Explicit formulas for two state Kalman, H/sub 2/ and H/sub /spl infin// target tracking filters

The continuous time, two state, target tracking problem is considered from the Kalman, H/sub 2/, and H/sub /spl infin// filter viewpoint. While previous treatments were numerical in nature, analytic transient responses and infinite horizon solutions with analytic performance expressions are presented here. Tracking indices, involving the maneuver and measurement uncertainties, are shown to have a role for both the steady state and transient responses. In addition, the H/sub /spl infin// tracker has a sensor index involving the performance bound and measurement uncertainty, which, along with the tracking index, plays a significant role in the H/sub /spl infin// tracker expressions. Analytical expressions for the probability of target escape, the probability that the target position will be outside the radar beamwidth (BW), are developed not only to compare the performance of various trackers, but also as a design tool to meet tracking specifications. Examples illustrate the performance of the target trackers as a function of the error gain upper bound.

[1]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[2]  G. Zames,et al.  On H ∞ -optimal sensitivity theory for SISO feedback systems , 1984 .

[3]  Paul Zarchan,et al.  Comparison of Four Filtering Options for a Radar Tracking Problem , 1998 .

[4]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[5]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[6]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[7]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[8]  U. Shaked,et al.  H/sub infinity /-optimal estimation: a tutorial , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[9]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[10]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

[11]  U. Shaked,et al.  Design of linear tracking filters via robust H/sub 2/ optimization , 1996, IEEE Transactions on Aerospace and Electronic Systems.

[12]  G. Zames.  Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[13]  Jeffrey B. Burl,et al.  Linear Optimal Control , 1998 .

[14]  U. Shaked,et al.  H,-OPTIMAL ESTIMATION: A TUTORIAL , 1992 .

[15]  On Kalman, H/sub /spl infin// and H/sub 2/ target tracking: probability of target escape , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[16]  Amir Averbuch,et al.  Interacting Multiple Model Methods in Target Tracking: A Survey , 1988 .

[17]  P. Kalata.  The Tracking Index: A Generalized Parameter for α-β and α-β-γ Target Trackers , 1984, IEEE Transactions on Aerospace and Electronic Systems.

[18]  Uri Shaked,et al.  Game theory approach to finite-time horizon optimal estimation , 1993, IEEE Trans. Autom. Control..

[19]  Samuel S. Blackman,et al.  Design and Analysis of Modern Tracking Systems , 1999 .

[20]  Eric R. Ziegel,et al.  Handbook of Mathematical Sciences , 1989 .

[21]  G. A. Watson,et al.  IMMPDAF for radar management and tracking benchmark with ECM , 1998 .

[22]  G. Zames,et al.  Feedback, minimax sensitivity, and optimal robustness , 1983 .

[23]  Yaakov Bar-Shalom,et al.  Benchmark for radar allocation and tracking in ECM , 1998 .

[24]  Michael J. Grimble.  Robust filter design for uncertain systems defined by both hard and soft bounds , 1996, IEEE Trans. Signal Process..

[25]  G. Zames,et al.  H ∞ -optimal feedback controllers for linear multivariable systems , 1984 .

[26]  Dominick Andrisani,et al.  Design of a robust estimator for target tracking , 1993 .

[27]  Richard A. Brown,et al.  Introduction to random signals and applied kalman filtering (3rd ed , 2012 .

[28]  Paul Kalata,et al.  The Tracking Index for Continuous Target Trackers , 1992, 1992 American Control Conference.

[29]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[30]  Tamer Başar,et al.  H1-Optimal Control and Related Minimax Design Problems , 1995 .