Quadratic constrained weighted least-squares method for TDOA source localization in the presence of clock synchronization bias: Analysis and solution

Wang, Ding; Yin, Jianxin; Tang, Tao; Chen, Xin; Wu, Zhidong

doi:10.1016/j.dsp.2018.08.002

Cited by 24 publications

(9 citation statements)

References 42 publications

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“…Here, we need to derive the analytical MSE ofρ s2 . Substituting (2) into (57) and neglecting the second-and higher-order error terms produces…”

Section: Mse Expression Ofρ S2mentioning

confidence: 99%

“…In [24,56], the mean square error (MSE) of source position estimate is derived when an optimum estimator assumes the sensor positions are exact but, in fact, they have errors. In [57], the effects of synchronization errors on TDOA localization accuracy are analyzed in terms of estimation bias, MSE, and success probability. In [58,59], the degradation in localization accuracy caused by synchronization offsets and sensor position perturbations is examined through the CRB analysis.…”

Section: Introductionmentioning

confidence: 99%

“…In other words, these sensors are partially synchronized. Based on this localization scenario, some efficient localization approaches are developed in [57,59,70].…”

Section: Introductionmentioning

confidence: 99%

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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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“…Here, we need to derive the analytical MSE ofρ s2 . Substituting (2) into (57) and neglecting the second-and higher-order error terms produces…”

Section: Mse Expression Ofρ S2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Typical positioning parameters include time of arrival (TOA) [16], time difference of arrival (TDOA) [17], angle of arrival (AOA) [18], received signal strength (RSS) [19], and a combination of them [20]. When there is relative motion between the target and the sensors, frequency differences of arrival (FDOA) can be exploited not only to further improve the estimation accuracy of the target position, but also to provide an estimate of the target velocity.…”

Section: Introductionmentioning

confidence: 99%

A Novel Estimator for TDOA and FDOA Positioning of Multiple Disjoint Sources in the Presence of Calibration Emitters

et al. 2020

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Multiple-target localization is extensively applied in wireless connected networks. However, sensor location uncertainty is known to degrade significantly the target localization accuracy. Fortunately, calibration emitters such as unmanned aerial vehicles (UAV) with known location can be used to reduce the loss in localization accuracy due to sensor location errors. This paper is devoted to the use of UAV calibration emitters for time differences of arrival (TDOA) and frequency differences of arrival (FDOA) positioning of multiple targets. The study starts with deriving the Cramér-Rao bound (CRB) for TDOA/FDOA-based target location estimate when several UAV calibration signals are available. Subsequently, the paper presents an iterative constrained weighted least squares (ICWLS) estimator for multiple-target joint localization using TDOA/FDOA measurements from both target sources and UAV calibration emitters. The newly proposed method consists of two stages. In the first phase, the sensor locations are refined based on the calibration measurements as well as the prior knowledge of sensor locations. The second step provides the estimate of multiple-target locations by combining the measurements of target signals as well as the estimated values in the first phase. An efficient ICWLS algorithm is presented at each stage. Both the two algorithms are implemented by using matrix singular value decomposition (SVD), which is able to provide a closed-form solution and update the weighting matrix at every iteration. Finally, the convergence behavior and estimation mean-square-error (MSE) of the new estimator are deduced. Both theoretical analysis and simulation results show that the developed method can improve the TDOA/FDOA localization accuracy obviously with the help of UAV calibration emitters. INDEX TERMS Target localization, unmanned aerial vehicle (UAV), time difference of arrival (TDOA), frequency difference of arrival (FDOA), multiple targets, calibration emitters, constrained weighted least squares (CWLS), Cramér-Rao bound (CRB), singular value decomposition (SVD).

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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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Quadratic constrained weighted least-squares method for TDOA source localization in the presence of clock synchronization bias: Analysis and solution

Cited by 24 publications

References 42 publications

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

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

A Novel Estimator for TDOA and FDOA Positioning of Multiple Disjoint Sources in the Presence of Calibration Emitters

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

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