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

Kalman filtering 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

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 and specifically comprises the following steps: considering modeling interference and state time lag, taking actuator and sensor faults as additional variables, and establishing a time lag generalized system model; designing a non-singular robust Kalman filter; expanding nonlinear terms and nonlinear time-lag terms of a time-lag generalized system based on a Taylor series, and providing a robust upper bound; optimizing a noise covariance matrix through an improved whale optimization algorithm, and replacing the original noise covariance with the optimized noise covariance matrix; and executing state estimation and modeling interference estimation of the time-lag generalized system to complete state estimation and composite fault estimation of the satellite attitude control system. By adopting the Kalman filtering method for the satellite attitude control system fault estimation, the problems of various fault estimation of the satellite attitude control system in a complex operating environment are solved, and the precision of the fault estimation is improved.

Description

Kalman filtering method for fault estimation of satellite attitude control system
Technical Field
The invention relates to the technical field of spacecraft fault diagnosis, in particular to a Kalman filtering method for satellite attitude control system fault estimation.
Background
With the rapid development of satellite in-orbit services, the number of in-orbit satellites is increasing. Accordingly, the demands for satellite stability and security are also increasing. Attitude Control Systems (ACSs) act as important sub-systems for satellites, whose normal operation is related to the efficient deployment of important tasks such as on-board payload, remote control, telemetry and orbit control. However, ACSs are also relatively prone to failure due to the numerous system devices and complex operating mechanisms. Therefore, the fault of ACSs needs to be diagnosed, and the abnormality of the system is found in time, so that the occurrence of safety accidents is avoided, and the on-orbit normal operation of satellites is ensured. Therefore, by combining with the modern fault diagnosis technology, the fault of ACSs is effectively diagnosed, and the method has important practical significance.
In the model-based fault diagnosis method, designing a residual generator is an effective method. Currently, residual generators such as observers, filters, etc. have been widely used for fault diagnosis of acs. To achieve the first two task phases of ACSs, namely: fault Detection and Isolation (FDI), unknown Input Observer (UIO) has combined H - /H ∞ The detection method is widely applied. And for the last task phase of fault diagnosis: the fault estimation is particularly important because the process not only can judge the specific form and amplitude of the fault signal, but also can provide a basis for active fault-tolerant control. In view of this, adaptive observers, sliding mode observers, interval observers, etc. have combined with robust H ∞ The method ensures the stability and the robustness of the system. However, when there is operational noise in the system, the influence of noise on the fault estimation accuracy needs to be considered. For this purpose, another residual generator, a Kalman filter, has been used for ACSs fault estimation under noise.
In view of the nonlinear characteristics of ACSs systems, extended Kalman filters based on the parity vector method, fused unscented Kalman filters, strong tracking volume Kalman filters, and other improved nonlinear filters have been used to estimate the failure of ACSs. In addition, the unknown characteristics of ACSs noise are considered, and methods such as adaptive filtering, variational Bayesian filtering and the like are combined with the nonlinear Kalman filter to better estimate system noise, so that better fault estimation is realized. However, the nonlinear Kalman filtering method of ACSs still has certain drawbacks. First, the accuracy of concurrent actuator and sensor concurrent fault (composite fault) estimation of the system still needs to be further improved. Typically, satellite actuator failures are manifested as flywheel stuck, lost motion, and ramp drift, etc.; the sensor failure is mainly represented by: the gyro sensor is locked, constant deviation, slope change and the like. In extreme cases, if compound faults occur simultaneously, the coupling of fault signals may result in poor estimation accuracy. While sensor failure may be considered a false actuator failure, deviations from the equivalent method may affect the accuracy of the estimation. Second, external disturbances of the system have a certain impact on the accuracy of the fault estimation. Although methods such as disturbance observers have been used to estimate the external disturbances of ACSs, random noise and unknown external disturbances are often present at the same time, which presents certain challenges to the design of Kalman filters. Again, the speed lag of ACSs can also affect the filtering accuracy. At present, the Kalman filter design for ACSs with time-lag links mainly focuses on ACSs with measurement time-lag, but the essence of the methods is high-dimensional transformation of a system, so that the defects of high variable dimension, larger algorithm load and the like are caused. Therefore, it is necessary to design an effective fault estimation Kalman filter to improve the composite fault estimation accuracy of acs, taking the comprehensive influence of the above factors into consideration.
In addition, for ACSs, because the ACSs operate under complex working conditions for a long time, a plurality of uncertain factors can cause the abnormality of a measuring element, so that a certain deviation exists between a measured value and a true value of noise, and the filtering precision is further reduced. Currently, population intelligent algorithms such as locust algorithm, wild goat algorithm, gray wolf algorithm and Whale Optimization Algorithm (WOA) are used for optimizing system noise, so that the influence of measurement deviation of the system noise on filtering precision is reduced. However, the existing researches and applications show that the method has the defects of low convergence speed, low optimizing precision, easiness in sinking into local optimal solution and the like to different degrees. Therefore, the method for optimizing the intelligent group by combining the effective method improves the existing intelligent group optimizing method, and has important significance for enhancing the algorithm performance, improving the noise optimizing precision and further improving the fault estimating precision of ACSs.
Considering the speed time lag of ACSs, modeling disturbance and system measurement deviation, and obtaining a time lag generalized system according to the faults of an actuator and a sensor as additional state variables of the system. Thus, the fault estimation of the ACSs translates into a state estimation of the time-lapse generalized system. In recent years, kalman filtering estimation of a generalized system becomes a hot spot for domestic and foreign research. Because of the singular matrix in the dynamic term of the generalized system, the Kalman filter with the existing singular structure is difficult to solve, singular values may appear in the covariance matrix, and the method is not easy to apply. Meanwhile, the Kalman filtering estimation method for the state time lag generalized system is still limited at present. In addition, the external interference and system measurement bias described above present additional challenges to the Kalman filter design of nonlinear generalized systems. Therefore, the invention builds a time lag generalized system according to the additional variables of ACSs as the composite faults of the executor and the sensor; a robust Kalman filter is designed based on a disturbance observer, and robust parameters are designed to solve the problem of linearization errors of a nonlinear term and a nonlinear time-lag term of a system; improved annealing simulation algorithm (ISA) and adaptive parameter improved WOA based on elite set strategy to better optimize system noise and reduce the influence of noise measurement bias on filtering accuracy. Combining robust H method, kalman
∞
The filter and disturbance estimation idea are that an improved group intelligent algorithm is utilized to design an optimized robust Kalman filter, so that ACSs composite fault estimation accuracy under complex working conditions is improved, and the method has important practical significance.
Disclosure of Invention
The invention aims to provide a Kalman filtering method for fault estimation of a satellite attitude control system, which realizes high-precision fault estimation of a spacecraft.
In order to achieve the above purpose, the invention provides a Kalman filtering method for satellite attitude control system fault estimation, which comprises 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.
Preferably, in step S1,
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.
Preferably, the model of the satellite attitude control system is:
Figure BDA0004082139010000041
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 2 ,η k+1 ＝Wη k
wherein ,ηk For exogenous disturbance, D 1 、D 2 And W is a constant matrix;
let x= [ x ] T f T s T ] T ，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 The time lag generalized system is obtained as follows:
Figure BDA0004082139010000051
wherein: e=diag (I, 0), I representing a unit array of set dimensions;
Figure BDA0004082139010000052
as a state variable of the time-lapse generalized system,
Figure BDA0004082139010000053
for state time lag variable, ++>
Figure BDA0004082139010000054
Figure BDA0004082139010000055
Figure BDA0004082139010000056
White noise w of system k and vk Covariance of Q k and Rk ，
Figure BDA0004082139010000057
and
Figure BDA0004082139010000058
Covariance of +.>
Figure BDA0004082139010000059
And
Figure BDA00040821390100000510
preferably, the non-singular matrices G and H related to the time-lag generalized system and the designed non-singular robust Kalman filter satisfy the following formula:
Figure BDA00040821390100000511
the general solution of the non-singular matrix G and the matrix H is:
Figure BDA00040821390100000512
wherein ,
Figure BDA00040821390100000513
y is a degree of freedom matrix>
Figure BDA00040821390100000514
Is pseudo-inverse.
Preferably, the structure of the non-singular robust Kalman filter is as follows:
Figure BDA00040821390100000515
wherein ,
Figure BDA00040821390100000516
and
Figure BDA00040821390100000517
State variables for estimating time-lag generalized system, respectively>
Figure BDA00040821390100000518
State time lag variable->
Figure BDA00040821390100000519
And exogenous interference eta k ；K k and Vk A gain matrix to be designed;
order the
Figure BDA00040821390100000520
Figure BDA0004082139010000061
Define the error of variable J as +.>
Figure BDA0004082139010000062
Obtain->
Figure BDA0004082139010000063
The joint estimation error of η is:
Figure BDA0004082139010000064
wherein ,
Figure BDA0004082139010000065
preferably, the nonlinear error term
Figure BDA0004082139010000066
and
Figure BDA0004082139010000067
Linearization using Taylor series expansionAfter the equation represents the nonlinear higher-order term and the nonlinear time-lag higher-order term, it is obtained that:
Figure BDA0004082139010000068
wherein ,
Figure BDA0004082139010000069
N i,k (i=1, 2) is +.>
Figure BDA00040821390100000610
About->
Figure BDA00040821390100000611
Figure BDA00040821390100000612
About->
Figure BDA00040821390100000613
Deriving the obtained matrix;
Figure BDA00040821390100000614
L 1 and L2 Is a constant matrix phi 1,k and φ2,k For an unknown bounded matrix, satisfy +.>
Figure BDA00040821390100000615
Based on inequality quotation, get
Figure BDA00040821390100000616
Covariance matrix robust upper bound P of (2) k+1 The method comprises the following steps:
Figure BDA00040821390100000617
wherein the scalar mu > 0, gamma 1 and γ2 For the robust parameters of the design,
Figure BDA00040821390100000618
Figure BDA00040821390100000619
the filter gain matrix satisfies:
Figure BDA00040821390100000620
and estimate the error
Figure BDA00040821390100000621
For amplifying noise->
Figure BDA00040821390100000622
and
Figure BDA00040821390100000623
The robustness of (c) is guaranteed by the following inequality:
Figure BDA00040821390100000624
wherein ,P0 -1 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 BDA00040821390100000625
Preferably, 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 BDA0004082139010000071
wherein p is a random number between 0 and 1, U i,k+1 Is the current particle position, U i,k * Is the location of the optimal particle(s),
Figure BDA0004082139010000072
is a constant defining a spiral shape, ω is between-1 and 1, < >>
Figure BDA0004082139010000073
Figure BDA0004082139010000074
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 BDA0004082139010000075
wherein ,
Figure BDA0004082139010000076
Figure BDA0004082139010000077
is the location of the random particles in the current population.
Step S43a: judgment by elite set policy
Figure BDA0004082139010000078
Whether to enter a collection, define +.>
Figure BDA0004082139010000079
The elite aggregation policy steps are:
(1) for the fitness function ψ, if
Figure BDA00040821390100000710
Then->
Figure BDA00040821390100000711
Entering a collection; otherwise, turning to the step (4);
(2) if j < Y, j=j+1,
Figure BDA00040821390100000712
entering a collection; if j=Y-1, then +.>
Figure BDA00040821390100000713
Enter collection, adjust>
Figure BDA00040821390100000714
Exiting the collection;
(3) arranging elements in a collection from large to small, i.e.
Figure BDA00040821390100000715
(4) Ending the judgment;
step S44a: based on elite set strategy, executing simulated annealing algorithm, and accepting probability by Mertopolis
Figure BDA00040821390100000716
Judging whether to accept the new solution:
Figure BDA00040821390100000717
wherein ,
Figure BDA0004082139010000081
is the position of the random particle in the elite set,/->
Figure BDA0004082139010000082
If it is
Figure BDA0004082139010000083
Then->
Figure BDA0004082139010000084
Otherwise->
Figure BDA0004082139010000085
If it is
Figure BDA0004082139010000086
Then->
Figure BDA0004082139010000087
Otherwise U i,k+1 ＝U i,k 。
Preferably, the noise covariance matrix of the system is optimized by a modified whale optimization algorithm
Figure BDA0004082139010000088
and
Figure BDA0004082139010000089
The obtained optimized values are +.>
Figure BDA00040821390100000810
and
Figure BDA00040821390100000811
Will->
Figure BDA00040821390100000812
and
Figure BDA00040821390100000813
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 BDA00040821390100000814
and
Figure BDA00040821390100000815
Optimal value +.>
Figure BDA00040821390100000816
And
Figure BDA00040821390100000817
step S43b: performing filtering estimation to obtain a time-lag generalized system state variable
Figure BDA00040821390100000818
And exogenous interference eta k+1 Is>
Figure BDA00040821390100000819
The corresponding covariance robust upper bound and the filter gain matrix calculation mode are as follows:
Figure BDA00040821390100000820
Figure BDA00040821390100000821
step S44b: step S41 b-step S43b are repeated for the next set of samples.
Preferably, the joint estimation is obtained
Figure BDA00040821390100000822
Thereafter, the following estimation values are calculated:
calculating state estimation value of time-lag generalized system
Figure BDA00040821390100000823
And estimate of exogenous interference->
Figure BDA00040821390100000824
From the following components
Figure BDA00040821390100000825
Calculating a modelable interference estimate +.>
Figure BDA00040821390100000826
Calculating state estimation value of satellite attitude control system
Figure BDA00040821390100000827
And calculating an actuator and sensor composite fault estimation value +.>
Figure BDA00040821390100000828
and
Figure BDA00040821390100000829
Preferably, the obtained filtering algorithm result comprises 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.
Therefore, the Kalman filtering method for satellite attitude control system fault estimation has the following beneficial effects:
(1) According to the technical scheme, modeling interference and state time lag are considered, faults of an actuator and a sensor are taken as additional variables of a satellite attitude control system, a time lag generalized system model is established, influences of complex factors such as ACSs (active sensor system) actuator faults, sensor faults, modeling interference, state timing time lag and system measurement deviation are fully considered, then a fault estimation Kalman filter is designed, the problem of complex fault estimation of the satellite attitude control system in a complex operation environment is solved, and the application range of the Kalman filter in the time lag generalized system is widened.
(2) According to the technical scheme, a non-singular robust Kalman filter is designed based on a robust filter and a disturbance observer aiming at an established time-lag generalized system; the non-singular robust Kalman filter has a non-singular structure, has the advantages of simple calculation, easy realization and the like, realizes multiple fault estimation and simultaneously realizes the estimation of modeling external interference; through the designed robust upper bound, linearization errors of nonlinear terms and nonlinear time-lag terms caused by Taylor series expansion are reduced, so that filtering precision is improved, and more accurate ACSs state estimation results, modeling interference estimation results, actuator and sensor fault estimation results are obtained.
(3) According to the technical scheme, aiming at noise measurement deviation of a system, an annealing simulation algorithm is improved based on an elite set strategy, and a Whale Optimization Algorithm (WOA) is improved based on the improved annealing simulation algorithm and adaptive parameters. The Improved Whale Optimization Algorithm (IWOA) effectively avoids the defects of low WOA optimization accuracy, low convergence speed, easiness in sinking into a local optimal solution and the like to a certain extent, so that system noise is better optimized, and an optimized filtering algorithm is executed based on a process noise and measurement noise covariance matrix obtained by improving whale algorithm optimization. The algorithm effectively reduces the problem of filtering precision reduction caused by system noise measurement deviation, so that the state value, the modeling interference value and various fault values of the satellite attitude control system are estimated more effectively; compared with the prior optimized filtering algorithm, the method has higher estimation accuracy.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a schematic diagram of a Kalman filtering method for fault estimation of a satellite attitude control system according to the present invention;
FIG. 2a is a graph of the result of estimating the X-axis state of the satellite attitude control system according to the present invention;
FIG. 2b is a diagram of the Y-axis state estimation result of the satellite attitude control system according to the present invention;
FIG. 2c is a graph of the Z-axis state estimation results of the satellite attitude control system of the present invention;
FIG. 3 is a graph of a modeled disturbance estimation result;
FIG. 4 is an actuator fault estimation result;
FIG. 5 is a sensor fault estimation result;
FIG. 6 is a graph comparing the iteration results of the adaptive functions of IWOA-ODORKF and WOA-ORDRKF.
Detailed Description
Examples
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Referring to fig. 1, a Kalman filtering method for fault estimation of a satellite attitude control system specifically includes the following steps:
step S1: and taking modeling interference and state time lag into consideration, taking the faults of the actuator and the sensor as additional variables of the satellite attitude control system, and establishing a time lag generalized system model. The fault distribution matrix and the modelable disturbance distribution matrix of the actuator and the sensor are both a column full order matrix.
The model of the satellite attitude control system of the present embodiment is:
Figure BDA0004082139010000111
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 (f) k and sk Indicating actuator and sensor failure; 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 For its distribution matrix.
The modelable disturbance has harmonic characteristics and can be equivalently an exogenous disturbance;
the equivalent formula for modeling interference is as follows:
d k ＝D 1 η k +D 2 ,η k+1 ＝Wη k
wherein ,ηk For exogenous disturbance, D 1 、D 2 And W is a constant matrix;
order the
Figure BDA0004082139010000112
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 The time lag generalized system is obtained as follows:
Figure BDA0004082139010000113
wherein: e=diag (I, 0), I representing a unit array of appropriate dimensions,
Figure BDA0004082139010000114
as a state variable of the time-lapse generalized system,
Figure BDA0004082139010000115
is a state time lag variable->
Figure BDA0004082139010000116
Figure BDA0004082139010000117
The specific form of the other matrix is:
Figure BDA0004082139010000118
in addition, system white noise w k and vk Covariance of Q k and Rk ，
Figure BDA0004082139010000119
and
Figure BDA00040821390100001110
Covariance of +.>
Figure BDA00040821390100001111
And
Figure BDA00040821390100001112
from matrix->
Figure BDA00040821390100001113
and D1 The full detectability of the time-lapse generalized system and the feasibility of filter design are guaranteed.
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:
HE+GC＝I n ，
the general solution of the non-singular matrix G and the matrix H is:
Figure BDA0004082139010000121
wherein ,
Figure BDA0004082139010000122
y is a degree of freedom matrix>
Figure BDA0004082139010000123
Is pseudo-inverse.
Step S2: aiming at the established time lag generalized system, a non-singular robust Kalman filter is designed based on the robust filtering and the disturbance observer.
The non-singular robust Kalman filter includes an interference estimation term and a nonlinear state estimation term. The disturbance observer based disturbance estimation terms are used to estimate the modelable disturbance. The nonlinear state estimation term is used to estimate the state variable of the time-lag generalized system.
The structure of the non-singular robust Kalman filter is as follows:
Figure BDA0004082139010000124
wherein ,
Figure BDA0004082139010000125
and
Figure BDA0004082139010000126
State variables for estimating time-lag generalized system, respectively>
Figure BDA0004082139010000127
State time lag variable->
Figure BDA0004082139010000128
And exogenous interference eta k ；K k and Vk A gain matrix to be designed;
order the
Figure BDA0004082139010000129
Figure BDA00040821390100001210
Define the error of variable J as +.>
Figure BDA00040821390100001211
Obtain->
Figure BDA00040821390100001212
The joint estimation error of η is:
Figure BDA00040821390100001213
wherein ,
Figure BDA00040821390100001214
Figure BDA00040821390100001215
step S3: nonlinear terms and nonlinear time-lag terms of a Taylor series expansion time-lag generalized system are based, and a robust upper bound of a Taylor series expansion truncation error is given.
Given the robust upper bound of the nonlinear higher order term and the nonlinear time-lag higher order term, the nonlinear error term
Figure BDA0004082139010000131
And
Figure BDA0004082139010000132
linearization is performed by adopting a Taylor series expansion mode, after a nonlinear higher-order term and a nonlinear time-lag higher-order term are expressed by using an equation, a first derivative term is reserved as a linear error term, and a truncation error is expressed as follows:
Figure BDA0004082139010000133
the method comprises the following steps:
Figure BDA0004082139010000134
wherein ,
Figure BDA0004082139010000135
N i,k (i=1, 2) is +.>
Figure BDA0004082139010000136
About->
Figure BDA0004082139010000137
With respect to
Figure BDA0004082139010000138
Deriving the resulting matrix.
Based on inequality quotation, given positive scalar μ, design robust parameter γ 1 and γ2 Obtaining
Figure BDA0004082139010000139
Covariance matrix robust upper bound P of (2) k+1 The method comprises the following steps:
Figure BDA00040821390100001310
wherein the scalar mu > 0, gamma 1 and γ2 For the robust parameters of the design,
Figure BDA00040821390100001311
Figure BDA00040821390100001312
meanwhile, the designed filter gain matrix satisfies the following conditions:
Figure BDA00040821390100001313
and estimate the error
Figure BDA00040821390100001314
For amplifying noise->
Figure BDA00040821390100001315
and
Figure BDA00040821390100001316
The robustness of (c) is guaranteed by the following inequality:
Figure BDA00040821390100001317
wherein, P 0 -1 Represents an initial value P of an estimated error covariance upper bound 0 For matrix or variable X, Z, there is
Figure BDA00040821390100001318
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.
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 BDA0004082139010000141
wherein p is a random number between 0 and 1, U i,k+1 Is the current particle position, U i,k * Is the location of the optimal particle(s),
Figure BDA0004082139010000142
is a constant defining a spiral shape, ω is between-1 and 1, < >>
Figure BDA0004082139010000143
Figure BDA0004082139010000144
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 BDA0004082139010000145
wherein ,
Figure BDA0004082139010000146
Figure BDA0004082139010000147
is the location of the random particles in the current population.
Step S43a: judgment by elite set policy
Figure BDA0004082139010000148
Whether to enter a collection, define +.>
Figure BDA0004082139010000149
The elite aggregation policy steps are:
(1) for the fitness function ψ, if
Figure BDA00040821390100001410
Then->
Figure BDA00040821390100001411
Entering a collection; otherwise, turning to the step (4);
(2) if j < Y, j=j+1,
Figure BDA00040821390100001412
entering a collection; if j=Y-1, then +.>
Figure BDA00040821390100001413
Enter collection, adjust>
Figure BDA00040821390100001414
Exiting the collection;
(3) arranging elements in a collection from large to small, i.e.
Figure BDA00040821390100001415
(4) Ending the judgment;
step S44a: based on elite set strategy, executing simulated annealing algorithm, and accepting probability by Mertopolis
Figure BDA0004082139010000151
Judging whether to accept the new solution:
Figure BDA0004082139010000152
wherein ,
Figure BDA0004082139010000153
is the position of the random particle in the elite set,/->
Figure BDA0004082139010000154
If it is
Figure BDA0004082139010000155
Then->
Figure BDA0004082139010000156
Otherwise->
Figure BDA0004082139010000157
If it is
Figure BDA0004082139010000158
Then->
Figure BDA0004082139010000159
Otherwise U i,k+1 ＝U i,k 。
Optimizing noise covariance matrix of system by improved whale optimization algorithm
Figure BDA00040821390100001510
and
Figure BDA00040821390100001511
The obtained optimized values are +.>
Figure BDA00040821390100001512
and
Figure BDA00040821390100001513
Will->
Figure BDA00040821390100001514
and
Figure BDA00040821390100001515
Substituting the filtered signal into a non-singular robust Kalman filter to obtain an IWA-DORKF filtering flow, wherein 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 BDA00040821390100001516
and
Figure BDA00040821390100001517
Optimal value +.>
Figure BDA00040821390100001518
And
Figure BDA00040821390100001519
step S43b: performing filtering estimation to obtain a time-lag generalized system state variable
Figure BDA00040821390100001520
And exogenous interference eta k+1 Is>
Figure BDA00040821390100001521
The corresponding covariance robust upper bound and the filter gain matrix calculation mode are as follows:
Figure BDA00040821390100001522
Figure BDA00040821390100001523
step S44b: step S41 b-step S43b are repeated for the next set of samples.
Step S5: and executing state estimation and modeling interference estimation of the time-lag generalized system to complete state estimation and composite fault estimation of the satellite attitude control system. Obtaining the joint estimation value
Figure BDA00040821390100001524
Thereafter, the following estimation values are calculated:
(1) Calculating state estimation value of time-lag generalized system
Figure BDA00040821390100001525
And estimate of exogenous interference->
Figure BDA00040821390100001529
(2) From the following components
Figure BDA00040821390100001526
Calculating a modelable interference estimate +.>
Figure BDA00040821390100001527
(3) Calculating state estimation value of satellite attitude control system
Figure BDA00040821390100001528
And calculating an actuator and sensor composite fault estimation value +.>
Figure BDA0004082139010000161
and
Figure BDA0004082139010000162
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.
To verify the performance of the present implementation, three filters are used to estimate the failure of the target acs, etc., and the three obtained filter estimation results are compared. The three filters are respectively: DORKF, WOA-DORKF, and IWOA-DORKF.
The test results are shown in fig. 2a, 2b, 2c, 3, 4 and 5, and the IWOA-DORKF filtering method based on the embodiment has the advantages of faster convergence speed, higher calculation accuracy and better capability of jumping out of the global optimal solution, and the fault estimation result of modeling interference and actuator and sensor composite to the state of the target ACSs is closest to the actual value of the corresponding variable of the target ACSs, so that the fault estimation method provided by the invention has more accurate estimation effect. At the same time, as shown in FIG. 6, the WOA-DORKF and the IWAA-DORKF adaptive function of the invention are iteratively compared. The estimation accuracy is ensured by a better adaptive function iteration mode of the IWAA in the estimation period.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the 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 2 ,η k+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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