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Despite the existence of different error metrics for trajectory evaluation inSLAM, their theoretical justifications and connections are rarely studied, andfew methods handle temporal association properly. In this work, we propose toformulate the trajectory evaluation problem in a probabilistic, continuous-timeframework. By modeling the groundtruth as random variables, the concepts ofabsolute and relative error are generalized to be likelihood. Moreover, thegroundtruth is represented as a piecewise Gaussian Process in continuous-time.Within this framework, we are able to establish theoretical connections betweenrelative and absolute error metrics and handle temporal association in aprincipled manner.

Rethinking Trajectory Evaluation for SLAM: a Probabilistic, Continuous-Time Approach