Tire Stiffness Identification in Vehicle Dynamics via Differentiable Moving Horizon Estimation

This paper presents a novel approach for tire stiffness estimation in vehicle dynamics using Differentiable Moving Horizon Estimation (DMHE). The method leverages the OptNet framework, which enables embedding convex optimization as a differentiable layer, allowing gradient-based learning of physical parameters. Unlike traditional Moving Horizon Estimation (MHE) or the Dual Extended Kalman Filter (DEKF), the proposed DMHE algorithm jointly estimates vehicle states and unknown stiffness parameters by backpropagating through the optimization layer. The approach is validated using simulations under varying initial conditions and noise, showing faster convergence and improved accuracy. While lateral velocity is assumed measurable-consistent with standard IMU-based vehicle sensing practices-the framework is extensible to observer-based architectures. Additionally, the paper discusses how DMHE can be generalized to handle time-varying stiffness, thereby enhancing its applicability to realworld driving scenarios where tire properties evolve over time. The results suggest DMHE is a promising tool for robust, real-time parameter identification in intelligent vehicle control systems.