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新近引入的$\text{SE}_2(3)$李群定义的机器人状态估计度量。该度量与SLAM领域先前的度量相关，但显式考虑了状态估计的线速度，从而改进了当前基于位姿的轨迹分析方法。其优势在于提供单一量化指标以评估状态估计算法，同时兼容现有工具和库。由于地面真值数据通常源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值线速度的方法。通过切比雪夫插值与伪谱参数化，我们能够以最佳逼近误差最优地估计轨迹的地面真值线速度。我们在多个对精确状态估计至关重要的机器人平台上验证了该方法的性能，并将其与有限差分法等替代方法进行对比。伪谱参数化还额外提供了轨迹数据压缩的功能。实验结果表明，该方法提供了一种有效且精确的状态估计系统比较手段，同时易于解释和报告。