Continuous-time trajectory estimation is an attractive alternative to discrete-time batch estimation due to the ability to incorporate high-frequency measurements from asynchronous sensors while keeping the number of optimization parameters bounded. Two types of continuous-time estimation have become prevalent in the literature: Gaussian process regression and spline-based estimation. In this paper, we present a direct comparison between these two methods. We first compare them using a simple linear system, and then compare them in a camera and IMU sensor fusion scenario on SE(3) in both simulation and hardware. Our results show that if the same measurements and motion model are used, the two methods achieve similar trajectory accuracy. In addition, if the spline order is chosen so that the degree-of-differentiability of the two trajectory representations match, then they achieve similar solve times as well.

翻译：连续时间轨迹估计是离散时间批量估计的一种有吸引力的替代方案，因为它能够融合异步传感器的高频测量数据，同时保持优化参数数量有界。文献中主流采用两种连续时间估计方法：高斯过程回归和基于样条的估计。本文对这两种方法进行了直接比较。我们首先在简单线性系统中进行对比，随后在SE(3)上的相机与惯性测量单元（IMU）传感器融合场景中通过仿真和硬件实验进行对比。结果表明，若采用相同测量数据与运动模型，两种方法可实现相近的轨迹精度。此外，当样条阶数选择使得两种轨迹表示的可微性阶数匹配时，它们也能达到相近的求解时间。