# 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 state-space model incorporates suspension deformation, sprung mass acceleration, and tire deformation as states, assuming the derivative of tire deformation and road surface vertical position changes follow white Gaussian noise. The proposed observer relies on measurable quantities, such as suspension deformation (distance between sprung and unsprung masses) and sprung mass acceleration. The authors of [7] design an estimation system for vertical tire forces in a four-axle truck used for vehicle dynamic control based on an adaptive treble-extend Kalman filter.The vertical force estimation method relies on a four-axle truck model, which introduces challenges due to the over-constrained nature of the system and the variability in center of gravity positions caused by uneven load distributions. The method also depends on roll dynamics, requiring accurate measurements of roll angle, roll acceleration, and rotational inertia, which can vary significantly in heavy vehicles with irregular load placements. Additionally, the model involves complex parameterization, including suspension stiffness, damping coefficients, and rotational inertia, necessitating precise calibration and updates for different operating conditions. While the approach aims to minimize sensor usage, it still relies on critical sensor data, such as roll rate measurements, which are essential for accurate dynamic updates and can impact the overall reliability of the model. [PERSON] et al. in [8] present a parameterization procedure for tire vertical stiffness, focusing on measured tire geometry and air pressure, particularly for applications where high-fidelity tire models are deemed unnecessary. Vertical forces are computed through an air volume optimization approach. They compare this approach, known as the \"Energy method\", developed by [PERSON] et al. introduced in [9], for force estimation based on tire shape, with a proposed contact area-based approach (Area method) and an approach by [PERSON] (Rotta method). These methods are employed for estimating vertical forces acting on a tire on flat ground with various deflections, with the Energy method outperforming the others.The vertical force estimation method in the paper relies heavily on the geometric properties of the tire, including free radius, sidewall length, and rim diameter. The method requires accurate measurements of these parameters to calculate the contact patch length, which directly influences the predicted vertical force. The reliance on specific tire geometries and contact patch characteristics makes the model sensitive to parameter variations and limits its generalizability to other tire types or dynamic scenarios. Moreover, the use of fitting coefficients derived from experimental data introduces a dependency on specific conditions, necessitating recalibration for diverse applications. The sensitivity of the model to parameter variations is demonstrated in the tables within the paper, where a 5% change in parameters, such as free radius or sidewall length, results in significant deviations in force estimation. This highlights the importance of precise geometric measurements and calibration. Additionally, the requirement for sensor data, such as radial acceleration, adds complexity to the implementation, as sensor noise and environmental factors may further affect prediction accuracy. These limitations underscore the method's reliance on accurate parameterization and robust calibration. The authors of [10] propose an estimator based on an unscented Kalman filter (UKF) for estimating the roll angle and lateral acceleration using the UKF algorithm for a Three-Degree-of-Freedom (3-DOF) model. Subsequently, the research employs lateral load transfer and longitudinal load transfer models to estimate the vertical load force on each tire.The proposed vertical force estimation method relies on a 3-DOF vehicle model and a lateral-longitudinal load transfer model, both of which require a range of dynamic parameters.