Conditional Joint Decision and Estimation with Application to Joint Tracking and Classification

The joint decision and estimation (JDE) algorithm is for solving problems involving simultaneous interdependent decision and estimation. Based on the JDE approach with a generalized Bayes risk and its recursive implementation (RJDE) for a dynamic system proposed recently, this paper proposes a conditional JDE (CJDE) risk, which is a generalization of the Bayes decision and estimation risks conditioning on data. We derive the optimal solution that minimizes the CJDE risk and present an optimal CJDE algorithm. For dynamic JDE problems, a recursive version of CJDE (RCJDE) is also proposed by following the same spirit of CJDE. To improve the joint performance of CJDE for a dynamic system, we propose a modified CJDE (MJDE) risk, by incorporating on-line prediction information, and present a corresponding MJDE algorithm. Because parameters play important roles in the JDE and CJDE risks, we analyze their effect to provide guidance for practical applications. The power of the proposed CJDE approach is illustrated by applying it to the joint target tracking and classification problem, which has received a great deal of attention in recent years. Simulation results show that CJDE can beat the traditional two-stage strategies and it involves less computation than RJDE. Furthermore, the superiority of MJDE is verified by comparing it with RCJDE. Moreover, it is shown that with appropriate parameters, CJDE can outperform separate optimal decision and optimal estimation in the joint performance metric.