CN115062416A - Fast regression orbit design method based on discrete space combination optimization - Google Patents
Fast regression orbit design method based on discrete space combination optimization Download PDFInfo
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Abstract
The invention discloses a regression orbit rapid design method based on discrete space combination optimization, which comprises the following steps: establishing a sun synchronous orbit analysis model and a regression orbit analysis model, and establishing a discrete solution set by combining the sun synchronous orbit analysis model and the regression orbit analysis model; optimizing the discrete solution set to obtain regression orbit parameters, and establishing a regression orbit based on the regression orbit parameters; and correcting the regression characteristic of the regression orbit to obtain a target regression orbit. The invention adopts the differential correction strategy of the expanded dimensionality to correct the regression characteristics of the designed orbit, takes the radial vector into consideration, increases the regression constraint of the satellite space position and realizes the design of the high-precision regression orbit.
Description
Technical Field
The invention belongs to the field of regression orbit design, and particularly relates to a fast regression orbit design method based on discrete space combination optimization.
Background
The regression orbit design method in the prior art has the following defects:
a strict regression orbit design method considering a high-order gravity field is provided in a patent CN110378012A, Newton iteration and NSGA-II are adopted to carry out mixed optimization orbit design, a continuous optimization method is adopted, the optimization time is long, and the conditions of premature convergence and the like can occur; secondly, the patent only considers the regression characteristic of the satellite, namely realizes the regression of the initial and final state vectors in the regression period, does not consider load constraint, and cannot meet the actual task requirement.
The patent CN106092105A provides a method for determining a strict regression orbit of a near-earth satellite, and the patent adopts a continuous optimization method, so that the optimization speed is low and the time is long; secondly, the patent also considers regression characteristics constraints, not the loads of the satellites for the actual mission.
Disclosure of Invention
The invention aims to provide a regression orbit rapid design method based on discrete space combination optimization, so as to solve the problems in the prior art.
In order to achieve the purpose, the invention provides a regression orbit rapid design method based on discrete space combination optimization, which comprises the following steps:
constructing a sun synchronous orbit analysis model and a regression orbit analysis model, and obtaining a discrete solution set according to the sun synchronous orbit analysis model and the regression orbit analysis model;
optimizing the discrete solution set to obtain regression orbit parameters, and establishing a regression orbit based on the regression orbit parameters;
and correcting the regression characteristic of the regression orbit to obtain a target regression orbit.
Preferably, the process of constructing the sun-synchronous orbit analysis model includes: according to the second of a year, the long-term influence of the earth second-order harmonic perturbation term and the earth fourth-order harmonic perturbation term on the orbit ascension point right ascension is obtained, the precession value of the satellite orbit ascension point right ascension is obtained, and the solar synchronization constraint is established.
Preferably, the process for obtaining the long-term influence of the second-order band harmonic perturbation term of the earth and the fourth-order band harmonic perturbation term of the earth on the ascension of the orbit ascending intersection comprises the following steps: obtaining the average angular velocity of the satellite according to the earth gravitational constant and the satellite orbit semimajor axis; and obtaining the long-term influence of the earth second-order harmonic perturbation term and the earth fourth-order harmonic perturbation term on the orbit ascent point right ascension according to the average angular velocity of the satellite, the satellite orbit semi-major axis, the earth equatorial radius, the earth second-order harmonic perturbation coefficient and the earth fourth-order harmonic perturbation coefficient.
Preferably, the process of constructing the regression orbit analysis model comprises: and establishing an orbit regression constraint according to the precession value of the right ascension of the satellite orbit intersection point, the earth equator radius and the satellite orbit node period.
Preferably, the obtaining of the satellite orbit node cycle comprises: and obtaining the satellite orbit node period according to the second-order band harmonic perturbation coefficient of the earth, the satellite near-location amplitude angle under the influence of the fourth-order band harmonic perturbation coefficient of the earth and the long-term change of the satellite mean near point angle.
Preferably, the sun synchronous orbit analysis model and the regression orbit analysis model are simultaneously established, and the process of establishing the discrete solution set comprises the following steps:
presetting value ranges of regression days and regression turns, and obtaining a semimajor axis and a track inclination angle of a regression track through simultaneous sun synchronization constraint and track regression constraint based on the value ranges; and establishing a discrete solution set according to the mapping relation between the regression days and the regression turns and the inclination angles of the semi-major axis and the orbit.
Preferably, the process of optimizing the discrete solution set includes:
obtaining the least number of covering turns according to the load width and the load wave position of the satellite; establishing an optimization function, and obtaining regression turns according to the minimum coverage turns; and obtaining regression days based on the regression turns and the orbit height of the satellite.
Preferably, the process of performing regression characteristic correction on the regression trajectory includes:
acquiring latitude, longitude and radial vectors after satellite regression based on orbital elements, wherein the orbital elements comprise a semi-major axis, an inclination angle and a true paraxial point angle;
establishing a differential correction formula based on the difference values of the latitude, longitude and radial vector at the beginning and end of the regression cycle;
and based on the differential correction formula, performing regression characteristic correction on the regression orbit to obtain a corrected semimajor axis, an inclination angle and a true anomaly angle, and further obtaining a target regression orbit.
The invention has the technical effects that:
(1) compared with the traditional establishment of the earth J2 perturbation model, the method considers the earth J4 perturbation during the construction of the sun synchronous regression orbit analysis model, and solves the problem that the sun synchronous regression orbit analysis model is not accurate enough, so that the initial orbit value designed by the method has higher regression precision.
(2) The invention maps the continuous optimization space into the discrete space by utilizing the one-to-one mapping relation of integer variables including the regression period and the days and the track elements, realizes the establishment of a discrete solution set, and greatly accelerates the track design time based on the processing of discrete space combination optimization in the subsequent optimization problem.
(3) The invention adopts the differential correction strategy of the expanded dimensionality to correct the regression characteristic of the designed orbit, thereby obtaining a more accurate regression orbit. Compared with the traditional correction method only considering the longitude and latitude of the satellite points, the method provided by the invention expands the dimensionality and takes the sagittal vector into consideration, thereby increasing the regression constraint of the satellite spatial position and realizing the design of a high-precision regression orbit.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application. In the drawings:
FIG. 1 is a flow chart of a method in an embodiment of the invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
Example one
As shown in fig. 1, the embodiment provides a regression trajectory fast design method based on discrete spatial combination optimization, including:
aiming at the sun synchronous regression orbit characteristic of a near circular orbit satellite, establishing an analytic model of a semi-long axis and an orbit inclination angle according to the sun synchronous characteristic; establishing an analysis model of regression days, regression turns and a node period of the satellite according to the regression orbit characteristics;
in the first step, when the sun synchronous regression orbit model is established, the influence of perturbation of the earth J4 is further considered, and the established sun synchronous analysis model and the established regression orbit analysis model have higher precision. The detailed steps are as follows:
and establishing sun synchronization constraint. Assuming that the eccentricity e of the near-circular orbit is 0, considering the long-term influence of the earth J2 and J4 items on the right ascension of the orbit intersection point, establishing a precession formula of the right ascension of the satellite orbit intersection point by solar synchronization constraint:
wherein year represents the number of seconds of a year,
the long-term effects of the earth's J2 and J4 terms on the orbital ascension crossing right ascension, respectively, are expressed as follows:
wherein, the first and the second end of the pipe are connected with each other,
a is the semi-major axis of the satellite orbit,
is the equatorial radius of the earth and is,
is the average angular velocity of the satellite(s),
is the earth's gravitational constant. J. the design is a square 2 、J 4 Respectively corresponding perturbation coefficients.
Secondly, regression characteristic constraints are established, which satisfy the following formula:
the formula of the satellite orbit node period is as follows:
the earth J can be obtained by the two constraints of the equations (1) and (4) 4 Semi-long axis satisfying sun synchronization characteristic and regression characteristic under influence of terms
And track inclination
And step two, simultaneously establishing a sun synchronous orbit analysis model and a regression orbit model, establishing a one-to-one mapping relation between integer variable regression days and regression turns and continuous variable semi-major axis and orbit inclination angle, realizing mapping from a continuous space to a discrete space, and establishing a discrete solution set in a limited space.
In the second step, the range of regression days and regression turns of integer variables is appointed, and the orbit inclination angles under different semi-major axes are obtained in the range by simultaneously establishing the constraints (1) and (4), so that a discrete solution set of a discrete space containing the regression days, the regression turns, the semi-major axes and the orbit inclination angles is established, and the list of the discrete solution set is given as an example: assuming that the regression days range is set to 6-12 days and the regression turns range is 80-200 turns, the resulting discretized solution set format is as follows:
| days of regression | Number of return turns | Semi-major axis | Inclination angle of track |
| 6 | 89 | 6991235 | 97.8744 |
| 6 | 89 | 6991235 | 97.8744 |
| 8 | 119 | 6978145 | 97.8227 |
| 10 | 149 | 6970321 | 97.7919 |
| 11 | 164 | 6967481 | 97.7808 |
| … | … | … | … |
And step three, considering the task requirement of the load, establishing a task-related optimization function, and performing optimization processing based on the established discrete solution set.
In the third step, the process of establishing the optimization function based on the load constraint comprises the following steps:
from the load capacity, the satellite regressive orbit parameters can be determined, including the number of regressive days and the number of regressive turns. The satellite regression Number (Orbit Number) is related to the load width and the wave position, and the determination formula is as follows:
the minimum number of coverage turns for which the satellite can achieve global coverage is determined by (8). Based on the regression turn number and the track height, the regression Day may be determined, with the following formula:
wherein a ═ R e + H is the semi-major axis of the satellite orbit, mu-398600.4405 km 3 /s 2 Is a constant of the earth's gravity.
To achieve global coverage, the number of regression orbit turns should be designed to be greater than the minimum number of coverage turns, but considering the conservation of satellite load resources, the optimization function is designed as follows:
the optimization objective function is:
wherein R is d The regression turns of the designed regression orbit.
And step four, performing regression characteristic correction of the extended dimensionality on the regression orbit meeting the task requirement to obtain the regression orbit with higher regression precision.
In the fourth step, a regression orbit correction model of the extension dimensionality is established, and the nonlinear relation between the regression longitude and latitude and the satellite radial vector and the orbit elements is established as follows:
regressive latitude
And the longitude λ and the sagittal are functions of the semi-major axis a, the inclination i and the true paraxial angle f:
and establishing a differential correction formula by the difference value of the latitude, longitude and radial vector at the beginning and end of a regression cycle as follows:
where Δ represents the difference operator over the entire regression cycle. And obtaining the corrected semimajor axis, inclination angle and true paraxial point angle through differential correction, thereby obtaining the track with higher regression precision.
In summary, the invention provides a fast regression orbit design method based on discrete space combination optimization, which establishes a high-precision one-to-one mapping relationship between regression characteristic integer variables including regression days and regression turns and continuous orbit element variables including half-field axes and orbit inclination angles by establishing a sun synchronous regression orbit analysis model, thereby mapping a continuous optimization space into a discrete space and providing a solution space for optimization problems. Then, based on the load task requirement, an optimization function is established, based on the obtained discrete solution set in the discrete space, the solution of the optimization problem is realized, so that the designed orbit meets the task requirement, and the regression characteristic is further corrected by using the differential correction method of the expanded dimensionality, so that the regression orbit with high regression precision meeting the task requirement is obtained.
The above description is only for the preferred embodiment of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (8)
1. A regression orbit rapid design method based on discrete space combination optimization is characterized by comprising the following steps:
constructing a sun synchronous orbit analysis model and a regression orbit analysis model, and obtaining a discrete solution set according to the sun synchronous orbit analysis model and the regression orbit analysis model;
optimizing the discrete solution set to obtain regression orbit parameters, and establishing a regression orbit based on the regression orbit parameters;
and correcting the regression characteristic of the regression orbit to obtain a target regression orbit.
2. The fast design method of regression trajectory based on discrete spatial combination optimization according to claim 1,
the process of constructing the sun synchronous orbit analysis model comprises the following steps: according to the second of a year, the long-term influence of the earth second-order harmonic perturbation term and the earth fourth-order harmonic perturbation term on the orbit ascension point right ascension is obtained, the precession value of the satellite orbit ascension point right ascension is obtained, and the solar synchronization constraint is established.
3. The fast design method of regression trajectory based on discrete spatial combination optimization according to claim 2,
the acquisition process of the long-term influence of the second-order harmonic perturbation item of the earth and the fourth-order harmonic perturbation item of the earth on the right ascension of the orbit ascending intersection comprises the following steps: obtaining the average angular velocity of the satellite according to the earth gravity constant and the satellite orbit semimajor axis; and obtaining the long-term influence of the earth second-order harmonic perturbation term and the earth fourth-order harmonic perturbation term on the orbit ascent point right ascension according to the average angular velocity of the satellite, the satellite orbit semi-major axis, the earth equatorial radius, the earth second-order harmonic perturbation coefficient and the earth fourth-order harmonic perturbation coefficient.
4. The fast design method of regression trajectory based on discrete spatial combination optimization according to claim 1,
the process of constructing the regression orbit analysis model comprises the following steps: and establishing an orbit regression constraint according to the precession value of the right ascension point of the satellite orbit, the earth equator radius and the satellite orbit node period.
5. The regression trajectory rapid design method based on discrete spatial combination optimization according to claim 4,
the acquisition process of the satellite orbit node cycle comprises the following steps: and obtaining the satellite orbit node period according to the second-order band harmonic perturbation coefficient of the earth, the satellite near-location amplitude angle under the influence of the fourth-order band harmonic perturbation coefficient of the earth and the long-term change of the satellite mean near point angle.
6. The fast design method of regression trajectory based on discrete spatial combination optimization according to claim 1,
and (3) simultaneously establishing the sun synchronous orbit analysis model and the regression orbit analysis model, wherein the process of establishing a discrete solution set comprises the following steps:
presetting value ranges of regression days and regression turns, and obtaining a semimajor axis and a track inclination angle of a regression track through simultaneous sun synchronization constraint and track regression constraint based on the value ranges; and establishing a discrete solution set according to the mapping relation between the regression days and the regression turns and the inclination angles of the semi-major axis and the orbit.
7. The fast design method of regression trajectory based on discrete spatial combination optimization according to claim 1,
the process of optimizing the discrete solution set comprises the following steps:
obtaining the least number of covering turns according to the load width and the load wave position of the satellite; establishing an optimization function, and obtaining regression turns according to the minimum coverage turns; and obtaining regression days based on the regression turns and the orbit height of the satellite.
8. The fast design method of regression trajectory based on discrete spatial combination optimization according to claim 1,
the process of performing regression characteristic correction on the regression trajectory includes:
acquiring latitude, longitude and radial vectors after satellite regression based on orbital elements, wherein the orbital elements comprise a semi-major axis, an inclination angle and a true paraxial point angle;
establishing a differential correction formula based on the difference values of the latitude, longitude and radial vector at the beginning and end of the regression cycle;
and based on the differential correction formula, performing regression characteristic correction on the regression orbit to obtain a corrected semimajor axis, an inclination angle and a true anomaly angle, and further obtaining a target regression orbit.
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