Generalized Cramer-Rao Bound for Joint Estimation of Target Position and Velocity for Active and Passive Radar Networks

TL;DR

This paper derives a generalized Cramer-Rao bound for joint target position and velocity estimation in radar networks, accommodating practical conditions like nonorthogonal signals and spatially dependent clutter, aiding performance assessment of estimation algorithms.

Contribution

It provides a comprehensive CRB formulation under realistic conditions, including nonorthogonal signals and unknown parameters, extending prior bounds and supporting practical radar system design.

Findings

CRB derived for nonorthogonal signals and spatially dependent clutter

Numerical validation confirms the bounds' accuracy

Application demonstrated on GSM-based passive radar

Abstract

In this paper, we derive the Cramer-Rao bound (CRB) for joint target position and velocity estimation using an active or passive distributed radar network under more general, and practically occurring, conditions than assumed in previous work. In particular, the presented results allow nonorthogonal signals, spatially dependent Gaussian reflection coefficients, and spatially dependent Gaussian clutter-plus-noise. These bounds allow designers to compare the performance of their developed approaches, which are deemed to be of acceptable complexity, to the best achievable performance. If their developed approaches lead to performance close to the bounds, these developed approaches can be deemed "good enough". A particular recent study where algorithms have been developed for a practical radar application which must involve nonorthogonal signals, for which the best performance is unknown, is a great example. The presented results in our paper do not make any assumptions about the approximate location of the target being known from previous target detection signal processing. In addition, for situations in which we do not know some parameters accurately, we also derive the mismatched CRB. Numerical investigations of the mean squared error of the maximum likelihood estimation are employed to support the validity of the CRBs. In order to demonstrate the utility of the provided results to a topic of great current interest, the numerical results focus on a passive radar system using the Global System for Mobile communication (GSM) cellar system.