Investigation of performance improvement in GNSS PPP-RTK ambiguity resolution via Gaussian overbounding for heavy-tailed error modeling

Abstract

Global Navigation Satellite System (GNSS) is essential for many autonomous system applications. Its degradation directly threatens the operational safety. Precise Point Positioning (PPP) based on real-time kinematic (RTK) networks (PPP-RTK) is a popular candidate for providing precise positioning service. This technology needs to resolve integer ambiguities of GNSS carrier phase measurements, which is key to achieving centimeter-level accuracy (also known as a fixed solution). However, there are times when the fixed solution is falsely locked to an incorrect set of integers, leading to errors of several meters. This miss detection can occur even when a rigorous ambiguity resolution (AR) algorithm, such as the least squares ambiguity decorrelation adjustment (LAMBDA) method, is applied. This is sometimes because GNSS measurements often exhibit heavy-tailed error distributions. To address this issue, this paper investigates the use of a Gaussian overbounding method to stochastically model the noise of pseudorange and carrier phase measurements. The Gaussian overbounding method can better describe the tail characteristics of the error distribution, aiming to reduce the miss detection rate of AR and thereby improve positioning performance. A PPP-RTK simulation platform is developed to validate the effectiveness of the Gaussian overbounding method under various degrees of heavy-tailed error distribution scenarios. Through Monte Carlo simulations, we demonstrate that the overbound-based stochastic model can reduce the miss detection rate under heavy-tailed distributions and mitigate the degradation of AR reliability caused by underestimating measurement uncertainty, serving as a confirmation and complement to existing studies. Real experiments demonstrate that the 3D RMSE of the fixed solution decreases by 18.34 % on average.