PROCESSING OF DIFFERENCED DATA |
There
are a number of comments that can be made with regards to the
various
differenced phase data solutions:
GPS phase data
processing sequence.
The following are some characteristics
of triple-difference solutions:
The triple-differences solution algorithm :Difference epoch data between-satellites, form double-differences. Difference double-differences between epochs at some sample rate (for example, every 5th observation epoch), form triple-differences. Assume all triple-difference observations are independent when forming Weight Matrix (no correlations taken into account), define P matrix. Form Observation Equations, construct the A matrix. Accumulate Normal Equations, scaled by the Weight Matrix A^{T}PA. At end of data set, invert Normal Matrix and obtain geodetic parameter solution, = (A^{T}PA)^{-1}.A^{T}P . Update parameters. Optionally scan triple-difference residuals for cycle slips in double-difference observables. |
The following are some
characteristics of double-differenced phase
(ambiguity-free)
solutions:
The double-difference solution algorithm:Difference epoch data between-satellites, form double-differences. Apply data reductions, such as a troposphere bias model. Construct Weight Matrix (depending on whether correlations are to be taken into account), define the P matrix. Form Observation Equations --> construct the A matrix. Accumulate Normal Equations, scaled by the Weight Matrix A^{T}PA. At end of session, invert Normal Matrix and obtain geodetic and ambiguity parameter solution, = (A^{T}PA)^{-1}.A^{T}P . Update parameters. Decide (a) iterate solution, or (b) iterate solution only after ambiguity resolution attempted. |
The following are some
characteristics of double-differenced phase
(ambiguity-fixed)
solutions:
The ambiguity-fixed solution algorithm:Difference epoch data between-satellites, form double-differences as before but without ambiguities as solve-for parameters. Apply data reductions, such as a troposphere bias model. Construct Weight Matrix (depending on whether correlations are to be taken into account), define the P matrix. Form Observation Equations, construct the A matrix. Accumulate Normal Equations, scaled by the Weight Matrix A^{T}PA. At end of session, invert Normal Matrix and obtain geodetic parameter solution, = (A^{T}PA)^{-1}.A^{T}P . Update parameters. This process can be iterated to resolve other ambiguities until (a) all have been resolved (and "fixed" to integers), or (b) no more can be reliably resolved. |
Once ambiguities have been resolved, the ambiguous phase measurements are converted to precise range observations. As in conventional GPS navigation, single epoch positioning is now possible and hence "carrier-range" observations are ideal for kinematic positioning applications.
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© Chris Rizos, SNAP-UNSW, 1999