Integer ambiguity validation in high accuracy GNSS positioning

Abstract

Carrier phase observations are required for high-accuracy positioning with Global Navigation Satellite Systems. This requires that the correct number of whole carrier cycles in each observation (integer ambiguity) is determined. The existing methods have been shown to perform differently depending on the observables. Subsequently, the ratio test used for ambiguity validation was developed further including combining it with the integer aperture concept. The key challenges in using the ratio test are the existence of biases in float solutions and stochastic dependence between the two elements of the ratio. The current methods either make assumptions of independence and nonexistence of biases or use simulations together with the bias-free assumption. We propose a new method taking into account both challenges which result in an unknown distribution of the ratio test statistic. A doubly non-central F distribution (DNCF) is proposed for the determination of threshold. The cumulative distribution function (CDF) of DNCF over-bounds the CDF of ratio test statistic distribution in case there is a bias in the float solution and a correlation between the two elements of the ratio. The Precise Point Positioning (PPP) method with products from CNES and measurement data from 10 NOAA stations are used to verify the proposed method. The test results show that the proposed method improves the performance of ambiguity resolution achieving a lower rate of wrong fixing than current state of the art.