The Free Running Detection Problem: The Detection of Randomly Occurring Pulses as They Occur

摘要

The study provides an extension of classical detection theory by defining and analyzing two classes of decision devices that both operate in real time to detect the presence of each pulse in a sequence of randomly occurring pulses while that pulse is still present. The respond-once device seeks to detect each pulse once and only once whereas the other device, the respond-and-hold device, seeks to respond at each instant of time at which a pulse is present. The problem of obtaining the decision devices that are optimum in the above setting is the free running detection problem. It is assumed that all pulses are identically shaped and known up to their arrival times and that it is possible to observe these pulses only through an observation that contains additive noise. It is also assumed that the decision devices are allowed to make decisions on the presence or absence of pulses only at discrete, equally spaced points in time. The mathematical model is constructed in terms of the general decision theory model providing the theoretical basis for describing the performance of both classes of decision devices and for obtaining decision devices that are optimum with respect to the Bayes criteria. The performance of the respondance decision device is described in terms of the average number of pulses detected, the average number of false alarms, and the average number of times a pulse is detected more than once. (Author)