Improved Kalman filter design for three-dimensional radar tracking

The problem of three-dimensional (3D) radar tracking is considered. The usual tracking filter design relying on first-order (or linear) approximations leads to poor convergence and erratic filter behavior in highly nonlinear situations. Simple filter algorithms that can overcome these ill effects are developed for two different types of 3D radar measurement. For each type of radar measurement, an accurate expression for the measurement covariance is obtained by evaluating inherent nonlinearities of radar measurements via coordinate transformation. Then algebraic manipulations and reasonable approximations are employed to yield a simple filter formulation based on the expression. The resulting filter equations are similar to the extended Kalman filter (EKF) and provide some useful insights into the behavior of linearized Kalman filters designed with radar measurements. Finally, simulation results show that the proposed approach is very effective in accounting for the measurement nonlinearities.