GPS Observables

7/31/2019 GPS Observables

1/24

GPSObservables


2/24

en a rece ver measures e me o seneeds to apply to its replica of the code to reachmaximum correlation with received si nal what isit measuring?

It is measuring the time difference between when

a s gna was ransm e ase on sa e e c ocand when it was received (based on receiverclock .

If the satellite and receiver clocks were

synchronized, this would be a measure of range Since they are not synchronized, it is calledpseudorange


3/24

Pseudorange:

p

p

Where Ppk is the pseudorange between receiver k and satellite p; tkis the receiver clock time tp is the satellite transmit time and c is

k k

the speed of light

This expression can be related to the true range by introducingcorrections to the clock times

k and p are true times; tk and tp are clock corrections


4/24

u s u ng n o e equa on o e

pseudorange yields

kp is true range, and the ionospheric and

the propagation velocity is not c.


5/24

e equa on or e pseu orange uses e rue

range and corrections applied for propagationdela s because the ro a ation velocit is not thein-vacuum value, c, 2.99792458x108 m/s

To convert times to distance c is used and then

correc ons app e or e ac ua ve oc y noequaling c. In RINEX data files, pseudorange isiven in distance units.

The true range is related to the positions of the

ground receiver and satellite. Also need to account for noise in measurements


6/24

seu orange no se ran om an no so ran om errors nmeasurements) contributions:

inversely proportional to the bandwidth of the signal. Therefore

the 1MHz bandwidth of C/A produces a peak 1 sec wide

(300m) compared to the P(Y) code 10MHz bandwidth whichproduces 0.1 sec peak (30 m)

Rough rule is that peak o correlation unction can be determined

to 1% of width (with care). Therefore 3 m for C/A code and 0.3

.


7/24

ore no se sources Thermal noise: Effects of other random radio noise in the GPS

bandsBlack body radiation: I=2kT/2 where Iis the specific intensity in,for example, watts/(m2Hz ster), kis Boltzmans constant,1.380 x10-23 watts/Hz/K and is wavelength.

Depends on area of antenna, area of sky seen (ster=ster-radians), temperature T (Kelvin) and frequency. Since C/A codehas narrower bandwidth, tracking it in theory has 10 times less

erma no se power epen s on rac ng an w p us efactor of 2 more because of transmission power).

Thermal noise is general smallest effect Multipath: Reflected signals (discussed later)


8/24

e ma n no se sources are re a e o re ec e

signals and tracking approximations. g qua y rece ver: no se a ou cm

Low cost receiver ($200): noise is a few meters

In general: C/A code pseudoranges are of similar.

narrowband tracking which reduces amount of

thermal noise Precise positioning (P-) code is not really the case.


9/24

Carrier phase measurements are similar to

seudoran e in that the are thedifference in phase between the

.Integration of the oscillator frequency

.

Basic notion in carrierphase: =ftwhere is phase and fis frequency


10/24

kp(tr) k(tr) r

p(tr) Nk

p(1)

between phase of receiver oscillator and

at the initial start of tracking

The received phase is related to the

rp(tr) t

p(tt) t

p(tr k

p/c) t

p(tr)

p(tr) k

p/c


11/24

e rate o c ange o p ase s requency.

Notice that the phase difference changesas /c changes. If clocks perfect andnothing moving then would be constant.

Subtle effects in phase equation =

at t-(riding the wave)

(used later). Also possible to formulate astransmit time.


12/24

When phase is used it is converted to

distance usin the standard L1 and L2frequencies and vacuum speed of light.

difference between true frequencies andnominal frequencies. As with range

ionospheric and atmospheric delaysaccount for propagation velocity


13/24


14/24

GPSobservables

GPSreceiverscanrecordupto5observables: an :p asemeasuremen son an

frequencies,incycles

PlusDopplerphase=d/dt


15/24

GPSobservablesstoredinreceiversinbinary

ro rietar format ReceiverIndependentExchangeformat

=

Formatdescription:ftp://igscb.jpl.nasa.gov/igscb/data/format/rin

ex2.txt


16/24


17/24

Pseudorange measurements(C/A,P1,P2): eometr crange+c oc o set+no se:

=r+ t c ~

ofcorrelationpeakwidth:

3mwithC/Acode .

Lowaccuracybutabsolutemeasurements

Phasemeasurements L1,L2 : Geometricrange+clockoffset initialphaseambiguityN:

=r f/c+ t fN~ .

(0.005x20cm=0.2mm)millimeter accuracytheoreticallypossible

eryaccura emeasuremen s u am guous


18/24

Absolutepositioning

e a vepos on ng

biases.

Datadifferencing


19/24

Positioningprinciples:Absolute

Positioning=

Tj =timeofreceptionofthesignalatreceiverj

Xi,Yi,andZi =theknowncoordinatesofthefourobservedsatellites , , t =theunknownreceiverclockerror c =isthespeedofelectromagneticradiationinspace.


20/24


21/24


22/24

GPSPhaseObservationEquation

i = receiversatellite ran e as com uted usin the hase observable

( )i i i

j j j jT n

Tj =timeofreceptionofasignalatreceiverj ij =truerangebetweensatellitei andreceiverj

=lengthoftheobservedwave nij =istheintegernumberofcycleambiguity a mos =p asea e ue o ea mosp er c e ay atmos =phaseduetounmodeled errors.

Thetruerange ij couldbeestimatedonlyiftheclockerrors,atmosphericdelayandcycleambiguitiesareresolvedoreliminatedbydatadifferencing.


23/24


24/24

Datadifferencin :DoubleDifferencin

GPS Observables

Documents

Transcript of GPS Observables