A Robust Backtracking CKF Based on Krein Space Theory for In-Motion Alignment Process

Abstract

The large misalignment angle errors generated by coarse alignment and the uncertainty time-varying calibration errors generated by the inertial measurement unit reduce the alignment accuracy, increase the alignment time, and ultimately limit the application of backtracking Kalman filters into In-motion fine alignment scene. This paper proposes a robust backtracking cubature Kalman filter (CKF) approach based on Krein space theory to overcome these issues. Specifically, considering the effect of dynamic model uncertainties of the alignment process, a linear robust filter and the existence conditions of optimal estimation are constructed to restrain the uncertainty interference according to Krein space theory. Meanwhile, an adaptive window adjustment algorithm is designed to intelligently determine the backtracking interval in different backtracking filtering stages and cross-scene motion environments, which is founded on the innovation variance gradient detection. Furthermore, using the statistical linearization scheme, the quasi-linear CKF model is derived to assist in resolving the nonlinear large misalignment angle within the Krein linear space framework for In-motion alignment. Experimental verification results from a vehicle In-motion alignment test illustrate that the proposed Krein backtracking CKF approach is effective in improving the alignment accuracy and shortening the alignment time simultaneously.