An iterative solution to the min-max simultaneous detection and estimation problem

Min-max simultaneous signal detection and parameter estimation requires the solution to a nonlinear optimization problem. Under certain conditions, the solution can be obtained by equalizing the probabilities of correctly estimating the signal parameter over the parameter range. We present an iterative algorithm based on Newton´s root finding method to solve the nonlinear min-max optimization problem through explicit use of the equalization criterion. The proposed iterative algorithm does not require prior proof of whether an equalizer rule exists: convergence of the algorithm implies existence. A theoretical study of algorithm convergence is followed by an amplitude estimation example which shows that decoupling detection from estimation entails a very significant loss in estimation performance even when optimal decoupled decision rules rules are implemented