H:\EXCERC\geod98e.e10.wpd

Department of Geophysics, Julian Maries Vej 30, 2100 Copenhagen Ø.

Geodesy Course, Exercise 10.

10.1. Process the GPS data with the manufacturer program GPSurvey. What are the geographical coordinates for the points in WGS84, when the coordinates of the Rockefeller Tower antenna are kept fixed ? What is the estimated errors of the coordinate differences ? (Follow the attached instructions for the processing).

10.2. The preliminary coordinates for a point are (in WGS84):

(X',Y',Z') = ( 3496719 m, 743242 m, 5264456 m).

There has been observed 4 distances from satellites no. 16, 23, 26 og 27. The coordinates for the satellites, the observed distances, and the calculated ones for satellites 16, 23, 26 are found in the table below. (You must calculate the last distance yourself). All quantities are in units of m.

Sat. X Y Z Obser. Calcul.

Distance

16 19882818.3 -4007732.6 17137390.1 20785631.1 20785633.8

23 -8318660.0 -15394931.9 20196264.6 24960037.2 24960023.0

26 9358156.0 -18567258.8 16719423.9 23204925.3 23204917.0

27 14687857.1 7259303.2 20670310.0 20125624.5

Use Taylors formula to establish the 4 linearized observation equations. Suppose first that the receiver clock is without error, and use the 3 first satellites to determine the improvements (dX, dY, dZ) to the preliminary coordinates.

Now, suppose the clock has an error. What are now (dX, dY, dZ, dt), where dt is the clock error. The calculations must be made with a precision of 0.1 m, so take care that your pocket calculator has enough significant digits !

For the more advanced: Suppose all 4 distances are observed with an estimated error of 1 m, and that the errors are uncorrelated. What are then the variance covariance matrix of the calculated quantities (dX, dY, dZ, dt) ?