Large Deviations Performance of Consensus+Innovations Distributed Detection with Non-Gaussian Observations

TL;DR

This paper analyzes the large deviations performance of consensus+innovations distributed detection in non-Gaussian sensor networks, revealing a phase transition in detection efficacy based on network connectivity and observation distribution.

Contribution

It establishes the error exponent for non-Gaussian distributed detection and identifies a critical network connectivity threshold for optimal performance.

Findings

Distributed detection matches centralized performance above threshold.

Below threshold, distributed detection is suboptimal.

Observation distribution affects detection performance and thresholds.

Abstract

We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs with the decision variables of their neighbors (consensus) and 2) assimilate their new observations (innovations). This paper shows for general non-Gaussian distributions that consensus+innovations distributed detection exhibits a phase transition behavior with respect to the network degree of connectivity. Above a threshold, distributed is as good as centralized, with the same optimal asymptotic detection performance, but, below the threshold, distributed detection is suboptimal with respect to centralized detection. We determine this threshold and quantify the performance loss below threshold. Finally, we show the dependence of the threshold and performance on the distribution of the observations: distributed detectors over the same random network, but with different observations' distributions, for example, Gaussian, Laplace, or quantized, may have different asymptotic performance, even when the corresponding centralized detectors have the same asymptotic performance.