Receiver-Operating-Characteristic for Several Multiple Hypothesis Range-Rate Filter Algorithms

Several multiple-hypothesis range-rate algorithms are investigated to determine initial target acquisition capabilities of a direct detection ladar operating under low photo-electron return conditions. During initial acquisition of an object, the location of the object is not known, therefore the ladar returns cannot be simply summed in order to improve detection statistics. Analogous to classical radar multiple hypothesis algorithm approaches a "shift and sum," a "shift and accumulate," and a "numerically shift and histogram" algorithm are investigated. The probability density function for the maximum of the multiple-hypothesis range-rate algorithm matrix output is developed so that a threshold crossing probability can be determined and a "detection" declared (receiver-operating-characteristic). This is expressed as a function of false alarm rate which is a function of the number of ladar returns processed in the acquisition process and the length of the acquisition window.