CN103954289B - The quick motor-driven attitude determination method of a kind of Optical Imaging Satellite - Google Patents

Abstract

The quick motor-driven attitude determination method of a kind of Optical Imaging Satellite, relates to the attitude of satellite and determines field。Solving existing satellite attitude determination method in determining calculating process, the attitude of satellite large angle maneuver initial stage produces big vibration, and this vibration reduces the attitude control accuracy of satellite, causes the problem that optical satellite imaging task cannot be smoothed out。The method comprises the following steps: step one, obtain system state equation and observational equation according to satellite attitude kinematics equation；Step 2, obtain the gain matrix of Kalman filter according to system state equation and observational equation；Step 3, utilize Kalman filter the change according to the filtering parameter of Kalman filter to realize quick motor-driven attitude to determine。The present invention is applicable to determine the quick motor-driven attitude of satellite。

Description

Method for determining agile maneuvering attitude of optical imaging satellite

Technical Field

The present invention relates to the field of satellite attitude determination.

Background

An optical imaging system of an optical imaging satellite is usually fixed on a satellite body, and when earth is photographed, the attitude of the whole satellite needs to be frequently and rapidly maneuvered so as to realize observation of different regions, and the satellite usually needs to be maneuvered in a large-angle rapid attitude. Typically, a large-angle fast-gesture maneuver is also referred to as an agile maneuver. The problem of attitude determination in agile maneuvers has been a hotspot and difficulty of research. The attitude determination in the agile maneuvering process is the premise of ensuring the control precision of the optical imaging satellite and the guarantee of successfully completing the imaging task. The kalman filtering method has received wide attention from the world since its introduction and has been applied to various industrial fields. Because of its advantages of simplicity and reliability, the current satellite attitude control system also widely adopts the kalman filtering method to determine the attitude. However, when the attitude determination is performed by using the kalman filtering method, large vibration is generated at the initial stage of large-angle maneuvering of the satellite attitude, which greatly reduces the attitude control precision of the satellite and does not meet the imaging conditions of the optical imaging system, so that the imaging task of the optical satellite cannot be smoothly performed.

Disclosure of Invention

The invention provides a method for determining an agile maneuvering posture of an optical imaging satellite, which aims to solve the problem that the imaging task of the optical satellite cannot be smoothly performed due to the fact that large vibration is generated at the initial stage of large-angle maneuvering of the satellite posture in the determination and calculation process of the conventional satellite posture determination method, and the vibration reduces the posture control precision of the satellite.

An optical imaging satellite agile maneuver attitude determination method comprises the following steps:

the method comprises the following steps of firstly, obtaining a system state equation and an observation equation according to a satellite attitude kinematics equation;

step two, obtaining a gain matrix of the Kalman filter according to a system state equation and an observation equation;

thirdly, the agile maneuver attitude determination is realized by using the Kalman filter according to the change of the filter parameters of the Kalman filter, and the specific realization process is as follows:

△ q error quaternion vector part between the target attitude quaternion and the currently calculated acquired attitude quaternion₁₃Whether any item is greater than 0.01, and whether the satellite attitude working mode is a photographing mode or a data transmission mode is judged;

if there is an errorQuaternion vector portion △ q₁₃Is more than 0.01, the satellite attitude working mode is a photographing mode or a data transmission mode, and when the satellite is in an agile maneuvering process, the gain matrix K of the Kalman filter at the previous moment, namely the moment K-1, is saved_k-1Is a reaction of K_k-1The constant gain matrix is used as a constant gain matrix in the agile maneuvering process of the satellite to determine the attitude;

if the error quaternion vector portion △ q₁₃When the agile maneuver process of the satellite is finished, updating the gain matrixes of the Kalman filters at different moments and circularly executing the first step and the second step to realize the determination of the agile maneuver attitude of the satellite.

Has the advantages that: the satellite attitude can be determined by the determination method provided by the invention through a simple switching criterion, when the satellite is in agile maneuver, the gain matrix of the Kalman filter is kept unchanged, namely the attitude of the agile maneuver of the satellite is determined by adopting a constant Kalman filter; when the agile maneuver of the satellite is finished, updating the gain matrix of the Kalman filter so as to determine the attitude of the satellite in real time; when the satellite attitude large-angle maneuvering is in the initial stage, even large vibration is generated, the determination method provided by the invention cannot be influenced, and the smooth performance of the optical satellite imaging task is ensured.

Drawings

Fig. 1 is a flowchart for determining an agile maneuver attitude by using a kalman filter according to a variation of a filter parameter of the kalman filter according to the fourth embodiment.

Detailed Description

In a first embodiment, a method for determining an agile maneuver attitude of an optical imaging satellite in the first embodiment includes the following steps:

the method comprises the following steps of firstly, obtaining a system state equation and an observation equation according to a satellite attitude kinematics equation;

step two, obtaining a gain matrix of the Kalman filter according to a system state equation and an observation equation;

thirdly, the agile maneuver attitude determination is realized by using the Kalman filter according to the change of the filter parameters of the Kalman filter, and the specific realization process is as follows:

△ q error quaternion vector part between the target attitude quaternion and the currently calculated acquired attitude quaternion₁₃Whether any item is greater than 0.01, and whether the satellite attitude working mode is a photographing mode or a data transmission mode is judged;

if the error quaternion vector portion △ q₁₃Is more than 0.01, the satellite attitude working mode is a photographing mode or a data transmission mode, and when the satellite is in an agile maneuvering process, the gain matrix K of the Kalman filter at the previous moment, namely the moment K-1, is saved_k-1Is a reaction of K_k-1The constant gain matrix is used as a constant gain matrix in the agile maneuvering process of the satellite to determine the attitude;

if the error quaternion vector portion △ q₁₃When the agile maneuver process of the satellite is finished, updating the gain matrixes of the Kalman filters at different moments and circularly executing the first step and the second step to realize the determination of the agile maneuver attitude of the satellite.

The difference between the second specific embodiment and the first specific embodiment in the method for determining the agile maneuver attitude of the optical imaging satellite is that the process of establishing a system state equation and an observation equation according to the satellite attitude kinematics model in the first step is as follows:

is provided with $q=\left[\begin{array}{c}{q}_{13}\\ q_{14}\end{array}\right]=\left[\begin{array}{c}{q}_1\\ q_2\\ q_3\\ q_4\end{array}\right]$ Is a quaternion of the satellite attitude, $\mathrm{\ω}=\left[\begin{array}{c}{\mathrm{\ω}}_x\\ {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z\end{array}\right]$ expressed as the angular velocity of the satellite attitude, the quaternion q and the gyro drift b form the attitudeDetermined state vectors, i.e. $x=\left[\begin{array}{c}q\\ b\end{array}\right],$ The quaternion has the property of being normalized, i.e. the quaternion q has a modulo of 1,

kinematic equation based on satellite attitudeObtaining a system state equation $\stackrel{\·}{x}=f\left(x\right)+\mathrm{Gn}=\left[\begin{array}{c}\frac{1}{2}\mathrm{\Ω}\left(\mathrm{\ω}\right)q-\frac{1}{2}\mathrm{\Ξ}\left(q\right)b\\ 0_{3\×1}\end{array}\right]+\left[\begin{array}{cc}-\frac{1}{2}\mathrm{\Ψ}\left(q\right)& \\ & I_{3\×3}\end{array}\right]n,$ Wherein, $\widetilde{\mathrm{\ω}}=\left[\begin{array}{c}\mathrm{\ω}\\ 0\end{array}\right],$ $\mathrm{\Ξ}\left(q\right)=\left[\begin{array}{c}{q}_4{I}_{3\×3}+[q_{13}\×]\\ {-q}_{13}^T\end{array}\right],\mathrm{\Ω}\left(\mathrm{\ω}\right)=\left[\begin{array}{cc}-[\mathrm{\ω}\×]& \mathrm{\ω}\\ {-\mathrm{\ω}}^T& 0\end{array}\right],$ I_3×3is a third order unit array, 0_3×1Is a zero matrix of 3 × 1, n is the systematic process noise vector, and $n={\left[\begin{array}{cc}{\mathrm{\η}}_{\mathrm{\ω}}^T& {\mathrm{\η}}_b^T\end{array}\right]}^T,$ η_ωprocess noise vector for attitude angular velocity, η_bProcess noise vector for gyro drift, process noise covariance matrix $Q=\left[\begin{array}{cc}{\mathrm{\σ}}_{\mathrm{\ω}}^2{I}_{3\×3}& \\ & {\mathrm{\σ}}_b^2{I}_{3\×3}\end{array}\right],$ Is the error covariance of the attitude angular velocity,is the error covariance of the gyro drift,

setting state error vector $\mathrm{\δx}={\left[\begin{array}{cc}{\mathrm{\δq}}_{13}^T& {\mathrm{\δb}}^T\end{array}\right]}^T,$ Wherein q is₁₃Is the vector part of the quaternion error, b is the gyro drift error vector, and $\mathrm{\δq}={\hat{q}}^{-1}\⊗q,\mathrm{\δ\ω}=\mathrm{\ω}-\widehat{\mathrm{\ω}=-(b-\hat{b})-{\mathrm{\η}}_{\mathrm{\ω}}}=-\mathrm{\δb}-{\mathrm{\η}}_{\mathrm{\ω}},$ the symbol a represents the variable estimation result,

obtaining a differential equation from the system state equation and the state error vectorWherein, $F\left(\hat{x}\right)=\left[\begin{array}{cc}-\left[\widehat{\mathrm{\ω}\×}\right]& {-05I}_{3\×3}\\ 0_{3\×3}& 0_{3\×3}\end{array}\right],$ 0_3×3is a three-order zero matrix,

if the control period is dt, the discrete form of the differential equation corresponding to the kth time is: x is the number of_k＝Φ_k,k-1x_k-1+_k-1n_k-1Wherein _k-1＝Gdt，I_6×6for a six-order unit matrix, the system observation equation is: z_k＝H_kx_k+v_kWherein the observation matrix H_k＝[I_3×30_3×3]，v_kTo measure noise.

The difference between the third specific embodiment and the second specific embodiment in the method for determining the agile maneuver attitude of the optical imaging satellite is that the process of obtaining the gain matrix of the kalman filter according to the system state equation and the observation equation in the second step is as follows:

according to the covariance matrix $P_{k/k-1}={\mathrm{\Φ}}_{k,k-1}{P}_{k-1}{\mathrm{\Φ}}_{k,k-1}^T+{\mathrm{\Γ}}_{k-1}{Q}_{k-1}{\mathrm{\Γ}}_{k-1}^T,$ Wherein, P_k-1Is the system covariance matrix, Q, at time k-1_k-1Updating a gain matrix for the system process noise covariance matrix at the k-1 moment: $K_k=P_{k/k-1}{H}_k^T{[H_k{P}_{k/k-1}{H}_k^T+R_k]}^{-1},$ wherein R is_kMeasuring a noise covariance matrix;

updating the covariance matrix P_k＝(I-K_kH_k)P_k/k-1Wherein I is a 6 th order unit matrix, P₀Taking a 6-order unit array;

correcting the state error vector in the discrete form to obtain:wherein, $\mathrm{\δ}{\hat{x}}_k={\left[\begin{array}{cc}{\mathrm{\δ}\hat{q}}_{13,k}^T& {{\mathrm{\δ}\hat{b}}_k}^T\end{array}\right]}^T$ for the discrete form of the state error vector corrected at time k,the vector portion of the discrete-form quaternion error corrected at time k,for the discrete form of the gyro drift error vector corrected at time k,for one-step prediction of state, Z_kIs the measured value at the time of the k-th instant,namely 6-order zero array;

according to the characteristics of quaternion normalization, according to the vector part of quaternion errorCalculating to obtain corresponding quaternion errorUpdating the quaternion q to obtain:wherein q is_kThe system quaternion at the kth moment;

updating the gyro drift b to obtain:wherein, b_kThe system gyro drift at the kth moment;

updating the system state to obtain: $x_k=\left[\begin{array}{c}{q}_k\\ b_k\end{array}\right],{\hat{x}}_k=\left[\begin{array}{c}{\hat{q}}_k\\ {\hat{b}}_k\end{array}\right],$ whereinIs a system discrete quaternion at the kth time,The drift of the system discrete gyro at the kth moment meets the system state equation, ${\hat{x}}_0={\left[\begin{array}{ccccccc}0& 0& 0& 1& 0& 0& 0\end{array}\right]}^T;$

and substituting the updated quaternion q and the gyro drift b into the step one to repeatedly calculate.

The method for determining the attitude can determine the attitude of the satellite through a simple switching criterion, and when the satellite is in agile maneuver, the gain matrix of the Kalman filter is kept unchanged, namely the attitude of the agile maneuver of the satellite is determined by adopting a constant Kalman filter; when the satellite is not in agile maneuver, updating the gain matrix of the Kalman filter so as to realize real-time determination of the satellite attitude; when the satellite attitude large-angle maneuvering is in the initial stage, even if large vibration is generated, the determination method for determining the attitude cannot be influenced, and the optical satellite imaging task is ensured to be smoothly carried out.

Claims (3)

1. An optical imaging satellite agile maneuver attitude determination method is characterized by comprising the following steps:

the method comprises the following steps of firstly, obtaining a system state equation and an observation equation according to a satellite attitude kinematics equation;

step two, obtaining a gain matrix of the Kalman filter according to a system state equation and an observation equation;

thirdly, the agile maneuver attitude determination is realized by utilizing the Kalman filter according to the change of the gain matrix of the Kalman filter, and the specific realization process is as follows:

judging an error quaternion vector part q between the target attitude quaternion and the attitude quaternion obtained by current calculation₁₃Whether any item is greater than 0.01, and whether the satellite attitude working mode is a photographing mode or a data transmission mode is judged;

if the error quaternion vector portion q₁₃Is more than 0.01, the satellite attitude working mode is a photographing mode or a data transmission mode, and when the satellite is in an agile maneuvering process, the gain matrix K of the Kalman filter at the previous moment, namely the moment K-1, is saved_k-1Is a reaction of K_k-1The constant gain matrix is used as a constant gain matrix in the agile maneuvering process of the satellite to determine the attitude;

if the error quaternion vector portion q₁₃When the agile maneuver process of the satellite is finished, updating the gain matrixes of the Kalman filters at different moments and circularly executing the first step and the second step to realize the determination of the agile maneuver attitude of the satellite.

2. The method for determining the agile maneuver attitude of the optical imaging satellite according to claim 1, wherein the process of establishing the system state equation and the observation equation according to the kinematic model of the attitude of the satellite in the first step is as follows:

is provided withIs a quaternion of the satellite attitude,expressed as the satellite attitude angular velocity, the quaternion q and the gyro drift b form the attitude-determining state vector, i.e.The quaternion has the property of being normalized, i.e. the quaternion q has a modulo of 1,

kinematic equation based on satellite attitudeObtaining a system state equationWherein, I_3×3is a third order unit array, 0_3×1Is a zero matrix of 3 × 1, n is the systematic process noise vector, andη_ωprocess noise vector for attitude angular velocity, η_bProcess noise vector for gyro drift, process noise covariance matrix Is the error covariance of the attitude angular velocity,is the error covariance of the gyro drift,

setting state error vectorWherein q is₁₃Is the vector part of the quaternion error, b is the gyro drift error vector, andthe symbol a represents the variable estimation result,

basis systemObtaining a differential equation from the system state equation and the state error vectorWherein,0_3×3is a three-order zero matrix,

if the control period is dt, the discrete form of the differential equation corresponding to the kth time is: x is the number of_k＝Φ_k,k-1x_k-1+_k-1n_k-1Wherein _k-1＝Gdt，I_6×6for a six-order unit matrix, the system observation equation is: z_k＝H_kx_k+v_kWherein the observation matrix H_k＝[I_3×30_3×3]，v_kTo measure noise.

3. The method for determining the agile maneuver attitude of the optical imaging satellite according to claim 2, wherein the process of obtaining the gain matrix of the kalman filter according to the system state equation and the observation equation in the second step is:

according to the covariance matrixWherein, P_k-1Is the system covariance matrix, Q, at time k-1_k-1Updating a gain matrix for the system process noise covariance matrix at the k-1 moment:wherein R is_kMeasuring a noise covariance matrix;

updating the covariance matrix P_k＝(I-K_kH_k)P_k/k-1Wherein I is a 6 th order unit matrix, P₀Taking a 6-order unit array;

correcting the state error vector in the discrete form to obtain:wherein,for the discrete form of the state error vector corrected at time k,the vector portion of the discrete-form quaternion error corrected at time k,for the discrete form of the gyro drift error vector corrected at time k,for one-step prediction of state, Y_kIs the measured value at the time of the k-th instant,namely 6-order zero array;

according to the characteristics of quaternion normalization, according to the vector part of quaternion errorCalculating to obtain corresponding quaternion errorUpdating the quaternion q to obtain:wherein q is_kThe system quaternion at the kth moment;

updating the gyro drift b to obtain:wherein, b_kThe system gyro drift at the kth moment;

updating the system state to obtain:whereinIs a system discrete quaternion at the kth time,The drift of the system discrete gyro at the kth moment meets the system state equation,

and substituting the updated quaternion q and the gyro drift b into the step one to repeatedly calculate.