Optimal Sequential Joint Detection and Estimation

TL;DR

This paper introduces the first optimal solution for the sequential joint detection and estimation problem, aiming to minimize average stopping time while satisfying detection and estimation constraints.

Contribution

It develops the first optimal framework for sequential joint detection and estimation, including the optimal stopping time, detector, and estimator.

Findings

Optimal triplet of stopping time, detector, and estimator derived.

Solution minimizes average stopping time under combined constraints.

Addresses complexity of sequential decision-making in joint detection and estimation.

Abstract

This paper has been withdrawn by the authors. Please see arXiv:1302.6058. We consider the sequential joint detection and estimation problem. Minimizing the average stopping time subject to a combination of detection and estimation constraints we obtain the optimal triplet of stopping time, detector and estimator. In the joint detection and estimation problem the primary goal is to detect and estimate together, as opposed to the conventional testing of composite hypotheses where the primary goal is to detect only. For the first time in the literature we develop optimal solution to the sequential joint detection and estimation problem. In the sequential version of the problem, different from the fixed sample size version, optimal stopping time is also sought, complicating the solution considerably.