Decentralized Quantized Kalman Filtering With Scalable Communication Cost

Estimation and tracking of generally nonstationary Markov processes is of paramount importance for applications such as localization and navigation. In this context, ad hoc wireless sensor networks (WSNs) offer decentralized Kalman filtering (KF) based algorithms with documented merits over centralized alternatives. Adhering to the limited power and bandwidth resources WSNs must operate with, this paper introduces two novel decentralized KF estimators based on quantized measurement innovations. In the first quantization approach, the region of an observation is partitioned into N contiguous, nonoverlapping intervals where each partition is binary encoded using a block of m bits. Analysis and Monte Carlo simulations reveal that with minimal communication overhead, the mean-square error (MSE) of a novel decentralized KF tracker based on 2-3 bits comes stunningly close to that of the clairvoyant KF. In the second quantization approach, if intersensor communications can afford m bits at time n, then the ith bit is iteratively formed using the sign of the difference between the nth observation and its estimate based on past observations (up to time n-1) along with previous bits (up to i-1) of the current observation. Analysis and simulations show that KF-like tracking based on m bits of iteratively quantized innovations communicated among sensors exhibits MSE performance identical to a KF based on analog-amplitude observations applied to an observation model with noise variance increased by a factor of [1-(1-2/pi)m]-1.

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

[2]  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.

[3]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[4]  Alejandro Ribeiro,et al.  Bandwidth-constrained distributed estimation for wireless sensor Networks-part I: Gaussian case , 2006, IEEE Transactions on Signal Processing.

[5]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[6]  Chee-Yee Chong,et al.  Sensor networks: evolution, opportunities, and challenges , 2003, Proc. IEEE.

[7]  Yaakov Bar-Shalom,et al.  Estimation and Tracking: Principles, Techniques, and Software , 1993 .

[8]  Richard M. Murray,et al.  On a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage , 2006, Autom..

[9]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[10]  Haralabos C. Papadopoulos,et al.  Sequential signal encoding from noisy measurements using quantizers with dynamic bias control , 2001, IEEE Trans. Inf. Theory.

[11]  RibeiroA..  Bandwidth-constrained distributed estimation for wireless sensor Networks-part I , 2006 .

[12]  Mani Srivastava,et al.  Overview of sensor networks , 2004 .

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

[14]  Joel Max,et al.  Quantizing for minimum distortion , 1960, IRE Trans. Inf. Theory.

[15]  Deborah Estrin,et al.  Guest Editors' Introduction: Overview of Sensor Networks , 2004, Computer.

[16]  R C Robertson,et al.  Digital Communications Over Fading Channels , 2004 .

[17]  Mark G. Terwilliger,et al.  Overview of Sensor Networks , 2004 .

[18]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[19]  Robert M. Gray.  Quantization in Task-Driven Sensing and Distributed Processing , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[20]  Kazufumi Ito,et al.  Gaussian filters for nonlinear filtering problems , 2000, IEEE Trans. Autom. Control..

[21]  Stergios I. Roumeliotis,et al.  Optimal Sensing Strategies for Mobile Robot Formations: Resource-Constrained Localization , 2005, Robotics: Science and Systems.

[22]  John Anderson,et al.  Wireless sensor networks for habitat monitoring , 2002, WSNA '02.

[23]  Petar M. Djuric,et al.  Gaussian particle filtering , 2003, IEEE Trans. Signal Process..

[24]  J. Doob.  Stochastic processes , 1953 .

[25]  Stergios I. Roumeliotis,et al.  Optimal sensor scheduling for resource-constrained localization of mobile robot formations , 2006, IEEE Transactions on Robotics.