CN106325099B - A kind of spacecraft real-time track improved method based on pseudo- relative motion - Google Patents
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Abstract
The spacecraft real-time track improved method based on pseudo- relative motion that the present invention provides a kind of, the present invention by solve respectively without/have Spacecraft Relative Motion kinetic model under perturbation conditions, obtain without/have relative motion analytical expression under perturbation conditions, and it is corresponding with orbital drift data, orbital drift data are handled with Fourier transformation method, resolving obtains spacecraft initial position error and velocity error, finally can inverting obtain spacecraft real time position vector sum velocity vector.Orbit determination accuracy can be improved into a nearly magnitude on the basis of initial orbit determination technology using the above method；And there is universal adaptability, using CW equation and considers that the improvement equation under perturbation realizes that circle/nearly circle spacecraft orbit is improved, Lawden equation can also be used and its consider that the deformation under perturbation realizes that oval spacecraft orbit is improved.
Description
Technical Field
The invention belongs to the field of spacecraft orbit determination, and particularly relates to a spacecraft real-time orbit improvement method based on pseudo relative motion.
Background
The spacecraft orbit determination is a process of estimating the spacecraft orbit by using a statistical principle on spacecraft motion state data containing measurement errors. The motion state of the spacecraft at any time in the past, the current and the future can be obtained through orbit determination.
The orbit determination method can be divided into kinematic orbit determination, dynamic orbit determination and simplified dynamic orbit determination according to whether a mechanical model of the perturbation force borne by the spacecraft is adopted and the relation with the mechanical model; the method can be divided into a batch method and a sequential recursion method according to a data processing strategy; the method can be divided into a short arc section method and a long arc section method according to the length of the arc section; there are a single-step method and a multi-step method according to the integration method.
At present, the common spacecraft orbit determination methods are least square estimation methods and Kalman filtering methods in various forms. The least squares estimation method requires a large amount of data to be stored in the iteration process for the next iteration; the Kalman filtering method can cause the divergence of the filtering orbit determination result due to poor observability of data, initial orbit difference, strong nonlinearity of measured data and the like; in addition, the least square estimation method and the kalman filtering method also have the numerical problem of ill-condition of the normal equation matrix and the covariance matrix due to observability.
Since the measurement accuracy of the conventional track determination method is limited, the track determination accuracy cannot be further improved without greatly improving the accuracy of the observation data, and therefore, a novel track improvement method needs to be researched to improve the track determination accuracy.
Disclosure of Invention
The invention aims to provide a spacecraft real-time orbit improvement method based on pseudo relative motion, aiming at solving the technical problem of low measurement accuracy of the existing spacecraft orbit determination method.
In order to achieve the above object, the invention provides a spacecraft real-time orbit improvement method based on pseudo relative motion, which comprises the following steps:
step 1) taking a measurement orbit of a spacecraft as a reference orbit, taking an initial state of the spacecraft determined by the measurement orbit at an initial moment as a starting point of a forecast orbit, and generating the forecast orbit according to an orbit dynamics model;
step 2) taking the difference value between the forecast orbit and the measured orbit as orbit drift data, and defining a track formed by the orbit drift data as pseudo relative motion of the spacecraft;
step 3) respectively solving the dynamic models of the pseudo-relative motion under the perturbation-free and perturbation-free conditions to obtain analytical expressions of the pseudo-relative motion under the perturbation-free and perturbation-free conditions, and inverting the estimated value of the initial state error of the spacecraft by the analytical expressions obtained by the calculation after processing the orbit drift data by using a Fourier transform method;
and 4) using the difference between the estimated value of the initial state error and the initial state error value of the reference orbit as an improved value of the spacecraft orbit.
As a further improvement of the above technical solution, the analytic expression of the pseudo relative motion under the perturbation-free condition in step 3) is as follows:
where n is the average angular motion of the orbit, i.e. the angular frequency of the reference orbit, t represents time, and the parameters and their relationships are set as:
wherein (x)0,y0,z0) The error of the initial position of the three axes is shown,representing the triaxial initial speed error;
processing orbit drift data by using a Fourier transform method, and resolving to obtain a constant item xcycLong term 3xcnt/2 and period termsEach coefficient x in csin (nt + phi)c,b,ycC, phi, and using the above analytical expression to perform inversion to obtain the error of the initial stateDifference (D)Is estimated value of
As a further improvement of the above technical solution, the analytic expression of the pseudo relative motion under the perturbation condition in step 3) is as follows:
wherein, the parameters and the relation thereof are set as follows:
where n is the orbital mean angular motion, i.e., the reference orbital angular frequency, t represents time, u is the coefficient of gravity, rrefFor reference of orbital center-to-earth distance, irefFor reference to the inclination of the track, J2Is a second band harmonic term, ReIs the radius of the earth, n1、n2、n3、n4、n5The angular frequency of each periodic component in the relative motion respectively;
processing orbit drift data by using a Fourier transform method, and resolving to obtain a constant value item A3,A7Long term A6t and period term A1cos(n1t+θ1),A2cos(n2t+θ2),A4cos(n3t+θ3),A5cos(n4t+θ4),A8sin(n5t+θ5) Each coefficient A in (1)1,θ1,A2,θ2,A3,A4,θ3,A5,θ4,A6,A7,A8,θ5And using the above analytical expressionsPerforming inversion to obtain initial state errorIs estimated value of
The spacecraft real-time orbit improvement method based on the pseudo relative motion has the advantages that:
1. the orbit determination precision is high, and can be improved by nearly one magnitude on the basis of the initial orbit determination technology;
2. the method has the advantages that the method is real-time, and can be used for reversely integrating time to obtain a position vector and a speed vector of the spacecraft at the current moment;
3. the method has universal adaptability, realizes the improvement of the orbit of the circular/near-circular spacecraft by using a CW equation and an improvement equation under the consideration of perturbation, and also can realize the improvement of the orbit of the elliptical spacecraft by using a Lawden equation and deformation under the consideration of perturbation.
Drawings
Fig. 1 is a flow chart of a spacecraft real-time orbit improvement method based on pseudo relative motion according to the invention.
Fig. 2 is a schematic diagram of a trajectory of pseudo relative motion of a spacecraft, which is shown in an embodiment of the present invention.
Fig. 3 is an amplitude-frequency curve obtained by radial drift data and fourier transform processing of a spacecraft orbit in an embodiment of the invention.
Fig. 4 is an amplitude-frequency curve obtained by processing the spacecraft orbit trajectory drift data and fourier transform in the embodiment of the present invention.
Fig. 5 is an amplitude-frequency curve obtained by processing spacecraft orbit normal drift data and fourier transform in the embodiment of the invention.
Detailed Description
The invention relates to a spacecraft real-time orbit improvement method based on pseudo relative motion, which is described in detail in the following with reference to the accompanying drawings and embodiments.
The invention provides a spacecraft real-time orbit improvement method based on pseudo relative motion, which can realize spacecraft orbit improvement under the condition of initial orbit determination.
According to the method, a spacecraft relative motion dynamics model under the perturbation-free/perturbation-free condition is respectively solved to obtain a relative motion analytical expression under the perturbation-free/perturbation-free condition, the relative motion analytical expression corresponds to orbit drift data, a Fourier transform method is used for resolving to obtain an initial position error and a velocity error of the spacecraft, and finally a real-time position vector and a velocity vector of the spacecraft can be obtained through inversion.
Specifically, a spacecraft real-time orbit improvement method based on pseudo relative motion comprises the following steps:
①, taking the idea of flying formation of spacecraft as reference, taking the measurement orbit (initial orbit determination orbit) of the spacecraft as a reference orbit, and taking the forecast orbit based on the initial orbit determination state as the corresponding orbit of the pseudolite, wherein the difference between the measurement orbit and the forecast orbit can be understood as a relative motion, namely a pseudo relative motion, because the deviation between the two orbits is small;
②, taking the initial state of the spacecraft determined by initial orbit determination at the initial moment as the starting point of the forecast orbit, generating a forecast orbit according to the orbit dynamics model, and subtracting the forecast orbit from the measured orbit to obtain orbit drift data;
③ respectively solving the dynamic model of pseudo-relative motion under the condition of no perturbation and perturbation, and under the condition of not considering perturbation, when the reference orbit of the spacecraft is a near-earth circle/near-circle orbit, the relative motion between the reference orbit and the forecast orbit satisfies CW equation, that is to say
Wherein (x)0,y0,z0) The error of the initial position of the three axes is shown,representing the error of the three-axis initial speed (on the track coordinate system of the reference track), n is the average angular motion of the track, namely the angular frequency of the reference track, t represents time, and the quantities are theoretical known quantities;
converting the CW equation into a form of a combination of constant, periodic and long term terms, i.e.
Wherein the parameters and the relationship thereof are set as follows:
④ the orbit drift data between the reference orbit and the forecast orbit satisfies the above CW equation, the orbit drift data is processed by Fourier transform method, and the constant term x is obtained by calculationcycLong term 3xcnt/2 and period termscsin (nt + phi) coefficient xc,b,ycC, phi, and obtaining the initial state error by inversion with the formula (3)Is estimated value of
⑤ estimation of initial state error by inversionError from initial stateThe difference is a real-time orbit improvement precision value of the spacecraft based on the pseudo relative motion;
if the starting point of the forecast orbit is placed at a moment before the current moment, the orbit state improvement precision value at that moment is finally obtained by utilizing the steps ① - ⑤, and similarly, if the starting point of the forecast orbit is placed at the current moment, the orbit state improvement precision value at the current moment is finally obtained, thereby realizing the real-time improvement of the spacecraft orbit.
⑥ the pseudo-relative motion dynamics model of the spacecraft under consideration of J2 perturbation is represented as:
wherein,the second derivative of the triaxial motion quantity respectively represents the dynamic process.
Wherein the parameters and the relationship thereof are set as follows:
wherein n is the orbital mean angular motion, t represents time, u is the coefficient of gravity of the earth, rrefFor reference of orbital center-to-earth distance, irefFor reference to the inclination of the track, J2Is a second band harmonic term, ReThe radius of the earth.
Because the variation of the geocentric distance and the orbit inclination angle of the spacecraft under the perturbation of J2 is very small, and in consideration of practical engineering application, if the reference orbit of the spacecraft is a circular orbit, the orbit inclination angle is 28.5 degrees and the orbit height is 500km, the variation range of the geocentric distance under the perturbation of J2 is 4.48km, and the relative variation is 0.065 percent; the variation range of the track inclination angle is 0.03 degrees, and the relative variation is 0.11 percent. And in order to obtain a relative motion analytic form under J2 perturbation, reasonably assuming that the earth-center distance and the orbit inclination angle of the spacecraft are constants, and respectively taking specific values as a reference orbit average semi-major axis and an average orbit inclination angle, so as to obtain a pseudo relative motion kinetic equation of the spacecraft under J2 perturbation:
wherein the parameters and the relationship thereof are set as follows:
the analytic expression of the solved pseudo relative motion is as follows:
it should be noted that decoupling of the z-axis relative motion component from the xy-plane relative motion component, realization of non-surmounting of the z-axis relative motion require more assumption conditions, and the influence of the z-axis relative motion orbit determination accuracy on the overall orbit determination accuracy is small, so that the z-axis relative motion is directly taken as the z-axis motion form in the CW equation, that is, the z-axis relative motion is taken as the z-axis motion form in the CW equation
Wherein:
converting the formula (9) into a form of constant term, periodic term and long term combination:
wherein:
where n is the orbital mean angular motion, i.e., the reference orbital angular frequency, t represents time, u is the coefficient of gravity, rrefFor reference of orbital center-to-earth distance, irefFor reference to the inclination of the track, J2Is a second band harmonic term, ReIs the radius of the earth, n1、n2、n3、n4、n5The angular frequency of each periodic component in the relative motion respectively;
⑦ the orbit drift data between the reference orbit and the forecast orbit under J2 perturbation satisfies the above motion form, and the Fourier transform method is also used to process the pseudo relative motion orbit drift data to obtain the constant value item A3,A7Long term A6t and period term A1cos(n1t+θ1),A2cos(n2t+θ2),A4cos(n3t+θ3),A5cos(n4t+θ4),A8sin(n5t+θ5) Each coefficient A in (1)1,θ1,A2,θ2,A3,A4,θ3,A5,θ4,A6,A7,A8,θ5And using the formula (12) to carry out inverse solution to obtain the initial state errorIs estimated value of
⑧ estimated value of initial state error obtained by resolvingError from initial stateThe difference is the real-time orbit improvement precision value of the spacecraft based on the pseudo relative motion under the perturbation of J2;
in addition, under the condition of simultaneously considering J2 perturbation and atmospheric resistance perturbation, the position deviation of the near-earth spacecraft orbit caused by the atmospheric resistance perturbation is only in the order of several meters to dozens of meters, so that the spacecraft pseudo relative motion equation under the atmospheric resistance perturbation does not need to be solved in the spacecraft orbit determination, the spacecraft pseudo relative motion equation (formula 9) under the J2 perturbation is directly used for determining the spacecraft orbit, and the orbit improvement precision is basically not influenced.
Example one
As shown in fig. 1, it is noted at an initial time t0The actual position of the spacecraft is located at the point A, the initial orbit determination (measurement orbit) determines that the spacecraft is located at the point B, the actual position A and the measurement position B do not coincide due to the existence of the initial orbit determination error, and the initial orbit determination error is recorded as(in the orbit coordinate system of the reference orbit, for assuming a known quantity)The state error is also the initial state error of the spacecraft, and the state error is extended in time and space, namely, the difference between the forecast orbit and the measured orbit is made to obtain the orbit drift data in a period of time, namely, the state drift amount in the period of time. Because the state drift amount is small relative to the state amount, the deviation between the forecast orbit and the measurement orbit can be regarded as relative motion and meets a certain rule.
(1) The first situation is as follows: the processing steps are as follows without considering the external perturbation force:
① the spacecraft orbit is a near earth circle/near circle orbit, the relative motion between the reference orbit and the forecast orbit satisfies the CW equation, i.e.
② the CW motion equation contains constant term, periodic term and long term, and can be obtained by sorting the CW motion equation:
wherein the parameters and the relationship thereof are set as follows:
③ Fourier transform the acquired orbit state drift data satisfying the form of the CW equation:
F{af1(t)+bf2(t)}＝aF1(w)+bF2(w)
obtaining a corresponding amplitude-frequency response curve;
④ extracting corresponding frequency, amplitude and phase information according to the amplitude-frequency response curve, and Fourier transforming to process X-axis track drift data to obtain Xc,b,n, processing Y-axis drift data by Fourier transform to obtain YcAnd processing the Z axis to obtain c and phi. Using this information to bias the initial statePerforming identification to obtain identification resultI.e. the estimated value of the initial state error, and the difference between the two is the track improvement precision value.
(2) Case two: in the case of considering the external perturbation force, for a near-earth spacecraft, the external perturbation force is mainly J2 perturbation and atmospheric resistance perturbation. The processing steps are as follows:
① consider first only J2 perturbation, in which case the spacecraft pseudo relative kinematics equation is expressed as:
wherein the parameters and the relationship thereof are set as follows:
wherein r isrefFor reference to the real-time centre-to-centre distance of the star irefIs the real-time orbit inclination of the reference star.
② under J2 perturbation, the ground center distance and the orbit inclination of the spacecraft in the above formula show sinusoidal oscillation trend, which causes the above formula differential equation to be an transcendental equation, and an analytic solution form cannot be obtained, but the ground center distance and the orbit inclination change amplitude are small compared with the average value, therefore, the ground center distance and the orbit inclination are reasonably assumed to be constant values on the premise of meeting the precision, and the value is obtained by the average orbit number:
therefore, the pseudo relative motion kinetic equation of the spacecraft under the J2 perturbation is converted into a non-transcendental equation by the transcendental equation.
At this time, the analytical expression of the pseudo relative motion under the J2 perturbation condition is:
③ Fourier transform processing is performed on orbit state drift data satisfying the form of the equation of motion:
F{af1(t)+bf2(t)}＝aF1(w)+bF2(w)
④ error for initial statePerforming identification to obtain the identification resultNamely an estimated value of the initial state error, and the difference between the two is an improved precision value of the spacecraft orbit.
In addition, under the condition of simultaneously considering J2 perturbation and atmospheric resistance perturbation, for a conventional profile spacecraft, the atmospheric resistance perturbation only has a large relation with the surface-to-mass ratio and the orbit height of the spacecraft. The method is characterized in that the method runs for two periods at an orbit height of 500km, atmospheric resistance perturbation only generates a position error of about 10 meters, when the orbit height is increased, the magnitude of the atmospheric resistance perturbation influence decreases exponentially, the atmospheric resistance only influences relative motion of a spacecraft trace, the influence on radial and normal relative motion is small, and the calculation amount is increased by introducing an atmospheric model, so that the influence of the atmospheric resistance can be not considered, a pseudo relative motion equation under the J2 perturbation is directly used as a relative motion equation under the condition of considering the J2 perturbation and the atmospheric resistance perturbation at the same time, then a Fourier transform method is used for processing relative motion data under the perturbation condition, and finally the orbit improvement of the spacecraft is realized.
As shown in table 1, the initial state vector and the initial state error of the spacecraft selected in this embodiment and the data of the initial error obtained by inversion by the method of the present invention are respectively:
TABLE 1 simulation initial data and simulation results
FIG. 3 is an amplitude-frequency curve obtained by the radial drift data and Fourier transform processing of the corresponding spacecraft orbit; three groups of frequency, amplitude and phase information A can be extracted from the first 2 peak values and the starting point in the amplitude-frequency response curve1,n1,θ1,A2,n2,θ2,A3。
FIG. 4 is an amplitude-frequency curve obtained by the corresponding spacecraft orbit trajectory drift data and Fourier transform processing; three groups of frequency, amplitude and phase information A can be extracted from the first 2 peak values and the starting point in the amplitude-frequency response curve4,n3,θ3,A5,n4,θ4,A6,A7。
Fig. 5 is an amplitude-frequency curve obtained by the corresponding spacecraft orbit normal drift data and fourier transform processing. From the 1 st peak in the amplitude-frequency response curve, a set of frequency, amplitude and phase information A can be extracted8,n5,θ5。
The frequency, amplitude and phase information extracted from fig. 3 to 5 are integrated together, and finally, the inverse calculation is performed by using the formula (12), so that the estimated value of the initial state error can be obtained(i.e., Fourier transform inversion position error and Fourier transform inversion velocity error in Table 1), the estimated value and initial state error(i.e., the initial spacecraft position error and the initial spacecraft velocity error in table 1) is the spacecraft real-time orbit improvement accuracy based on the pseudo relative motion.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (3)
1. A spacecraft real-time orbit improving method based on pseudo relative motion is characterized by comprising the following steps:
step 1) taking a measurement orbit of a spacecraft as a reference orbit, taking an initial state of the spacecraft determined by the measurement orbit at an initial moment as a starting point of a forecast orbit, and generating the forecast orbit according to an orbit dynamics model;
step 2) taking the difference value between the forecast orbit and the measured orbit as orbit drift data, and defining a track formed by the orbit drift data as pseudo relative motion of the spacecraft;
step 3) respectively solving the dynamic models of the pseudo-relative motion under the perturbation-free and perturbation-free conditions to obtain analytical expressions of the pseudo-relative motion under the perturbation-free and perturbation-free conditions, and inverting the estimated value of the initial state error of the spacecraft by the analytical expressions obtained by the calculation after processing the orbit drift data by using a Fourier transform method;
and 4) using the difference between the estimated value of the initial state error and the initial state error value of the reference orbit as an improved value of the spacecraft orbit.
2. The pseudo relative motion-based spacecraft real-time orbit improvement method of claim 1,
the analytic expression of the pseudo relative motion under the perturbation-free condition in the step 3) is as follows:
where n is the average angular motion of the orbit, i.e. the angular frequency of the reference orbit, t represents time, and the parameters and their relationships are set as:
wherein (x)0,y0,z0) The error of the initial position of the three axes is shown,representing the triaxial initial speed error;
processing orbit drift data by using a Fourier transform method, and resolving to obtain a constant item xcycLong term 3xcnt/2 and period termsEach coefficient x in csin (nt + phi)c,b,ycC, phi, and using the above analytical expression to carry out inversion to obtain the initial state errorIs estimated value of
3. The pseudo relative motion-based spacecraft real-time orbit improvement method of claim 1,
the analytic expression of the pseudo relative motion under the perturbation condition in the step 3) is as follows:
wherein, the parameters and the relation thereof are set as follows:
where n is the orbital mean angular motion, i.e., the reference orbital angular frequency, t represents time, u is the coefficient of gravity, rrefFor reference of orbital center-to-earth distance, irefFor reference to the inclination of the track, J2Is a second band harmonic term, ReIs the radius of the earth, n1、n2、n3、n4、n5The angular frequency of each periodic component in the relative motion respectively; (x)0,y0,z0) The error of the initial position of the three axes is shown,representing the triaxial initial speed error;
processing orbit drift data by using a Fourier transform method, and resolving to obtain a constant value item A3,A7Long term A6t and period term A1cos(n1t+θ1),A2cos(n2t+θ2),A4cos(n3t+θ3),A5cos(n4t+θ4),A8sin(n5t+θ5) Each coefficient A in (1)1,θ1,A2,θ2,A3,A4,θ3,A5,θ4,A6,A7,A8,θ5And performing inversion by using the analytical expression to obtain initial state errorIs estimated value of
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