Recursive Distributed Detection for Composite Hypothesis Testing: Nonlinear Observation Models in Additive Gaussian Noise

Abstract

This paper studies recursive composite hypothesis testing in a network of sparsely connected agents. The network objective is to test a simple null hypothesis against a composite alternative concerning the state of the field, modeled as a vector of (continuous) unknown parameters determining the parametric family of probability measures induced on the agents' observation spaces under the hypotheses. Specifically, under the alternative hypothesis, each agent sequentially observes an independent and identically distributed time-series consisting of a (nonlinear) function of the true but unknown parameter corrupted by Gaussian noise, whereas, under the null, they obtain noise only. Two distributed recursive generalized likelihood ratio test type algorithms of the consensus+innovations form are proposed, namely CIGLRT − L and CIGLRT − N L, in which the agents estimate the underlying parameter and in parallel also update their test decision statistics by simultaneously processing the latest local sensed information and information obtained from neighboring agents. For CIGLRT − N L, for a broad class of nonlinear observation models and under a global observability condition, algorithm parameters which ensure asymptotically decaying probabilities of errors (probability of miss and probability of false detection) are characterized. For CIGLRT − L, a linear observation model is considered and upper bounds on large deviations decay exponent for the error probabilities are obtained.

Node-Specific Diffusion LMS-Based Distributed Detection Over Adaptive Networks

“…Given communication and computational constraints in networks, an approximation can prove rewarding. Recalling the expression (20) for K k,i and assuming the matrices {K k,i } of temporally growing dimensions are not exchanged among neighboring nodes (by setting A ℓk to W k , if ℓ = k, and 0, otherwise), and that the stepsizes {µ k } are sufficiently small, then, a good approximation for Q k,c,i is Q k,c,i = I Mc . A detailed derivation is given in Appendix B.…”

“…It was shown in [13] that diffusion strategies enjoy enhanced stability and performance relative to consensus strategies, achieving centralized performance in the slow adaptation regime [4], [10], [14], [15]. Building upon parameter estimation is detection, investigated in both the consensus [16]- [20] and diffusion [21]- [25] contexts.…”

Classification techniques for adaptive distributed networks and aeronautical structures.

“…Detection using adaptive networks has received considerable attention due to its energy saving capability, less communication resource requirements, robustness to node and link failure, scalability and tracking performance [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], employing different detection strategies depending on the application. For instance, several works focus on distributed Neyman-Pearson (NP) detectors [36], an approach appropriate, for example, to detect the presence of a target in a radar, since this detector maximizes the probability of detection of an event given a maximum desirable probability of false alarm.…”

“…The decision algorithm is based on the estimation technique diffusion LMS [19,44], which was applied in [23][24][25][26][27][28][29][30][31] to design distributed NP detectors. These works use a diffusion learning process among the nodes [45,46], but there are several others relying on the consensus technique [32][33][34][35].…”

“…The statistic variance σ 2 k (i) is obtained, by definition, from the kth diagonal entry of the matrix R t (i). Thus, it holds from (3.33), and recalling the definition of matrix W in (3.25), that 34) in which Rw k (i) is the kth M×M diagonal block of matrix Rw(i) and also the covariance matrix ofw k (i). We now obtain a non-recursive expression for Rw(i), in order to compute approximations to c k (i) in (3.32) in the next subsection.…”