Statistical Signal Processing for Data Fusion

In this dissertation we focus on statistical signal processing for Data Fusion, with a particular focus on wireless sensor networks. Six topics are studied: (i) Data Fusion for classification under model uncertainty; (ii) Decision Fusion over coherent MIMO channels; (iii) Performance analysis of Maximum Ratio Combining in MIMO decision fusion; (iv) Decision Fusion over non-coherent MIMO channels; (v) Decision Fusion for distributed classification of multiple targets; (vi) Data Fusion for inverse localization problems, with application to wideband passive sonar platform estimation. The first topic of this thesis addresses the problem of lack of knowledge of the prior distribution in classification problems that operate on small data sets that may make the application of Bayes’ rule questionable. Uniform or arbitrary priors may provide classification answers that, even in simple examples, may end up contradicting our common sense about the problem. Entropic priors (EP via application of the maximum entropy (ME) principle, seem to provide good objective answers in practical cases leading to more conservative Bayesian inferences. EP are derived and applied to classification tasks when only the likelihood functions are available. When inference is based only on one sample, we review the use of the EP also in comparison to priors that are obtained from maximization of the mutual information between observations and classes. This last criterion coincides with the maximization of the KL divergence between posteriors and priors that for large sample sets leads to the well-known reference (or Bernardo’s) priors. The comparison on single samples considers both approaches in prospective and clarifies differences and potentials. A combinatorial justification for EP, inspired by Wallis’ combinatorial argument for entropy definition, is also included. The application of the EP to sequences (multiple samples) that may be affected by excessive domination of the class with the maximum entropy is also considered with a solution that guarantees posterior consistency. An explicit iterative algorithm is proposed for EP determination solely from knowledge of the likelihood functions. Simulations that compare EP with uniform priors on short sequences are also included. In the second topic, we study channel-aware binary-decision fusion over a shared Rayleigh flat-fading channel with multiple antennas at the Decision Fusion Center (DFC). We present the optimal rule and derive sub-optimal fusion rules, as alternatives with improved numerical stability, reduced complexity and lower system knowledge required. The set of rules is derived following both ?Decode-and-Fuse? and ?Decode-then-Fuse? approaches. Simulation results for performances are presented both under Neyman-Pearson and Bayesian frameworks. The effect of multiple antennas at the DFC for the presented rules is analyzed, showing corresponding benefits and limitations. Also, the effect on performances as a function of the number of sensors is studied under a total power constraint. The third part covers a theoretical performance analysis of the maximum ratio combining (MRC) rule for channel-aware decision fusion over multiple-input multiple-output channels, in the general case of both dependent and independent local decisions. The performances are evaluated through the closed form of the conditional moment generating function (MGF) of the MRC statistic, along with Gauss-Chebyshev quadrature rules. Also, the conditional MGF allows to derive the explicit expression of the deflection coefficients. Finally, all the theoretical results are confirmed through Monte Carlo simulations. The fourth part of this dissertation presents a generalized optimality analysis of received-energy test for non-coherent decision fusion over a Rayleigh fading multiple access channel (MAC). More specifically, we provide a twofold generalization w.r.t the existing literature, allowing sensors to be non identical on one hand and introducing diversity on the other hand. Along with the derivation, we provide also a general tool to verify optimality of the the received energy test in scenarios with correlated sensor decisions. Finally, we derive an analytical expression of the effect of the diversity on the large-system performances, under both individual and total power constraints. The fifth topic deals with the derivation of two sub-optimal decision fusion algorithms in the context of distributed classification of multiple moving targets, as a low complexity alternative to the optimal decision fusion. At the fusion center, all the the binary decisions coming from a wireless sensor network (WSN) designed for single target classification are exploited for a multiple classification task. Based on the concept of maximum detection range of each sensor and approximating the joint posterior as a product of the posterior marginal, we derive the RLM (Range Limited Marginalization) and PRLM (Parallel Range Limited Marginalization) algorithms. Comparison between these suboptimal algorithms and the optimal decision fusion are performed for different scenarios, in terms of probabilities of detection and false alarm and metrics related to complexity theory. Finally we study an advanced topic in target motion analysis with wideband passive sonar. Maximum-likelihood probabilistic data-association represents an asymptotically efficient estimator for deterministic target motion, dealing with low-observable targets. Here we study the inverse problem, namely, how to identify the observing platform (following a “two-leg” motion model), from its results of the target estimation process, i.e. the estimated target state and the Fisher information matrix. We tackle the problem and we present observability properties, with supporting simulation results.