Double-factor Fading Memory Kalman Filter for Compensating Model Uncertainty

In order to solve the divergence problem of Kalman filter caused by the model uncertainty in the dynamic system, this paper proposes an adaptive filter called double-factor fading memory Kalman filter. In fact, the recursive formulas of state estimations in Kalman filter can be derived by minimizing a quadratic cost function. To compensate for the different degrees of model uncertainty in the motion equation and the measurement equation, this paper introduces two fading factors into the weight matrices of the lost function. The values of fading factors can be calculated by iteratively solving the equations that assume the theoretic covariance matrices of innovations and residuals equals to the sample covariance matrices of innovations and residuals respectively, and then state estimations expressed by fading factors can be obtained.