Performance of the NCV Kalman Filter with ECAE for Tracking Maneuvering Targets

When tracking maneuvering targets with a nearly constant velocity (NCV) Kalman filter, the selection of the process noise variance is complicated by the fact that the process errors are modeled as white Gaussian, while target maneuvers are deterministic or highly correlated in time. Due to this model mismatch, the NCV Kalman filter is a biased estimator for an accelerating target. In recent years, the deterministic tracking index was introduced and used to develop a relationship between the maximum acceleration of the target and the process noise variance that minimizes the maximum mean squared error (MMSE) in position. A lower bound on the process noise variance was also expressed in terms of the maximum acceleration and deterministic tracking index. In this paper, the NCV model Kalman filter with exponentially-correlated acceleration errors (ECAE) is studied. While the model mismatch of the NCV Kalman filter with ECAE is less than that for the NCV Kalman filter with white noise errors for a constant acceleration target, it is a biased estimator. Expressions for the MMSE of an NCV Kalman filter with ECAE tracking a constant acceleration target are developed and those expressions are verified via Monte Carlo simulations.

[1]  T. R. Rice,et al.  A Two-Stage Filter for State Estimation in the Presence of Dynamical Stochastic Bias , 1992, 1992 American Control Conference.

[2]  W. Blair,et al.  Note on Sensor Resource Allocations: Higher Rate or Better Measurements? , 2019, 2019 IEEE Aerospace Conference.

[3]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[4]  W.D. Blair,et al.  Tracking maneuvering targets with multiple sensors: does more data always mean better estimates? , 1996, IEEE Transactions on Aerospace and Electronic Systems.

[5]  William Dale Blair,et al.  Steady-state tracking with LFM waveforms , 2000, IEEE Trans. Aerosp. Electron. Syst..

[6]  William Dale Blair,et al.  Design of nearly constant velocity track filters for tracking maneuvering targets , 2008, 2008 11th International Conference on Information Fusion.

[7]  B. Friedland.  Treatment of bias in recursive filtering , 1969 .

[8]  V. Jain,et al.  Filter Design for Steady-State Tracking of Maneuvering Targets with LFM Waveforms , 2007, 2007 Thirty-Ninth Southeastern Symposium on System Theory.

[9]  W. D. Blair,et al.  NCV Filter Design for Radar Tracking of Maneuvering Targets with LFM Waveforms , 2019, 2019 IEEE Radar Conference (RadarConf).

[10]  Robert J. Fitzgerald,et al.  Effects of Range-Doppler Coupling on Chirp Radar Tracking Accuracy , 1974, IEEE Transactions on Aerospace and Electronic Systems.

[11]  T. R. Rice,et al.  On the optimality of two-stage state estimation in the presence of random bias , 1993, IEEE Trans. Autom. Control..

[12]  Robert Fitzgerald,et al.  Simple Tracking Filters: Closed-Form Solutions , 1981, IEEE Transactions on Aerospace and Electronic Systems.

[13]  W. Blair.  Design of nearly constant velocity filters for radar tracking of maneuvering targets , 2012, 2012 IEEE Radar Conference.

[14]  Ali T. Alouani,et al.  Two-stage Kalman estimator for tracking maneuvering targets , 1991, Conference Proceedings 1991 IEEE International Conference on Systems, Man, and Cybernetics.

[15]  William Dale Blair,et al.  Fixed-gain two-stage estimators for tracking maneuvering targets , 1993 .

[16]  Ali T. Alouani,et al.  A two-stage Kalman estimator for state estimation in the presence of random bias and for tracking maneuvering targets , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.