Decentralized Kalman filtering algorithm with uncertain signal model for heterogeneous sensor networks

This paper investigates the problem of designing decentralized robust Kalman filters for sensor networks observing a physical process with parametric uncertainty. A sensor network consists of distributed collection of nodes, each of which has sensing, communication and computation capabilities. We consider a heterogeneous sensor network consisting of two class of nodes (type A and type B) and central base station. Type A nodes undertake the sensing and make noisy observations of the same physical process while type B nodes play the role of cluster-heads. We derive the information form of robust Kalman filter by using the Krein space approach which proves to be useful to combine the local estimates. We obtain the decentralized robust Kalman filter for each type B node for the state estimation of uncertain physical phenomena of interest by taking into consideration the sensing model of each cluster and the information form of robust Kalman filter. The type B nodes transmit their estimates along with the inverse of error covariance matrix to the central base station which fuses these local estimates to produce the global estimate. Simulation results indicate that the performance of the centralized estimate is comparable to the performance of the global estimate and this suggest that they are identical.

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

[2]  Mahbub Gani,et al.  Optimal Deployment Control for a Heterogeneous Mobile Sensor Network , 2006, 2006 9th International Conference on Control, Automation, Robotics and Vision.

[3]  Jason Speyer,et al.  Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[4]  Duncan McFarlane,et al.  Robust state estimation for uncertain systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[5]  Ossama Younis,et al.  Node clustering in wireless sensor networks: recent developments and deployment challenges , 2006, IEEE Network.

[6]  Ian R. Petersen,et al.  Robust state estimation and model validation for discrete-time uncertain systems with a deterministic description of noise and uncertainty , 1998, Autom..

[7]  Jin-Bae Park,et al.  Robust Kalman filtering via Krein space estimation , 2004 .

[8]  Garry A. Einicke,et al.  Robust extended Kalman filtering , 1999, IEEE Trans. Signal Process..

[9]  François Baccelli,et al.  Stochastic geometry and architecture of communication networks , 1997, Telecommun. Syst..

[10]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

[11]  Catherine Rosenberg,et al.  A minimum cost heterogeneous sensor network with a lifetime constraint , 2005, IEEE Transactions on Mobile Computing.

[12]  Edward J. Coyle,et al.  An energy efficient hierarchical clustering algorithm for wireless sensor networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[13]  Qiang Du,et al.  Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations , 2002, Parallel Comput..

[14]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[16]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Ian R. Petersen,et al.  Robust Kalman Filtering for Signals and Systems with Large Uncertainties , 1999 .

[18]  Chee-Yee Chong,et al.  Distributed Tracking in Distributed Sensor Networks , 1986 .

[19]  Zhi Tian,et al.  Performance evaluation of track fusion with information matrix filter , 2002 .

[20]  Michael Athans,et al.  Proceedings of the MIT/ONR Workshop on Distributed Communication and Decision Problems Motivated by Naval C3 Systems (2nd). Held in Monterey, California on 16-27 July 1979. Volume 2 , 1980 .

[21]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[22]  Babak Hassibi,et al.  Indefinite-Quadratic Estimation And Control , 1987 .

[23]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.