# Vertical Force Monitoring of Racing Tires: A Novel Deep Neural Network-Based Estimation Method
## 2 Related Works
### Observer and Filter-Based Estimation of Vertical Force
In [14], the contact angle between the tire and the road surface is calculated using an intelligent tire and is subsequently employed for tire load estimation.The vertical force estimation method described in this study demonstrates certain limitations that could affect its effectiveness in real-world applications. The simplified vehicle model used does not account for factors like air resistance or road surface irregularities, which could restrict its applicability in more complex environments. While dynamic load estimation has been validated against a vehicle dynamics model, further verification using direct measurements with wheel force transducers would strengthen its reliability. Additionally, reliance on geometric assumptions may reduce its accuracy on inclined or uneven road surfaces. Research by [15] proposes a method for estimating vertical load by deriving peak radial displacement from the radial acceleration signal. While effective within the tested conditions, this approach exhibits certain limitations. The integration process for the acceleration signal can introduce errors, including drift, which necessitates mitigation through high-pass filtering. Furthermore, the method assumes a linear relationship between peak radial displacement and load, but this assumption holds only within specific pressure and load ranges, potentially restricting its applicability to broader or more variable operating conditions. [PERSON] et al. [16] propose an innovative observer for estimating one-sided lateral load transfer employing a linear Kalman filter. The estimated lateral load transfer, along with longitudinal acceleration measurements, is utilized for estimating vertical forces.The vertical force estimation method utilizes suspension deflection measurements to calculate the roll angle, which serves as a key component in determining the tire load distribution. While effective in controlled scenarios, the method presents some practical challenges. Suspension deflection measurements require precise sensors on each wheel, which can increase the complexity and cost of the system. Additionally, the accuracy of the estimations may be affected by sensor calibration issues or drift over time. The approach assumes linear roll dynamics and a fixed roll center position, which might not fully capture the complexities of real-world conditions, such as high-speed maneuvers or uneven road surfaces. Furthermore, factors like road surface variations, tire wear, and temperature changes are not explicitly accounted for, which could impact the model's performance in diverse environments. In [17], an empirical model is developed and comprises a basic shape function for acceleration and relationships that connect the parameters of this function to tire conditions. Furthermore, a model-based estimator is designed for vertical force using this model, which consists of a peak synchronization algorithm and an extended Kalman filter. An increase in the complexity of vehicle or tire models does not necessarily translate to proportional improvements in prediction accuracy, and there are certain errors and uncertainties in the prediction of the tire force based on the signals collected by on-board sensors [1]. While increasing model complexity aims to capture the intricate dynamics of tire forces, it also introduces significant challenges in terms of parameter tunability and practical implementation. Complex models require highly accurate parameter estimation, which is often impractical due to variations in vehicle dynamics, road conditions, and tire wear. Additionally, the reliance on a larger number of sensors to improve model accuracy further escalates system costs and increases the likelihood of sensor malfunctions or failures. These limitations highlight the inherent trade-offs in traditional model-based approaches, where greater complexity does not necessarily lead to better performance, but instead adds layers of calibration difficulties and operational risks.