# Vehicle Lateral Velocity Estimation Based on Long Short-Term Memory Network

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## Abstract

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## 1. Introduction

- Proposing a method of estimating vehicle lateral velocity based on LSTM using the most common sensor measurements in mass production vehicles.
- Testing on roads with different road friction coefficients. The results show that the proposed method is robust to the change of road friction coefficient.
- Collecting a data set from multiple measurement data under generally standard working conditions rather than verification working conditions. The verification results show that training set can well reflect vehicle characteristics.

## 2. Related Work

#### 2.1. Model Based Approach

#### 2.2. Neural Network Based Approach

## 3. Method

#### 3.1. Preliminary: LSTM Neural Network

#### 3.2. Definition of Lateral Velocity Estimation Problem

#### 3.3. Lateral Velocity Estimation Model

#### 3.3.1. Sensor Input Layer

#### 3.3.2. LSTM Layer

#### 3.3.3. Fully Connected Layer

#### 3.4. Model Training

#### 3.4.1. Data Set

#### 3.4.2. Hyperparameters Tuning

## 4. Verification and Discussion

#### 4.1. Results

#### 4.1.1. DLC at 30 km/h

#### 4.1.2. DLC at 50 km/h

#### 4.1.3. DLC at 70 km/h

#### 4.1.4. Comparison of the Results

#### 4.2. Quantitative Analysed Metrics

#### 4.3. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Estimation Results under 30 km/h DLC condition: (

**a**) road friction coefficient of 0.3; (

**b**) road friction coefficient of 0.5; (

**c**) road friction coefficient of 0.85; (

**d**) road friction coefficient of 1.0.

**Figure 7.**Estimation Results under 50 km/h DLC condition: (

**a**) road friction coefficient of 0.3; (

**b**) road friction coefficient of 0.5; (

**c**) road friction coefficient of 0.85; (

**d**) road friction coefficient of 1.0.

**Figure 8.**Estimation Results under 70 km/h DLC condition: (

**a**) road friction coefficient of 0.3; (

**b**) road friction coefficient of 0.5; (

**c**) road friction coefficient of 0.85; (

**d**) road friction coefficient of 1.0.

Sensor | Symbol | Unit |
---|---|---|

Steering wheel angle | $\delta $ | deg |

Throttle opening | $\alpha $ | % |

Engine speed | ${n}_{e}$ | rpm |

Gear | $G$ | - |

Left front wheel speed | ${\omega}_{fl}$ | rpm |

Right front wheel speed | ${\omega}_{fr}$ | rpm |

Left rear wheel speed | ${\omega}_{rl}$ | rpm |

Right rear wheel speed | ${\omega}_{rr}$ | rpm |

Longitudinal acceleration | ${a}_{x}$ | g |

Lateral acceleration | ${a}_{y}$ | g |

Yaw rate | $r$ | deg/s |

Longitudinal speed | ${V}_{x}$ | km/h |

Category | Parameter | Value |
---|---|---|

LSTM Layer | Hidden Layers | 1 |

Hidden Units | 128 | |

Full connection layer | Hidden Layers | 1 |

Hidden Units | 64 | |

Output Layer Units | 1 | |

Overall Architecture | Input Sequence length | 5 |

Number of Parameters | 80,513 | |

Activation Function | Relu | |

Training Process | Batch Size | 32 |

Initial Value of Learning Rate | 0.001 | |

Early Stop Patience Value | 5 | |

Training Algorithm | Gradient Attenuation Factor | 0.9 |

Square Gradient Attenuation Factor | 0.99 | |

Bias Term | 1 × 10^{−8} |

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## Share and Cite

**MDPI and ACS Style**

Kong, D.; Wen, W.; Zhao, R.; Lv, Z.; Liu, K.; Liu, Y.; Gao, Z.
Vehicle Lateral Velocity Estimation Based on Long Short-Term Memory Network. *World Electr. Veh. J.* **2022**, *13*, 1.
https://doi.org/10.3390/wevj13010001

**AMA Style**

Kong D, Wen W, Zhao R, Lv Z, Liu K, Liu Y, Gao Z.
Vehicle Lateral Velocity Estimation Based on Long Short-Term Memory Network. *World Electric Vehicle Journal*. 2022; 13(1):1.
https://doi.org/10.3390/wevj13010001

**Chicago/Turabian Style**

Kong, Debao, Wenhao Wen, Rui Zhao, Zheng Lv, Kewang Liu, Yujie Liu, and Zhenhai Gao.
2022. "Vehicle Lateral Velocity Estimation Based on Long Short-Term Memory Network" *World Electric Vehicle Journal* 13, no. 1: 1.
https://doi.org/10.3390/wevj13010001