CN112257343B - High-precision ground track repetitive track optimization method and system - Google Patents

High-precision ground track repetitive track optimization method and system Download PDF

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CN112257343B
CN112257343B CN202011138645.3A CN202011138645A CN112257343B CN 112257343 B CN112257343 B CN 112257343B CN 202011138645 A CN202011138645 A CN 202011138645A CN 112257343 B CN112257343 B CN 112257343B
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李楠
陈筠力
陈重华
信太林
陈国忠
凌惠祥
孙英梅
刘艳阳
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Shanghai Institute of Satellite Engineering
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Abstract

The invention provides a high-precision ground track repetitive orbit optimization method and system, wherein a corresponding satellite orbit dynamics recursion model is established according to the requirement analysis of an earth gravity field non-spherical perturbation order; the method comprises the steps of providing heavy rail interference track parameters under a J2 low-order gravity field according to an analytical formula, and obtaining correction parameters under J4 perturbation through iterative calculation to serve as initial values of a high-precision ground track repeated track parameter self-adaptive setting algorithm; and according to the requirement of the repeated track precision, carrying out self-adaptive optimization setting on the repeated track parameters of the high-precision ground track. The method solves the problems that the traditional low-order gravity field orbit model is low in ground track repetition precision, the high-order gravity field orbit model is high in nonlinearity, many in iterative correction parameters, incapable of resolving and the like, and has more general engineering practicability.

Description

High-precision ground track repetitive track optimization method and system
Technical Field
The invention relates to astronavigation aircraft orbital dynamics, in particular to a high-precision ground track repeated orbit optimization method and system.
Background
The revisiting characteristic of the track of the sub-satellite points is an important index for the design of the earth observation satellite track, the requirement of the traditional satellite ground track on the return precision of the track is not high, the track deviation can be from several kilometers to dozens of kilometers, and the flying task of the satellite is not influenced. In recent years, with the requirement of imaging precision greatly improved, the limitation of the existing regression orbit design method is increasingly obvious, and particularly for a surveying and mapping task, in order to realize accurate surveying and mapping and efficient task planning, high-precision regression of a satellite reference orbit ground track needs to be ensured.
At present, a plurality of regression orbit design schemes are applied at home and abroad, but most of the regression orbit design schemes are based on an analysis method of a low-order gravity field model, and the regression precision deviation is as high as 3km to 10km. In the Chinese patent "a method for determining a strict regression orbit of a near earth satellite" (CN 106092105A), the popchengqing, ducuke, wang etime and the like perform iterative correction by establishing a relationship between a semi-major axis of the orbit, an inclination angle of the orbit and a longitude and latitude of a sub-satellite by taking regression accuracy as an index; and aiming at the characteristic of the eccentricity ratio vector limit cycle, repeatedly carrying out iterative correction on the eccentricity ratio and the perigee argument by adopting an averaging method. In the method, the perturbation of the earth 2-order gravity field is only considered in the functional relation between the satellite points for iterative correction and the orbit semi-major axis and inclination angle, so that the regression precision is influenced; each iteration correction of eccentricity and argument of near place needs to acquire 4-month period data for averaging, the calculated amount is large, and the iteration convergence speed is influenced; the regression precision of the obtained orbit can only reach the meter level, and engineering application is influenced.
In summary, a high-precision ground track repetitive track design under the influence of high-order gravity field perturbation needs to be developed for centimeter-level regression precision requirements.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a high-precision ground track repetitive track optimization method and system.
The invention provides a high-precision ground track repetitive track optimization method, which comprises the following steps:
step A: according to the requirement analysis of the earth gravity field non-spherical perturbation order, establishing a corresponding satellite orbit dynamics recursion model;
and B: the method comprises the steps of providing heavy rail interference track parameters under a J2 low-order gravity field according to an analytical formula, and obtaining correction parameters under J4 perturbation through iterative calculation to serve as initial values of a high-precision ground track repeated track parameter self-adaptive setting algorithm;
step C: and according to the requirement of the repeated track precision, carrying out self-adaptive optimization setting on the repeated track parameters of the high-precision ground track.
Preferably, the precision of the heavy rail track is less than 0.01m.
Preferably, the step a includes:
taking a numerical simulation test result as a basis, comprehensively considering ground track repetition precision and track recursion calculation amount, establishing a satellite track dynamic model corresponding to the following steps by adopting an expression method of an earth gravity field potential function:
Figure BDA0002737567200000021
wherein the content of the first and second substances,
Figure BDA0002737567200000022
is the earth-centered position vector of the satellite;
Figure BDA0002737567200000023
is the function of the field potential of the earth gravity;
the gravity field potential function comprises two parts of earth central gravity and earth non-spherical gravity, and if the earth is considered as a rigid body and an equatorial plane is superposed with a basic plane of an epoch inertial system, the gravity field potential function is expanded into a series form in the earth central inertial system as follows:
Figure BDA0002737567200000024
wherein mu is the gravitational constant of the earth, r is the earth center distance of the satellite, C n0 And C nm And S nm All are spherical harmonic coefficients, R e Is the equatorial radius,
Figure BDA0002737567200000025
The geocentric latitude and the lambda are geocentric longitude which are obtained by calculating a position vector in a satellite geostationary system;
Figure BDA0002737567200000026
and
Figure BDA0002737567200000027
the terms are Legendre and associated Legendre polynomials respectively, are correction parts of a real earth gravitational potential pair uniform sphere and comprise a band harmonic term and a field harmonic term;
and obtaining coefficient values of each order of a gravitational field potential function through an earth gravitational field table, calculating to obtain a perturbation force expression under a satellite geostationary system, and further integrating to obtain the position and the speed of the satellite.
Preferably, the step B includes:
step S4.1: according to the overall design constraint, giving a semi-major axis analytic solution a of the heavy rail interference track under the J2 low-order gravity field J2 Orbit dip angle analytic solution i J2 A heavy rail period T and a rail turn number Q;
according to the load working power, the satellite weight, the carrying and launching capacity and other overall constraints, the semi-major axis a of the heavy-rail interference orbit can be determined J2 ；
Orbit dip analytic solution i J2 ：
Figure BDA0002737567200000031
Wherein J2=0.001082,
Figure BDA0002737567200000032
Track number of turns Q, heavy rail period T:
Figure BDA0002737567200000033
Figure BDA0002737567200000034
T＝T n ×Q
wherein, T n Is a point of intersectionPeriod, w e Is the rotational angular velocity of the earth;
step S4.2: according to the J2 perturbation analysis orbit, a J4 perturbation correction orbit based on a Newton iteration method is provided, and the method comprises the following steps:
step S4.2.1: selecting t according to the ground track arrangement requirement of the satellite task 0 Latitude and longitude lambda of time sub-satellite point 0 、
Figure BDA0002737567200000035
Establishing a functional relation of longitude and latitude about a semi-long axis and an inclination angle after the following track is repeated;
Figure BDA0002737567200000036
wherein the content of the first and second substances,
Figure BDA0002737567200000037
Figure BDA0002737567200000038
Figure BDA0002737567200000039
Figure BDA00027375672000000310
Figure BDA00027375672000000311
M＝n(t-t 0 )
G 0 is t 0 At time Greenwich mean sidereal time omega 0 Is t 0 The right ascension at the ascending crossing point of the moment,
Figure BDA00027375672000000312
is J 4 Perturbation of the rising point right ascension drift rate;
step S4.2.2: obtaining the following heavy rail interference track eccentricity e by utilizing the constraint relation of the frozen track J3 And estimating the initial value of the argument w of the near place:
Figure BDA0002737567200000041
step S4.2.3: first with the satellite t 0 Time ground track initial longitude and latitude lambda 0 、
Figure BDA0002737567200000042
Taking the starting point as the point of the second track, performing the integration of the second track period T to obtain T 0 Satellite ground track longitude and latitude lambda at + T moment n 、
Figure BDA0002737567200000043
Then calculating to obtain the longitude and latitude deviation delta lambda = lambda of the initial end and the final end of the heavy rail n -λ 0 ，
Figure BDA0002737567200000044
Judging whether the deviation meets the heavy rail interference precision index or not; if the index is satisfied, outputting a semimajor axis and a tilt angle correction value a J4 、i J4 If the iteration parameter is out of tolerance, the following parameter correction is carried out, and the integral judgment process is converted back again until the iteration parameter meets the precision index;
a k ＝a k-1 +Δa k-1
i k ＝i k-1 +Δi k-1
wherein the content of the first and second substances,
Figure BDA0002737567200000045
a k for the semi-major axis of the orbit at time k, a k-1 Is the half-major axis of the track at time k-1, i k For the track inclination at time k, i k-1 For track inclination at time k-1；
Step S4.2.4: calculating to obtain t by using the functional relationship between the semi-major axis and the inclination angle of the track in the step S4.2.1 and the longitude and latitude of the subsatellite point 0 Time a J4 、i J4 Corresponding rising point right ascension omega J4 Angle M close to the mean J4 。
Preferably, the step C includes:
step S5.1: the method comprises the steps of converting a track repeated nonlinear parameter solving problem under a high-order gravity field into a multivariable and multi-target optimization problem, guiding parameter self-adaptive setting by combining target track characteristic information, and describing an optimization model as follows:
optimizing the target:
Figure BDA0002737567200000046
optimizing variables: [ Δ a, Δ e, Δ i, Δ Ω, Δ w, Δ M ]
Initial conditions were as follows: [ a ] A J4 ,e J3 ,i J4 ,Ω J4 ,w＝90°,M J4 ]
Constraint conditions are as follows:
Figure BDA0002737567200000047
delta a is correction of track semimajor axis, delta e is correction of track eccentricity, delta i is correction of track inclination angle, delta omega is correction of right ascension at track ascending intersection point, delta w is correction of amplitude at track perigee, delta M is correction of angle at track mean perigee,
Figure BDA0002737567200000048
is a vector of the acceleration of the satellite,
Figure BDA0002737567200000049
in order to be a satellite position deviation,
Figure BDA00027375672000000410
for the satellite position vector at time T,
Figure BDA00027375672000000411
is t 0 A time satellite position vector;
step S5.2: selecting individuals through a binary system tournament method, and performing crossing and variation to generate a new population;
step S5.3: calculating and updating a new population objective function value, namely the position and speed deviation of the satellite earth-fixed system;
step S5.4: generating a new combined population by a merging method, and carrying out non-dominant sorting;
step S5.5: selecting individuals to form a new generation of population through a displacement and elite retention strategy;
step S5.6: and skipping to the step S5.2, and circularly updating until the termination condition is met.
The invention provides a high-precision ground track repetitive track optimization system, which comprises:
a module A: according to the demand analysis of the earth gravity field non-spherical perturbation order, establishing a corresponding satellite orbit dynamics recursion model;
and a module B: according to an analytical formula, heavy-rail interference track parameters under a J2 low-order gravity field are given, correction parameters under J4 perturbation are obtained through iterative calculation and serve as initial values of a high-precision ground track repeated track parameter self-adaptive setting algorithm;
and a module C: and performing self-adaptive optimization setting of the high-precision ground track repeated track parameters according to the repeated track precision requirement.
Preferably, the precision of the heavy rail track is less than 0.01m.
Preferably, the module a comprises:
taking the numerical simulation test result as a basis, comprehensively considering the ground track repetition precision and the orbit recursion computation amount, establishing a satellite orbit dynamics model corresponding to the following steps, and adopting an expression method of an earth gravity field potential function:
Figure BDA0002737567200000051
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002737567200000052
is the earth-centered position vector of the satellite;
Figure BDA0002737567200000053
is a function of the field potential of the earth gravity;
the gravity field potential function comprises two parts of earth central gravity and earth non-spherical gravity, and if the earth is considered as a rigid body and an equatorial plane is superposed with a basic plane of an epoch inertial system, the gravity field potential function is expanded into a series form in the earth central inertial system as follows:
Figure BDA0002737567200000054
wherein mu is the gravitational constant of the earth, r is the earth center distance of the satellite, C n0 And C nm And S nm All are spherical harmonic coefficients, R e Is the equatorial radius,
Figure BDA0002737567200000055
The geocentric latitude and the lambda are geocentric longitude which are obtained by calculating a position vector in a satellite geostationary system;
Figure BDA0002737567200000056
and
Figure BDA0002737567200000057
the terms are Legendre and associated Legendre polynomials respectively, are correction parts of a real earth gravitational potential pair uniform sphere and comprise a band harmonic term and a field harmonic term;
and obtaining coefficient values of each order of a gravitational field potential function through an earth gravitational field table, calculating to obtain a perturbation force expression under a satellite geostationary system, and further integrating to obtain the position and the speed of the satellite.
Preferably, the module B comprises:
module S4.1: according to the overall design constraint, giving a semi-major axis analytic solution a of the heavy rail interference track under the J2 low-order gravity field J2 Orbit dip angle analytic solution i J2 And heavy track period T, trackThe number of turns Q;
according to the load working power, the satellite weight, the carrying and launching capacity and other overall constraints, the semi-major axis a of the heavy-rail interference orbit can be determined J2 ；
Orbit dip analytic solution i J2 ：
Figure BDA0002737567200000061
Wherein J2=0.001082,
Figure BDA0002737567200000062
Track turn number Q, heavy track period T:
Figure BDA0002737567200000063
Figure BDA0002737567200000064
T＝T n ×Q
wherein, T n Is a period of intersection, w e Is the rotational angular velocity of the earth;
module S4.2: according to the J2 perturbation analysis orbit, a J4 perturbation correction orbit based on a Newton iteration method is provided, and the method comprises the following steps:
module s4.2.1: selecting t according to the ground track arrangement requirement of the satellite task 0 Latitude and longitude lambda of time point under star 0 、
Figure BDA0002737567200000065
Establishing a functional relation of longitude and latitude about a semi-major axis and an inclination angle after the following tracks are repeated;
Figure BDA0002737567200000066
wherein the content of the first and second substances,
Figure BDA0002737567200000071
Figure BDA0002737567200000072
Figure BDA0002737567200000073
Figure BDA0002737567200000074
Figure BDA0002737567200000075
M＝n(t-t 0 )
G 0 is t 0 At time Greenwich mean sidereal time omega 0 Is t 0 The right ascension at the ascending crossing point of the moment,
Figure BDA0002737567200000076
is J 4 Perturbation of the rising point right ascension drift rate;
module s4.2.2: obtaining the following heavy rail interference track eccentricity e by utilizing the constraint relation of the frozen track J3 And estimating the initial value of the argument w of the near place:
Figure BDA0002737567200000077
module s4.2.3: firstly, with the satellite t 0 Time ground track initial longitude and latitude lambda 0 、
Figure BDA0002737567200000078
Taking the starting point as the point of integration of the heavy track period T to obtain T 0 Satellite ground track longitude and latitude lambda at + T moment n 、
Figure BDA0002737567200000079
Then calculating to obtain the longitude and latitude deviation delta lambda = lambda of the initial end of the heavy rail n -λ 0 ，
Figure BDA00027375672000000710
Judging whether the deviation meets the heavy rail interference precision index or not; if the index is satisfied, outputting a semimajor axis and inclination angle correction value a J4 、i J4 If the iteration parameter is out of tolerance, the following parameter correction is carried out, and the integral judgment process is converted back again until the iteration parameter meets the precision index;
a k ＝a k-1 +Δa k-1
i k ＝i k-1 +Δi k-1
wherein the content of the first and second substances,
Figure BDA00027375672000000711
a k for the semi-major axis of the orbit at time k, a k-1 Is the half-major axis of the track at time k-1, i k For the track inclination at time k, i k-1 Is the inclination angle of the orbit at the moment of k-1;
module s4.2.4: t is obtained by calculation according to the function relation between the semi-major axis and the inclination angle of the orbit in the module S4.2.1 and the longitude and latitude of the satellite point 0 Time a J4 、i J4 Corresponding rising point right ascension omega J4 Angle M close to the mean J4 。
Preferably, the module C comprises:
module S5.1: the method comprises the following steps of converting a track repetition nonlinear parameter solving problem under a high-order gravity field into a multivariable and multi-target optimization problem, guiding parameter self-adaptive setting by combining target track characteristic information, and describing an optimization model as follows:
optimizing the target:
Figure BDA0002737567200000081
optimizing variables: [ Δ a, Δ e, Δ i, Δ Ω, Δ w, Δ M ]
Initial conditions were as follows: [ a ] A J4 ,e J3 ,i J4 ,Ω J4 ,w＝90°,M J4 ]
Constraint conditions are as follows:
Figure BDA0002737567200000082
delta a is correction of track semimajor axis, delta e is correction of track eccentricity, delta i is correction of track inclination angle, delta omega is correction of right ascension at track ascending intersection point, delta w is correction of amplitude at track perigee, delta M is correction of angle at track mean perigee,
Figure BDA0002737567200000083
as a vector of the acceleration of the satellite,
Figure BDA0002737567200000084
in order to be a satellite position deviation,
Figure BDA0002737567200000085
for the satellite position vector at time T,
Figure BDA0002737567200000086
is t 0 A time satellite position vector;
module S5.2: selecting individuals through a binary tournament method, and performing crossing and variation to generate a new population;
module S5.3: calculating and updating a new population objective function value, namely the position and speed deviation of the satellite earth-fixed system;
module S5.4: generating a new combined population by a merging method, and carrying out non-dominant sorting;
module S5.5: selecting individuals to form a new generation of population through a displacement and elite retention strategy;
module S5.6: and jumping to a module S5.2, and circularly updating until a termination condition is met.
Compared with the prior art, the invention has the following beneficial effects:
the method solves the problems that the traditional low-order gravity field orbit model is low in ground track repetition precision, the high-order gravity field orbit model is high in nonlinearity, many in iterative correction parameters, incapable of resolving and the like, and has more general engineering practicability.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic block diagram of a high-precision ground track repetitive orbit optimization method;
FIG. 2 is a schematic block diagram of iterative correction of an initial value of a high-precision ground track repetitive orbit J4;
FIG. 3 is a schematic diagram of high-precision ground track repetitive orbit parameter adaptive setting optimization;
FIG. 4 is a high-precision ground track repetitive orbit high-order gravity field model order determination simulation diagram.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will aid those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any manner. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the concept of the invention. All falling within the scope of the present invention.
As shown in the attached figure 1, the invention provides a high-precision ground track repetitive track optimization method with self-adaptive parameter setting under the influence of high-order gravity field perturbation. The method specifically comprises the following steps:
step A: according to the requirement analysis of the earth gravity field non-spherical perturbation order, establishing a corresponding satellite orbit dynamics recursion model;
and B, step B: giving out heavy-rail interference track parameters under a J2 low-order gravity field according to an analytical formula, and iteratively calculating on the basis to obtain correction parameters under J4 perturbation as initial values of a high-precision ground track repeated track parameter self-adaptive setting algorithm;
and C: and according to the requirement of the repeated track precision, carrying out self-adaptive optimization setting on the repeated track parameters of the high-precision ground track.
In this embodiment, the regression accuracy is better than 0.01m.
In the step A: as shown in fig. 4, the orbit repetition position precision of the regression orbit under each other low-order perturbation model is calculated by a numerical simulation test method with 120 × 120-order earth gravity field as a standard, and then the orbit recursion computation amount is considered comprehensively, so that a suggestion that the order of the gravity field model is selected to be 90 × 90 is given, and the following corresponding satellite orbit dynamics model is established.
In order to facilitate the description of the numerical integration of the satellite orbit in the gravity field, a representation method of the potential function of the earth gravity field is adopted, namely:
Figure BDA0002737567200000091
wherein the content of the first and second substances,
Figure BDA0002737567200000092
is the earth-centered position vector of the satellite;
Figure BDA0002737567200000093
is a function of the field potential of the earth's gravity.
The gravity field potential function includes two parts of earth central gravity and earth non-spherical gravity, and if the earth is considered as a rigid body and an equatorial plane is superposed with a basic plane of an epoch inertial system, the gravity field potential function can be expanded into a series form in the earth central inertial system as follows:
Figure BDA0002737567200000094
wherein mu is the gravitational constant of the earth, r is the earth center distance of the satellite, C n0 And C nm And S nm All are spherical harmonic coefficients, R e Is the equatorial radius,
Figure BDA0002737567200000101
Latitude of geocentric, λ of geocentricLongitude, both calculated from the position vector in the satellite earth's system;
Figure BDA0002737567200000102
and
Figure BDA0002737567200000103
the terms are Legendre and associated Legendre polynomials respectively, are correction parts of a real earth gravitational potential pair uniform sphere, comprise a band harmonic term and a field harmonic term, and reflect the unevenness of the earth.
The coefficient values of each order of the gravitational field potential function are obtained through the earth gravitational field table, the perturbation force expression under the satellite earth-fixed system can be obtained through calculation, and then the satellite position and the satellite speed are obtained through integration.
Preferably, the step B comprises the following steps:
step S4.1: according to the overall design constraint, giving a semi-major axis analytic solution a of the heavy rail interference track under the J2 low-order gravity field J2 Orbit dip angle analytic solution i J2 And a heavy track period T, a track turn number Q.
According to the load working power, the satellite weight, the carrying and launching capacity and other overall constraints, the semi-major axis a of the heavy-rail interference orbit can be determined J2 ；
Orbit dip analytic solution i J2 ：
Figure BDA0002737567200000104
Wherein J2=0.001082,
Figure BDA0002737567200000105
Track turn number Q, heavy track period T:
Figure BDA0002737567200000106
Figure BDA0002737567200000107
T＝T n ×Q
wherein, T n Is a period of intersection, w e Is the rotational angular velocity of the earth.
Step S4.2: and (4) according to the J2 perturbation analysis orbit, providing a J4 perturbation correction orbit based on a Newton iteration method. The research idea of the method is as follows:
step S4.2.1: selecting t according to the requirement of satellite task on ground track arrangement 0 Latitude and longitude lambda of time sub-satellite point 0 、
Figure BDA0002737567200000108
And establishing the following functional relationship of longitude and latitude of the repeated track with respect to the semi-major axis and the inclination angle.
Figure BDA0002737567200000109
Wherein the content of the first and second substances,
Figure BDA0002737567200000111
Figure BDA0002737567200000112
Figure BDA0002737567200000113
Figure BDA0002737567200000114
Figure BDA0002737567200000115
M＝n(t-t 0 )
G 0 is t 0 At time Greenwich mean sidereal time omega 0 Is t 0 The right ascension at the ascending crossing point of the moment,
Figure BDA0002737567200000116
is J 4 Ascension point right ascension drift rate in perturbation.
Step S4.2.2: and obtaining the following heavy rail interference track eccentricity and near-place argument initial value estimation by utilizing the constraint relation of the frozen track.
Figure BDA0002737567200000117
Step S4.2.3: as shown in the calculation flow of FIG. 2, firstly, the satellite t is used 0 Time ground track initial longitude and latitude lambda 0 、
Figure BDA0002737567200000118
Taking the starting point as the point of integration of the heavy track period T to obtain T 0 Satellite ground track longitude and latitude lambda at + T moment n 、
Figure BDA0002737567200000119
Then calculating to obtain the longitude and latitude deviation delta lambda = lambda of the initial end and the final end of the heavy rail n -λ 0 ，
Figure BDA00027375672000001110
Judging whether the deviation meets the heavy rail interference precision index or not; if the index is satisfied, outputting a semimajor axis and a tilt angle correction value a J4 、i J4 And if the iteration parameter is out of tolerance, the following parameter correction is carried out, and the integral judgment process is converted back until the iteration parameter meets the precision index.
a k ＝a k-1 +Δa k-1
i k ＝i k-1 +Δi k-1
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00027375672000001111
a k for the semi-major axis of the orbit at time k, a k-1 Is the semimajor axis of the track at time k-1, i k For the track inclination at time k, i k-1 Is the inclination angle of the orbit at the moment of k-1;
step S4.2.4: by utilizing the functional relationship between the semi-major axis and the inclination angle of the orbit and the longitude and latitude of the satellite point in the step S4.2.1, t can be obtained by calculation 0 Time a J4 、i J4 Corresponding rising point right ascension omega J4 Angle M close to the mean J4 。
As shown in fig. 3, the step C includes the following steps:
step S5.1: the problem of solving the track repeated nonlinear parameters under the high-order gravity field is converted into a multivariable and multi-target optimization problem, and the parameters are guided to be self-adaptively adjusted by combining target track characteristic information (freezing performance and regression period). The optimization model is described below.
Optimizing the target:
Figure BDA0002737567200000121
optimizing variables: [ Δ a, Δ e, Δ i, Δ Ω, Δ w, Δ M ]
Initial conditions: [ a ] A J4 ,e J3 ,i J4 ,Ω J4 ,w＝90°,M J4 ]
Constraint conditions are as follows:
Figure BDA0002737567200000122
delta a is correction of track semimajor axis, delta e is correction of track eccentricity, delta i is correction of track inclination angle, delta omega is correction of right ascension at track ascending intersection point, delta w is correction of amplitude at track perigee, delta M is correction of angle at track mean perigee,
Figure BDA0002737567200000123
is a vector of the acceleration of the satellite,
Figure BDA0002737567200000124
in order to be a satellite position deviation,
Figure BDA0002737567200000125
for the satellite position vector at time T,
Figure BDA0002737567200000126
is t 0 A time satellite position vector;
step S5.2: selecting individuals through a binary tournament method, and performing crossing and variation to generate a new population;
step S5.3: calculating and updating a new population target function value, namely satellite geostationary system position and speed deviation;
step S5.4: generating a new combined population by a merging method, and carrying out non-dominated sorting;
step S5.5: selecting individuals to form a new generation of population through a displacement and elite retention strategy;
step S5.6: and skipping to the step S5.2, and circularly updating until the termination condition is met.
In this embodiment, the design input is the orbit height 6989.90km, and the satellite initial starting point longitude and latitude are 0.135 ° S and 90.019 ° W. The 90 × 90-order earth gravity field model of the EGM2008 model is selected for orbit recursion, and the initial epoch is 0 minute 0 second (UTCG) at 6 months, 1 day, 12 hours, 2023 years.
As shown in table 1, firstly, according to the design constraint, obtaining an analytic solution and regression characteristics under the perturbation of the regression trajectory J2 according to step a; then obtaining a correction value under J4 perturbation on the basis according to the step B, and taking the correction value as an initial value of high-precision ground track repetitive orbit parameter adaptive optimization design; and finally, according to the step C, combining the track freezing characteristic and the regression characteristic determined in the initial value solving process to perform parameter self-adaptive optimization of the high-precision ground track repeated track until the regression precision meets centimeter-level design requirements (shown in a table 2), and outputting a group of high-precision ground track repeated track parameters.
TABLE 1 high-precision ground track repetitive orbit initial value and high-order optimization solution
Figure BDA0002737567200000127
Figure BDA0002737567200000131
TABLE 2 ground track position repeat accuracy
Figure BDA0002737567200000132
The invention provides a high-precision ground track repetitive track optimization system, which comprises:
a module A: and establishing a corresponding satellite orbit dynamics recursion model according to the requirement analysis of the earth gravity field non-spherical perturbation order.
And a module B: and (3) giving out heavy rail interference track parameters under the J2 low-order gravity field according to an analytical formula, and performing iterative calculation to obtain correction parameters under J4 perturbation, wherein the correction parameters are used as initial values of a high-precision ground track repeated track parameter adaptive setting algorithm.
And a module C: and according to the requirement of the repeated track precision, carrying out self-adaptive optimization setting on the target track parameter of the high-precision ground track repeated track parameter self-adaptive setting algorithm.
Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, units provided by the present invention as pure computer readable program code, the system and its various devices, modules, units provided by the present invention can be fully implemented by logically programming method steps in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system and various devices, modules and units thereof provided by the invention can be regarded as a hardware component, and the devices, modules and units included in the system for realizing various functions can also be regarded as structures in the hardware component; means, modules, units for realizing various functions can also be regarded as structures in both software modules and hardware components for realizing the methods.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (6)

1. A high-precision ground track repetitive track optimization method is characterized by comprising the following steps:
step A: according to the demand analysis of the earth gravity field non-spherical perturbation order, establishing a corresponding satellite orbit dynamics recursion model;
and B, step B: the method comprises the steps of providing heavy rail interference track parameters under a J2 low-order gravity field according to an analytical formula, and obtaining correction parameters under J4 perturbation through iterative calculation to serve as initial values of a high-precision ground track repeated track parameter self-adaptive setting algorithm;
and C: according to the requirement of the repeated track precision, carrying out self-adaptive optimization setting on the repeated track parameters of the high-precision ground track;
the step A comprises the following steps:
taking the numerical simulation test result as a basis, comprehensively considering the ground track repetition precision and the orbit recursion computation amount, establishing a satellite orbit dynamics model corresponding to the following steps, and adopting an expression method of an earth gravity field potential function:
Figure FDA0003883811350000011
wherein the content of the first and second substances,
Figure FDA0003883811350000012
is the earth-centered position vector of the satellite;
Figure FDA0003883811350000013
is the function of the field potential of the earth gravity;
the gravity field potential function comprises two parts of earth central gravity and earth non-spherical gravity, and if the earth is considered as a rigid body and an equatorial plane is superposed with a basic plane of an epoch inertial system, the gravity field potential function is expanded into a series form in the earth central inertial system as follows:
Figure FDA0003883811350000014
wherein mu is the gravitational constant of the earth, r is the earth center distance of the satellite, C n0 And C nm And S nm All are spherical harmonic coefficients, R e Is the equatorial radius,
Figure FDA0003883811350000015
The geocentric latitude and the lambda are geocentric longitude which are obtained by calculating a position vector in a satellite geostationary system;
Figure FDA0003883811350000016
and
Figure FDA0003883811350000017
the terms are Legendre and associated Legendre polynomials respectively, are correction parts of a real earth gravitational potential pair uniform sphere and comprise a band harmonic term and a field harmonic term;
acquiring each order coefficient value of a gravitational field potential function through an earth gravitational field table, calculating to obtain a perturbation force expression under a satellite geostationary system, and further integrating to obtain the position and the speed of the satellite;
the step B comprises the following steps:
step S4.1: according to the overall design constraint, giving a semi-major axis analytic solution a of the heavy rail interference track under the J2 low-order gravity field J2 And resolving the track inclination angle i J2 A heavy rail period T and a rail turn number Q;
according to load working power, satellite weight and carrying and launching capacity total constraints, a heavy-orbit interference orbit semi-major axis analytical solution a can be determined J2 ；
Orbit dip analytic solution i J2 ：
Figure FDA0003883811350000021
Wherein J2=0.001082,
Figure FDA0003883811350000022
Track number of turns Q, heavy rail period T:
Figure FDA0003883811350000023
Figure FDA0003883811350000024
T＝T n ×Q
wherein, T n Is a period of intersection, w e Is the angular velocity of rotation of the earth i J2 Resolving the orbit inclination angle;
step S4.2: according to the J2 perturbation analysis orbit, a J4 perturbation correction orbit based on a Newton iteration method is provided, and the method comprises the following steps:
step S4.2.1: selecting t according to the ground track arrangement requirement of the satellite task 0 Latitude and longitude lambda of time point under star 0 、
Figure FDA0003883811350000025
Establishing a functional relation of longitude and latitude about a semi-long axis and an inclination angle after the following track is repeated;
Figure FDA0003883811350000026
wherein the content of the first and second substances,
Figure FDA0003883811350000027
Figure FDA0003883811350000028
Figure FDA0003883811350000029
p＝a(1-e 2 ),J4＝-1.619×10 -6
A 2 ＝1.5R e ×J2,
Figure FDA00038838113500000210
Figure FDA00038838113500000211
M＝n(t-t 0 )
G 0 is t 0 At time Greenwich mean sidereal time omega 0 Is t 0 The right ascension point of the moment,
Figure FDA00038838113500000212
is the rising point right ascension drift rate under J4 perturbation;
step S4.2.2: obtaining the following heavy rail interference track eccentricity e by utilizing the constraint relation of the frozen track J3 And estimating the initial value of the argument w of the near place:
Figure FDA0003883811350000031
step S4.2.3: first with the satellite t 0 Time ground track initial longitude and latitude lambda 0 、
Figure FDA0003883811350000032
Taking the starting point as the point of integration of the heavy track period T to obtain T 0 Satellite ground track longitude and latitude lambda at + T moment n 、
Figure FDA0003883811350000033
Then calculating to obtain the longitude and latitude deviation delta lambda = lambda of the initial end of the heavy rail n -λ 0 ，
Figure FDA0003883811350000034
Judging whether the deviation meets the heavy rail interference precision index or not; if the index is satisfied, outputting a semimajor axis and a tilt angle correction value a J4 、i J4 If the iteration parameter is out of tolerance, the following parameter correction is carried out, and the integral judgment process is converted back again until the iteration parameter meets the precision index;
a k ＝a k-1 +Δa k-1
i k ＝i k-1 +Δi k-1
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003883811350000035
a k for the semi-major axis of the orbit at time k, a k-1 Is the semimajor axis of the track at time k-1, i k For the track inclination at time k, i k-1 Is the inclination angle of the orbit at the moment of k-1;
step S4.2.4: using the function relationship between the semi-major axis and the inclination angle of the orbit and the longitude and latitude of the satellite point in the step S4.2.1 to calculate and obtain t 0 Time a J4 、i J4 Corresponding rising point right ascension omega J4 Angle M close to the mean J4 。
2. A high accuracy ground track repeat trajectory optimization method as claimed in claim 1, wherein said repeat trajectory accuracy is less than 0.01m.
3. The high accuracy ground track repetitive orbit optimization method of claim 1, wherein the step C comprises:
step S5.1: the method comprises the steps of converting a track repeated nonlinear parameter solving problem under a high-order gravity field into a multivariable and multi-target optimization problem, guiding parameter self-adaptive setting by combining target track characteristic information, and describing an optimization model as follows:
optimizing the target:
Figure FDA0003883811350000036
optimizing variables: [ Δ a, Δ e, Δ i, Δ Ω, Δ w, Δ M ]
Initial conditions: [ a ] A J4 ,e J3 ,i J4 ,Ω J4 ,w＝90°,M J4 ]
Constraint conditions are as follows:
Figure FDA0003883811350000037
delta a is correction of track semimajor axis, delta e is correction of track eccentricity, delta i is correction of track inclination angle, delta omega is correction of right ascension at track ascending intersection point, delta w is correction of amplitude at track perigee, delta M is correction of angle at track mean perigee,
Figure FDA0003883811350000041
as a vector of the acceleration of the satellite,
Figure FDA0003883811350000042
in order to be a satellite position deviation,
Figure FDA0003883811350000043
for the satellite position vector at time T,
Figure FDA0003883811350000044
is t 0 A time satellite position vector;
step S5.2: selecting individuals through a binary system tournament method, and performing crossing and variation to generate a new population;
step S5.3: calculating and updating a new population objective function value, namely the position and speed deviation of the satellite earth-fixed system;
step S5.4: generating a new combined population by a merging method, and carrying out non-dominated sorting;
step S5.5: selecting individuals to form a new generation of population through a displacement and elite retention strategy;
step S5.6: and jumping to the step S5.2, and circularly updating until the termination condition is met.
4. A high-precision ground track repeat trajectory optimization system, comprising:
a module A: according to the requirement analysis of the earth gravity field non-spherical perturbation order, establishing a corresponding satellite orbit dynamics recursion model;
and a module B: according to an analytical formula, heavy-rail interference track parameters under a J2 low-order gravity field are given, correction parameters under J4 perturbation are obtained through iterative calculation and serve as initial values of a high-precision ground track repeated track parameter self-adaptive setting algorithm;
and a module C: according to the requirement of the repeated track precision, carrying out self-adaptive optimization setting on the repeated track parameters of the high-precision ground track;
the module A comprises:
taking the numerical simulation test result as a basis, comprehensively considering the ground track repetition precision and the orbit recursion computation amount, establishing a satellite orbit dynamics model corresponding to the following steps, and adopting an expression method of an earth gravity field potential function:
Figure FDA0003883811350000045
wherein the content of the first and second substances,
Figure FDA0003883811350000046
is the earth-centered position vector of the satellite;
Figure FDA0003883811350000047
is the function of the field potential of the earth gravity;
the gravity field potential function comprises two parts of earth central gravity and earth non-spherical gravity, and if the earth is considered as a rigid body and an equatorial plane is superposed with a basic plane of an epoch inertial system, the gravity field potential function is expanded into a series form in the earth central inertial system as follows:
Figure FDA0003883811350000048
wherein mu is the gravitational constant of the earth, r is the earth center distance of the satellite, C n0 And C nm And S nm All are spherical harmonic coefficients, R e Is the equatorial radius,
Figure FDA0003883811350000049
The geocentric latitude and the lambda are geocentric longitude which are obtained by calculating a position vector in a satellite geostationary system;
Figure FDA00038838113500000410
and
Figure FDA00038838113500000411
legendre and associated Legendre polynomials are respectively a correction part of a real earth gravitational potential to a uniform sphere, and comprise a band harmonic term and a field harmonic term;
obtaining each order coefficient value of a gravitational field potential function through an earth gravitational field table, calculating to obtain a perturbation force expression under a satellite geostationary system, and further integrating to obtain the position and the speed of the satellite;
the module B comprises:
module S4.1: according to the overall design constraint, giving a semi-major axis analytic solution a of the heavy rail interference track under the J2 low-order gravity field J2 And resolving the track inclination angle i J2 A heavy rail period T and a rail turn number Q;
according to load working power, satellite weight and total constraint of carrying and launching capacity, a heavy-orbit interference orbit semi-major axis analytic solution a can be determined J2 ；
Orbit dip analytic solution i J2 ：
Figure FDA0003883811350000051
Wherein J2=0.001082,
Figure FDA0003883811350000052
Track number of turns Q, heavy rail period T:
Figure FDA0003883811350000053
Figure FDA0003883811350000054
T＝T n ×Q
wherein, T n Is a period of intersection, w e Is the angular velocity of rotation of the earth i J2 Resolving the orbit inclination angle;
module S4.2: according to the J2 perturbation analysis orbit, a J4 perturbation correction orbit based on a Newton iteration method is provided, and the method comprises the following steps:
module s4.2.1: selecting t according to the requirement of satellite task on ground track arrangement 0 Latitude and longitude lambda of time sub-satellite point 0 、
Figure FDA0003883811350000055
Establishing a functional relation of longitude and latitude about a semi-major axis and an inclination angle after the following tracks are repeated;
Figure FDA0003883811350000056
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003883811350000061
Figure FDA0003883811350000062
Figure FDA0003883811350000063
p＝a(1-e 2 ),J4＝-1.619×10 -6
A 2 ＝1.5R e ×J2,
Figure FDA0003883811350000064
Figure FDA0003883811350000065
M＝n(t-t 0 )
G 0 is t 0 At time Greenwich mean sidereal time omega 0 Is t 0 The right ascension at the ascending crossing point of the moment,
Figure FDA0003883811350000066
is the ascent point right ascension drift rate under J4 perturbation;
module s4.2.2: obtaining the following heavy rail interference track eccentricity e by utilizing the constraint relation of the frozen track J3 And estimating the initial value of the argument w of the near place:
Figure FDA0003883811350000067
module s4.2.3: first with the satellite t 0 Time ground track initial longitude and latitude lambda 0 、
Figure FDA0003883811350000068
Taking the starting point as the point of integration of the heavy track period T to obtain T 0 Satellite ground track longitude and latitude lambda at + T moment n 、
Figure FDA0003883811350000069
Then calculateObtaining the longitude and latitude deviation delta lambda = lambda of the initial end and the final end of the heavy rail n -λ 0 ，
Figure FDA00038838113500000610
Judging whether the deviation meets the heavy rail interference precision index or not; if the index is satisfied, outputting a semimajor axis and a tilt angle correction value a J4 、i J4 If the iteration parameter is out of tolerance, the following parameter correction is carried out, and the integral judgment process is converted back again until the iteration parameter meets the precision index;
a k ＝a k-1 +Δa k-1
i k ＝i k-1 +Δi k-1
wherein the content of the first and second substances,
Figure FDA00038838113500000611
a k for the semi-major axis of the orbit at time k, a k-1 Is the semimajor axis of the track at time k-1, i k For the track inclination at time k, i k-1 Is the inclination angle of the orbit at the moment of k-1;
module s4.2.4: t is obtained by calculation according to the function relation between the semi-major axis and the inclination angle of the orbit in the module S4.2.1 and the longitude and latitude of the satellite point 0 Time a J4 、i J4 Corresponding rising point right ascension omega J4 Angle M close to the mean J4 。
5. A high accuracy ground track repetitive track optimization system as set forth in claim 4, wherein said repetitive track accuracy is less than 0.01m.
6. The high accuracy ground track repetitive track optimization system of claim 4, wherein the module C comprises:
module S5.1: the method comprises the steps of converting a track repeated nonlinear parameter solving problem under a high-order gravity field into a multivariable and multi-target optimization problem, guiding parameter self-adaptive setting by combining target track characteristic information, and describing an optimization model as follows:
optimizing the target:
Figure FDA0003883811350000071
optimizing variables: [ Δ a, Δ e, Δ i, Δ Ω, Δ w, Δ M ]
Initial conditions: [ a ] A J4 ,e J3 ,i J4 ,Ω J4 ,w＝90°,M J4 ]
Constraint conditions are as follows:
Figure FDA0003883811350000072
delta a is correction of track semimajor axis, delta e is correction of track eccentricity, delta i is correction of track inclination angle, delta omega is correction of right ascension at track ascending intersection point, delta w is correction of amplitude at track perigee, delta M is correction of angle at track mean perigee,
Figure FDA0003883811350000073
as a vector of the acceleration of the satellite,
Figure FDA0003883811350000074
in order to be a satellite position deviation,
Figure FDA0003883811350000075
for the satellite position vector at time T,
Figure FDA0003883811350000076
is t 0 A time satellite position vector;
module S5.2: selecting individuals through a binary system tournament method, and performing crossing and variation to generate a new population;
module S5.3: calculating and updating a new population objective function value, namely the position and speed deviation of the satellite earth-fixed system;
module S5.4: generating a new combined population by a merging method, and carrying out non-dominant sorting;
module S5.5: selecting individuals to form a new generation of population through a displacement and elite retention strategy;
module S5.6: and jumping to a module S5.2, and circularly updating until a termination condition is met.
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