Particle filtering for high-dimensional systems

Particle filtering methods aim at tracking probability distributions sequentially in time. One of the main challenges of these methods is their accuracy in high-dimensional state spaces. Namely, it can be shown that if the dimensions of these spaces are sufficiently high, the obtained results by particle filtering are practically useless. In this paper, we propose an approach for addressing this problem. It is based on breaking the high-dimensional distribution of the complete state into smaller dimensional (marginalized) distributions and attempting to track these distributions in a novel way as accurately as possible. We demonstrate the proposed approach with computer simulations.

[1]  Bo Yang,et al.  Multi-target device-free tracking using radio frequency tomography , 2011, 2011 Seventh International Conference on Intelligent Sensors, Sensor Networks and Information Processing.

[2]  A. Budhiraja,et al.  Modified particle filter methods for assimilating Lagrangian data into a point-vortex model , 2008 .

[3]  Andrew J. Majda,et al.  Filtering Complex Turbulent Systems , 2012 .

[4]  Mónica F. Bugallo,et al.  Multiple Particle Filtering , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[5]  J. Huang,et al.  Curse of dimensionality and particle filters , 2003, 2003 IEEE Aerospace Conference Proceedings (Cat. No.03TH8652).

[6]  Jeffrey L. Anderson,et al.  A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts , 1999 .

[7]  Nicholas G. Polson,et al.  Particle Filtering , 2006 .

[8]  Andrew M. Wallace,et al.  Tracking With a Hierarchical Partitioned Particle Filter and Movement Modelling , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  P.M. Djuric,et al.  Target Tracking by Multiple Particle Filtering , 2007, 2007 IEEE Aerospace Conference.

[10]  P. Bickel,et al.  Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems , 2008, 0805.3034.

[11]  Michael Isard,et al.  Partitioned Sampling, Articulated Objects, and Interface-Quality Hand Tracking , 2000, ECCV.

[12]  P. Djurić,et al.  Particle filtering , 2003, IEEE Signal Process. Mag..

[13]  Phani Chavali,et al.  Scheduling and Power Allocation in a Cognitive Radar Network for Multiple-Target Tracking , 2012, IEEE Transactions on Signal Processing.

[14]  T. Higuchi,et al.  Merging particle filter for sequential data assimilation , 2007 .

[15]  Bo Yang,et al.  Radio-Frequency Tomography for Passive Indoor Multitarget Tracking , 2013, IEEE Transactions on Mobile Computing.

[16]  Peter Jan,et al.  Particle Filtering in Geophysical Systems , 2009 .

[17]  A. Doucet,et al.  A Tutorial on Particle Filtering and Smoothing: Fifteen years later , 2008 .

[18]  Chaitali Chakrabarti,et al.  Efficient Bayesian Tracking of Multiple Sources of Neural Activity: Algorithms and Real-Time FPGA Implementation , 2013, IEEE Transactions on Signal Processing.