Optimality of the maximum average correlation height filter for detection of targets in noise

A statistical analysis is provided for the properties of the recently developed maximum average correlation height (MACH) filter (Mahalanobis et al. 1994). It is shown that the MACH filter can be interpreted as an optimum filter for the detection of targets in additive noise. A rationale is given for using a popular peak-to-sidelobe ratio metric to characterize the output of the MACH filter. Finally, the performance of the MACH filter is compared to that of the matched spatial filter in terms of the relation between the probabilities of correct detection and false alarm, which is represented as a receiver operating characteristic curve.