Aircraft trajectory filtering method based on Gaussian‐sum and maximum correntropy square‐root cubature Kalman filter

Abstract

Aiming at meetiing the need to filtering flight trajectory data for aircraft testing, a novel adaptive cubature Kalman filter (CKF) is proposed based on the maximum correntropy and Gaussian-sum in this paper. Firstly, based on the traditional CKF algorithm, we introduced a Gaussian-sum method to approximate non-Gaussian noise to get more accurate filtering results in view of the problem of reduced filtering accuracy caused by the inherent non-Gaussian nature of the noise and the system non-linearity. Secondly, the maximum correntropy criterion is introduced to solve further the problem of improving the filtering accuracy of the system in the case of non-linearity. Simulation results and actual data verification showed that the Square-root cubature Kalman filter algorithm based on the maximum correntropy and Gaussian-sum has higher accuracy than traditional filtering algorithms, which verified the algorithm's effectiveness in the application.

An Improved Gaussian Sum Extended Kalman Filter With Colored Noise for GNSS/SINS Tightly Coupled Positioning and Attitude Determination Systems

“…This approach may result in overly conservative covariance estimates for filtering estimation [39]. Consequently, the above studies are incapable of effectively addressing the more common problem of non-Gaussian colored noise in GNSS/SINS tightly coupled positioning and attitude determination systems data processing [40], [41].…”

A novel Gaussian sum quaternion constrained cubature Kalman filter algorithm for GNSS/SINS integrated attitude determination and positioning system

“…In recent years, the filter random model has been optimized by GMM, which has gradually been recognized as a superior approach, attracting attention in target tracking, speech recognition, signal analysis, navigation integrity monitoring, and other aspects ( Sun et al, 2020 ; Zickert and Yarman, 2021 ; Zhu et al, 2022 ; Yu et al, 2023 ). The literature sequentially delves into the nonlinear optimization problem associated with the Gaussian sum filter (GSF) algorithm grounded in GMM, such as the Gaussian sum extended Kalman filter (GSEKF) algorithm, Gaussian sum unscented Kalman filter (GSUKF) algorithm, Gaussian sum quadrature Kalman Filter (GSQKF) algorithm, and Gaussian sum cubature Kalman filter (GSCKF) algorithm, and these studies have to some extent optimized the integrated navigation information fusion algorithm ( Wang and Cheng, 2015 ; Qian et al, 2021 ; Wang et al, 2021 ; Bai et al, 2022 ). While numerous algorithms have been put forward to optimize the random model of nonlinear filter algorithms under non-Gaussian noise conditions based on GMM, there are limited reports on research on quaternion-based algorithm in GNSS/SINS-IADPS data processing for UAVs.…”