<p>Accurate lateral state estimation is crucial for ensuring the stability and safety of vehicles. The Kalman filter is widely utilized to estimate the lateral state of vehicles. However, vehicle state measurement suffers from inherent time delays and model discrepancies. The existence of fractional and random delays necessitates long sampling periods for the inputs of the Kalman filter, leading to update mismatch and deterioration of the accuracy of the estimation. This situation poses a threat to driving safety. In addition, the tire cornering stiffness, a critical model parameter, exhibits nonlinear and dynamic variations that cannot be measured in real time. This inherent variability significantly affects the accuracy of lateral state estimation. Considering internal and external uncertainties, an observer framework for vehicle lateral state estimation based on the Kalman filter was designed in this work. First, a modified delayed Kalman filter method that considers the random fractional delays was developed. The relationship correlation between the delayed measurement and the prior state was constructed based on a likelihood algorithm. Then, the tire cornering stiffness was estimated online by an algorithm based on recursive least squares. This parameter was used to dynamically adjust the vehicle model for the Kalman filter. Finally, two simulations and a real vehicle experiment were performed to verify the effectiveness of the proposed method. In particular, the root mean squared error (RMSE) of the slip angle decreased by 30.70%, and that of the yaw rate decreased by 61.03% in the double lane change scenario. Actual vehicle experiments demonstrated that the algorithm can be effectively applied in real situations.</p>