# Longitudinal Velocity Estimation of Driverless Vehicle by Fusing LiDAR and Inertial Measurement Unit

^{*}

## Abstract

**:**

## 1. Introduction

- To address the issue of point cloud distortion during the motion of LiDAR, IMU is used to predict the pose changes of LiDAR to reduce the impact of motion distortion on odometry accuracy.
- Time-series analysis is introduced into the motion equation to predict the trend of longitudinal acceleration changes through multiple sets of IMU historical data, thereby improving the estimation accuracy of the filtering algorithm.

## 2. LiDAR-IMU Odometry

#### 2.1. Correction of Point Cloud Motion Distortion

#### 2.2. LiDAR Point Cloud Clustering

#### 2.3. Feature Extraction of Point Cloud

#### 2.4. Feature Matching of Point Cloud

#### 2.4.1. Edge Point Matching

#### 2.4.2. Planar Point Matching

#### 2.5. Pose Estimation

## 3. Fusion Method of LiDAR and IMU

#### 3.1. AUKF

#### 3.2. Longitudinal Acceleration Prediction

## 4. Simulation and Experimental Results

#### 4.1. Carla Simulation Experiment

#### 4.2. Real-Vehicle Experiment

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- He, H.W.; Peng, J.K.; Xiong, R.; Fan, H. An acceleration slip regulation strategy for four-wheel drive electric vehicles based on sliding mode control. Energies
**2014**, 7, 3748–3763. [Google Scholar] [CrossRef] [Green Version] - Zhao, B.; Xu, N.; Chen, H.; Guo, K.; Huang, Y. Stability control of electric vehicles with in-wheel motors by considering tire slip energy. Mech. Syst. Sig. Process.
**2019**, 118, 340–359. [Google Scholar] [CrossRef] - Arnold, E.; Al-Jarrah, O.; Dianati, M.; Fallah, S.; Oxtoby, D.; Mouzakitis, A. A survey on 3D object detection methods for autonomous driving applications. IEEE Trans. Intell. Transp. Syst.
**2019**, 20, 3782–3795. [Google Scholar] [CrossRef] [Green Version] - Chen, W.; Tan, D.; Zhao, L. Vehicle sideslip angle and road friction estimation using online gradient descent algorithm. IEEE Trans. Veh. Technol.
**2018**, 67, 11475–11485. [Google Scholar] [CrossRef] - Napolitano Dell’Annunziata, G.; Arricale, V.M.; Farroni, F.; Genovese, A.; Pasquino, N.; Tranquillo, G. Estimation of Vehicle Longitudinal Velocity with Artificial Neural Network. Sensors
**2022**, 22, 9516. [Google Scholar] [CrossRef] [PubMed] - Karlsson, R.; Hendeby, G. Speed Estimation From Vibrations Using a Deep Learning CNN Approach. IEEE Sens. Lett.
**2021**, 5, 1–4. [Google Scholar] [CrossRef] - Zhang, D.; Song, Q.; Wang, G.; Liu, C. A Novel Longitudinal Speed Estimator for Four-Wheel Slip in Snowy Conditions. Appl. Sci.
**2021**, 11, 2809. [Google Scholar] [CrossRef] - Xin, X.S.; Chen, J.X.; Zou, J.X. Vehicle state estimation using cubature Kalman filter. In Proceedings of the 2014 IEEE the 17th International Conference on Computational Science and Engineering, Chengdu, China, 19–21 December 2014; pp. 44–48. [Google Scholar]
- Antonov, S.; Fehn, A.; Kugi, A. Unscented Kalman filter for vehicle state estimation. Veh. Syst. Dyn.
**2011**, 49, 1497–1520. [Google Scholar] [CrossRef] - Li, J.; Zhang, J.X. Vehicle sideslip angle estimation based on hybrid Kalman filter. Math. Probl. Eng.
**2016**, 3269142, 1–10. [Google Scholar] [CrossRef] [Green Version] - Xiong, L.; Xia, X.; Lu, Y.; Liu, W.; Gao, L.; Song, S.; Han, Y.; Yu, Z. IMU-Based Automated Vehicle Slip Angle and Attitude Estimation Aided by Vehicle Dynamics. Sensors
**2019**, 19, 1930. [Google Scholar] [CrossRef] [Green Version] - Wang, Y.; Li, Y.; Zhao, Z. State Parameter Estimation of Intelligent Vehicles Based on an Adaptive Unscented Kalman Filter. Electronics
**2023**, 12, 1500. [Google Scholar] [CrossRef] - van Zanten, A.T. Bosch ESP system: 5 years of experience. SAE Trans.
**2000**, 109, 428–436. [Google Scholar] - Du, H.P.; Li, W.H. Kinematics-based parameter-varying observer design for sideslip angle estimation. In Proceedings of the 2014 International Conference on Mechatronics and Control, Jinzhou, China, 3–5 July 2014; pp. 2042–2047. [Google Scholar]
- Madhusudhanan, A.K.; Corno, M.; Holweg, E. Vehicle sideslip estimation using tyre force measurements. In Proceedings of the 2015 the 23rd Mediterranean Conference on Control and Automation, Torremolinos, Spain, 16–19 June 2015; pp. 88–93. [Google Scholar]
- Rezaeian, A.; Khajepour, A.; Melek, W.; Chen, S.K.; Moshchuk, N. Simultaneous Vehicle Real-Time Longitudinal and Lateral Velocity Estimation. IEEE Trans. Veh. Technol.
**2017**, 66, 1950–1962. [Google Scholar] [CrossRef] - Pi, D.W.; Chen, N.; Wang, J.X.; Zhang, B.J. Design and evaluation of sideslip angle observer for vehicle stability control. Int. J. Automot. Technol.
**2011**, 12, 391–399. [Google Scholar] [CrossRef] - Li, X.; Chan, C.Y.; Wang, Y. A reliable fusion methodology for simultaneous estimation of vehicle sideslip and yaw angles. IEEE Trans. Veh. Technol.
**2016**, 65, 4440–4458. [Google Scholar] [CrossRef] - Farrell, J.A.; Tan, H.S.; Yang, Y. Carrier phase gps-aided ins-based vehicle lateral control. J. Dyn. Syst. Meas. Control
**2003**, 125, 339–353. [Google Scholar] [CrossRef] - Yoon, J.H.; Peng, H. A cost-effective sideslip estimation method using velocity measurements from two gps receivers. IEEE Trans. Veh. Technol.
**2014**, 63, 2589–2599. [Google Scholar] [CrossRef] - Song, R.; Fang, Y. Vehicle state estimation for INS/GPS aided by sensors fusion and SCKF-based algorithm. Mech. Syst. Signal Process.
**2021**, 107315, 0888–3270. [Google Scholar] [CrossRef] - Gao, L.; Ma, F.; Jin, C. A Model-Based Method for Estimating the Attitude of Underground Articulated Vehicles. Sensors
**2019**, 19, 5245. [Google Scholar] [CrossRef] [Green Version] - Talebi, S.P.; Godsill, S.J.; Mandic, D.P. Filtering Structures for α-Stable Systems. IEEE Control Syst. Lett.
**2023**, 7, 553–558. [Google Scholar] [CrossRef] - Lv, J.; He, H.; Liu, W.; Chen, Y.; Sun, F. Vehicle Velocity Estimation Fusion with Kinematic Integral and Empirical Correction on Multi-Timescales. Energies
**2019**, 12, 1242. [Google Scholar] [CrossRef] [Green Version] - Wang, X.; You, Z.; Zhao, K. Inertial/celestial-based fuzzy adaptive unscented Kalman filter with Covariance Intersection algorithm for satellite attitude determination. Aerosp. Sci. Technol.
**2016**, 48, 214–222. [Google Scholar] [CrossRef]

**Figure 2.**The principle of motion distortion generation: (

**a**) LiDAR scanning starting point; (

**b**) LiDAR motion process; (

**c**) Point cloud distortion caused by motion.

**Figure 3.**The comparison of motion distortion removal: (

**a**) The point cloud of the same laser beam in the red box cannot be aligned before removing motion distortion; (

**b**) Aligning point cloud of the same laser beam after distortion removal.

**Figure 5.**Edge point feature matching: (

**a**) Edge feature point set at time ${t}_{k}$; (

**b**) Edge feature point set at time ${t}_{k+1}$.

**Figure 6.**Planar point feature matching; (

**a**) Planar feature point set at time ${t}_{k}$; (

**b**) Planar feature point set at time ${t}_{k+1}$.

Equipment | Model |
---|---|

CPU | I7–7700HQ |

GPU | GTX 1050Ti |

Scenario (Velocity) | LiDAR-IMU Odometry | AUKF | TSA-AUKF |
---|---|---|---|

0–15 m/s | 1.828 | 2.597 | 1.149 |

0–30 m/s | 4.708 | 3.201 | 1.573 |

Sensor | Quantity | Performance |
---|---|---|

Gyroscopes | Bias stability | 4 $\mathrm{deg}/\mathrm{hr}$ |

Angular random walk | 0.12 $\mathrm{deg}/\surd \mathrm{hr}$ | |

Accelerometers | Bias stability | 25 $\mathrm{ug}$ |

Velocity random walk | 0.045 $\mathrm{m}/\mathrm{s}/\surd \mathrm{hr}$ |

^{2}, deg = degree, u = $1.0\times {10}^{-6}$, m = meter.

LiDAR-IMU Odometry | GPS-IMU | TSA-AUKF |
---|---|---|

0.279 | 0.158 | 0.113 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, C.; Guo, Z.; Dang, M.
Longitudinal Velocity Estimation of Driverless Vehicle by Fusing LiDAR and Inertial Measurement Unit. *World Electr. Veh. J.* **2023**, *14*, 175.
https://doi.org/10.3390/wevj14070175

**AMA Style**

Zhang C, Guo Z, Dang M.
Longitudinal Velocity Estimation of Driverless Vehicle by Fusing LiDAR and Inertial Measurement Unit. *World Electric Vehicle Journal*. 2023; 14(7):175.
https://doi.org/10.3390/wevj14070175

**Chicago/Turabian Style**

Zhang, Chuanwei, Zhongyu Guo, and Meng Dang.
2023. "Longitudinal Velocity Estimation of Driverless Vehicle by Fusing LiDAR and Inertial Measurement Unit" *World Electric Vehicle Journal* 14, no. 7: 175.
https://doi.org/10.3390/wevj14070175