A New Method of Instantaneous Ambiguity Resolution

Don Knight

Abstract:	The objective of the work reported here was to develop a method of ambiguity resolution that is fast and robust in the face of the signal reception environment of commer- cially-viable attitude determination systems. The method achieved is fully optimum. If there are a trillion integer combinations, the method finds the single most likely combination out of all trillion, and makes it possible to prove that this has actually occurred. The method avoids double differencing. With short antenna separations, it can withstand phase measurement errors up to 40” RMS. With the more typical interferometry measurement accu- racy of 10” RMS, with antenna cable drifts of 5” RMS, with 4 satellites in track, and with 4 antennas on the cor- ners of a 2-meter square, the method produces attitude solutions on 99.3% of update cycles,’ with an average computation time of 0.24 seconds on a 486 PC, and with an RMS azimuth solution accuracy of 0.07’. The method is the basis of instantaneous ambiguity resolution in one operating regime2 of Trimble’s new Vector Attitude Determination System. Performance results being ob- tained with Trimble’s equipment are summarized. The significance of this work is in developing a general, op- timal solution for resolving carrier cycle ambiguities in a wide range of applications. The attitude determination problem is formulated as a maximum-likelihood optimization, in which vehicle attitude and the carrier cycle integers are regarded as parameters to be adjusted to maximize the probability of interferometric measurements obtained by GPS receiving hardware. The formulation results in weighted-fit-error W as the objective criterion to minimize. A Kalman filter is introduced, having the same objective criterion. Minimizing computation in the Kalman filter leads to a decision tree for the integers. Two ways are shown to prune the tree. The first is to exclude impossible combi- nations, and the second is to generate a lower bound for W at each branch of the tree. A running sum is kept at each stage moving down the tree. When that sum ex- ceeds the current best W found elsewhere in the search, it is guaranteed that all subsequent integer combinations further down the current branch will produce an even larger W, and cannot be optimum. The remainder of the current branch is then cut off, speeding up the search.
Published in:	Proceedings of the 7th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1994) September 20 - 23, 1994 Salt Palace Convention Center Salt Lake City, UT
Pages:	707 - 716
Cite this article:	Knight, Don, "A New Method of Instantaneous Ambiguity Resolution," Proceedings of the 7th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1994), Salt Lake City, UT, September 1994, pp. 707-716.
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