Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.01919 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913821739712512 |
|---|---|
| author | Liu, Xinghua Cao, Ming |
| author_facet | Liu, Xinghua Cao, Ming |
| contents | In this work, we propose a high-order regularization method to solve the ill-conditioned problems in robot localization. Numerical solutions to robot localization problems are often unstable when the problems are ill-conditioned. A typical way to solve ill-conditioned problems is regularization, and a classical regularization method is the Tikhonov regularization. It is shown that the Tikhonov regularization is a low-order case of our method. We find that the proposed method is superior to the Tikhonov regularization in approximating some ill-conditioned inverse problems, such as some basic robot localization problems. The proposed method overcomes the over-smoothing problem in the Tikhonov regularization as it uses more than one term in the approximation of the matrix inverse, and an explanation for the over-smoothing of the Tikhonov regularization is given. Moreover, one a priori criterion, which improves the numerical stability of the ill-conditioned problem, is proposed to obtain an optimal regularization matrix. As most of the regularization solutions are biased, we also provide two bias-correction techniques for the proposed high-order regularization. The simulation and experimental results using an Ultra-Wideband sensor network in a 3D environment are discussed, demonstrating the performance of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-order regularization dealing with ill-conditioned robot localization problems Liu, Xinghua Cao, Ming Robotics In this work, we propose a high-order regularization method to solve the ill-conditioned problems in robot localization. Numerical solutions to robot localization problems are often unstable when the problems are ill-conditioned. A typical way to solve ill-conditioned problems is regularization, and a classical regularization method is the Tikhonov regularization. It is shown that the Tikhonov regularization is a low-order case of our method. We find that the proposed method is superior to the Tikhonov regularization in approximating some ill-conditioned inverse problems, such as some basic robot localization problems. The proposed method overcomes the over-smoothing problem in the Tikhonov regularization as it uses more than one term in the approximation of the matrix inverse, and an explanation for the over-smoothing of the Tikhonov regularization is given. Moreover, one a priori criterion, which improves the numerical stability of the ill-conditioned problem, is proposed to obtain an optimal regularization matrix. As most of the regularization solutions are biased, we also provide two bias-correction techniques for the proposed high-order regularization. The simulation and experimental results using an Ultra-Wideband sensor network in a 3D environment are discussed, demonstrating the performance of the proposed method. |
| title | High-order regularization dealing with ill-conditioned robot localization problems |
| topic | Robotics |
| url | https://arxiv.org/abs/2410.01919 |