Accession Number : ADA292473

Title :   A Page Test With Nuisance Parameter Estimation.

Descriptive Note : Final rept.,

Corporate Author : NAVAL UNDERSEA WARFARE CENTER NEWPORT DIV NEW LONDON CT NEW LONDON DETACHMENT

Personal Author(s) : Abraham, Douglas A.

PDF Url : ADA292473

Report Date : 01 MAR 1995

Pagination or Media Count : 45

Abstract : The detection of the onset of a signal or the detection of a finite duration signal is a common and relevant problem in sonar signal processing. The Page test using the log-likelihood ratio is the optimal detector structure for signal onset detection when it is desired to minimize the average time before detection (D) while constraining the average time between false alarms (T). Parameterizations of realistic detection problems typically include unknown parameters having the same value under the signal-present and signal-absent hypotheses, known as nuisance parameters. When testing a finite set of data, nuisance parameters may be dealt with through the use of uniformly most powerful tests, invariant tests, Bayesian approaches, or the generalized likelihood ratio test. Unfortunately, these techniques do not always extend to sequential detection problems. In this report, the Page test generalized to account for nuisance parameters. The inherent signal-absent decision-making of the Page test is exploited to identify signal-free data (i.e., auxiliary data) to estimate the nuisance parameters. Due to the independence of the auxiliary data and the current Page test statistic, analysis is feasible. Wald- and Siegmund-based approximations to D and Tare derived and shown to simplify to those of the standard Page test when the nuisance parameters are known exactly. Closed forms for the average sample numbers (D and T) for the Page test with nuisance parameter estimation for a Gaussian shift in mean signal with unknown variance are derived. The approximations are verified through comparison with simulation results, where it is seen, as in the standard Page test, that the Siegmund-based approximation provides more accuracy.

Descriptors :   *SIGNAL PROCESSING, *SONAR SIGNALS, ALGORITHMS, COMPUTERIZED SIMULATION, OPTIMIZATION, PARAMETERS, THRESHOLD EFFECTS, MAXIMUM LIKELIHOOD ESTIMATION, STATISTICAL TESTS, SIGNAL TO NOISE RATIO, ANALYSIS OF VARIANCE, ACOUSTIC DETECTION, ACCURACY, FALSE ALARMS, APPROXIMATION(MATHEMATICS), BAYES THEOREM, STATISTICAL PROCESSES, ACOUSTIC DATA.

Subject Categories : Acoustic Detection and Detectors
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE