Abstract: The broken line constitutive model has few control parameters and clear physical meaning, but its mathematical expression is complex. Thusly, it is difficult to identify. Aiming at the parameter identification of the broken line constitutive model, a global iteration parametric Kalman filter algorithm based on Sigma point transform is proposed. The method proposed takes the parameters to be identified as the state vector to reduce the dimension of the state vector and the amount of calculation. Based on Sigma point Kalman filter, the Jacobian matrix is avoided, and the parameter identification of a discontinuous function constitutive model is realized. By setting the objective function for a global iteration, the optimal solution can be obtained. Because the next time response of the nonlinear system is related to the historical path, the measurement update is calculated from the initial time to the current time. Finally, under seismic loading, the isolated bearing system is simplified as a single degree of freedom with a bilinear model, and the pier is simplified as a single degree of freedom with a Takeda model. According to the method proposed, the broken line constitutive model parameters are identified based on different sampling rules, such as unscented Kalman filter (UKF), cubature Kalman filter (CKF) and spherical simplex-radial cubature quadrature Kalman filter (SSRCQKF). The results demonstrate that the method proposed can accurately identify the nonlinear parameters and has strong robustness. The convergence process and results of different filters are also different.