Sequential Joint Detection and Estimation

TL;DR

This paper introduces a sequential framework for joint detection and estimation, emphasizing that optimal performance requires integrating estimation considerations into the hypothesis testing process.

Contribution

It proposes a unified approach that combines detection and estimation in a sequential setting, improving over separate strategies by considering the estimator during testing.

Findings

Optimal joint detection and estimation strategy outperforms separate approaches.

Treating detection and estimation separately is suboptimal.

Incorporating the estimator into the testing phase enhances performance.

Abstract

We consider the problem of simultaneous detection and estimation under a sequential framework. In particular we are interested in sequential tests that distinguish between the null and the alternative hypothesis and every time the decision is in favor of the alternative they provide an estimate of a random parameter. As we demonstrate with our analysis treating the two subproblems separately with the corresponding optimal strategies does not result in the best possible performance. To enjoy optimality one needs to take into account the optimum estimator during the hypothesis testing phase.