CN110736468A - Spacecraft attitude estimation method assisted by self-adaptive kinematics model - Google Patents

Abstract

The invention discloses a spacecraft attitude estimation method assisted by an adaptive kinematics model. By establishing a state space model of the spacecraft at the kth time, when the observation vector at the kth time is available, according to the kth time The state space model uses the Kalman filtering result at the k-1 time to perform Kalman filtering, extract the rotation vector in the posterior estimation of the state vector, update the attitude matrix according to the rotation vector, and determine the attitude of the spacecraft at the k-th time. Accurately obtain the attitude of the spacecraft at the kth moment, after updating the attitude matrix, set the rotation vector to zero, and update other parameters, so that when a new observation vector is available, set k=k+1, and return to execute the establishment of the spacecraft In the process of the state space model at the kth moment, the estimation of the attitude of the spacecraft at a new moment is continued to estimate the attitude of the spacecraft at each moment in real time, which effectively improves the accuracy of the obtained attitude of the spacecraft.

Description

Spacecraft Attitude Estimation Method Aided by Adaptive Kinematics Model

technical field

The invention relates to the technical field of spacecraft attitude estimation, in particular to a spacecraft attitude estimation method assisted by an adaptive kinematics model.

Background technique

Attitude is an important parameter of a spacecraft. Accurate attitude estimation plays an important role in spacecraft operation control and mission execution. Insufficient attitude estimation accuracy will shorten the operating life of the spacecraft, reduce the quality of spacecraft products, and even cause spacecraft mission failure. fail.

Gyroscopes and star trackers are the most commonly employed spacecraft attitude estimation devices. The angular velocity measured by the gyroscope contains the relative information of the attitude, where the relative information refers to the time-varying information of the attitude; while the star tracker provides the absolute information of the attitude, and the absolute information here refers to the specific size of the attitude at the measurement moment. Therefore, the two have obvious complementarity, and they can and should be fused. The method used is generally Kalman filtering. In short, the use of Kalman filtering to fuse the gyroscope and star tracker installed on the spacecraft for accurate spacecraft attitude estimation has become the most commonly used method.

As an actual physical process, the attitude change of the spacecraft generally has a certain continuity. Specifically, in a short period of time between two consecutive observations, the attitude of the spacecraft will not change too much, which shows that the time-varying process of the attitude of the spacecraft can be modeled, that is, its kinematic model can be established. Introducing this kinematic model into the attitude estimation problem is equivalent to introducing additional information, when the model can reflect the real dynamics of the spacecraft to a certain extent. However, the attitude dynamics of the spacecraft are generally time-varying. Accordingly, the kinematic model should also be dynamically adjusted. The traditional scheme uses a predetermined kinematic model, which often limits the attitude estimation accuracy of the spacecraft. If the kinematic model appears Errors will also cause a decrease in the accuracy of pose estimation, and even filter divergence.

SUMMARY OF THE INVENTION

In view of the above problems, the present invention proposes a spacecraft attitude estimation method assisted by an adaptive kinematics model.

In order to achieve the purpose of the present invention, a spacecraft attitude estimation method assisted by an adaptive kinematics model is provided, comprising the following steps:

S10, establishing a state space model of the spacecraft at the kth moment, where the state space model includes a process model and an observation model;

状态向量后验估计

先验协方差矩阵P_k|k-1和后验协方差矩阵P_k|k；S30, when the observation vector at the kth time is available, perform Kalman filtering according to the state space model at the kth time and use the Kalman filtering result at the k-1th time to obtain the state vector prior at the kth time estimate

State Vector Posterior Estimation

Prior covariance matrix P _k|k-1 and posterior covariance matrix P _k|k ;

的旋转矢量，根据所述旋转矢量更新姿态矩阵，根据更新后的姿态矩阵确定航天器在第k个时刻的姿态，在更新姿态矩阵之后，将旋转矢量置零，设置

并进行如下赋值操作：P_k|k←JP_k|kJ^T，其中，符号←表示赋值操作，符号T表示转置，P_k|k表示后验协方差矩阵，

表示第k个时刻的姿态矩阵的后部分分量，

为的转置矩阵，I₉表示9行9列单位阵；S50, extract the posterior estimation of the state vector

The rotation vector of , update the attitude matrix according to the rotation vector, determine the attitude of the spacecraft at the k-th moment according to the updated attitude matrix, after updating the attitude matrix, set the rotation vector to zero, set

And perform the following assignment operation: P _k|k ←JP _k|k J ^T , where the symbol ← represents the assignment operation, the symbol T represents the transposition, and P _k|k represents the posterior covariance matrix,

Represents the rear component of the attitude matrix at the kth moment,

for The transpose matrix of , I ₉ represents a unit matrix with 9 rows and 9 columns;

S60, when there is a new observation vector, set k=k+1, and return to step S10.

In one of the embodiments, before S10, it further includes:

Set the initial filter parameters of the Kalman filter.

In one embodiment, after step S30, it further includes:

联立为一个伪观测向量，建立所述伪观测向量的观测方程，根据所述观测方程采用BIQUE对待调节参数进行估计得到

并根据下式进行参数调节：

将

P_k|k-1和

保存用于下一时刻的滤波；其中，μ表示学习率。S40, estimate the observation model and the state vector a priori

Simultaneously form a pseudo-observation vector, establish an observation equation of the pseudo-observation vector, and use BIQUE to estimate the parameters to be adjusted according to the observation equation.

And adjust the parameters according to the following formula:

Will

P _k|k-1 and

Save the filtering for the next moment; where μ is the learning rate.

In one of the embodiments, the process model at the kth moment includes:

x _k =F _k-1 x _k-1 +w _k-1 ,

Among them, x _k-1 represents the state vector at the k-1 time, x _k represents the state vector at the k time, F _k-1 represents the state transition matrix, and w _k-1 represents the process noise.

As an embodiment, the acquisition process of the process model includes:

其中，ω_t表示t时刻的角速度向量，φ_t表示t时刻的旋转矢量，

表示φ_t的时间微分；Obtain the differential equation of the rotation vector; the differential equation of the rotation vector includes:

Among them, ω _t represents the angular velocity vector at time t, φ _t represents the rotation vector at time t,

represents the time differential of φ _t ;

其中，

表示ω_t的时间微分，ξ_t表示t时刻的角加速度，

表示ξ_t的时间微分，η_t表示t时刻的第一噪声，μ_t表示t时刻的第二噪声；Obtain a velocity kinematic model, the velocity kinematic model includes:

in,

represents the time differential of ω _t , ξ _t represents the angular acceleration at time t,

represents the time differential of ξ _t , η _t represents the first noise at time t, and μ _t represents the second noise at time t;

其中，θ_t表示t时刻的噪声，

表示t时刻的陀螺零偏，

表示的时间微分；Obtain a gyro bias model, where the gyro bias model includes:

where θ _t represents the noise at time t,

represents the zero bias of the gyro at time t,

express time differential;

The initial process model is obtained by combining the differential equation of the rotation vector, the velocity kinematic model and the gyro bias model;

The process model is obtained by discretizing the initial process model.

In one of the embodiments, the observation model at the kth moment includes:

y _k =H _k x _k +e _k ,

表示第k个时刻的姿态矩阵的第二分量，

表示从第k时刻的参考系r_k到第k-1时刻的参考系r_k-1的方向余弦矩阵或旋转矩阵，表示第k个时刻的观测向量在参考系的坐标向量，符号×表示求位于×前的一个向量的斜对称矩阵，e_k表示第k个时刻的，I₃表示3行3列单位阵。Among them, x _k represents the state vector at the k-th moment, y _k represents the observation vector at the k-th moment,

represents the second component of the attitude matrix at the kth moment,

represents the direction cosine matrix or rotation matrix from the reference frame r _k at the k-th moment to the reference frame r _k- 1 at the k-1th moment, Represents the coordinate vector of the observation vector at the kth time in the reference frame, the symbol × represents the oblique symmetric matrix of a vector located before the ×, e _k represents the kth time, and I ₃ represents the unit matrix with 3 rows and 3 columns.

As an embodiment, the acquisition process of the observation model includes:

Obtain the first observation model of the star tracker, and obtain the second observation model of the gyroscope;

The observation model is obtained by combining the first observation model and the second observation model.

In one embodiment, the process of Kalman filtering at the k-th time includes:

P _k|k =P _k|k-1 -K _k H _k P _k|k-1 ,

R _k =cov[e _k ],

表示第k个时刻的状态向量先验估计，

第k-1个时刻的状态向量后验估计，F_k-1表示第k-1个时刻的状态转移矩阵，

表示第k个时刻的状态向量后验估计，P_k|k-1表示第k个时刻的先验协方差矩阵，P_k|k表示第k个时刻的后验协方差矩阵，P_k-1|k-1表示第k-1个时刻的后验协方差矩阵，Q_k-1表示第k-1个时刻的过程噪声的协方差矩阵，上标T表示转置，上标-1表示求逆，K_k表示滤波增益矩阵，

表示第k个时刻的姿态矩阵的第二分量，

表示从第k时刻的参考系r_k到第k-1时刻的参考系r_k-1的方向余弦矩阵，

表示第k个时刻的观测向量在参考系的坐标向量，符号×表示求位于×前的一个矩阵的斜对称矩阵，e_k表示第k个时刻的观测噪声向量，I₃表示3行3列单位阵，y_k表示第k个时刻的观测向量。in,

represents the prior estimate of the state vector at the kth moment,

The posterior estimation of the state vector at the k-1th time, F _k-1 represents the state transition matrix at the k-1th time,

Represents the posterior estimation of the state vector at the k-th time, P _k|k-1 represents the prior covariance matrix at the k-th time, P _k|k represents the posterior covariance matrix at the k-th time, and P _{k-1 |k-1} represents the posterior covariance matrix of the k-1th time, Q _k-1 represents the covariance matrix of the process noise at the k-1th time, the superscript T represents the transpose, and the superscript -1 represents the calculation Inverse, K _k represents the filter gain matrix,

represents the second component of the attitude matrix at the kth moment,

represents the direction cosine matrix from the reference frame r _k at the k-th moment to the reference frame r _k- 1 at the k-1th moment,

Represents the coordinate vector of the observation vector at the kth time in the reference frame, the symbol × represents the oblique symmetric matrix of a matrix located in front of ×, e _k represents the observation noise vector at the kth time, and I ₃ represents the unit of 3 rows and 3 columns matrix, y _k represents the observation vector at the kth moment.

状态向量后验估计

先验协方差矩阵P_k|k-1和后验协方差矩阵P_k|k，再提取状态向量后验估计

中的旋转矢量，根据所述旋转矢量更新姿态矩阵，根据更新后的姿态矩阵确定航天器在第k个时刻的姿态，以准确获取航天器在第k个时刻的姿态，在更新姿态矩阵之后，将旋转矢量置零，并更新其他参数，以当具备新的观测向量时，令k＝k+1，返回执行建立航天器在第k个时刻的状态空间模型的过程，以继续进行航天器在新的时刻的姿态的估计，这样便可以对航天器在各个时刻的姿态进行准确估计，其中采用的状态空间模型和滤波参数得到实时准确更新，有效提高了所获得的航天器姿态的精度。The above-mentioned adaptive kinematic model-assisted spacecraft attitude estimation method, by establishing the state space model of the spacecraft at the kth time, when the observation vector at the kth time is available, according to the state space model of the kth time, and Using the Kalman filtering result at the k-1 time, Kalman filtering is performed to obtain the prior estimation of the state vector at the k time.

State Vector Posterior Estimation

Prior covariance matrix P _k|k-1 and posterior covariance matrix P _k|k , and then extract state vector posterior estimation

The rotation vector in , the attitude matrix is updated according to the rotation vector, and the attitude of the spacecraft at the kth moment is determined according to the updated attitude matrix, so as to accurately obtain the attitude of the spacecraft at the kth moment. After updating the attitude matrix, Set the rotation vector to zero, and update other parameters, so that when there is a new observation vector, let k=k+1, and return to the process of establishing the state space model of the spacecraft at the k-th time to continue the spacecraft at The attitude of the new moment can be estimated, so that the attitude of the spacecraft at each moment can be accurately estimated, and the adopted state space model and filtering parameters are updated accurately in real time, which effectively improves the accuracy of the obtained spacecraft attitude.

Description of drawings

1 is a flowchart of an adaptive kinematic model-assisted spacecraft attitude estimation method according to an embodiment;

FIG. 2 is a flowchart of a method for estimating a spacecraft attitude assisted by an adaptive kinematics model according to another embodiment.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present application more clearly understood, the present application will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, but not to limit the present application.

Reference herein to an "embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor a separate or alternative embodiment that is mutually exclusive of other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

Referring to FIG. 1, FIG. 1 is a flowchart of an adaptive kinematic model-assisted spacecraft attitude estimation method according to an embodiment, including the following steps:

S10, establishing a state space model of the spacecraft at the kth moment, where the state space model includes a process model and an observation model;

Specifically, the state space model of the spacecraft at each moment includes two parts: the process model and the observation model. The process model includes the following three parts: a1) the attitude model (differential equation of the rotation vector) defined by the attitude differential equation, a2) the angular velocity and angular acceleration model (velocity kinematics model) represented by the random constant angular acceleration model, a3) random The gyroscope bias model represented by the constant value model. The purpose of the velocity kinematics model shown in a2) is to assist attitude estimation and improve estimation accuracy. The observation model includes the following two parts: b1) the observation model of the star tracker (the first observation model), and b2) the observation model of the gyroscope (the second observation model). In the traditional algorithm, the observation model of the gyroscope generally appears in the process. model, which in this embodiment is part of the observation model. The model parameters of the state space model include the following: c1) The process noise variance of the gyroscope bias model (such as α1, α2 and α3), these parameters correspond to the gyroscope’s bias stability performance index, according to the gyroscope factory performance index manual or The calibration results are manually set; c2) The star tracker vector observation noise variance (such as α4, α5 and α6), these parameters are manually set according to the star tracker factory performance index manual or the calibration results; c3) The gyroscope observation noise variance (such as α7, α8, α9), these parameters correspond to the random walk performance index of the gyroscope, and are manually set according to the factory performance index manual or calibration results of the gyroscope; c4) The noise variance of the angular velocity process in the random constant angular acceleration model (such as β1, β2 and β3), these parameters will be adaptively adjusted during the filtering process; c5) The noise variance of the angular acceleration process in the random constant angular acceleration model (such as β4, β5 and β6), these parameters will be in the filtering process. adaptive adjustment.

In an example, the state vector in the established process model includes 3 error angles, 3 angular velocities, 3 angular accelerations, and 3 gyro biases, totaling 12 dimensions, and the state vector at the kth moment is represented as x _k ; The observations at the kth moment in the established observation model include the angular rate measured by 3 gyroscopes and the vector observations measured by 3nk star trackers, where nk represents the number of vectors observed by the star tracker at the kth moment , denote the observation vector at the k-th moment as y _k .

The process model part in the established state space model of the above-mentioned steps, in addition to comprising the attitude kinematics model a1) and the gyroscope bias model a3) in the traditional method, also introduced the kinematics model a2) of angular velocity and angular acceleration; Correspondingly, the state vector includes angular velocity and angular acceleration in addition to attitude angle or error attitude angle and gyroscope bias. It is suitable for spacecraft attitude estimation problem using a three-axis gyroscope and one or more star trackers, and an adaptive kinematics model can also be introduced to assist attitude estimation to improve attitude estimation accuracy.

状态向量后验估计

先验协方差矩阵P_k|k-1和后验协方差矩阵P_k|k；S30, when the observation vector at the kth time is available, perform Kalman filtering according to the state space model at the kth time and use the Kalman filtering result at the k-1th time to obtain the state vector prior at the kth time estimate

State Vector Posterior Estimation

Prior covariance matrix P _k|k-1 and posterior covariance matrix P _k|k ;

以及先验协方差矩阵P_k|k-1和后验协方差矩阵P_k|k。When the observation vector y _k at the kth time is available, according to the above state space model, and using the filtering result of the previous time (ie time k-1), standard Kalman filtering is performed to obtain a priori estimate of the state vector at this time. and a posteriori estimate

and the prior covariance matrix P _k|k-1 and the posterior covariance matrix P _k|k .

)。In the actual estimation process of the spacecraft attitude, the Kalman filter involves the parameter β to be adjusted, and its value is the estimated value obtained after the filtering at the previous moment (such as

).

的旋转矢量，根据所述旋转矢量更新姿态矩阵，根据更新后的姿态矩阵确定航天器在第k个时刻的姿态，在更新姿态矩阵之后，将旋转矢量置零，设置

并进行如下赋值操作：P_k|k←JP_k|kJ^T，其中，符号←表示赋值操作，符号T表示转置，P_k|k表示后验协方差矩阵，

表示第k个时刻的姿态矩阵的后部分分量，

为的转置矩阵，I₉表示9行9列单位阵；S50, extract the posterior estimation of the state vector

The rotation vector of , update the attitude matrix according to the rotation vector, determine the attitude of the spacecraft at the k-th moment according to the updated attitude matrix, after updating the attitude matrix, set the rotation vector to zero, set

And perform the following assignment operation: P _k|k ←JP _k|k J ^T , where the symbol ← represents the assignment operation, the symbol T represents the transposition, and P _k|k represents the posterior covariance matrix,

Represents the rear component of the attitude matrix at the kth moment,

for The transpose matrix of , I ₉ represents a unit matrix with 9 rows and 9 columns;

的各个分量(即

将

中前三个分量提取出来，作为的旋转矢量，进行姿态矩阵的更新，即以及

然后根据中的旋转矢量置零，计算

并进行如下赋值操作，即：P_k|k←JP_k|kJ^T，其中←表示赋值操作；其中J为引入的辅助变量。Specifically, it can be estimated a posteriori based on the state vector

each component of (i.e.

Will

The first three components are extracted as The rotation vector of , to update the attitude matrix, that is as well as

then according to The rotation vector in is zeroed out, computing

And perform the following assignment operation, namely: P _k|k ←JP _k|k J ^T , where ← represents assignment operation; where J is the introduced auxiliary variable.

Further, after the rotation vector is set to zero in the above steps, the corresponding covariance matrix (eg P _k|k ) should also be adjusted accordingly to ensure the accuracy of the attitude matrix acquisition at subsequent moments.

S60, when there is a new observation vector, set k=k+1, and return to step S10.

When there is a new observation amount, the above-mentioned new observation amount means that the gyroscope and the star tracker output a new observation amount, so that the time k is incremented by 1, and the filter is transferred to the next time, that is, returning to step S10, and re-establishing The state space model of the spacecraft at the k-th time is updated with a new attitude matrix to obtain the new attitude information of the spacecraft; this is performed in sequence until the filtering ends, that is, no new observations appear.

状态向量后验估计

先验协方差矩阵P_k|k-1和后验协方差矩阵P_k|k，再提取状态向量后验估计

的旋转矢量，根据所述旋转矢量更新姿态矩阵，根据更新后的姿态矩阵确定航天器在第k个时刻的姿态，以准确获取航天器在第k个时刻的姿态，在更新姿态矩阵之后，将旋转矢量置零，并更新其他参数，以当具备新的观测向量时，令k＝k+1，返回执行建立航天器在第k个时刻的状态空间模型的过程，以继续进行航天器在新的时刻的姿态的估计，这样便可以对航天器在各个时刻的姿态进行准确估计，其中采用的状态空间模型和滤波参数得到实时准确更新，有效提高了所获得的航天器姿态的精度。The above-mentioned adaptive kinematic model-assisted spacecraft attitude estimation method, by establishing the state space model of the spacecraft at the kth time, when the observation vector at the kth time is available, according to the state space model of the kth time, and Using the Kalman filtering result at the k-1 time, Kalman filtering is performed to obtain the prior estimation of the state vector at the k time.

State Vector Posterior Estimation

Prior covariance matrix P _k|k-1 and posterior covariance matrix P _k|k , and then extract state vector posterior estimation

According to the rotation vector of the rotation vector, the attitude matrix is updated according to the rotation vector, and the attitude of the spacecraft at the kth moment is determined according to the updated attitude matrix, so as to accurately obtain the attitude of the spacecraft at the kth moment. After updating the attitude matrix, the The rotation vector is set to zero, and other parameters are updated, so that when there is a new observation vector, let k=k+1, and return to execute the process of establishing the state space model of the spacecraft at the kth time, so as to continue the process of the spacecraft in the new In this way, the attitude of the spacecraft at each moment can be accurately estimated, and the adopted state space model and filtering parameters are updated accurately in real time, which effectively improves the accuracy of the obtained spacecraft attitude.

状态向量后验估计

先验协方差矩阵P_1|0和后验协方差矩阵P_1|1之前，还包括：In one embodiment, before step S10, specifically, when the observation vector at the first moment is available, the Kalman filter may be performed according to the state space model at the first moment and using the Kalman filtering result at the 0th moment. Filter to obtain a priori estimate of the state vector at the first moment

State Vector Posterior Estimation

Before the prior covariance matrix P _1|0 and the posterior covariance matrix P _1|1 , it also includes:

Set the initial filter parameters of the Kalman filter.

其中x表示状态向量，状态向量顶部的^表示估计值，下标中竖线前(左边)的0表示估计的是第0时刻的变量，下标中竖线后(右边)的0表示估计值采用了0时刻及其之前时刻的观测值，此处“0时刻及其之前时刻的观测值”实际上是指没有任何观测值；2)状态向量协方差矩阵初值，将其表示为P_0|0，下标的含义与前述保持一致，3)待调节参数β1-β6的初值，将这6个参数组成的向量表示为β，即β＝(β1，β2，β3，β4，β5，β6)，该向量的初值表示为

下标0表示该变量为第0时刻的变量，顶部符号^表示估计值；其中1)中状态向量估计初值

与2)中状态向量协方差矩阵初值P_0|0应具有统计一致性，即前者的不确定性(即其真实的协方差矩阵P₀表示)应不大于后者，其中协方差矩阵的大小定义如下，y_k协方差矩阵A不大于协方差矩阵B是指矩阵B-A非负定；令首次具备观测量的时刻为第一个滤波时刻，即k＝1。In an example, the following initial filtering parameters may be set, for example, the filtering time corresponding to these initial values is set to zero time, that is, k=0. Further, the initial filtering parameters may also include: 1) the initial value of state vector estimation, which is expressed as

Where x represents the state vector, the ^ at the top of the state vector represents the estimated value, the 0 before the vertical line in the subscript (on the left) indicates that the variable at time 0 is estimated, and the 0 after the vertical line in the subscript (on the right) represents the estimated value The observations at time 0 and its previous moments are used, where "observed values at time 0 and its previous moments" actually means that there are no observed values; 2) The initial value of the state vector covariance matrix is expressed as P _{0 |0} , the meaning of the subscript is the same as the above, 3) the initial value of the parameters to be adjusted β1-β6, the vector composed of these 6 parameters is expressed as β, that is, β=(β1, β2, β3, β4, β5, β6 ), the initial value of this vector is expressed as

The subscript 0 indicates that the variable is the variable at the 0th moment, and the top symbol ^ indicates the estimated value; the initial value of the state vector estimation in 1)

The initial value of the state vector covariance matrix P _0|0 in 2) should have statistical consistency, that is, the uncertainty of the former (that is, its real covariance matrix P ₀ representation) should not be greater than the latter, where the covariance matrix of The size is defined as follows, the covariance matrix A of y _k is not greater than the covariance matrix B, which means that the matrix BA is non-negative definite; let the moment when the observed quantity is available for the first time be the first filtering moment, that is, k=1.

先验协方差矩阵P_k|k-1和后验协方差矩阵P_k|k之后，还包括：In one embodiment, in S30, when the observation vector at the kth time is available, Kalman filtering is performed according to the state space model at the kth time, and the Kalman filtering result at the k-1th time is used to obtain the kth time. State vector prior estimates at moments State Vector Posterior Estimation

After the prior covariance matrix P _k|k-1 and the posterior covariance matrix P _k|k , it also includes:

联立为一个伪观测向量，建立所述伪观测向量的观测方程，根据所述观测方程采用BIQUE对待调节参数进行估计得到

并根据下式进行参数调节：

将

P_k|k-1和保存用于下一时刻的滤波；其中，μ表示学习率。S40, estimate the observation model and the state vector a priori

Simultaneously form a pseudo-observation vector, establish an observation equation of the pseudo-observation vector, and use BIQUE to estimate the parameters to be adjusted according to the observation equation.

And adjust the parameters according to the following formula:

Will

P _k|k-1 and Save the filtering for the next moment; where μ is the learning rate.

并根据下式进行参数调节：

学习率μ需要人为设置，一般情况下的设置范围为[0.001 0.1]，当航天器的角动态较大时采用较小的μ，否则采用较大的μ。将

保存用于下一时刻的滤波。Specifically, the observation vector y _k at the k-th moment and the state vector at the k-th moment can be estimated a priori Simultaneously form a pseudo-observation vector, denote the pseudo-observation vector as z _k , and establish the observation equation of the pseudo-observation vector. According to this observation equation, the parameters to be adjusted are estimated by BIQUE.

And adjust the parameters according to the following formula:

The learning rate μ needs to be set manually. Generally, the setting range is [0.001 0.1]. When the angular dynamics of the spacecraft is large, a smaller μ is used, otherwise a larger μ is used. Will

Save the filter for the next moment.

包括6个元素，即

依据其中前3个元素可以进行下一个时刻(第k+1个时刻)η_t的协方差矩阵的确定，依据其中后3个元素可以进行下一个时刻μ_t的协方差矩阵的确定，依据下一个时刻的η_t和μ_t进一步进行速度运动学模型的确定，从而确定下一时刻的过程模型，以对下一时刻的过程模型进行准确确定。specifically,

includes 6 elements, namely

According to the first 3 elements, the covariance matrix of the next moment (the k+1th moment) η _t can be determined, and the covariance matrix of the next moment μ _t can be determined according to the last 3 elements, according to the following The velocity kinematics model is further determined at one time η _t and μ _t , so as to determine the process model at the next time, so as to accurately determine the process model at the next time.

In one example, the pseudo-observation equation including the above pseudo-observation vector is:

观测矩阵

伪观测噪声

其中，I₁₂表示12×12维的单位矩阵，符号d表示求微分，e_k表示实际观测噪声。该伪观测噪声的协方差矩阵表示如下：where the pseudo-observation vector

observation matrix

Pseudo-observation noise

Among them, I ₁₂ represents a 12×12-dimensional unit matrix, the symbol d represents the differentiation, and e _k represents the actual observation noise. The covariance matrix of this pseudo-observation noise is expressed as:

in,

Ψ＝[Ψ_ij]＝[tr[VΩ_iVΩ_j]],i,j＝1,2,…,6(其中tr[]表示矩阵求迹算子)、

然后待调节参数的估计值如下：Among them, the 12 × 12-dimensional matrix Θ _ij (i represents the first subscript, j represents the second subscript) means that all elements are 0 except for the elements located on the i-th row and the j-th column at the same time. . According to the BIQUE theory of variance component estimation, firstly, the parameter estimates obtained after filtering at the previous moment are substituted into the covariance matrix of the observed noise to calculate Q _υυ , and then calculate

Ψ=[Ψ _ij ]=[tr[VΩ _i VΩ _j ]], i,j=1,2,...,6 (where tr[] represents the matrix trace operator),

Then the estimated values of the parameters to be adjusted are as follows:

will finally The estimated value in and the estimated value obtained in the filtering at the previous moment are linearly combined, and the combined value is used as the latest parameter estimated value: as shown below

Among them, ← represents the assignment operation, μ represents the learning rate, which needs to be set manually. In general, the setting range is [0.001 0.1]. When the angular dynamics of the spacecraft is large, a smaller μ is used, otherwise a larger μ is used.

In one embodiment, the process model at the kth moment includes:

x _k =F _k-1 x _k-1 +w _k-1 ,

Among them, x _k-1 represents the state vector of the k-1th time, x _k represents the state vector of the kth time, F _k-1 represents the state transition matrix, and w _k-1 represents the process noise.

As an embodiment, the acquisition process of the process model includes:

其中，ω_t表示t时刻的角速度向量，φ_t表示t时刻的旋转矢量，

表示φ_t的时间微分；Obtain the differential equation of the rotation vector; the differential equation of the rotation vector includes:

Among them, ω _t represents the angular velocity vector at time t, φ _t represents the rotation vector at time t,

represents the time differential of φ _t ;

其中，

表示ω_t的时间微分，ξ_t表示t时刻的角加速度，

表示ξ_t的时间微分，η_t表示t时刻的第一噪声，μ_t表示t时刻的第二噪声；Obtain a velocity kinematic model, the velocity kinematic model includes:

in,

represents the time differential of ω _t , ξ _t represents the angular acceleration at time t,

represents the time differential of ξ _t , η _t represents the first noise at time t, and μ _t represents the second noise at time t;

其中，θ_t表示t时刻的表示t时刻的，

表示t时刻的陀螺零偏，

表示

的时间微分；Obtain a gyro bias model; the gyro bias model includes:

Among them, θ _t represents time t at time t,

represents the zero bias of the gyro at time t,

express

time differential;

The initial process model is obtained by combining the differential equation of the rotation vector, the velocity kinematic model and the gyro bias model;

The process model is obtained by discretizing the initial process model.

其中r_k表示第k时刻的参考坐标系，b_k表示第k时刻的航天器载体坐标系。根据姿态矩阵的链式法则，可以得到姿态矩阵为：In one example, the attitude matrix, ie, the direction cosine matrix (DCM), can be expressed as

where r _k represents the reference coordinate system at the k-th time, and b _k represents the spacecraft carrier coordinate system at the k-th time. According to the chain rule of the attitude matrix, the attitude matrix can be obtained as:

表示

的前部分分量，

表示第k-1时刻的姿态矩阵，表示

的后部分分量。可选地，将参考系r选为惯性系i，则有

I₃为3行3列的单位阵。在第k时刻的姿态估计过程中，第k-1时刻的姿态矩阵

采用上一时刻滤波过程中得到的值，在当前时刻的滤波中视为已知。根据姿态表示相关理论，上式中右边最后一项表示为：

其中φ_k被称为旋转矢量，根据姿态运动学理论，旋转矢量的微分方程可以表示为in,

express

the front component of ,

represents the attitude matrix at the k-1th moment, express

the rear part of the component. Optionally, the reference frame r is selected as the inertial frame i, then we have

I ₃ is an identity matrix with 3 rows and 3 columns. During the attitude estimation process at the kth moment, the attitude matrix at the k-1th moment

The value obtained in the filtering process at the previous moment is used, and it is regarded as known in the filtering at the current moment. According to the relevant theory of attitude representation, the last term on the right side of the above formula is expressed as:

where φ _k is called the rotation vector. According to the theory of attitude kinematics, the differential equation of the rotation vector can be expressed as

表示φ_t的时间微分，变量顶部的一“点”表示时间微分，下标t与前述下标k的关系如下：对于任一变量a，有其中t_k表示第k时刻对应的时间。Among them, ω _t represents the angular velocity vector at time t, φ _t represents the rotation vector at time t,

Represents the time differential of φ _t , a "dot" at the top of the variable represents the time differential, and the relationship between the subscript t and the aforementioned subscript k is as follows: For any variable a, there are where t _k represents the time corresponding to the kth moment.

Angular velocity and angular acceleration kinematics model (velocity kinematics model): The aforementioned attitude kinematics model (differential equation of rotation vector) is obtained according to attitude kinematics theory, and the angular velocity and angular acceleration kinematics model here can be set by the user based on experience. The following kinematics model is adopted in the present invention:

表示ω_t的时间微分，ξ_t表示t时刻的角加速度，表示ξ_t的时间微分，η_t表示t时刻的第一噪声，μ_t表示t时刻的第二噪声。η_t的协方差矩阵为：in,

represents the time differential of ω _t , ξ _t represents the angular acceleration at time t, represents the time differential of ξ _t , η _t represents the first noise at time t, and μ _t represents the second noise at time t. The covariance matrix of η _t is:

The covariance matrix of μ _t is:

Among them, cov[] represents the covariance matrix operator. β1-β6 are the parameters to be adjusted, specifically, β=(β1, β2, β3, β4, β5, β6), in the β at the kth moment, β1, β2, β3 are the first 3 elements of β, β4 , β5 and β6 are the last three elements of β.

The gyro bias model is as follows:

表示t时刻的陀螺零偏，

表示

的时间微分，θ_t的协方差为

其中参数α₁、α₁和α₃表示了陀螺仪的零偏稳定性指标，需要使用者根据陀螺仪的出厂性能指标手册或标定结果进行人为设置，设置完成后在滤波过程中保持不变。where θ _t represents the noise at time t,

represents the zero bias of the gyro at time t,

express

The time differential of , the covariance of θ _t is

The parameters α ₁ , α ₁ and α ₃ represent the zero bias stability index of the gyroscope, which needs to be manually set by the user according to the factory performance index manual or the calibration result of the gyroscope. After the setting is completed, it will remain unchanged during the filtering process.

Further, the initial process model of the state space model is obtained by combining the differential equation of the rotation vector, the velocity kinematic model and the gyro bias model, which is expressed as the following differential equation:

可见x_t可以分解为4个元素；where x _t represents the state vector at time t,

It can be seen that x _t can be decomposed into 4 elements;

and have

Discretizing the initial process model yields the difference equation (i.e. the final process model) as shown below:

x _k+1 =F _k x _k +w _k ,

The state transition matrix F _k is F _k ≈I ₁₂ +Φ _t △, Δ=t _k -t _k-1 , and has the covariance matrix of the process noise w _k as follows:

In one embodiment, the observation model at the kth moment includes:

y _k =H _k x _k +e _k ,

表示第k个时刻的姿态矩阵的第二分量，

表示从第k时刻的参考系r_k到第k-1时刻的参考系r_k-1的方向余弦矩阵或旋转矩阵，其中下标k或k-1表示时刻，根据姿态表示相关理论，从坐标系r_k-1旋转到坐标系r_k的姿态矩阵，即

为

的转置矩阵，其他类同，

表示第k个时刻的观测向量在参考系的坐标向量，符号×表示求位于×前的一个向量的斜对称矩阵，e_k表示第k个时刻的观测噪声，I₃表示3行3列单位阵。Among them, x _k represents the state vector at the k-th moment, y _k represents the observation vector at the k-th moment,

represents the second component of the attitude matrix at the kth moment,

Represents the direction cosine matrix or rotation matrix from the reference frame r _k at the k-th moment to the reference frame r _k-1 at the k-1th moment, where the subscript k or k-1 represents the moment, according to the relevant theory of attitude representation, from the coordinates The attitude matrix of the system r _k-1 rotated to the coordinate system r _k , namely

for

The transpose matrix of , other similarities,

Represents the coordinate vector of the observation vector at the k-th time in the reference frame, the symbol × represents the oblique symmetric matrix of a vector located before the ×, e _k represents the observation noise at the k-th time, I ₃ represents the unit matrix with 3 rows and 3 columns .

As an embodiment, the acquisition process of the observation model includes:

Obtain the first observation model of the star tracker, and obtain the second observation model of the gyroscope;

The observation model is obtained by combining the first observation model and the second observation model.

In one example, the observation model of the star tracker is as follows (a vector is used as an example, the others are similar):

和

分别为第k个时刻的观测向量在参考系和在载体系中的坐标向量。上式中[φ_k×]表示向量φ_k的斜对称矩阵，其他类同，斜对称矩阵的定义如下：任给一个向量其斜对称矩阵为

上式中ε_k为相应的观测误差，其协方差矩阵为

其中参数α₄，α₅，α₅表示星跟踪器的精度，根据星跟踪器的出厂性能指标手册或者标定结果进行人为设置，设置完成后在滤波过程中保持不变。in

and

are the coordinate vectors of the observation vector at the kth moment in the reference frame and in the carrier system, respectively. In the above formula, [φ _k ×] represents the oblique symmetric matrix of the vector φ _k , and other similarities. The definition of the oblique symmetric matrix is as follows: Any given vector Its obliquely symmetric matrix is

In the above formula, ε _k is the corresponding observation error, and its covariance matrix is

The parameters α ₄ , α ₅ , and α ₅ represent the accuracy of the star tracker, which are manually set according to the factory performance index manual or the calibration result of the star tracker, and remain unchanged during the filtering process after the setting is completed.

Further, the first observation model of the star tracker can be determined according to the observation model of each vector of the star tracker.

The observation model (second observation model) of the gyroscope is as follows:

where the covariance matrix of the observation noise ζ _k is: The parameters α ₇ , α ₈ , and α ₉ represent the random walk performance index of the gyroscope, which is manually set according to the factory performance index manual of the gyroscope or the calibration result, and remains unchanged during the filtering process after the setting is completed. By combining the first observation model and the second observation model, the total observation model and the observation equation of the observation model are obtained as follows:

y _k =H _k x _k +e _k

in

In one embodiment, the process of Kalman filtering at the k-th time includes:

P _k|k =P _k|k-1 -K _k H _k P _k|k-1 ,

R _k =cov[e _k ],

表示第k个时刻的状态向量先验估计，

第k-1个时刻的状态向量后验估计，F_k-1表示第k-1个时刻的状态转移矩阵，

表示第k个时刻的状态向量后验估计，P_k|k-1表示第k个时刻的先验协方差矩阵，P_k|k表示第k个时刻的后验协方差矩阵，P_k-1|k-1表示第k-1个时刻的后验协方差矩阵，Q_k-1表示第k-1个时刻的过程噪声的协方差矩阵，上标T表示转置，上标-1表示求逆，K_k表示滤波增益矩阵，

表示第k个时刻的姿态矩阵的第二分量，

表示从第k时刻的参考系r_k到第k-1时刻的参考系r_k-1的方向余弦矩阵，

表示第k个时刻的观测向量在参考系的坐标向量，符号×表示求位于×前的一个向量的斜对称矩阵，R_k表示e_k的协方差矩阵，e_k表示第k个时刻的观测噪声，y_k表示第k个时刻的观测向量。in,

represents the prior estimate of the state vector at the kth moment,

The posterior estimation of the state vector at the k-1th time, F _k-1 represents the state transition matrix at the k-1th time,

Represents the posterior estimation of the state vector at the k-th time, P _k|k-1 represents the prior covariance matrix at the k-th time, P _k|k represents the posterior covariance matrix at the k-th time, and P _{k-1 |k-1} represents the posterior covariance matrix of the k-1th time, Q _k-1 represents the covariance matrix of the process noise at the k-1th time, the superscript T represents the transpose, and the superscript -1 represents the calculation Inverse, K _k represents the filter gain matrix,

represents the second component of the attitude matrix at the kth moment,

represents the direction cosine matrix from the reference frame r _k at the k-th moment to the reference frame r _k- 1 at the k-1th moment,

Represents the coordinate vector of the observation vector at the kth time in the reference frame, the symbol × represents the oblique symmetric matrix of a vector located before ×, R _k represents the covariance matrix of e _k , and e _k represents the observation noise at the kth time. , y _k represents the observation vector at the kth moment.

In an example, the above-mentioned flow chart of the spacecraft attitude estimation method assisted by the adaptive kinematics model can also be referred to as shown in FIG. 2 , including:

其中x表示状态向量，变量顶部的^表示估计值，下标中竖线前(左边)的0表示估计的是第0时刻的变量，下标中竖线后(右边)的0表示估计值采用了0时刻及其之前时刻的观测值，注意此处“0时刻及其之前时刻的观测值”实际上是指没有任何观测值，2)状态向量协方差矩阵初值，将其表示为P_0|0，下标的含义与前述保持一致，3)待调节参数β1-β6的初值，不妨将这6个参数组成的向量表示为β，该向量的初值表示为

下标0表示该变量为第0时刻的变量，顶部符号^表示估计值；其中1)中状态向量估计初值

与2)中状态向量协方差矩阵初值P_0|0应具有统计一致性，即前者的不确定性(即其真实的协方差矩阵P₀表示)应不大于后者，其中协方差矩阵的大小定义如下，y_k协方差矩阵A不大于协方差矩阵B是指矩阵B-A非负定；令首次具备观测量的时刻为第一个滤波时刻，即k＝1。(1) Determine the initial filtering parameters, set the initial values of the following parameters, and set the filtering time corresponding to these initial values to zero time, that is, k=0. These parameters include: 1) The initial value of state vector estimation, which is expressed as

Where x represents the state vector, ^ at the top of the variable represents the estimated value, 0 in front of the vertical line in the subscript (on the left) indicates that the variable at time 0 is estimated, and 0 after the vertical line in the subscript (on the right) represents the estimated value using Observations at time 0 and before, note that "observed values at time 0 and before" actually means that there are no observations, 2) the initial value of the state vector covariance matrix, which is represented as P _{0 |0} , the meaning of the subscript is the same as the above, 3) the initial value of the parameters to be adjusted β1-β6, may wish to express the vector composed of these 6 parameters as β, and the initial value of the vector is expressed as

The subscript 0 indicates that the variable is the variable at the 0th moment, and the top symbol ^ indicates the estimated value; the initial value of the state vector estimation in 1)

The initial value of the state vector covariance matrix P _0|0 in 2) should have statistical consistency, that is, the uncertainty of the former (that is, its real covariance matrix P ₀ representation) should not be greater than the latter, where the covariance matrix of The size is defined as follows, the covariance matrix A of y _k is not greater than the covariance matrix B, which means that the matrix BA is non-negative definite; let the moment when the observed quantity is available for the first time be the first filtering moment, that is, k=1.

(2) Establish a state space model, which includes two parts: a process model and an observation model, and the process model includes the following three parts: a1) The attitude model (differential equation of the rotation vector) defined by the attitude differential equation, a2) The angular velocity and angular acceleration model represented by the random constant angular acceleration model, a3) The gyroscope bias model represented by the random constant value model, wherein the model shown in a2) is a newly introduced part in the present invention, and its purpose is to assist Attitude estimation to improve estimation accuracy; the observation model includes the following two parts: b1) the observation model of the star tracker, b2) the observation model of the gyroscope, in which the observation model of the gyroscope generally appears in the process model in the traditional algorithm, In the present invention, however, the model is part of the observation model. The model parameters include the following: c1) The process noise variance α1-α3 of the gyroscope bias model, these parameters correspond to the gyroscope’s bias stability performance index, and are manually set according to the gyroscope’s factory performance index manual or calibration results; c2) Star tracker vector observation noise variance α4-α6, these parameters are artificially set according to the star tracker factory performance index manual or calibration results; c3) gyroscope observation noise variance α7-α9, these parameters correspond to the random walk of the gyroscope The performance index is manually set according to the gyroscope factory performance index manual or calibration results; c4) The noise variance β1-β3 of the angular velocity process in the random constant angular acceleration model, these parameters will be adaptively adjusted during the filtering process; c5) Random The noise variance β4-β6 of the angular acceleration process in the constant angular acceleration model, these parameters will be adaptively adjusted in the filtering process; the state vector in the established model includes 3 error angles, 3 angular velocities, 3 angular accelerations, 3 gyro biases, totaling 12 dimensions, the state vector at the kth moment is represented as x _k ; the kth moment observation in the established model includes the angular rate measured by 3 gyroscopes and the vector observations measured by 3nk star trackers , where nk represents the number of vectors observed by the star tracker at the kth moment, and the observed vector at the kth moment is denoted as y _k .

和后验估计

以及先验协方差矩阵P_k|k-1和后验协方差矩阵P_k|k，其中的变量符号及其下标、顶部符号的定义与前述保持一致。在这一步骤的Kalman滤波中涉及待调节参数β，其值取为上一时刻滤波结束后得到的估计值。(3) When the observation vector y _k at the kth time is available, according to the above state model, and using the filtering result of the previous time (ie time k-1), perform standard Kalman filtering to obtain a priori estimate of the state vector at this time.

and a posteriori estimate

As well as the prior covariance matrix P _k|k-1 and the posterior covariance matrix P _k|k , the definitions of variable symbols, subscripts, and top symbols are consistent with the above. The parameter β to be adjusted is involved in the Kalman filtering of this step, and its value is the estimated value obtained after the end of the filtering at the previous moment.

联立为一个伪观测向量，不妨将此伪观测向量表示为z_k，并建立此伪观测向量的观测方程，据此观测方程采用BIQUE对待调节参数进行估计得到

并根据下式进行参数调节：

其中μ表示学习率，需要人为设置，一般情况下的设置范围为[0.001 0.1]，当航天器的角动态较大时采用较小的μ，否则采用较大的μ。将

保存用于下一时刻的滤波。相较于采用传统Kalman滤波的方法，该步骤为本发明新引入的部分；相较于其他自适应方法，该步骤中采用BIQUE为本发明新提出的方法。(4) Priori estimation of observation vector _yk and state vector

Simultaneously as a pseudo-observation vector, it is advisable to denote this pseudo-observation vector as z _k , and establish the observation equation of this pseudo-observation vector, according to which the observation equation uses BIQUE to estimate the parameters to be adjusted.

And adjust the parameters according to the following formula:

Among them, μ represents the learning rate, which needs to be set manually. In general, the setting range is [0.001 0.1]. When the angular dynamics of the spacecraft is large, a smaller μ is used, otherwise a larger μ is used. Will

Save the filter for the next moment. Compared with the traditional Kalman filtering method, this step is a newly introduced part of the present invention; compared with other adaptive methods, BIQUE is used in this step, which is a newly proposed method of the present invention.

以及

然后将状态向量估计中的旋转矢量置零，计算

并进行如下赋值操作，即：P_k|k←JP_k|kJ^T，其中←表示赋值操作。(5) Zeroing the rotation vector and transforming the covariance matrix: According to the rotation vector in the state vector estimation, the attitude matrix is updated, that is

as well as

Then zero the rotation vector in the state vector estimate, compute

And perform the following assignment operation, namely: P _k|k ←JP _k|k J ^T , where ← represents an assignment operation.

(6) The time k is increased by 1, and then steps (2), (3), (4) and (5) are executed repeatedly in sequence until the filtering ends.

The technical features of the above embodiments can be combined arbitrarily. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features It is considered to be the range described in this specification.

It should be noted that the term "first\second\third" involved in the embodiments of the present application is only to distinguish similar objects, and does not represent a specific ordering of objects. It is understandable that "first\second\third" "Three" may be interchanged in a particular order or sequence where permitted. It should be understood that the "first\second\third" distinctions may be interchanged under appropriate circumstances to enable the embodiments of the application described herein to be practiced in sequences other than those illustrated or described herein.

The terms "comprising" and "having" and any variations thereof in the embodiments of the present application are intended to cover non-exclusive inclusion. For example, a process, method, apparatus, product or device comprising a series of steps or modules is not limited to the listed steps or modules, but optionally also includes unlisted steps or modules, or optionally also includes Other steps or modules inherent to these processes, methods, products or devices.

The above-mentioned embodiments only represent several embodiments of the present application, and the descriptions thereof are specific and detailed, but should not be construed as a limitation on the scope of the invention patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which all belong to the protection scope of the present application. Therefore, the scope of protection of the patent of the present application shall be subject to the appended claims.

Claims (8)

1, A spacecraft attitude estimation method assisted by an adaptive kinematics model, which is characterized by comprising the following steps:

s10, establishing a state space model of the spacecraft at the kth moment, wherein the state space model comprises a process model and an observation model;

s30, when the observation vector of the kth moment is provided, Kalman filtering is carried out according to the state space model of the kth moment and by using the Kalman filtering result of the kth-1 moment to obtain the prior estimation of the state vector of the kth moment

State vector posterior estimation

A priori covariance matrix P_k|k-1Sum a posteriori covariance matrix P_k|k；

S50, extracting the posterior estimation of the state vector

Updating an attitude matrix according to the rotation vector, determining the attitude of the spacecraft at the kth moment according to the updated attitude matrix, zeroing the rotation vector after updating the attitude matrix, and setting

And carrying out the following assignment operations: p_k|k←JP_k|kJ^TWherein the symbol ← represents the assignment operation, the symbol T represents the transposition, P_k|kA matrix of the a posteriori covariance is represented,the back component of the attitude matrix representing the kth time instant,

is composed of

Transposed matrix of (I)₉Representing a 9-row 9-column unit array;

in step S60, when a new observation vector is present, k is set to k +1, and the process returns to step S10.

2. The adaptive kinematics model-assisted spacecraft attitude estimation method according to claim 1, further comprising, before S10:

and setting initial filtering parameters of Kalman filtering.

3. The adaptive kinematics model-assisted spacecraft attitude estimation method according to claim 1, further comprising, after step S30:

s40, estimating the observation model and the state vector a prioriSimultaneously setting pseudo-observation vectors, establishing an observation equation of the pseudo-observation vectors, and estimating parameters to be adjusted by adopting BIQUE according to the observation equation to obtain

And parameter adjustments are made according to the following formula:

will be provided with

P_k|k-1And

the filter for the next time instant is saved, where μ represents the learning rate.

4. The adaptive kinematic model-assisted spacecraft attitude estimation method of any of claims 1 to 3 and , wherein the process model at the kth time instant comprises:

x_k＝F_k-1x_k-1+w_k-1，

wherein x is_k-1Representing the state vector, x, at the (k-1) th instant_kRepresenting the state vector at the kth time, F_k-1Representing a state transition matrix, w_k-1Representing process noise.

5. The adaptive kinematics model-assisted spacecraft attitude estimation method according to claim 4, wherein the process model obtaining procedure comprises:

acquiring a differential equation of the rotation vector; the differential equation of the rotation vector includes:

wherein, ω is_tRepresents the angular velocity vector at time t, phi_tThe rotation vector representing the time t is shown,

is indicative of phi_tTime differentiation of (d);

obtaining a velocity kinematics model, the velocity kinematics model comprising:

wherein,

represents omega_tTime differentiation of ξ_tThe angular acceleration at the time t is indicated,

representation ξ_tTime differentiation of η_t th noise, μ, at time t_tA second noise representing time t;

obtaining a gyro zero-bias model, wherein the gyro zero-bias model comprises:

wherein, theta_tWhich represents the noise at the time t,representing the gyro zero offset at time t,

to represent

Time differentiation of (d);

simultaneously establishing a differential equation of the rotation vector, a velocity kinematics model and a gyro zero-offset model to obtain an initial process model;

and discretizing the initial process model to obtain the process model.

6. The adaptive kinematic model-assisted spacecraft attitude estimation method of any of claims 1 to 3 and , wherein the observation model at the kth time comprises:

y_k＝H_kx_k+e_k，

wherein x is_kRepresenting the state vector at the k-th instant, y_kRepresents the observation vector at the k-th time instant,

representing the second component of the attitude matrix at the kth time instant,representing the reference frame r from the k-th instant_kReference frame r to time k-1_k-1The direction cosine matrix of (a) is,coordinate vectors in the reference system representing observation vectors at the k-th time, symbol x represents the determination of a skew-symmetric matrix of vectors located before x, e_kIndicating the k-th time instant, I₃Representing a3 row 3 column unit array.

7. The adaptive kinematics model-assisted spacecraft attitude estimation method according to claim 6, wherein the acquisition of the observation model comprises:

obtaining an th observation model of the star tracker, and obtaining a second observation model of the gyroscope;

and simultaneously obtaining the observation model by combining the th observation model and the second observation model.

8. The adaptive kinematic model-assisted spacecraft attitude estimation method of any of claims 1 to 3 and , wherein the Kalman filtering at the kth time comprises:

P_k|k＝P_k|k-1-K_kH_kP_k|k-1，

R_k＝cov[e_k]，

wherein,

representing the state vector a priori estimate at the k-th time instant,

posterior estimation of the state vector at the k-1 th instant, F_k-1Representing the state transition matrix at time k-1,

state vector a posteriori estimate, P, representing the k-th time instant_k|k-1Representing the prior covariance matrix, P, at the k-th time instant_k|kRepresenting the posterior covariance matrix, P, at the k-th time instant_k-1|k-1Representing the a posteriori covariance matrix, Q, at time k-1_k-1Covariance matrix representing process noise at time K-1, superscript T representing transposition, superscript-1 representing inversion, K_kA matrix of filter gains is represented by,

representing the second component of the attitude matrix at the kth time instant,

representing the reference frame r from the k-th instant_kReference frame r to time k-1_k-1The direction cosine matrix of (a) is,

coordinate vector of observation vector at k-th time in reference system, symbol x represents the oblique symmetric matrix of matrixes before x, e_kRepresenting the observed noise vector at the k-th time instant, I₃Represents a 3-row and 3-column unit array, y_kRepresenting the observation vector at the k-th time instant.

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