A linear Kalman filter-based integrity monitoring considering colored measurement noise

Abstract

Apart from positioning accuracy, the reliability of a navigation system is also significant, especially for safety-critical applications, such as intelligent vehicle navigation. Generally, the Global Navigation Satellite System (GNSS) positioning algorithm assumed that measurement noise is uncorrelated white noise. However, the appearance of colored noise, which comes from various noise sources, does not follow the Gaussian white noise assumption in the Kalman filter and would degrade both the accuracy and reliability of positioning. To deal with this problem, we propose a linear Kalman filter-based integrity monitoring method, which is based on a linear colored Kalman filter (CKF) considering measurement time correlation colored noise by a first-order Gauss-Markov model. Both simulated and real dynamic experiments were conducted to test the proposed algorithm. The results proved that CKF is capable of modeling time correlation with a realistic filter covariance in both simulated static and in-field dynamic tests. Furthermore, the performance of an integrity monitoring system with a protection level based on the CKF has proved to be more feasible and effective to bound position errors. Besides, the simulated results demonstrate that it can typically reduce false alarm by 24.81% in the horizontal direction and 39.47% in the vertical direction in a simulated experiment. The dynamic test shows that the proposed method can reduce the false alarm rate by 22.11% and 15.62% in the horizontal and vertical directions, respectively.

A modified between‐receiver single‐difference‐based fault detection and exclusion algorithm for real‐time kinematic positioning

“…After that, according to the DD technique of RTK positioning, most error sources in undifferenced observations would be reduced or mitigated in short baseline tests [22, 23]. Then, the DD observation formulations are expressed as follows: $$${P}_{A,B,f}^{i,j}={\rho }_{A,B}^{i,j}+{{\epsilon}}_{A,B,f,P}^{i,j}$$$ $$${{\Phi}}_{A,B,f}^{i,j}={\rho }_{A,B}^{i,j}+{\lambda }_{f}{N}_{A,B,f}^{i,j}+{{\epsilon}}_{A,B,f,{\Phi}}^{i,j}$$$ where $${\rho }_{A,B}^{i,j}$$ represents the DD geometric distance; $${N}_{A,B,f}^{i,j}$$ signifies the DD ambiguity, and $${{\epsilon}}_{A,B,f,P}^{i,j},\,$$ and $${{\epsilon}}_{A,B,f,{\Phi}}^{i,j}$$ denote the code and the carrier phase measurement noise, respectively.…”

“…After that, according to the DD technique of RTK positioning, most error sources in undifferenced observations would be reduced or mitigated in short baseline tests [22, 23]. Then, the DD observation formulations are expressed as follows: where represents the DD geometric distance; signifies the DD ambiguity, and and denote the code and the carrier phase measurement noise, respectively.…”

“…After that, according to the DD technique of RTK positioning, most error sources in undifferenced observations would be reduced or mitigated in short baseline tests [22,23]. Then, the DD observation formulations are expressed as follows:…”

Integrity monitoring scheme for single-epoch GNSS PPP-RTK positioning

“…In this study, the risks of incorrect ambiguity fixing are considered as ignorable. While this assumption is widely used in existing studies (Jokinen et al, 2013a;Jokinen et al, 2013b;Feng et al, 2014;Wang et al, 2020;Wang et al 2022;Gao et al, 2021), the effects of wrong ambiguity fixing on the protection level computations are analyzed in Sect. "Effects of fault probabilities on protection level computations".…”

Adaptive Kalman filter based on integer ambiguity validation in moving base RTK

“…A Gaussian sum filter was proposed based on a Gaussian mixed model, which provides a more conservative PL and minimum detectable bias (MDB) for an integrity monitoring system (Yun et al 2008). Other methods mainly consider a stochastic noise model, which can provide a real-time protection level for integrity monitoring by adjusting the observation weight according to the satellite elevation and signal-to-noise ratio to reduce the influence of colored noise (Gao et al 2021). However, in the case of high-precision dynamic positioning, these methods do not consider the impact of the correct fixed carrier phase ambiguity on the positioning error and integrity monitoring performance.…”