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In this paper, we discuss a class of distributed detection algorithms which can be viewed as implementations of Bayes law in distributed settings. Some of the algorithms are proposed in the literature most recently, and others are first developed in this paper. The common feature of these algorithms is that they all combine (i) certain kinds of consensus protocols with (ii) Bayesian updates. They are different mainly in the aspect of the type of consensus protocol and the order of the two operations. After discussing their similarities and differences, we compare these distributed algorithms by numerical examples. We focus on the rate at which these algorithms detect the underlying true state of an object. We find that (a) The algorithms with consensus via geometric average is more efficient than that via arithmetic average; (b) The order of consensus aggregation and Bayesian update does not apparently influence the performance of the algorithms; (c) The existence of communication delay dramatically slows down the rate of convergence; (d) More communication between agents with different signal structures improves the rate of convergence.
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In this article, we present a finite time stopping criterion for consensus algorithms in networks with dynamic communication topology. Recent results provide asymptotic convergence to the consensus algorithm. However, the asymptotic convergence of these algorithms pose a challenge in the practical settings where the response from agents is required in finite time. To this end, we propose a Maximum-Minimum protocol which propagates the global maximum and minimum values of agent states (while running consensus algorithm) in the network. We establish that global maximum and minimum values are strictly monotonic even for a dynamic topology and can be utilized to distributively ascertain the closeness to convergence in finite time. We show that each node can have access to the global maximum and minimum by running the proposed Maximum-Minimum protocol and use it as a finite time stopping criterion for the otherwise asymptotic consensus algorithm. The practical utility of the algorithm is illustrated through experiments where each agent is instantiated by a NodeJS socket.io server.
Opinion Dynamics lacks a theoretical basis. In this article, I propose to use a decision-theoretic framework, based on the updating of subjective probabilities, as that basis. We will see we get a basic tool for a better understanding of the interaction between the agents in Opinion Dynamics problems and for creating new models. I will review the few existing applications of Bayesian update rules to both discrete and continuous opinion problems and show that several traditional models can be obtained as special cases or approximations from these Bayesian models. The empirical basis and useful properties of the framework will be discussed and examples of how the framework can be used to describe different problems given.
A protocol for distributed estimation of discrete distributions is proposed. Each agent begins with a single sample from the distribution, and the goal is to learn the empirical distribution of the samples. The protocol is based on a simple message-passing model motivated by communication in social networks. Agents sample a message randomly from their current estimates of the distribution, resulting in a protocol with quantized messages. Using tools from stochastic approximation, the algorithm is shown to converge almost surely. Examples illustrate three regimes with different consensus phenomena. Simulations demonstrate this convergence and give some insight into the effect of network topology.
We address the optimal transmit power allocation problem (from the sensor nodes (SNs) to the fusion center (FC)) for the decentralized detection of an unknown deterministic spatially uncorrelated signal which is being observed by a distributed wireless sensor network. We propose a novel fully distributed algorithm, in order to calculate the optimal transmit power allocation for each sensor node (SN) and the optimal number of quantization bits for the test statistic in order to match the channel capacity. The SNs send their quantized information over orthogonal uncorrelated channels to the FC which linearly combines them and makes a final decision. What makes this scheme attractive is that the SNs share with their neighbours just their individual transmit powers at the current states. As a result, the SN processing complexity is further reduced.
This paper considers the problem of simultaneous sensor fault detection, isolation, and networked estimation of linear full-rank dynamical systems. The proposed networked estimation is a variant of single time-scale protocol and is based on (i) consensus on textit{a-priori} estimates and (ii) measurement innovation. The necessary connectivity condition on the sensor network and stabilizing block-diagonal gain matrix is derived based on our previous works. Considering additive faults in the presence of system and measurement noise, the estimation error at sensors is derived and proper residuals are defined for fault detection. Unlike many works in the literature, no simplifying upper-bound condition on the noise is considered and we assume Gaussian system/measurement noise. A probabilistic threshold is then defined for fault detection based on the estimation error covariance norm. Finally, a graph-theoretic sensor replacement scenario is proposed to recover possible loss of networked observability due to removing the faulty sensor. We examine the proposed fault detection and isolation scheme on an illustrative academic example to verify the results and make a comparison study with related literature.
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