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

Abstract

Abstract 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.

Keywords

• adaptive filters
• Kalman filters
• navigation
• nonlinear dynamical systems