BETWEEN-STATION DIFFERENCING |
The satellite clock phase errors may be (almost) eliminated by forming the
difference between observations by two GPS receivers to one satellite, at
the same time (see Figure below). The operator 
indicates a between-station
difference, also sometimes referred to confusingly as a single-difference.
Although the nominal observation or reception times of the two measurements
may be the same, the actual time of measurement may differ between one receiver
and another because of receiver time-tag errors. The differenced
observation can be constructed from:
 |
(6.3-3) |
where t is the nominal receiver clock time, and Tj is the true time-of-reception of the signal at receiver i.
Using eqn (6.1-13), the between-station difference involving receivers 1 and 2 is:
 |
(6.3-4) |
The satellite clock phase errors may not completely cancel because they refer to different transmission times. The transit times of the satellite signals are not equal because of the different satellite - receiver ranges, and this difference may be up to 1 millisecond for a 300km baseline. However, as the satellites use stable atomic oscillators, it is usual to assume that the satellite clock phase errors are identical and thus cancel when the between-station difference is formed (RIZOS & GRANT, 1990):
 |
(6.3-5) |
Note that the clock bias terms that remain are the between-station clock phase errors and the between-station cycle ambiguity. (The influence of the orbit error terms e1ori and e2ori for satellite i is such that they have approximately equal magnitude, and will therefore cancel in between-receiver differencing; though this assumption starts to break down with increasing receiver separation.) As in the case of the between-satellite difference, it is possible to either use individual ambiguity modelling for n1i and n2i, or to adopt a new definition for the ambiguity parameter consisting of the between-station cycle ambiguity k12i (= n1i – n2i).
Between-station differencing to eliminate or reduce satellite dependent
biases.
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© Chris Rizos, SNAP-UNSW, 1999