Nonlinear Kalman Filter Using Cramer Rao Bound

Abstract: This paper studies the optimal state estimation for a dynamic system, whose transfer function can be nonlinear and the input noise can be of arbitrary distribution. Our algorithm differs from the conventional extended Kalman filter (EKF) and the particle filter (PF) in that it estimates not only the state vector but also the Cramer-Rao bound (CRB), which serves as an accuracy indicator. Combining the state estimation, the CRB, and the incoming new measurement, the algorithm updates the state estimation according to the maximum likelihood (ML) criterion. To illustrate the effectiveness of the proposed method for autonomous driving, we apply it to estimate the position and velocity of a vehicle based on the noisy measurements of distance and Doppler offset. Simulation results show that the proposed algorithm can achieve estimation significantly more accurate than the standard EKF and the PF.