A Novel Joint Multitarget Estimator for Multi-Bernoulli Models

In this paper, the joint multitarget (JoM) estimator proposed for the joint target detection and tracking (JoTT) filter is reformulated for the Gaussian mixture (GM) implementations of the multitarget multi-Bernoulli (MeMBer) filters. For this purpose, a mode-finding algorithm is employed to search for the most significant mode of a GM density. Thus, the maximum a posterior (MAP) estimates of Bernoulli targets are determined. In addition, the multi-Bernoulli versions of the two conflicting objective functions for the Pareto-optimal value of the unknown JoM estimation constant are derived. Simulations compare the performance of the proposed JoM estimator with that of the marginal multitarget (MaM) estimator in a multitarget tracking scenario, where the probability of target detection is a function of target states. The simulation results demonstrate that the proposed JoM estimator outperforms the MaM estimator under moderately low-observable conditions. This is because the incomplete cost function of the MaM estimator is not adequate to obtain accurate cardinality estimates of targets without considering how well targets are localized. Nevertheless, the proposed JoM estimator may suffer from track termination latency more than the MaM estimator due to the definition of its cost function.

[1]  Thia Kirubarajan,et al.  Improved multi-target multi-Bernoulli filter with modelling of spurious targets , 2016 .

[2]  Ba-Ngu Vo,et al.  Labeled Random Finite Sets and the Bayes Multi-Target Tracking Filter , 2013, IEEE Transactions on Signal Processing.

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

[4]  Ba-Ngu Vo,et al.  On performance evaluation of multi-object filters , 2008, 2008 11th International Conference on Information Fusion.

[5]  Ba-Ngu Vo,et al.  A Consistent Metric for Performance Evaluation of Multi-Object Filters , 2008, IEEE Transactions on Signal Processing.

[6]  Ba-Ngu Vo,et al.  Labeled Random Finite Sets and Multi-Object Conjugate Priors , 2013, IEEE Transactions on Signal Processing.

[7]  Marco Lops,et al.  Random-Set Theory and Wireless Communications , 2012, Found. Trends Commun. Inf. Theory.

[8]  Ronald P. S. Mahler,et al.  Statistical Multisource-Multitarget Information Fusion , 2007 .

[9]  Jason L. Williams,et al.  An Efficient, Variational Approximation of the Best Fitting Multi-Bernoulli Filter , 2014, IEEE Transactions on Signal Processing.

[10]  Marco Lops,et al.  Multiuser Detection in a Dynamic Environment— Part II: Joint User Identification and Parameter Estimation , 2009, IEEE Transactions on Information Theory.

[11]  Ba Tuong Vo,et al.  Random finite sets in Multi-object filtering , 2008 .

[12]  Ronald P. S. Mahler,et al.  “Statistics 102” for Multisource-Multitarget Detection and Tracking , 2013, IEEE Journal of Selected Topics in Signal Processing.

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

[14]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[15]  Miguel Á. Carreira-Perpiñán,et al.  Mode-Finding for Mixtures of Gaussian Distributions , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Ba-Ngu Vo,et al.  Generalized Labeled Multi-Bernoulli Approximation of Multi-Object Densities , 2014, IEEE Transactions on Signal Processing.

[17]  Klaus C. J. Dietmayer,et al.  The Labeled Multi-Bernoulli Filter , 2014, IEEE Transactions on Signal Processing.

[18]  Ronald P. Mahler,et al.  Why Multi-Source, Multi-Target Data Fusion is Tricky , 1999 .

[19]  Ba-Ngu Vo,et al.  Robust Multi-Bernoulli Filtering , 2013, IEEE Journal of Selected Topics in Signal Processing.

[20]  Y. Bar-Shalom,et al.  Probability hypothesis density filter for multitarget multisensor tracking , 2005, 2005 7th International Conference on Information Fusion.

[21]  Yaakov Bar-Shalom,et al.  A physical-space approach for the probability hypothesis density and cardinalized probability hypothesis density filters , 2006, SPIE Defense + Commercial Sensing.

[22]  Ba-Ngu Vo,et al.  Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter , 2007, IEEE Transactions on Signal Processing.

[23]  I. R. Goodman,et al.  Mathematics of Data Fusion , 1997 .

[24]  Ba-Ngu Vo,et al.  A Tutorial on Bernoulli Filters: Theory, Implementation and Applications , 2013, IEEE Transactions on Signal Processing.

[25]  Thia Kirubarajan,et al.  Improved MeMBer filter with modeling of spurious targets , 2013, Proceedings of the 16th International Conference on Information Fusion.

[26]  Thia Kirubarajan,et al.  A Joint Multitarget Estimator for the Joint Target Detection and Tracking Filter , 2015, IEEE Transactions on Signal Processing.

[27]  R. Mahler,et al.  PHD filters of higher order in target number , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[28]  Miguel Á. Carreira-Perpiñán,et al.  Gaussian Mean-Shift Is an EM Algorithm , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  Jason L. Williams,et al.  Marginal multi-bernoulli filters: RFS derivation of MHT, JIPDA, and association-based member , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[30]  Ba-Ngu Vo,et al.  The Cardinality Balanced Multi-Target Multi-Bernoulli Filter and Its Implementations , 2009, IEEE Transactions on Signal Processing.

[31]  Lewis D. Griffin,et al.  Scale Space Methods in Computer Vision , 2003, Lecture Notes in Computer Science.

[32]  M.A. El-Sharkawi,et al.  Pareto Multi Objective Optimization , 2005, Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems.

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

[34]  Robin J. Evans,et al.  Integrated probabilistic data association , 1994, IEEE Trans. Autom. Control..

[35]  Miguel Á. Carreira-Perpiñán,et al.  Continuous latent variable models for dimensionality reduction and sequential data reconstruction , 2001 .

[36]  Oleksandr Romanko,et al.  Discussions on Normalization and Other Topics in Multi-Objective Optimization Algorithmics Group, Fields Industrial Problem Solving Workshop , 2006 .

[37]  Peter Willett,et al.  The Bin-Occupancy Filter and Its Connection to the PHD Filters , 2009, IEEE Transactions on Signal Processing.

[38]  Miguel Á. Carreira-Perpiñán,et al.  On the Number of Modes of a Gaussian Mixture , 2003, Scale-Space.

[39]  M. Ulmke,et al.  "Spooky Action at a Distance" in the Cardinalized Probability Hypothesis Density Filter , 2009, IEEE Transactions on Aerospace and Electronic Systems.

[40]  B. Vo,et al.  Bayesian approaches to track existence - IPDA and random sets , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[41]  Branko Ristic,et al.  A Metric for Performance Evaluation of Multi-Target Tracking Algorithms , 2011, IEEE Transactions on Signal Processing.