Filter Design for Steady-State Tracking of Maneuvering Targets with LFM Waveforms

The equation for the Kalman filter assumes that the model or process noise is white Gaussian. However, for maneuvering targets, the acceleration changes in a deterministic manner, and hence, the process noise is non-white. Therefore, while tracking maneuvering targets, the Kalman filter develops a bias (lag) in its estimates and the state covariance does not accurately represent the error. This paper derives expressions for the sensor noise only (SNO) covariance matrix and the position and velocity lag parameters due to maneuvers, which are used to perform an RMSE analysis for tracking with LFM waveforms. In doing so, the concept of the deterministic tracking index and its relation to the typical tracking index for random maneuvers is introduced. Using these relations, the paper also proposes a method to calculate the optimal process noise variance to be used in the Kalman filter for a given deterministic tracking index.