Adaptive Tests for Object Detection

• Activity Number: 229 - Statistical Process Monitoring of High-Volume Data Streams
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Grigory Sokolov* and Alexander G. Tartakovsky
• Companies: and Moscow Institute of Physics and Technology
• Keywords: adaptive sequential probability ratio test; asymptotic optimality; composite hypotheses; generalized sequential probability ratio test; operating characteristics

Abstract

Target detection in a cluttered environment, involving noisy measurements of signals over time, is a central problem in radar, sonar and communications applications.

We consider the problem of detecting an object assuming that the distributions of the observed data are not exactly specified; more specifically, the hypotheses to be tested are composite. We use an adaptive version of the SPRT, built upon the one-stage delayed estimators of the unknown parameters. An alternative, also an asymptotically optimal test, is the generalized SPRT. It has certain drawbacks in selecting thresholds to guarantee the upper bounds on the probabilities of errors, but may appear to be slightly more efficient than the adaptive SPRT if the error probabilities match.

We study the relative efficiency of these tests asymptotically, as well as for realistic probabilities of errors using Monte Carlo simulations in a problem of detecting a target with unknown intensity in clutter.