Nearly Optimal Adaptive Sequential Tests for Object Detection

Object detection in a cluttered environment, involving noisy measurements of signal over time, is a central problem in radar, sonar, optical, and communications applications. We consider the problem of detecting an object assuming that the distributions of the observed data are not exactly specified. As a result, the hypotheses to be tested are composite. We propose an adaptive version of the SPRT, named adaptive double SPRT developed by Tartakovsky (2014), who showed that this test is uniformly asymptotically optimal in the sense that it minimizes the average sample size for all parameter values when the probabilities of errors are small. This test is based on the parallel implementation of two one-sided adaptive SPRTs, each of these SPRTs is based on the comparison of the adaptive likelihood ratio statistic to a threshold. An alternative, also asymptotically optimal test is the popular generalized SPRT that has certain drawbacks in selecting thresholds to guarantee the upper bounds on the probabilities of errors but may appear to be more efficient than the adaptive SPRT if the error probabilities match. We study the relative efficiency of the adaptive SPRT, the generalized SPRT, and the non-adaptive 2-SPRT asymptotically as well as for realistic probabilities of errors using Monte Carlo simulations in a problem of detecting a signal with unknown intensity in clutter. The results demonstrate the robustness and high performance of the adaptive double SPRT algorithm.