## 3 Slip-Based Road Friction Monitoring
### Lateral Dynamics
[108], where the one-directional friction potential coefficients \(\mu_{\max,x},\mu_{\max,y}\) were estimated using a UKF structure and a modified _Dugoff_ tyre model. The tyre forces were obtained from a discrete EKF using chassis acceleration and yaw acceleration measurements. A Mean Square Error (MSE) weighted fusion method is proposed to obtain the resultant friction potential estimate depending on the uncertainty associated with each one-directional estimate. Such uncertainties are computed from second-order surfaces that depend on the lateral and longitudinal tyre slips. Despite this simulation results are presented on surfaces of different grip potentials, a discussion on grip utilisation levels is omitted. [PERSON] et al. [103] proposed a proportional-integral-derivative (PID) controller to estimate the road friction potential. Specifically, the responses obtained from a two-track vehicle model equipped with an analytical model developed by the authors in [115] are compared to wheel speed and yaw rate measurements, following the structure depicted in Figure 15. The model was validated experimentally in dry asphalt and gravel terrains and friction potential estimates were obtained from the wheel speed and yaw rate signal errors. Finally, a weighting strategy was proposed to fuse these estimates based on the steering wheel angle and the longitudinal velocity signals. A similar reference vehicle model-based approach has been reported in the Europen project \"Friction\" [104] and in [PERSON] [23]. This algorithm was developed by VDO Automotive AG and compares yaw rate sensor measurements with the responses obtained from a reference vehicle model. Additional details regarding the tyre parameterisation employed in the reference vehicle model were not found in these works. The friction estimator was integrated with a steering wheel torque-based friction observer (provided by Centro Ricerche Fiat S.C.p.A.) and a Vehicle Feature Fusion (VFF) block was formed. After performing  
Figure 14: Estimation structure proposed by [PERSON] et al. [101]. Figure adapted by the authors from [101]. a detailed experimental assessment of the proposed solutions on dry asphalt, snow, and ice surfaces, [PERSON] remarks that acceleration levels higher than 3 m/s\({}^{2}\) are required by both structures to achieve an accurate estimation. In [PERSON] et al. [106] an observer is proposed to estimate the lateral velocity and the road friction potential. The authors used separated strategies for the linear and nonlinear lateral dynamics. In the linear dynamics case, it is assumed that the friction potential does not affect the vehicle response, and the tyre cornering stiffness (\(C_{a}\)) is considered unaltered. The estimation of the Tyre Road Friction Coefficient (TRFC) is therefore limited to the nonlinear lateral dynamics and is carried out using an observation law based on the resultant lateral force error obtained from lateral acceleration measurements and a _Magic Formula_ type model. A kinematic-based observer is used to estimate the lateral velocity required by the _Magic Formula_ type model during the operation in the nonlinear region. The authors proposed a similar approach in [109]. In this case, the vehicle body slip is assumed to be measured, and the one-directional friction potential coefficients \(\mu_{\max,x},\mu_{\max,y}\) are estimated using the adaptation laws  
\[\hat{\mu}_{\max,xi}=k_{p1}(F_{xi}-\hat{F}_{xi}),\quad\hat{\mu}_{\max,yi}=k_{p2 }(F_{yi}-\hat{F}_{yi}) \tag{46}\]  
with \(i\in\{fl,fr,rl,rr\}\) and \(k_{p1},k_{p2}\) being suitable gains. \(F_{xi}\) is the measured longitudinal force (inferred from the current of an electric motor) and \(F_{yi}\) is the tyre lateral force (assumed to be measured by a sensor). Finally, the authors proposed a weighting function based on the tyre longitudinal and lateral slips to fuse the one-directional grip potential estimates. As occurred in the previous cases, a detail discussion regarding grip utilisation levels is not provided.