Filter Design for Radar Tracking of Maneuvering Targets

Although the Kalman filter has been widely applied to target tracking applications since its introduction in the early 1960s, until recently, no systematic design methodology was available to predict tracking performance for maneuvering targets and optimize filter parameter selection. When tracking maneuvering targets with a Kalman filter, the selection of the process noise (e.g., acceleration errors) variance is complicated by the fact that the motion modeling errors are represented as white Gaussian, while target maneuvers are deterministic or highly correlated in time. In recent years, relationships between the maximum acceleration of the target and the variance of the process noise errors were developed to minimize the maximum mean squared error (MaxMSE) in position for multiple filter types. Lower bounds on the variance of the motion modeling errors were also expressed in terms of the maximum acceleration. This tutorial presents rigorous procedures for selecting the optimal process noise variance for radar tracking filters based on the properties of the sensor and target motion model. Design methods are presented for the nearly constant velocity (NCV) Kalman filter with discrete white noise acceleration (DWNA), continuous white noise acceleration (CWNA), or exponentially-correlated acceleration errors (ECAE), the nearly constant acceleration (NCA) Kalman filter with Discrete Wiener Process Acceleration (DWPA), and the Interacting Multiple Model (IMM) estimators. Filter design for tracking maneuvering targets with linear frequency modulated (LFM) waveforms is also addressed and tracking with LFM waveforms is shown to be significantly better than tracking with a monotone waveform. Guidelines on the inclusion of acceleration in your track filter are provided. In other words, guidelines on the use of an NCV Kalman filter versus an NCA Kalman filter are given along with guidelines on the inclusion of the NCA model in the IMM estimator. Numerous radar tracking examples are used to illustrate the validity of the design methods. The benefit of tracking with LFM waveforms for mode estimation in the IMM estimator is also demonstrated via simulation examples.