For accurate state estimation in the process of vehicle lateral motion，an estimation algorithm considering the tire nonlinear cornering mechanical characteristics is proposed. In order to accurately reflect the evolution law of vehicle lateral dynamics under special driving conditions，a vehicle dynamics model considering the tire nonlinear cornering mechanical characteristics is established by using the piecewise affine identification method，and then the piecewise affine model of vehicle lateral dynamics is constructed. On this basis，a "multi-mode switching" state estimation strategy for the piecewise affine model of the system is designed based on the strong tracking square root cubature Kalman filter algorithm to maintain good state estimation accuracy when the system state changes suddenly. Based on CarSim and MATLAB/Simulink，a Co-Simulation platform for vehicle driving state estimation performance is established. By setting up two typical working conditions，the state estimation effect of vehicle yaw rate and sideslip angle is verified. The results show that the proposed estimation algorithm can achieve high-precision estimation of vehicle driving state under special driving conditions.