Fault Estimation Based On The Two-stage Kalman Filtering In The Spacecraft Attitude Control System

In order to complete specific space missions,the attitude of the spacecraft need to be controlled precisely so that it can point to a specific target or maneuver.And then the spacecraft attitude control system(ACS)keep working throughout its designed life,and hence is prone to failures,especially actuators and sensors in it.For the purpose of enhancing the reliability,safety,and completion of space missions of the on-orbit spacecraft,the design and development of the fault detection,isolation and recovery systems have attracted more and more attention.Considering the non-ignorable nonlinear nature of the ACS during maneuvering,the two-stage Kalman filter-based nonlinear filtering methods for the simultaneous estimation problems of the attitude state and the fault were investigated in this paper under the background that recoverable faults of actuators and sensors attack the spacecraft ACS.The main contents and contributions of this paper are listed as follows.Considering the ACS model with actuator/sensor faults while the attitude was maneuvering,the simultaneous estimation problem of actuator/sensor fault and attitude information was proposed based on the TSUKF algorithm.Firstly,the basic unscented Kalman filtering method based on the unscented transformation was introduced.For fault and state estimation,the high-dimensional augmented-stage UKF was easy to diverge,and the computational cost was large.Considering the above disadvantages and the characteristics that the ACS model was conditional linear in actuator/sensor faults,the two-stage unscented Kalman filtering method was derived based on the unscented transformation and the two-stage Kalman filtering.On one hand,the unscented transformation was introduced to provide estimates with higher precision.On the other hand,by separating the bias/fault from the state,the high-dimensional filter could be decomposed into two low-dimensional filters,which could remove the unnecessary sigma point calculations in the unscented transformation,lower the computational cost,and reduce the risk of filter divergence.Based on the proposed TSUKF method,a TSUKF estimator for the ACS model during maneuvering was designed to estimate the attitude information and the actuator/sensor faults simultaneously.Finally,numerical simulation results demonstrated the effectiveness of the TSUKF estimator for the maneuvering attitude and the actuator/sensor fault estimation in the spacecraft ACS under pre-set fault conditions.In the presence of actuator faults with time-varying magnitudes in the ACS during maneuvering,the TSXKF method was presented to estimate the attitude information and the fault.Firstly,the TSEKF method was presented.Accordingly,a TSEKF estimator was designed for attitude information and actuator fault estimation simultaneously considering actuators were attacked by faults during attitude maneuvering.Next,the basic idea of the XKF together with its stability analysis was introduced.Then considering actuator faults with time-varying magnitudes,the two-stage exogenous Kalman filtering scheme was proposed to enhance the estimation performance based on the XKF theory and the TSEKF method.Finally,numerical simulations were employed to verify the effectiveness of the TSXKF method.For comparison,the TSEKF estimator was applied in simulations too.The simulation results showed that although the estimation performance of TSXKF was not as good as TSEKF before the fault occurred or the magnitude of the fault was constant,the TSXKF estimator could achieve estimates with higher precision than the TSEKF estimator after actuator faults with time-varying magnitudes attacked the ACS,and the dynamic performance of TSXKF was better than that of TSEKF.Besides,compared to the observer's sensitivity to the initial values,TSXKF could converge quickly even under the condition of inaccurate initial values,which was inherited from TSEKF.The problem of estimating the attitude information and the actuator/sensor faults simultaneously was addressed based on the TSMKF method and the modified two-stage exogenous Kalman filtering scheme,respectively.Firstly,considering the orthogonal constraint of attitude quaternions,attitude error quaternions were brought in and thereby the two-stage multiplicative Kalman filtering method was proposed.On one hand,the estimation error covariance matrix of the state containing the attitude quaternion could be propagated in the reduced dimension space.On the other hand,the dimension of the filter was effectively reduced to prevent the filter form diverging.However,the estimation performance of TEMKF would be degraded in face of faults with time-varying magnitudes.Accordingly,a modified two-stage exogenous Kalman filtering method was derived based on the XKF method.Compared with the TSXKF scheme in the previous chapter,the local linearization in the modified TSXKF here was completely dependent on the observation values offered by those global nonlinear observers,which was a 'complete'exogenous filtering scheme.Finally,numerical simulations were investigated to verify the effectiveness of the proposed TSMKF and the modified TSXKF.For comparison,the observers were used in numerical simulations too.The simulation results indicated that,the proposed TSMKF algorithm could estimate attitude information and actuator/sensor faults effectively when the faults' magnitudes were constant.When the faults'magnitudes were time-varying,the modified TSXKF scheme achieved both better dynamic and steady-state performances than TSMKF.Meanwhile,the two filtering methods obtained better sensor fault estimates than the observers.In addition,the modified TSXKF also inherited the TSMKF's insensitivity nature to inaccurate initial value.Under the simulation conditions with inaccurate values of attitude quaternions,the attitude quaternion estimate and the attitude angular velocity estimate of the two filtering methods could converge faster than those of the observer estimates.