Statistical Error Analysis of a DOA Estimator for a PCL System Using the Cramer-RAO Bound Theorem

摘要

Direction of Arrival (DOA) estimation of signals has been a popular research area in Signal Processing. DOA estimation also has a significant role in the object location process of Passive Coherent Location (PCL) systems. PCL systems have been in open literature since 1986 and their applications are not as clearly understood as the DOA estimation problem. However, they are the focus of many current research efforts and show much promise. The purpose of this research is to analyze the DOA estimation errors in a PCL system. The performance of DOA estimators is studied using the Cramer-Rao Bound (CRB) theorem. The CRB provides a lower bound on the variance of unbiased DOA estimators. Since variance is a desirable property for measuring the accuracy of an estimator, the CRB gives a good indication about the performance of an estimator. Previous DOA estimators configured with array antennas used the array antenna manifold, or the properties of the array antenna structure, to estimate signal DOA. Conventional DOA estimators use arbitrary signal (AS) structures. Constant Modulus (CM) DOA estimators restrict the input signals to a family of constant envelope signals, and when there are multiple signals in the environment, CM DOA estimators are able to separate signals from each other using the CM signal property. CM estimators then estimate the DOA for each signal individually. This research compares the CRB for AS and CM DOA estimators for a selected system. The CRB is also computed for this system when single and multiple and moving objects are present. The CRB(sub AS) and CRB(sub CM) are found to be different for the multiple signal case and moving object cases.