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.

Robust cubature Kalman filter method for the nonlinear alignment of SINS

Nonlinear initial alignment is a significant research topic for strapdown inertial navigation system(SINS).Cubature Kalman filter(CKF)is a popular tool for nonlinear initial alignment.Standard CKF assumes that the statics of the observation noise are pre-given before the filtering process.Therefore,any unpredicted outliers in observation noise will decrease the stability of the filter.In view of this problem,improved CKF method with robustness is proposed.Multiple fading factors are introduced to rescale the observation noise covariance.Then the update stage of the filter can be autonomously tuned,and if there are outliers exist in the observations,the update should be less weighted.Under the Gaussian assumption of KF,the Mahalanobis distance of the innovation vector is supposed to be Chi-square distributed.Therefore a judging index based on Chi-square test is designed to detect the noise outliers,determining whether the fading tune are required.The proposed method is applied in the nonlinear alignment of SINS,and vehicle experiment proves the effective of the proposed method.

Adaptive robust cubature Kalman filtering for satellite attitude estimation

This paper is concerned with the adaptive robust cubature Kalman filtering problem for the case that the dynamics model error and the measurement model error exist simultaneously in the satellite attitude estimation system. By using Hubel-based robust filtering methodology to correct the measurement covariance formulation of cubature Kalman filter, the proposed filtering algorithm could effectively suppress the measurement model error. To further enhance this effect and reduce the impact of the dynamics model error, two different adaptively robust filtering algorithms,one with the optimal adaptive factor based on the estimated covariance matrix of the predicted residuals and the other with multiple fading factors based on strong tracking algorithm, are developed and applied for the satellite attitude estimation. The quaternion is employed to represent the global attitude parameter, and three-dimensional generalized Rodrigues parameters are introduced to define the local attitude error. A multiplicative quaternion error is derived from the local attitude error to maintain quaternion normalization constraint in the filter. Simulation results indicate that the proposed novel algorithm could exhibit higher accuracy and faster convergence compared with the multiplicative extended Kalman filter, the unscented quaternion estimator, and the adaptive robust unscented Kalman filter.