Optimal Sequential Joint Detection and Estimation

This paper has been withdrawn by the authors.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.