Analysis of a signal starting time estimator based on the Page test statistic

Abstract

The time of the most recent reset to zero of the Page test statistic is proposed as an estimator of the starting time of a signal. The probability mass function of the estimator is determined analytically subject to a quantization of the Page test statistic update. Closed form results for the first three uncorrected moments of the estimator are presented. The analytical results are verified by comparison with simulation results and the fineness of the quantization required for accurate representation is investigated by evaluation of the

Kolmogorov-Srnirnov statistic. The bias, standard deviation, and skewness of the estimator as a function of the signal strength and detector threshold are evaluated for Gaussian shift-in-mean and noncentral chi-squared signal types.