Reliable Probabilistic Human Trajectory Prediction for Autonomous Applications

TL;DR

This work tackles probabilistic human trajectory prediction (HTP) for autonomous systems by proposing a lightweight architecture that combines stacked LSTM encoding with a Mixture Density Network head to output multi-modal future position distributions. It emphasizes reliability and calibrated uncertainty through novel metrics (R_avg, R_min, S_68, S_95) and confidence-set construction, and validates performance across four large-scale traffic datasets on both standard benchmarks and embedded hardware. The results demonstrate strong reliability and competitive ADE/FDE with real-time inference feasibility, highlighting practical suitability for path planning and human–machine interaction in autonomous platforms. By prioritizing uncertainty quantification and transferability, the approach offers a robust, deployment-friendly alternative to more resource-intensive or purely accuracy-focused HTP methods, with open-source code for broader adoption.

Abstract

Autonomous systems, like vehicles or robots, require reliable, accurate, fast, resource-efficient, scalable, and low-latency trajectory predictions to get initial knowledge about future locations and movements of surrounding objects for safe human-machine interaction. Furthermore, they need to know the uncertainty of the predictions for risk assessment to provide safe path planning. This paper presents a lightweight method to address these requirements, combining Long Short-Term Memory and Mixture Density Networks. Our method predicts probability distributions, including confidence level estimations for positional uncertainty to support subsequent risk management applications and runs on a low-power embedded platform. We discuss essential requirements for human trajectory prediction in autonomous vehicle applications and demonstrate our method's performance using multiple traffic-related datasets. Furthermore, we explain reliability and sharpness metrics and show how important they are to guarantee the correctness and robustness of a model's predictions and uncertainty assessments. These essential evaluations have so far received little attention for no good reason. Our approach focuses entirely on real-world applicability. Verifying prediction uncertainties and a model's reliability are central to autonomous real-world applications. Our framework and code are available at: https://github.com/kav-institute/mdn_trajectory_forecasting.

Figures (5)

• Figure 1: Network architecture. We use a stacked LSTM for dynamic input horizon handling and a bivariate Mixture Density Head for the probabilistic predictions.
• Figure 2: Confidence level $1-\alpha(\hbox{\boldmath$p$})$ (black curve) of $\hbox{\boldmath$p$}$ (orange dot), with $N$ random samples $\hbox{\boldmath$z$}\in \mathbf{Z}$ with $\mathcal{D}(\hbox{\boldmath$z$})\geq\mathcal{D}(\hbox{\boldmath$p$})$ as green, and $\mathcal{D}(\hbox{\boldmath$z$})<\mathcal{D}(\hbox{\boldmath$p$})$ as blue markers.
• Figure 3: Calibration plots for reliability and usability check. Curves for predictions at ${t+0.8s}$ (blue), at ${t+1.6s}$ (orange), at ${t+2.4s}$ (green), at ${t+3.2s}$ (red), at ${t+4.0s}$ (purple), at ${t+4.8s}$ (brown) and ideal behavior (black dashed line). The horizontal axis is the expected CL, and the vertical axis is the observed frequency of CLs.
• Figure 4: Example results for the IMPTC dataset. Past input trajectory (red), ground truth (black line), predicted CLs at $t{+1s}$ (blue area), $t{+2s}$ (orange area), and $t{+3s}$ (green area). Inner contours represent the 68 %, and outer contours the 95 % CL.
• Figure 5: Reliability calibration plots for method comparison using ETH/UCY dataset. Colors and axis are equal to \ref{['fig:overall_reliability_plots']}. Upper row show ETH subtest, lower row is Univ subtest.