Continuous-time Trajectory Estimation: A Comparative Study Between Gaussian Process and Spline-based Approaches

Abstract: 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.