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The road adhesion coefficient has a great impact on the performance of vehicle tires, which in turn affects vehicle safety and stability. A low coefficient of adhesion can significantly reduce the tire's traction limit. Therefore, the measurement of the coefficient is much helpful for automated vehicle control and stability control. Considering that the road adhesion coefficient is an inherent parameter of the road and it cannot be known directly from the information of the on-vehicle sensors. The novelty of this paper is to construct a road adhesion coefficient observer which considers the noise of sensors and measures the unknown state variable by the trained neural network. A Butterworth filter and Adaptive Neural Fuzzy Interference System (ANFIS) are combined to provide the lateral and longitudinal velocity which cannot be measured by regular sensors.