Multiple Adaptive Fading Schmidt-Kalman Filter for Unknown Bias

Abstract

Unknown biases in dynamic and measurement models of the dynamic systems can bring greatly negative effects to the state estimates when using a conventional Kalman filter algorithm. Schmidt introduces the “consider” analysis to account for errors in both the dynamic and measurement models due to the unknown biases. Although the Schmidt-Kalman filter “considers” the biases, the uncertain initial values and incorrect covariance matrices of the unknown biases still are not considered. To solve this problem, a multiple adaptive fading Schmidt-Kalman filter (MAFSKF) is designed by using the proposed multiple adaptive fading Kalman filter to mitigate the negative effects of the unknown biases in dynamic or measurement model. The performance of the MAFSKF algorithm is verified by simulation.

Robust Partially Strong Tracking Extended Consider Kalman Filtering for INS/GNSS Integrated Navigation

“…To overcome the uncertainties in state-space system model and satisfy the accuracy and adaptability of the filtering, a mutually orthogonal principle of the predicted measurement residual sequences is proposed by Zhou and Frank [31] and Zhou et al [32]. Based on the mutually orthogonal principle, a time-varying suboptimal adaptive fading factor is introduced into the predicted state error covariance matrix to adjust the gain matrix K k in real time, and then improve the filtering precision [27], [32]. Here, to improve the robustness and adaptability of the ECKF, a suboptimal adaptive fading factor is partially introduced into in Eq.…”

“…This handling method about the biases could consider the effects of the biases and reduce the computation cost by not estimating them. Then, many modified CKF are proposed to improve estimation accuracy, such as unscented CKF [26], norm-constrained CKF [24], multiple adaptive fading CKF [27], ensemble CKF [25], Gaussian mixture CKF [28].…”

Multiple Adaptive Fading Cubature Kalman Filter for INS/GPS Integrated Navigation

“…Based on the comment in the literature [5], a multiple fading factorwhich is premultiplicated to the priori error covariance equation for the linear Kalman filter are calculatedfor the CKF as follows. …”

“…The INS/GPS integrated navigation is often realized using the Kalman filter to estimate the host platform attitude. However, if the system parameters which are used to update the state and covariance estimates are not accurately modeled, the accuracy of the state estimates may significantly degrade.Fortunately, a single adaptive fading factor can be introduced as a multiplier to the dynamic or measurement noise covariance to adjust the priori covariance when the information of the dynamic or measurement model is incomplete [2][3][4][5]. Then, considering the complex systems with multivariable, the multiple fading factor is proposed to reflect corrective effects of the multivariable in filtering [2,5].…”

“…However, if the system parameters which are used to update the state and covariance estimates are not accurately modeled, the accuracy of the state estimates may significantly degrade.Fortunately, a single adaptive fading factor can be introduced as a multiplier to the dynamic or measurement noise covariance to adjust the priori covariance when the information of the dynamic or measurement model is incomplete [2][3][4][5]. Then, considering the complex systems with multivariable, the multiple fading factor is proposed to reflect corrective effects of the multivariable in filtering [2,5]. For the nonlinear of the INS/GPS integrated navigation, the cubature Kalmanfilter (CKF) [6,7] is introduced to avoid calculating Jacobians or Hessiansas the extended Kalman filter [1].…”