# A White-Noise-On-Jerk Motion Prior for Continuous-Time Trajectory Estimation on SE(3)

arXiv: https://arxiv.org/abs/1809.06518 · HTML: https://mlsanity.com/paper/1809.06518/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2018.

## Built on by (most cited first, 5 of 5)

- [Asynchronous Multi-View SLAM](https://mlsanity.com/paper/2101.06562/) (2021)
- [Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)](https://mlsanity.com/paper/2508.07775/) (2025)
- [Traj-LIO: A Resilient Multi-LiDAR Multi-IMU State Estimator Through Sparse Gaussian Process](https://mlsanity.com/paper/2402.09189/) (2024)
- [Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations](https://mlsanity.com/paper/2506.06780/) (2025)
- [AsynEIO: Asynchronous Monocular Event-Inertial Odometry Using Gaussian Process Regression](https://mlsanity.com/paper/2411.12175/) (2024)

## Abstract (arXiv)

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