gps positioning and surveying

7/23/2019 Gps Positioning and Surveying

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GPS Positioning and Surveying

Research Center for Seismology, Volcanology and Disaster Mitigation

Graduate School of Environmental StudiesNagoya University, 5 February 2007

Hasanuddin Z. AbidinGeodesy Research Division

Institute of Technology BandungJl. Ganesha 10, Bandung, IndonesiaE-mail : [email protected]


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Positioning with GPS

Position is given in 3-D, i.e. (X,Y,Z) or (L,B,h). Height (h) given by GPS is an ellipsoidal height.

Positioning datum is WGS (World Geodetic System) 1984which uses reference ellipsoid : WGS84.

Point to be positioned could be stationary or moving.

Positioning could be done relative to the Earths center orrelative to the other known point.

Positioning could be done using several methods :absolutepositioning, differential positioning, static surveying, rapidstatic, pseudo-kinematic and kinematic positioning.

Positioning accuracy :mm to several of m level. Positioning accuracy would depend on several factors :

positioning method, satellite geometry, data quality, anddata processing strategy.

Hasanuddin Z. Abidin, 2006


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Basic Pr inciple of Positioni ng with GPS

However, with GPS we can only measurethedistances, not theposition vectors.

GPS overcome this positioning problem bysimultaneouslymeasuring distancesto several GPS satellites.


GPS

Observer

Earth s center

r (known)_

(required)_

R (sought)

_

R = r - _

_ _

Geocentric position of satellite( r )is known.

If the topocentric vector position ofsatellite ( ) can be measured, thenthe geocentric position vector ofthe observer can be determined as :

_

_

d1

d2d3 d4 d5


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The Principle is Not New !!

The basic principle of GPS positioningis actually not a new one.

It is actually the same astraditional terrestrial principleof resection by distancesto the known control points.


d1

d2d3

(x,y)3

(x,y)2(x,y)1

measured

known

(x,y) = ?? sought

In case of GPS, the knownpoints are lift up to the skyas the satellites,

the satellites can be seenas the rotating 3D-knowncontrol points

d1

d2d3 d4 d5

(X,Y,Z)1(X,Y,Z)2

(X,Y,Z)3 (X,Y,Z)4 (X,Y,Z)5

(X,Y,Z)

measured

known

sought

Satellites coordinatesare computed based

on Navigation Message


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Besides containing the ranging codes, GPS signals also aremodulated by the 'navigation message'.

This message contains information such as :- the satellite's orbital data (the so-calledbroadcast ephemeris),- satellite almanac data,

- satellite clock correction parameters,- satellite health and constellation status,- ionospheric model parameters for single-frequency users, and- the offset between the GPS and UTC

(Universal Time Coordinated) time systems.

The content of the navigation message isdetermined by the GPS Control Segment andbroadcast to the users by the GPS satellites.

GPS Navigation Message



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Structure of GPS Navigation Message

1 2 3 4 5

0 1 2 3 4 5 6 7 8 9

Dataframe (30 sec)

Subframe (6 sec)

Information/Control

24 bits 6 bits

TLM H OW

2,3

4,5

Block I Data(Clock Parameters)

Block II Data(Broadcast Ephemeris)

Block III Data(Almanac, UTC,

Ion. cor. parameters,Special information)

Subframes

1


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Time Parameters

toe Reference time for the ephemeris parameters (s)

toc Reference time for the clock parameters (s) ao, a1, a2 Polynomial coefficients for satellite clock correction, i.e. representing the

bias (s), drift (s/s), and drift-rate (s/s2) components.

IOD Issue of Data (arbitrary identification number)Satellite Orbit Parameters

a Square root of the semi-major axis (m1/2) e Eccentricity of the orbit (dimensionless) io Inclination of the orbit at toe (semicircles)

o Longitude of the ascending node at toe (semicircles) Argument of perigee (semicircles) Mo Mean anomaly at toe (semicircles)

Orbital Perturbation Parameters

n Mean motion difference from computed value (semicircles/s) Rate of change of right ascension (semicircles/s) idot Rate of change of inclination (semicircles/s)

Cus and Cuc Amplitude of the sine and cosine harmonic correction terms to theargument of latitude (rad) Cisand C ic Amplitude of the sine and cosine harmonic correction terms to the

inclination angle (m)

Crsand Crc Amplitude of the sine and cosine harmonic correction terms to the orbitradius (m)

Content of GPS Broadcast Ephemeris



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Perigee

Reference epoch

io

idot

k

Equator

Mo

o

a,e

Ascending node

.e.

Geocenter

Vernalequinox

n

ZT

Satell i te

Cic, Cis

Crc, CrsCuc, Cus

YT

XT

Perigee

Reference epoch

io

idot

k

Equator

Mo

o

o

a,e

Ascending node

..e.e.

Geocenter

Vernalequinox

nn

ZT

Satell i te

Cic, Cis

Crc, CrsCrc, CrsCuc, Cus

YT

XT

Geometric Visualizationof the GPS Broadcast

Ephemeris Parameters


In BROADCAST EPHEMERIS :Coordinates of GPS

satellites are not givendirectly in (X,Y,Z).

Instead the Keplerianelements of the orbitare given.


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Other GPS Orbit Information

GPS OrbitInformation:

AlmanacBroadcast EphemerisIGS Ultra Rapid EphemerisIGS Rapid EphemerisIGS Final (Precise) Ephemeris

http://igscb.jpl.nasa.gov/components/prods.html

Keplerian elements

Position andvelocity ofsatellites

ph = predicted half; oh = observed half

Broadcast ~160 cm real time -- daily

Ultra-Rapid (ph) ~10 cm real time 4 times daily 15 min

Ultra-Rapid (oh)


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Distances to GPS Satellites

PSEUDORANGES

based on the travel time of the signal derived using code measurements

PHASE RANGES

based on the phase of the signal

derived using carrier phasemeasurements4



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GPS PRN-Codes

1 chips C/A-code = 1sec293 m

P(Y)-code = 0.1sec29.3 m GPS codes--

1 chips C/A-code = 1 sec

P(Y)-code = 0.1 sec GPS codes--

1 chips C/A-code = 1sec293 m

P(Y)-code = 0.1sec29.3 m GPS codes--

1 chips C/A-code = 1 sec

P(Y)-code = 0.1 sec GPS codes--

There are two pseudo-randomnoise (PRN) codes which aretransmitted by a GPS satellite: the P(Y)-code and the C/A-code.

The two main roles of these codes are- to provide time delay measurements so the user can obtain

the distance to the observed satellite , and- to help the receiver in differentiating the incoming signals

from different satellites.These codes are sequences of binary values (zeros and ones, or +1 and -1),

and although the sequence appears to be random, each code has its uniquestructure generated by a mathematical algorithm.



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The basic principle for obtaining this range is the so-called 'code-correlation'technique whereby the incoming code from the satellite is correlated with areplica of the corresponding code generated inside the receiver(see the Figure).

Both codes are generated using the same mathematical algorithm.The time shift (dt) required to align the two codes is, in principle, the time

required by the signal carrying the code to travel from the satellite to the receiver. Multiplying dt with the speed of light, one can obtain an estimate

of the range to the satellite.

This range is usually termed pseudorange, since it is still biased by the timeoffset between the satellite and receiver clocks used to measured the time delay dt.


DETERMINING PSEUDORANGE USING CODE

dt

Code coming from GPS satellite

Code replica generated

inside GPS receiver

Distance from observer to satellite = c . dt

Observer

Satellite


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GPS Carrier Waves

The main function of the GPS carrier waves, L1 and L2, is to

'carry' the codes and navigation messages to the receiver.

The codes and navigation messages are modulated onto thecarrier waves using the bi-phase shift key modulation technique.

The phase measurements made on the carrier waves can also beused to derive very precise range measurements to the satellites,

which are often referred to as 'phase ranges' or 'carrier ranges',


carrier wave

data-modulatedcarrier wave

data (code andnavigation message)

+ 1

- 1


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PHASE RANGE DETERMINATION


GPS phase range is not an 'absolute' range from receiver to the satellite asin the case of pseudorange, but is an ambiguous range.

There is an unobserved part of the range caused by the initial cycle ambiguityof the phase (N).

To convert this ambiguous range into an absolute range, N has to be estimated.If the integer value of N can be correctly estimated, then the carrier range will

become a very precise range measurement (at the few mm precision level),and can be used for high precision positioning.

The integer cycle ambiguity resolution is not an easy task.

Range from observer to satellite =wavelength . (

+ N)Range from observer to satellite =wavelength . ( + N)Range from observer to satellite =wavelength .( + N)

Counted number of full cycles, from toto t1

Unobserved numberof full cycles; called

initial integerambiguity (N)

Satellite

Observer

Range from observer to satellite =. ( + N)

Measured phase (fraction of cycle) at epoch ti

ti to

Phase observation () at epoch t1


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GEOMETRICAL INTERPRETATION OFCARRIER RANGE AND CYCLE AMBIGUITY

(ti) = Fr((ti)) + Int(;to, ti) + N(to)= N(to) +i

i= Fr((ti)) + Int(;to, ti)

Phase observationat each epoch ti:


N(to)

GPS Orbit

GPS Receiver

N(to)

N(to)

12

3

t1t2

t3


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Pseudorange vs Phase Range


PSEUDORANGE PHASE RANGE

Noise(1% of

)

P(Y)-code : 0.3 mC/A-code : 3 m

L1 : 1.9 mmL2 : 2.4 mm

Ambiguity None cycle ambiguity

Ionospheric bias delayed fasten

Multipath

1 code width (max) :

P(Y)-code : 30 mC/A-code : 300 m

0.25 (max) :

L1 : 4.8 cmL2 : 6.1 cm


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Factors InfluencingGPS Positioning Accuracy

SatelliteGeometry

Data ProcessingStrategy

Data Quality

PositioningMethod


4


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type of data used (pseudorange or phase)

GPS receiver quality level of errors and biases

number of satellites

location and distribution of satellites

length of measurement period

absolute & differential positioning

static, rapid static, pseudo-kinematic, stop-and-go, kinematic

one & multi monitor stations

real-time & post processing

strategy for correcting errors and biases estimation method to be used

baseline processing and network adjustment

quality control mechanism

DATA QUALITY

SATELLITEGEOMETRY

POSITIONINGMETHOD

DATAPROCESSING

STRATEGY

Factors Influencing GPS Positioning Accuracy


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One-Way Pseudorange


P = pseudorange = geometric range between the antenna and satellited = ephemeris (orbital) errordtrop = tropospheric biasdion = ionospheric bias

dt,dT = receiver and satellite clock errorsMP = pseudorange multipathP = pseudorange noise

Subscript i indicates a certain frequency of signal (i=1,2, or 5)

4

Pi=+ d + dtrop + dioni+ (dt - dT) + MPi+Pi


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One-Way Phase Range


L = phase measurement in range unit = geometric range between the antenna and satellited = ephemeris (orbital) errordtrop = tropospheric biasdion = ionospheric biasdt,dT = receiver and satellite clock errors

= signal wavelengthN = phase ambiguity (integer)MC = phase multipathC = phase noise

Subscript i indicates a certain frequency of signal (i=1,2, or 5)

4

Li=+ d + dtrop - dioni+ (dt - dT) i.Ni+ MCi+Ci


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GPS Errors and Biases


?

Orbital errorsSatellite clock errors

Phase AmbiguityCycle Slips

Tropospheric bias

Ionospheric bias

Receiver clock errors Antenna errors Receiver noise

MultipathImaging


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SPS = Standard Positioning Service (for civilian).

PPS = Precise Positioning Service (for military and authorized users).

PPP = Precise Point Positioning (using phases)

1 mm 1 cm 1 m10 cm 10 m 100 m

DIFFERENTIALPOSITIONING

ABSOLUTE

POSITIONING

3 mm

static survey (carrier phase)

5 cm

1 mcarrier-smoothed code

2 mdifferential code

3 m

PPS with anti-spoofing

5 m

SPS without selective availability50 m

SPS with selective availability

ambiguity-resolved carrier phase

Since2 May

2000

PPP surveying

10 cm

Spectrum of GPS Positioning Accuracy


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GPS Positioning Methods

STATIC(point is static, receiver is static)

KINEMATIC

(point is moving, receiver is moving)

RAPID STATIC(point is static, receiver is static (short period))

PSEUDO-KINEMATIC(point is static, receiver is static and moving)

STOP AND GO(point is static, receiver is stopping and moving)

ABSOLUTE(one receiver)

DIFFERENTIAL(minimal 2 receivers)


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Post-processing

Pseudo-kinematic

Real-Time

Static

Kinematic

Stop-and-Go

Rapid Static

Navigation

RTK DGPS

PPP(PrecisePoint

Poitioning)

Surveying

Positioning with GPS

Differential AbsoluteDifferentialAbsolute

GPS Positioning Methods


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Absolute Positioning


It is also called point positioning

Position is given in WGS-84 system, relative to mass center of the Earth. Uses only one receiver.

Basic principle : simultaneous distance measurements to several satellites.


Usually based onpseudoranges

The phases could also be used if the initial phase ambiguities have been

previously determined or they are estimated together with the position. Precise Point Positioning (PPP) is using phases in static mode.

Positioning accuracystrongly dependent onthe data quality andsatellite geometry.

It is not intended foraccurate positioning.

Main applications :navigation andreconnaissance.

GPS Satellite

Kinematic

GPS Satellite

Static


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Using a single epoch observations.

Usually based on pseudoranges.

Basic positioning mode used bythe navigation-type GPS receiver.

At each epoch, there are 4 parametersthat should be estimated :

- 3 parameters of coordinate (X,Y,Z or,h)- 1 parameter of receiver clock errors

In order to estimate the parameters, observations tominimal of 4 GPS satellites are required.


Real-Time Absolute Positioning (1)


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http://www.math.tamu.edu/~dallen/physics/gps/gps.htm

A single epochobservation equations

using psudoranges :

Position of GPS receiverto be estimated : (x,y,z)

Coordinates of satellitesare known.

Psudoranges are measured.

Real-Time Absolute Positioning (2)


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Before May 2000 :Before May 2000 :2525--100 m100 m

33--5 m5 m

USC-USDC (2002)

RealReal--Time Absolute Positioning (3)Time Absolute Positioning (3)

Todays typical accuracy ofTodays typical accuracy ofhorizontal position based onhorizontal position based on

C/A Code on L1C/A Code on L1Hasanuddin Z. Abidin, 2006


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Modernization of GPS Signals

P(Y)

C/A

C/A

P(Y)

P(Y)

P(Y)

ML2C

M

C/A

P(Y)

M

P(Y)

L2CM

P(Y)

C/A

C/A

P(Y)

P(Y)

P(Y)

ML2C

M

Current signals(Block II/IIA/IIR)

C/A

P(Y)

M

P(Y)

L2CM

1176 MHz 1227 MHz 1575 MHz1176 MHz

(L5)

1227 MHz

(L2)

1575 MHz

(L1)

Full modernizedSignals (Block IIF)

Next GenerationSignals (Block IIR-M)



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11--3 m3 m

Better resistance toBetter resistance to

interferenceinterference

Eliminates need for costlyEliminates need for costlyDGPS in many nonDGPS in many non--safetysafetyapplicationsapplications

USC-USDC (2002)

RealReal--Time Absolute Positioning (4)Time Absolute Positioning (4)

Tomorrows typical accuracy ofTomorrows typical accuracy ofhorizontal position based onhorizontal position based on

C/A Code on L1C/A Code on L1L2C Code on L2L2C Code on L2New Code on L5New Code on L5



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Static Absolute Positioning

Using many epochs of observations (e.g. a few hours or more). Requires the use of mapping or geodetic-type receiver.

Can based on pseudoranges, phases and phase-smoothedpseudoranges.

Typical accuracy spectrum :dm to a few meters

Accuracy will be mainly affected by :- type of data being used

- data length Can be used for establishing the initial

(temporary) control station.


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Differential Positioning It is also calledrelative positioning.

Required at least 2receivers, where one of themis located on the point withknown coordinates(reference station).

Position is determinedrelative to thereferencestation.

Basic concept:differencing processcould eliminate and/or reduce the effects ofsome errors and biases, and therefore enhancing the positioning accuracy.

Effectiveness of differencing process would strongly depend on the distancebetween the monitor station and the point to be positioned (the shorter the moreeffective, and vice versa).


Could usepseudoranges, phases, or phase-smoothed pseudoranges. Positioning accuracy level ranges from medium to high.

Main applications:survey and mapping, geodetic surveys, and precisenavigation.


Observer

GPS Satellite

Monitorstation

Observer

STATIC

KINEMATIC

GPS Satellite

Referencestation


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Effect of GPS Data Differencing


ERRORS AND BIASESCOULD BE

ELIMINATED

COULD BE

REDUCED

COULD NOT BEELIMINATED

OR REDUCED

Satellite clock

Receiver clock

Orbit (Ephemeris)

IonosfirTroposfir

Multipath

Noise

The effectiveness of error-and-bias reduction will mainly depend on

the distance between stations (baseline length) the longer the baseline, reduction will be less effective, and vice-versa.

For high precision applications, the residual errors and biases shouldbe further modeled and/or estimated.


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Receiver # 1 Receiver # 2

Satellite # 1,epoch # 1

Satellite # 1,epoch # 2 BETWEEN

EPOCHS

Satellite # 2,epoch # 2

Data Differencing Modes

BETWEENRECEIVERS

BETWEENSATELLITES


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Differencing TypesSD = OW - OW

DD = SD - SDTD = DD - DD between-receiver

between-satellite

between-epoch OW = ONE-WAY data

SD = SINGLE-DIFFERENCE data

DD = DOUBLE-DIFFERENCE data

TD = TRIPLE-DIFFERENCE data


valid forpseudoranges,phase ranges,

or otherdata combination

Data that are mainly used fordifferential GPS positioning are :

Receiver-Satellite Double-DifferenceTriple Difference


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Receiver-Satellite Double-Difference


Eliminates the receiver andsatellite clock errors and biases.

Reduces the effects of orbital,ionospheric and troposphericerrors and biases.

Cycle ambiguity still needto be resolved and fixed.

Observation noiseincreases by factor of 2.

Data generally used for GPS differential positioning.

2 receivers, 2 satellites, 1 epoch

GPS-1 GPS-2


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Eliminates the receiver and satellite

clock errors and biases. Eliminates cycle ambiguity (when

there is no cycle slips between epochs).

Reduces the effects of orbital,ionospheric and troposphericerrors and biases.

Observation noiseincreases by factor of

8.

Generally used for automaticediting ofcycle slips.

In GPS differential positioningis generally used to provide an approximate baseline solution.

Triple Difference Observation

d dtrop dion P

L d dtrop dion MC C

2 receivers, 2 satellites, 2 epochs

GPS-2, epoch-2GPS-2,

epoch-1

GPS-1,

epoch-2

GPS-1,

epoch-1


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DGPS System


DGPS (Differential GPS) system is a termusedto represent a real-time differentialpositioning system using pseudorange data.

In order to establish a real time mode,Reference Station has to send the differentialcorrection to the user in real-time by usinga certain data communication system.

Two types of differential correction :

- pseudorange correction (RTCM SC-104)- position correction

Generally used :pseudorange correction

Typical positioning accuracy : 1 - 3 m

It is generally used to positionthe moving objects.

Main applications:marine surveysand medium accuracy navigation.

GPS

ReferenceStation

DifferentialCorrection

Vessel


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RTK System


RTK (Real-Time Kinematic) system isa term used to representa real-timedifferential positioning system using

phase data.

Could be used to position the stationaryand moving objects.

In order to establish a realtime mode, Reference Stationhas to sendboth phaseand pseudorange datato the user in real-timeby using a certain datacommunication system.

Typical positioning accuracy : 1 - 5 cm

Main applications :staking out, cadastral survey, mining survey, andhigh precision navigation.

Phases andPseudoranges

MonitorStation

Rover

GPS satellites


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RTK Positioning: TodayRTK Positioning: Today

10 km10 km

2 cm accuracy2 cm accuracy

USC-USDC (2002)

Todays typical accuracy of positioning based onTodays typical accuracy of positioning based onL1 Code and CarrierL1 Code and Carrier

L2 CarrierL2 CarrierData LinkData Link


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100+ km100+ kmFaster recoveryFaster recoveryfollowing signalfollowing signalinterruptionsinterruptions(ex., under bridges)(ex., under bridges)

2 cm accuracy2 cm accuracyFewer referenceFewer referencestations neededstations needed

USC-USDC (2002)

RTK Positioning: TomorrowRTK Positioning: Tomorrow

Tomorrows typical accuracy of positioning based onTomorrows typical accuracy of positioning based onL1 Code and CarrierL1 Code and CarrierL2 Code and CarrierL2 Code and Carrier

L5 Code and CarrierL5 Code and CarrierData LinkData Link


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GPS Static Sur veying

All points to be positionedare stationary.

Observations are usuallyperformed to cover a certainnetwork of points.

The coordinates are determined relative to

the fixed points with known coordinates.

Observation is usually performed in baseline mode for a few hours or days.

Usually based on differential positioning using phase data.

Achievable positioning accuracy is usually high (mm to cm level).

Applications :control surveys, monitoring surveys, etc..

Other Methods : - RAPID STATIC - STOP AND GO- PSEUDO-KINEMATIC - KINEMATIC


F ixed points

Points to be

positioned

observed baseline

vectors


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Network vs. Radial Mode of Surveying


NETWORK MODERADIAN MODE

(from Reference Point)

Achievable AccuracySurvey TimeSurvey Cost

The adopted modewill affects :


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GPS survey data processing is usually performed inthree stages, namely :

Data processing could be done usingeithercommercial softwareorscientific software, depending onthe accuracy level being sought.

GPS Survey Data Processing

1. Baseline processing

2. Network adjustment

3. Datum and coordinatetransformation


Fixedpoint


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GPS Data Processing Software


SKIPro

GPSurvey

Pinnacle

BERNESSE University of Berne, Swiss

DIPOP University of New Brunswick, Kanada

GAMIT Massachussets Institute of Technology, USA

GIPSY Jet Propulsion Laboratory, USA

TOPAS University of Federal Armed Forces, Jerman

Leica

Trimble

Topcon

Commercial Software Author

Scientific Software Author


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On-line GPS Data Processing Software


AUSPOS : http://www.ga.gov.au/geodesy/sgc/wwwgps/CSRS-PPP : http://www.geod.nrcan.gc.ca/ppp_e.php

SCOUT : http://sopac.ucsd.edu/cgi-bin/SCOUT.cgiAUTO GIPSY : http://milhouse.jpl.nasa.gov/ag/OPUS : http://www.ngs.noaa.gov/OPUS/

It provides users with the facility to submit dual frequency geodeticquality GPS RINEX data observed in a 'static' mode, to website-basedGPS processing system and the user receive rapid turn-around ITRFcoordinates.

It is a FREE service.

This service takes advantage of both the IGS Stations Network andthe IGS product range, and works with data collected anywhere on Earth.

Examples :


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1

10

100

1985 1986 1987 1988 1989 1990 1991 1992 1993

milimeter

Ref. : UNAVCO (1995)

Achievable Precision ofHorizontal Component


GPS Positioning Precision (1)


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GPS Positioning Precision (2)

0

5

10

20

30

40

50

1985 1986 1987 1988 1989 1990 1991 1992 1993

milim

eter

Achievable Precision ofVertical Component

Ref. : UNAVCO (1995) Hasanuddin Z. Abidin, 1996


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Rapid Static Surveying Static surveywith shorter session length

(5-20 minutes instead of 1-2 hours or more).

Observation procedure is basically the same asin static survey.

Observation length depends on baselinelength, number of observed satellites andsatellite geometry).

Based ondifferential positioningusing carrier

phase data. Fundamental requirement :fast cycle

ambiguity resolution


Requires a sophisticated data processing software.

Requires good satellite geometry, minimal residual errors and biases,multipath-minimal environment.

Dual-frequency GPS data is preferred. Typical achievable (relative) accuracy : cm level.

Main applications :survey and mapping, network densification, engineeringsurvey, utility survey, etc.

Fixed point

baselin

e

Points to bepositioned


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Rapid Static vs. Static Surveying Rapid static has a higher productivity than static survey.

Static survey yield a relatively higher accuracy of coordinates.

Compared to static survey, rapid static has a more stringent requirementon GPS receiver, observation geometry, and data processing software tobe used.

Rapid static survey is more prone toward the effects of errors and biases.

A better utilization scenario is to integrate the two survey methods

according to their characteristics, as shown in the following.


Static surveyRapid static survey

Fixed point

Points to be positionedusing static survey

Points to be positionedusing rapid static survey


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Pseudo-Kinematic Surveying (1)

Also calledintermittent staticorreoccupationmethod.

It is the same as two rapid static surveys(duration of a few minutes each) separatedwith a relatively longer period (more thanan hour).

Fundamental argument :Observations intwo separated sessions can cover requiredgeometrical changes for successfulambiguity resolution.

Requires good satellite geometry, minimalresidual errors and biases, multipath-minimal environment


FixedStation

1st observation

2nd observationafter > 1 hour

Geometricalchages

Observer

GPS

2nd

observat

ion

1 s

t

observation


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Based on differential positioning using carrier phase data.

GPS receiver can be turned off during the move between stations.

Coordinates are estimated using data from both sessions.

Not all GPS receivers have operational mode forpseudo-kinematic surveying.

Requires a sophisticated data processing software.

Typical achievable (relative) accuracy : cm level.

Ideal for positioning the points along the road.

Static

Rapid Static

Pseudo-kinematic

Pseudo-Kinematic Surveying (2)



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Stop-and-Go Survey (1)

Characteristic :rover moves and stop

(for several seconds) from point to point. Also called semi-kinematic survey.

Similar to kinematic positioning;only the receiver stops for a whileat each points.

Cycle ambiguity at the first pointhas to be determined prior toreceiver movement to next points.

During the movement between points,receiver has to always lock on toGPS signal.

If the receiver loss the signal (cycle slip),receiver has to stop and re-determine the cycle ambiguity,and afterward moves on again to other points.

Typical achievable (relative) accuracy : cm level.

stopstop

stop

stop

stop

stop

stopstop

go

go

go

go

gogo

go

go

Rover

Receiver movement

Base

Point



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Based on differential positioning using

carrier phase data. Rover trajectory between points is not

required, although was observed.

Requires a sophisticateddata processing software.

Requires good satellite geometry,minimal residual errors and biases,multipath-minimal environment.

Position determination can be performedin real-time or post-processing mode.

Real-time requires stringent operational

strategy. Coordinates are determined relative to a fixed point

This method is suitable for surveys inan open area with points close to each other.

Coordinates are determinedrelative to a fixed point

Fixed point

Rover

Stop-and-Go Survey (2)Stop-and-Go Survey (2)



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Points to be positioned are moving.

Besides position, the velocity, acceleration,and attitude of the moving object could alsobe determined by GPS.

Could be absolute or differential positioning.

Could use pseudorange and/or phase data.

Data processing to obtain positioncould be done in real-time or in post-processing.

For real-time differential kinematic positioning,data communication between monitor stationand moving receiver is required.

Precise kinematic positioning required the use of phase data.

The main problem ison-the-fly ambiguity resolution. Positioning accuracy ranges from low to high level.

Applications : navigation, surveillance, guidance, photogrammetry,airborne gravimetry, hydrographic survey, etc.

Kinematic Positioning

GPS

MonitorStation


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GPS Height

Geocentre

H

h

Earths Surface

Geoid

Ellipsoid

Height of point given by GPS (h)is the height above WGS84 referenceellipsoid.

Thisellipsoidal height(h) is notthe same as anorthometric height

which is generally used for practicalapplications and obtained fromlevelling measurement.

Orthometric heightof a point is its height abovegeoidmeasured

along the plumb line on that point.

Ellipsoidal heightof a point is its height aboveellipsoidmeasuredalong the ellipsoidal normal line on that point.


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Ellipsoidal Height to Orthometric Height

h = ellipsoidal heightH = orthometric heightN = geoid undulation = deflection of vertical

Approximated formula :

The above formula is accurate enoughfor practical applications.

The maximum value of deflection ofvertical () is about 30.

In order to achieve a higher accuracy,the height determination is done inrelative positioning mode :

H = h - N

dH = dh - dN

Geocentre

H

h

Earths Surface

Geoid

Ellipsoid


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Why height component is less accurate ?

GPS-derived height component is usually2-3 times less accurate than its horizontalcomponent.

One-sided geometry :

- only satellites above horizon can be observed.- geometrically is not an optimal situation.

- noup-and-down reduction schemeof errorsas in the case of horizontal component(i.e. East-West and North-South schemes)

Effects of the errors and biases on observedranges are usually lengthening or shorteningthese observed distances. height component will be mostly affected


GPS

Earth

GPSHorizontalComponents

REASONS :


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The above accuracy figuresare derived by basing on the misclosuresof height differences obtained by GPS survey method.

Accuracy of GPS (Surveying) Height

Reported AccuracyReported Accuracy ResearcherResearcher

Engelis & Rapp (1984)


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GPS Leveling vs. Leveling


0

40

80

120

160

200

240

280

320

0 20 40 60 80 100

Leveling - Orde 1

Leveling - Orde 2

Leveling - Orde 3

GPS leveling - 1 ppm

GPS leveling - 3 ppm

Distance (km)

Accuracy

(mm)

In this graphic for GPS levelingit is assumed that relative undulation error(N) is negligible (about zero).


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Velocity and AccelerationDetermination using GPS


dt

dt

dt

dt

Phase Data

Frequency (Phase rate) Velocity

Acceleration

PositionEP #1

Estimation process

Differentialoperator

Frequency Rate

EP #2

EP #3

Estimation process

Estimation process


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1. http://www.gmat.unsw.edu.au/snap/gps/about_gps.htm2. http://www3.sympatico.ca/craymer/geodesy/gps.html3. http://igscb.jpl.nasa.gov/4. http://www.gpsy.com/gpsinfo/5. http://www.ga.gov.au/geodesy/sgc/wwwgps/6. http://www.geod.nrcan.gc.ca/ppp_e.php7. http://sopac.ucsd.edu/cgi-bin/SCOUT.cgi

8. http://milhouse.jpl.nasa.gov/ag/9. http://www.ngs.noaa.gov/OPUS/10. http://sideshow.jpl.nasa.gov/mbh/series.html11. http://www.ngs.noaa.gov/gps-toolbox/12. http://www.navcen.uscg.gov/gps/modernization/default.htm13. http://www.usace.army.mil/publications/eng-manuals/

em1110-1-1003/toc.htm

14. http://bowie.mit.edu/%7Esimon/gtgk/15. http://facility.unavco.org/software/processing/gipsy/gipsy_info.html16. http://www.gpsworld.com/gpsworld/17. http://www.navtechgps.com/

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