Distributed Sequential Bayesian Estimation of a Diffusive Source in Wireless Sensor Networks

Abstract

We develop an efficient distributed sequential Bayesian estimation method for applications relating to diffusive sources-localizing a diffusive source, determining its space-time concentration distribution, and predicting its cloud envelope evolution using wireless sensor networks. Potential applications include security, environmental and industrial monitoring, as well as pollution control. We first derive the physical model of the substance dispersion by solving the diffusion equations under different environment scenarios and then integrate the physical model into the distributed processing technologies. We propose a distributed sequential Bayesian estimation method in which the state belief is transmitted in the wireless sensor networks and updated using the measurements from the new sensor node. We propose two belief representation methods: a Gaussian density approximation and a new LPG function (linear combination of polynomial Gaussian density functions) approximation. These approximations are suitable for the distributed processing in wireless sensor networks and are applicable to different sensor network situations. We implement the idea of information-driven sensor collaboration and select the next sensor node according to certain criterions, which provides an optimal subset and an optimal order of incorporating the measurements into our belief update, reduces response time, and saves energy consumption of the sensor network. Numerical examples demonstrate the effectiveness and efficiency of the proposed methods