A Geometric Approach to Integer Ambiguity Validation

Takafumi Nagano, Shoji Yoshikawa, Takashi Iwamoto and Katsuhiko Yamada

Abstract:	Satellite navigation systems have been offering a large variety of applications for positioning and navigation. For precise positioning, the carrier phase measurements give us more precise information than the pseudo-range measurements. However, the unknown integer cycle ambiguities of the carrier phase measurements must be determined. The integer ambiguities are usually resolved using integer least-squares techniques. The resolved integer ambiguities are then validated, because the resolved integer ambiguities are not necessarily the correct ambiguities. There are various ambiguity validation procedures based on several statistical assumptions. One of the most popular tests is the ratio test which discriminates between the best solution and the second-best solution. The test statistic of the ratio test is the ratio of the least squares residuals of the second-best solution to the best solution. The ratio test is considered as a useful validation procedure and is commonly used, although the ratio test has a problem in the statistical assumption. It is worthy to note here that the ratio test has a drawback in that it is insensitive to the magnitude of the covariances for a float solution. If a fixed threshold for the ratio is used, the ratio test is likely to accept incorrect integer ambiguities in some cases where the magnitude of the covariances for a float solution is large. There is another problem in previous ambiguity validation procedures. Ambiguity validation procedures should give consideration to cases where a float solution has bias errors especially in decimal fractions caused by various error sources, such as atmospheric biases and multipath. From the above mentioned points of view, we propose a new integer ambiguity validation procedure which introduces the concept of a margin. The difference between the ratio test and the proposed one will be discussed and the numerical results will be shown.
Published in:	Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005) September 13 - 16, 2005 Long Beach Convention Center Long Beach, CA
Pages:	88 - 93
Cite this article:	Nagano, Takafumi, Yoshikawa, Shoji, Iwamoto, Takashi, Yamada, Katsuhiko, "A Geometric Approach to Integer Ambiguity Validation," Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, CA, September 2005, pp. 88-93.
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