Multiple Fading Factors Kalman Filter for SINS Static Alignment Application

To solve the problem that the standard Kalman filter cannot give the optimal solution when the system model and stochastic information are unknown accurately, single fading factor Kalman filter is suitable for simple systems. But for complex systems with multi-variable, it may not be sufficient to use single fading factor as a multiplier for the covariance matrices. In this paper, a new multiple fading factors Kalman filtering algorithm is presented. By calculating the unbiased estimate of the innovation sequence covariance using fenestration, the fading factor matrix is obtained. Adjusting the covariance matrix of prediction error Pk｜k-1 using fading factor matrix, the algorithm provides different rates of fading for different filter channels. The proposed algorithm is applied to strapdown inertial navigation system （SINS） initial alignment, and simulation and experimental results demonstrate that, the alignment accuracy can be upgraded dramatically when the actual system noise characteristics are different from the pre-set values. The new algorithm is less sensitive to uncertainty noise and has better estimation effect of the parameters. Therefore, it is of significant value in practical applications.