Sequential Detection with Mutual Information Stopping Cost

TL;DR

This paper develops a sequential detection framework based on mutual information for Gaussian processes with noisy, incomplete observations, providing a monotone policy structure for efficient decision-making in radar applications.

Contribution

It introduces a monotone policy characterization for sequential detection using mutual information, enabling efficient algorithms for Gaussian processes with missing data.

Findings

Monotone policies effectively control mutual information in radar scenarios.

Numerical examples demonstrate the approach's applicability in surveillance tasks.

The method improves decision efficiency in noisy, incomplete observation settings.

Abstract

This paper formulates and solves a sequential detection problem that involves the mutual information (stochastic observability) of a Gaussian process observed in noise with missing measurements. The main result is that the optimal decision is characterized by a monotone policy on the partially ordered set of positive definite covariance matrices. This monotone structure implies that numerically efficient algorithms can be designed to estimate and implement monotone parametrized decision policies.The sequential detection problem is motivated by applications in radar scheduling where the aim is to maintain the mutual information of all targets within a specified bound. We illustrate the problem formulation and performance of monotone parametrized policies via numerical examples in fly-by and persistent-surveillance applications involving a GMTI (Ground Moving Target Indicator) radar.