Source localization using TDOA and FDOA measurements based on semidefinite programming and reformulation linearization

Zhi, Zheng; Zhang, Hongwang; Wang, Wen-Qin; So, Hing Cheung

doi:10.1016/j.jfranklin.2019.10.029

Cited by 11 publications

(13 citation statements)

References 36 publications

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“…The traditional bias-reduced method is based on (21). The solution to (21) neglects the constraint relationship between and 1 in the first stage. A second step to reduce the nonlinear error is necessary.…”

Section: Iterative Constrained Weighted Least Squares Methods For Bias Reductionmentioning

confidence: 99%

“…They generally outperform the closed-form solution methods when the noise is considerable. Besides, the semidefinite programming (SDP) methods combined with reformulation linearization (RLT) [21] and the mixed SDP/ second-order cone program(SOCP) [22] were proposed to improve the location accuracy. Both of the methods show superior performance over the TWLS method.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Constrained Weighted Least Squares Method With Bias Reduction for TDOA-Based Localization

Zhang

Shin

2021

IEEE Sensors J.

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This paper addresses the source location problem by using time-difference-of-arrival (TDOA) measurements. The twostage weighted least squares (TWLS) algorithm has been widely used in the TDOA location. However, the estimation accuracy of the source location is poor and the bias is significant when the measurement noise is large. Owing to the nonlinear nature of the system model, we reformulate the localization problem as a constrained weighted least squares problem and derive the theoretical bias of the source location estimate from the maximumlikelihood (ML) estimation. To reduce the location bias and improve location accuracy, a novel bias-reduced method is developed based on an iterative constrained weighted least squares algorithm. The new method imposes a set of linear equality constraints instead of the quadratic constraints to suppress the bias. Numerical simulations demonstrate the significant performance improvement of the proposed method over the traditional methods. The bias is reduced significantly and the Cramér-Rao lower bound accuracy can also be achieved.

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Section: Iterative Constrained Weighted Least Squares Methods For Bias Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient Constrained Weighted Least Squares Method With Bias Reduction for TDOA-Based Localization

Zhang

Shin

2021

IEEE Sensors J.

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“…It is clear that (29) is a non-convex problem due to the equality constraint Y t = θ t θ t T . A feasible way is to convert (29) into a SDP problem and use interior point methods to solve the SDP problem efficiently.…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…Many TDOA/FDOA-based localisation methods have been developed during the last decade. They can be roughly classified into the following categories: the two-step WLS (TSWLS) method [8][9][10][11][12][13][14][15], the constrained WLS (CWLS) method [16][17][18][19][20][21][22], the non-linear WLS (NWLS) method [23], the multidimensional scaling (MDS) method [24], and the semidefinite programming (SDP)-based method [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Source localisation using TDOA and FDOA measurements under unknown noise power knowledge

Zhang

Zheng

Wang

et al. 2020

IET signal process.

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In this study, the authors develop a new algorithm for passive source localisation using time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements. In this algorithm, the position and velocity of the target source are successively estimated by formulating two alone semidefinite programming problems, where the variances of the TDOA and FDOA measurement noises can be separated and neglected. Unlike the traditional methods, the authors' approach does not require the prior knowledge of the TDOA/FDOA measurement noise power. Simulation results indicate that the proposed algorithm outperforms the existing methods under unknown noise power knowledge. the Fundamental Research Funds for the Central Universities of China under grant no. 2672018ZYGX2018J003. Fig. 2 Comparison of RMSEs using various methods in the far-field scenario (a) Position estimation, (b) Velocity estimation

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“…The algorithm ToA is often used with TDoA (Time Difference of Arrival) [ 25 ] and FDoA (Frequency difference of arrival) [ 26 ], which are also often used together [ 27 , 28 , 29 , 30 ]. TDoA is a very popular algorithm for different applications and measures the difference in the time of arrival of a signal from an object to several base stations [ 31 , 32 , 33 ]. FDoA, which is also named DD (Differential Doppler), is a method analogous to TDoA for estimating the location of a radio emitter based on observations from other points according to different Doppler shift observations of the emitter at different locations [ 34 , 35 ].…”

Section: Introductionmentioning

confidence: 99%

Method for Remote Determination of Object Coordinates in Space Based on Exact Analytical Solution of Hyperbolic Equations

Kuptsov

Badenko

Ivanov

et al. 2020

Sensors

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Accurate remote determination of the object coordinates in 3D space is one of the main questions in many applications. In one of the most popular methods, such determination of the location of an object uses the measurement by receiving an electromagnetic signal transmitted by several spatially distributed base stations (BS). The main problem is that it is necessary to reduce errors and computation time. To overcome these difficulties, an analytical method for determining the position of an object based on the analysis of time difference of arrival (TDoA) of signals from the transmitter of the object to the receivers of the BS is proposed. One of the main advantages of this method is that it is possible to eliminate the ambiguity in determining the coordinates of the object in space and to increase the accuracy of determining the coordinates when the TDoA measurement between base stations fluctuates. Applications for autonomous automotive vehicles and spacebased positioning systems are analyzed. The results obtained show that the proposed algorithm has an accuracy of determining coordinates several times higher than the method of linearization of hyperbolic equations and is less sensitive to TDoA fluctuations at base stations.

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Source localization using TDOA and FDOA measurements based on semidefinite programming and reformulation linearization

Cited by 11 publications

References 36 publications

An Efficient Constrained Weighted Least Squares Method With Bias Reduction for TDOA-Based Localization

An Efficient Constrained Weighted Least Squares Method With Bias Reduction for TDOA-Based Localization

Source localisation using TDOA and FDOA measurements under unknown noise power knowledge

Method for Remote Determination of Object Coordinates in Space Based on Exact Analytical Solution of Hyperbolic Equations

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