CN106325099B - A kind of spacecraft real-time track improved method based on pseudo- relative motion - Google Patents

Abstract

The present invention provides a real-time trajectory improvement method for spacecraft based on pseudo-relative motion. The present invention obtains the relative motion analysis under the condition of no/with perturbation by separately solving the relative motion dynamics model of the spacecraft under the condition of no/with perturbation Expression, and corresponding to the orbital drift data, use the Fourier transform method to process the orbital drift data, solve the initial position error and velocity error of the spacecraft, and finally obtain the real-time position vector and velocity vector of the spacecraft. Using the above method can improve the orbit determination accuracy by nearly an order of magnitude on the basis of the initial orbit determination technology; and it has universal adaptability, using the CW equation and the improved equation considering the perturbation to realize the improvement of the circular/near-circular spacecraft orbit, and also The improvement of the elliptical spacecraft orbit can be realized by using the Lawden equation and its deformation considering the perturbation.

Description

A real-time trajectory improvement method for spacecraft based on pseudo-relative motion

technical field

The invention belongs to the field of orbit determination of spacecraft, in particular to a method for improving real-time orbit of spacecraft based on pseudo relative motion.

Background technique

Spacecraft orbit determination is the process of estimating the spacecraft orbit using statistical principles for the spacecraft motion state data that contains measurement errors. Through orbit determination, the motion state of the spacecraft at any time in the past, current and future period can be obtained.

According to whether to use the mechanical model of the perturbed force of the spacecraft and the relationship with the mechanical model, the orbit determination method can be divided into kinematic orbit determination, dynamic orbit determination and simplified dynamic orbit determination; according to the data processing strategy, it can be divided into batch Processing method and sequential recursion method; according to the length of the arc, it can be divided into short arc method and long arc method; according to the integration method, it can be divided into single-step method and multi-step method.

At present, the commonly used spacecraft orbit determination methods are the least square estimation method and various forms of Kalman filter methods. The least squares estimation method needs to store a large amount of data in the iterative process for the next iteration; the Kalman filter method will cause divergence of the filter orbit determination results due to poor data observability, initial orbit difference, and strong nonlinearity of the measurement data; in addition , the least squares estimation method and the Kalman filter method also have the numerical problem that the normal equation matrix and the covariance matrix are ill-conditioned due to observability.

Since the measurement accuracy of the above-mentioned traditional orbit determination methods is limited, the accuracy of orbit determination cannot be further improved without a substantial improvement in the accuracy of observation data. Therefore, it is necessary to study new orbit improvement methods to improve the accuracy of orbit determination .

Contents of the invention

The object of the present invention is to provide a method for improving real-time orbit of spacecraft based on pseudo relative motion in order to solve the technical problem of low measurement accuracy of existing spacecraft orbit determination methods.

In order to achieve the above object, a method for improving real-time orbit of spacecraft based on pseudo-relative motion provided by the present invention includes:

Step 1) taking the measured orbit of the spacecraft as the reference orbit, taking the initial state of the spacecraft determined by the measured orbit at the initial moment as the starting point of the predicted orbit, and generating the predicted orbit according to the orbital dynamics model;

Step 2) using the difference between the predicted orbit and the measured orbit as the orbital drift data, and defining the trajectory formed by the orbital drift data as the pseudo-relative motion of the spacecraft;

Step 3) Solve the dynamic model of pseudo relative motion under the condition of no perturbation and presence of perturbation respectively, obtain the analytical expression of pseudo relative motion under the condition of no perturbation and presence of perturbation, and use the Fourier transform method to process the orbital drift data to solve The calculated analytical expression is used to invert the estimated value of the initial state error of the spacecraft;

Step 4) Use the difference between the estimated value of the initial state error and the initial state error value of the reference orbit as the spacecraft orbit improvement value.

As a further improvement of the above-mentioned technical solution, the analytical expression of the pseudo-relative motion under the condition of no perturbation in the step 3) is:

Among them, n is the average angular motion of the orbit, that is, the reference orbital angular frequency, t represents the time, and the parameters and their relationships are set as:

Among them, (x ₀ , y ₀ , z ₀ ) represents the three-axis initial position error, Indicates the three-axis initial velocity error;

Using the Fourier transform method to process the orbital drift data, the constant value term x _c y _c , the long-term term 3x _c nt/2 and the periodic term are obtained Each coefficient x _c ,b, in csin(nt+φ) y _c ,c,φ, and use the above analytic expression to invert to get the initial state error estimated value of

As a further improvement of the above-mentioned technical solution, the analytical expression of the pseudo-relative motion under the perturbation condition in the step 3) is:

Among them, the parameters and their relationships are set as:

Among them, n is the average orbital angular motion, that is, the reference orbital angular frequency, t is the time, u is the gravitational coefficient of the earth, _rref is the reference orbital center distance, _iref is the reference orbital inclination, _J2 is the second harmonic term, R _e is the radius of the earth, n ₁ , n ₂ , n ₃ , n ₄ , n ₅ are the angular frequencies of each periodic component in relative motion;

Using the Fourier transform method to process the orbital drift data, the constant value items A ₃ , A ₇ , the long-term item A ₆ t and the periodic item A ₁ cos(n ₁ t+θ ₁ ), A ₂ cos(n ₂ t +θ ₂ ), A ₄ cos(n ₃ t+θ ₃ ), A ₅ cos(n ₄ t+θ ₄ ), A ₈ sin(n ₅ t+θ ₅ ), A ₁ , θ ₁ , A ₂ , θ ₂ , A ₃ , A ₄ , θ ₃ , A ₅ , θ ₄ , A ₆ , A ₇ , A ₈ , θ ₅ , and use the above analytical expressions to perform inversion to obtain the initial state error estimated value of

The advantage of a kind of spacecraft real-time track improvement method based on pseudo-relative motion of the present invention is:

1. High orbit determination accuracy, which can improve the orbit determination accuracy by nearly an order of magnitude on the basis of the initial orbit determination technology;

2. Real-time, it can reversely integrate time to obtain the position vector and velocity vector of the spacecraft at the current moment;

3. Universal adaptability, use the CW equation and the improved equation considering perturbation to realize the improvement of circular/near-circular spacecraft orbit, and also use the Lawden equation and its deformation considering perturbation to realize the improvement of elliptical spacecraft orbit.

Description of drawings

Fig. 1 is a flow chart of a real-time orbit improvement method for a spacecraft based on pseudo relative motion in the present invention.

Fig. 2 is a schematic diagram of the trajectory of the pseudo relative motion of the spacecraft shown in the embodiment of the present invention.

Fig. 3 is an amplitude-frequency curve obtained by processing radial drift data of spacecraft orbit and Fourier transform in an embodiment of the present invention.

Fig. 4 is an amplitude-frequency curve obtained by processing spacecraft trajectory drift data and Fourier transform in an embodiment of the present invention.

Fig. 5 is an amplitude-frequency curve obtained by processing normal drift data of spacecraft orbit and Fourier transform in an embodiment of the present invention.

Detailed ways

A method for improving real-time orbit of a spacecraft based on pseudo-relative motion according to the present invention will be described in detail below in conjunction with the accompanying drawings and embodiments.

The invention provides a method for improving the real-time orbit of a spacecraft based on pseudo relative motion, which can realize the improvement of the orbit of the spacecraft under the condition of determining the initial orbit.

The present invention obtains the analytical expression of relative motion under the condition of no/with perturbation by separately solving the relative motion dynamics model of the spacecraft under the condition of no/with perturbation, and corresponds to the orbital drift data, and uses the Fourier transform method to solve The initial position error and velocity error of the spacecraft are calculated, and finally the real-time position vector and velocity vector of the spacecraft can be obtained by inversion.

Specifically, a method for improving real-time orbit of a spacecraft based on pseudo-relative motion, comprising the steps of:

①Referring to the idea of spacecraft formation flight, the spacecraft's measurement orbit (preliminary orbit orbit) is used as the reference orbit, and the predicted orbit based on the initial orbit status is used as the corresponding "pseudo-satellite" orbit. Due to the deviation between the measured orbit and the predicted orbit Small, the difference between the two can be understood as a kind of relative motion, that is, pseudo relative motion;

②The initial state of the spacecraft determined by the initial orbit determination at the initial moment is used as the starting point of the predicted orbit, and a predicted orbit is generated according to the orbital dynamics model, and the difference between the predicted orbit and the measured orbit is the orbit drift data;

③ Solve the dynamic model of pseudo-relative motion under the conditions of no perturbation and presence of perturbation respectively. Without considering the perturbation force, when the reference orbit of the spacecraft is a near-earth circular/near-circular orbit, the relative relationship between the reference orbit and the predicted orbit The motion satisfies the CW equation, namely

Among them, (x ₀ , y ₀ , z ₀ ) represents the three-axis initial position error, Indicates the three-axis initial velocity error (on the orbital coordinate system of the reference orbit), n is the average angular motion of the orbit, that is, the angular frequency of the reference orbit, and t represents the time, and these quantities are all theoretically known quantities;

Transform the CW equation into the form of a combination of constant term, periodic term and long-term term, namely

The parameters and their relationships are set as follows:

④ The orbital drift data between the reference orbit and the predicted orbit satisfies the above CW equation, and the Fourier transform method is used to process the orbital drift data, and the constant item x _c y _c , the long-term item 3x _c nt/2 and the periodic item are obtained by solving csin(nt+φ) coefficient x _c ,b, y _c , c, φ, and use formula (3) to invert to get the initial state error estimated value of

⑤ Estimated value of initial state error obtained by inversion error from the initial state The difference is the improved accuracy value of the real-time orbit of the spacecraft based on pseudo-relative motion;

Since the predicted orbit is obtained by time forward integration, the satellite orbit state at a certain moment before the current moment is finally obtained; in the same way, if the orbit dynamics model is time-reversely integrated, the current moment state can be obtained is the predicted orbit of the initial value. If the starting point of the predicted orbit is placed at a certain moment before the current moment, the last step ①-⑤ above is used to obtain the improved accuracy value of the orbital state at that moment; similarly, if the starting point of the predicted orbit is placed at the current moment, The final result is the improved accuracy value of the orbit state at the current moment, thus realizing the real-time improvement of the orbit of the spacecraft.

⑥ Considering the J2 perturbation, the pseudo-relative dynamics model of the spacecraft is expressed as:

in, Respectively are the second derivatives of the three-axis motion, representing the dynamic process.

The parameters and their relationships are set as follows:

Among them, n is the average orbital angular motion, t is time, u is the gravitational coefficient of the earth, r _ref is the reference orbit geocentric distance, i _ref is the reference orbit inclination, J ₂ is the second harmonic term, R _e is the radius of the earth.

Due to the small changes in the distance from the center of the earth and the orbital inclination of the spacecraft under the J2 perturbation, and considering the practical engineering application, assuming that the reference orbit of the spacecraft is a circular orbit, the orbital inclination is 28.5°, and the orbital altitude is 500km, the J2 perturbation The variation range of the earth center distance below is 4.48km, and the relative variation is 0.065%; the variation range of the orbital inclination is 0.03°, and the relative variation is 0.11%. , in order to obtain the analytical form of relative motion under J2 perturbation, it is reasonable to assume that the spacecraft's center distance and orbital inclination are constant, and the specific values are respectively taken as the average semi-major axis of the reference orbit and the average orbital inclination, then the spacecraft pseudo Relative motion dynamic equation:

The parameters and their relationships are set as follows:

The analytical expression of the pseudo-relative motion can be obtained as follows:

It should be noted that the decoupling of the z-axis relative motion component from the xy-plane relative motion component, and the realization of non-transcendence of the z-axis relative motion requires more assumptions, and the z-axis relative motion orbit determination accuracy has little effect on the overall orbit determination accuracy , therefore, the z-axis relative motion is directly taken as the z-axis motion form in the CW equation, namely

in:

Transform formula (9) into the form of constant value item, periodic item, and long-term item combination:

in:

Among them, n is the average orbital angular motion, that is, the reference orbital angular frequency, t is the time, u is the gravitational coefficient of the earth, _rref is the reference orbital center distance, _iref is the reference orbital inclination, _J2 is the second harmonic term, R _e is the radius of the earth, n ₁ , n ₂ , n ₃ , n ₄ , n ₅ are the angular frequencies of each periodic component in relative motion;

⑦ Under J2 perturbation, the orbit drift data between the reference orbit and the predicted orbit satisfies the above motion form, and the Fourier transform method is also used to process the pseudo relative motion orbit drift data, and the constant items A ₃ , A ₇ and the long-term item A ₆ t and periodic terms A ₁ cos(n ₁ t+θ ₁ ), A ₂ cos(n ₂ t+θ ₂ ), A ₄ cos(n ₃ t+θ ₃ ), A ₅ cos(n ₄ t+θ 3 ₄ ), each coefficient A ₁ , θ ₁ , A 2 , θ _{2 , A 3 , A 4 ,} θ ₃ , A _{5 , θ 4 ,} A ₆ , A ₇ in A 8 sin(n 5 t+θ _{5 )} ,A ₈ ,θ ₅ , and use the formula (12) to carry out the reverse solution to get the initial state error estimated value of

⑧ The estimated value of the initial state error obtained from the solution error from the initial state The difference is the improved precision value of the real-time orbit of the spacecraft based on pseudo-relative motion under J2 perturbation;

In addition, considering J2 perturbation and atmospheric drag perturbation at the same time, the position deviation of near-Earth spacecraft orbit due to atmospheric drag perturbation is only on the order of a few meters to tens of meters, so it is not necessary to solve The pseudo-relative motion equation of the spacecraft under the perturbation of atmospheric drag can be directly used to determine the orbit of the spacecraft using the pseudo-relative motion equation of the spacecraft under the J2 perturbation (Formula 9), and the accuracy of the orbit improvement is basically not affected.

Embodiment one

As shown in Figure 1, recorded at the initial time t ₀ , the real position of the spacecraft is at point A, and the initial orbit (measurement orbit) determines that the spacecraft is at point B. Due to the existence of the initial orbit error, the actual position A and the measured position B does not coincide, and the initially determined orbit error is (On the orbital coordinate system of the reference orbit, it is assumed to be a known quantity), this is also the initial state error of the spacecraft, and this state error is extended in time and space, that is, to make a difference between the predicted orbit and the measured orbit, and obtain a period of time The orbital drift data in , that is, the amount of state drift within this period of time. Since the state drift is small relative to the state quantity, the deviation between the predicted orbit and the measured orbit can be regarded as a kind of relative motion, which satisfies a certain law.

(1) Situation 1: Without considering the external perturbation force, the processing steps are as follows:

①The orbit of the spacecraft is a near-earth circular/near-circular orbit, then the relative motion between the reference orbit and the predicted orbit satisfies the CW equation, that is,

②The CW motion equation contains constant value term, periodic term and long-term term. After sorting out the CW motion equation, we can get:

The parameters and their relationships are set as follows:

③ Perform Fourier transform processing on the obtained orbital state drift data satisfying the above CW equation form:

F{af ₁ (t)+bf ₂ (t)}＝aF ₁ (w)+bF ₂ (w)

Get the corresponding amplitude-frequency response curve;

④ According to the amplitude-frequency response curve, extract the corresponding frequency, amplitude, and phase information, and process the X-axis orbital drift data by Fourier transform to obtain x _c , b, n, the Fourier transform processes the Y-axis drift data to obtain y _c , and processes the Z-axis to obtain c, φ. Use this information to bias the initial state Identify and get the identification result That is, the estimated value of the initial state error, and the difference between the two is the orbit improvement accuracy value.

(2) Scenario 2: In the case of considering the external perturbation force, for the near-Earth spacecraft, the external perturbation force is mainly J2 perturbation and atmospheric resistance perturbation. The processing steps are as follows:

① Firstly, only the J2 perturbation is considered. In this case, the dynamic equation of the pseudo-relative motion of the spacecraft is expressed as:

The parameters and their relationships are set as follows:

Among them, r _ref is the real-time geocentric distance of the reference star, and i _ref is the real-time orbit inclination of the reference star.

②Under the J2 perturbation, the earth center distance and orbit inclination of the spacecraft in the above formula show a sinusoidal oscillation trend, so the differential equation in the above formula is a transcendental equation, and the form of analytical solution cannot be obtained, but the change amplitude of the earth center distance and orbit inclination is similar It is smaller than its average value, so it can be reasonably assumed that the earth center distance and orbital inclination angle are constant values under the premise of satisfying the accuracy, and its value is obtained from the average orbital element:

Therefore, under the J2 perturbation, the dynamic equation of the pseudo-relative motion of the spacecraft is transformed from a transcendental equation to a non-transcendental equation.

At this time, the analytical expression of the pseudo-relative motion under the J2 perturbation condition is:

③ Perform Fourier transform processing on the orbital state drift data satisfying the above motion equation:

F{af ₁ (t)+bf ₂ (t)}＝aF ₁ (w)+bF ₂ (w)

④ For the initial state error Identify and get the result That is, the estimated value of the initial state error, and the difference between the two is the improved accuracy value of the spacecraft orbit.

In addition, considering the J2 perturbation and the atmospheric drag perturbation at the same time, for a spacecraft with a conventional shape, the atmospheric drag perturbation only has a greater relationship with the spacecraft's area-to-mass ratio and orbital altitude. At an orbital altitude of 500km, after two cycles of operation, the atmospheric drag perturbation will only produce a position error of about 10 meters. When the orbital altitude increases, the magnitude of the influence of the atmospheric drag perturbation decreases exponentially, and the atmospheric drag only affects the spacecraft The impact on the relative motion in the track direction has little effect on the relative motion in the radial and normal directions, and the introduction of the atmospheric model will increase the amount of calculation. Therefore, the pseudo relative motion equation under the J2 perturbation can be directly used as the simultaneous Consider the relative motion equation of J2 perturbation and atmospheric drag perturbation, and then use the Fourier transform method to process the relative motion data in the perturbation case, and finally realize the orbit improvement of the spacecraft.

As shown in Table 1, the initial state vector and initial state error of the spacecraft selected in this embodiment and the data of the initial error obtained by inversion using the method of the present invention are respectively:

Table 1 Simulation initial data and simulation results

Figure 3 is the amplitude-frequency curve obtained from the corresponding spacecraft orbit radial drift data and Fourier transform processing; from the first two peaks and the starting point in the amplitude-frequency response curve, three groups of frequency, amplitude and Phase information A ₁ , n ₁ , θ ₁ , A ₂ , n ₂ , θ ₂ , A ₃ .

Figure 4 is the amplitude-frequency curve obtained from the corresponding spacecraft track drift data and Fourier transform processing; from the first two peaks and the starting point in the amplitude-frequency response curve, three groups of frequency, amplitude and Phase information A ₄ , n ₃ , θ ₃ , A ₅ , n ₄ , θ ₄ , A ₆ , A ₇ .

Figure 5 is the amplitude-frequency curve obtained from the corresponding spacecraft orbital normal drift data and Fourier transform processing. A set of frequency, amplitude and phase information A ₈ , n ₅ , θ ₅ can be extracted from the first peak in the amplitude-frequency response curve.

Integrating the frequency, amplitude and phase information extracted from Fig. 3 to Fig. 5, and finally using the formula (12) for reverse calculation, the estimated value of the initial state error can be obtained (that is, the Fourier transform inversion position error and the Fourier transform inversion velocity error in Table 1), this estimated value is different from the initial state error (That is, the difference between the initial spacecraft position error and the initial spacecraft velocity error in Table 1) is the improved accuracy of the real-time orbit of the spacecraft based on pseudo relative motion.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than limit them. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent replacements to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all of them should be included in the scope of the present invention. within the scope of the claims.

Claims (3)

1. A real-time orbit improvement method for spacecraft based on pseudo-relative motion, characterized in that it comprises: Step 1) taking the measured orbit of the spacecraft as the reference orbit, taking the initial state of the spacecraft determined by the measured orbit at the initial moment as the starting point of the predicted orbit, and generating the predicted orbit according to the orbital dynamics model; Step 2) using the difference between the predicted orbit and the measured orbit as the orbital drift data, and defining the trajectory formed by the orbital drift data as the pseudo-relative motion of the spacecraft; Step 3) Solve the dynamic model of pseudo relative motion under the condition of no perturbation and presence of perturbation respectively, obtain the analytical expression of pseudo relative motion under the condition of no perturbation and presence of perturbation, and use the Fourier transform method to process the orbital drift data to solve The calculated analytical expression is used to invert the estimated value of the initial state error of the spacecraft; Step 4) Use the difference between the estimated value of the initial state error and the initial state error value of the reference orbit as the spacecraft orbit improvement value. 2. the spacecraft real-time orbit improvement method based on pseudo-relative motion according to claim 1, is characterized in that, The analytical expression of pseudo-relative motion under the condition of no perturbation in described step 3) is: Among them, n is the average angular motion of the orbit, that is, the reference orbital angular frequency, t represents the time, and the parameters and their relationships are set as: Among them, (x ₀ , y ₀ , z ₀ ) represents the three-axis initial position error, Indicates the three-axis initial velocity error; Using the Fourier transform method to process the orbital drift data, the constant value term x _c y _c , the long-term term 3x _c nt/2 and the periodic term are obtained Each coefficient x _c ,b, in csin(nt+φ) y _c ,c,φ, and use the above analytic expression to invert to get the initial state error estimated value of 3. the spacecraft real-time orbit improvement method based on pseudo-relative motion according to claim 1, is characterized in that, The analytical expression of pseudo-relative motion under the perturbation condition in described step 3) is: Among them, the parameters and their relationships are set as: Among them, n is the average orbital angular motion, that is, the reference orbital angular frequency, t is the time, u is the gravitational coefficient of the earth, _rref is the reference orbital center distance, _iref is the reference orbital inclination, _J2 is the second harmonic term, R _e is the radius of the earth, n ₁ , n ₂ , n ₃ , n ₄ , and n ₅ are the angular frequencies of each periodic component in the relative motion, respectively; (x ₀ , y ₀ , z ₀ ) represent the three-axis initial position error, Indicates the three-axis initial velocity error; Using the Fourier transform method to process the orbital drift data, the constant value items A ₃ , A ₇ , the long-term item A ₆ t and the periodic item A ₁ cos(n ₁ t+θ ₁ ), A ₂ cos(n ₂ t +θ ₂ ), A ₄ cos(n ₃ t+θ ₃ ), A ₅ cos(n ₄ t+θ ₄ ), A ₈ sin(n ₅ t+θ ₅ ), A ₁ , θ ₁ , A ₂ , θ ₂ , A ₃ , A ₄ , θ ₃ , A ₅ , θ ₄ , A ₆ , A ₇ , A ₈ , θ ₅ , and use the above analytical expressions to perform inversion to obtain the initial state error estimated value of