Adaptive Kalman filtering based on optimal autoregressive predictive model

Conventional Kalman filter (KF) relies heavily on a priori knowledge of the potentially unstable process and measurement noise statistics. Insufficiently known a priori filter statistics will reduce the precision of the estimated states or introduce biases to the estimates. We propose an adaptive KF based on the autoregressive (AR) predictive model for vehicle navigation. First, the AR model is incorporated into the KF for state estimation. The closed-form solution of the AR model coefficients is obtained by solving a convex quadratic programming problem, which is according to the criterion of minimizing the mean-square error, and subject to the polynomial constraint of vehicle motion. Then, an innovation-based adaptive approach is improved based on the KF with the AR predictive model. In the proposed adaptive algorithm, the process noise covariance is computed using the real-time information of the innovation sequence. Simulation results demonstrate that the KF with the AR model has a higher estimated precision than the KF with the traditional discrete-time differential model under the condition of the same parameter setting. Field tests show that the positioning accuracy of the proposed adaptive algorithm is superior to the conventional adaptive KF.