# A Novel Longitudinal Speed Estimator for Four-Wheel Slip in Snowy Conditions
## 2 Materials and Methods
### Longitudinal Speed Estimator of Four-Wheel Drive Slipping Vehicle on Split Roads
#### 2.1.5 Final Fuzzy Logic Algorithm  
Both the Kalman filter and the fuzzy control algorithm can satisfy the accuracy requirement with the application of speed sensors. However, longitudinal speed estimation using the Kalman filter is restricted by its linearization and sensor information-based models. The combination of speed and acceleration sensors does not provide good estimates in single wheel slip cases, let alone high slip level conditions.  
The proposed algorithm is aimed at longitudinal speed estimation on snowy surfaces. This estimator has two layers: the first layer calculates a relatively-accurate value, while the second layer consider slip rate and the number of slipping wheels using fuzzy logic. The basic idea is to introduce a confidence coefficient to judge conditions. If the number of slipping wheels is less than two, it directs toward the wheel speed-based estimator, otherwise, toward the vehicle accelerometer-based estimator.  
Thus, we obtain the final estimate of longitudinal vehicle speed \(v_{E}\) in the second layer, which is believed accurate in the large and multiple-wheel slip conditions considered in this paper. To balance the estimates of vehicle speed (\(v_{E,w}\), \(v_{E,a}\)) in final fuzzy logic algorithm, the final estimated longitudinal vehicle speed is optimized for the highest confidence level.  
To achieve the logic algorithm, the final fuzzy logic approach begins by defining Slip and No Slip as input variables. For a No Slip condition, the slip ratio, monitored by the slip ratio calculator, is less than 0.1. Slip ratios larger than 0.1 indicate wheel slip on a snowy road. The weighting coefficient definition for the vehicle speed estimate of slipping wheels is shown in Figure 4.  
Estimated longitudinal speed based on wheel sensor speeds becomes less accurate during the experiment, and fuzzy control is adopted when more than two wheels' slip. Moreover, if four wheels slip simultaneously, the algorithm performance will decline rapidly because of inaccurate input. However, after calibration, the longitudinal speed estimate from the wheel sensor speed remains accurate without wheel slip. According to the findings above, the output variable definition for zero to four slipping wheels is shown in Figure 5.  
Although simple estimation of \(v_{E,J}\) from the local vehicle speed estimator is not sufficiently accurate, it can still judge the slip condition for the final fuzzy control logic.  
The confidence coefficients of \(V_{E\_w}\) and \(V_{E\_a}\) are different depending on how many wheels slip. The basic rule is that the more wheels' slip, the higher the confidence of estimating the vehicle speed from the acceleration sensor. The lower the number of slipping wheels, the higher the confidence of estimating vehicle speed from the wheel encoder speeds is. The fuzzy control logic algorithm is shown in Figure 6.  
Figure 4: Final fuzzy logic algorithm input variables.  
Figure 5: Final fuzzy logic algorithm output variables.