The cornering stiffness of automobile tires is closely linked to the vehicle's handling characteristics, and accurately estimating the tire cornering stiffness in real time is of significant importance for enhancing the stability of vehicle handling. Addressing the challenge of direct measurement of cornering stiffness, a real-time identification method based on the estimation of tire lateral force and slip angle was proposed. Firstly, considering the influence of longitudinal force on lateral force, a tire lateral force estimator was designed based on the yaw dynamics model and sliding mode observer algorithm, followed by the design of a slip angle feedback estimator based on the estimation error of lateral force. Secondly, a nonlinear tire force model that describes the relationship among tire lateral force, slip angle, and cornering stiffness was established. Taking the real-time estimated lateral force and slip angle as inputs, a recursive least squares online identification algorithm with limited memory was designed to address the issue of estimation error due to "data saturation" and improve identification accuracy. Finally, joint simulation experiments using Simulink and CarSim were conducted. The experimental results indicate that the estimation error of tire lateral force is approximately 4.153 9% on average, while the estimation error of tire slip angle is 3.285 2% on average. The identification model based on the recursive least squares method is robust to changes in road conditions, demonstrating good tracking accuracy and stability under both high and low adhesion conditions, with an average estimation accuracy of tire cornering stiffness of approximately 98.379 3%.