Online clutter estimation using a Gaussian kernel density estimator for target tracking

In this paper, based on non-homogeneous Poisson point processes (NHPP), a kernel clutter spatial intensity estimation method is proposed. Here, the clutter spatial intensity estimation problem is decomposed into two parts: (1) estimate the probability distribution of the clutter number per scan; (2) estimate the spatial variation of the clutter intensity in the measurement space. Under the NHPP assumption, the empirical mean is used to get a maximum likelihood estimate for the first problem. For the second problem, an online locally adaptive Gaussian kernel density estimator is proposed. In addition, the proposed clutter estimation method is integrated with standard multitarget trackers, like Multiple Hypothesis Tracker (MHT), Joint Integrated Probabilistic Data Association (JIPDA) tracker, Probability Hypothesis Density (PHD) filter. Simulation results show that the proposed clutter spatial intensity estimator can improve the performance of the multitarget tracker in the presence of non-homogeneous clutter background.

[1]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[2]  Thia Kirubarajan,et al.  Integrated Clutter Estimation and Target Tracking using Poisson Point Processes , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[3]  Evgueni A. Haroutunian,et al.  Information Theory and Statistics , 2011, International Encyclopedia of Statistical Science.

[4]  Y. Bar-Shalom,et al.  Dimensionless score function for multiple hypothesis tracking , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[5]  Ratnasingham Tharmarasa,et al.  Integrated Bayesian Clutter Estimation with JIPDA/MHT Trackers , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[6]  Tarn Dunong Bandwidth selectors for multivariate kernel density estimation , 2005, Bulletin of the Australian Mathematical Society.

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

[8]  Stergios B. Fotopoulos,et al.  All of Nonparametric Statistics , 2007, Technometrics.

[9]  Joti Jain,et al.  Statistical Inference and Simulation , 2006 .

[10]  Ning Li,et al.  Target perceivability and its applications , 2001, IEEE Trans. Signal Process..

[11]  Thiagalingam Kirubarajan,et al.  Integrated clutter estimation and target tracking using Poisson point process , 2009, Optical Engineering + Applications.

[12]  K. G. Murty An Algorithm for Ranking All the Assignment in Order of Increasing Cost , 1968 .

[13]  B. Moran,et al.  Clutter map and target tracking , 2005, 2005 7th International Conference on Information Fusion.

[14]  M. Hazelton,et al.  Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation , 2005 .

[15]  Yakov Bar-Shalom,et al.  Multitarget-Multisensor Tracking: Principles and Techniques , 1995 .

[16]  Marimuthu Palaniswami,et al.  Adaptive Target Tracking in Slowly Changing Clutter , 2006, 2006 9th International Conference on Information Fusion.

[17]  Ba-Ngu Vo,et al.  The Gaussian Mixture Probability Hypothesis Density Filter , 2006, IEEE Transactions on Signal Processing.

[18]  R. Evans,et al.  Clutter map information for data association and track initialization , 2004, IEEE Transactions on Aerospace and Electronic Systems.

[19]  Jeffrey D. Scargle,et al.  An Introduction to the Theory of Point Processes, Vol. I: Elementary Theory and Methods , 2004, Technometrics.

[20]  Inderjit S. Dhillon,et al.  Differential Entropic Clustering of Multivariate Gaussians , 2006, NIPS.

[21]  S. Godsill,et al.  Auxiliary Particle Implementation of the Probability Hypothesis Density Filter , 2007, 2007 5th International Symposium on Image and Signal Processing and Analysis.

[22]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[23]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[24]  Ning Li,et al.  Integrated real-time estimation of clutter density for tracking , 2000, IEEE Trans. Signal Process..

[25]  Ronald Mahler,et al.  CPHD and PHD filters for unknown backgrounds I: dynamic data clustering , 2009, Defense + Commercial Sensing.

[26]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[27]  G. Terrell The Maximal Smoothing Principle in Density Estimation , 1990 .

[28]  Esko Valkeila,et al.  An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure, 2nd Edition by Daryl J. Daley, David Vere‐Jones , 2008 .

[29]  J. Møller,et al.  Statistical Inference and Simulation for Spatial Point Processes , 2003 .

[30]  Ronald Mahler,et al.  CPHD and PHD filters for unknown backgrounds II: multitarget filtering in dynamic clutter , 2009, Defense + Commercial Sensing.

[31]  Darko Musicki,et al.  Joint Integrated Probabilistic Data Association - JIPDA , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[32]  Hugh L. Kennedy,et al.  Clutter-based Test Statistics for Automatic Track Initiation , 2008 .

[33]  Ronald Mahler,et al.  CPHD and PHD filters for unknown backgrounds, part III: tractable multitarget filtering in dynamic clutter , 2010, Defense + Commercial Sensing.

[34]  Oliver E. Drummond,et al.  Performance metrics for multiple-sensor multiple-target tracking , 2000, SPIE Defense + Commercial Sensing.

[35]  Kaare Brandt Petersen,et al.  The Matrix Cookbook , 2006 .