Improved GPS Phase-Ambiguity Resolution by Second-Order Statistical Filtering

Haywood Satz

Abstract:	Resolution of phase-ambiguity in GPS carrier phase measurements was examined for its application in GPS-derived range and attitude determination. Statistical filtering of phase differences, gathered from two GPS antennas over a baseline defined by antenna placements, enabled the observation of ambiguity errors. As those errors converged, the unknown ambiguity integers were resolved, thus determining the baseline orientation relative to the GPS line-of-sight. Both first-order and second-order statistical filtering algorithms were implemented to process GPS phase-differences. Exact measurement sensitivities were approached by truncating the observation-model Taylor expansion, as normally done in nonlinear filtering, and thus contributing an error (due to model truncation) in measurement residuals. For the second-order implementation, quadratic variations of the observation model expansion were added to the update equations in an attempt to reduce that truncation error. Each algorithm was tested with several types of physical models. A model of baseline-phase-differences, contained entirely within a geometric plane, was used for it simplicity and relative ease of computing second variations. A simulation of a spacecraft in low Earth orbit, with 3 GPS antenna/receiver complements, was used to include all details of GPS processing and measurement errors. Second-order filtering showed significant improvement, in estimation convergence and ambiguity resolution, over that attainable with first-order algorithms. Second-order measurement residuals (containing less truncation error) improved the convergence characteristics, and shortened ambiguity resolution intervals. The Appendix outlines the equations needed to implement a second order nonlinear filtering algorithm. Mean and covariance evolution was developed, at measurement transitions, and measurement model nonlinearities and error state probability densities were specified.
Published in:	Proceedings of the 52nd Annual Meeting of The Institute of Navigation (1996) June 19 - 21, 1996 Royal Sonesta Hotel Cambridge, MA
Pages:	779 - 786
Cite this article:	Satz, Haywood, "Improved GPS Phase-Ambiguity Resolution by Second-Order Statistical Filtering," Proceedings of the 52nd Annual Meeting of The Institute of Navigation (1996), Cambridge, MA, June 1996, pp. 779-786.
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