Simultaneous trajectory estimation and mapping (STEAM) offers an efficient\napproach to continuous-time trajectory estimation, by representing the\ntrajectory as a Gaussian process (GP). Previous formulations of the STEAM\nframework use a GP prior that assumes white-noise-on-acceleration, with the\nprior mean encouraging constant body-centric velocity. We show that such a\nprior cannot sufficiently represent trajectory sections with non-zero\nacceleration, resulting in a bias to the posterior estimates.\n This paper derives a novel motion prior that assumes white-noise-on-jerk,\nwhere the prior mean encourages constant body-centric acceleration. With the\nnew prior, we formulate a variation of STEAM that estimates the pose,\nbody-centric velocity, and body-centric acceleration. By evaluating across\nseveral datasets, we show that the new prior greatly outperforms the\nwhite-noise-on-acceleration prior in terms of solution accuracy.\n