Random Field Reconstruction With Quantization in Wireless Sensor Networks

Abstract

We develop new and novel algorithms for spatial field reconstruction and spatial exceedance level estimation. We consider spatial physical phenomena which are partially observed by a wireless sensor network. We focus on the practical scenario in which, due to bandwidth and power constraints, the observations at the sensors are quantized and transmitted over imperfect wireless channels. We first develop the Spatial-Best Linear Unbiased Estimator (S-BLUE) algorithm for the spatial field reconstruction estimation. We then develop an algorithm that is based on a multivariate series expansion approach resulting in a Saddle-point type approximation to solve both problems of spatial field reconstruction and exceedance level estimation. We derive the Posterior Cramér Rao Lower Bound (PCRLB) and quantify the achievable MSE in the estimation. The estimation accuracy of the proposed algorithms is quantified via numerical comparisons between the two algorithms and the PCRLB.