We propose a new metric for robot state estimation based on the recently introduced $\text{SE}_2(3)$ Lie group definition. Our metric is related to prior metrics for SLAM but explicitly takes into account the linear velocity of the state estimate, improving over current pose-based trajectory analysis. This has the benefit of providing a single, quantitative metric to evaluate state estimation algorithms against, while being compatible with existing tools and libraries. Since ground truth data generally consists of pose data from motion capture systems, we also propose an approach to compute the ground truth linear velocity based on polynomial interpolation. Using Chebyshev interpolation and a pseudospectral parameterization, we can accurately estimate the ground truth linear velocity of the trajectory in an optimal fashion with best approximation error. We demonstrate how this approach performs on multiple robotic platforms where accurate state estimation is vital, and compare it to alternative approaches such as finite differences. The pseudospectral parameterization also provides a means of trajectory data compression as an additional benefit. Experimental results show our method provides a valid and accurate means of comparing state estimation systems, which is also easy to interpret and report.

翻译：我们提出了一种基于最近引入的 $\text{SE}_2(3)$ 李群定义的机器人状态估计新度量。该度量与先前的SLAM度量相关，但显式考虑了状态估计的线速度，改进了当前基于位姿的轨迹分析方法。其优势在于既能提供一个统一的定量指标来评估状态估计算法，又与现有工具和库兼容。由于地面真实数据通常来自运动捕捉系统的位姿数据，我们还提出了一种基于多项式插值计算地面真实线速度的方法。通过利用切比雪夫插值和伪谱参数化，我们能够在最优框架下以最佳逼近误差精确估计轨迹的地面真实线速度。我们展示了该方法在多个需要精确状态估计的机器人平台上的性能，并与有限差分等替代方法进行了比较。此外，伪谱参数化还提供了轨迹数据压缩的附加优势。实验结果表明，我们的方法为比较状态估计系统提供了有效且精确的评估手段，同时易于解释和报告。