Multi-Hypothesis Joint Detection and Estimation with Worst-Case Mean Square Error

Detection and estimation, as the basic uncertainty handling technologies, have attached increasingly attention in control and robotics engineering. This work tackles multiple hypotheses joint detection and estimation (JDE) problems with non-convexity performance measures (i.e., worst-case mean square error, MSE) using low-complexity frameworks. Most previous works mainly use numerical search to minimize the worst-case MSE under detection error probability constrains. This is computationally expensive because of the non-convexity of the loss function, and the optimality is not guaranteed in finite number of iterations. To address this issue, this work proposes an estimation-cost constrained decision-cost minimization (ECDM) framework. The central idea is to use the decision-cost (detection error probability) as linear loss function and the upper-bound of the estimation-cost as the constrains, such that the optimal solution is guaranteed to be obtained by linear programming efficiently. We theoretically prove that the solution of a linear ECDM optimization is still optimal to the conventional non- convexity optimizations. A range of simulations verify that, the proposed ECDM framework obtains less worst-case MSE and detection error probabilities and is significantly more efficient than the state-of-the-art algorithms in terms of runtime.