1. Introduction
The joint problem of distinguishing between different hypotheses and estimating the unknown parameters based on the outcome of the hypotheses test has received considerable attention in the literature [1]–[6]. Such a problem arises in a wide range of applications, including (i) radiographic inspection for detecting anomalies in manufactured objects and estimating their position and size [7], (ii) retrospective changepoint hypotheses testing to detect change in the statistics and simultaneously estimate the time of change [8], [9], (iii) jointly detecting the presence of multiple objects and estimating their states using image observations [10], and (iv) distinguishing between two hypotheses and at the same time estimating the unknown parameters in the accepted hypothesis in a distributed framework [11]. Some popular techniques to address this problem include reformulating the composite detection problem as a pure estimation problem [12], while the maximum a posteriori estimate was shown to provide a solution to the joint detection and estimation problem in a Bayesian context [13]. The problem has also been addressed in a sequential setting, where the objective is to minimize the number of samples subject to a constraint on the combined detection and estimation cost [14], [15]. The generalized sequential probability ratio test was presented in [16], where a decision was obtained using the maximum likelihood estimate of the unknown parameter.