High-order regularization dealing with ill-conditioned robot localization problems
<|reference_start|>High-order regularization dealing with ill-conditioned robot localization problems: 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 can be seen as 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 robot localization problems. The proposed method overcomes the over-smoothing problem in the Tikhonov regularization as it can use 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 experiment results using a sensor network in a 3D environment are discussed, demonstrating the performance of the proposed method.<|reference_end|>
@article{liu2024high-order,
    title={High-order regularization dealing with ill-conditioned robot
  localization problems},
    author={Xinghua Liu and Ming Cao},
    journal={arXiv preprint arXiv:2410.01919},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.01919},
    primaryClass={cs.RO}
}