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
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.
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) ?