CN110203424B - Method and device for estimating spacecraft spin motion by using speed measurement data - Google Patents
Method and device for estimating spacecraft spin motion by using speed measurement data Download PDFInfo
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Abstract
The invention provides a method and equipment for estimating spacecraft spinning motion by using speed measurement data, which are suitable for estimating the spacecraft spinning motion under the condition that the spacecraft attitude has spinning faults and the ground cannot obtain stable telemetering data, so that ground engineering technicians are assisted to judge and process attitude faults in time. The invention selects the spin angular velocity and the spin angular velocity direction of the spacecraft as parameters and establishes a speed measurement data observation model. The method estimates the spinning motion of the spacecraft through the spacecraft speed measurement data, and has strong adaptability and rapid convergence. The scheme does not depend on the telemetering information of the spacecraft, and can provide an effective basis for attitude fault diagnosis and treatment under the condition of abnormal attitude of the spacecraft.
Description
Technical Field
The present invention relates generally to the field of spacecraft measurement and control technology. More particularly, the invention relates to a method and apparatus for estimating spacecraft spin motion using velocity measurement data.
Background
The measurement, maneuvering, pointing and the like of the spacecraft attitude are mainly taken charge of an attitude control system, and are the basis for on-orbit power supply, remote measurement and control, scientific target realization and the like of the spacecraft. At present, the ground mainly obtains spacecraft attitude information through downlink telemetering data of a spacecraft-mounted attitude sensor. Once the attitude control system of the in-orbit spacecraft breaks down, the spacecraft gradually forms stable spinning motion under the action of internal and external moments. Under the spinning state, the spacecraft measurement and control antenna loses stable pointing, and the ground receiving spacecraft telemetering 'flash lock' and even 'lock losing' can be caused under the condition that measurement and control links such as moon and deep space exploration tasks are tense. Under the condition, the ground cannot know the spinning state of the spacecraft in time through remote measurement, and effective attitude control cannot be implemented. If spinning for a long time, the spacecraft faces significant risks of power supply exhaustion, structure disintegration and the like. Therefore, in the case that the spacecraft attitude fault causes the spin motion, and the ground has no stable telemetry data, the spin motion state of the spacecraft must be estimated in time, which is a basic premise of fault diagnosis and fault treatment.
The spin motion causes the spacecraft measurement and control antenna to generate periodic motion relative to the spacecraft centroid, and causes the spacecraft (measurement and control antenna) to add Doppler to ground measurement and control equipment, and the Doppler is expressed in speed measurement data; moreover, in general, the link margin of the ground measurement and control equipment locking detector downlink carrier is larger than that of downlink telemetry (generally about 10dB larger for deep space measurement and control). In other words, when the spacecraft performs spin motion, the ground measurement and control equipment can still lock the downlink carrier wave of the spacecraft to acquire effective speed measurement data, and the ground measurement and control equipment is expected to be used for spacecraft spin motion estimation.
Disclosure of Invention
Based on the background, the invention aims at the problem of spin motion estimation under the condition that the ground has no stable telemetering data due to the spin fault of the spacecraft, selects the magnitude and the direction of the spin angular velocity of the spacecraft as parameters to establish a speed measurement data observation model, and provides a method for estimating the spin motion of the spacecraft, which determines the magnitude of the spin angular velocity based on spectral estimation and estimates the direction of the spin angular velocity based on indirect adjustment.
To this end, in one aspect, the invention provides a method of estimating spacecraft spin motion using velocimetry data, comprising:
step 1): according to the precise orbit of the spacecraft, determining the speed of the mass center of the spacecraft relative to the plurality of ground measurement and control equipment in an observation arc section relative to the spacecraft and determining the additional speed caused by the spinning motion;
step 2): transforming the spacecraft spin motion speed obtained by each ground measurement and control device to obtain a spectrum estimation;
step 3): determining the frequency corresponding to the strongest frequency spectrum component of each ground measurement and control device according to the spectrum estimation of each ground measurement and control device so as to determine the estimated value of the magnitude of the spinning angular velocity of the spacecraft;
step 4): establishing an observation equation of the spacecraft spinning motion speed based on the estimated value;
step 5): selecting a state vector X and deriving a Jacobi matrix based on the observation equation and the state vector;
step 6): determining the correction of the state vector X based on an indirect adjustment method
Step 7): updating an estimate of a state vector X based on an iterative operation, wherein the estimate is
X0An initial estimate representing a state vector X; and
step 8): and determining the first to third elements of the estimated value after the iteration operation as the estimated value of the projection of the direction of the spin angular velocity on three coordinate axes of the spacecraft body coordinate system.
In one embodiment, wherein step 1) comprises:
according to the precise orbit of the spacecraft, calculating the speed v of the mass center of the spacecraft relative to a ground measurement and control device N (N is 1, 2orbit(n, i), and then calculating an additional velocity v due to spin motion according to equation (1)obs.spin(n，i)。
vobs.spin(n，i)＝vobs(n，i)-vorbit(n，i) (1)
In another embodiment, wherein step 2) comprises:
fourier transform is carried out on the spacecraft spin motion speed obtained by each ground measurement and control device according to the formula (2) to complete spectrum estimation,
P(n，f)＝FT(vobs.spin(n，i)) (2)
where FT denotes spectral estimation based on fourier transform.
In one embodiment, wherein step 3) comprises:
finding out the frequency f corresponding to the strongest frequency spectrum component of the frequency spectrum obtained from the measured data of each ground measurement and control devicenAnd determining an estimated value of the magnitude of the spacecraft spin angular velocity according to the following formula (3),
in yet another embodiment, wherein step 4) comprises:
establishing an observation equation of the spinning motion speed of the spacecraft according to the formula (4),
wherein I3Is a 3 × 3 identity matrix, er(n, i) is from moment idt to spacecraft barycenter direction of ground measurement and control equipment nUnit vector, H0＝[H01 H02 H03]TIs a constant unknown vector independent of time and ground measurement and control equipment, EωDetermined according to the following formula (5),
wherein eωx、eωy、eωzThe following constraint conditions (6) are satisfied,
in one embodiment, wherein step 5) comprises:
the following pending parameters are selected as the state vector X,
X＝[eωx eωy eωz H01 H02 H03]T (7)
the Jacobi matrix B (n, i) that determines the observation equation pair state vector is given by the following equation (8)
In yet another embodiment, wherein step 6) comprises:
the correction amount of the state vector X is obtained by the following equation (9)
(vector quantity) of the vector quantity,
wherein [. ]]NIThe data of all the ground measurement and control equipment 1-N and time 0-1 are combined into a column vector of NI multiplied by 1, the sequence of the column vector is not limited, and all [ · in the formula (9)]NIIn a consistent order [. ]]|X0Express calculation [ ·]At X0As a result, P is a weight matrix (NI multiplied by NI) matrix of all data of the ground measurement and control equipment 1 to N and time 0 to (I-1), and the element sequence is equal to [ · [ ]]NIAre arranged in a uniform order, X0Is an initial estimation value of the state vector X, and is taken according to the following formula (10) under the condition of lacking enough prior information,
wherein A is0When the initial time i is equal to 0, the spacecraft body coordinate system Ob-XbYbZbA coordinate transformation matrix to the earth's equatorial inertial coordinate system O-XYZ and, if no prior information, a 3 x 3 identity matrix, ρantennaFor spacecraft antenna in a body coordinate system Ob-XbYbZbA lower mounting position.
In a further embodiment, wherein step 7) comprises:
updating the parameter estimation value, and iteratively solving until convergence, wherein the step of updating the parameter estimation value comprises the following steps:
determining parameter correction
And the size of the convergence threshold Tol:
when in use
Exiting the iteration;
otherwise, get
As a new initialization value X0Calculating the parameter correction amount corresponding to the new initialization value according to equation (9)
When the iteration is over, the estimated value of the parameter is obtained according to the following formula (11):
wherein
The 1 st, 2 nd and 3 th elements of (A) represent projections e of the direction of the spin angular velocity on three coordinate axes of a spacecraft body coordinate systemωx、eωy、eωzAn estimate of (d).
In another aspect, the invention provides an apparatus for estimating spacecraft spin motion using velocimetry data, comprising:
a processor;
a memory comprising computer instructions that, when executed by the processor, cause the apparatus to perform the steps of:
step 1): according to the precise orbit of the spacecraft, determining the speed of the mass center of the spacecraft relative to the plurality of ground measurement and control equipment in an observation arc section relative to the spacecraft and determining the additional speed caused by the spinning motion;
step 2): transforming the spacecraft spin motion speed obtained by each ground measurement and control device to obtain a spectrum estimation;
step 3): determining the frequency corresponding to the strongest frequency spectrum component of each ground measurement and control device according to the spectrum estimation of each ground measurement and control device so as to determine the estimated value of the magnitude of the spinning angular velocity of the spacecraft;
step 4): establishing an observation equation of the spacecraft spinning motion speed based on the estimated value;
step 5): selecting a state vector X and deriving a Jacobi matrix based on the observation equation and the state vector;
step 6): determining the correction of the state vector X based on an indirect adjustment method
Step 7): updating based on iterative operationsAn estimate of a state vector X, wherein the estimate is
X0An initial estimate representing a state vector X; and
step 8): and determining the first to third elements of the estimated value after the iteration operation as the estimated value of the projection of the direction of the spin angular velocity on three coordinate axes of the spacecraft body coordinate system.
In yet another aspect, the invention provides a computer readable storage medium comprising a program for estimating spacecraft spin motion using tachometer data, the program, when executed by a processor, performing the following operational steps:
step 1): according to the precise orbit of the spacecraft, determining the speed of the mass center of the spacecraft relative to the plurality of ground measurement and control equipment in an observation arc section relative to the spacecraft and determining the additional speed caused by the spinning motion;
step 2): transforming the spacecraft spin motion speed obtained by each ground measurement and control device to obtain a spectrum estimation;
step 3): determining the frequency corresponding to the strongest frequency spectrum component of each ground measurement and control device according to the spectrum estimation of each ground measurement and control device so as to determine the estimated value of the magnitude of the spinning angular velocity of the spacecraft;
step 4): establishing an observation equation of the spacecraft spinning motion speed based on the estimated value;
step 5): selecting a state vector X and deriving a Jacobi matrix based on the observation equation and the state vector;
step 6): determining the correction of the state vector X based on an indirect adjustment method
Step 7): updating an estimate of a state vector X based on an iterative operation, wherein the estimate is
X0To representAn initial estimate of the state vector X; and
step 8): and determining the first to third elements of the estimated value after the iteration operation as the estimated value of the projection of the direction of the spin angular velocity on three coordinate axes of the spacecraft body coordinate system.
According to the technical scheme, the spinning motion state of the spacecraft is estimated through spacecraft speed measurement data, so that the adaptability is strong, and the convergence is rapid. The method does not need spacecraft telemetering information, and can provide effective basis for fault diagnosis and treatment under the condition of spacecraft spinning faults.
Drawings
The invention and its advantages will be better understood by reading the following description, provided by way of example only, and made with reference to the accompanying drawings, in which:
FIG. 1 shows a flow diagram of a method of estimating spacecraft spin motion using velocity measurement data in accordance with an embodiment of the invention;
FIG. 2 shows a projected representation of spacecraft spin angular velocity in a body coordinate system in accordance with an embodiment of the present invention;
FIG. 3 is a geometric diagram of a spacecraft speed measurement performed by a ground measurement and control device according to an embodiment of the present invention;
FIG. 4 shows a graphical representation of spacecraft spin motion velocity and frequency spectrum obtained with a ground test control device according to the present invention; and
fig. 5 shows the convergence process of estimating the spacecraft spin angular velocity direction using velocity measurement data.
Detailed Description
Based on the background, the invention selects the spin angular velocity and the direction of the spacecraft as parameters to establish a speed measurement data observation model for the problem of spin motion estimation under the condition that the ground has no stable telemetering data due to the spin fault of the spacecraft, and provides a method for estimating the spin motion of the spacecraft, which determines the spin angular velocity based on spectral estimation and estimates the spin angular velocity direction based on indirect adjustment.
In order to facilitate a further understanding of the invention, the establishment of the coordinate system will first be described. In one embodiment, the solution of the invention selects the Earth's equatorial inertial frame O-XYZ (original)The point is positioned in the center of the earth, the X axis points to the vernal point in the equatorial plane of the earth, the Z axis is superposed with the rotation axis of the earth, and the Y axis, the X axis and the Z axis form a right-handed system) and a spacecraft body coordinate system Ob-XbYbZb. Spacecraft in body coordinate system Ob-XbYbZbThe lower spin angular velocity is omega, the magnitude of the lower spin angular velocity is omega, and the projections on three coordinate axes of the body coordinate system are respectively omegax、ωy、ωz(ii) a The direction of spin angular velocity being the unit vector eωThe projections on the three coordinate axes of the body coordinate system are respectively eωx、eωy、eωzAs shown in fig. 2.
Fig. 1 shows a flow diagram of a method 100 for estimating spacecraft spin motion using velocity measurement data according to an embodiment of the invention. The process of the invention is as follows:
during the spinning motion of the spacecraft, the speed measurement result of the ground measurement and control equipment N (N is 1, 2.., N) on the spacecraft at the time I × dt (dt is a sampling interval, I is 0, 1.., I-1) is vobs(n，i)。
In step 1: according to the precise orbit of the spacecraft, calculating the speed v of the mass center of the spacecraft relative to a ground measurement and control device N (N is 1, 2orbit(n, i), and then calculating an additional velocity v due to spin motion according to equation (1)obs.spin(n，i)。
vobs.spin(n，i)＝vobs(n，i)-vorbit(n，i) (1)
Step 2: fourier Transform is carried out on the spacecraft spinning motion speed (time sequence) obtained by each ground measurement and control device to complete spectrum estimation, and the formula (2) is shown.
P(n，f)＝FT(vobs.spin(n，i)) (2)
In equation (2), FT represents spectral estimation based on fourier transform (such as periodogram method).
And step 3: finding out the frequency f corresponding to the strongest frequency spectrum component of the frequency spectrum obtained from the measured data of each ground measurement and control devicenObtaining the spin angle of the spacecraftThe estimated value of the velocity magnitude is shown in equation (3).
And 4, step 4: the observation equation for establishing the spinning motion speed of the spacecraft is as follows:
in the formula (4), I3Is a 3 × 3 identity matrix, er(n, i) is a unit vector (as shown in fig. 3, a known quantity in the case of a known spacecraft precise orbit) from the ground measurement and control equipment n to the spacecraft centroid direction at the moment idt, and H0＝[H01 H02H03]TIs a constant unknown vector independent of time and ground measurement and control equipment, EωIt is determined according to the following (5),
furthermore, eωx、eωy、eωzThe following constraint should be satisfied,
and 5: the following pending parameters are selected as the state vector X,
X＝[eωx eωy eωz H01 H02 H03]T (7)
the Jacobi matrix B (n, i) of the observation equation in step 4 to the state vector is derived, namely:
step 6: the correction amount of the state vector X is solved using the following formula according to the correlation model and theory of the indirect adjustment method (e.g., "constrained indirect adjustment")
(vector quantity) of the vector quantity,
in formula (9) [. ]]NIThe column vector (the order of the column vectors is not limited, but all [ · in the formula (9)) representing that all data of the ground measurement and control devices 1 to N and the time 0 to (I-1) are combined into NI × 1]NIShould be in the same order), [. cndot.]|X0Express calculation [ ·]At X0As a result, P is a weight matrix (NI multiplied by NI square matrix, element sequence and [. cndot. ] of all data of the ground measurement and control devices 1 to N and time 0 to (I-1)]NIThe element arrangement order of (1) is the same), X0Which is an initial estimate of the state vector X, in the absence of sufficient prior information, can be taken as follows,
in the formula (10), A0As an initial time (i ═ 0) spacecraft body coordinate system Ob-XbYbZbCoordinate conversion matrix to the earth's equator inertial coordinate system O-XYZ (if no prior information, then 3 × 3 unit matrix), ρantennaFor spacecraft antenna in a body coordinate system Ob-XbYbZbA lower mounting position.
And 7: updating the parameter estimation value, and iteratively solving until convergence. Determining parameter correction
Is calculated from the absolute value of each element and the convergence threshold Tol (set according to actual needs, reference value 1 × 10-8) The size of (2):
1. if it is
Exiting the iteration;
2. otherwise, get
As a new initialization value X0Calculating the parameter correction corresponding to the new initialization value according to equation (9)
And (5) finishing iteration to obtain an estimated value of the parameter:
the 1 st, 2 nd and 3 rd elements of the parameter (vector), namely the projection e of the direction of the spin angular velocity on three coordinate axes of the spacecraft body coordinate systemωx、eωy、eωzAn estimate of (d).
The technical scheme and a plurality of embodiments of the invention are described above with reference to the accompanying drawings, and the specific implementation of the invention will be further explained below by simulating and generating speed measurement data of two stations under the condition that a spacecraft has a spin fault in combination with a typical moon transfer orbit of a moon-exploring task in China.
The orbit number of the spacecraft is assumed as follows: 196478km for half-length axis, 0.9665 eccentricity, 28.5 degree of orbit inclination, 205.5 degree of right ascension at ascending intersection, 173.8 degree of argument of perigee, and 150.0 degree of true perigee (initial time). Antenna mounting position ρantenna＝[-1.0 2.0 -1.5]T(m) of the reaction mixture. The spin motion state is: omegax＝60°/s、ωy＝-20°/s、ω z10 DEG/s, i.e. omega 1.11756rad/s, eωx＝0.9370、eωy＝-0.3123、eωz0.1562. The obtained speed measurement data is the measurement result of the ground measurement and control devices 1 and 2 (i.e. N is 2), and the coordinates of the ground measurement and control devices 1 and 2 under the earth fixed coordinate system are (-2872, 3331, 460), respectively3) km, (1150, 4870, 3943) km. Based on the above data, the velocity measurement data v of the ground measurement and control devices 1 and 2 to the spacecraft at the moment idt (dt ═ 0.2s, I ═ 0, 1, 2, 3.., 600, I ═ 601) is generated in a simulation mannerobs(n, i) and adding zero mean white noise (1 σ ═ 5 × 10) to the tachometer data-3m/s)。
Based on the model and the data, the spacecraft spin motion estimation is carried out according to the following process.
Step 2-1: according to the orbit number of the spacecraft, calculating the speed v of the spacecraft at the moment idt of the mass center of the spacecraft relative to the ground measurement and control equipment 1 and 2orbit(n, i), and then calculates an additional velocity v due to spin motion according to equation (12)obs.spin(n，i)。
vobs.spin(n，i)＝vobs(n，i)-vorbit(n，i) (12)
For the sake of understanding, the additional velocity due to the spacecraft spin motion obtained by the ground measurement and control device 1 is shown in the upper diagram of fig. 4.
Step 2-1: fourier Transform (Fourier Transform) is carried out on the spacecraft spin motion speed (time sequence) obtained by the ground measurement and control equipment 1 and 2, and spectral estimation is completed by adopting a Welch method, as shown in a formula (13).
P(n，f)＝FT(vobs.spin(n，i)) (13)
In equation (13), FT represents spectrum estimation based on fourier transform. For the convenience of understanding, the lower graph of fig. 4 shows a frequency spectrum obtained by performing spectrum estimation on the spacecraft spin motion speed obtained by the ground measurement and control device 1.
Step 2-3: the frequency spectrum obtained according to the measurement data of the ground measurement and control equipment 1 and 2 has the frequency f corresponding to the strongest frequency spectrum component1＝0.17790Hz、f20.17785Hz, the estimated value of the magnitude of the spacecraft spin angular velocity is:
step 2-4: the observation equation for establishing the spinning motion speed of the spacecraft is as follows:
in the formula (15), I3Is a 3 × 3 identity matrix, er(n, i) is a unit vector (shown in fig. 4, which is a known quantity) from the ground measurement and control device n to the spacecraft centroid direction at the moment idt, and H0＝[H01 H02 H03]TIs a constant unknown vector independent of time and ground measurement and control equipment, EωCan be expressed as follows:
furthermore, eωx、eωy、eωzThe following constraint should be satisfied,
step 2-5: the following pending parameters are selected as the state vector X,
X＝[eωx eωy eωz H01 H02 H03]T (18)
the Jacobi matrix B (n, i) of the observation equations in step 2-4 for the state vector is derived, i.e.:
step 2-6: according to a correlation model and theory of 'indirect adjustment with constraint conditions', the correction quantity of the state vector X is solved by using the following formula
(vector quantity) of the vector quantity,
in formula (20) [. ]]1202Representing that all data of the ground measurement and control equipment 1-2 and the time 0-600 are combined into column vector 1202 x 1 (the 1 st-601 st row is the measurement data of the ground measurement and control equipment 1, the 602 st-1202 st row is the measurement data of the ground measurement and control equipment 2) [ ·]|X0Express calculation [ ·]At X0As a result, P is a weight matrix of all measurement data (1202 × 1202 matrix, the 1 st-601 st row/column represents the measurement data of the ground measurement and control equipment 1, the 602 st-1202 st row/column represents the measurement data of the ground measurement and control equipment 2), X0Is an initial estimation value of the state vector X, and takes the following values according to the current prior information,
step 2-7: updating the parameter estimation value, and iteratively solving until convergence. According to the formula (20), the method is obtained by solving for one time:
setting the convergence threshold Tol to 1 × 10-8Due to the fact
Then get
As a new initialization value X0Calculating the parameter correction corresponding to the new initialization value according to equation (20)
Repeating the judging and calculating steps until the 6 th iteration calculation reaches a convergence condition, ending the iteration, and obtaining an estimated value of the parameter:
i.e. the projection e of the direction of the spin angular velocity on three coordinate axes of the spacecraft body coordinate systemωx、eωy、eωzThe estimates of (d) were 0.9365, -0.3117, 0.1604, respectively.
Fig. 5 shows the convergence process of estimating the spacecraft spin angular velocity direction using velocity measurement data. In particular, as shown in FIG. 5 as eωx、eωy、eωzThe iterative convergence process of the estimated value, wherein the horizontal axis in the figure is iteration times, and the vertical axis is the projection of the spin angular velocity direction of the spacecraft under the system; meanwhile, the true values of the spin angular velocity directions are shown in the figure by black dashed lines. It can be seen from the figure that the parameter estimation of the spacecraft spin angular velocity direction is converged to the vicinity of the true value rapidly.
In this example, the comparison of the estimated values and the true values of the spin angular velocity and the direction of the spacecraft is shown in table 1 below. From table 1, it is seen that the estimation of the magnitude and direction of the spacecraft spin angular velocity is accurate, and the fault diagnosis and treatment requirements under the spacecraft spin fault condition can be met.
TABLE 1 estimated and true values of spin angular velocity magnitude and direction for spacecraft
In some embodiments, aspects of the present invention can also be embodied in computer-readable codes in a computer-readable recording medium. The computer-readable recording medium includes all kinds of recording media storing data that can be interpreted by a computer system. The recording medium may include, for example, but is not limited to, a Read Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, an optical disk, a flash Memory, and the like. Further, these computer-readable recording media can be propagated or spread among various communication entities over a communication network (including a computer communication network, a cellular communication network, or a local area communication network), so that the computer-readable instructions or computer-executable code stored on the computer-readable storage media can also be executed in any manner.
Although the present invention is described in the above embodiments, the description is only for the convenience of understanding the present invention, and is not intended to limit the scope and application of the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A method of estimating spacecraft spin motion using velocity measurement data, comprising:
step 1): according to the precise orbit of the spacecraft, determining the speed of the mass center of the spacecraft relative to the plurality of ground measurement and control equipment in an observation arc section relative to the spacecraft and determining the additional speed caused by the spinning motion;
step 2): transforming the spacecraft spin motion speed obtained by each ground measurement and control device to obtain a spectrum estimation;
step 3): determining the frequency corresponding to the strongest frequency spectrum component of each ground measurement and control device according to the spectrum estimation of each ground measurement and control device so as to determine the estimated value of the magnitude of the spinning angular velocity of the spacecraft;
step 4): establishing an observation equation of the spacecraft spinning motion speed based on the estimated value;
step 5): selecting a state vector X and deriving a Jacobi matrix based on the observation equation and the state vector;
step 6): determining the correction of the state vector X based on an indirect adjustment method
Step 7): updating an estimate of a state vector X based on iterative operationsEvaluating, wherein the evaluation value
X0An initial estimate representing a state vector X; and
step 8): and determining the first to third elements of the estimated value after the iteration operation as the estimated value of the projection of the direction of the spin angular velocity on three coordinate axes of the spacecraft body coordinate system.
2. The method of claim 1, wherein step 1) comprises:
according to the precise orbit of the spacecraft, calculating the speed v of the mass center of the spacecraft relative to a ground measurement and control device N (N is 1, 2orbit(n, i), and then calculating an additional velocity v due to spin motion according to equation (1)obs.spin(n，i)：
vobs.spin(n，i)＝vobs(n，i)-vorbit(n，i) (1)
Wherein v isobsAnd (n, i) is the speed measurement result of the ground measurement and control equipment n on the spacecraft at the moment idt.
3. The method of claim 1, wherein step 2) comprises:
fourier transform is carried out on the spacecraft spin motion speed obtained by each ground measurement and control device according to the formula (2) to complete spectrum estimation,
P(n，f)＝FT(vobs.spin(n，i)) (2)
wherein v isobs.spin(n, i) represents additional velocity due to spin motion, and FT represents spectral estimation based on Fourier transform.
4. The method of claim 1, wherein step 3) comprises:
finding out the frequency f corresponding to the strongest frequency spectrum component of the frequency spectrum obtained from the measured data of each ground measurement and control devicenAnd determining an estimated value of the magnitude of the spacecraft spin angular velocity according to the following formula (3),
and N is the total number of the ground measurement and control equipment.
5. The method of claim 1, wherein step 4) comprises:
establishing an observation equation of the spinning motion speed of the spacecraft according to the formula (4),
wherein I3Is a 3 × 3 identity matrix, er(n, i) is a unit vector of the ground measurement and control equipment n from moment idt to the direction of the mass center of the spacecraft, H0＝[H01 H02 H03]TIs a constant unknown vector irrelevant to time and ground measurement and control equipment,
as an estimate of the magnitude of the spin angular velocity of the spacecraft, EωDetermined according to the following formula (5),
wherein e isωx、eωy、eωzThe projections of the spin angular velocity direction on three coordinate axes of the spacecraft body coordinate system respectively satisfy the constraint condition of the following formula (6),
6. the method of claim 1, wherein step 5) comprises:
the following pending parameters are selected as the state vector X,
X＝[eωx eωy eωz H01 H02 H03]T (7)
wherein e isωx、eωy、eωzProjections of the spin angular velocity direction on three coordinate axes of a spacecraft body coordinate system, H0＝[H01 H02 H03]TThe constant unknown vector is irrelevant to time and ground measurement and control equipment;
the Jacobi matrix B (n, i) that determines the observation equation pair state vector is given by the following equation (8)
Wherein v isspin(n, i) represents an observation equation of the spacecraft spin motion velocity.
7. The method of claim 1, wherein step 6) comprises:
the correction amount of the state vector X is obtained by the following equation (9)
(vector quantity) of the vector quantity,
wherein B (n, i) is a Jacobi matrix of the observation equation to a state vector; e.g. of the typeωx、eωy、eωzProjection of spin angular velocity direction on three coordinate axes of spacecraft body coordinate system [ ·]NIThe data of all the ground measurement and control equipment 1-N and time 0-1 are combined into a column vector of NI multiplied by 1, the sequence of the column vector is not limited, and all [ · in the formula (9)]NIIn a consistent order [. ]]|X0Indicating meterCalculation []At X0As a result, P is a weight matrix (NI multiplied by NI) matrix of all data of the ground measurement and control equipment 1 to N and time 0 to (I-1), and the element sequence is equal to [ · [ ]]NIAre arranged in a uniform order, X0Is an initial estimation value of the state vector X, and is taken according to the following formula (10) under the condition of lacking enough prior information,
wherein,
is an estimate of the magnitude of the spacecraft spin angular velocity, vobs.spin(n, i) denotes additional velocity due to spin motion, A0When the initial time i is equal to 0, the spacecraft body coordinate system Ob-XbYbZbA coordinate transformation matrix to the earth's equatorial inertial coordinate system O-XYZ and, if no prior information, a 3 x 3 identity matrix, ρantennaFor spacecraft antenna in a body coordinate system Ob-XbYbZbA lower mounting position; v. ofspin(n, i) represents an observation equation of the spacecraft spin motion velocity.
8. The method of claim 7, wherein step 7) comprises:
updating the parameter estimation value, and iteratively solving until convergence, wherein the step of updating the parameter estimation value comprises the following steps:
determining parameter correction
And the size of the convergence threshold Tol:
when in use
Exiting the iteration;
otherwise, get
As a new initialization value X0According to said formula (9):
NBB＝BTPB
W＝BTPl
calculating a parameter correction corresponding to the new initialization value
When the iteration is over, the estimated value of the parameter is obtained according to the following formula (11):
wherein
The 1 st, 2 nd and 3 th elements of (A) represent projections e of the direction of the spin angular velocity on three coordinate axes of a spacecraft body coordinate systemωx、eωy、eωzAn estimate of (d).
9. An apparatus for estimating spacecraft spin motion using velocity measurement data, comprising:
a processor;
a memory comprising computer instructions that, when executed by the processor, cause the apparatus to perform the steps of:
step 1): according to the precise orbit of the spacecraft, determining the speed of the mass center of the spacecraft relative to the plurality of ground measurement and control equipment in an observation arc section relative to the spacecraft and determining the additional speed caused by the spinning motion;
step 2): transforming the spacecraft spin motion speed obtained by each ground measurement and control device to obtain a spectrum estimation;
step 3): determining the frequency corresponding to the strongest frequency spectrum component of each ground measurement and control device according to the spectrum estimation of each ground measurement and control device so as to determine the estimated value of the magnitude of the spinning angular velocity of the spacecraft;
step 4): establishing an observation equation of the spacecraft spinning motion speed based on the estimated value;
step 5): selecting a state vector X and deriving a Jacobi matrix based on the observation equation and the state vector;
step 6): determining the correction of the state vector X based on an indirect adjustment method
Step 7): updating an estimate of a state vector X based on an iterative operation, wherein the estimate is
X0An initial estimate representing a state vector X; and
step 8): and determining the first to third elements of the estimated value after the iteration operation as the estimated value of the projection of the direction of the spin angular velocity on three coordinate axes of the spacecraft body coordinate system.
10. A computer readable storage medium comprising a program for estimating spacecraft spin motion using velocity measurement data executed by a processor, which when executed by the processor performs the following operational steps:
step 1): according to the precise orbit of the spacecraft, determining the speed of the mass center of the spacecraft relative to the plurality of ground measurement and control equipment in an observation arc section relative to the spacecraft and determining the additional speed caused by the spinning motion;
step 2): transforming the spacecraft spin motion speed obtained by each ground measurement and control device to obtain a spectrum estimation;
step 3): determining the frequency corresponding to the strongest frequency spectrum component of each ground measurement and control device according to the spectrum estimation of each ground measurement and control device so as to determine the estimated value of the magnitude of the spinning angular velocity of the spacecraft;
step 4): establishing an observation equation of the spacecraft spinning motion speed based on the estimated value;
step 5): selecting a state vector X and deriving a Jacobi matrix based on the observation equation and the state vector;
step 6): determining the correction of the state vector X based on an indirect adjustment method
Step 7): updating an estimate of a state vector X based on an iterative operation, wherein the estimate is
X0An initial estimate representing a state vector X; and
step 8): and determining the first to third elements of the estimated value after the iteration operation as the estimated value of the projection of the direction of the spin angular velocity on three coordinate axes of the spacecraft body coordinate system.
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