Nonlinear Kalman Filter Using Cramer Rao Bound

TL;DR

This paper introduces a nonlinear Kalman filter that estimates both the state and the Cramer-Rao bound to improve accuracy in dynamic systems with nonlinear transfer functions and arbitrary noise distributions.

Contribution

It presents a novel algorithm that jointly estimates the state and the CRB, enhancing accuracy over traditional filters like EKF and PF.

Findings

Achieves more accurate state estimation than EKF and PF.

Effectively estimates vehicle position and velocity in autonomous driving scenarios.

Demonstrates robustness with arbitrary noise distributions.

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.