The application of the Bayesian fusion detection criterion to the case of two disparate signals

Abstract

A Bayesian fusion criterion is described and applied to estimate improvements in detection range for two collocated sensors of disparate signals. The amplitude detection threshold selected for each sensor is expressed in terms of a likelihood threshold. The likelihood function is the ratio of the area under the probability density function beyond a threshold for a given signal to that for noise. The Bayesian criterion allows tying the likelihood threshold for one sensor to that for the other. When one can be set high, the other can be set low, thereby optimizing the use of the two sensor types. The assumption of Gaussian signal and noise probability density functions enables solving for the combined probability of detection versus range using an error function. An example is given for two signal types where each is subject to a different spreading loss. Estimates indicate that when the two individual detection ranges are comparable, the improvement in detection range through the application of a Bayesian criterion when compared to a simple ‘‘or’’ criterion (each sensor used separately with fixed nonrelated likelihood thresholds) can be as much as 30%. [Work supported by ONR.]