Initialization of SINS/GNSS Error Covariance Matrix Based on Error States Correlation

Abstract

The traditional Strapdown Inertial Navigation System (SINS)/Global Navigation Satellite System (GNSS) integrated system uses standard Kalman Filter (KF) to estimate the error states, which weakens the correlation between the different error components to directly initialed the Error Covariance Matrix (ECM) into diagonalization. This initialed method is also widely applied in State Transformation Extended Kalman Filter (STEKF) and Invariant Extended Kalman Filter (IEKF), which results in state estimation failing to achieve the optimal performance. To solve this problem, this paper first analyses the transformed relationship from traditional linear error state to the nonlinear error state redefined in STEKF and IEKF, and the strong correlation is found between the redefined error state components, namely the ECM in STEKF or IEKF no longer appears as a diagonal matrix. Then, aiming at the nonlinear error states, the transformed models of ECM in STEKF and IEKF are derived respectively, which establishes the theoretical basis for ECM initialization based on the error states correlation. Finally, the accuracy, feasibility and general applicability of the proposed method are verified by a boat-mounted field trial.

Keywords

• Correlation
• error covariance matrix
• IEKF
• SINS/GNSS
• STEKF