Mid-State Kalman Filter for Nonlinear Problems

When tracking very long-range targets, wide-band radars capable of measuring targets with high precision at ranges have severe measurement nonlinearities. The existing nonlinear filtering technology, such as the extended Kalman filter and untracked Kalman filter, will have significant consistency problems and loss in tracking accuracy. A novel mid-state Kalman filter is proposed to avoid loss and preserve the filtering consistency. The observed state and its first-order state derivative are selected as the mid-state vector. The update process is transformed into the measurement space to ensure the Gaussian measurement distribution and the linearization of the measurement equation. In order to verify the filter performance in comparison, an iterative formulation of Cramér-Rao Low Bound for the nonlinear system is further derived and given in this paper. Simulation results show that the proposed method has excellent performance of high filtering accuracy and fast convergence by comparing the filter state estimation accuracy and consistency.