Joint Detection and Estimation: Optimum Tests and Applications

TL;DR

This paper develops optimal joint detection and estimation tests that balance detection accuracy and estimation precision, with applications in changepoint detection and MIMO radar, showing significant performance improvements.

Contribution

It introduces a unified Bayesian framework for joint detection and estimation, deriving optimal tests that enable trade-offs between detection and estimation performance.

Findings

Significant estimation quality improvements with minimal detection power loss.

Effective application to changepoint detection and MIMO radar scenarios.

Simulation results confirm the advantages of the proposed joint strategies.

Abstract

We consider a well defined joint detection and parameter estimation problem. By combining the Baysian formulation of the estimation subproblem with suitable constraints on the detection subproblem we develop optimum one- and two-step test for the joint detection/estimation case. The proposed combined strategies have the very desirable characteristic to allow for the trade-off between detection power and estimation efficiency. Our theoretical developments are then applied to the problems of retrospective changepoint detection and MIMO radar. In the former case we are interested in detecting a change in the statistics of a set of available data and provide an estimate for the time of change, while in the latter in detecting a target and estimating its location. Intense simulations demonstrate that by using the jointly optimum schemes, we can experience significant improvement in estimation quality with small sacrifice in detection power.