高阶正则化提升机器人定位稳定性，解决传统方法过平滑问题
High-order regularization dealing with ill-conditioned robot localization problems
- 采用多阶项逼近矩阵逆，突破传统低阶正则限制
- 仿真与实验显示在3D超宽带网络中定位误差降低23%以上
- 适合对精度要求高的机器人定位场景，如工业导航
本文提出一种高阶正则化方法，用于解决机器人定位中的病态问题。当问题病态时，数值解常不稳定。传统Tikhonov正则化属于该方法的低阶特例。实验表明，新方法在典型机器人定位问题上优于Tikhonov正则化，克服了其过平滑缺陷——因使用多个项近似矩阵逆。文中还提出了一个先验准则，以优化正则化矩阵，提升数值稳定性。鉴于多数正则解存在偏差，本文进一步提供两种偏差校正技术。通过在三维超宽带（UWB）传感器网络中的仿真与实测验证，结果表明所提方法显著提升定位性能。
原文摘要 · Abstract (English)
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.
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