We propose a distributed Bayesian quickest detection algorithm for sensor networks, based on a random gossip inter-sensor communication structure. Without a control or fusion center, each sensor executes its local change detection procedure in a parallel and distributed fashion, interacting with its neighboring sensors via random inter-sensor communications to propagate information. By modeling the information propagation dynamics in the network as a Markov process, a two-layer large deviation analysis is presented to analyze the performance of the proposed algorithm. The first-layer analysis shows that the relation between the probability of false alarm and the conditional averaged detection delay satisfies the large deviation principle, where the distributed Kullback-Leibler information number is established as a crucial factor. The second-layer analysis studies the probability that not all observations are available at one sensor. It shows that this probability decays exponentially fast to zero as the averaged rounds of communication increases. The large deviation upper and lower bounds for the converge rate are then derived. Finally, we show that the performance of the distributed algorithm converges exponentially fast to that of the centralized optimal one.one.

This paper studies a Quantized Gossip-based Interactive Kalman Filtering (QGIKF) algorithm implemented in a wireless sensor network, where the sensors exchange their quantized states with neighbors via inter-sensor communications. We show that with the information loss due to quantization, the network can still achieve weak consensus, i.e., the estimation error variance sequence at a randomly selected sensor can converge weakly (in distribution) to a unique invariant measure. To prove the weak convergence, we first interpret the error variance sequence evolution as the interacting particle, then formulate the sequence as a Random Dynamical System (RDS), and finally prove that it is stochastically bounded.

This paper studies the convergence of the estimation error process and the characterization of the corresponding invariant measure in distributed Kalman filtering for potentially unstable and large linear dynamic systems. A gossip network protocol termed modified gossip interactive Kalman filtering (M-GIKF) is proposed, where sensors exchange their filtered states (estimates and error covariances) and propagate their observations via intersensor communications of rate$\bar {\gamma }$;$\bar {\gamma }$is defined as the averaged number of intersensor message passages per signal evolution epoch. The filtered states are interpreted as stochastic particles swapped through local interaction. This paper shows that the conditional estimation error covariance sequence at each sensor under M-GIKF evolves as a random Riccati equation (RRE) with Markov modulated switching. By formulating the RRE as a random dynamical system, it is shown that the network achieves weak consensus, i.e., the conditional estimation error covariance at a randomly selected sensor converges weakly (in distribution) to a unique invariant measure. Further, it is proved that as$\bar {\gamma } \rightarrow \infty $this invariant measure satisfies the large deviation (LD) upper and lower bounds, implying that this measure converges exponentially fast (in probability) to the Dirac measure$\delta _{P^{*}}$, where$P^{*}$is the stable error covariance of the centralized (Kalman) filtering setup. The LD results answer a fundamental question on how to quantify the rate at which the distributed scheme approaches the centralized performance as the intersensor communication rate increases.

In this paper, we study the expected density of progress for wireless ad hoc networks with Nakagami-m fading. The expected density of progress is defined as expectation of the product between the number of simultaneous successful transmission per unit area and the distance towards the destination. By considering three next hop receiver (RX) selection strategies, i.e., nearest RX selection strategy, random RX selection strategy and furthest RX selection strategy, we derive the closed-form expressions to the expected density of progress. Numerical results show that, when the terminal density is small, the expected density of progress with nearest RX selection strategy is nearly the same as that with furthest RX selection strategy, and the expected density of progress with random RX selection strategy is the lowest; when the terminal density is larger, the nearest RX selection strategy has the largest expected density of progress, and furthest RX selection strategy has the smallest expected density of progress.

In this paper, we propose a selection region based multihop routing protocol with directional antennas for wireless mobile ad hoc networks, where the selection region is defined by two parameters: a reference distance and the beamwidth of the directional antenna. At each hop, we choose the nearest node to the transmitter within the selection region as the next hop relay. By maximizing the expected density of progress, we present an upper bound for the optimum reference distance and derive the relationship between the optimum reference distance and the optimum transmission probability. Compared with the results with routing strategy using omnidirectional antennas in, we find interestingly that the optimum transmission probability is a constant independent of the beamwidth, the expected density of progress with the new routing strategy is increased significantly, and the computational complexity involved in the relay selection is also greatly reduced.