CN116149186A - A Kalman filter method for fault estimation of satellite attitude control system - Google Patents

A Kalman filter method for fault estimation of satellite attitude control system Download PDF

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CN116149186A
CN116149186A CN202310122951.5A CN202310122951A CN116149186A CN 116149186 A CN116149186 A CN 116149186A CN 202310122951 A CN202310122951 A CN 202310122951A CN 116149186 A CN116149186 A CN 116149186A
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梁天添
王英东
杨建雄
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Dalian Jiaotong University
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Abstract

本发明公开了一种卫星姿态控制系统故障估计的Kalman滤波方法,属于航天器故障诊断技术领域,具体为:考虑可建模干扰和状态时滞,执行器和传感器故障为附加变量,建立时滞广义系统模型;设计非奇异鲁棒Kalman滤波器;基于泰勒级数展开时滞广义系统的非线性项和非线性时滞项,并给出鲁棒上界;通过改进的鲸鱼优化算法优化噪声协方差矩阵,并用优化后的噪声协方差矩阵代替原有噪声协方差;执行时滞广义系统的状态估计和可建模干扰估计,完成卫星姿态控制系统的状态估计和复合故障估计。采用上述一种卫星姿态控制系统故障估计的Kalman滤波方法,解决了复杂运行环境下卫星姿态控制系统的多种故障估计问题,提高了故障估计的精度。

Figure 202310122951

The invention discloses a Kalman filtering method for fault estimation of a satellite attitude control system, which belongs to the technical field of spacecraft fault diagnosis. Generalized system model; design non-singular robust Kalman filter; expand the nonlinear term and nonlinear time-delay term of the time-delay generalized system based on Taylor series, and give a robust upper bound; optimize the noise coherence through the improved whale optimization algorithm variance matrix, and replace the original noise covariance with the optimized noise covariance matrix; perform state estimation and modelable interference estimation for time-delay generalized systems, and complete state estimation and composite fault estimation for satellite attitude control systems. Using the Kalman filter method for fault estimation of the satellite attitude control system mentioned above, various fault estimation problems of the satellite attitude control system in complex operating environments are solved, and the accuracy of fault estimation is improved.

Figure 202310122951

Description

一种卫星姿态控制系统故障估计的Kalman滤波方法A Kalman Filtering Method for Fault Estimation of Satellite Attitude Control System

技术领域Technical Field

本发明涉及航天器故障诊断技术领域,尤其是涉及一种卫星姿态控制系统故障估计的Kalman滤波方法。The invention relates to the technical field of spacecraft fault diagnosis, and in particular to a Kalman filtering method for fault estimation of a satellite attitude control system.

背景技术Background Art

随着卫星在轨服务的快速发展,在轨卫星数量不断增加。相应地,对卫星稳定性和安全性的要求也日益提升。姿态控制系统(ACSs)作为卫星的重要分系统,其正常工作关系到星上有效载荷、遥控、遥测和轨道控制等重要任务的有效展开。但是,由于系统设备众多、运行机制复杂,ACSs也较易发生故障。因此,需要对ACSs的故障进行诊断,以及时发现系统异常,避免安全事故发生,保证卫星的在轨正常运行。因此,结合现代故障诊断技术,有效诊断出ACSs的故障,具有重要的现实意义。With the rapid development of satellite on-orbit services, the number of satellites in orbit continues to increase. Correspondingly, the requirements for satellite stability and safety are also increasing. As an important subsystem of the satellite, the normal operation of the attitude control system (ACSs) is related to the effective implementation of important tasks such as on-board payload, remote control, telemetry and orbit control. However, due to the large number of system equipment and complex operating mechanisms, ACSs are also prone to failure. Therefore, it is necessary to diagnose the faults of ACSs to detect system anomalies in time, avoid safety accidents, and ensure the normal operation of satellites in orbit. Therefore, it is of great practical significance to effectively diagnose the faults of ACSs in combination with modern fault diagnosis technology.

在基于模型的故障诊断方法中,设计残差生成器是一种行之有效的方法。目前,诸如观测器、滤波器等残差生成器已广泛用于ACSs的故障诊断。为实现ACSs的前两个任务阶段,即:故障检测与分离(FDI),未知输入观测器(UIO)已结合H-/H检测方法得到了广泛应用。而对于故障诊断的最后一个任务阶段:故障估计,因该过程不仅能够判断故障信号的具体形式和幅值,而且能够为主动容错控制提供基础,故尤为重要。有鉴于此,自适应观测器、滑模观测器、区间观测器等已结合鲁棒H方法,保证了系统的稳定性和鲁棒性。但是,当系统存在运行噪声时,需要考虑噪声对于故障估计精度的影响。为此,另一种残差生成器-Kalman滤波器已被用于噪声下的ACSs故障估计。In the model-based fault diagnosis method, designing residual generators is an effective method. At present, residual generators such as observers and filters have been widely used in fault diagnosis of ACSs. To achieve the first two task stages of ACSs, namely, fault detection and isolation (FDI), unknown input observers (UIO) have been widely used in combination with H- / H∞ detection methods. As for the last task stage of fault diagnosis: fault estimation, it is particularly important because this process can not only determine the specific form and amplitude of the fault signal, but also provide a basis for active fault-tolerant control. In view of this, adaptive observers, sliding mode observers, interval observers, etc. have been combined with robust H∞ methods to ensure the stability and robustness of the system. However, when there is operating noise in the system, it is necessary to consider the impact of noise on the accuracy of fault estimation. For this reason, another residual generator-Kalman filter has been used for ACSs fault estimation under noise.

鉴于ACSs系统的非线性特性,基于奇偶向量法的扩展Kalman滤波器、融合无迹Kalman滤波器、强跟踪容积Kalman滤波器等改进的非线性滤波器已用于估计ACSs的故障。另外,考虑ACSs噪声的未知特性,自适应滤波、变分贝叶斯滤波等方法已结合上述非线性Kalman器,用于更好地估计系统噪声,从而实现更优的故障估计。然而,ACSs的非线性Kalman滤波方法仍有一定不足。首先,系统的并发执行器、传感器并发故障(复合故障)估计精度仍需进一步提高。通常,卫星的执行器故障表现为飞轮卡死、空转和斜坡漂移等;传感器故障主要表现为:陀螺敏感器卡死、恒偏差、斜坡变化等。极端情况下,若复合故障同时发生,故障信号的耦合可能导致估计精度不高。尽管传感器故障可视为伪执行器故障,但该等效方法的偏差可能影响估计精度。其次,系统的外部干扰对故障估计的精度具有一定的影响。尽管扰动观测器等方法已用于估计ACSs的外部干扰,但随机噪声和未知外部干扰通常同时存在,给Kalman滤波器的设计带来了一定的挑战。再次,ACSs的速度时滞也会影响滤波精度。目前,针对具有时滞环节ACSs的Kalman滤波器设计主要集中于具有测量时滞的ACSs,但这些方法的本质是系统的高维变换,导致变量维度高、算法负载较大等不足。因此,考虑上述因素的综合影响,设计行之有效的故障估计Kalman滤波器,以提高ACSs的复合故障估计精度,是十分必要的。In view of the nonlinear characteristics of ACSs, improved nonlinear filters such as extended Kalman filter based on parity vector method, fused unscented Kalman filter, and strong tracking cubature Kalman filter have been used to estimate the faults of ACSs. In addition, considering the unknown characteristics of ACSs noise, adaptive filtering, variational Bayesian filtering and other methods have been combined with the above nonlinear Kalman filter to better estimate the system noise, thereby achieving better fault estimation. However, the nonlinear Kalman filtering method of ACSs still has certain shortcomings. First, the estimation accuracy of concurrent actuator and sensor concurrent faults (compound faults) of the system still needs to be further improved. Usually, the actuator faults of satellites are manifested as flywheel jamming, idling and slope drift; sensor faults are mainly manifested as gyro sensor jamming, constant deviation, slope change, etc. In extreme cases, if compound faults occur at the same time, the coupling of fault signals may lead to low estimation accuracy. Although sensor faults can be regarded as pseudo-actuator faults, the deviation of this equivalent method may affect the estimation accuracy. Secondly, the external interference of the system has a certain impact on the accuracy of fault estimation. Although methods such as disturbance observers have been used to estimate external disturbances of ACSs, random noise and unknown external disturbances usually exist at the same time, which brings certain challenges to the design of Kalman filters. Thirdly, the speed delay of ACSs will also affect the filtering accuracy. At present, the design of Kalman filters for ACSs with time-delay links mainly focuses on ACSs with measurement delays, but the essence of these methods is the high-dimensional transformation of the system, which leads to shortcomings such as high variable dimension and heavy algorithm load. Therefore, considering the combined influence of the above factors, it is necessary to design an effective fault estimation Kalman filter to improve the estimation accuracy of composite faults of ACSs.

另外,对于ACSs而言,因其长期运行于复杂工况下,诸多不确定因素可能导致测量元件异常,从而导致噪声的测量值和真实值存在一定的偏差,进一步降低了滤波精度。目前,已有诸如蝗虫算法、野山羊算法、灰狼算法和鲸鱼优化算法(WOA)等群体智能算法用于优化系统噪声,从而降低系统噪声测量偏差对于滤波精度的影响。但已有的研究和应用表明,上述方法不同程度地具有收敛速度慢、寻优精度低和易陷入局部最优解等不足。因此,结合有效的方法改进现有的群体智能寻优方法,对于增强算法性能、提高噪声寻优精度,进而提高ACSs的故障估计精度,具有重要的意义。In addition, for ACSs, because they operate under complex working conditions for a long time, many uncertain factors may cause abnormal measurement components, resulting in a certain deviation between the measured value and the true value of the noise, further reducing the filtering accuracy. At present, swarm intelligence algorithms such as locust algorithm, wild goat algorithm, gray wolf algorithm and whale optimization algorithm (WOA) have been used to optimize system noise, thereby reducing the impact of system noise measurement deviation on filtering accuracy. However, existing research and applications have shown that the above methods have shortcomings such as slow convergence speed, low optimization accuracy and easy to fall into local optimal solutions to varying degrees. Therefore, combining effective methods to improve the existing swarm intelligence optimization method is of great significance for enhancing algorithm performance, improving noise optimization accuracy, and thus improving the fault estimation accuracy of ACSs.

考虑ACSs的速度时滞、可建模扰动和系统测量偏差,视执行器、传感器故障为系统的附加状态变量,则得到时滞广义系统。故而,ACSs的故障估计转化为时滞广义系统的状态估计。近年来,广义系统的Kalman滤波估计成为国内外研究的热点。由于广义系统的动态项中存在奇异矩阵,导致现有奇异结构的Kalman滤波器解算困难,且其协方差矩阵可能出现奇异值,不易于应用。同时,目前针对状态时滞广义系统的Kalman滤波估计方法仍较为有限。另外,上述的外部干扰和系统测量偏差给非线性广义系统的Kalman滤波器设计带来了额外的挑战。因此,本发明视执行器、传感器复合故障为ACSs的附加变量,建立时滞广义系统;基于扰动观测器设计鲁棒Kalman滤波器,设计鲁棒参数以解决系统非线性项和非线性时滞项的线性化误差问题;基于精英集合策略的改进退火模拟算法(ISA)和自适应参数改进WOA,以更好地寻优系统噪声,降低噪声测量偏差对滤波精度的影响。结合鲁棒H方法、KalmanConsidering the speed time delay, modelable disturbance and system measurement deviation of ACSs, and regarding the actuator and sensor faults as additional state variables of the system, a time-delay generalized system is obtained. Therefore, the fault estimation of ACSs is transformed into the state estimation of the time-delay generalized system. In recent years, Kalman filter estimation of generalized systems has become a hot topic of research at home and abroad. Due to the existence of singular matrices in the dynamic terms of generalized systems, the existing singular structure Kalman filter is difficult to solve, and its covariance matrix may have singular values, which is not easy to apply. At the same time, the current Kalman filter estimation methods for state-delay generalized systems are still relatively limited. In addition, the above-mentioned external disturbances and system measurement deviations bring additional challenges to the design of Kalman filters for nonlinear generalized systems. Therefore, the present invention regards the combined faults of actuators and sensors as additional variables of ACSs and establishes a time-delay generalized system; designs a robust Kalman filter based on a disturbance observer and designs robust parameters to solve the linearization error problem of the system nonlinear terms and nonlinear time-delay terms; improves the WOA based on the improved annealing simulation algorithm (ISA) of the elite set strategy and adaptive parameters to better optimize the system noise and reduce the influence of noise measurement deviation on the filtering accuracy.

滤波器和扰动估计思想,利用改进的群体智能算法设计优化的鲁棒Kalman滤波器,从而提高复杂工况下的ACSs复合故障估计精度,具有重要的现实意义。The idea of filter and disturbance estimation is used to design an optimized robust Kalman filter using an improved swarm intelligence algorithm, thereby improving the estimation accuracy of ACSs compound faults under complex working conditions, which has important practical significance.

发明内容Summary of the invention

本发明的目的是提供一种卫星姿态控制系统故障估计的Kalman滤波方法,实现航天器的高精度故障估计。The purpose of the present invention is to provide a Kalman filtering method for fault estimation of a satellite attitude control system, so as to achieve high-precision fault estimation of a spacecraft.

为实现上述目的,本发明提供了一种卫星姿态控制系统故障估计的Kalman滤波方法,具体步骤如下:To achieve the above object, the present invention provides a Kalman filtering method for satellite attitude control system fault estimation, and the specific steps are as follows:

步骤S1:考虑可建模干扰和状态时滞,将执行器故障和传感器故障为卫星姿态控制系统的附加变量,建立时滞广义系统模型;Step S1: Considering the modelable disturbance and state time delay, actuator failure and sensor failure are taken as additional variables of the satellite attitude control system, and a time-delay generalized system model is established;

步骤S2:针对建立的时滞广义系统,基于鲁棒滤波和扰动观测器设计非奇异鲁棒Kalman滤波器;Step S2: for the established time-delay descriptor system, a non-singular robust Kalman filter is designed based on robust filtering and disturbance observer;

非奇异鲁棒Kalman滤波器包括干扰估计项和非线性状态估计项,The non-singular robust Kalman filter includes interference estimation terms and nonlinear state estimation terms.

基于扰动观测器的干扰估计项用于估计可建模干扰;The disturbance estimation term based on the disturbance observer is used to estimate the modelable disturbance;

非线性状态估计项用于估计时滞广义系统的状态变量;The nonlinear state estimation term is used to estimate the state variables of the time-delay descriptor system;

步骤S3:基于泰勒级数展开时滞广义系统的非线性项和非线性时滞项,并给出泰勒级数展开截断误差的鲁棒上界;Step S3: Based on the Taylor series expansion of the nonlinear term and the nonlinear time-delay term of the time-delay descriptor system, a robust upper bound of the Taylor series expansion truncation error is given;

步骤S4:基于精英集合策略得到改进的模拟退火算法,通过改进的模拟退火算法和自适应参数改进鲸鱼优化算法,得到改进的鲸鱼优化算法,通过改进的鲸鱼优化算法优化系统的噪声协方差矩阵,并用优化后的噪声协方差矩阵代替系统原有噪声协方差;Step S4: an improved simulated annealing algorithm is obtained based on the elite set strategy, and the whale optimization algorithm is improved by the improved simulated annealing algorithm and adaptive parameters to obtain an improved whale optimization algorithm, and the noise covariance matrix of the system is optimized by the improved whale optimization algorithm, and the original noise covariance of the system is replaced by the optimized noise covariance matrix;

步骤S5:执行时滞广义系统的状态估计和可建模干扰估计,完成卫星姿态控制系统的状态估计和多种故障估计。Step S5: Execute state estimation and modelable interference estimation of the time-delay generalized system, and complete state estimation and multiple fault estimation of the satellite attitude control system.

优选的,在步骤S1中,Preferably, in step S1,

所述可建模干扰具有谐波特性,且等效为外源干扰;The modelable interference has harmonic characteristics and is equivalent to external interference;

所述时滞为定常时滞,即时滞常数为正整数;The time lag is a steady-state time lag, that is, the time lag constant is a positive integer;

所述执行器和所述传感器的故障分布矩阵和可建模干扰分布矩阵均为列满秩矩阵。The fault distribution matrix and the modelable interference distribution matrix of the actuator and the sensor are both column full rank matrices.

优选的,所述卫星姿态控制系统的模型为:Preferably, the model of the satellite attitude control system is:

Figure BDA0004082139010000041
Figure BDA0004082139010000041

其中,xk、xk-l、g(xk)、gd(xk-l)、uk、yk分别为:卫星的三轴角速度、角速度时滞、非线性项、非线性时滞项、控制输入、测量输出;l代表时滞常数且为正整数,fk和sk分别表示执行器故障和传感器故障;A、Ad和C为常数矩阵;常数矩阵B为控制输入uk的系数矩阵;Fa和Fs分别为执行器故障fk和传感器故障sk的分布矩阵;wk和vk分别为过程白噪声和测量白噪声,dk为可建模干扰,常数矩阵Fd为其分布矩阵;Among them, xk , xkl , g( xk ), gd ( xkl ), uk , yk are: the satellite's three-axis angular velocity, angular velocity time delay, nonlinear term, nonlinear time delay term, control input, and measurement output, respectively; l represents the time delay constant and is a positive integer, fk and sk represent actuator fault and sensor fault, respectively; A, Ad , and C are constant matrices; the constant matrix B is the coefficient matrix of the control input uk ; Fa and Fs are the distribution matrices of actuator fault fk and sensor fault sk , respectively; wk and vk are process white noise and measurement white noise, respectively; dk is the modelable interference, and the constant matrix Fd is its distribution matrix;

可建模干扰的等效公式如下:The equivalent formula for modeling interference is as follows:

dk=D1ηk+D2k+1=Wηk d k =D 1 η k +D 2 , η k+1 =Wη k

其中,ηk为外源干扰,D1、D2和W为常数矩阵;Among them, η k is the external interference, D 1 , D 2 and W are constant matrices;

令x=[xT fT sT]T,yr,k=Crfk+vr,k,vr,k为白噪声,且其协方差矩阵为Rr,k,令fk+1≈fk,则得到时滞广义系统如下:Let x = [x T f T s T ] T , y r,k = C r f k + v r,k , v r,k is white noise, and its covariance matrix is R r,k , let f k+1 ≈ f k , then the time-delay generalized system is as follows:

Figure BDA0004082139010000051
Figure BDA0004082139010000051

其中:E=diag(I,0),I代表设定维数的单位阵;

Figure BDA0004082139010000052
为时滞广义系统的状态变量,
Figure BDA0004082139010000053
为状态时滞变量,
Figure BDA0004082139010000054
Figure BDA0004082139010000055
Where: E = diag(I,0), I represents the unit matrix of set dimension;
Figure BDA0004082139010000052
is the state variable of the time-delay descriptor system,
Figure BDA0004082139010000053
is the state lag variable,
Figure BDA0004082139010000054
Figure BDA0004082139010000055

Figure BDA0004082139010000056
Figure BDA0004082139010000056

系统白噪声wk和vk的协方差为Qk和Rk

Figure BDA0004082139010000057
Figure BDA0004082139010000058
的协方差为
Figure BDA0004082139010000059
Figure BDA00040821390100000510
The covariance of the system white noise w k and v k is Q k and R k ,
Figure BDA0004082139010000057
and
Figure BDA0004082139010000058
The covariance of
Figure BDA0004082139010000059
and
Figure BDA00040821390100000510

优选的,与时滞广义系统和所设计的非奇异鲁棒Kalman滤波器有关的非奇异矩阵G和矩阵H满足如下公式:Preferably, the non-singular matrix G and the matrix H related to the time-delay descriptor system and the designed non-singular robust Kalman filter satisfy the following formula:

Figure BDA00040821390100000511
Figure BDA00040821390100000511

非奇异矩阵G和矩阵H的通解为:The general solution for non-singular matrices G and H is:

Figure BDA00040821390100000512
Figure BDA00040821390100000512

其中,

Figure BDA00040821390100000513
Y为自由度矩阵,
Figure BDA00040821390100000514
为伪逆。in,
Figure BDA00040821390100000513
Y is the degree of freedom matrix,
Figure BDA00040821390100000514
It is a pseudo-reverse.

优选的,所述非奇异鲁棒Kalman滤波器结构为:Preferably, the non-singular robust Kalman filter structure is:

Figure BDA00040821390100000515
Figure BDA00040821390100000515

其中,

Figure BDA00040821390100000516
Figure BDA00040821390100000517
分别用以估计时滞广义系统的状态变量
Figure BDA00040821390100000518
状态时滞变量
Figure BDA00040821390100000519
和外源干扰ηk;Kk和Vk为待设计的增益矩阵;in,
Figure BDA00040821390100000516
and
Figure BDA00040821390100000517
They are used to estimate the state variables of the time-delay descriptor system
Figure BDA00040821390100000518
State Delay Variable
Figure BDA00040821390100000519
and external interference η k ; K k and V k are gain matrices to be designed;

Figure BDA00040821390100000520
Figure BDA0004082139010000061
定义变量J的误差为
Figure BDA0004082139010000062
得到
Figure BDA0004082139010000063
和η的联合估计误差为:make
Figure BDA00040821390100000520
Figure BDA0004082139010000061
Define the error of variable J as
Figure BDA0004082139010000062
get
Figure BDA0004082139010000063
The joint estimation error of and η is:

Figure BDA0004082139010000064
Figure BDA0004082139010000064

其中,

Figure BDA0004082139010000065
in,
Figure BDA0004082139010000065

优选的,非线性误差项

Figure BDA0004082139010000066
Figure BDA0004082139010000067
采用泰勒级数展开方式进行线性化,利用等式表示非线性高阶项和非线性时滞高阶项后,得到:Preferably, the nonlinear error term
Figure BDA0004082139010000066
and
Figure BDA0004082139010000067
After linearization using Taylor series expansion and using equations to represent nonlinear high-order terms and nonlinear time-delay high-order terms, we get:

Figure BDA0004082139010000068
Figure BDA0004082139010000068

其中,

Figure BDA0004082139010000069
Ni,k(i=1,2)为
Figure BDA00040821390100000610
关于
Figure BDA00040821390100000611
Figure BDA00040821390100000612
关于
Figure BDA00040821390100000613
求导得到的矩阵;
Figure BDA00040821390100000614
L1和L2为常数矩阵,φ1,k和φ2,k为未知有界矩阵,满足
Figure BDA00040821390100000615
in,
Figure BDA0004082139010000069
N i,k (i=1,2) is
Figure BDA00040821390100000610
about
Figure BDA00040821390100000611
Figure BDA00040821390100000612
about
Figure BDA00040821390100000613
The matrix obtained by derivative;
Figure BDA00040821390100000614
L 1 and L 2 are constant matrices, φ 1,k and φ 2,k are unknown bounded matrices satisfying
Figure BDA00040821390100000615

基于不等式引理,得到

Figure BDA00040821390100000616
的协方差矩阵鲁棒上界Pk+1为:Based on the inequality lemma, we get
Figure BDA00040821390100000616
The robust upper bound P k+1 of the covariance matrix is:

Figure BDA00040821390100000617
Figure BDA00040821390100000617

其中,标量μ>0,γ1和γ2为设计的鲁棒参数,

Figure BDA00040821390100000618
Figure BDA00040821390100000619
Among them, the scalar μ>0, γ1 and γ2 are the designed robust parameters,
Figure BDA00040821390100000618
Figure BDA00040821390100000619

滤波增益矩阵满足:The filter gain matrix satisfies:

Figure BDA00040821390100000620
Figure BDA00040821390100000620

且估计误差

Figure BDA00040821390100000621
对于增广噪声
Figure BDA00040821390100000622
Figure BDA00040821390100000623
的鲁棒性由如下不等式保证:And the estimated error
Figure BDA00040821390100000621
For the augmented noise
Figure BDA00040821390100000622
and
Figure BDA00040821390100000623
The robustness of is guaranteed by the following inequality:

Figure BDA00040821390100000624
Figure BDA00040821390100000624

其中,P0 -1代表估计误差协方差上界初始值P0的逆;对于矩阵或变量X、Z,有

Figure BDA00040821390100000625
Among them, P 0 -1 represents the inverse of the initial value P 0 of the upper bound of the estimated error covariance; for matrices or variables X, Z, there is
Figure BDA00040821390100000625

优选的,改进的鲸鱼优化算法具体步骤如下:Preferably, the specific steps of the improved whale optimization algorithm are as follows:

步骤S41a:设置自适应参数psStep S41a: setting the adaptive parameter ps ;

步骤S42a:基于自适应参数ps,执行鲸鱼优化算法的搜索过程:Step S42a: Based on the adaptive parameter ps , the search process of the whale optimization algorithm is performed:

若rand()>ps,鲸鱼对猎物进行局部搜索:If rand()> ps , the whale performs a local search for prey:

Figure BDA0004082139010000071
Figure BDA0004082139010000071

其中,p是0和1之间的随机数,Ui,k+1是当前粒子位置,Ui,k *是最优粒子的位置,

Figure BDA0004082139010000072
是定义螺旋形状的常数,ω在-1和1之间,
Figure BDA0004082139010000073
Figure BDA0004082139010000074
ζ=2arl1-a,ξ=2rl2,rl1和rl2是0和1之间的随机数,a是收敛因子,从2线性下降到0;Where p is a random number between 0 and 1, U i,k+1 is the current particle position, U i,k * is the position of the optimal particle,
Figure BDA0004082139010000072
is a constant that defines the shape of the spiral, ω is between -1 and 1,
Figure BDA0004082139010000073
Figure BDA0004082139010000074
ζ=2ar l1 -a,ξ=2r l2 ,r l1 and r l2 are random numbers between 0 and 1, a is the convergence factor, which decreases linearly from 2 to 0;

若rand()≤ps,鲸鱼对猎物进行全局搜索:If rand() ≤ps , the whale conducts a global search for prey:

Figure BDA0004082139010000075
Figure BDA0004082139010000075

其中,

Figure BDA0004082139010000076
Figure BDA0004082139010000077
是随机粒子在当前总体中的位置。in,
Figure BDA0004082139010000076
Figure BDA0004082139010000077
is the position of the random particle in the current population.

步骤S43a:通过精英集合策略判断

Figure BDA0004082139010000078
是否进入集合,假设选择集合的大小为Y,定义
Figure BDA0004082139010000079
则精英集合策略步骤为:Step S43a: Determine by elite set strategy
Figure BDA0004082139010000078
Whether to enter the collection, assuming that the size of the selected collection is Y, define
Figure BDA0004082139010000079
Then the steps of elite set strategy are:

①对于适应度函数ψ,若

Figure BDA00040821390100000710
Figure BDA00040821390100000711
进入集合;否则,转至步骤④;①For the fitness function ψ, if
Figure BDA00040821390100000710
but
Figure BDA00040821390100000711
Enter the collection; otherwise, go to step ④;

②若j<Y,则j=j+1,

Figure BDA00040821390100000712
进入集合;若j=Y-1,则
Figure BDA00040821390100000713
进入集合,
Figure BDA00040821390100000714
退出集合;②If j<Y, then j=j+1,
Figure BDA00040821390100000712
Enter the set; if j = Y-1, then
Figure BDA00040821390100000713
Enter the collection,
Figure BDA00040821390100000714
Exit the collection;

③将集合中的元素从大到小排列,即

Figure BDA00040821390100000715
③ Arrange the elements in the set from large to small, that is
Figure BDA00040821390100000715

④结束判断;④End the judgment;

步骤S44a:基于精英集合策略,执行模拟退火算法,用Mertopolis接受概率

Figure BDA00040821390100000716
判断是否接受新的解:Step S44a: Based on the elite set strategy, execute the simulated annealing algorithm and use the Mertopolis acceptance probability
Figure BDA00040821390100000716
Determine whether to accept the new solution:

Figure BDA00040821390100000717
Figure BDA00040821390100000717

其中,

Figure BDA0004082139010000081
是随机粒子在精英集合中的位置,
Figure BDA0004082139010000082
in,
Figure BDA0004082139010000081
is the position of the random particle in the elite set,
Figure BDA0004082139010000082

Figure BDA0004082139010000083
Figure BDA0004082139010000084
否则
Figure BDA0004082139010000085
like
Figure BDA0004082139010000083
but
Figure BDA0004082139010000084
otherwise
Figure BDA0004082139010000085

Figure BDA0004082139010000086
Figure BDA0004082139010000087
否则Ui,k+1=Ui,k。like
Figure BDA0004082139010000086
but
Figure BDA0004082139010000087
Otherwise U i,k+1 =U i,k .

优选的,通过改进的鲸鱼优化算法优化系统的噪声协方差矩阵

Figure BDA0004082139010000088
Figure BDA0004082139010000089
得到的优化值分别为
Figure BDA00040821390100000810
Figure BDA00040821390100000811
Figure BDA00040821390100000812
Figure BDA00040821390100000813
代入非奇异鲁棒Kalman滤波器,具体步骤如下:Preferably, the noise covariance matrix of the system is optimized by an improved whale optimization algorithm
Figure BDA0004082139010000088
and
Figure BDA0004082139010000089
The optimized values obtained are
Figure BDA00040821390100000810
and
Figure BDA00040821390100000811
Will
Figure BDA00040821390100000812
and
Figure BDA00040821390100000813
Substitute into the non-singular robust Kalman filter, the specific steps are as follows:

步骤S41b:初始化,给定状态估计及其相应协方差矩阵的初始值;Step S41b: Initialization, giving the initial value of the state estimate and its corresponding covariance matrix;

步骤S42b:寻找最优噪声,通过改进的鲸鱼优化算法寻优到

Figure BDA00040821390100000814
Figure BDA00040821390100000815
的最优值
Figure BDA00040821390100000816
Figure BDA00040821390100000817
Step S42b: Find the optimal noise, and use the improved whale optimization algorithm to find the optimal
Figure BDA00040821390100000814
and
Figure BDA00040821390100000815
The optimal value of
Figure BDA00040821390100000816
and
Figure BDA00040821390100000817

步骤S43b:执行滤波估计,得到时滞广义系统状态变量

Figure BDA00040821390100000818
和外源干扰ηk+1的联合估计值
Figure BDA00040821390100000819
其相应的协方差鲁棒上界和滤波增益矩阵计算方式为:Step S43b: Execute filtering estimation to obtain the state variables of the time-delay generalized system
Figure BDA00040821390100000818
and the joint estimate of the external interference η k+1
Figure BDA00040821390100000819
The corresponding covariance robust upper bound and filter gain matrix are calculated as follows:

Figure BDA00040821390100000820
Figure BDA00040821390100000820

Figure BDA00040821390100000821
Figure BDA00040821390100000821

步骤S44b:对下一组样本重复步骤S41b-步骤S43b。Step S44b: Repeat steps S41b to S43b for the next set of samples.

优选的,得到所述的联合估计值

Figure BDA00040821390100000822
后,计算如下的估计值:Preferably, the joint estimate is obtained
Figure BDA00040821390100000822
Then, the following estimates are calculated:

计算时滞广义系统的状态估计值

Figure BDA00040821390100000823
和外源干扰的估计值
Figure BDA00040821390100000824
Compute state estimates for time-delay descriptor systems
Figure BDA00040821390100000823
and estimates of external interference
Figure BDA00040821390100000824

Figure BDA00040821390100000825
计算可建模干扰估计值
Figure BDA00040821390100000826
Depend on
Figure BDA00040821390100000825
Compute modelable interference estimates
Figure BDA00040821390100000826

计算卫星姿态控制系统的状态估计值

Figure BDA00040821390100000827
且计算执行器与传感器复合故障估计值
Figure BDA00040821390100000828
Figure BDA00040821390100000829
Compute state estimates for satellite attitude control systems
Figure BDA00040821390100000827
And calculate the estimated value of the combined fault of the actuator and sensor
Figure BDA00040821390100000828
and
Figure BDA00040821390100000829

优选的,得到滤波算法的结果包括卫星状态估计曲线、基于执行器与传感器的复合故障估计曲线、改进的鲸鱼优化算法适应度函数迭代曲线以及用于评价滤波算法的指标数据,指标数据为均方根误差。Preferably, the results of the filtering algorithm include a satellite state estimation curve, a composite fault estimation curve based on actuators and sensors, an improved whale optimization algorithm fitness function iteration curve, and indicator data for evaluating the filtering algorithm, wherein the indicator data is a root mean square error.

因此,本发明采用上述一种卫星姿态控制系统故障估计的Kalman滤波方法,具有以下有益效果:Therefore, the present invention adopts the above-mentioned Kalman filtering method for satellite attitude control system fault estimation, which has the following beneficial effects:

(1)本发明的技术方案考虑可建模干扰和状态时滞,将执行器和传感器故障为卫星姿态控制系统的附加变量,建立时滞广义系统模型,充分考虑了ACSs的执行器故障、传感器故障、可建模干扰、状态定常时滞和系统测量偏差等复杂因素的影响,然后设计故障估计Kalman滤波器,不仅解决了复杂运行环境下卫星姿态控制系统的复合故障估计问题,而且拓展了Kalman滤波在时滞广义系统中的应用范围。(1) The technical solution of the present invention takes into account modelable interference and state time delay, regards actuator and sensor faults as additional variables of the satellite attitude control system, establishes a time-delay generalized system model, and fully considers the influence of complex factors such as actuator failure, sensor failure, modelable interference, state steady-state time delay and system measurement deviation of ACSs. Then, a fault estimation Kalman filter is designed, which not only solves the complex fault estimation problem of satellite attitude control systems under complex operating environments, but also expands the application scope of Kalman filtering in time-delay generalized systems.

(2)本发明的技术方案,针对建立的时滞广义系统,基于鲁棒滤波和扰动观测器设计非奇异鲁棒Kalman滤波器;非奇异鲁棒Kalman滤波器具有非奇异的结构,具有计算简单、实现容易等优点,在实现多种故障估计的同时,也实现了可建模外部干扰的估计;通过设计的鲁棒上界,降低了非线性项和非线性时滞项因泰勒级数展开导致的线性化误差,从而提高了滤波精度,进而得到了更精确的ACSs状态估计结果、可建模干扰估计结果和执行器、传感器故障估计结果。(2) The technical solution of the present invention is to design a non-singular robust Kalman filter based on robust filtering and disturbance observer for the established time-delay generalized system; the non-singular robust Kalman filter has a non-singular structure and has the advantages of simple calculation and easy implementation. While realizing multiple fault estimations, it also realizes the estimation of modelable external disturbances; through the designed robust upper bound, the linearization error of nonlinear terms and nonlinear time-delay terms caused by Taylor series expansion is reduced, thereby improving the filtering accuracy, and further obtaining more accurate ACSs state estimation results, modelable disturbance estimation results, and actuator and sensor fault estimation results.

(3)本发明的技术方案,针对系统的噪声测量偏差,基于精英集合策略改进退火模拟算法,并基于改进的退火模拟算法和自适应参数改进鲸鱼优化算法(WOA)。得到的改进的鲸鱼优化算法(IWOA)在一定程度上有效地避免了WOA优化精度低、收敛速度较慢和易陷入局部最优解等缺陷,从而更好地寻优了系统噪声,基于改进鲸鱼算法寻优得到的过程噪声和测量噪声协方差矩阵,执行优化滤波算法。该算法有效地降低了系统噪声测量偏差导致的滤波精度降低问题,从而更有效地估计出卫星姿态控制系统的状态值、可建模干扰值和多种故障值;相较于以往的优化滤波算法,得到了更高的估计精度。(3) The technical solution of the present invention aims at the noise measurement deviation of the system, improves the annealing simulation algorithm based on the elite set strategy, and improves the whale optimization algorithm (WOA) based on the improved annealing simulation algorithm and adaptive parameters. The obtained improved whale optimization algorithm (IWOA) effectively avoids the defects of low optimization accuracy, slow convergence speed and easy to fall into local optimal solution of WOA to a certain extent, so as to better optimize the system noise, and executes the optimization filtering algorithm based on the process noise and measurement noise covariance matrix obtained by optimizing the improved whale algorithm. The algorithm effectively reduces the problem of reduced filtering accuracy caused by the system noise measurement deviation, so as to more effectively estimate the state value, modelable interference value and various fault values of the satellite attitude control system; compared with the previous optimization filtering algorithm, a higher estimation accuracy is obtained.

下面通过附图和实施例,对本发明的技术方案做进一步的详细描述。The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为本发明一种卫星姿态控制系统故障估计的Kalman滤波方法的结构示意图;FIG1 is a schematic diagram of the structure of a Kalman filtering method for fault estimation of a satellite attitude control system according to the present invention;

图2a为本发明卫星姿态控制系统的X轴状态估计结果图;FIG2a is a diagram showing the X-axis state estimation result of the satellite attitude control system of the present invention;

图2b为本发明卫星姿态控制系统的Y轴状态估计结果图;FIG2 b is a diagram showing the Y-axis state estimation result of the satellite attitude control system of the present invention;

图2c为本发明卫星姿态控制系统的Z轴状态估计结果图;FIG2c is a diagram showing the Z-axis state estimation result of the satellite attitude control system of the present invention;

图3为可建模扰动估计结果图;Figure 3 is a diagram of the modelable disturbance estimation results;

图4为执行器故障估计结果;Figure 4 shows the actuator fault estimation results;

图5为传感器故障估计结果;Figure 5 shows the sensor fault estimation results;

图6为IWOA-ODORKF与WOA-ORDRKF自适应函数迭代结果对比图。Figure 6 is a comparison of the iterative results of the adaptive functions of IWOA-ODORKF and WOA-ORDRKF.

具体实施方式DETAILED DESCRIPTION

实施例Example

为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。通常在此处附图中描述和示出的本发明实施例的组件可以以各种不同的配置来布置和设计。In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

因此,以下对在附图中提供的本发明的实施例的详细描述并非旨在限制要求保护的本发明的范围,而是仅仅表示本发明的选定实施例。基于本发明中的实施例,本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

下面结合附图,对本发明的实施方式作详细说明。The embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

参考图1,一种卫星姿态控制系统故障估计的Kalman滤波方法,具体步骤如下:Referring to FIG1 , a Kalman filtering method for satellite attitude control system fault estimation is shown in the following specific steps:

步骤S1:考虑可建模干扰和状态时滞,将执行器和传感器故障为卫星姿态控制系统的附加变量,建立时滞广义系统模型。所述执行器和所述传感器的故障分布矩阵和可建模干扰分布矩阵均为列满秩矩阵。Step S1: Considering modelable interference and state time delay, actuator and sensor faults are taken as additional variables of the satellite attitude control system, and a time-delay generalized system model is established. The fault distribution matrix of the actuator and the sensor and the modelable interference distribution matrix are both column full rank matrices.

本实施例的卫星姿态控制系统的模型为:The model of the satellite attitude control system of this embodiment is:

Figure BDA0004082139010000111
Figure BDA0004082139010000111

其中,xk、xk-l、g(xk)、gd(xk-l)、uk、yk分别为:卫星的三轴角速度、角速度时滞、非线性项、非线性时滞项、控制输入、测量输出;l代表时滞常数且为正整数;fk和sk表示执行器和传感器故障;A、Ad和C为常数矩阵;常数矩阵B为控制输入uk的系数矩阵;Fa和Fs分别为执行器故障fk和传感器故障sk的分布矩阵;wk和vk分别为过程白噪声和测量白噪声,dk为可建模干扰,常数矩阵Fd为其分布矩阵。Among them, xk , xkl , g( xk ), gd ( xkl ), uk , and yk are the satellite's three-axis angular velocity, angular velocity lag, nonlinear term, nonlinear lag term, control input, and measurement output, respectively; l represents the lag constant and is a positive integer; fk and sk represent actuator and sensor faults; A, Ad, and C are constant matrices; the constant matrix B is the coefficient matrix of the control input uk ; Fa and Fs are the distribution matrices of actuator fault fk and sensor fault sk, respectively; wk and vk are process white noise and measurement white noise, respectively; dk is the modelable interference, and the constant matrix Fd is its distribution matrix.

可建模干扰具有谐波特性,且可等效为外源干扰;The modelable interference has harmonic characteristics and can be equivalent to external interference;

可建模干扰的等效公式如下:The equivalent formula for modeling interference is as follows:

dk=D1ηk+D2k+1=Wηk d k =D 1 η k +D 2 , η k+1 =Wη k

其中,ηk为外源干扰,D1、D2和W为常数矩阵;Among them, η k is the external interference, D 1 , D 2 and W are constant matrices;

Figure BDA0004082139010000112
yr,k=Crfk+vr,k,vr,k为白噪声,且其协方差矩阵为Rr,k,令fk+1≈fk,则得到时滞广义系统如下:make
Figure BDA0004082139010000112
yr ,k = C rfk + vr,k , vr ,k is white noise, and its covariance matrix is Rr,k . Let fk+1fk , then the time-delay generalized system is as follows:

Figure BDA0004082139010000113
Figure BDA0004082139010000113

其中:E=diag(I,0),I代表适当维数的单位阵,

Figure BDA0004082139010000114
为时滞广义系统的状态变量,
Figure BDA0004082139010000115
为状态时滞变量
Figure BDA0004082139010000116
Figure BDA0004082139010000117
其他矩阵的具体形式为:Where: E = diag(I,0), I represents the unit matrix of appropriate dimension,
Figure BDA0004082139010000114
is the state variable of the time-delay descriptor system,
Figure BDA0004082139010000115
is the state lag variable
Figure BDA0004082139010000116
Figure BDA0004082139010000117
The specific forms of other matrices are:

Figure BDA0004082139010000118
Figure BDA0004082139010000118

另外,系统白噪声wk和vk的协方差为Qk和Rk

Figure BDA0004082139010000119
Figure BDA00040821390100001110
的协方差为
Figure BDA00040821390100001111
Figure BDA00040821390100001112
由矩阵
Figure BDA00040821390100001113
和D1的性质,保证了时滞广义系统的完全可检测性和滤波器设计的可行性。In addition, the covariance of the system white noise w k and v k is Q k and R k ,
Figure BDA0004082139010000119
and
Figure BDA00040821390100001110
The covariance of
Figure BDA00040821390100001111
and
Figure BDA00040821390100001112
By matrix
Figure BDA00040821390100001113
The properties of D1 and D2 guarantee the complete detectability of the time-delay descriptor system and the feasibility of filter design.

与时滞广义系统和所设计的非奇异鲁棒Kalman滤波器有关的非奇异矩阵G和矩阵H满足如下公式:The non-singular matrices G and H related to the time-delay descriptor system and the designed non-singular robust Kalman filter satisfy the following formulas:

HE+GC=InHE+GC=I n

非奇异矩阵G和矩阵H的通解为:The general solution for non-singular matrices G and H is:

Figure BDA0004082139010000121
Figure BDA0004082139010000121

其中,

Figure BDA0004082139010000122
Y为自由度矩阵,
Figure BDA0004082139010000123
为伪逆。in,
Figure BDA0004082139010000122
Y is the degree of freedom matrix,
Figure BDA0004082139010000123
It is a pseudo-reverse.

步骤S2:针对建立的时滞广义系统,基于鲁棒滤波和扰动观测器设计非奇异鲁棒Kalman滤波器。Step S2: For the established time-delay descriptor system, a non-singular robust Kalman filter is designed based on robust filtering and disturbance observer.

非奇异鲁棒Kalman滤波器包括干扰估计项和非线性状态估计项。基于扰动观测器的干扰估计项用于估计可建模干扰。非线性状态估计项用于估计时滞广义系统的状态变量。The non-singular robust Kalman filter includes disturbance estimation term and nonlinear state estimation term. The disturbance estimation term based on disturbance observer is used to estimate the modelable disturbance. The nonlinear state estimation term is used to estimate the state variables of the time-delay descriptor system.

非奇异鲁棒Kalman滤波器结构为:The structure of the non-singular robust Kalman filter is:

Figure BDA0004082139010000124
Figure BDA0004082139010000124

其中,

Figure BDA0004082139010000125
Figure BDA0004082139010000126
分别用以估计时滞广义系统的状态变量
Figure BDA0004082139010000127
状态时滞变量
Figure BDA0004082139010000128
和外源干扰ηk;Kk和Vk为待设计的增益矩阵;in,
Figure BDA0004082139010000125
and
Figure BDA0004082139010000126
They are used to estimate the state variables of the time-delay descriptor system
Figure BDA0004082139010000127
State Delay Variable
Figure BDA0004082139010000128
and external interference η k ; K k and V k are gain matrices to be designed;

Figure BDA0004082139010000129
Figure BDA00040821390100001210
定义变量J的误差为
Figure BDA00040821390100001211
得到
Figure BDA00040821390100001212
和η的联合估计误差为:make
Figure BDA0004082139010000129
Figure BDA00040821390100001210
Define the error of variable J as
Figure BDA00040821390100001211
get
Figure BDA00040821390100001212
The joint estimation error of and η is:

Figure BDA00040821390100001213
Figure BDA00040821390100001213

其中,

Figure BDA00040821390100001214
Figure BDA00040821390100001215
in,
Figure BDA00040821390100001214
Figure BDA00040821390100001215

步骤S3:基于泰勒级数展开时滞广义系统的非线性项和非线性时滞项,并给出泰勒级数展开截断误差的鲁棒上界。Step S3: Based on the Taylor series expansion, the nonlinear terms and nonlinear time-delay terms of the time-delay descriptor system are obtained, and a robust upper bound of the Taylor series expansion truncation error is given.

给定非线性高阶项和非线性时滞高阶项的鲁棒上界,非线性误差项

Figure BDA0004082139010000131
Figure BDA0004082139010000132
采用泰勒级数展开方式进行线性化,利用等式表示非线性高阶项和非线性时滞高阶项后,保留一阶导数项作为线性误差项,且截断误差表示为:
Figure BDA0004082139010000133
得到:Given the robust upper bounds of the nonlinear high-order terms and the nonlinear time-delay high-order terms, the nonlinear error term
Figure BDA0004082139010000131
and
Figure BDA0004082139010000132
The Taylor series expansion method is used for linearization. After the nonlinear high-order terms and nonlinear time-delay high-order terms are expressed by equations, the first-order derivative terms are retained as linear error terms, and the truncation error is expressed as:
Figure BDA0004082139010000133
get:

Figure BDA0004082139010000134
Figure BDA0004082139010000134

其中,

Figure BDA0004082139010000135
Ni,k(i=1,2)为
Figure BDA0004082139010000136
关于
Figure BDA0004082139010000137
关于
Figure BDA0004082139010000138
求导得到的矩阵。in,
Figure BDA0004082139010000135
N i,k (i=1,2) is
Figure BDA0004082139010000136
about
Figure BDA0004082139010000137
about
Figure BDA0004082139010000138
The matrix obtained by derivative.

基于不等式引理,给定正标量μ,设计鲁棒参数γ1和γ2,,得到

Figure BDA0004082139010000139
的协方差矩阵鲁棒上界Pk+1为:Based on the inequality lemma, given a positive scalar μ, we design robust parameters γ 1 and γ 2 , and obtain
Figure BDA0004082139010000139
The robust upper bound P k+1 of the covariance matrix is:

Figure BDA00040821390100001310
Figure BDA00040821390100001310

其中,标量μ>0,γ1和γ2为设计的鲁棒参数,

Figure BDA00040821390100001311
Figure BDA00040821390100001312
Among them, the scalar μ>0, γ1 and γ2 are the designed robust parameters,
Figure BDA00040821390100001311
Figure BDA00040821390100001312

同时,设计的滤波增益矩阵满足:At the same time, the designed filter gain matrix satisfies:

Figure BDA00040821390100001313
Figure BDA00040821390100001313

且估计误差

Figure BDA00040821390100001314
对于增广噪声
Figure BDA00040821390100001315
Figure BDA00040821390100001316
的鲁棒性由如下不等式保证:And the estimated error
Figure BDA00040821390100001314
For the augmented noise
Figure BDA00040821390100001315
and
Figure BDA00040821390100001316
The robustness of is guaranteed by the following inequality:

Figure BDA00040821390100001317
Figure BDA00040821390100001317

其中,其中,P0 -1代表估计误差协方差上界初始值P0的逆,对于矩阵或变量X、Z,有

Figure BDA00040821390100001318
Among them, P 0 -1 represents the inverse of the initial value P 0 of the upper bound of the estimated error covariance. For matrices or variables X and Z, there is
Figure BDA00040821390100001318

步骤S4:基于精英集合策略得到改进的模拟退火算法,通过改进的模拟退火算法和自适应参数改进鲸鱼优化算法,得到改进的鲸鱼优化算法,通过改进的鲸鱼优化算法优化系统的噪声协方差矩阵,并用优化后的噪声协方差矩阵代替系统原有噪声协方差。Step S4: Based on the elite set strategy, an improved simulated annealing algorithm is obtained, and the whale optimization algorithm is improved by the improved simulated annealing algorithm and adaptive parameters to obtain an improved whale optimization algorithm. The noise covariance matrix of the system is optimized by the improved whale optimization algorithm, and the original noise covariance of the system is replaced by the optimized noise covariance matrix.

改进的鲸鱼优化算法具体步骤如下:The specific steps of the improved whale optimization algorithm are as follows:

步骤S41a:设置自适应参数psStep S41a: setting the adaptive parameter ps ;

步骤S42a:基于自适应参数ps,执行鲸鱼优化算法的搜索过程:Step S42a: Based on the adaptive parameter ps , the search process of the whale optimization algorithm is performed:

若rand()>ps,鲸鱼对猎物进行局部搜索:If rand()> ps , the whale performs a local search for prey:

Figure BDA0004082139010000141
Figure BDA0004082139010000141

其中,p是0和1之间的随机数,Ui,k+1是当前粒子位置,Ui,k *是最优粒子的位置,

Figure BDA0004082139010000142
是定义螺旋形状的常数,ω在-1和1之间,
Figure BDA0004082139010000143
Figure BDA0004082139010000144
ζ=2arl1-a,ξ=2rl2,rl1和rl2是0和1之间的随机数,a是收敛因子,从2线性下降到0。Where p is a random number between 0 and 1, U i,k+1 is the current particle position, U i,k * is the position of the optimal particle,
Figure BDA0004082139010000142
is a constant that defines the shape of the spiral, ω is between -1 and 1,
Figure BDA0004082139010000143
Figure BDA0004082139010000144
ζ=2ar l1 -a, ξ=2r l2 , r l1 and r l2 are random numbers between 0 and 1, and a is the convergence factor, which decreases linearly from 2 to 0.

若rand()≤ps,鲸鱼对猎物进行全局搜索:If rand() ≤ps , the whale conducts a global search for prey:

Figure BDA0004082139010000145
Figure BDA0004082139010000145

其中,

Figure BDA0004082139010000146
Figure BDA0004082139010000147
是随机粒子在当前总体中的位置。in,
Figure BDA0004082139010000146
Figure BDA0004082139010000147
is the position of the random particle in the current population.

步骤S43a:通过精英集合策略判断

Figure BDA0004082139010000148
是否进入集合,假设选择集合的大小为Y,定义
Figure BDA0004082139010000149
则精英集合策略步骤为:Step S43a: Determine by elite set strategy
Figure BDA0004082139010000148
Whether to enter the collection, assuming that the size of the selected collection is Y, define
Figure BDA0004082139010000149
Then the steps of elite set strategy are:

①对于适应度函数ψ,若

Figure BDA00040821390100001410
Figure BDA00040821390100001411
进入集合;否则,转至步骤④;①For the fitness function ψ, if
Figure BDA00040821390100001410
but
Figure BDA00040821390100001411
Enter the collection; otherwise, go to step ④;

②若j<Y,则j=j+1,

Figure BDA00040821390100001412
进入集合;若j=Y-1,则
Figure BDA00040821390100001413
进入集合,
Figure BDA00040821390100001414
退出集合;②If j<Y, then j=j+1,
Figure BDA00040821390100001412
Enter the set; if j = Y-1, then
Figure BDA00040821390100001413
Enter the collection,
Figure BDA00040821390100001414
Exit the collection;

③将集合中的元素从大到小排列,即

Figure BDA00040821390100001415
③ Arrange the elements in the set from large to small, that is
Figure BDA00040821390100001415

④结束判断;④End the judgment;

步骤S44a:基于精英集合策略,执行模拟退火算法,用Mertopolis接受概率

Figure BDA0004082139010000151
判断是否接受新的解:Step S44a: Based on the elite set strategy, execute the simulated annealing algorithm and use the Mertopolis acceptance probability
Figure BDA0004082139010000151
Determine whether to accept the new solution:

Figure BDA0004082139010000152
Figure BDA0004082139010000152

其中,

Figure BDA0004082139010000153
是随机粒子在精英集合中的位置,
Figure BDA0004082139010000154
in,
Figure BDA0004082139010000153
is the position of the random particle in the elite set,
Figure BDA0004082139010000154

Figure BDA0004082139010000155
Figure BDA0004082139010000156
否则
Figure BDA0004082139010000157
like
Figure BDA0004082139010000155
but
Figure BDA0004082139010000156
otherwise
Figure BDA0004082139010000157

Figure BDA0004082139010000158
Figure BDA0004082139010000159
否则Ui,k+1=Ui,k。like
Figure BDA0004082139010000158
but
Figure BDA0004082139010000159
Otherwise U i,k+1 =U i,k .

通过改进的鲸鱼优化算法优化系统的噪声协方差矩阵

Figure BDA00040821390100001510
Figure BDA00040821390100001511
得到的优化值分别为
Figure BDA00040821390100001512
Figure BDA00040821390100001513
Figure BDA00040821390100001514
Figure BDA00040821390100001515
代入非奇异鲁棒Kalman滤波器,得到的IWOA-DORKF滤波流程具体步骤如下:Optimizing the noise covariance matrix of the system by using the improved whale optimization algorithm
Figure BDA00040821390100001510
and
Figure BDA00040821390100001511
The optimized values obtained are
Figure BDA00040821390100001512
and
Figure BDA00040821390100001513
Will
Figure BDA00040821390100001514
and
Figure BDA00040821390100001515
Substituting into the non-singular robust Kalman filter, the specific steps of the IWOA-DORKF filtering process are as follows:

步骤S41b:初始化,给定状态估计及其相应协方差矩阵的初始值;Step S41b: Initialization, giving the initial value of the state estimate and its corresponding covariance matrix;

步骤S42b:寻找最优噪声,通过改进的鲸鱼优化算法寻优到

Figure BDA00040821390100001516
Figure BDA00040821390100001517
的最优值
Figure BDA00040821390100001518
Figure BDA00040821390100001519
Step S42b: Find the optimal noise, and use the improved whale optimization algorithm to find the optimal
Figure BDA00040821390100001516
and
Figure BDA00040821390100001517
The optimal value of
Figure BDA00040821390100001518
and
Figure BDA00040821390100001519

步骤S43b:执行滤波估计,得到时滞广义系统状态变量

Figure BDA00040821390100001520
和外源干扰ηk+1的联合估计值
Figure BDA00040821390100001521
其相应的协方差鲁棒上界和滤波增益矩阵计算方式为:Step S43b: Execute filtering estimation to obtain the state variables of the time-delay generalized system
Figure BDA00040821390100001520
and the joint estimate of the external interference η k+1
Figure BDA00040821390100001521
The corresponding covariance robust upper bound and filter gain matrix are calculated as follows:

Figure BDA00040821390100001522
Figure BDA00040821390100001522

Figure BDA00040821390100001523
Figure BDA00040821390100001523

步骤S44b:对下一组样本重复步骤S41b-步骤S43b。Step S44b: Repeat steps S41b to S43b for the next set of samples.

步骤S5:执行时滞广义系统的状态估计和可建模干扰估计,完成卫星姿态控制系统的状态估计和复合故障估计。得到所述的联合估计值

Figure BDA00040821390100001524
后,计算如下的估计值:Step S5: Execute the state estimation and modelable interference estimation of the time-delay generalized system to complete the state estimation and composite fault estimation of the satellite attitude control system. Obtain the joint estimation value
Figure BDA00040821390100001524
Then, the following estimates are calculated:

(1)计算时滞广义系统的状态估计值

Figure BDA00040821390100001525
和外源干扰的估计值
Figure BDA00040821390100001529
(1) Calculate the state estimate of the time-delay descriptor system
Figure BDA00040821390100001525
and estimates of external interference
Figure BDA00040821390100001529

(2)由

Figure BDA00040821390100001526
计算可建模干扰估计值
Figure BDA00040821390100001527
(2) By
Figure BDA00040821390100001526
Compute modelable interference estimates
Figure BDA00040821390100001527

(3)计算卫星姿态控制系统的状态估计值

Figure BDA00040821390100001528
且计算执行器与传感器复合故障估计值
Figure BDA0004082139010000161
Figure BDA0004082139010000162
(3) Calculate the state estimate of the satellite attitude control system
Figure BDA00040821390100001528
And calculate the estimated value of the combined fault of the actuator and sensor
Figure BDA0004082139010000161
and
Figure BDA0004082139010000162

得到滤波算法的结果包括卫星状态估计曲线、基于执行器与传感器的复合故障估计曲线、改进的鲸鱼优化算法适应度函数迭代曲线以及用于评价滤波算法的指标数据,指标数据为均方根误差。The results of the filtering algorithm include the satellite state estimation curve, the composite fault estimation curve based on actuators and sensors, the improved whale optimization algorithm fitness function iteration curve, and the indicator data used to evaluate the filtering algorithm, the indicator data is the root mean square error.

为了验证本实施的性能,采用三种滤波器对目标ACSs的故障等进行估计,且将所获得的三种滤波器估计结果进行对比。三种滤波器分别为:DORKF、WOA-DORKF以及IWOA-DORKF。In order to verify the performance of this implementation, three filters are used to estimate the faults of target ACSs, and the estimation results of the three filters are compared. The three filters are DORKF, WOA-DORKF and IWOA-DORKF.

试验结果如图2a、图2b、图2c、图3、图4以及图5所示,基于本实施例的IWOA-DORKF滤波方法具有更快收敛速度、更高计算精度和更好跳出全局最优解能力,对目标ACSs的状态、可建模干扰和执行器、传感器复合故障估计结果最接近目标ACSs相应变量的真实值,因此表明本发明所提供的故障估计方法具有更精确的估计效果。于此同时,如图6所示,WOA-DORKF和本发明的IWOA-DORKF自适应函数迭代对比图。所述的估计精度由IWOA在估计期间内的更优自适应函数迭代方式保证。The test results are shown in Figures 2a, 2b, 2c, 3, 4 and 5. The IWOA-DORKF filtering method based on this embodiment has a faster convergence speed, higher calculation accuracy and better ability to jump out of the global optimal solution. The estimation results of the state of the target ACSs, modelable interference and actuator and sensor composite faults are closest to the true values of the corresponding variables of the target ACSs, thus indicating that the fault estimation method provided by the present invention has a more accurate estimation effect. At the same time, as shown in Figure 6, the WOA-DORKF and the IWOA-DORKF adaptive function iteration comparison diagram of the present invention. The estimation accuracy is guaranteed by the more optimal adaptive function iteration method of IWOA during the estimation period.

最后应说明的是:以上实施例仅用以说明本发明的技术方案而非对其进行限制,尽管参照较佳实施例对本发明进行了详细的说明,本领域的普通技术人员应当理解:其依然可以对本发明的技术方案进行修改或者等同替换,而这些修改或者等同替换亦不能使修改后的技术方案脱离本发明技术方案的精神和范围。Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims (10)

1. A Kalman filtering method for satellite attitude control system fault estimation is characterized by comprising the following specific steps:
step S1: taking modeling interference and state time lag into consideration, taking actuator faults and sensor faults as additional variables of a satellite attitude control system, and establishing a time lag generalized system model;
step S2: aiming at the established time lag generalized system, a non-singular robust Kalman filter is designed based on a robust filter and a disturbance observer;
the non-singular robust Kalman filter includes an interference estimation term and a nonlinear state estimation term,
an interference estimation term based on the disturbance observer is used for estimating modelable interference;
the nonlinear state estimation term is used for estimating state variables of the time lag generalized system;
step S3: based on a nonlinear term and a nonlinear time-lag term of a Taylor series expansion time-lag generalized system, a robust upper bound of a Taylor series expansion truncation error is given;
step S4: an improved simulated annealing algorithm is obtained based on an elite set strategy, a whale optimization algorithm is improved through the improved simulated annealing algorithm and the adaptive parameters, an improved whale optimization algorithm is obtained, a noise covariance matrix of a system is optimized through the improved whale optimization algorithm, and the optimized noise covariance matrix is used for replacing the original noise covariance of the system;
step S5: and executing state estimation and modeling interference estimation of the time-lag generalized system to complete state estimation and various fault estimation of the satellite attitude control system.
2. A Kalman filtering method for fault estimation of satellite attitude control system according to claim 1, wherein: in the step S1 of the process,
the modelable disturbance has harmonic characteristics and is equivalent to an exogenous disturbance;
the time lag is constant time lag, and the instant time lag constant is a positive integer;
the fault distribution matrix and the modelable disturbance distribution matrix of the actuator and the sensor are both a column full order matrix.
3. A Kalman filtering method for fault estimation of satellite attitude control system according to claim 2, wherein: the satellite attitude control system model is as follows:
Figure FDA0004082139000000021
wherein ,xk 、x k-l 、g(x k )、g d (x k-l )、u k 、y k The method comprises the following steps of: triaxial angular velocity, angular velocity time lag, nonlinear term, nonlinear time lag term, control input and measurement output of the satellite; l represents a time lag constant and is a positive integer, f k and sk Representing an actuator failure and a sensor failure, respectively; A. a is that d And C is a constant matrix; the constant matrix B is the control input u k Coefficient matrix of (a); f (F) a and Fs Respectively the actuator faults f k And sensor faults s k Is a distribution matrix of (a); w (w) k and vk Respectively, process white noise and measurement white noise, d k To model interference, a constant matrix F d A distribution matrix for the same;
the equivalent formula for modeling interference is as follows:
d k =D 1 η k +D 2k+1 =Wη k
wherein ,ηk For exogenous disturbance, D 1 、D 2 And W is a constant matrix;
order the
Figure FDA0004082139000000022
y r,k =C r f k +v r,k ,v r,k White noise and its covariance matrix is R r,k Let f k+1 ≈f k Then get time lagThe generalized system is as follows:
Figure FDA0004082139000000023
wherein: e=diag (I, 0), I representing a unit array of set dimensions;
Figure FDA0004082139000000024
for the state variable of the time-lag generalized system, +.>
Figure FDA0004082139000000025
For state time lag variable, ++>
Figure FDA0004082139000000026
Figure FDA0004082139000000027
Figure FDA0004082139000000028
White noise w of system k and vk Covariance of Q k and Rk
Figure FDA0004082139000000029
and
Figure FDA00040821390000000210
Covariance of +.>
Figure FDA00040821390000000211
And
Figure FDA00040821390000000212
4. a Kalman filtering method for fault estimation of satellite attitude control system according to claim 3, wherein: the non-singular matrix G and matrix H related to the time-lag generalized system and the designed non-singular robust Kalman filter satisfy the following formula:
Figure FDA0004082139000000031
the general solution of the non-singular matrix G and the matrix H is:
Figure FDA0004082139000000032
wherein ,
Figure FDA0004082139000000033
y is a degree of freedom matrix>
Figure FDA0004082139000000034
Is pseudo-inverse.
5. The Kalman filtering method for satellite attitude control system fault estimation according to claim 4, wherein: the structure of the non-singular robust Kalman filter is as follows:
Figure FDA0004082139000000035
wherein ,
Figure FDA0004082139000000036
and
Figure FDA0004082139000000037
Respectively used for estimating state variables x of time lag generalized system k State time lag variable->
Figure FDA0004082139000000038
And exogenous interference eta k ;K k and Vk A gain matrix to be designed;
order the
Figure FDA0004082139000000039
Figure FDA00040821390000000310
Define the error of variable J as +.>
Figure FDA00040821390000000311
Obtain->
Figure FDA00040821390000000312
The joint estimation error of η is:
Figure FDA00040821390000000313
wherein ,
Figure FDA00040821390000000314
6. the Kalman filtering method for satellite attitude control system fault estimation according to claim 5, wherein: nonlinear error term
Figure FDA00040821390000000315
and
Figure FDA00040821390000000316
Linearization is performed by adopting a Taylor series expansion mode, and after a nonlinear high-order term and a nonlinear time-lag high-order term are expressed by using an equation, the method is characterized in that:
Figure FDA00040821390000000317
wherein ,
Figure FDA00040821390000000318
N i,k (i=1, 2) is +.>
Figure FDA00040821390000000319
About->
Figure FDA00040821390000000320
About->
Figure FDA00040821390000000324
Deriving the obtained matrix;
Figure FDA00040821390000000321
L 1 and L2 Is a constant matrix phi 1,k and φ2,k For an unknown bounded matrix, satisfy +.>
Figure FDA00040821390000000322
Based on inequality quotation, get
Figure FDA00040821390000000323
Covariance matrix robust upper bound P of (2) k+1 The method comprises the following steps:
Figure FDA0004082139000000041
wherein the scalar mu > 0, gamma 1 and γ2 For the robust parameters of the design,
Figure FDA0004082139000000042
Figure FDA0004082139000000043
the filter gain matrix satisfies:
Figure FDA0004082139000000044
and estimate the error
Figure FDA0004082139000000045
For amplifying noise->
Figure FDA0004082139000000046
and
Figure FDA0004082139000000047
The robustness of (c) is guaranteed by the following inequality:
Figure FDA0004082139000000048
wherein ,
Figure FDA0004082139000000049
represents an initial value P of an estimated error covariance upper bound 0 Is the inverse of (2); for matrix or variable X, Z, there are
Figure FDA00040821390000000410
7. The Kalman filtering method for fault estimation of satellite attitude control system according to claim 6, wherein: the improved whale optimization algorithm comprises the following specific steps:
step S41a: setting an adaptive parameter p s
Step S42a: based on adaptive parameter p s Performing a search process of a whale optimization algorithm:
if rand () > p s Whale performs a local search for prey:
Figure FDA00040821390000000411
wherein p is a random number between 0 and 1, U i,k+1 Is the current particle position, U i,k * Is the position of the optimal particle, θ is a constant defining the helical shape, ω is between-1 and 1,
Figure FDA00040821390000000412
Figure FDA00040821390000000413
ζ=2ar l1 -a,ξ=2r l2 ,r l1 and rl2 Is a random number between 0 and 1, a is a convergence factor, and decreases linearly from 2 to 0;
if rand (). Ltoreq.p s Whale performs a global search for prey:
Figure FDA0004082139000000051
wherein ,
Figure FDA0004082139000000052
is the location of the random particles in the current population.
Step S43a: judgment by elite set policy
Figure FDA0004082139000000053
If the set is entered, define that the size of the selected set is Y
Figure FDA0004082139000000054
The elite aggregation policy steps are:
(1) for the fitness function ψ, if
Figure FDA0004082139000000055
Then->
Figure FDA0004082139000000056
Entering a collection; otherwise, turning to the step (4); />
(2) If j < Y, j=j+1,
Figure FDA0004082139000000057
entering a collection; if j=Y-1, then +.>
Figure FDA0004082139000000058
Enter collection, adjust>
Figure FDA0004082139000000059
Exiting the collection;
(3) arranging elements in a collection from large to small, i.e.
Figure FDA00040821390000000510
(4) Ending the judgment;
step S44a: based on elite set strategy, executing simulated annealing algorithm, and accepting probability by Mertopolis
Figure FDA00040821390000000511
Judging whether to accept the new solution:
Figure FDA00040821390000000512
wherein ,
Figure FDA00040821390000000513
is the position of the random particle in the elite set,/->
Figure FDA00040821390000000514
If it is
Figure FDA00040821390000000515
Then->
Figure FDA00040821390000000516
Otherwise->
Figure FDA00040821390000000517
If it is
Figure FDA00040821390000000518
Then->
Figure FDA00040821390000000519
Otherwise U i,k+1 =U i,k
8. The Kalman filtering method for fault estimation of satellite attitude control system according to claim 7, wherein: optimizing noise covariance matrix of system by improved whale optimization algorithm
Figure FDA00040821390000000520
and
Figure FDA00040821390000000521
The obtained optimized values are respectively
Figure FDA00040821390000000522
and
Figure FDA00040821390000000523
Will->
Figure FDA00040821390000000524
and
Figure FDA00040821390000000525
Substituting into a non-singular robust Kalman filter, the specific steps are as follows:
step S41b: initializing, wherein initial values of state estimation and corresponding covariance matrixes are given;
step S42b: searching for optimal noise, optimizing by improved whale optimizing algorithm
Figure FDA00040821390000000526
and
Figure FDA00040821390000000527
Optimal value +.>
Figure FDA00040821390000000528
and
Figure FDA00040821390000000529
Step S43b: performing filtering estimation to obtain a time-lag generalized system state variable
Figure FDA00040821390000000530
And exogenous interference eta k+1 Joint estimation of (a)
Figure FDA0004082139000000061
The corresponding covariance robust upper bound and the filter gain matrix calculation mode are as follows:
Figure FDA0004082139000000062
Figure FDA0004082139000000063
step S44b: step S41 b-step S43b are repeated for the next set of samples.
9. The Kalman filtering method for fault estimation of satellite attitude control system according to claim 8, wherein: obtaining said joint estimateValue of
Figure FDA0004082139000000064
Thereafter, the following estimation values are calculated:
calculating state estimation value of time-lag generalized system
Figure FDA0004082139000000065
And estimate of exogenous interference->
Figure FDA0004082139000000066
From the following components
Figure FDA00040821390000000611
Calculating a modelable interference estimate +.>
Figure FDA0004082139000000067
Calculating state estimation value of satellite attitude control system
Figure FDA0004082139000000068
And calculating an actuator and sensor composite fault estimation value +.>
Figure FDA0004082139000000069
and
Figure FDA00040821390000000610
10. The Kalman filtering method for fault estimation of satellite attitude control system according to claim 9, wherein: the obtained filtering algorithm results comprise a satellite state estimation curve, a composite fault estimation curve based on an actuator and a sensor, an improved whale optimization algorithm fitness function iteration curve and index data for evaluating the filtering algorithm, wherein the index data is root mean square error.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118938685A (en) * 2024-08-23 2024-11-12 大连交通大学 A Neural Adaptive Sliding Mode Observer Design Method for Fault Estimation of Satellite ACSs

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1999010783A1 (en) * 1997-08-22 1999-03-04 Voyan Technology A method for real-time nonlinear system state estimation and control
WO2014030054A2 (en) * 2012-08-21 2014-02-27 Gonzalez Juan Valdes Method and device for determining the electrical properties of materials
EP2784445A2 (en) * 2013-03-26 2014-10-01 Honeywell International Inc. Selected aspects of advanced receiver autonomous integrity monitoring application to kalman filter based navigation filter
CN109885075A (en) * 2019-03-06 2019-06-14 扬州大学 A Fault Tolerant Control Method for Satellite Attitude Anti-jamming Based on T-S Fuzzy Modeling
CN110955231A (en) * 2019-12-18 2020-04-03 中国科学院长春光学精密机械与物理研究所 Satellite attitude control system tiny fault detection method based on robust observer
CN111999747A (en) * 2020-08-28 2020-11-27 大连海事大学 Robust fault detection method for inertial navigation-satellite combined navigation system
CN112212860A (en) * 2020-08-28 2021-01-12 山东航天电子技术研究所 Distributed filtering micro-nano satellite attitude determination method with fault tolerance
CN113253050A (en) * 2021-05-08 2021-08-13 南昌大学 Traveling wave fault location method based on whale optimization Kalman filtering algorithm

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1999010783A1 (en) * 1997-08-22 1999-03-04 Voyan Technology A method for real-time nonlinear system state estimation and control
WO2014030054A2 (en) * 2012-08-21 2014-02-27 Gonzalez Juan Valdes Method and device for determining the electrical properties of materials
EP2784445A2 (en) * 2013-03-26 2014-10-01 Honeywell International Inc. Selected aspects of advanced receiver autonomous integrity monitoring application to kalman filter based navigation filter
CN109885075A (en) * 2019-03-06 2019-06-14 扬州大学 A Fault Tolerant Control Method for Satellite Attitude Anti-jamming Based on T-S Fuzzy Modeling
CN110955231A (en) * 2019-12-18 2020-04-03 中国科学院长春光学精密机械与物理研究所 Satellite attitude control system tiny fault detection method based on robust observer
CN111999747A (en) * 2020-08-28 2020-11-27 大连海事大学 Robust fault detection method for inertial navigation-satellite combined navigation system
CN112212860A (en) * 2020-08-28 2021-01-12 山东航天电子技术研究所 Distributed filtering micro-nano satellite attitude determination method with fault tolerance
CN113253050A (en) * 2021-05-08 2021-08-13 南昌大学 Traveling wave fault location method based on whale optimization Kalman filtering algorithm

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
赵琳;邱海洋;郝勇;: "范数有界的鲁棒卫星姿态估计方法", 华中科技大学学报(自然科学版), no. 04 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118938685A (en) * 2024-08-23 2024-11-12 大连交通大学 A Neural Adaptive Sliding Mode Observer Design Method for Fault Estimation of Satellite ACSs

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