无需数据关联即可全局最优定位，提升机器人定位精度与收敛性。
Globally Optimal Data-Association-Free Landmark-Based Localization Using Semidefinite Relaxations
- 通过半定松弛法同时求解最优位姿与数据关联
- 在中等噪声下多数情况可实现紧致松弛，保证全局最优
- 相比传统方法显著提升收敛到全局最优的能力
本文提出一种针对平面环境中基于地标且数据关联未知的定位问题的半定松弛方法。该方法能够以全局最优方式同时求解机器人的最优状态和数据关联。利用已知地标的相对位置测量，但机器人无法确定每条测量对应的是哪个地标。所提松弛方法在中等噪声水平下多数情况下具有紧致性。算法在仿真和实验中与基于死区推算轨迹初始化的局部高斯-牛顿基线方法对比，显著提升了收敛至全局最优解的能力。配套代码与补充材料可在 https://github.com/decargroup/certifiable_uda_loc 获取。
原文摘要 · Abstract (English)
This paper proposes a semidefinite relaxation for landmark-based localization with unknown data associations in planar environments. The proposed method simultaneously solves for the optimal robot states and data associations in a globally optimal fashion. Relative position measurements to known landmarks are used, but the data association is unknown in tha tthe robot does not know which landmark each measurement is generated from. The relaxation is shown to be tight in a majority of cases for moderate noise levels. The proposed algorithm is compared to local Gauss-Newton baselines initialized at the dead-reckoned trajectory, and is shown to significantly improve convergence to the problem's global optimum in simulation and experiment. Accompanying software and supplementary material may be found at https://github.com/decargroup/certifiable_uda_loc .
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