Cramér–Rao lower bound for tracking multiple targets

The derivation and computation of the theoretical Crame/spl acute/r-Rao lower bounds for multiple target tracking has traditionally been considered to be a notoriously difficult problem. The authors present a simple and exact solution based on the assumption that raw sensor data (before thresholding) are available. The multi-target tracking problem can then be formulated as recursive Bayesian track-before-detect estimation. The advantage of this formulation is that it is identical to nonlinear filtering, for which the exact posterior Crame/spl acute/r-Rao bound is already known. The paper presents several numerical examples in support of the theoretical findings.

[1]  Petr Tichavský,et al.  Filtering, predictive, and smoothing Cramér-Rao bounds for discrete-time nonlinear dynamic systems , 2001, Autom..

[2]  Lawrence D. Stone,et al.  Bayesian Multiple Target Tracking , 1999 .

[3]  Branko Ristic,et al.  Cramer-Rao bound for nonlinear filtering with Pd<1 and its application to target tracking , 2002, IEEE Trans. Signal Process..

[4]  Carlos H. Muravchik,et al.  Posterior Cramer-Rao bounds for discrete-time nonlinear filtering , 1998, IEEE Trans. Signal Process..

[5]  D. J. Salmond,et al.  A particle filter for track-before-detect , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[6]  Branko Ristic,et al.  Performance bounds and comparison of nonlinear filters for tracking a ballistic object on re-entry , 2003 .

[7]  F. Daum.  Bounds on performance for multiple target tracking , 1990 .

[8]  Edward W. Kamen,et al.  Multiple target tracking using products of position measurements , 1993 .

[9]  Yaakov Bar-Shalom,et al.  Track formation with bearing and frequency measurements in clutter , 1990 .

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

[11]  T. Kerr.  Status of CR-like lower bounds for nonlinear filtering , 1989 .

[12]  S. M. Tonissen,et al.  Maximum likelihood track-before-detect with fluctuating target amplitude , 1998 .

[13]  Branko Ristic,et al.  Bearings-Only Tracking of Manoeuvring Targets Using Particle Filters , 2004, EURASIP J. Adv. Signal Process..

[14]  H. Gauvrit,et al.  Approximations of the Cramer-Rao bound for multiple-target motion analysis , 2000 .

[15]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[16]  Leonid I. Perlovsky,et al.  Cramer-Rao bound for tracking in clutter and tracking multiple objects , 1997, Pattern Recognit. Lett..

[17]  James H. Taylor.  The Cramer-Rao estimation error lower bound computation for deterministic nonlinear systems , 1978 .

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