# An Empirical Bayes Analysis of Object Trajectory Representation Models

arXiv: https://arxiv.org/abs/2211.01696 · HTML: https://mlsanity.com/paper/2211.01696/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 3 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [What the Constant Velocity Model Can Teach Us About Pedestrian Motion Prediction](https://mlsanity.com/paper/1903.07933/) (2019)
- [Vehicle trajectory prediction works, but not everywhere](https://mlsanity.com/paper/2112.03909/) (2021)
- [Self-Driving like a Human driver instead of a Robocar: Personalized comfortable driving experience for autonomous vehicles](https://mlsanity.com/paper/2001.03908/) (2020)
- [PLOP: Probabilistic poLynomial Objects trajectory Planning for autonomous driving](https://mlsanity.com/paper/2003.08744/) (2020)
- [Temporally-Continuous Probabilistic Prediction using Polynomial Trajectory Parameterization](https://mlsanity.com/paper/2011.00399/) (2020)

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

- [Improving Out-of-Distribution Generalization of Trajectory Prediction for Autonomous Driving via Polynomial Representations](https://mlsanity.com/paper/2407.13431/) (2024)
- [Uncertainty-Aware Trajectory Prediction via Rule-Regularized Heteroscedastic Deep Classification](https://mlsanity.com/paper/2504.13111/) (2025)
- [EP-Diffuser: An Efficient Diffusion Model for Traffic Scene Generation and Prediction via Polynomial Representations](https://mlsanity.com/paper/2504.05422/) (2025)
- [TPK: Trustworthy Trajectory Prediction Integrating Prior Knowledge For Interpretability and Kinematic Feasibility](https://mlsanity.com/paper/2505.06743/) (2025)
- [Boundary-Guided Trajectory Prediction for Road Aware and Physically Feasible Autonomous Driving](https://mlsanity.com/paper/2505.06740/) (2025)

## Abstract (arXiv)

Linear trajectory models provide mathematical advantages to autonomous driving applications such as motion prediction. However, linear models' expressive power and bias for real-world trajectories have not been thoroughly analyzed. We present an in-depth empirical analysis of the trade-off between model complexity and fit error in modelling object trajectories. We analyze vehicle, cyclist, and pedestrian trajectories. Our methodology estimates observation noise and prior distributions over model parameters from several large-scale datasets. Incorporating these priors can then regularize prediction models. Our results show that linear models do represent real-world trajectories with high fidelity at very moderate model complexity. This suggests the feasibility of using linear trajectory models in future motion prediction systems with inherent mathematical advantages.