Field Estimation From Randomly Located Binary Noisy Sensors

The estimation of bounded multivariate fields from 1-bit quantized and dithered noisy observations is considered. We consider two models for random sensor deployment based on regular Monte Carlo (simple random sampling) and stratified sampling. We propose linear estimators, and for both sensors deployment methods we establish exact expressions for the bias and variance of the estimates (including integrated mean-square errors). We show in particular that estimates of the field on the basis of stratified sensor locations always outperform estimates based on regular Monte Carlo sensor locations. For both estimation schemes, we also establish central limit theorems which can be used to compute the probability of events involving the estimates including confidence intervals.