CN112762925A - Low-orbit satellite attitude determination method based on geomagnetism meter and gyroscope - Google Patents

Low-orbit satellite attitude determination method based on geomagnetism meter and gyroscope Download PDF

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CN112762925A
CN112762925A CN202011581356.0A CN202011581356A CN112762925A CN 112762925 A CN112762925 A CN 112762925A CN 202011581356 A CN202011581356 A CN 202011581356A CN 112762925 A CN112762925 A CN 112762925A
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向高军
王文斌
王艳峰
李涛
胡俊
杨轶
蒋博
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Dongfanghong Satellite Mobile Communication Co Ltd
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    • G—PHYSICS
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Abstract

The invention belongs to the field of low-orbit satellite attitude determination, and particularly relates to a low-orbit satellite attitude determination method based on a magnetometer and a gyroscope, which comprises the following steps: acquiring initial low-orbit satellite attitude parameters before the low-orbit satellite is launched, and measuring a geomagnetic field by using a geomagnetic meter carried on the low-orbit satellite; calculating the attitude of the low-orbit satellite by adopting an attitude algorithm; establishing a four-element attitude updating equation of a gyroscope, and updating the attitude of the low-earth orbit satellite in real time; fusing the low-orbit satellite attitude and the low-orbit satellite attitude updated by the gyroscope by adopting an extended Kalman filtering equation, and outputting a low-orbit satellite attitude angle with higher precision; the method provides a high-precision data source for the low-orbit satellite orbit control without depending on systems such as an external GNSS and the like, and avoids the uncontrollable performance of the low-orbit satellite in orbit transfer when the low-orbit satellite is disconnected with the ground.

Description

Low-orbit satellite attitude determination method based on geomagnetism meter and gyroscope
Technical Field
The invention belongs to the field of low-orbit satellite attitude determination, and particularly relates to a low-orbit satellite attitude determination method based on a magnetometer and a gyroscope.
Background
At present, there are 4 main technical means for determining the orbit and attitude of a low-orbit Satellite with high precision, including a Satellite Laser Ranging (SLR), a Doppler terrestrial radio positioning (dorsi) technology, a precision Ranging and velocity measuring (PRARE) technology, and a Global positioning (GNSS) technology. However, SLR is expensive, heavy, and difficult to perform alone for the precise positioning task of low orbit satellites with a height of about 500km due to the limited observation coverage area and the severe influence of weather. The DORIS system in France has relatively slow data acquisition and processing speed, and the ground tracking network coverage is relatively weak. The PRARE system in Germany has fewer stations around the world, more expensive equipment and fewer satellites to load. However, GNSS cannot meet the requirements of orbit determination and attitude determination in extreme periods such as failure, and cannot realize full-arc orbit determination and attitude determination in working period, and there are many difficulties in the autonomous orbit determination and attitude determination method and system for low-orbit satellites based on non-navigation satellite signals.
When the low-orbit satellite is subjected to attitude determination, the roll angle, the pitch angle and the course angle of the low-orbit satellite are accurately measured, and the attitude determination is performed on the low-orbit satellite by referring to the roll angle, the pitch angle and the course angle, so that the motion state and the motion track of the low-orbit satellite can be better controlled. However, due to the limitation of factors such as volume, mass and power consumption, the traditional method for measuring the attitude of the low-orbit satellite is difficult to meet the requirement for measuring the attitude of the low-orbit satellite, and therefore a method capable of measuring the attitude of the low-orbit satellite more accurately is urgently needed.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a low-orbit satellite attitude determination method based on a geomagnetic meter and a gyroscope, which comprises the following steps:
s1: acquiring initial attitude parameters of a low-earth-orbit satellite;
s2: establishing an orbit coordinate system of the low-orbit satellite, measuring the satellite angular velocity of the low-orbit satellite in the coordinate system by adopting a gyroscope, and measuring the geomagnetic component of the low-orbit satellite in the coordinate system by adopting a geomagnetic meter;
s3: inputting the angular velocity of the satellite into a gyro four-element attitude updating model, and calculating attitude information of the low-orbit satellite to obtain the state of the satellite at the next moment;
s4: inputting the geomagnetic component under the body coordinate system of the low-orbit satellite and the attitude information of the low-orbit satellite into a geomagnetic attitude measurement model to obtain an observation equation of the low-orbit satellite;
s5: processing an observation equation obtained by measurement by adopting an extended Kalman filtering fusion algorithm to obtain multi-point information of the low-orbit satellite;
s6: the attitude information of the low-orbit satellite is continuously corrected by carrying out iteration and filtering processing on the multi-point information of the low-orbit satellite;
s7: it is determined whether the low-earth orbit satellite attitude determination task is finished, that is, whether the satellite has reached the predetermined attitude, and if the condition is not satisfied, the process returns to S2.
Preferably, the initial low-orbit satellite attitude parameters before low-orbit satellite transmission include: satellite roll angle
Figure BDA0002864486030000021
A satellite pitch angle theta and a satellite course angle psi;
preferably, the gyro four-element posture updating model is as follows:
Figure BDA0002864486030000022
Figure BDA0002864486030000023
preferably, the attitude four-element state equation is:
X(k+1)＝F·X(k)+V
further, the expression of the state transition equation F is:
Figure BDA0002864486030000024
Figure BDA0002864486030000025
preferably, the geomagnetism attitude measurement model under the small angle is as follows:
Figure BDA0002864486030000031
Figure BDA0002864486030000032
preferably, the observation equation for the low earth orbit satellite is:
Y(k+1)＝HX(k+1)+N
Figure BDA0002864486030000033
preferably, the processing the measured attitude by using the extended kalman filter fusion algorithm includes: updating the observation equation by adopting a covariance updating formula, calculating a gain matrix of the updated observation equation, and updating the attitude information of the low-earth orbit satellite according to the gain matrix;
the covariance update equation is:
P-(k+1)＝FP(k)FT+R
P(k+1)＝[I-K(k+1)H(k+1)]P-(k+1)
the gain matrix is:
K(k+1)＝P-(k+1)H[HP-(k+1)HT+Q]-1
the state update equation is:
X(k+1)＝X-(k+1)+K(k+1)(Y(k+1)-HX-(k+1))
preferably, the process of performing iteration and filtering processing on the multipoint information of the low earth orbit satellite comprises: and resolving initial four elements by combining the initial attitude of the low-earth orbit satellite, updating the four elements by using the gyroscope, correcting the accumulated error of the gyroscope by adopting an extended Kalman filtering fusion algorithm, and outputting an attitude angle with higher precision.
The invention can complete the low-orbit satellite attitude measurement with higher precision on the premise of consuming less low-orbit satellite resources; under the condition of not depending on systems such as an external GNSS and the like, the method provides a high-precision data source for the low-orbit satellite orbit control, and avoids the uncontrollable performance of the low-orbit satellite in orbit change when the low-orbit satellite is disconnected with the ground.
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FIG. 1 is a block flow diagram of the present invention;
FIG. 2 is a view of the course angle fusion result of the attitude angle according to the embodiment of the present invention;
FIG. 3 is a table of the blending results of the roll angles of the attitude angles of the embodiment of the present invention;
fig. 4 is a diagram of the result of the pitch angle fusion of attitude angles in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A low-earth orbit satellite attitude determination method based on a magnetometer and a gyroscope, as shown in fig. 1, the method comprises:
s1: acquiring initial low-orbit satellite attitude parameters before the low-orbit satellite is transmitted;
s2: measuring satellite angular velocity under a low-orbit satellite local coordinate system by adopting a gyroscope, and measuring geomagnetic components under a low-orbit satellite local coordinate system by adopting a geomagnetic meter;
s3: acquiring attitude information of a low-earth orbit satellite by adopting a gyro four-element attitude updating model and a geomagnetism attitude measurement model;
s4: calculating the attitude information of the low-orbit satellite by adopting an attitude four-element state equation according to the angular velocity of the satellite to obtain the state of the satellite at the next moment; establishing a geomagnetism attitude measurement equation according to the geomagnetic component in the low-orbit satellite body coordinate system, and carrying out attitude measurement on the state of the satellite at the next moment;
s5: processing the measured attitude by adopting an extended Kalman filtering fusion algorithm to obtain multi-point information of the low-orbit satellite;
s6: the attitude information of the low-orbit satellite is continuously corrected by carrying out iteration and filtering processing on the multi-point information of the low-orbit satellite;
s7: and judging whether the low-orbit satellite attitude determination task is finished or not, and returning to the step S2 if the low-orbit satellite attitude determination task is not finished.
The initial low-orbit satellite attitude parameters before low-orbit satellite transmission comprise: satellite roll angle
Figure BDA0002864486030000041
Satellite pitch angle theta and satellite heading angle psi.
As shown in fig. 2, in the chart of the fusion result of the heading angles of the attitude angles of the present invention, a line indicates heading angle information obtained by separately using a magnetometer model, a line indicates heading angle information obtained by separately using a gyroscope model, and a solid line indicates heading angle information obtained by fusing the two.
As shown in fig. 3, a graph of the result of blending roll angles of the attitude angles of the present invention is shown, in which a profile indicates roll angle information obtained by using a magnetometer model alone, a profile indicates roll angle information updated by using a gyroscope model alone, and a solid line indicates roll angle information obtained by blending both.
As shown in fig. 4, a diagram of a pitch angle fusion result of the attitude angle of the present invention is shown, where a line indicates pitch angle information obtained by using a magnetometer model alone, a line indicates pitch angle information obtained by using a gyroscope model alone, and a solid line indicates pitch angle information obtained by fusing the two.
The gyroscope is a three-axis gyroscope, and the geomagnetism meter is a three-axis geomagnetism meter; and installing the triaxial gyroscope and the triaxial geomagnetism along a low-earth orbit satellite body coordinate system. In the invention, the sensitive data of the gyroscope and the geomagnetism are synchronized in time.
The process of constructing the gyro four-element posture updating model comprises the following steps:
Figure BDA0002864486030000051
wherein,
Figure BDA0002864486030000052
representing roll angle, theta pitch angle, psi heading angle, q0、q1、q2、q3Are four elements respectively.
The process of constructing the geomagnetism attitude measurement model comprises the following steps:
Figure BDA0002864486030000053
Figure BDA0002864486030000054
wherein, Bx、By、BzRespectively representing the magnetic strength measurements in the measurement coordinate, Bbx、Bby、BbzRespectively represent geomagnetic components in a low orbit satellite body coordinate system.
The attitude four element state equation is:
X(k+1)＝F·X(k)+V
wherein x (k) ═ q0(k) q1(k) q2(k) q3(k)]TRepresenting four elements of attitude, F representing the state transition equation, and V representing white gaussian noise with a mean value of zero.
The equation for calculating the state transition equation F is:
Figure BDA0002864486030000061
Figure BDA0002864486030000062
wherein, ω isx、ωy、ωzThe three-axis angular velocity measurement values of the low-orbit satellite under the low-orbit satellite body coordinate are respectively, and delta t is time variation.
The covariance of the attitude four-element state equation is calculated from the white gaussian noise V with a mean of zero, and the expression of the covariance is shown as:
E{VVT}＝R
wherein E {. means solving covariance, R means covariance of attitude four-element state equation, and VTRepresenting a gaussian white noise transpose matrix.
Establishing an observation equation of the relationship between the geomagnetic field vector and the low-orbit satellite attitude according to the IGRF geomagnetic field model:
Y(k+1)＝HX(k+1)+N
y (k +1) represents a magnetic strength matrix under the measurement coordinate, H represents an observation matrix, and N represents white Gaussian noise with a mean value of zero. Wherein:
Figure BDA0002864486030000063
Figure BDA0002864486030000064
calculating the covariance of an observation equation of the attitude relation of the low-orbit satellite according to Gaussian white noise N with the mean value of zero; the expression is as follows:
E{NNT}＝Q
wherein E {. means solving the covariance, Q means the covariance of the observation equation of the low-earth satellite,NTrepresenting a gaussian white noise transpose matrix.
Figure BDA0002864486030000065
The conversion relation of the geomagnetic field vector under the track coordinate system and the measurement coordinate is as follows:
Figure BDA0002864486030000071
wherein, Bx、By、BzRepresenting the three-axis component of the geomagnetic intensity in orbital coordinates, Bbx Bby BbzThe geomagnetic intensity measurement value is shown when the geomagnetic meter is installed along the coordinate system of the low-orbit satellite body.
Calculating the roll angle in the attitude angle of the low-orbit satellite according to the conversion relation of the geomagnetic field vector under the orbit coordinate system and the measurement coordinate
Figure BDA0002864486030000072
The pitch angle theta and the heading angle psi are expressed as follows:
Figure BDA0002864486030000073
θ＝arcsin[2(q0q2-q1q3)]
Figure BDA0002864486030000074
the process of carrying out iteration and filtering processing on the multipoint information of the low-orbit satellite comprises the following steps: and resolving initial four elements by combining the initial attitude of the low-orbit satellite, updating the four elements by using the gyroscope, and correcting the accumulated error of the gyroscope by combining magnetometer information and adopting an extended Kalman filter fusion algorithm, thereby outputting an attitude angle with higher precision.
The covariance calculation equation expression in the fusion process is as follows:
P-(k+1)＝FP(k)FT+R
the corresponding gain matrix expression is:
K(k+1)＝P-(k+1)H[HP-(k+1)HT+Q]-1
updating the covariance according to a covariance expression and a gain matrix, wherein the expression is as follows:
P(k+1)＝[I-K(k+1)H(k+1)]P-(k+1)
updating the attitude of the low orbit satellite according to the gain matrix and the covariance expression, wherein the updating expression is as follows:
X(k+1)＝X-(k+1)+K(k+1)(Y(k+1)-HX-(k+1))
wherein, P-(K +1) represents the covariance of the error prior to the time K +1, K represents the sampling time, F represents the state-transfer equation, R represents the value of the covariance of the attitude four-element state equation, T represents the transpose, K (K +1) represents the gain matrix at the time K +1, H (K +1) represents the observation matrix, Q represents the covariance of the observation equation for low-orbit satellites, and X represents the covariance of the observation equation for low-orbit satellites-And (k +1) represents a k +1 moment antecedent attitude four-element state equation.
The invention provides a combined geomagnetism/gyroscope low-orbit satellite attitude determination technology. The low-orbit satellite attitude measured by the technology can provide an accurate data source for the motion control of the low-orbit satellite, and meanwhile, the accurate control of the orbit of the low-orbit satellite is realized, so that the ground measurement and control station can be ensured to stably track the low-orbit satellite, and further guarantee is provided for the related application based on the low-orbit satellite.
The above-mentioned embodiments, which further illustrate the objects, technical solutions and advantages of the present invention, should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and should not be construed as limiting the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. A low-orbit satellite attitude determination method based on a geomagnetic meter and a gyroscope is characterized by comprising the following steps:
s1: acquiring initial attitude parameters of a low-earth-orbit satellite;
s2: establishing an orbit coordinate system of the low-orbit satellite, measuring the satellite angular velocity of the low-orbit satellite in the coordinate system by adopting a gyroscope, and measuring the geomagnetic component of the low-orbit satellite in the coordinate system by adopting a geomagnetic meter;
s3: inputting the angular velocity of the satellite into a gyro four-element attitude updating model, and calculating attitude information of the low-orbit satellite to obtain the state of the satellite at the next moment;
s4: inputting the geomagnetic component under the body coordinate system of the low-orbit satellite and the attitude information of the low-orbit satellite into a geomagnetic attitude measurement model to obtain an observation equation of the low-orbit satellite;
s5: processing an observation equation obtained by measurement by adopting an extended Kalman filtering fusion algorithm to obtain multi-point information of the low-orbit satellite;
s6: the attitude information of the low-orbit satellite is continuously corrected by carrying out iteration and filtering processing on the multi-point information of the low-orbit satellite;
s7: it is determined whether the low-earth orbit satellite attitude determination task is finished, that is, whether the satellite has reached the predetermined attitude, and if the condition is not satisfied, the process returns to S2.
2. The geomagnetic-and-gyroscope-based low-orbit satellite attitude determination method according to claim 1, wherein the initial low-orbit satellite attitude parameters before low-orbit satellite transmission comprise: satellite roll angle
Figure FDA0002864486020000014
The satellite pitch angle θ, the satellite heading angle ψ, are determined by the ground-assisted equipment at initial power-on.
3. The method of claim 1, wherein the gyro four-element attitude update model is:
Figure FDA0002864486020000011
θ＝arcsin[2(q0q2-q1q3)]、
Figure FDA0002864486020000012
Figure FDA0002864486020000013
calculating an attitude angle through the four elements, and updating the four elements by utilizing the angular velocity of the gyroscope;
wherein,
Figure FDA0002864486020000025
representing roll angle, theta pitch angle, psi heading angle, q0、q1、q2、q3Are respectively four elements, omegax、ωy、ωzRespectively are the measurement values of the three-axis angular velocity of the low-orbit satellite under the low-orbit satellite body coordinates.
4. The method of claim 1, wherein the attitude four-element state equation is:
X(k+1)＝F·X(k)+V
X(k)＝[q0(k) q1(k) q2(k) q3(k)]T
wherein X (k) represents attitude four elements, F represents a state transition equation, V represents white Gaussian noise with a mean of zero, and covariance is E { VVTR, T denotes transpose, R denotes covariance of the pose four-element state equation.
5. The method of claim 4, wherein the state transition equation F is expressed as:
Figure FDA0002864486020000021
Figure FDA0002864486020000022
wherein, ω isx、ωy、ωzThe three-axis angular velocity measurement values of the low-orbit satellite under the low-orbit satellite body coordinate are respectively, and delta t is time variation.
6. A method for determining attitude of a low earth orbit satellite based on a geomagnetic meter and a gyroscope according to claim 1, wherein the geomagnetic meter attitude measurement model is:
Figure FDA0002864486020000023
Figure FDA0002864486020000024
wherein, Bx、By、BzRespectively representing the magnetic strength measurements in the measurement coordinate, Bbx、Bby、BbzRespectively represent geomagnetic components in a low orbit satellite body coordinate system.
7. The method of claim 1, wherein the observation equation of the low earth orbit satellite is as follows:
Y(k+1)＝HX(k+1)+N
Figure FDA0002864486020000031
wherein Y (k +1) represents a magnetic strength matrix under a measurement coordinate, H represents an observation matrix, N represents white Gaussian noise with a mean value of zero, and the covariance of the white Gaussian noise is E { NN }TQ, T denotes the transpose, Q denotes the observation side of the low earth satelliteCovariance of the equation, Bx、By、BzRespectively, represent the magnetic strength measurements at the measurement coordinates.
8. The method of claim 1, wherein the processing the measured attitude by using the extended kalman filter fusion algorithm comprises:
updating the observation equation by adopting a covariance updating formula, calculating a gain matrix of the updated observation equation, and updating the attitude information of the low-earth orbit satellite according to the gain matrix;
the covariance update equation is:
P-(k+1)＝FP(k)FT+R
P(k+1)＝[I-K(k+1)H(k+1)]P-(k+1)
the gain matrix is:
K(k+1)＝P-(k+1)H(k+1)[H(k+1)P-(k+1)HT(k+1)+Q]-1
the state update equation is:
X(k+1)＝X-(k+1)+K(k+1)(Y(k+1)-HX-(k+1))
wherein, P-(K +1) represents the covariance of the error prior to the time K +1, K represents the sampling time, F represents the state-transfer equation, R represents the value of the covariance of the attitude four-element state equation, T represents the transpose, K (K +1) represents the gain matrix at the time K +1, H (K +1) represents the observation matrix, Q represents the covariance of the observation equation for low-orbit satellites, and X represents the covariance of the observation equation for low-orbit satellites-And (k +1) represents a k +1 moment antecedent attitude four-element state equation.
9. The method of claim 1, wherein the iterative and filtering process of the multi-point information of the low earth orbit satellite comprises: solving initial four elements according to the initial attitude of the low-earth orbit satellite, updating the four elements by adopting a gyroscope, correcting the accumulated error of the gyroscope by adopting an extended Kalman filtering fusion algorithm, and outputting an attitude angle with higher precision.
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TWI831466B (en) * 2022-11-11 2024-02-01 耀登科技股份有限公司 Heading and attitude correction method and heading and attitude correction system

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