# Uncertainty estimation of pedestrian future trajectory using Bayesian approximation

arXiv: https://arxiv.org/abs/2205.01887 · HTML: https://mlsanity.com/paper/2205.01887/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 4 May 2022.

## Builds on (most cited first, 16 of 16)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks](https://mlsanity.com/paper/1907.03395/) (2019)
- [The inD Dataset: A Drone Dataset of Naturalistic Road User Trajectories at German Intersections](https://mlsanity.com/paper/1911.07602/) (2019)
- [Uncertainty-Aware Reinforcement Learning for Collision Avoidance](https://mlsanity.com/paper/1702.01182/) (2017)
- [An LSTM Network for Highway Trajectory Prediction](https://mlsanity.com/paper/1801.07962/) (2018)
- [Probabilistic Vehicle Trajectory Prediction over Occupancy Grid Map via Recurrent Neural Network](https://mlsanity.com/paper/1704.07049/) (2017)
- [Sequence-to-Sequence Prediction of Vehicle Trajectory via LSTM Encoder-Decoder Architecture](https://mlsanity.com/paper/1802.06338/) (2018)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Scene-LSTM: A Model for Human Trajectory Prediction](https://mlsanity.com/paper/1808.04018/) (2018)
- [Pedestrian Trajectory Prediction with Convolutional Neural Networks](https://mlsanity.com/paper/2010.05796/) (2020)
- [Convolutional Neural Network for Trajectory Prediction](https://mlsanity.com/paper/1809.00696/) (2018)
- [A Quality Index Metric and Method for Online Self-Assessment of Autonomous Vehicles Sensory Perception](https://mlsanity.com/paper/2203.02588/) (2022)
- [Attention-based Neural Network for Driving Environment Complexity Perception](https://mlsanity.com/paper/2106.11277/) (2021)

## Built on by (most cited first, 12 of 12)

- [V2XP-ASG: Generating Adversarial Scenes for Vehicle-to-Everything Perception](https://mlsanity.com/paper/2209.13679/) (2022)
- [Bridging the Gap Between Multi-Step and One-Shot Trajectory Prediction via Self-Supervision](https://mlsanity.com/paper/2306.03367/) (2023)
- [Hypergraph-Transformer (HGT) for Interactive Event Prediction in Laparoscopic and Robotic Surgery](https://mlsanity.com/paper/2402.01974/) (2024)
- [Motion Forecasting via Model-Based Risk Minimization](https://mlsanity.com/paper/2409.10585/) (2024)
- [Pedestrian Trajectory Forecasting Using Deep Ensembles Under Sensing Uncertainty](https://mlsanity.com/paper/2305.16620/) (2023)
- [Multi-scale Temporal Fusion Transformer for Incomplete Vehicle Trajectory Prediction](https://mlsanity.com/paper/2409.00904/) (2024)
- [MSTF: Multiscale Transformer for Incomplete Trajectory Prediction](https://mlsanity.com/paper/2407.05671/) (2024)
- [DD-MDN: Human Trajectory Forecasting with Diffusion-Based Dual Mixture Density Networks and Uncertainty Self-Calibration](https://mlsanity.com/paper/2602.11214/) (2026)
- [Leveraging Multi-stream Information Fusion for Trajectory Prediction in Low-illumination Scenarios: A Multi-channel Graph Convolutional Approach](https://mlsanity.com/paper/2211.10226/) (2022)
- [Cooperative Probabilistic Trajectory Forecasting under Occlusion](https://mlsanity.com/paper/2312.03296/) (2023)
- [Adaptive Multi-Mode Out-of-Distribution Detection for Trajectory Prediction in Autonomous Vehicles](https://mlsanity.com/paper/2509.13577/) (2025)
- [Uncertainty-Aware Adaptive Sensor Fusion for Autonomous Navigation](https://mlsanity.com/paper/2606.05437/) (2026)

## Abstract (arXiv)

Past research on pedestrian trajectory forecasting mainly focused on deterministic predictions which provide only point estimates of future states. These future estimates can help an autonomous vehicle plan its trajectory and avoid collision. However, under dynamic traffic scenarios, planning based on deterministic predictions is not trustworthy. Rather, estimating the uncertainty associated with the predicted states with a certain level of confidence can lead to robust path planning. Hence, the authors propose to quantify this uncertainty during forecasting using stochastic approximation which deterministic approaches fail to capture. The current method is simple and applies Bayesian approximation during inference to standard neural network architectures for estimating uncertainty. The authors compared the predictions between the probabilistic neural network (NN) models with the standard deterministic models. The results indicate that the mean predicted path of probabilistic models was closer to the ground truth when compared with the deterministic prediction. Further, the effect of stochastic dropout of weights and long-term prediction on future state uncertainty has been studied. It was found that the probabilistic models produced better performance metrics like average displacement error (ADE) and final displacement error (FDE). Finally, the study has been extended to multiple datasets providing a comprehensive comparison for each model.