Identifying the local nonlinear hysteretic behaviors in structures arises as an important issue in structural health monitoring. This paper develops a new hysteresis identification framework where rather than identifying the hysteretic parameters, the restoring forces are reconstructed so as to identify the hysteretic loops. Under this new framework, there is no need to get a priori knowledge on the hysteretic models, enabling a wider range of applications, and the involved system equation is linear with unknown restoring forces, tending to be more efficient. Then, the Kalman filter is adopted for real-time restoring force reconstruction because the Kalman filter is celebrated for its efficiency, effectiveness and reliability in linear system estimation with noisy measured data. In doing so, the restoring forces are additionally augmented as state variables and such augmentation is shown to act as the role of Tikhonov regularization, by which the proper covariance of the augmentation as the regularization parameter is selected via the L-curve method. Numerical examples are presented and an experimental test is conducted to verify the effectiveness and robustness of the proposed real-time hysteresis identification method.