# Practical Modeling of GNSS for Autonomous Vehicles in Urban Environments

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## Abstract

**:**

## 1. Introduction

## 2. Integration of Odometry and GNSS

#### 2.1. Extended Kalman Filter (EKF)

#### 2.2. The Conventional Odometry Motion Model

#### 2.3. Improved Odometry Motion Model for Vehicles

## 3. Improved GNSS Sensor Model

## 4. Experimental Results

#### 4.1. Experimental Setup

#### 4.2. Motion Model Construction

#### 4.2.1. Calibration of Wheel Diameter Through Straight Driving

#### 4.2.2. Wheelbase Calibration Through Circular Driving

#### 4.2.3. Non-Systematic Error Parameter Estimation

#### 4.2.4. Motion Model Verification Experiment

#### 4.3. Sensor Model Construction

#### 4.3.1. RE Measurement

#### 4.3.2. ASE Measurement

#### 4.3.3. LCE Measurement

#### 4.3.4. GNSS Sensor Model Verification

#### 4.4. EKF Localization Using the Proposed Models

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

GNSS | Global navigation space system |

RTK | Real-time kinematic |

NTRIP | Networked transport of RTCM via internet protocol |

LIDAR | Light detection and ranging |

RE | Ranging error |

ASE | Atmospheric effect and Satellite-oriented error |

LCE | Local characteristic error |

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**Figure 3.**Experimental platform: Santa Fe DM 2.0 2WD with an Autonics E40HB wheel encoder, Novatel Propak-V3, and SICK LMS111. Note: GNSS = global navigation satellite system; LRF = laser range finder.

**Figure 4.**Comparison of the straight driving paths before and after wheel diameter error calibration.

**Figure 5.**Result for the circular path before and after calibration. Comparison of circular path results: (

**a**) counterclockwise (CCW); (

**b**) clockwise (CW).

**Figure 6.**Comparison of the circular driving paths before and after wheel diameter and wheelbase calibration.

**Figure 7.**Driving environment in an urban environment with multipath effect that interferes with GNSS satellite signals due to high buildings.

**Figure 8.**(

**a**) GNSS measurement data measured in 9 driving tasks. (

**b**) Results of the local characteristic error map generation.

**Figure 9.**Comparison of the estimated error between the proposed method (blue line) and the conventional method (green line).

**Figure 10.**Comparison of the Extended Kalman filter (EKF) localization results of the proposed and conventional methods.

Test Run | |||
---|---|---|---|

Straight | CCW | CW | |

${k}_{l}$ | 0.0047 | 0.0279 | 0.0141 |

${k}_{r}$ | 0.0048 | 0.0176 | 0.0292 |

State | ASE (state) |
---|---|

None | 0.89 m |

Float Solution | 0.69 m |

Integer RTK | 0.00 m |

RMS between Measurement Error and Estimated Error $\left(2\mathsf{\sigma}\right)$ | Number of Epochs in the $2\mathsf{\sigma}$ Ellipse | |
---|---|---|

Proposed | 0.42 m | 97.6% |

Conventional | 1.08 m | 72.8% |

Error | Conventional Model | Proposed Model | Difference |
---|---|---|---|

Experiment place 1 | |||

Position | |||

Avg. | 28.5 m | 4.9 m | 96.50% |

Max. | 56.7 m | 8.5 m | |

Experiment place 2 | |||

Position | |||

Avg. | 4.4 m | 3.6 m | 18.20% |

Max. | 15.4 m | 10.6 m | |

Experiment place 3 | |||

Position | |||

Avg. | 7.0 m | 5.3 m | 24.30% |

Max. | 56.2 m | 14.0 m |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lee, W.; Cho, H.; Hyeong, S.; Chung, W.
Practical Modeling of GNSS for Autonomous Vehicles in Urban Environments. *Sensors* **2019**, *19*, 4236.
https://doi.org/10.3390/s19194236

**AMA Style**

Lee W, Cho H, Hyeong S, Chung W.
Practical Modeling of GNSS for Autonomous Vehicles in Urban Environments. *Sensors*. 2019; 19(19):4236.
https://doi.org/10.3390/s19194236

**Chicago/Turabian Style**

Lee, Woosik, Hyojoo Cho, Seungho Hyeong, and Woojin Chung.
2019. "Practical Modeling of GNSS for Autonomous Vehicles in Urban Environments" *Sensors* 19, no. 19: 4236.
https://doi.org/10.3390/s19194236