The Kalman filter is widely used to solve the state estimation problem of linear Gaussian systems. Due to the unknown prior knowledge of the process noise and state model, and outliers in measurement, accuracy state estimation is difficult. In this paper, a general interactive multiple model adaptive filter is proposed to estimate the state of the system with uncertain state model and noise information. The algorithm designs a bank of filters in parallel to deal with the system model uncertainy. In each filter, the Skew-T distribution is used to model asymmetric Heavy-tailed measurement noise. To deal with the problem the process noise and system parameter are coupled, the covariance matrix of the system is assumed as inverse Wishart distributed. Then, the posterior distribution of the system state are joint recursively calculated by variational inference. The simulation and experimental results demonstrate that the proposed algorithm has better estimation accuracy with uncertain system models and noise information.