Rank Properties for Matrices Constructed From Time Differences of Arrival

Le, Trung-Kien; Ho, K. C.; TrungHieu, Le

doi:10.1109/tsp.2018.2827327

Cited by 16 publications

(5 citation statements)

References 27 publications

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“…As mentioned in Section I, the reference sensor is commonly used to employ nonredundant TDs [3], [23], [30]- [32], with the first sensor often serving as the reference. Then, before solving (12), let us consider the problem of choosing the optimal reference sensor as follows.…”

Section: B Reference-based Solutionmentioning

confidence: 99%

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Minimum-Spanning-Tree-Based Time Delay Estimation Robust to Outliers

Yamaoka,

Nakashima,

Wakabayashi

et al. 2023

IEEE Access

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In this paper, we present a novel approach to estimating multiple time delays (TDs) in sensor arrays that is robust to outliers of TD measurements. These measurements are typically obtained from the peak of the cross correlation of two sensor signals but may contain outliers due to noise, significantly degrading the performance of downstream applications. To address this issue, we propose an approach to leverage only the best minimum-necessary TD measurements. First, we describe the general properties of TDs and show that the degree of freedom of TDs is the number of sensors minus one for a signal source, which indicates that the full set of TDs is redundant in this case. We then consider selecting nonredundant TDs from all measurements given the necessary and sufficient condition to reconstruct all TDs uniquely. We represent this condition by utilizing the graph theory, and then, formulate an optimization problem to select the optimal nonredundant TDs while satisfying the condition above. We reduce this problem to the problem of finding a minimum spanning tree and propose an efficient algorithm for TD estimation. Experimental evaluation shows that our method successfully eliminates outliers while ensuring that all TDs can be restored.

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Section: B Reference-based Solutionmentioning

confidence: 99%

“…Another approach is to choose a reference sensor and only use nonredundant M − 1 TDs between the reference sensor and the others [3], [23], [30]. Fig.…”

Section: Introductionmentioning

confidence: 99%

Minimum-Spanning-Tree-Based Time Delay Estimation Robust to Outliers

Yamaoka,

Nakashima,

Wakabayashi

et al. 2023

IEEE Access

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“…This is an advantage and from that we can combine our method with other methods to get better results. This idea that improving the observations based on their algebraic or geometrical properties can be found in (Velasco et al, 2016;Le et al, 2018) on studying the signal-based localization.…”

Section: Accuracy Of Correspondencesmentioning

confidence: 99%

Multi-view Geometry: Correspondences Refinement Based on Algebraic Properties

Le¹,

Li²

2022

Preprint

Self Cite

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Correspondences estimation or feature matching is a key step in the image-based 3D reconstruction problem. In this paper, we propose two algebraic properties for correspondences. The first is a rank deficient matrix construct from the correspondences of at least nine key-points on two images (two-view correspondences) and the second is also another rank deficient matrix built from the other correspondences of six key-points on at least five images (multi-view correspondences). To our knowledge, there are no theoretical results for multi-view correspondences prior to this paper. To obtain accurate correspondences, multi-view correspondences seem to be more useful than two-view correspondences. From these two algebraic properties, we propose an refinement algorithm for correspondences. This algorithm is a combination of correspondences refinement, outliers recognition and missing key-points recovery. Real experiments from the project of reconstructing Buddha statue show that the proposed refinement algorithm can reduce the average error from 77 pixels to 55 pixels on the correspondences estimation. This drop is substantial and it validates our results.

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“…Targets can be located by a single transmission, which leads to a reduction in power emission. For further enhanced observations in radar, microphone array, sonar, and particularly in passive scenarios, the authors of [36] developed two TDOA algebraic properties in sensor network and simultaneous source-sensor localization problem. Singular value decomposition, geometrical knowledge, and low rank property were exploited to improve the qualities of the TDOA, which led to a higher positioning accuracy.…”

Section: Wsn Localization Problemmentioning

confidence: 99%

An Efficient Distributed Elliptic Positioning for Underground Remote Sensing

Al-Samahi

Ansaf

2021

Electronics

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Remote surveying of unknown bound geometries, such as the mapping of underground water supplies and tunnels, remains a challenging task. The obstacles and absorption in media make the long-distance telecommunication and localization process inefficient due to mobile sensors’ power limitations. This work develops a new short-range sequential localization approach to reduce the required amount of signal transmission power. The developed algorithm is based on a sequential localization process that can utilize a multitude of randomly distributed wireless sensors while only employing several anchors in the process. Time delay elliptic and frequency range techniques are employed in developing the proposed algebraic closed-form solution. The proposed method is highly effective as it reaches the Cramer–Rao Lower Bound performance level. The estimated positions can act as initializations for the iterative Maximum Likelihood Estimator (MLE) via the Taylor series linearization to acquire even higher positioning accuracy as needed. By reducing the need for high power at the transmit modules in the sensors, the developed localization approach can be used to design a compact sensor with low power consumption and greater longevity that can be utilized to explore unknown bounded geometries for life-long efficient observation mapping.

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Rank Properties for Matrices Constructed From Time Differences of Arrival

Cited by 16 publications

References 27 publications

Minimum-Spanning-Tree-Based Time Delay Estimation Robust to Outliers

Minimum-Spanning-Tree-Based Time Delay Estimation Robust to Outliers

Multi-view Geometry: Correspondences Refinement Based on Algebraic Properties

An Efficient Distributed Elliptic Positioning for Underground Remote Sensing

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