# Reliable Estimation of Urban Link Travel Time Using Multi-Sensor Data Fusion

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## Abstract

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## 1. Introduction

## 2. Link Travel Time Extraction Algorithms Based on Single-Sensor Traffic Data

#### 2.1. Travel Time Extraction from License Plate Recognition Data

#### 2.2. Travel Time Extraction from Geomagnetic Detector Data

_{i}, v

_{j}) in free flow state; ${q}_{ij,GDD}^{t}$ is the actual traffic flow of observed link $({v}_{i},{v}_{j})$ obtained from the GDD at the timestep t; c

_{ij}is the capacity of observed link $({v}_{i},{v}_{j})$; $\alpha $ and $\beta $ are impedance parameters. The BPR function shows three important relationship characteristics: (i) the link travel time is close to the free-flow travel time when actual traffic flow is small enough; (ii) the link travel time varies slowly and is proportional to traffic flow when actual flow is far less than the link capacity; (iii) the link travel time increases rapidly with the change of traffic flow when actual flow approaches or exceeds capacity. Unlike the highway environment, there are signal controls in urban road networks. As traffic congestion is increasingly heavier, urban link travel time will not get continuous growth. This means that when traffic flow exceeds the capacity and road link reaches the certain congested level, the flow begins to decrease and the travel time increases to a stable high value. So, the BPR function model cannot be directly applied to urban roads, and the uniformly calibrated BPR model achieves poor estimation in the congested state. In view of this, the BPR model is calibrated by differentiating traffic conditions, so as to make better use of the GDD to estimate urban link travel time [29]. This paper considers the product of traffic flow and occupancy rate from the GDD as road traffic state index. The specific calculation formula is as follows:

#### 2.3. Travel Time Extraction from Floating Car Data

## 3. Urban Link Travel Time Estimation Method Using Multi-Sensor Data Fusion

#### 3.1. Support Degree Algorithm of Multi-Sensor Traffic Data

_{t}is obtained by:

#### 3.2. Credibility Algorithm of Multi-Sensor Traffic Data

#### 3.3. Reliable Fusion of Average Link Travel Time

## 4. Case Study and Results

#### 4.1. Distribution Fitting of Average Link Travel Time Series

#### 4.2. Analysis of Case Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Probability histogram and probability density function (PDF) curve of average travel time based on license plate recognition (LPR) data.

**Figure 5.**Probability histogram and PDF curve of average travel time based on geomagnetic detector data (GDD).

**Figure 6.**Probability histogram and PDF curve of average travel time based on floating car data (FCD).

**Table 1.**Parameters and goodness of fit test results of three average link travel time distributions.

Traffic Sensor Data | Distribution Parameter | Kolmogorov–Smirnov Test | |||
---|---|---|---|---|---|

Mean μ_{α} | Standard Deviation δ_{α} | Test Statistics | Critical Value at 0.05 Significance Level | Result | |

LPR | 4.5276 | 0.5612 | 0.0823 | 0.1388 | Accepted |

GDD | 4.6254 | 0.5561 | 0.1206 | 0.1388 | Accepted |

FCD | 4.6923 | 0.6410 | 0.0873 | 0.1388 | Accepted |

Methods | MAPE/% | MAE | RMSE |
---|---|---|---|

GDD extraction method | 22.34 | 26.82 | 35.59 |

FCD extraction method | 27.43 | 31.37 | 44.72 |

LPR extraction method | 12.31 | 15.43 | 22.72 |

Weight distribution fusion method | 10.39 | 11.46 | 16.07 |

The proposed fusion method | 9.34 | 10.43 | 13.41 |

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**MDPI and ACS Style**

Guo, Y.; Yang, L.
Reliable Estimation of Urban Link Travel Time Using Multi-Sensor Data Fusion. *Information* **2020**, *11*, 267.
https://doi.org/10.3390/info11050267

**AMA Style**

Guo Y, Yang L.
Reliable Estimation of Urban Link Travel Time Using Multi-Sensor Data Fusion. *Information*. 2020; 11(5):267.
https://doi.org/10.3390/info11050267

**Chicago/Turabian Style**

Guo, Yajuan, and Licai Yang.
2020. "Reliable Estimation of Urban Link Travel Time Using Multi-Sensor Data Fusion" *Information* 11, no. 5: 267.
https://doi.org/10.3390/info11050267