Generalized Cramér–Rao Bound for Joint Estimation of Target Position and Velocity for Active and Passive Radar Networks

Abstract

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 nonorthognal 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.

A novel distributed fusion algorithm for multi-sensor nonlinear tracking

“…Then, we evaluate the performance of fusion with three radars, i.e., one active and two passive radars. Following [25], the aforementioned parameters are set as s T The simulation setting may be applied to a composite guidance scenario [26], in which there are one active and two passive radars [27,28]. Although we simplify the observation equation in a 2-D scenario, the simulation scenario is still suitable for the practical application of tracking and surveillance in network centric warfare (NCW) [29].…”

Modified Cramér‐Rao lower bounds for joint position and velocity estimation of a Rician target in OFDM‐based passive radar networks

“…It is introduced in Godrich et al [] that the mean square error (MSE) of the maximum likelihood estimator (MLE) is close to the CRLB when certain conditions are satisfied. Recently, significant attention has been drawn to the CRLB for target parameter estimation with both noncoherent and coherent observations [ Godrich et al , ; He and Blum , ; He et al , , ; Wei et al , ; Zhao and Huang , ]. In [ Godrich et al , ], the closed‐form expressions of CRLB are derived for noncoherent and coherent MIMO radar systems, and it is demonstrated that the CRLB is inversely proportional to the carrier frequency and signals averaged effective bandwidth.…”

“…Zhao and Huang [] compute the CRLBs for the joint time delay and Doppler stretch estimation of an extended target, which analyzes the effects of waveform parameters on the CRLB of both the time delay and the Doppler stretch for the extended target. In Gogineni et al [], Stinco et al [], Filip and Shutin , , He and Blum , , , Javed et al [], and Shi et al [], the CRLB has been investigated and applied to passive radar systems employing Gaussian pulse signals, FM commercial radio signals, UMTS signals, global system for mobile communications (GSM) signals, and orthogonal frequency‐division multiplexing (OFDM)‐based L band digital aeronautical communication system type 1 (LDACS1) communication signals as signals of opportunity for the passive radar networks implementation. In He et al [], a generalized CRLB and mismatched CRLB for distributed active and passive radar networks are derived, where it is assumed that the approximation state of the target is unknown without previous target detection.…”

Power allocation for target detection in radar networks based on low probability of intercept: A cooperative game theoretical strategy

“…Distributed radar network systems have received contentiously growing attention in a novel class of radar system and on a path from theory to practical use owing to their advantage of signal and spatial diversities [Fisher et al, 2006;Haimovich et al, 2008;Li and Stoica, 2009;Pace, 2009], where the term radar networks refer to the use of multiple-transmit as well as multiple-receive antennas. In recent years, the study of distributed radar network architectures has received sizeable impetus, which has been extensively studied from various perspectives [Chen et al, 2013;Fisher et al, 2006;Godrich et al, 2010Godrich et al, , 2012He et al, 2016;Shi et al, 2015Shi et al, , 2016aShi et al, , 2016cShi et al, , 2016d. In Fisher et al [2006], the authors introduce the concept of distributed multiple-input multiple-output (MIMO) radar and investigate the inherent performance limitations of both conventional phased array radars and the newly proposed radars.…”