The Multiple-Hypothesis Wald Sequential Probability Ratio Test for GPS Integer Ambiguity Resolution

Abstract

: An algorithm for resolving the GPS integer ambiguity is introduced. This algorithm is based on a log formulation of the Multiple-Hypothesis Wald Sequential Probability Test (MHWSPT) and is called the Multiple-Hypothesis Wald Sequential Probability Ratio Test (MHWSPRT). Given a set of integer hypotheses, the computational time of the MHWSPT is reduced, and convergence to the correct integer vector is achieved within a given probability in minimal time. The convergence characteristics of the proposed method allow independent testing of the various integer candidates hypothesized and therefore permit eliminating the hypotheses that are proven wrong, with high probability in the sequential processing of obtaining the true integer ambiguity. The proposed method is seen as a generalization of the classic two-hypothesis sequential probability ratio test (THSPRT). The method's relationship to the THSPRT is also derived.