Surveying with Satellites GS609

Winter Quarter 2009

Distributed: February 6, 2009

Date Due: February 27, 2009

Problem Set 3

Given RINEX observation and navigation data files for a stationary GPS receiver with unknown location, perform the following:

  1. Linearize the pseudorange observation equation and compute the partial derivatives (receiver coordinates and clock correction!) using satellite coordinates from (2) below (note that the approximate coordinates of the GPS antenna are given in the RINEX observation header file).
  1. Compute the satellites’ positions [Earth-Centered-Earth-Fixed (ECEF) Cartesian coordinates] at the epoch corresponding to the epochof observation, based on RINEX navigation data, using the algorithm that you developed for Lab #2.
  1. Use pseudorange data given in the RINEX observation file to compute 3D Cartesian coordinates of the location of the GPS antenna and the receiver clock correction (Hint: based on RINEX navigation data compute and apply the satellite clock correction first; neglect all other unknowns in the equation). What is the minimum number of observations that you need to obtain the solution? Perform the minimum-constellation solution based on P1-code range.
  1. Use pseudorange data given in the RINEX observation file to compute 3D Cartesian coordinates of the location of the GPS antenna and the receiver clock correction (Hint: based on RINEX navigation data compute and apply the satellite clock correction first; neglect all other unknowns in the equation). Obtain separate solutions from P1-code range and C/A-code observable, respectively. This time, use all the satellite observation data provided to get solution. Compare the results and discuss (P1-code range vs. C/A-code).
  1. Compare the results from (3) and (4) above. Discuss.
  1. Prove the relationship: t=k/f2 from the enclosed handout (distributed in class earlier), where t is the ionospheric delay of the signal, k is a constant and f is the signal frequency. (Hint: start from the relationship between time, velocity and distance, and find the change in time as a function of varying velocity; assume fixed travel distance).

NOTE THAT RINEX files are provided on the GS609 web site and are shown here for reference only!

Navigation File (Lab301.99n)

2 NAVIGATION DATA RINEX VERSION / TYPE

GPS Data Logger GRDL 22-Mar-199912:01 PGM / RUN BY / DATE

COMMENT

END OF HEADER

7 99 3 22 18 0 0.0 .813954044133D-03 .147792889038D-11 .000000000000D+00

.170000000000D+03 .603750000000D+02 .481091467962D-08 .272033290081D+01

.302121043205D-05 .102233515354D-01 .410713255405D-05 .515360291672D+04

.151200000000D+06 -.447034835815D-07 .225165927234D+01 -.165775418282D-06

.955617560370D+00 .294500000000D+03 -.216826844627D+01 -.827677333226D-08

.539308178636D-10 .000000000000D+00 .100200000000D+04 .000000000000D+00

.700000000000D+01 .000000000000D+00 -.931322574615D-09 .682000000000D+03

.147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00

13 99 3 22 17 59 44.0 -.690338201821D-04 -.210320649785D-10 .000000000000D+00

.000000000000D+00 .275000000000D+01 .470412451710D-08 -.162968136300D+01

.251457095146D-06 .212027202360D-02 .709854066372D-05 .515377128983D+04

.151184000000D+06 -.745058059692D-08 -.874646144797D+00 .149011611938D-07

.961259925683D+00 .243750000000D+03 -.109490109393D+01 -.815426822943D-08

.333228166005D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00

.700000000000D+01 .000000000000D+00 .558793544769D-08 .256000000000D+03

.147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00

15 99 3 22 18 0 0.0 .664619728923D-03 .397903932026D-11 .000000000000D+00

.213000000000D+03 -.826875000000D+02 .416767360033D-08 -.539578337546D+00

-.423565506935D-05 .714090676047D-02 .632181763649D-05 .515359841728D+04

.151200000000D+06 -.521540641785D-07 -.290786742981D+01 .689178705215D-07

.983325919289D+00 .267781250000D+03 .151707954902D+01 -.821319925557D-08

-.277868717205D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00

.200000000000D+01 .000000000000D+00 -.931322574615D-09 .725000000000D+03

.147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00

26 99 3 22 18 0 0.0 .357320066541D-03 .470663508167D-10 .000000000000D+00

.128000000000D+03 .225000000000D+01 .477769901034D-08 .241671187380D+01

.175088644028D-06 .111072373111D-01 .674650073051D-05 .515358551025D+04

.151200000000D+06 -.169500708580D-06 -.868448606462D+00 .210478901863D-06

.960262099982D+00 .249031250000D+03 -.103266892749D+00 -.818176937496D-08

.240009997380D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00

.700000000000D+01 .000000000000D+00 .000000000000D+00 .384000000000D+03

.147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00

27 99 3 22 17 59 44.0 .148387625813D-04 .113686837722D-11 .000000000000D+00

.660000000000D+02 -.188750000000D+02 .522878922863D-08 -.530517243864D+00

-.964850187302D-06 .133102550171D-01 .775977969170D-05 .515368167686D+04

.151184000000D+06 .281259417534D-06 .143695736910D+00 -.111758708954D-07

.941077547360D+00 .216000000000D+03 -.294706393665D+01 -.848785355317D-08

-.260725145963D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00

.700000000000D+01 .000000000000D+00 .465661287308D-09 .660000000000D+02

.147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00

31 99 3 22 18 0 0.0 .154948793352D-04 .568434188608D-12 .000000000000D+00

.165000000000D+03 .688437500000D+02 .504806741513D-08 .152727803811D+01

.359117984772D-05 .886761641596D-02 .414252281189D-05 .515370834351D+04

.151200000000D+06 -.167638063431D-06 .225269650320D+01 .502914190292D-07

.955064555392D+00 .299562500000D+03 .778139664206D+00 -.863857411700D-08

.564309220030D-10 .000000000000D+00 .100200000000D+04 .000000000000D+00

.700000000000D+01 .000000000000D+00 .139698386192D-08 .165000000000D+03

.147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00

Observation File (Lab301.99o)

2 OBSERVATION DATA G (GPS) RINEX VERSION / TYPE

GPS Data Logger GRDL 22-Mar-199912:01 PGM / RUN BY / DATE

holl COMMENT

topex1 COMMENT

COMMENT

NOS MARKER NAME

7031 D 1977 MARKER NUMBER

dmm NOS OBSERVER / AGENCY

UZ01286 ASHTECH Z-SURVEYOR UE00 REC # / TYPE / VERS

CD16199 ashtech chokering ANT # / TYPE

310880.617 -4679087.195 4308925.762 APPROX POSITION XYZ

2.0 0 0 ANTENNA: DELTA H/E/N

1 1 WAVELENGTH FACT L1/2

5 C1 L1 L2 P1 P2 # / TYPES OF OBSERV

1 INTERVAL

1999 3 22 17 1 22 TIME OF FIRST OBS

1999 3 22 21 51 5 TIME OF LAST OBS

END OF HEADER

99 3 22 17 1 22.0000000 0 6 15312726 713

21594940.921 11609407.06401 9047549.64101 21594939.245 21594947.336

22563844.186 13226364.74301 10294014.15201 22563842.766 22563850.920

20261148.335 12073632.93801 9406275.67801 20261147.263 20261152.933

24634912.090 -789202.16501 -615223.99801 24634912.480 24634921.398

23260563.863 11270500.28501 8787740.46301 23260562.980 23260573.029

23494472.305 13044704.23601 10154322.73801 23494471.963 23494481.281

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