Evaluation of covariance and information performance measures for dynamic object tracking

ABSTRACT In surveillance and reconnaissance applications, dynamic objects are dynamically followed by track filters with sequential measurements. There are two popular implementations of tracking filters: one is the covariance or Kalman filter and the other is the information filter. Evaluation of tracking filters is important in performance optimization not only for tracking filter design but also for resource manageme nt. Typically, the information matrix is the inverse of the covariance matrix. The covariance filter-based approaches attempt to minimize the covariance matrix-based scalar indexes whereas the information filter-based methods aim at maximizing the information matrix-based scalar indexes. Such scalar performance measures include the trace, determin ant, norms (1-norm, 2-norm, infinite-norm, and Forbenius norm), and eigenstructure of the covariance matrix or the information matrix and their variants. One natural question to ask is if the scalar track filter performa nce measures applied to the covariance matrix are equivalent to those applied to the information matrix? In this paper we show most of the scalar performance indexes are equivalent yet some are not. As a result, the indexes if used improperly would provide an “optimized” solution but in the wrong sense relative to track accuracy. The simulation indicated that all the seven indexes were successful when applied to the covariance matrix. However, the failed indexes for the information filter include the trace and the four norms (as defined in MATLAB) of the information matrix. Nevertheless, the determinant and the properly selected eigenvalue of the information matrix were successful to select the optimal sensor update configuration. The evaluation analysis of track measures can serve as a guideline to determine the suitability of performance measures for tracking filter design and resource management. Keywords: Target Tracking, Performance Evaluation, Covari ance Matrix, Information Ma trix, Performance Measures, Index Equivalence, Tracking F ilter Design, Resource Management 1. INTRODUCTION In surveillance and reconnaisiance applications, dynamic objects are dynamically by track filters with sequential measurements [1, 2, 6]. There are two popular im plementations of tracking filters: one is the covariance or Kalman filter [1, 2, 6] and the other is the information filter [5]. Most tracking filters are implemented using the Kalman filter or one of its variants [1, 2, 6], which is useful for centralized tracking. The KF updates the state x and the estimation error covariance P . The information filter (IF) is designed using the inve rse of the covariance matrix, termed the information matrix P