# Estimating Traffic Speeds using Probe Data: A Deep Neural Network Approach

arXiv: https://arxiv.org/abs/2104.09686 · HTML: https://mlsanity.com/paper/2104.09686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 70 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
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- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Learning Traffic as Images: A Deep Convolutional Neural Network for Large-Scale Transportation Network Speed Prediction](https://mlsanity.com/paper/1701.04245/) (2017)
- [Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications](https://mlsanity.com/paper/2002.02374/) (2020)
- [Incorporating Kinematic Wave Theory into a Deep Learning Method for High-Resolution Traffic Speed Estimation](https://mlsanity.com/paper/2102.02906/) (2021)
- [Learning-based Traffic State Reconstruction using Probe Vehicles](https://mlsanity.com/paper/2011.05031/) (2020)
- [Highway Traffic State Estimation with Mixed Connected and Conventional Vehicles](https://mlsanity.com/paper/1504.06879/) (2015)
- [Traffic Data Imputation using Deep Convolutional Neural Networks](https://mlsanity.com/paper/2002.04406/) (2020)

## Abstract (arXiv)

This paper presents a dedicated Deep Neural Network (DNN) architecture that reconstructs space-time traffic speeds on freeways given sparse data. The DNN is constructed in such a way, that it learns heterogeneous congestion patterns using a large dataset of sparse speed data, in particular from probe vehicles. Input to the DNN are two equally sized input matrices: one containing raw measurement data, and the other indicates the cells occupied with data. The DNN, comprising multiple stacked convolutional layers with an encoding-decoding structure and feed-forward paths, transforms the input into a full matrix of traffic speeds. The proposed DNN architecture is evaluated with respect to its ability to accurately reconstruct heterogeneous congestion patterns under varying input data sparsity. Therefore, a large set of empirical Floating-Car Data (FCD) collected on German freeway A9 during two months is utilized. In total, 43 congestion distinct scenarios are observed which comprise moving and stationary congestion patterns. A data augmentation technique is applied to generate input-output samples of the data, which makes the DNN shift-invariant as well as capable of managing varying data sparsities. The DNN is trained and subsequently applied to sparse data of an unseen congestion scenario. The results show that the DNN is able to apply learned patterns, and reconstructs moving as well as stationary congested traffic with high accuracy; even given highly sparse input data. Reconstructed speeds are compared qualitatively and quantitatively with the results of several state-of-the-art methods such as the Adaptive Smoothing Method (ASM), the Phase-Based Smoothing Method (PSM) and a standard Convolutional Neural Network (CNN) architecture. As a result, the DNN outperforms the other methods significantly.