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

Abstract

Modified fast recursive algorithm for efficient MMSE-SIC detection of the V-BLAST system," IEEE Trans.Abstract-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 closedform 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.

Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking

“…However, it is worth noting that the GA results we show here might be improved if numerical approximations such as those developed in [64,19,65,66] were used in place of the analytic approximation (49).…”

“…and probability density functions (PDFs), for which the fusion is referred to as vfusion and f -fusion, respectively. While it seems that the AA fusion is more common in the former [7,8,4,9], the GA fusion is vibrant in the latter [3,14,15], which coincides with the Chernoff fusion [16,17,18,19] and is also known as covariance intersection (CI) when Gaussian functions that are uniquely characterized by the first and second order statistics are particularly considered [20,21,22,23,24,25]. The CI approach was originally proposed for fusing unknown-correlated estimates produced at distinct but not necessarily independent sensors to avoid information double accounting in the fusion.…”

“…5] such as the PHD [38] factories into a cardinality distribution on the number of objects and a localization density conditioned on the cardinality. In this case, while the AA of a sum can be straightforwardly expressed as a cascaded sum of the fusing sums (after re-weighting them) that remains in the same form [42,43]te, the fractional order exponential power of a sum does not remain as a sum of the same form, and typically approximation must be resorted to; see, e.g., [64,19,31,65,66].…”

Distributed Sequential Estimation in Asynchronous Wireless Sensor Networks

“…of the LP is computed from the particle representation by means of the weighted EM algorithm [19], and the GM parameters are broadcast to all neighbor sensors .…”

“…of the predictive pdf is computed from the particle representation by means of the weighted EM algorithm [19].…”