A Novel Enhancement to Kalman Filter: When Kalman Meets Cramér and Rao

This paper revisits the classic problem of state estimation and tracking of a dynamic nonlinear system from the perspective of sequential minimum mean squared error (MMSE) and maximum
a posteriori
(MAP) estimation. We propose a new method, which condenses all the existing measurements into a MAP estimate of the current state of the system, and calculates the Cramér-Rao Bound (CRB) to gauge the reliability of the estimate. This method, termed as the CRB-Kalman filter (CRB-KF), can deal with nonlinearity better than the widely-used extended Kalman filter (EKF) and is computation-wise much more efficient than the particle filter (PF). We then apply the CRB-KF to the localization and tracking of a vehicle aided by some roadside base-stations, which would be important for the emerging application of autonomous driving. Simulation results show that the proposed method, where Cramér and Rao meet with Kalman, can significantly outperform the state-of-the-art methods, including the EKF, the cubature KF and the PF.