Accurate knowledge of wheel-individual friction brake torques, and thus of the effective brake coefficient of friction (BCF) between brake pad and disc can significantly enhance advanced vehicle control functions. It improves comfort-oriented brake blending by enabling a smoother transition from regenerative to friction braking and supports control algorithms by replacing the common assumption of a constant BCF with a time-varying estimate. Furthermore, it provides a basis for long-term assessment of brake condition and brake performance. This paper presents an Extended Kalman Filter for the simultaneous estimation of vehicle states and wheel-individual drive and brake torques, also considering and estimating the road gradient (inclination and banking) that commonly occurs on public roads. A sensitivity analysis of the vehicle model parameters is conducted to identify parameters that need to be known precisely to improve the estimation results, which is the dynamic wheel radius for the proposed algorithm. Extensive experimental validation is performed using an Audi A6 test vehicle, including proving ground tests, scenarios with inclined roads, and a 40-min public road measurement. The results demonstrate accurate brake torque estimation across a wide range of driving conditions, particularly during pure longitudinal braking. Estimation accuracy is only reduced during emergency braking or very high deceleration events, which is attributed to the underlying model assumptions. These results highlight the suitability of the approach for real-world applications and its potential to improve comfort- and safety-related vehicle control systems.
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Heinemann et al. (2026) studied this question.
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