Performance Measures of Covariance and Information Matrices in Resource Management for Target State Estimation

In target tracking, sensor resource management (SRM) assigns to each target a best combination of sensors, which requires performance analysis of track filter updates. Two popular implementations of track filters are the Kalman filter (or covariance filter) and the information filter. SRM with Kalman filters attempts to minimize the estimation error covariance matrix-based scalar performance measures, whereas SRM with information filters aims to maximize the information matrix-based counterpart. In this paper, we investigate issues related to scalar performance measures and, in particular, compare the use of trace, determinant, and eigenvalues of the covariance matrix or information matrix as scalar performance measures. The study demonstrates which matrix measures are appropriate for resource management applications. Furthermore, the study shows when the matrix measures lead to equivalent goals. While this analysis is agnostic to the type of measurement, the paper demonstrates how to accommodate bearing and range measurements. Overall, the analysis provides insight about how sensor measurements best reduce uncertainty so that we can properly exploit performance measures to satisfy requirements of practical tracking and SRM applications.