Approximate Cramer-Rao Bounds for Multiple Target Tracking
Leven, William Franklin
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The main objective of this dissertation is to develop mean-squared error performance predictions for multiple target tracking. Envisioned as an approximate Cramer-Rao lower bound, these performance predictions allow a tracking system designer to quickly and efficiently predict the general performance trends of a tracking system. The symmetric measurement equation (SME) approach to multiple target tracking (MTT) lies at the heart of our method. The SME approach, developed by Kamen et al., offers a unique solution to the data association problem. Rather than deal directly with this problem, the SME approach transforms it into a nonlinear estimation problem. In this way, the SME approach sidesteps report-to-track associations. Developing performance predictions using the SME approach requires work in several areas: (1) extending SME tracking theory, (2) developing nonlinear filters for SME tracking, and (3) understanding techniques for computing Cramer-Rao error bounds in nonlinear filtering. First, on the SME front, we extend SME tracking theory by deriving a new set of SME equations for motion in two dimensions. We also develop the first realistic and efficient method for SME tracking in three dimensions. Second, we apply, for the first time, the unscented Kalman filter (UKF) and the particle filter to SME tracking. Using Taylor series analysis, we show how different SME implementations affect the performance of the EKF and UKF and show how Kalman filtering degrades for the SME approach as the number of targets rises. Third, we explore the Cramer-Rao lower bound (CRLB) and the posterior Cramer-Rao lower bound (PCRB) for computing MTT error predictions using the SME. We show how to compute performance predictions for multiple target tracking using the PCRB, as well as address confusion in the tracking community about the proper interpretation of the PCRB for tracking scenarios.