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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.15619 |
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| _version_ | 1866912009556066304 |
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| author | Xiong, Wenxin Chen, Yuming He, Jiajun Shi, Zhang-Lei Hu, Keyuan So, Hing Cheung Leung, Chi-Sing |
| author_facet | Xiong, Wenxin Chen, Yuming He, Jiajun Shi, Zhang-Lei Hu, Keyuan So, Hing Cheung Leung, Chi-Sing |
| contents | This short communication addresses the problem of elliptic localization with outlier measurements. Outliers are prevalent in various location-enabled applications, and can significantly compromise the positioning performance if not adequately handled. Instead of following the common trend of using $M$-estimation or adjusting the conventional least squares formulation by integrating extra error variables, we take a different path. Specifically, we explore the worst-case robust approximation criterion to bolster resistance of the elliptic location estimator against outliers. From a geometric standpoint, our method boils down to pinpointing the Chebyshev center of a feasible set, which is defined by the available bistatic ranges with bounded measurement errors. For a practical approach to the associated min-max problem, we convert it into the convex optimization framework of semidefinite programming (SDP). Numerical simulations confirm that our SDP-based technique can outperform a number of existing elliptic localization schemes in terms of positioning accuracy in Gaussian mixture noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A semidefinite programming approach for robust elliptic localization Xiong, Wenxin Chen, Yuming He, Jiajun Shi, Zhang-Lei Hu, Keyuan So, Hing Cheung Leung, Chi-Sing Signal Processing This short communication addresses the problem of elliptic localization with outlier measurements. Outliers are prevalent in various location-enabled applications, and can significantly compromise the positioning performance if not adequately handled. Instead of following the common trend of using $M$-estimation or adjusting the conventional least squares formulation by integrating extra error variables, we take a different path. Specifically, we explore the worst-case robust approximation criterion to bolster resistance of the elliptic location estimator against outliers. From a geometric standpoint, our method boils down to pinpointing the Chebyshev center of a feasible set, which is defined by the available bistatic ranges with bounded measurement errors. For a practical approach to the associated min-max problem, we convert it into the convex optimization framework of semidefinite programming (SDP). Numerical simulations confirm that our SDP-based technique can outperform a number of existing elliptic localization schemes in terms of positioning accuracy in Gaussian mixture noise. |
| title | A semidefinite programming approach for robust elliptic localization |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2401.15619 |