基于ATSUKF算法的卫星姿控系统故障估计
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摘要
针对卫星姿态控制过程中可能发生的执行机构或敏感器故障,提出了一种基于无损卡尔曼滤波(UKF)及偏差分离原理的自适应二阶无损卡尔曼滤波(ATSUKF)算法。首先,提出TSUKF算法,通过UKF处理姿态机动时的非线性并通过偏差分离原理将非线性系统的状态及故障分别估计,避免非线性模型的线性化过程同时降低了计算过程中的矩阵维度。然后,在TSUKF算法的基础上提出了ATSUKF算法,通过滑动窗口内的残差计算自适应矩阵,使滤波器在统计特性不准确的情况下仍然具有较快的收敛速度,特别适用于卫星快速机动过程中的姿态与故障估计。数值仿真结果表明,ATSUKF算法相较于TSUKF算法能有效降低统计特性不准对系统造成的不利影响,实现卫星姿态、执行机构/敏感器故障的快速估计。
Based on the bias-separate principle and the Unscented Kalman Filter(UKF),an Adaptive Two-Stage Unscented Kalman Filter(ATSUKF)is proposed to address the fault estimation of actuators/sensors in the satellite attitude control system.First,the TSUKF is presented.The decoupled state and faults are estimated by applying the bias-separate principle and using the nonlinearity by the UKF when the attitude is maneuvered without linearization of the system model.This avoids lowering the dimension of the matrix during the estimating process.Based on the TSUKF,an adaptive version is proposed.The adaptive matrices are calculated by the residuals in the sliding data window to make the noise covariance matrices change adaptively.With the ATSUKF estimator,the convergence rate is enhanced when the prior knowledge of the noise covariance matrices are inaccurate or the fault changes.Numerical simulations demonstrate the effectiveness of the approach proposed.
Based on the bias-separate principle and the Unscented Kalman Filter(UKF),an Adaptive Two-Stage Unscented Kalman Filter(ATSUKF)is proposed to address the fault estimation of actuators/sensors in the satellite attitude control system.First,the TSUKF is presented.The decoupled state and faults are estimated by applying the bias-separate principle and using the nonlinearity by the UKF when the attitude is maneuvered without linearization of the system model.This avoids lowering the dimension of the matrix during the estimating process.Based on the TSUKF,an adaptive version is proposed.The adaptive matrices are calculated by the residuals in the sliding data window to make the noise covariance matrices change adaptively.With the ATSUKF estimator,the convergence rate is enhanced when the prior knowledge of the noise covariance matrices are inaccurate or the fault changes.Numerical simulations demonstrate the effectiveness of the approach proposed.
引文
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[25]CHENG H,HAO Y,XIONG K.An adaptive two-stage unscented Kalman filter and its application in un-known random bias[J].Aerospace Control&Application,2010,21(4):625-635.
[26]HAJIYEV C,SOKEN H E.Robust adaptive Kalman filter for estimation of UAV dynamics in the presence of sensor/actuator faults[J].Aerospace Science&Technology,2013,28(1):376-383.
[2]KELLER J Y,SUMMERER L,DAROUACH M.Extension of Friedland’s bias filtering technique to discrete-time systems with unknown inputs[J].International Journal of Systems Science,1996,27(12):1219-1229.
[3]KELLER J Y,DAROUACH M.Optimal two-stage Kalman filter in the presence of random bias[J].Automatica,1997,33(9):1745-1748.
[4]MENDEL J M.Extension of Friedland’s bias filtering technique to a class of nonlinear systems[J].IEEE Transactions on Automatic Control,1976,21(2):296-298.
[5]MENDEL J M,WASHBURN H D.Multistage estimation of bias states in linear systems[J].International Journal of Control,1978,28(4):511-524.
[6]IGNAGNI M B.An alternate derivation and extension of Friendland’s two-stage Kalman estimator[J].IEEETransactions on Automatic Control,1981,26(3):746-750.
[7]IGNAGNI M B.Separate bias Kalman estimator with bias state noise[J].IEEE Transactions on Automatic Control,1990,35(3):338-341.
[8]IGNAGNI M B.Optimal and suboptimal separate-bias Kalman estimators for a stochastic bias[J].IEEE Transactions on Automatic Control,2000,45(3):547-551.
[9]ALOUANI A T,XIA P,RICE T R,et al.A two-stage Kalman estimator for state estimation in the presence of random bias and for tracking maneuvering targets[C]∥Proceedings of the 30th IEEE Conference on Decision and Control.Piscataway,NJ:IEEE Press,1991,2:2059-2062.
[10]ALOUANI A T,XIA P,RICE T R,et al.On the optimality of two-stage state estimation in the presence of random bias[J].IEEE Transactions on Automatic Control,1993,38(8):1279-1283.
[11]KELLER J Y,SAUTER D D J.Kalman filter for discrete-time stochastic linear systems subject to intermittent un-known inputs[J].IEEE Transactions on Automatic Control,2013,58(7):1882-1887.
[12]HSIEH C S,CHEN F C.Optimal solution of the twostage Kalman estimator[C]∥Proceedings of the 34th IEEE Conference on Decision and Control.Piscataway,NJ:IEEE Press,1995,2:1532-1537.
[13]HSIEH C S,CHEN F C.Optimal solution of the twostage Kalman estimator[J].IEEE Transactions on Automatic Control,1999,44(1):194-199.
[14]HSIEH C S,CHEN F C.General two-stage Kalman filters[J].IEEE Transactions on Automatic Control,2000,45(4):819-824.
[15]HSIEH C S.Robust two-stage Kalman filters for systems with unknown inputs[J].IEEE Transactions on Automatic Control,2000,45(12):2374-2378.
[16]XIAO Q,WU Y,FU H,et al.Two-stage robust extended Kalman filter in autonomous navigation for the powered descent phase of Mars EDL[J].IET Signal Processing,2015,9(3):277-287.
[17]YI B,KANG L,TAO S,et al.Adaptive two-stage extended Kalman filter theory in application of sensor-less control for permanent magnet synchronous motor[J].Mathematical Problems in Engineering,2013,2013(3):1-13.
[18]CHEN X Q,LIU M.A two-stage extended Kalman filter method for fault estimation of satellite attitude control systems[J].Journal of the Franklin Institute,2017,354(2):872-886.
[19]CHEN X Q,SUN R,JIANG W C,et al.A novel twostage extended Kalman filter algorithm for reaction flywheels fault estimation[J].Chinese Journal of Aeronautics,2016,29(2):462-469.
[20]郭泽,缪玲娟,赵洪松.一种改进的强跟踪UKF算法及其在SINS大方位失准角初始对准中的应用[J].航空学报,2014,35(1):203-214.GUO Z,MIAO L J,ZHAO H S.An improved strong tracking UKF algorithm and its application in SINS initial alignment under large azimuth misalignment angles[J].Acta Aeronautica et Astronautica Sinica,2014,35(1):203-214(in Chinese).
[21]COSTANZI R,FANELLI F,MELI E,et al.UKF-based navigation system for AUVs:Online experimental validation[J].IEEE Journal of Oceanic Engineering,2018:1-9.
[22]陈记争,袁建平,方群.基于Rodrigues参数的姿态估计算法[J].航空学报,2008,29(4):960-965.CHEN J Z,YUAN J P,FANG Q.Attitude estimation algorithm based on Rodrigues parameter[J].Acta Aeronautica et Astronautica Sinica,2008,29(4):960-965(in Chinese).
[23]HE Z,CHEN D,PAN C,et al.State of charge estimation of power Li-ion batteries using a hybrid estimation algorithm based on UKF[J].Electrochimica Acta,2016,211:101-109.
[24]XU J,JING Y,DIMIROVSKI G M,et al.Two-stage unscented Kalman filter for nonlinear systems in the presence of unknown random bias[C]∥American Control Conference.Piscataway,NJ:IEEE Press,2008:3530-3535.
[25]CHENG H,HAO Y,XIONG K.An adaptive two-stage unscented Kalman filter and its application in un-known random bias[J].Aerospace Control&Application,2010,21(4):625-635.
[26]HAJIYEV C,SOKEN H E.Robust adaptive Kalman filter for estimation of UAV dynamics in the presence of sensor/actuator faults[J].Aerospace Science&Technology,2013,28(1):376-383.