Rece iver clock phase errors may be eliminated by forming the difference between simultaneous observations by one GPS receiver to two satellites (see Figure below). The operator indicates a between-satellite difference. The differenced observable can be written as:
where it is assumed that the two observations from receiver j to satellites 1 and 2 have been made at the same time Tj. The new differenced observation is (based on eqn (6.1-13), with the inclusion of an orbit error term ejor that represents the mapping of orbit error along the line-of-sight between receiver and satellite):
Note that the receiver clock phase error has been eliminated and the clock bias terms that remain are the between-satellite clock phase error and the between-satellite cycle ambiguity. As far as setting up the design matrix for a Least Squares adjustment based on between-satellite differences is concerned, there is a choice in the cycle ambiguity modelling. Either use individual ambiguity modelling for nj1 and nj2, or adopt a new definition for the ambiguity parameter consisting of the between-satellite cycle ambiguity kj12 (= nj1 nj2).
Between-satellite differencing eliminates receiver dependent biases.
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© Chris Rizos, SNAP-UNSW, 1999