# A Novel Longitudinal Speed Estimator for Four-Wheel Slip in Snowy Conditions
###### Abstract  
This article proposes a novel longitudinal vehicle speed estimator for snowy roads in extreme conditions (four-wheel slip) based on low-cost wheel speed encoders and a longitudinal acceleration sensor. The tire rotation factor, \(\eta_{t}\) is introduced to reduce the deviation between the rotation tire radius and the manufacturer's marked tire radius. The Local Vehicle Speed Estimator is defined to eliminate longitudinal vehicle speed estimation error. It improves the tire slip accuracy of four-wheel slip, even with a high slip rate. The final vehicle speed is estimated using two fuzzy control strategies that use vehicle speed estimates from speed encoders and a longitudinal acceleration sensor. Experimental and simulation results confirm the algorithm's validity for estimating longitudinal vehicle speed for four-wheel slip in snowy road conditions. tire rotation factor; four-wheel drive vehicle speed estimation; maximum wheel slip; snowy road; fuzzy control +
Footnote †: 2021: 11, 2809. [[https://doi.org/10.3390/app11062809](https://doi.org/10.3390/app11062809)]([https://doi.org/10.3390/app11062809](https://doi.org/10.3390/app11062809))  
Footnote †: 2021: 11, 2809. [[https://doi.org/10.33390/app11062809](https://doi.org/10.33390/app11062809)]([https://doi.org/10.33390/app11062809](https://doi.org/10.33390/app11062809))  
Footnote †: 2021: 11, 2809. [[https://doi.org/10.3390/app11062809](https://doi.org/10.3390/app11062809)]([https://doi.org/10.3390/app11062809](https://doi.org/10.3390/app11062809))  
Footnote †: 2021: 11, 2809. [[https://doi.org/10.33390/app11062809](https://doi.org/10.33390/app11062809)]([https://doi.org/10.33390/app11062809](https://doi.org/10.33390/app11062809))  
Footnote †: 2021: 11, 2809. [[https://doi.org/10.3390/app11062809](https://doi.org/10.3390/app11062809)]([https://doi.org/10.3390/app11062809](https://doi.org/10.3390/app11062809))  
Footnote †: 2021: 11, 2809. [[https://doi.org/10.33390/app11062809](https://doi.org/10.33390/app11062809)]([https://doi.org/10.33390/app11062809](https://doi.org/10.33390/app11062809))was to quantify the tire operating conditions during anti-lock braking system (ABS) braking in terms of longitudinal wheel slip. ABS braking tests with two subcompact passenger cars were performed on dry and wet asphalt, as well as on snow and ice surfaces. Even though these methods show great improvements, it remains difficult to obtain accurate vehicle state estimation on snowy roads. Kalman filters are conventional tire-based approaches to address these difficulties. A UKF-based longitudinal force estimation strategy was investigated in [13]. The process validity was studied using simulation and test results in slippery road conditions. [PERSON] et al. designed an adaptive vehicle longitudinal velocity observer for the electronic stability control system [14]. The observer was designed based on fuzzy logic and the Kalman filter, and the observer's effectiveness was validated in a Carsim environment. [PERSON] et al. proposed a novel approach to model-based joint wheel-slip and motion estimation of four-wheeled ground vehicles [15]. The model following control (MFC) strategy effectively employed the Rao-Blackwellized particle-filtering framework using a kinematic model. Compared with the no-control and MFC cases, the approach in [2] is a feasible method to effectively maintain vehicle stability. However, Kalman filter longitudinal speed estimation is restricted by models which rely excessively on sensors. Different from the above-mentioned methods, [PERSON] et al. solved the problem of estimating the longitudinal velocity of a braking vehicle using accelerometer measurements and wheel speed data from standard antilock braking wheel speed sensors [16]. Based on low-cost wheel speed encoders, a novel longitudinal speed estimator for vehicles during a cornering manoeuvre was proposed [17]. A gain-varying Kalman estimator was designed to output the lateral states of a vehicle body.