Distributed Estimation of Fields Using a Sensor Network with Quantized Measurements

In this paper, the problem of estimating a scalar field (e.g., the spatial distribution of contaminants in an area) using a sensor network is considered. The sensors are assumed to have quantized measurements. We consider distributed estimation algorithms where each sensor forms its own estimate of the field, with sensors able to share information locally with its neighbours. Two schemes are proposed, called, respectively, measurement diffusion and estimate diffusion. In the measurement diffusion scheme, each sensor broadcasts to its neighbours the latest received measurements of every sensor in the network, while in the estimate diffusion scheme, each sensor will broadcast local estimates and Hessians to its neighbours. Information received from its neighbours will then be iteratively combined at each sensor to form the field estimates. Time-varying scalar fields can also be estimated using both the measurement diffusion and estimate diffusion schemes. Numerical studies illustrate the performance of the proposed algorithms, in particular demonstrating steady state performance close to that of centralized estimation.