# Estimation of Vehicle Longitudinal Velocity with Artificial Neural Network

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## Abstract

**:**

## 1. Introduction

## 2. Equipped Sensors and Acquired Channels

#### 2.1. Equipped Sensors

#### 2.2. Acquired Channels

- steering angle [deg];
- lateral acceleration [m/s
^{2}]; - longitudinal acceleration [m/s
^{2}]; - yaw rate [deg/s];
- wheels speed [m/s];
- vehicle longitudinal velocity [m/s].

## 3. A Feed-Forward Neural Network-Based Longitudinal Velocity Estimation System

#### 3.1. Input Data

- steering angle [deg];
- lateral acceleration [g];
- longitudinal acceleration [g];
- yaw rate [deg/s];
- wheels speed [km/h].

- vehicle longitudinal velocity [km/h].

#### 3.2. Data Scaling

#### 3.3. Preliminary Neural Network Design

#### 3.4. Rprop

#### 3.5. Analyzed Approaches

- All: Data from all laps and circuits are used to train and test the neural network. The system randomly selects the data to use for the training set while the remaining ones are used in the test set;
- Exclude: The neural network is trained with a set in which all data from a specific circuit or lap (either the first, intermediate or last one) are removed. These data are then used in the test set;
- Include: The neural network is trained with a set containing only data from a specific circuit or lap (either the first, intermediate or last one). These data are then excluded from the testing set.

#### 3.6. Models’ Evaluation

- AIC (Akaike information criterion): The AIC, evaluated on a given dataset, is an indicator of the relative quality of the developed statistical models. Obtained via a series of different models for the data target, the AIC estimates the quality of each model relative to each of the other models. Thus, the AIC provides a mean for model selection [53].
- BIC (Bayesian information criterion): In statistics, the BIC or Schwarz criterion is a criterion for model selection among a finite set of models which is based, in part, on the likelihood function, and it is closely related to the AIC [54].

## 4. Improvements in Velocity Estimation through a Recurrent Neural Network-Based System

#### Design of Recurrent Neural Network

## 5. Results

#### 5.1. Experimentation Results

- The “All” method shows a higher accuracy for each track because it involves a larger set of data, which includes data from all circuits, both for training and the testing phase;
- The “Exclude” circuit method shows a lower accuracy because, in such a case, the neural network is tested on a circuit not used for the testing phase so the different boundary conditions can alter the prediction;
- For each methodology, the highest error is registered for the artificial neural network configuration, which involved the rear wheels (i.e., driving wheels). This is caused by the highest value of slip being reached by the driving wheels, which allows the greatest accuracy. For the following considerations, a neural network that involved no-driving wheels has been considered.

#### 5.2. Feed-Forward ANN KPIs Comparisons

- By increasing the number of training samples after a certain value, the RMSE of the training phase increases as well due to an increase in the constraint condition numbers, which makes the training more difficult.
- Increasing the number of input samples produces an accuracy increment for the testing phase. It is important to notice that after a certain value of training samples, the RMSE of the testing phase reaches a horizontal asymptote.
- The AIC and BIC parameters have higher values for the “four wheels” configuration, which involves more parameters, in accordance with what has been reported previously. By increasing the number of training samples, the AIC and BIC increase as well due to the increment of the constraining condition.
- Concerning the RMSE results, in accordance with what has been reported in the previous analysis, the highest error is registered for the artificial neural networks’ configuration involving the rear wheels (i.e., driving wheels).

#### 5.3. Feed-Forward and Recurrent Neural Network Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/s22239516

**AMA Style**

Napolitano Dell’Annunziata G, Arricale VM, Farroni F, Genovese A, Pasquino N, Tranquillo G.
Estimation of Vehicle Longitudinal Velocity with Artificial Neural Network. *Sensors*. 2022; 22(23):9516.
https://doi.org/10.3390/s22239516

**Chicago/Turabian Style**

Napolitano Dell’Annunziata, Guido, Vincenzo Maria Arricale, Flavio Farroni, Andrea Genovese, Nicola Pasquino, and Giuseppe Tranquillo.
2022. "Estimation of Vehicle Longitudinal Velocity with Artificial Neural Network" *Sensors* 22, no. 23: 9516.
https://doi.org/10.3390/s22239516