# 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
The 3-DOF model incorporates roll dynamics and necessitates precise measurements of roll angle (\(\phi\)), roll rate (\(\phi\)), and lateral forces (\(F_{y}\)), as well as suspension stiffness and damping coefficients. Similarly, the lateral-longitudinal load transfer model depends on parameters such as wheel radius (\(R\)), vehicle width (\(B\)), and the height of the center of gravity (\(H\)), alongside lateral acceleration (\(a_{y}\)). While these models enhance the method's ability to capture dynamic effects, their reliance on detailed parameterization and accurate sensor measurements increases complexity. The study by [11] proposes an algorithm to estimate the dynamic components of vertical tire contact forces by measuring vehicle body acceleration and angular velocity at selected locations on a standard vehicle. This involves employing a Kalman filter with augmented tire forces in the system state vector.The vertical force estimation method employs simplified vehicle models, such as the half-car model, which are computationally efficient, but do not fully capture complex real-world dynamics, including suspension system interactions and detailed tire-road behavior. The method shows error rates under varying road roughness and vehicle speed conditions, which can limit its applicability across diverse scenarios. The use of body-mounted sensors restricts the precision of tire force estimation, as alternative sensing technologies, such as tire-mounted sensors, are not included. Additionally, the method adopts a random walk model for tire force evolution, which simplifies the estimation process, but does not incorporate physical relationships between time steps. The computational feasibility and real-time performance of the approach are not discussed in the study. Finally, the robustness of the Kalman filter to sensor noise and modeling errors is constrained by the method's design, potentially affecting its performance in practical applications. The research by [12] introduces new vehicle dynamics models for estimating vertical, longitudinal, and lateral tire forces. Nonlinear observers are utilized to predict tire forces.The proposed vehicle model for vertical force estimation captures suspension pitch and roll dynamics, offering a novel approach to link suspension motion with tire forces. However, it has certain limitations. The model simplifies real-world vehicle dynamics, which may reduce accuracy during extreme maneuvers or on highly variable road surfaces. Its reliance on ADAS map data, such as road slope and friction coefficients, makes it susceptible to inaccuracies or outdated information in these maps. Additionally, the model's performance is sensitive to sensor noise and requires precise parameter tuning, as small inaccuracies in input data or parameter settings can significantly affect the estimated forces. The authors of [13] put forward a method for estimating individual tire vertical forces using a steady-state weight transfer approach that takes into consideration the roll stiffness distribution. In this approach, unsprung masses and suspension dynamics are disregarded, and the front and rear roll center heights are assumed to be at ground level. Additionally, the road is assumed to be completely flat, and dynamic loads resulting from road irregularities are not considered. Lateral weight transfer is presumed to be dependent on the roll stiffness at each axle.The proposed method aims to reduce tuning efforts by avoiding the complexities of traditional tire models and instead relies on a steady-state weight transfer approach combined with roll stiffness distribution for vertical force estimation. However, this simplification introduces certain limitations. The neglect of suspension dynamics and transient effects restricts the model's accuracy under dynamic driving scenarios such as uneven road surfaces. Additionally, while the reliance on roll stiffness distribution reduces the need for extensive parameter tuning, inaccuracies in these parameters can still significantly impact the estimation performance.