Uncertainty-Aware Hierarchical MHE–EKF for Joint Estimation of Vehicle Lateral Velocity and Road Friction

Accurate joint estimation of vehicle lateral velocity and tire-road friction coefficient (TRFC) is critical for active safety systems. However, under near-limit conditions, strong nonlinear coupling and mutual error propagation severely degrade estimation accuracy. To address these challenges, this article proposes a novel uncertainty-aware hierarchical moving horizon estimation and extended Kalman filter (MHE–EKF) framework. This two-stage architecture employs a dual EKF (DEKF) to provide robust coarse priors, followed by a bidirectionally coupled MHE–EKF for high-precision joint estimation. The key novelty of this MHE–EKF structure lies in an embedded dual-innovation mechanism explicitly designed to manage uncertainty: first, an error-propagation model translates state errors into a high-confidence TRFC constraint interval, strictly bounding the MHE search space; second, a flag-driven adaptive arrival-cost strategy integrates multistage priors to accelerate mutual convergence. Vehicle experiments validate the algorithm. Compared to the conventional DEKF, the proposed framework reduces the lateral velocity mean absolute error to 28.8<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> and 42.1<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> of the DEKF baseline in dry-asphalt slalom and double-lane-change maneuvers, respectively, while concurrently decreasing the corresponding TRFC estimation errors from 5.73<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> to 0.11<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> and from 11.61<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> to 1.38<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula>. Extended evaluations on low-adhesion snow roads further confirm the algorithm's exceptional robustness and consistent accuracy across variable friction conditions.