Optimum Detection in the Presence of Random Transient Disturbance and White Gaussian Noise

Detection of a deterministic signal in white Gaussian noise and a random transient disturbance is considered. Instead of the usual likelihood ratio as the detection statistic, we propose the use of the conditional likelihood ratio given the disturbance where the disturbance is estimated by the maximum a posteriori likelihood method. Since the likelihood ratio is the conditional version averaged over all possible realizations of the disturbance but the disturbance in the data, if any, is one particular realization, use of the conditional version is more appropriate. The disturbance model chosen is a piece of Gaussian process multiplied by a Rayleigh-distributed constant where the starting time and the duration are uniformly distributed. Such a disturbance, together with white noise, constitutes the worst case of the contaminated Gaussian noise in the min-max robust detection.