## 1 Introduction
### Literature Review  
The first research approach involves detecting substances covering the road, such as water, ice, or snow, either visually, through temperature, or by using specialized sensors [4; 5; 6]. Current methods that employ light or ultrasonic sensors to estimate friction coefficient require expensive additional sensors. The friction characteristics of asphalt can vary significantly depending on the distributed conditions of dryness, moisture, snow, or ice and the presence of localized specificities, such as oil traces and potholes (associated with weather conditions). However, stable performance across various environmental scenarios is essential. The mentioned research approach has limited application in production vehicles owing to its real-time performance  
Figure 1: The concept of wheel spin predictive control. being compromised by accuracy fluctuations based on external conditions. In particular, methods involving light or ultrasonic sensors require additional costly equipment, making it challenging to apply them to production vehicles. Another method uses acceleration sensors in the vehicle body to estimate tire-road friction [7; 8]. Using vehicle acceleration sensors to convert the acceleration of the center of mass into sprung mass acceleration to calculate tire acceleration enables the estimation of the tire-road friction coefficient by calculating the dynamic tire force and effective vertical force, considering the amount of load transfer. This approach considers the amount of slip that reaches the maximum tire force and calculates the effective dynamic tire force, which is similar to the friction estimation technique proposed in this paper. However, this method involves calculating the friction coefficient using only the acceleration of the vehicle. Therefore, the calculated value is used as is in stable situations; in sections where there is no rapid acceleration, the problem of the friction coefficient falling to a lower value than the actual friction coefficient can occur. Additionally, it has only been verified in certain driving conditions where the vehicle brakes while driving straight. It is necessary to verify whether the friction estimation is also effective in various driving environments with different road conditions and in situations where there is significant lateral acceleration due to turning. In turning situations where both longitudinal and lateral accelerations increase, leading to an increase in both longitudinal and lateral tire forces, the accuracy of tire-road friction estimation decreases if the effective normal acceleration cannot be calculated. Therefore, the aforementioned method needs additional strategies to accurately estimate the friction coefficient in stable vehicle states, which is a section where longitudinal and lateral accelerations are small. The second approach uses the vehicle-tire model to estimate the tire-road friction coefficient based on wheel slip ratio and braking-force characteristics [9; 10; 11; 12]. Using a linear vehicle-tire model provides high friction estimates across various environments. However, as it relies on simulation-based data, its implementation in real vehicle environments is inappropriate. In situations where the friction coefficient changes with driving conditions, estimating the limit value of the tire-road friction coefficient based on maximum braking force results in decreased accuracy. Additionally, the virtual environment vehicle model may not align with the actual vehicle, leading to a decrease in the performance of real-time tire-road friction estimation when applying such systems. The third approach estimates tire-road friction based on a discrete-time extended Kalman filter using a nonlinear vehicle-tire dynamics model [13; 14]. Estimating the lateral velocity of the vehicle to calculate the slip angle of the wheels enables accurate estimation of tire-road friction. However, this method faces challenges in real-time application due to the computational complexity of the nonlinear model and time considerations.