

Poor occupation/incorrect

occupation of survey points

No checks on local control

Checks for RTK

One base station only

Double visitation of local

control and surveyed

points

If same points used for

datum transformation

no redundancy

errors absorbed into

transformation

parameters

Checks for RTK

One base, one rover

Invert rover

Only new integer ambiguity resolution

No check on correct occupation of base

station

No check on correct occupation of rover

station

No check on multipath or residual refraction,

satellite constellation errors

Checks for RTK

GOOD design of checks

Multiple base stations, one

or more rovers

Visit a local control point

after initialization

Visit all survey points

Repeat visits to survey

points

Datum transformations

Satellite coordinates are in WGS84

Using base station coordinates gives GPS derived

coordinates in base station system

TrigNet this is IRTF2008

Local base station – system of entered coordinates

If only once base used, shift only

To calculate swing and scale, use more than one control point

Datum transformations

To transform from base station system to Hart94

Use of published conversion packages use averages… not

accurate enough for cadastral work (up to 10m incorrect) …

local transformation is required

use a similarity/helmert transformation … min 3 points

For cadastral work, conversion of archival data in Cape Datum may

also be required prior to survey.

GPS for Engineering Surveys

Heights are needed, as well as positions - this can

be a problem

Topographic surveys: RTK or continuous kinematic

Problems with satellite visibility – buildings, cranes,

cliffs, etc:

use additional satellites (GLONASS)

use electronic tacheometer in conjunction with

use laser ranger, with tilt and orientation

sensors

Monitoring surveys need high accuracy, high data

rate and low multipath

GPS for GIS

DGPS systems are generally adequate (1-2m

accuracy)

Need not be real time, but need to record all code

measurements if not

Handheld unit must be able store attribute data, with

user-defined data dictionary

Results must be capable of conversion to standard

formats (e.g. DXF, Shape files)

GPS Heighting

GPS provides heights above the WGS84 ellipsoid.

Users need heights above MSL/geoid – orthometric

heights

In order to convert GPS-derived heights to orthometric

heights we need a good model of the geoid/ellipsoid

separation – the geoidal height N:

Terrain

Ellipsoid

Geoid modelling

Small areas (a few km in extent) modelled by a tilted

at least 3 points with known orthometric heights are

surveyed with GPS

this approach is often used in RTK

Larger areas

gravimetric model

model and the levelling network may have

systematic errors

A combination approach (hybrid geoid model) is best,

using GPS/levelling data to calibrate a gravimetric geoid

Hybrid Geoid Model

118 GPS/levelling

points

Accuracy of 7cm

International GNSS Service (IGS)

Consortium of agencies operating permanent

continuous tracking stations

Main product is post-computed precise ephemeris –

accuracy of 2 – 10cm

Also: precise satellite clock corrections; ionospheric

refraction correction model; raw data in RINEX

format

International GNSS Service

Precise Point Positioning (PPP)

Makes use of precise ephemeris and satellite clock

corrections to obtain precise stand-alone position.

Needs dual-frequency receiver to remove

ionospheric refraction; solves for tropospheric zenith

path delay.

Uses both carrier phase and code phase data.

Post-processing only, minimum of 1hour data

required (preferably 24hrs)

Accuracies of 1cm – 10cm

Internet-based GPS Processing

Involves collection of data, conversion to RINEX

format, uploading to web site, with results received

via e-mail (free processing)

Differential carrier phase post-processing using IGS

reference stations and precise ephemeris:

Relative accuracies of up to 1mm + 0.01ppm

Precise point positioning using IGS (or other)

precise ephemeris and satellite clock corrections:

Absolute accuracies of 1-2cm

GLONASS

Galileo

Compass

Others proposed

Module 6: Other GNSS183

GLONASS

USSR/Russia equivalent of GPS

24 satellites in three orbital planes

65° orbit inclination

19100km altitude

Period of 11h 15m

Two carrier signals, civil & military codes

GLONASS

Currently only 26 satellites available

Launch failure in December 2010, July 2013

Modernisation (2nd civil signal) GLONASS-M. First

launch in 2005

Not used as a stand-alone system. Supplements

GPS in urban canyon environment.

GLONASS-K launched in Feb 2011

GALILEO

Proposed ESA/EU civilian navigation system

Planned: 27 satellites, 56° inclination, 14 hour

orbits. First test satellite launched late 2005, 2nd in

April 2008. FOC in 2012 (or later?)

To be compatible with and interoperable with GPS -

common reference frame, broadcast of timing

offsets.

Open Access

Commercial

Safety of Life

Search and Rescue

Free to air; Mass market;

Simple positioning and

timing

Encrypted; High accuracy;

Guaranteed service

Open Service + Integrity and

Authentication of signal

Encrypted; Integrity;

Continuous availability

Near real-time; Precise;

Return link feasible

Public Regulated

GALILEO – proposed services

GALILEO Signal Structure

C/AOS/GPS III

(1575.42 MHz)

(1278.75 MHz)

(1227.6 MHz)

(1176.45

M P(Y)PRS

(1217.14

L5 E5a E5bOS CS, SoL

COMPASS

Proposed Chinese satellite navigation system

Planned: 27 medium earth orbit satellites,

5 geostationary satellites, 3 inclined

geosynchronous satellites

Currently: three geostationary, one MEO

THE END

Surveying, GPS and GNSS Geomatics lectures

Technology