Scalar estimation from unreliable binary observations

We consider a scalar signal estimator based on unreliable observations. The proposed architecture forms an estimate using redundant arrays of unreliable binary sensors with detection thresholds that can vary randomly about their nominal values. We analyze the achievable performance of the estimator in terms of mean square error. We also provide approximate expressions for the error of a mean square optimal estimator in terms of the degree of redundancy in the system and the distribution of the random thresholds. We show that calibration and redundancy can compensate for uncertainty in the observations to form a reliable estimate.