Robust Direct position determination against sensor gain and phase errors with the use of calibration sources
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Robust Direct position determination against sensor gain and phase errors with the use of calibration sources Zeyu Yang1,2 · Ding Wang1,2
· Bin Yang1,2 · Fushan Wei1,3
Received: 16 November 2019 / Revised: 17 February 2020 / Accepted: 26 February 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The direct position determination (DPD) method can provide high localization performance than conventional two-step localization methods. However, the existing DPD methods only consider the scenario of parameters of the receiving arrays, and the localization performance decreases dramatically when the array model is inaccurate in practice. This paper studies the problem for positioning a stationary emitter in the presence of sensor gain and phase errors (SGPEs) aided by calibration sources. To remove these negative effects caused by SGPEs, calibration sources with known positions are introduced. The extended relationship between parameters of calibration sources and errors is used to establish a structural objective function based on the maximum likelihood estimate. The calibration parameters are jointly optimized with target-related parameters and an alternating iterative algorithm is then developed to decouple the multidimensional search into several low-dimensional optimizations. We also derive the Cramér–Rao bound (CRB) to evaluate the performance of the proposed method. Simulation results demonstrate that the proposed method outperforms the existing DPD methods and two-step methods, which incorporates the error information, and the accuracy attains the associated CRB. Keywords Source localization · Direct position determination (DPD) · Calibration sources · Sensor gain and phase errors (SGPEs) · Maximum likelihood (ML) estimate criteria · Angle of arrival (AOA) · Time difference of arrival (TDOA) · Cramér–Rao bound (CRB)
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Ding Wang [email protected]
1
PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, People’s Republic of China
2
National Digital Switching System Engineering and Technology Research Center, Zhengzhou 450002, People’s Republic of China
3
State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, People’s Republic of China
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Multidimensional Systems and Signal Processing
1 Introduction Passive localization is a classical problem that has been investigated over a few decades. It has attracted significant attention in many fields, including signal processing, wireless communications, underwater acoustics and vehicular technology for both defense-oriented and civil applications. Most localization systems employ a two-step processing, where metrics including the angle of arrival (AOA) (Stoica and Nehorai 1990; Liao et al. 2016; Sun et al. 2016; Do˘gançay 2005; Lin et al. 2016), the time of arrival (TOA) (Cheung et al. 2004; Chan et al. 2008; Le 2016), time difference of arrival (TDOA) (Ho and Xu 2004; Yang and Ho 2009; Jiang et al. 2016), frequency of arrival (FOA) (Mason 2004), frequency di
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