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Affected by the measurement errors of sensors and vibration interferences of railways, there are computational errors accumulating with time for inertial measurement system of tilting train based on math platform. Combined the inertial algorithm with the measured data, methods of dynamic errors compensation based on Kalman filter are researched. Based on the error mathematical models, corresponding two kinds of state-space equations of Kalman filter, that are "compact-coupled" model and "loose-coupled" model respectively, were built up. Combined with Kalman filter algorithm with time-variant fading factor, state variables and model parameters can be estimated in the same time. Since the time-variant colored noises of system can be modeled on the real time, it not only increases the accuracy of models, but also because of the self-tune ability of gain matrix, it is of strong robustness to the noises and uncertainties of models. Finally simulations are shown that errors accumulating with time can be effectively compensated for with the proposed algorithm.