Fast Consistent Chernoff Fusion of Gaussian Mixtures for Ad Hoc Sensor Networks

This correspondence examines the Chernoff rule for robust decentralized fusion of non-Gaussian pdfs in dynamic ad hoc sensor networks. Although theoretically appealing, the Chernoff rule is challenging to implement since it leads to fusion pdfs that cannot be obtained in closed-form and requires analytically intractable optimizations. Existing heuristic approximations to the Chernoff rule are generally inconsistent and do not accurately represent the fusion pdf. A fast new procedure based on Monte Carlo importance sampling, convex optimization and weighted expectation maximization is presented here to overcome these drawbacks and enable accurate online Chernoff fusion for ad hoc distributed sensor networks with Gaussian mixtures. Numerical experiments demonstrate the superiority of the proposed procedure.

[1]  Simon J. Julier,et al.  An Empirical Study into the Use of Chernoff Information for Robust, Distributed Fusion of Gaussian Mixture Models , 2006, 2006 9th International Conference on Information Fusion.

[2]  K.C. Chang,et al.  A distributed data fusion approach for mobile ad hoc networks , 2005, 2005 7th International Conference on Information Fusion.

[3]  Jacob Benesty,et al.  A fast recursive algorithm for optimum sequential signal detection in a BLAST system , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[4]  M. Hurley An information theoretic justification for covariance intersection and its generalization , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[5]  Tsung-Hsien Liu Some results for the fast MMSE-SIC detection in spatially multiplexed MIMO systems , 2009, IEEE Transactions on Wireless Communications.

[6]  Simon J. Julier,et al.  On conservative fusion of information with unknown non-Gaussian dependence , 2012, 2012 15th International Conference on Information Fusion.

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

[8]  Jeffrey K. Uhlmann,et al.  Using Exponential Mixture Models for Suboptimal Distributed Data Fusion , 2006, 2006 IEEE Nonlinear Statistical Signal Processing Workshop.

[9]  Hugh F. Durrant-Whyte,et al.  Decentralised particle filtering for multiple target tracking in wireless sensor networks , 2008, 2008 11th International Conference on Information Fusion.

[10]  Erik G. Larsson,et al.  Allocation of Computational Resources for Soft MIMO Detection , 2011, IEEE Journal of Selected Topics in Signal Processing.

[11]  Alexander Vardy,et al.  Closest point search in lattices , 2002, IEEE Trans. Inf. Theory.

[12]  Chee-Yee Chong,et al.  Analytical and Computational Evaluation of Scalable Distributed Fusion Algorithms , 2010, IEEE Transactions on Aerospace and Electronic Systems.

[13]  S. Grime,et al.  Data fusion in decentralized sensor networks , 1994 .

[14]  Erik G. Larsson,et al.  Gaussian approximation of the LLR distribution for the ML and partial marginalization MIMO detectors , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[15]  A.R. Runnalls,et al.  A Kullback-Leibler Approach to Gaussian Mixture Reduction , 2007 .

[16]  Hayit Greenspan,et al.  Simplifying Mixture Models Using the Unscented Transform , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Charles J. Geyer,et al.  Estimation and Optimization of Functions , 1996 .

[18]  Jeffrey K. Uhlmann,et al.  A non-divergent estimation algorithm in the presence of unknown correlations , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[19]  William J. Farrell,et al.  Generalized chernoff fusion approximation for practical distributed data fusion , 2009, 2009 12th International Conference on Information Fusion.