Smoothing out the edges: continuous-time estimation with Gaussian process motion priors on factor graphs

Continuous-time state estimation is gaining in popularity due to its abilities to provide smooth solutions, handle asynchronous sensors and interpolate between data points. While there are two main paradigms, parametric (e.g., temporal basis functions, splines) and nonparametric (Gaussian processes [GP]), the latter has seen less adoption despite its technical advantages and relative ease of implementation. This paper seeks to rectify this situation by providing a new simplified explanation of GP continuous-time estimation rooted in the language of factor graphs, which have become the de facto estimation paradigm in much of robotics. To simplify onboarding, this paper also provides three working examples implemented in the popular Georgia Tech Smoothing and Mapping estimation framework.