The Kalman like particle filter: Optimal estimation with quantized innovations/measurements

We study the problem of optimal estimation using quantized innovations, with application to distributed estimation over sensor networks. We show that the state probability density conditioned on the quantized innovations can be expressed as the sum of a Gaussian random vector and a certain truncated Gaussian vector. This structure bears close resemblance to the full information Kalman filter and so allows us to effectively combine the Kalman structure with a particle filter to recursively compute the state estimate. We call the resuting filter the Kalman like particle filter (KLPF) and observe that it delivers close to optimal performance using far fewer particles than that of a particle filter directly applied to the original problem. We also note that the conditional state density follows a, so called, generalized closed skew-normal (GCSN) distribution.

[1]  Lihua Xie,et al.  Multiple-Level Quantized Innovation Kalman Filter , 2008 .

[2]  R. Curry Estimation and Control with Quantized Measurements , 1970 .

[3]  Zhi-Quan Luo,et al.  Universal decentralized estimation in a bandwidth constrained sensor network , 2005, IEEE Transactions on Information Theory.

[4]  Arnaud Doucet,et al.  A survey of convergence results on particle filtering methods for practitioners , 2002, IEEE Trans. Signal Process..

[5]  M. Genton,et al.  Moments of skew-normal random vectors and their quadratic forms , 2001 .

[6]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[7]  M. Genton Discussion of ‘‘The Skew‐normal’’ , 2005 .

[8]  P. Embrechts Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality , 2005 .

[9]  Ian F. Akyildiz,et al.  Sensor Networks , 2002, Encyclopedia of GIS.

[10]  Arnaud Doucet,et al.  Convergence of Sequential Monte Carlo Methods , 2007 .

[11]  Marc G. Genton,et al.  Skew-elliptical distributions and their applications : a journey beyond normality , 2004 .

[12]  Arjun K. Gupta,et al.  A multivariate skew normal distribution , 2004 .

[13]  R. Brockett,et al.  Systems with finite communication bandwidth constraints. I. State estimation problems , 1997, IEEE Trans. Autom. Control..

[14]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[15]  M. Genton,et al.  A skewed Kalman filter , 2005 .

[16]  S. Yüksel A random time stochastic drift result and application to stochastic stabilization over noisy channels , 2009 .

[17]  A. Doucet,et al.  Particle filtering for partially observed Gaussian state space models , 2002 .

[18]  M. Genton,et al.  On fundamental skew distributions , 2005 .

[19]  Edoardo S. Biagioni,et al.  The Application of Remote Sensor Technology To Assist the Recovery of Rare and Endangered Species , 2002, Int. J. High Perform. Comput. Appl..

[20]  Zhi-Quan Luo,et al.  Minimum energy decentralized estimation in sensor network with correlated sensor noise , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[21]  Wing Shing Wong,et al.  Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback , 1999, IEEE Trans. Autom. Control..

[22]  Fredrik Gustafsson,et al.  Particle filtering for quantized sensor information , 2005, 2005 13th European Signal Processing Conference.

[23]  Bruno Sinopoli,et al.  Kalman filtering with intermittent observations , 2004, IEEE Transactions on Automatic Control.

[24]  R. Handel Uniform time average consistency of Monte Carlo particle filters , 2008, 0812.0350.

[25]  Stergios I. Roumeliotis,et al.  SOI-KF: Distributed Kalman Filtering With Low-Cost Communications Using The Sign Of Innovations , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[26]  Sekhar Tatikonda,et al.  Stochastic linear control over a communication channel , 2004, IEEE Transactions on Automatic Control.

[27]  Renwick E. Curry,et al.  Nonlinear estimation with quantized measurements-PCM, predictive quantization, and data compression , 1970, IEEE Trans. Inf. Theory.

[28]  Haikady N. Nagaraja,et al.  Inference in Hidden Markov Models , 2006, Technometrics.

[29]  Eric Moulines,et al.  Inference in Hidden Markov Models (Springer Series in Statistics) , 2005 .

[30]  Babak Hassibi,et al.  Particle filtering for Quantized Innovations , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[31]  Kristine L. Bell,et al.  A Tutorial on Particle Filters for Online Nonlinear/NonGaussian Bayesian Tracking , 2007 .