A Controllable Success Fix Rate Threshold Determination Method for GNSS Ambiguity Acceptance Tests

Abstract

Global navigation satellite system (GNSS) integer ambiguity acceptance test is one of the open problems in GNSS data processing. A number of ambiguity acceptance tests have been proposed from different perspectives and then unified into the integer aperture estimation framework. The existing comparative studies indicate that the impact of test statistics form on the test performance is less critical, while how to construct an efficient, practical test threshold is still challenging. Based on the likelihood ratio test theory, a new computationally efficient ambiguity acceptance test with controllable success fix rate, namely the fixed likelihood ratio (FL-) approach is proposed, which does not require Monte Carlo simulation. The study indicates that the fixed failure rate (FF-) approach can only control the overall failure rate of the acceptance region, but the local failure rate is not controllable. The proposed FL-approach only accepts the fixed solution meeting the likelihood ratio requirement. With properly chosen likelihood ratio threshold, the FL-approach achieves comparable success rate as the FF-approach and even lower failure rate than the FF-approach for the strong underlying model cases. The fixed success fix rate of the FL-approach is verified with both simulation data and real GNSS data. The numerical results indicate that the success fix rate of the FL-approach achieves >98% while the failure rate is <1.5%. The real-time kinematic (RTK) positioning with ambiguities tested by the FL-approach achieved 1–2cm horizontal precision and 2–4 cm vertical precision for all tested baselines, which confirms that the FL-approach can serve as a reliable and efficient threshold determination method for the GNSS ambiguity acceptance test problem.

Keywords

• likelihood ratio test
• fixed failure rate approach
• success fix rate
• ambiguity acceptance test
• ambiguity resolution