Adaptive optimal array detection of targets of unknown spatial location
A primary reason that much attention has been given to array antenna systems is their ability to perform rapid inertialess scanning. 1,2 Despite this great interest in array processing,1-6 the concept of an overall Bayesian approach to the scanning-detection problem has attracted little attention.' Classically "beams" are pointed at discrete spatial locations and detection decisions made on a local basis. Other suggested solutions include several non-parametric approaches1-10 and a generalized likelihood ratio approach.11 None of the above methods is optimal if target location statistics are available or can be assumed. In this paper the array detection problem is formulated in Bayesian terms for detection of a target of unknown location. Although a specific geometrical situation is assumed, the results are thought to be more general. Statistics are assumed on target location and the required likelihood ratios and resulting performance characteristics are obtained for several examples. It is shown that for a given array size it is possible to loosely bound the knowledge of target location required to achieve approximately "known location" performance. It is further demonstrated that if target location is unknown, there is not a direct trade-off between array size and signal energy with respect to performance. Finally it is shown that the dominant uncertainty affecting detection performance is that on location when compared with uncertainty on signal energy and/or phase.
