Proceedings Article | 27 July 1999
KEYWORDS: Algorithm development, Silicon, Palladium, Chemical elements, Tolerancing, Binary data, Target recognition, Interference (communication), Astatine, Pulmonary function tests
We consider a problem in which exactly one of the n+1 distinct signals {S0, ...,Sn}, say S0, may be present in a noisy environment and the presence or absence of S0 needs to be determined. The performance is given by the false alarm probabilities Pfi, i=1, ...,n, where Pfi is the probability that Si is declared as S0, and the detection probability Pd which is the probability that S0 is correctly recognized. It is required that Pd be maximized while Pfi≤ci, i=1,...,n, where c1, ...,cn are prescribed non-negative constants. The solution is an extended Neyman-Pearson test in which p0(x) is tested against (w1p1(x)+ ...+wnpn(x)) where pi(x) is the probability density function of observation X when Si occurs. We propose two methods to obtain w1, ..., wn for any given c1, ..., cn. For certain simple cases, analytical or graphical solution is used. For the general case, we propose a search algorithm on w1, ..., wn which provides a sequence of extended Neyman-Pearson tests that converge to the optical solution. Numerical examples are given to illustrate these methods.
