## 2 Sensors and Test Methods
### Equipped Sensors  
The input channels for the neural network are obtained from various sensors properly mounted on the reference vehicle. For what concerns the steering angle and the wheels' speed of the four corners, these are acquired from the vehicle CAN-bus [43]. A controller area network (CAN-bus) is a standardized vehicle communication network, developed to facilitate communication between microcontrollers and a variety of sensors, all without the dependency on a central host computer [44; 45]. It employs a message-based protocol consisting of four frame types: Data, Remote, Error, and Overload. The Data frame is the only one for actual data transmission. Each device transmits data serially, and if multiple devices attempt to transmit simultaneously, the highest priority device continues while others yield. The CAN-bus is then essential because it enables communication among the various instruments mounted on the vehicle for data acquisition and provides crucial data for this research activity. Differently, the acquisition of the yaw rate and both lateral and longitudinal accelerations is achieved with an inertial platform (depicted in Figure 2a). A sensor module comprising three accelerometers and three gyroscope units, functioning as angular rate sensors, is employed to calculate all resultant outputs. It is based on mathematical algorithms used to make precise real-time measurements of motion. Utilizing the Global Navigation Satellite System (GNSS), the instrument has the capacity to rectify all recorded parameters, thereby ensuring the accurate assessment of metrics such as accelerations, roll, pitch, and yaw. All of the data are processed in real time, time-stamped, and synchronized with GPS time. This information is transmitted over the CAN-bus and can be viewed in real time on a laptop using specialized software. To determine the longitudinal velocity and the reference sideslip angle for training the artificial neural network, an optical sensor is employed (depicted in Figure 2b). This instrument, utilizing Correvit technology, is valuable for directly measuring vehicle velocity and its components through non-contact measurements. A built-in GPS receiver enables the acquisition of position and speed data, while integrated accelerometers allow for the detection of the vehicle's longitudinal and transverse accelerations. Additionally, integrated angular rate sensors measure pitch and roll angles, as well as the rotation around the vehicle's vertical axis. Furthermore, the sensor also calculates additional signals such as leveled acceleration and curve radius. A schematic representation that summarizes the associated instruments for the various neural network inputs is presented in Table 2.  
The described sensors are all linked through an external data acquisition system with the ability to collect a range of signal types and ensure their proper synchronization. In the motorsport field, the use of optical sensors on vehicles during races and official test sessions is constrained by specific regulations. This restriction leads to less information  
Figure 2: Equipped sensors. (**a**) Inertial platform. (**b**) Optical sensor. that is useful to improve the overall vehicle performance. Additionally, it is essential to note that the sensors presented are both expensive and delicate, making them impractical for installation on all vehicles. Hence, the proposed methodology, which relies on neural networks for estimating the sideslip angle, offers an effective solution for overcoming the challenges associated with sensor equipment. In particular, with regard to the input related to longitudinal velocity, this paper presents two cases: the first case uses the value from the optical sensor as input, while the second case employs the estimation of longitudinal velocity based on the procedure presented in [42].