Recursive joint decision and estimation based on generalized Bayes risk

Joint decision and estimation (JDE) is for solving problems involving inter-dependent decision and estimation and was proposed recently based on a generalized Bayes risk. The currently available JDE algorithm processes data in a batch manner. This batch method is computationally inefficient or infeasible for many dynamic JDE problems where measurements are made available sequentially. Therefore, this paper follows the same JDE framework based on the generalized Bayes risk and proposes a recursive version of the JDE algorithm, which fits the dynamic JDE problems more naturally and inherits JDE's theoretical superiorities. Further, a joint performance measure in the measurement space is proposed for dynamic JDE problems. To the authors' knowledge, this is the only performance evaluation framework currently available for JDE evaluation. Finally, an illustrative example of the recursive JDE algorithm is elaborated and numerical simulations comparing it with the traditional two-stage algorithms (i.e., decide-then-estimate and estimate-then-decide) are presented.