A noise estimation algorithm based on modified system model and its application on backtracking

In backtracking, since the priori knowledge on noise statistics is involved in both Forward Kalman Filter (FKF) and Backward Kalman Filter (BKF), the inaccurate parameter will deteriorate the performance more significantly than conventional Kalman Filter (KF). To solve this issue, some scholars have proposed adaptive KF where the noise statistics are determined by the observation sequence real-timely. However, these algorithms are model-based methods, which means the accuracy of estimated noise statistics depends on system model. Inaccurate system model would undermine the performance of noise estimation algorithm, especially for backtracking. The computational errors, which are caused by improper reference frame, would be accumulated with the repeated iteration of FKF and BKF. To avoid the negative effects of inaccurate system model on noise estimation algorithm, a modified system model is proposed with respect to computational frame rather than ideal navigation frame. Simulation and experiments are utilized to illustrate the effectiveness of the modified algorithm.