CN113701755B - Optical remote sensing satellite attitude determination method without high-precision gyroscope - Google Patents
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Abstract
The invention provides an optical remote sensing satellite attitude determination method without a high-precision gyroscope. Step 1: defining an error quaternion, an error angular velocity and an error interference moment by combining a satellite kinematics equation and a dynamics equation; step 2: acquiring a state equation and a measurement equation of error quaternion, error angular velocity and error interference moment based on the definition of the step 1; step 3; filtering and updating the state equation and the measurement equation of the error quaternion, the error angular velocity and the error interference moment in the step 2 through a linear Kalman filtering method; step 4: the estimator is compensated to the star gesture quaternion and angular velocity and the calculation is returned for star control. The invention aims at the problems that the satellite does not use a high-precision gyroscope, only uses star sensor measurement information and reaction flywheel angular momentum information to acquire an on-orbit attitude quaternion and angular velocity.
Description
Technical Field
The invention belongs to the field of aerospace; in particular to an optical remote sensing satellite attitude determination method without a high-precision gyroscope.
Background
In recent years, the optical remote sensing satellite industry has rapidly developed. The attitude determination and control system is one of the most important subsystems of the optical remote sensing satellite, and the accuracy of attitude determination directly relates to the control accuracy and the image production quality when the satellite platform is imaged. The commonly applied gesture determining method at present is based on the combination of a high-precision gyroscope and a star sensor to determine a gesture angle and a gesture angular speed. The high-precision gyroscope has high quality, high power consumption and high price, and the performance and reliability can be obviously reduced after long-term use, and even faults can occur; the MEMS gyroscope has low power consumption and low price, but the measurement precision is difficult to meet the requirement, and the function of the high-precision gyroscope cannot be replaced. In addition, although the method of estimating the angular velocity using the angle sensor difference method is simple, shortening the sampling time increases the measurement noise, which limits its application.
Therefore, the optical remote sensing satellite attitude determination technology without the high-precision gyroscope has important significance for realizing the low-quality, low-power consumption, low-cost and high-precision design of satellites.
Disclosure of Invention
The invention provides an optical remote sensing satellite attitude determination method without a high-precision gyroscope, which aims at the problems that an on-orbit attitude quaternion and angular velocity are acquired by using satellite sensor measurement information and reaction flywheel angular momentum information without using a high-precision gyroscope.
The invention is realized by the following technical scheme:
The optical remote sensing satellite attitude determination method without the high-precision gyroscope is characterized by comprising the following steps of:
Step 1: defining an error quaternion, an error angular velocity and an error interference moment by combining a satellite kinematics equation and a dynamics equation;
Step 2: acquiring a state equation and a measurement equation of error quaternion, error angular velocity and error interference moment based on the definition of the step 1;
Step 3; filtering and updating the state equation and the measurement equation of the error quaternion, the error angular velocity and the error interference moment in the step 2 through a linear Kalman filtering method;
step 4: the estimator is compensated to the star gesture quaternion and angular velocity and the calculation is returned for star control.
Further, the kinematic equation derivation process of the error quaternion in the step 2 is as follows;
The satellite kinematics expressed in terms of attitude quaternions are:
where q= [ q 0q1q2q3]T represents a satellite attitude quaternion, The attitude angular velocity of the satellite is represented,
Defining the spread angular velocity asThe kinematic equation is expressed as:
defining a true quaternion q and an estimated quaternion The error quaternion between is deltaq,Δq is defined by q and/>Is obtained by incremental operation of:
Δq 0 ≡1 at a small angle;
Differentiating the incremental two sides to obtain:
defining an estimated angular velocity Extended estimate of angular velocity/>The kinematic equation expressed by the spread angular velocity is taken in to be:
Defining the error angular velocity Extended error angular velocity/>The above kinetic equation is expressed as:
I.e. Is a kinematic equation for the error quaternion vector.
Further, the dynamic equation derivation process about the error angular velocity in the step 2 is as follows:
the satellite dynamics equation is:
wherein J represents the moment of inertia of the whole satellite, h represents the moment of momentum generated by the momentum wheel, T c represents the control moment generated by the momentum wheel, and T d represents the disturbance moment of the satellite;
Order the The disturbance moment of the estimated satellite is obtained after being brought into a satellite dynamics equation:
the differential of the error angular velocity is expressed as:
According to the taylor expansion formula, the satellite dynamics equation expressed by the error angular velocity is obtained by ignoring the second-order minima:
Wherein, Representing disturbance moment estimation error, an
Further, the step3 specifically includes the following steps:
step 3.1: performing incremental differentiation on the error quaternion and bringing the kinematic equation into the differential quaternion to obtain the kinematic equation about the error quantity;
step 3.2: differentiating the error angular velocity and bringing the satellite dynamics equation into the error angular velocity, and obtaining a dynamics equation about the error amount by a Taylor expansion formula;
Step 3.3: calculating a state transition matrix based on the kinematic equation of the error amount in the step 3.1 and the state equation obtained by the kinematic equation of the error amount in the step 3.2, calculating a measurement matrix by a measurement equation, and estimating by applying a linear discrete Kalman filter in combination with star sensitivity and flywheel measurement information;
step 3.5: and compensating the error amount calculation result to the star gesture and the angular velocity.
Further, the state equation in the step3 is specifically that,
From the kinematic equation and the kinetic equation about the error amount, the state equation using the error quaternion, the error angular velocity and the error disturbance moment as state variables can be obtained:
wherein w (t) represents system noise, satisfying Delta k-j is the Kronecker-delta function;
Partial derivative matrix is obtained by solving state variables for partial derivative through state equation Because the state equation is continuous, discretization is needed, and the discretized state transition matrix is as follows:
Fk＝I9×9+A·Δt。
further, the measurement equation in the step 3 using the error quaternion, the error angular velocity and the error disturbance moment as the state variables can be expressed as follows:
wherein v (t) represents measurement noise, satisfying And/>State variables are biased through a measurement equation to obtain a measurement matrix/>
Further, the Kalman filtering update of the step 3 is specifically that,
Since the above state equation and measurement equation are both linear equations for state variables, the calculation steps of the linear discrete kalman filter method can be directly applied,
Where P k denotes the covariance of the estimation error, K k denotes the kalman filter gain, Q denotes the system noise covariance matrix, and R denotes the measurement noise covariance matrix.
Further, the filtering update compensation in the step 3 is specifically,
The beneficial effects of the invention are as follows:
The linearized state equation and measurement equation are obtained by designing the kinematics and dynamics equation of the error quantity, and then the high-precision attitude quaternion and angular velocity estimation method is obtained by applying Kalman filtering. Simulation and test results prove that the method is effective, and the optical remote sensing satellite attitude determination system with low quality, low power consumption, low cost and high precision can be realized.
Drawings
FIG. 1 is a flow chart of the Kalman filter calculation of the present invention.
Fig. 2 is a flow chart of the filtered estimation of the present invention.
FIG. 3 is a schematic representation of the true and estimated star gesture quaternion of the present invention.
Fig. 4 is a schematic diagram of real and estimated star angular velocity under the inertial frame of the present invention.
Fig. 5 is a schematic diagram of the actual and estimated disturbance moment of the present invention.
FIG. 6 is a schematic diagram of the estimated pose and true pose error quaternion of the present invention.
Fig. 7 is a schematic diagram of the estimated and true angular velocity errors of the present invention.
Fig. 8 is a flow chart of the method of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. 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.
The optical remote sensing satellite attitude determination method without the high-precision gyroscope is characterized by comprising the following steps of:
Step 1: defining an error quaternion, an error angular velocity and an error interference moment by combining a satellite kinematics equation and a dynamics equation;
Step 2: acquiring a state equation and a measurement equation of error quaternion, error angular velocity and error interference moment based on the definition of the step 1;
Step 3; filtering and updating the state equation and the measurement equation of the error quaternion, the error angular velocity and the error interference moment in the step 2 through a linear Kalman filtering method;
step 4: the estimator is compensated to the star gesture quaternion and angular velocity and the calculation is returned for star control.
The method comprises the steps of obtaining a state equation and a measurement equation about error quaternion, error angular velocity and error disturbance moment by defining the error quaternion, error angular velocity and error disturbance moment and combining a satellite kinematics equation and a dynamics equation; and then, filtering and updating the error quantity (namely an error quaternion, an error angular velocity and an error interference moment) by a linear Kalman filtering method, and finally, compensating the estimated quantity to the star gesture quaternion and the angular velocity and returning a calculation result to be used for star control.
Further, the kinematic equation derivation process of the error quaternion in the step 2 is as follows;
The satellite kinematics expressed in terms of attitude quaternions are:
where q= [ q 0q1q2q3]T represents a satellite attitude quaternion, The attitude angular velocity of the satellite is represented,
Defining the spread angular velocity asThe kinematic equation is expressed as:
defining a true quaternion q and an estimated quaternion The error quaternion between is deltaq,
Δq is defined by q and/>Is obtained by incremental operation of:
Δq 0 ≡1 at a small angle;
Differentiating the incremental two sides to obtain:
defining an estimated angular velocity Extended estimate of angular velocity/>The kinematic equation expressed by the spread angular velocity is taken in to be:
Defining the error angular velocity Extended error angular velocity/>The above kinetic equation is expressed as:
I.e. Is a kinematic equation for the error quaternion vector.
Further, the dynamic equation derivation process about the error angular velocity in the step 2 is as follows:
the satellite dynamics equation is:
wherein J represents the moment of inertia of the whole satellite, h represents the moment of momentum generated by the momentum wheel, T c represents the control moment generated by the momentum wheel, and T d represents the disturbance moment of the satellite;
Order the The disturbance moment of the estimated satellite is obtained after being brought into a satellite dynamics equation:
the differential of the error angular velocity is expressed as:
According to the taylor expansion formula, the satellite dynamics equation expressed by the error angular velocity is obtained by ignoring the second-order minima:
Wherein, Representing disturbance moment estimation error, an
Further, the step3 specifically includes the following steps:
step 3.1: performing incremental differentiation on the error quaternion and bringing the kinematic equation into the differential quaternion to obtain the kinematic equation about the error quantity;
step 3.2: differentiating the error angular velocity and bringing the satellite dynamics equation into the error angular velocity, and obtaining a dynamics equation about the error amount by a Taylor expansion formula;
Step 3.3: inputting star-sensitive and flywheel measurement information;
Step 3.4: calculating a state transition matrix based on the kinematic equation of the error amount in the step 3.1, the kinematic equation of the error amount in the step 3.2 and the state equation obtained by the star sensor and flywheel measurement information in the step 3.3, calculating a measurement matrix by the measurement equation, and estimating by applying a linearization discrete Kalman filter;
step 3.5: and compensating the error amount calculation result to the star gesture and the angular velocity.
Further, the state equation in the step3 is specifically that,
From the kinematic equation and the kinetic equation about the error amount, the state equation using the error quaternion, the error angular velocity and the error disturbance moment as state variables can be obtained:
wherein w (t) represents system noise, satisfying Delta k-j is the Kronecker-delta function;
Partial derivative matrix is obtained by solving state variables for partial derivative through state equation Because the state equation is continuous, discretization is needed, and the discretized state transition matrix is as follows:
Fk＝I9×9+A·Δt。
further, the measurement equation in the step 3 using the error quaternion, the error angular velocity and the error disturbance moment as the state variables can be expressed as follows:
wherein v (t) represents measurement noise, satisfying And/>State variables are biased through a measurement equation to obtain a measurement matrix/>
Further, the Kalman filtering update of the step 3 is specifically that,
Since the above state equation and measurement equation are both linear equations for state variables, the calculation steps of the linear discrete kalman filtering method can be directly applied, as shown in fig. 1:
Wherein P k denotes the covariance of the estimation error, K k denotes the Kalman filtering gain, Q denotes the system noise covariance matrix, R denotes the measurement noise covariance matrix, Representing a priori estimates of state variables,/>Representing the result of the estimation of the state variable,/>For/>Estimate error covariance,/>For/>Is used for estimating the error covariance.
Further, the filtering update compensation in the step 3 is specifically,
The satellite simulation parameters implemented are as follows:
The quaternion of the initial attitude of the satellite is q= [0.0357 0.821 0,56636 0.062587], the angular speed of the initial attitude is ω= [ 000 ], and the rotational inertia of the satellite is The angular momentum of the flywheel is 0.05Nms, the moment of the flywheel is 2mNm, the system noise is q=2X10 -15 I, and the measurement noise is r=2.15X10 -10 I. The space disturbance moment model used for simulation consists of remanence moment and gravity gradient moment.
According to the steps shown in fig. 2, a filter estimator is constructed, and in the maneuvering process of stabilizing the earth triaxial to the earth sidesway of 15 degrees, the real and estimated star attitude quaternion, the real and estimated star angular velocity under the inertial system and the real and estimated interference moment are respectively shown in fig. 3-5, so that the algorithm can track the dynamic change process.
Under the condition of stabilizing the attitude with respect to the inertial space, the quaternion of the estimated and real attitude errors and the estimated and real angular velocity errors are respectively shown in fig. 6 and 7, and it can be seen that the attitude estimation precision of the filter is about 0.0003 degrees, and the attitude angular velocity estimation precision is about 0.0001 degrees/s.
Claims (6)
1. The optical remote sensing satellite attitude determination method without the high-precision gyroscope is characterized by comprising the following steps of:
Step 1: defining an error quaternion, an error angular velocity and an error interference moment by combining a satellite kinematics equation and a dynamics equation;
Step 2: acquiring a state equation and a measurement equation of error quaternion, error angular velocity and error interference moment based on the definition of the step 1;
Step 3; filtering and updating the state equation and the measurement equation of the error quaternion, the error angular velocity and the error interference moment in the step 2 through a linear Kalman filtering method;
Step 4: compensating the estimated quantity to a star gesture quaternion and an angular velocity, and returning a calculation result to be used for star control;
The kinematic equation derivation process of the error quaternion in the step 2 is as follows;
The satellite kinematics expressed in terms of attitude quaternions are:
where q= [ q 0 q1 q2 q3]T represents a satellite attitude quaternion, The attitude angular velocity of the satellite is represented,
Defining the spread angular velocity asThe kinematic equation is expressed as:
defining a true quaternion q and an estimated quaternion The error quaternion between is Δq,Δq＝[Δq0Δq1Δq2Δq3]T＝[Δq0Δqs T]T,Δq defined by q and/>Is obtained by incremental operation of:
Δq 0 ≡1 at a small angle;
Differentiating the incremental two sides to obtain:
defining an estimated angular velocity Extended estimate of angular velocity/>The kinematic equation expressed by the spread angular velocity is taken in to be:
Defining the error angular velocity Extended error angular velocity/>The kinematic equation described above is expressed as:
I.e. Is a kinematic equation about the error quaternion vector;
the dynamic equation derivation process about the error angular velocity in the step 2 is as follows:
the satellite dynamics equation is:
wherein J represents the moment of inertia of the whole satellite, h represents the moment of momentum generated by the momentum wheel, T c represents the control moment generated by the momentum wheel, and T d represents the disturbance moment of the satellite;
Order the The disturbance moment of the estimated satellite is obtained after being brought into a satellite dynamics equation:
the differential of the error angular velocity is expressed as:
According to the taylor expansion formula, the satellite dynamics equation expressed by the error angular velocity is obtained by ignoring the second-order minima:
Wherein, Representing disturbance moment estimation error, an
2. The method for determining the attitude of the optical remote sensing satellite without the high-precision gyroscope according to claim 1, wherein the step 3 specifically comprises the following steps:
step 3.1: performing incremental differentiation on the error quaternion and bringing the kinematic equation into the differential quaternion to obtain the kinematic equation about the error quantity;
step 3.2: differentiating the error angular velocity and bringing the satellite dynamics equation into the error angular velocity, and obtaining a dynamics equation about the error amount by a Taylor expansion formula;
Step 3.3: calculating a state transition matrix based on the kinematic equation of the error amount in the step 3.1 and the state equation obtained by the kinematic equation of the error amount in the step 3.2, calculating a measurement matrix by a measurement equation, and estimating by applying a linear discrete Kalman filter in combination with star sensitivity and flywheel measurement information;
Step 3.4: and compensating the error amount calculation result to the star gesture and the angular velocity.
3. The method for determining the attitude of the optical remote sensing satellite without the high-precision gyroscope according to claim 2, wherein the state equation in the step 3 is specifically as follows,
From the kinematic equation and the kinetic equation about the error amount, the state equation using the error quaternion, the error angular velocity and the error disturbance moment as state variables can be obtained:
wherein w (t) represents system noise, satisfying Delta k-j is the Kronecker-delta function;
Partial derivative matrix is obtained by solving state variables for partial derivative through state equation Because the state equation is continuous, discretization is needed, and the discretized state transition matrix is as follows:
Fk＝I9×9+A·Δt。
4. The method for determining the attitude of the optical remote sensing satellite without the high-precision gyroscope according to claim 1, wherein the measurement equation in the step 3 can be expressed as a measurement equation with an error quaternion, an error angular velocity and an error interference moment as state variables:
wherein v (t) represents measurement noise, satisfying And/>State variables are biased through a measurement equation to obtain a measurement matrix/>
5. The method for determining the attitude of the optical remote sensing satellite without the high-precision gyroscope according to claim 1, wherein the Kalman filtering updating in the step 3 is specifically that,
Since the above state equation and measurement equation are both linear equations for state variables, the calculation steps of the linear discrete kalman filter method can be directly applied,
Wherein P k denotes the covariance of the estimation error, K k denotes the Kalman filtering gain, Q denotes the system noise covariance matrix, R denotes the measurement noise covariance matrix,Representing a priori estimates of state variables,/>Representing the result of the estimation of the state variable,For/>Estimate error covariance,/>For/>Is used for estimating the error covariance.
6. The method for determining the attitude of the optical remote sensing satellite without the high-precision gyroscope according to claim 1, wherein the filtering update compensation in the step 3 is specifically that,
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