THE ROLES & MERITS OF VARIOUS PHASE OBSERVABLES IN GPS ADJUSTMENTS |
The "undifferenced" approach to GPS phase adjustment is identical to using single-, double- or triple-differences only if the mathematical correlations introduced during the differencing operation are included in the VCV matrix and any explicitly modelled clock biases are assumed to be offsets (on an epoch-by-epoch basis in the case of the clock phase errors, and on a session-by-session basis for the cycle ambiguity parameters). Often, however, these conditions for exact equivalence are not met. Nevertheless the various differenced observables do have their role to play.
The between-satellite and between-station differences, for example, are useful for cycle slip editing, while triple-differences are often used to obtain preliminary site coordinate solutions because of their relative insensitivity to cycle slips in the phase data (this arises because the mathematical correlations are ignored!). On the other hand, it is the double-differenced observable that is most commonly used in precise GPS phase adjustment. However, a solution based on double-differenced data is relatively intolerant of cycle slips. Furthermore, the mathematical correlations are generally neglected, and hence the results are not strictly equivalent to using the "undifferenced" approach, but they are nevertheless suitable for most survey applications requiring relative accuracies of a few parts per million (BEUTLER et al, 1987).
The impact of cycle slips on the various differenced observables is illustrated in the Table below. A cycle slip is assumed to have occurred at receiver j while observing satellite i between epochs e-1 and e. All double-differences starting with epoch e are offset by the same amount s, while only one triple-difference is affected by the cycle slip. Another thing to note is that it is not possible to identify which of the four one-way observations contains the original cycle slip, only that a cycle slip has occurred and is noticeable in the double-differenced data from epoch e onwards.
One-way Phase
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Double- Difference |
Triple- Difference | ||||||||||||||||||||||||||||||
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© Chris Rizos, SNAP-UNSW, 1999
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