Abstract
The presence of transmitter and receiver location uncertainties has been known to remarkably deteriorate the target localization accuracy in multi-static passive radar (MPR) system. This paper explores the use of calibration targets, the positions and velocities of which are known to the MPR system, to counter the loss in target localization accuracy arising from the transmitter/receiver location uncertainties. We firstly evaluate the Cramer-Rao lower bound (CRLB) for bistatic range (BR) and bistatic range rate (BRR)-based target localization in the presence of calibration targets, which analytically indicates the potential of calibration targets in enhancing localization accuracy. After that, a novel closed-form solution is proposed for target localization using the BR and BRR measurements from the unknown target as well as the additional BR and BRR measurements from the calibration targets. The proposed solution includes two processing steps, referred to as calibration step and localization step respectively. The calibration step is devoted to refine the inaccurate transmitter and receiver locations using the BR and BRR measurements from the calibration targets, and then the localization step is devoted to determine the target position and velocity based on the refined transmitter/receiver locations and the BR/BRR measurements from the unknown target. The accuracy of proposed solution is shown analytically to accomplish the CRLB under sufficiently small BR/BRR measurement noises and transmitter/receiver location errors. Simulation results verify the effectiveness and superiority of the proposed solution over existing algorithms.
Highlights
With no dedicated transmitter, passive radar detects and tracks potential targets by processing reflections from non-cooperative transmitters in the environment, such as commercial broadcast/communication transmission [1] and non-cooperative radar emitters [2]
By combining the passive radar geometry configuration, the time delay (TD) can be directly translated into the bistatic range (BR) which is defined as the sum of transmitter-target and target-receiver ranges [6], and the Doppler shift (DS) can be translated into the bistatic range rate (BRR)
In order to protrude the superiority of the proposed solution, the algorithm proposed in [10] which is regarded as the representative of the localization algorithms without considering the transmitter and receiver location errors, and that proposed in [15] which considers the statistical distributions of transmitter/receiver location error but does not use any calibration targets, are chosen as references for comparison
Summary
Passive radar detects and tracks potential targets by processing reflections from non-cooperative transmitters in the environment, such as commercial broadcast/communication transmission [1] and non-cooperative radar emitters [2]. By introducing multiple auxiliary variables, Zhao et al develop a novel algebraic solution for target position and velocity estimation in [10], where the first WLS step linearizes the BR and BRR measurement equations by introducing multiple auxiliary variables and produces a rough estimate using WLS minimization, the second step explores the relation between the auxiliary variables and the target location parameters to refine the estimate This method requires neither grouping and merging nor translating the BR and BRR measurements into the RD and RRD ones, and is proven analytically and numerically to reach the Cramér-Rao lower bound (CRLB) accuracy. Despite the fine prospects, up to now there does not exist any publication in the open literature that addresses using calibration targets to refine the nominal transmitter and receiver locations and reduce the loss in target localization accuracy caused by the transmitter and receiver location uncertainties for multi-static passive radar.
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