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Approximation of the Page Test Probability of Detection by the Cumulative Distribution of a Mixture of Poisson Random Variables.
NAVAL UNDERSEA WARFARE CENTER NEWPORT DIV NEW LONDON CT NEW LONDON DETACHMENT
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Sequential tests like the Page test have been suggested for the detection of finite, unknown duration signals occurring at unknown times. The standard performance measures for the Page test are the average number of samples between false alarms and the average number ot samples before detection. The average number of samples between false alarms is an appropriate false alarm performance measure as the time of occurrence of the signal is unknown. However, the probability of detection is a more appropriate performance measure than the average number of samples before detection for signals having finite duration. Unfortunately, there has been minimal research related to determining this performance measure for the Page test. The results of Han, Willett, and Abraham indicate that the probability of detecting a finite duration signal with the Page test may be accurately approximated through the use of a continuous-time Brownian motion model or a quantized continuous-time process with moment matching when the sequences submitted to the regulated cumulative summation in the Page test is Gaussian. As many problems of interest result in non-Gaussian sequences to be submitted to the Page test it is desired to obtain distribution-independent methods for accurate detection probability approximation. The method proposed and analyzed herein involves approximating the probability density function of the stopping time random variable i.e., the number of samples before detection by a mixture of Poisson random variables. The probability of detecting a signal as a function of its duration is then approximated by the cumulative distribution function of the Poisson mixture. AN
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