Constrained total least squares localization using angle of arrival and time difference of arrival measurements in the presence of synchronization clock bias and sensor position errors

Liu, Ruirui; Wang, Ding; Yin, Jianxin; Wu, Ying

doi:10.1177/1550147719858591

Cited by 6 publications

(5 citation statements)

References 14 publications

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“…The weighting matrix W should modify the optimization to suppress noisy measurements. In the following, we derive a weighting matrix W, which reduces the influence of the measurements which are most affected by errors in the azimuth estimation [17], [18], [22]. Since the measurements with the highest uncertainty should have the smallest influence, the inverse of the measurement covariance cov[y] is used as weighting matrix…”

Section: A Optimized Weighted Least Squaresmentioning

confidence: 99%

Optimized Phase-based Ego-Motion Estimation with Multi-Dimensional Radar Systems

Stockel,

Froehly,

Wallrath

et al. 2024

Preprint

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Radars on unmanned vehicles can be used in indoor rescue scenarios to detect missing people based on their motion. In this case, the phase of the radar signals, which provides information about sub-millimeter changes in distance, have to be evaluated. However, in order to detect or to evaluate the motion of a missing person, the motion of the unmanned vehicle itself must be known and compensated for. To estimate the ego-motion of the unmanned vehicle, the radar system measures the phase information for multiple static objects in the radar’s environment. A model describing how the motion of the radar affects the phase signals is used to estimate the ego-motion by solving a system of equations. The accuracy of the estimated position, depends on how accurately the phase measurements represent the model. By analytically decomposing the errors in the measurement model, it is shown that the radar’s limited angular resolution induces a significant error. To mitigate this source of error, a weighted least squares approach is derived that minimizes the influence of the angular resolution on the position error. By calculating the position error distribution with and without the weighting approach, the benefits of the proposed algorithms are stated. Furthermore, the results are validated using simulations and real world measurements, showing that the proposed algorithm achieves sub-millimeter position accuracy.

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Section: A Optimized Weighted Least Squaresmentioning

confidence: 99%

Optimized Phase-based Ego-Motion Estimation with Multi-Dimensional Radar Systems

Stockel,

Froehly,

Wallrath

et al. 2024

Preprint

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“…As is well known, the optimal step length

in line 10 of Algorithm 1 can be found using both the Armijo and Wolfe conditions at expenses of more computational cost [ 31 , 32 ]. For practical purposes,

was set to one.…”

Section: A Robust and Distributed Localization Algorithm Based On mentioning

confidence: 99%

A Weighted and Distributed Algorithm for Range-Based Multi-Hop Localization Using a Newton Method

Diaz-Roman

Mederos

Sifuentes

et al. 2021

Sensors

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Wireless sensor networks are used in many location-dependent applications. The location of sensor nodes is commonly carried out in a distributed way for energy saving and network robustness, where the handling of these characteristics is still a great challenge. It is very desirable that distributed algorithms invest as few iterations as possible with the highest accuracy on position estimates. This research proposes a range-based and robust localization method, derived from the Newton scheme, that can be applied over isotropic and anisotropic networks in presence of outliers in the pair-wise distance measurements. The algorithm minimizes the error of position estimates using a hop-weighted function and a scaling factor that allows a significant improvement on position estimates in only few iterations. Simulations demonstrate that our proposed algorithm outperforms other similar algorithms under anisotropic networks.

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“…Apart from the eigenvalue problems [45], the CTLS can be solved by the Newton's method (NM) [46]- [53]. The CTLS criterion solved by the NM is adopted for sensor localization by means of the bearing angles [46], the TDoA [47], [48], [51], differential received signal strength [53], joint TDoA and angle of arrival [50], joint TDoA and wave velocity [52], and a general framework [49]. In this work, we pay attention to only the TDoA localization.…”

Section: Introductionmentioning

confidence: 99%

TDoA Localization in Wireless Sensor Networks Using Constrained Total Least Squares and Newton’s Methods

Tausiesakul,

Asavaskulkiet

2024

IEEE Access

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An important service in the wireless systems for the human daily life is the information of a mobile user location. Wireless sensor network is a structure that can be used to determine the mobile user position. The time-difference-of-arrival (TDoA) technique is often considered for wireless localization due to the low cost of sensor network. In this work, the error covariance matrices are derived for predicting the error performance of the conventional closed-form constrained total least squares (CTLS) estimator. More importantly, three new Newton's methods are proposed for computing the CTLS solution in the TDoA localization. In addition, theoretical performance of both new Newton-based approaches is provided in closed forms. Numerical simulation is conducted to compare the derived theoretical prediction with the corresponding actual estimation error. It is illustrated that the two new Newton-based techniques provide better performance, in terms of lower bias and root mean square error, less computational time, and more reliability, than the former Newton-based algorithms. Furthermore, the derived expressions for the theoretical error covariance well coincide with the actual random estimation results.INDEX TERMS First-order Taylor's series expansion, error covariance, localization, time difference of arrival, Newton's method.

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Constrained total least squares localization using angle of arrival and time difference of arrival measurements in the presence of synchronization clock bias and sensor position errors

Cited by 6 publications

References 14 publications

Optimized Phase-based Ego-Motion Estimation with Multi-Dimensional Radar Systems

Optimized Phase-based Ego-Motion Estimation with Multi-Dimensional Radar Systems

A Weighted and Distributed Algorithm for Range-Based Multi-Hop Localization Using a Newton Method

TDoA Localization in Wireless Sensor Networks Using Constrained Total Least Squares and Newton’s Methods

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