## 1 Introduction  
Over the years, car safety tech and crash prevention systems have improved a lot, and this has made active safety tech even better at stopping car accidents [1]. Efforts to reduce traffic jams and boost overall traffic efficiency have also increased [2]. Through complete digitization, the vehicles and all the elements related to the transportation system are evolving into sophisticated, interconnected complex-networked mobile computers. In particular, this aspect includes various networked microprocessor-based electronic control units (ECU) that enhance their functions and serve as a foundation for continuous control [3, 4]. Notably, the real-time estimation of data regarding the changes in vehicle's velocity components plays a vital role in three key areas:  
* Driving assistance systems;* Autonomous driving;
* The motorsport field. For what concerns the driving assistance systems, the increasing level of vehicle dependence on software has made complex control systems essential for modern vehicle development. Advanced safety systems, such as the anti-lock braking system (ABS), traction control system (TCS), and stability control systems, have become common features in modern vehicles [5; 6]. To guarantee the optimal performance of these vehicle control systems, it is crucial that all the data collected from on-board instruments, combined with insights from predictive models, maintain a high level of quality [7; 8; 9; 10; 11; 12; 13]. An accurate estimation of the vehicle longitudinal speed [14], combined with the estimation of the sideslip angle, is crucial for the design and implementation of safety-related control integrated systems. Indeed, the knowledge of the mentioned quantities can be useful for emergency braking, by enabling systems to detect potential collisions and respond promptly; for traction control, by controlling wheel spin, maintaining grip on the road, especially in adverse conditions; and for stability control, for preventing skidding and maintaining control during aggressive maneuvers. The estimation of a vehicle's longitudinal velocity and sideslip angle is a crucial topic also in the autonomous driving field [15]. Indeed, it allows autonomous vehicles to continuously monitor their velocity and direction to adapt both of them appropriately to road conditions. Moreover, thanks to these quantities, the vehicle is able to predict the trajectories, maintaining stability during turns and thereby enhancing overall safety. Another field of interest for the estimation of a vehicle's longitudinal velocity and sideslip angle is motorsport. Indeed, accurately estimating tire dynamics requires reliable knowledge of the longitudinal velocity and sideslip angle to determine slip indices [16]. In addition, these quantities are really useful for selecting the best vehicle setup to ensure the proper use of tires during races. For this aspect, it is also essential to characterize the tires from both a mechanical and thermal point of view [17; 18; 19], and this is related to the evaluation of the forces acting on the tires and the optimal thermal window of the same. In this way, it is possible to understand how to maximize the best overall vehicle performance, taking into account the tire/road interaction phenomena. The sideslip angle estimation can be also useful to predict when the vehicle is going to saturate the tires and lose directional stability [20], allowing for easy identification of understeer and oversteer conditions [21]. In particular, the estimation of the sideslip angle can be combined with sideslip control, particularly in high-performance and sports driving scenarios. This approach is designed to maintain the vehicle's sideslip angle within a specific range by employing various controls [22; 23; 24]. Given the significant relationship between the sideslip angle and the tire's operating conditions, it plays a critical role as an input for estimating the maximum friction coefficient between the tire's contact patch and the road surface [25; 26; 27].