The GNSS ambiguity ratio-test revisited: a better way of using it

TLDR

Integer carrier‑phase ambiguity resolution underpins fast, high‑precision GNSS positioning, and the ratio‑test is a widely used acceptance test in this process. The study investigates the properties and underlying concepts of the GNSS ratio‑test. The authors propose a fixed failure‑rate ratio‑test within the integer aperture estimation framework, demonstrating its improved performance through illustrative examples. They show that the ratio‑test does not verify integer least‑squares solutions, that using a fixed critical value is problematic, and recommend a fixed failure‑rate approach that yields better performance.

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 is part of the more general theory of integer aperture estimation, and enables that the failure rate does not exceed a user-defined value. Results of the fixed failure-rate ratio-test and its improved performance are illustrated with a number of examples.