Double‐state chi‐square test based sparse grid quadrature filtering algorithm and its application in integrated navigation

• Published in: IET control theory & applications Vol. 17; no. 9; pp. 1203 - 1213
• Main Authors: WU, Yifei, Ma, Yinrui, Jiang, Ye
• Format: Journal Article
• Language: English
• Published: Stevenage John Wiley & Sons, Inc 01.06.2023; Wiley
• Subjects: Accuracy; adaptive filters; Algorithms; Approximation; Chi-square test; Discrete time systems; Error analysis; Filtration; Flight tests; Global navigation satellite system; Inertial navigation; Kalman filters; navigation; Navigation systems; Noise measurement; nonlinear dynamical systems; Nonlinear systems; Quadratures; Signal processing; Sin; Uncertainty
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/cth2.12450

Aiming to reduce the impact that the measurement uncertainty of nonlinear system brings to filtering accuracy, a novel sparse grid quadrature filter (SGQF) algorithm based on the double‐state chi‐square test is proposed. And the strap‐down inertial navigation system (SINS)/global navigation satellite system (GNSS) integrated navigation system is used to verify the algorithm. A discrete‐time system model with uncertain measurement is constructed, then the system state through the SGQF algorithm is estimated. To determine the uncertainty of the measurement, the double‐state chi‐square test is introduced. By comparing the results of the state recursor, the chi‐square test value is obtained and it is used to update the measurement noise. Further, the system state and error covariance are re‐estimated. So far a robust sparse grid filter algorithm with statistical adjustment of the measurement noise is obtained. The proposed algorithm can overcome the influence of error statistical characteristic amplification on system filtering accuracy. Taking the SINS/GNSS integrated navigation system as the application object, off‐line simulation experiments and online flight tests verify the robustness of the proposed algorithm. A fault‐tolerant nonlinear filtering algorithm is designed and applied to the long‐time integrated navgation. Aiming at the problem that the single‐state recursion cannot run for a long time, an improved sparse grid quadrature filter based on the double‐state chi‐square test is proposed, and two state recursions are designed to be used interactively.