# Survey on Modelling and Techniques for Friction Estimation in Automotive Brakes
## 2 Techniques for the Estimation of BLCF in Automotive Disc Brakes
### State Observer for BLCF Estimation  
The abovementioned approaches present several drawbacks that make them unsuitable for online applications. Above all, both the model-based approach and neural networks require a high experimental burden for parameter characterization and the training/learning process, respectively. In addition, they also cause a high computational burden when augmented with a set of differential equations describing the temperature evolution in the brake disc or the hysteresis behaviour of the brake pads. Regardless, these models are incapable of rightly capturing the blended abrasive and adhesive wear and are unreliable when the plant characteristics change due to brake wear itself or in case of replacement with aftermarket brake linings or owing to variations in weather conditions.  
The possibility of predicting the BLCF for each wheel of the vehicle online is an important challenge for control engineers designing more and more efficient controllers. Indeed, in recent years, new control methodologies have been developed with the aim of enhancing braking performance during hard braking to improve vehicle safety. Different vehicle characteristics in terms of weight and maximum speed mean that braking system performances have to be improved. The knowledge of BLCF is useful to maintain the braking in the safe operating region, avoid fading, and evaluate the actual braking torque for the enhancement of online control systems such as ABS, ESP and TC. In addition, electric vehicles demand the design of new controllers to handle the regenerative braking and the blending with frictional braking [33; 67]. The mentioned controllers require the estimation of physical quantities that are not directly measurable. In accordance with this need, the state observation technique has been applied in the automotive field as a valid substitute for the model-based approach.  
From the literature emerges the possibility of using a state observer as an estimator of the BLCF, but it is still a poorly investigated topic. Herein, a new approach based on the Kalman theory is featured, which aims at estimating the BLCF by drawing upon the observation of the wheel torque. Referring to the state of the art, research effort in the last two decades has been mainly conducted in the fields of observation of the tire-road friction coefficient [68; 69; 70] and direct observation of the tire forces [71; 72]. The bulk of the literature assumes the wheel torque as an input of the state equations; instead, for the matter in hand, it constitutes one of the states to observe in order to estimate BLCF [73]. Therefore, the state space formulation associated with the developed observer is rearranged in order to handle the wheel torque as an augmented state [74].  
It is worth mentioning that, in [43], [PERSON] proposes a tool based on the extended Kalman filter to estimate the brake torque for the enhancement of the blending between the conventional and the regenerative brake for driving safety and energy recovery purposes. In particular, [PERSON] applies the Kalman filter to observe the temperature of each brake disc; thus a static friction model, based on a modified version of the LuGre, that takes into account the speed and temperature dependence of BLCF, is used to predict the frictional torque. The drawback is that it relies upon a friction model that, as already underlined, is not reliable for online applications. Indeed, in the case of variation in the plant characteristics or environmental conditions, the model leads the Kalman filter to a wrong estimate. The present work proposes a Kalman filter whose prediction relies on a more consolidated tire model and the virtual sensor guarantees robustness against potential faults in the model itself (e.g., variation in road conditions).