An Improved Multiple-Outlier Robust Filter Based on Maximum Correntropy Criterion for Integrated Navigation
Zengke Li, Wangqi Chen, Yaowen Sun, Zhaobing Chen
Abstract
In the integrated navigation of Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS), the Kalman filter is frequently employed for state estimation. GNSS signals are subjected to interference from the outside environment, and it is difficult for the classical Kalman filter to handle observations with outliers. Numerous robust filters have been proposed based on the maximum correntropy criterion (MCC), which is insensitive to non-Gaussian noise, to address the issue of state estimation in the presence of outliers. However, a fixed prior covariance will restrict the use of a maximum correntropy criterion Kalman filter (MCKF) in integrated navigation systems because GNSS signals can be affected by both time-varying noise and outliers. Existing filters consider the prior measurement noise covariance matrix (MNCM) as a deterministic matrix and can only amplify signals unidirectionally during iteration cycles. The weight of effective observations is reduced despite these filters having strong robustness. To overcome this shortcoming, this article proposes a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> -based MCKF ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> -MCKF). A strategy based on the chi-square test is designed to optimize the covariance of GNSS observations. By introducing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> to bidirectionally adjust the initial MNCM, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> -MCKF makes full use of effective observations. Then, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> -corrected MNCM is used to weigh different elements of the innovation vector, and a robust estimation is calculated based on the multiple-outlier robust Kalman filter (MORKF) framework. The GNSS/INS integrated navigation system is taken as an example to verify the effectiveness of the filter through simulation and vehicular experiments.