重新审视通过高斯过程和马格努斯展开的连续时间轨迹估计
Revisiting Continuous-Time Trajectory Estimation via Gaussian Processes and the Magnus Expansion
AI总结：
本文通过马格努斯展开提出了一种更优雅且通用的连续时间轨迹估计方法，替代了传统的局部高斯过程方法。
摘要：
连续时间状态估计已被证明是处理异步和高率测量、引入估计的平滑性、事后在测量时间以外的时间查询估计以及解决与移动扫描传感器相关的某些可观测性问题的有效方法。一种常用的在连续时间内表示轨迹的方法是通过高斯过程（GP）先验，其先验的均值和协方差函数由白噪声驱动的线性时变（LTV）随机微分方程（SDE）生成。当状态包含李群元素时，先前的工作采用了由线性时不变SDE核的局部GP组成的拼凑方法，虽然在实践中有效，但缺乏理论上的优雅。在这里，我们重新审视完整的LTV GP方法来估计连续时间轨迹，通过马格努斯展开推导出李群上的全局GP先验，这提供了一个更加优雅且通用的解决方案。我们提供了两种方法之间的数值比较，并讨论了它们的相对优点。
英文摘要：
Continuous-time state estimation has been shown to be an effective means of (i) handling asynchronous and high-rate measurements, (ii) introducing smoothness to the estimate, (iii) post hoc querying the estimate at times other than those of the measurements, and (iv) addressing certain observability issues related to scanning-while-moving sensors. A popular means of representing the trajectory in continuous time is via a Gaussian process (GP) prior, with the prior's mean and covariance functions generated by a linear time-varying (LTV) stochastic differential equation (SDE) driven by white noise. When the state comprises elements of Lie groups, previous works have resorted to a patchwork of local GPs each with a linear time-invariant SDE kernel, which while effective in practice, lacks theoretical elegance. Here we revisit the full LTV GP approach to continuous-time trajectory estimation, deriving a global GP prior on Lie groups via the Magnus expansion, which offers a more elegant and general solution. We provide a numerical comparison between the two approaches and discuss their relative merits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
