Semidefinite Relaxation Algorithm for Multisource Localization Using TDOA Measurements with Range Constraints

Jia, Changgui; Yin, Jianxin; Wang, Ding; Wang, Yunlong; Zhang, Li

doi:10.1155/2018/9430180

Cited by 5 publications

(6 citation statements)

References 23 publications

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“…The proof of Proposition 2 begins with reformulating the estimated covariance expression of θ in (38). We first define that Z s o ð Þ is the Jacobian matrix of ϑ with respect to s o , which is given by According to the definition of F 1 ðϑÞ in (31), it is easy to check that…”

Section: Acknowledgementmentioning

confidence: 99%

See 1 more Smart Citation

A novel time difference of arrival source localization method based on constrained scoring algorithm with a calibration emitter

Jia

Wang

2022

IET Signal Processing

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In this paper, we focus on the radiation source localization problem based on timedifference-of-arrival (time difference of arrival (TDOA)) measurements in the presence of sensor position errors. In order to alleviate the estimation degradation in locating a radiation source caused by the sensor position uncertainty, we propose to use a single calibration source and develop a novel two-stage localization algorithm based on the constrained scoring algorithm (CSA). In the first stage, we use the information of the calibration source to reduce the sensor position deviation, and here the CSA method is utilised to solve a quadratic constrained maximum likelihood (ML) objective function which is formulated from a set of underdetermined pseudo-linear equations. In the second stage, using the updated sensor positions and the TDOA measurements of the radiation source, another ML estimation problem with quadratic constraints is formulated, and we again invoke the CSA method to jointly estimate the source and sensor positions. Moreover, the asymptotically optimal performance of the proposed algorithm is mathematically analysed and proved based on the first-order error analysis. The simulation results verify the excellent performance of our algorithm and also demonstrate its robustness of resisting large measurement noise and sensor position errors. K E Y W O R D Scalibration emitter, constrained scoring method, sensor position error, source localization, time difference of arrival (TDOA) This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Acknowledgementmentioning

confidence: 99%

“…Then, substituting (C5) and (C6) into (38) yields Based on (C7), the covariance matrix cov ŝ ð Þ in (40) can be further rewritten as…”

Section: Acknowledgementmentioning

confidence: 99%

A novel time difference of arrival source localization method based on constrained scoring algorithm with a calibration emitter

Jia

Wang

2022

IET Signal Processing

Self Cite

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“…Specifically, it can be estimated during calibration by using a source of known location and by measuring the amounts of perturbations in the sensor positions. The detailed estimation method can be found in [84,85]. On the other hand, according to the discussion in [24], some scattering models from the environment may also help to determine the covariance matrix.…”

Section: Determination Of Covariance Matricesmentioning

confidence: 99%

“…From (85), (49), and (67), we have MSEðρ s1 Þ ¼ CRBðρÞ, which means that the solutionρ s1 is asymptotically efficient.…”

Section: Mse Expression Ofρ S1mentioning

confidence: 99%

On the use of calibration emitters for TDOA source localization in the presence of synchronization clock bias and sensor location errors

Wang

Yin

Chen

et al. 2019

EURASIP J. Adv. Signal Process.

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Time difference of arrival (TDOA) positioning is one of the widely applied techniques for locating an emitting source. Unfortunately, synchronization clock bias and random sensor location perturbations are known to significantly degrade the TDOA localization accuracy. This paper studies the use of a set of calibration sources, whose locations are accurately known to an estimator, to reduce the loss in localization accuracy caused by synchronization offsets and sensor location errors. Under the Gaussian noise assumption, we first derive the Cramér-Rao bound (CRB) for parametric estimation with the use of calibration emitters. Some explicit CRB expressions are obtained, and the performance improvement due to the introduction of the calibration sources is also quantified through the CRB analysis. In order to achieve the optimum localization accuracy, we proceed to propose new localization methods using the TDOA measurements from both target source and calibration emitters. Specifically, two dimension-reduction Taylor-series iterative algorithms are developed, and both of them have two stages. The first stage estimates the clock bias and refines the sensor positions by using the calibration TDOA measurements and the prior knowledge of sensor locations. The second stage provides the estimates of source location by combining the TDOA measurements of target signal and the estimated values in the first phase. The mean square errors (MSEs) of the proposed methods are shown analytically to achieve the corresponding CRB by applying the first-order perturbation analysis. Simulations are used to corroborate and support the theoretical development in this paper.

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“…Instead of linearizing the likelihood functions simply, the introduction of semidefinite constraints makes SDP a better choice for dealing with the nonconvex problems in wireless locations. Researchers devised several kinds of SDP approaches to approximating the location problems using energy/received signal strength (RSS) [43][44][45], angle of arrivals (AOAs) [46], TOAs [47][48][49], or TDOAs/frequency difference of arrivals (FDOAs) [46,[50][51][52][53][54][55][56][57][58][59][60]. In most cases, post-processing is required to refine the SDP solutions.…”

Section: Introductionmentioning

confidence: 99%

A Semidefinite Relaxation Method for Elliptical Location

2020

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Wireless location is a supporting technology in many application scenarios of wireless communication systems. Recently, an increasing number of studies have been conducted on range-based elliptical location in a variety of backgrounds. Specifically, the design and implementation of position estimators are of great significance. The difficulties arising from implementing a maximum likelihood estimator for elliptical location come from the nonconvexity of the negative log-likelihood functions. The need for computational efficiency further enhances the difficulties. Traditional algorithms suffer from the problems of high computational cost and low initialization justifiability. On the other hand, existing closed-form solutions are sensitive to the measurement noise levels. We recognize that the root of these drawbacks lies in an oversimplified linear approximation of the nonconvex model, and accordingly design a maximum likelihood estimator through semidefinite relaxation for elliptical location. We relax the elliptical location problems to semidefinite programs, which can be solved efficiently with interior-point methods. Additionally, we theoretically analyze the complexity of the proposed algorithm. Finally, we design and carry out a series of simulation experiments, showing that the proposed algorithm outperforms several widely used closed-form solutions at a wide range of noise levels. Extensive results under extreme noise conditions verify the deployability of the algorithm.

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Semidefinite Relaxation Algorithm for Multisource Localization Using TDOA Measurements with Range Constraints

Cited by 5 publications

References 23 publications

A novel time difference of arrival source localization method based on constrained scoring algorithm with a calibration emitter

A novel time difference of arrival source localization method based on constrained scoring algorithm with a calibration emitter

On the use of calibration emitters for TDOA source localization in the presence of synchronization clock bias and sensor location errors

A Semidefinite Relaxation Method for Elliptical Location

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