On GNSS acceptance tests

Abstract

Integer carrier phase ambiguity resolution is the key to fast and high precision global navigation satellite system (GNSS) positioning and application. Apart from integer estimation, also acceptance tests are part of the ambiguity resolution process. A popular acceptance test is the so-called ratio-test. In this contribution we study the properties and the underlying concepts of the ratio-test. We discuss some misconceptions of the ratio-test and in particular show that the ratio-test is not a test for testing the correctness of the integer least-squares solution. We also show that the common usage of the ratio-test with a fixed critical value has shortcomings. Instead, the fixed failure rate approach is recommended. This approach, which is part of the more general theory of integer aperture estimation, has the advantage that the times to first fix are reduced, while it is guaranteed that the failure rate does not exceed a user-defined value. Results of the fixed failure-rate ratio test are illustrated with a number of examples.