Computationally Efficient and Robust Vehicle State and Road Friction Estimation under Sensor Faults Using a Two-Stage UKF*

Abstract

Sensor fault detection is crucial for safe vehicle control, requiring rapid and accurate estimation under highly nonlinear dynamics. While the unscented Kalman filter (UKF) provides a powerful framework, augmenting the state vector with faults and parameters significantly increases computational load. To address this, this paper proposes a numerically efficient, fault-tolerant vehicle state and road friction estimation architecture based on an adapted two-stage square-root spherical simplex UKF (TS3UKF) formulation. First, algorithmic optimization is achieved by implementing the spherical simplex method - which reduces the standard 2n+1 sigma points to n+1 points - within the two-stage architecture while directly updating Cholesky factors to guarantee numerical stability. Second, the system state dimension is minimized by integrating an efficient tire slip calculation scheme that avoids full sigma point propagation. Finally, the framework is experimentally verified under highly critical, low-friction conditions using an Audi SQ8 e-tron test vehicle. Real-world results demonstrate that the algorithm precisely tracks states under injected IMU sensor faults with minor delay. In the absence of sensor faults, the road friction is estimated with high accuracy. Under active sensor faults during steady-state limit cornering, the friction estimate remains safely bounded, whereas subsequent dynamic excitation significantly improves convergence accuracy. Consequently, the total number of nonlinear function evaluations is reduced by 62 %, proving the modified algorithm’s high suitability for production vehicles.