Association-free tracking of two closely spaced targets

This paper introduces a new concept for tracking closely spaced targets in Cartesian space based on position measurements corrupted with additive Gaussian noise. The basic idea is to select a special state representation that eliminates the target identity and avoids the explicit evaluation of association probabilities. One major advantage of this approach is that the resulting likelihood function for this special problem is unimodal. Hence, it is especially suitable for closely spaced targets. The resulting estimation problem can be tackled with a standard nonlinear estimator. In this work, we focus on two targets in two-dimensional Cartesian space. The Cartesian coordinates of the targets are represented by means of extreme values, i.e., minima and maxima. Simulation results demonstrate the feasibility of the new approach.

[1]  Herbert A. David,et al.  Order Statistics, Third Edition , 2003, Wiley Series in Probability and Statistics.

[2]  S. Godsill,et al.  Monte Carlo filtering for multi target tracking and data association , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[3]  Marco F. Huber,et al.  Gaussian Filter based on Deterministic Sampling for High Quality Nonlinear Estimation , 2008 .

[4]  Andreas Krause,et al.  Data association for topic intensity tracking , 2006, ICML '06.

[5]  A.D. Lanterman,et al.  Multiple target tracking with symmetric measurement equations using unscented Kalman and particle filters , 2004, Thirty-Sixth Southeastern Symposium on System Theory, 2004. Proceedings of the.

[6]  |Marcus Baum,et al.  Random Hypersurface Models for extended object tracking , 2009, 2009 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT).

[7]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[8]  R.P.S. Mahler,et al.  "Statistics 101" for multisensor, multitarget data fusion , 2004, IEEE Aerospace and Electronic Systems Magazine.

[9]  Joris De Schutter,et al.  Nonlinear Kalman Filtering for Force-Controlled Robot Tasks , 2010, Springer Tracts in Advanced Robotics.

[10]  Peter Willett,et al.  Set JPDA algorithm for tracking unordered sets of targets , 2009, 2009 12th International Conference on Information Fusion.

[11]  Oliver E. Drummond,et al.  A bibliography of cluster (group) tracking , 2004, SPIE Defense + Commercial Sensing.

[12]  Y. Bar-Shalom,et al.  Tracking in clutter with nearest neighbor filters: analysis and performance , 1996, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Simon J. Godsill,et al.  Extended object tracking with unknown association, missing observations, and clutter using particle filters , 2003, IEEE Workshop on Statistical Signal Processing, 2003.

[14]  Samuel Kotz,et al.  Exact Distribution of the Max/Min of Two Gaussian Random Variables , 2008, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[15]  Henk A. P. Blom,et al.  Permutation invariance in Bayesian estimation of two targets that maneuver in and out formation flight , 2009, 2009 12th International Conference on Information Fusion.

[16]  S.S. Blackman,et al.  Multiple hypothesis tracking for multiple target tracking , 2004, IEEE Aerospace and Electronic Systems Magazine.

[17]  R. Mahler.  Multitarget Bayes filtering via first-order multitarget moments , 2003 .

[18]  E. Kamen,et al.  Multiple Target Tracking based on Symmetric Measurement Equations , 1989, 1989 American Control Conference.

[19]  Y. Bar-Shalom,et al.  The probabilistic data association filter , 2009, IEEE Control Systems.

[20]  H. N. Nagaraja,et al.  Order Statistics, Third Edition , 2005, Wiley Series in Probability and Statistics.

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

[22]  U. Hanebeck.  Optimal filtering of nonlinear systems based on pseudo gaussian densities , 2003 .

[23]  James Llinas,et al.  Handbook of Multisensor Data Fusion , 2001 .

[24]  Roy L. Streit,et al.  A look at the PMHT , 2009, 2009 12th International Conference on Information Fusion.

[25]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[26]  Neil J. Gordon,et al.  Group and extended object tracking , 1999, Optics & Photonics.

[27]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .

[28]  Aaron D. Lanterman,et al.  Unscented Kalman Filters for Multiple Target Tracking With Symmetric Measurement Equations , 2009, IEEE Transactions on Automatic Control.

[29]  N. Ikoma,et al.  Extended object tracking using particle techniques , 2004, 2004 IEEE Aerospace Conference Proceedings (IEEE Cat. No.04TH8720).