On the Reliability of Integer Ambiguity Resolution

S. Verhagen

Peer Reviewed

Abstract: Global Navigation Satellite System (GNSS) carrier-phase observations are ambiguous by an unknown, integer number of cycles. These integer ambiguity parameters need to be resolved before carrier-phase observations can begin to serve as very precise pseudorange measurements. Optimal estimation of the integer ambiguities involves a complex mapping of real-valued least-squares estimates to integers, and should be applied only when one can have enough confidence in the integer solution. Therefore, it is important to have measures available that provide information on the reliability of ambiguity resolution. The success rate is a very important measure for determining whether an attempt to fix the ambiguities should be made. Only when the success rate is very close to 1 can the integer ambiguities be considered deterministic. In this paper, lower and upper bounds of the integer least-squares success rate are evaluated, since exact computation is not possible. Furthermore, the discrimination tests commonly used to validate the actual integer solution are evaluated, and the pitfalls inherent in these tests are discussed. Also, a theoretically sound, overall approach to the problem of integer estimation and validation is outlined.
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 52, Number 2
Pages: 99 - 110
Cite this article: Verhagen, S., "On the Reliability of Integer Ambiguity Resolution", NAVIGATION, Journal of The Institute of Navigation, Vol. 52, No. 2, Summer 2005, pp. 99-110.
https://doi.org/10.1002/j.2161-4296.2005.tb01736.x
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