CN115265540A - Method and device for acquiring strict regression orbit parameters - Google Patents

Abstract

The disclosure relates to a method and a device for acquiring strict regression orbit parameters, relates to the technical field of spacecrafts, and can solve the problem that the existing algorithm consumes a long time. The specific technical scheme is as follows: adopting an orbit analysis method, and considering an earth oblateness perturbation item J₂And J₃To obtain a set of rough regression trajectory flat roots; acquiring an instantaneous orbit root corresponding to the rough regression orbit root by adopting a calculation function of flat-to-instantaneous conversion; recursion of the orbit by using a numerical method, and iterative correction of a semimajor axis in the parameters of the instantaneous orbit root to obtain an initial value for optimizing the regression orbit root; and carrying out small-range optimization improvement on each orbit parameter and regression period in the regression orbit root number optimization initial value by adopting a nonlinear equation set so as to obtain a strict regression orbit parameter with higher regression precision. The method has the advantages of simple and easily understood calculation process, high solving efficiency and short calculation time, and can greatly save the design and analysis stage of the strict regression orbitAnd measuring the time.

Description

Method and device for acquiring strict regression orbit parameters

Technical Field

The disclosure relates to the technical field of spacecraft, in particular to a method and a device for acquiring strict regression orbit parameters.

Background

The strict regression orbit is a satellite operation reference orbit with new characteristics, which is provided for the recent satellite heavy-orbit earth observation task. The strict regression trajectory is characterized by the closeness of the beginning and end states in design. The trajectory of the intersatellite points of the rigorous regression trajectory obtained by iterative design is shown in fig. 1, and the trajectory is a set of completely determined reference points in a ground-fixed coordinate system. After the initial point orbit parameters and the regression period of the strict regression orbit are obtained, other space environment perturbation terms are ignored, only the earth gravitational field model is considered to carry out high-precision orbit extrapolation prediction, a target reference nominal orbit can be obtained, strict regression orbit keeping control is carried out, a satellite orbit heavy-orbit earth observation task is realized, the requirement of satellite load on satellite orbit precision is met, for example, for a long-term earth deformation or a revisit measurement task of geological disaster monitoring, the satellite orbit is controlled to move near a preset strict regression orbit in the whole service life, and the deviation is about hundreds of meters at most.

The existing traditional regression orbit design method only considers the perturbation of the earth oblateness term J2, adopts an analytic method to design a rough regression orbit, has poor ground orbit revisiting precision and has the deviation of several kilometers to dozens of kilometers, and the regression characteristic orbit can only meet the satellite orbit heavy orbit earth observation task with general precision. In another strict regression orbit design method using an intelligent optimization algorithm such as a genetic algorithm, the initial value of the intelligent optimization algorithm is not easy to obtain, for example, a differential iteration algorithm is used to solve the optimization initial value, a large number of partial derivative term formulas need to be derived, and the analytic design result is corrected; or by constructing a high-order Poincare mapping of the orbit state change of the satellite after a regression period from the initial state, a high-order Taylor expansion equation needs to be deduced, and the process is complex. In addition, the genetic algorithm is characterized in that the process of simulating the genetic variation and the gene selection in the nature is tried for a plurality of times, the calculation efficiency of solving the optimal solution is related to a variation probability set value, and generally, the calculation time is long in order to ensure the success of solving the global optimal solution.

Disclosure of Invention

In order to overcome the problems in the related art, embodiments of the present disclosure provide a method and an apparatus for obtaining a strict regression trajectory parameter. The technical scheme is as follows:

according to a first aspect of the embodiments of the present disclosure, there is provided a method for obtaining strict regression orbit parameters, including:

adopting an orbit analysis method, and considering an earth oblateness perturbation item J₂And J₃To obtain a set of rough regression trajectory flat roots;

acquiring an instantaneous orbit root corresponding to the rough regression orbit root by adopting a calculation function of flat-to-instantaneous conversion;

recursion of the orbit by using a numerical method, and iterative correction of a semimajor axis in the parameters of the instantaneous orbit number to obtain an initial regression orbit number optimization value;

and carrying out small-range optimization improvement on each orbit parameter and regression period in the regression orbit root number optimization initial value by adopting a nonlinear equation set so as to obtain a strict regression orbit parameter with higher regression precision.

In one embodiment, the orbit analysis method is adopted, and the earth oblateness perturbation item J is considered₂And J₃To obtain the rough regression orbit number, including:

according to the constraint relation between the satellite orbit intersection point period and the fixed star period parameter, the semimajor axis a is calculated according to the following iterative formula_k+1：

Wherein, a normalization unit is adopted

Calculating and iteratively calculating an initial value a_k＝1，

When | a_k+1-a_kWhen the absolute value is less than 0.00000001, the iteration is finished to obtain the semimajor axis a_k+1；

According to formula a'₀＝a_k+1·R_ePerforming a denormalization calculation;

according to the relation between the semi-major axis and the ground track, correcting the a 'by adopting the formula'₀：

a₀＝a′₀+Δa；

Wherein, the first and the second end of the pipe are connected with each other,

wherein, the N is_dayThe number of days of regression; said N is_cirThe number of regression total turns; μ is an earth gravity constant; the R is_eIs the average radius of the equator of the earth; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the ω is₀Is the argument of the perigee.

In one embodiment, the method further comprises:

obtaining the track inclination angle i according to the following formula₀：

Wherein the semi-major axis a'₀The initial estimate is given by the following formula:

wherein T is the satellite orbit period.

In one embodiment, the method further comprises:

calculating the eccentricity according to the frozen track characteristic and the following iterative formula:

wherein, said e_nThe initial value of (2) belongs to (0, 0.002);

when | e_n+1-e_n|＜10^-7The iteration is finished to obtain the eccentricity e₀。

In one embodiment, the obtaining, by using a flat transient transformation calculation function, an instantaneous orbit root corresponding to the rough regression orbit root includes:

obtaining the instantaneous orbit number corresponding to the rough regression orbit number through the following formula:

wherein the Mean2Osc (σ) is a computational function of a flat transient; a is a₀Is a semi-major axis; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the omega₀Is the original ascension crossing point, the omega₀Is the argument of the near place; said M₀Is a flat proximal angle.

In one embodiment, the iteratively correcting the semimajor axis in the parameter of the instantaneous orbit root by using a numerical method to recur the orbit to obtain an initial value for optimizing the regression orbit root includes:

starting epoch time t₀Instantaneous orbital radical of time σ_oscConverting the position speed into the position speed under the J2000 inertial coordinate system, and calculating the longitude Lon of the subsatellite point in the earth-fixed coordinate system ECEF₀；

The regression cycle was calculated according to the following formula:

using numerical integration to integrate the sigma_oscExtrapolation prediction of a regression cycle T_regressAcquiring the position and the speed of the satellite in the J2000 inertial system at the end time of the period, and calculating the longitude Lon of the point under the satellite in the earth-fixed coordinate system ECEF_T；

According to the relationship between the satellite orbit period and the semimajor axis, improving the initial value of the semimajor axis of the regression orbit parameter by adopting a numerical iteration method of the following formula:

wherein, the first and the second end of the pipe are connected with each other,

ΔLon＝Lon_T-Lon₀(ii) a The omega_eIs the earth rotation angular rate;

substituting the new orbit parameter semimajor axis as an initial value into a formula corresponding to the regression period, and repeating the steps until the absolute value delta T is obtained_orbit|＜ΔT_epsWherein, the Δ T_epsIteratively correcting a convergence threshold for a strict regression trajectory of the LEO;

after the iteration is finished, acquiring the orbit parameter sigma obtained by the iteration_oscThe regression period is T_regress。

In one embodiment, the performing, by using a nonlinear equation set, a small-range optimization improvement on each orbit parameter and regression cycle in the regression orbit root optimization initial value to obtain a strict regression orbit parameter with higher regression accuracy includes:

according to the earth gravity field data model file, selecting a high-order earth gravity field perturbation model order according to the initial orbit parameter (t)₀，σ_osc) Calculating the position velocity of the satellite under the earth-fixed coordinate system ECEF at the initial moment by using the coordinate conversion function, and recording as (r)₀，v₀)；

Recursion of satellite orbit by a regression period T_regressCalculating the position speed at the end of the regression period, calculating the position speed of the satellite in the earth-fixed coordinate system ECEF at the initial moment by using the coordinate transfer function, and recording as (r)_f，v_f)；

Calculating the position error and the speed error of the start-stop moment of the next regression period of the earth-fixed coordinate system ECEF:

Δr＝|r_f-r₀|

Δv＝|v_f-v_f|；

taking the process as a nonlinear equation set to be solved of the minpack algorithm:

{Δr_x，Δr_y，Δr_z，1000·Δv_x，1000·Δv_y，1000·Δv_z}＝F(σ_osc，T_regress)≈0；

due to a small speed error, the position error is quickly diverged under the action of time accumulation, and the precision requirement of strict regression cannot be met. The speed error is multiplied by 1000 as an amplification factor, which is similar to a constraint penalty factor when an optimization target is constructed in an intelligent optimization algorithm.

According to the variation range of searching and solving of each track parameter in the Minpack algorithm, a group of track initial roots and a corresponding strict regression period are obtained by utilizing the solving capability of a nonlinear equation set of the Minpack algorithm, so that the regression revisiting precision of the reference track under the earth-fixed system can meet the following formula:

according to a second aspect of the embodiments of the present disclosure, there is provided an apparatus for obtaining strict regression orbit parameters, including:

a first acquisition module for adopting an orbit analysis method and considering an earth oblateness perturbation item J₂And J₃To obtain a set of rough regression orbit flat roots

A is a₀Is a semi-major axis; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the omega₀Is the original ascension crossing point, the omega₀Is the argument of the near place; the M is₀Is a flat proximal angle;

the second acquisition module is used for acquiring the instantaneous orbit number corresponding to the rough regression orbit number by adopting a calculation function of flat transient conversion;

a third obtaining module, configured to recur the orbit by using a numerical method, and iteratively correct the semi-major axis in the parameter of the instantaneous orbit root to obtain an initial value σ for optimizing the regression orbit root_osc(a₁，e₁，i₁，Ω₁，ω₁，M₁)；

A fourth obtaining module, configured to perform small-range optimization and improvement on each orbit parameter and regression period in the regression orbit root optimization initial value by using a nonlinear equation set to obtain a strict regression orbit parameter σ with high regression accuracy^*(a^*，e^*，i^*，Ω^*，ω^*，M^*)。

According to a third aspect of the embodiments of the present disclosure, there is provided an apparatus for obtaining strict regression orbit parameters, including:

a processor;

a memory for storing processor-executable instructions;

wherein the processor is configured to:

an orbit analysis method is adopted, and an earth oblateness perturbation item J is considered₂And J₃To obtain a set of rough regression orbit flat roots

A is a₀Is a semi-major axis; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the omega₀Is the original ascension crossing point, the omega₀Is a perigee argument; said M₀Is a flat proximal angle;

acquiring an instantaneous orbit root corresponding to the rough regression orbit root by adopting a calculation function of flat-to-instantaneous conversion;

recursion of the orbit by using a numerical method, and iterative correction of the semimajor axis in the parameters of the instantaneous orbit root to obtain an initial value sigma of regression orbit root optimization_osc(a₁，e₁，i₁，Ω₁，ω₁，M₁)；

Performing small-range optimization improvement on each orbit parameter and regression period in the regression orbit root number optimization initial value by adopting a nonlinear equation set to obtain a strict regression orbit parameter sigma with higher regression precision^*(a^*，e^*，i^*，Ω^*，ω^*，M^*)。

According to a fourth aspect of embodiments of the present disclosure, there is provided a computer-readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method of any one of the first aspects.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure.

FIG. 1 is a diagram illustrating a trajectory of sub-satellite points of a strict regression orbit resulting from an iterative design, according to an exemplary embodiment.

FIG. 2 is a flow diagram illustrating a method of obtaining strict regression trajectory parameters, according to an exemplary embodiment.

FIG. 3 is a flow diagram illustrating a method of obtaining strict regression trajectory parameters, according to an example embodiment.

Fig. 4 is a block diagram illustrating an apparatus for obtaining strict regression trajectory parameters according to an example embodiment.

Detailed Description

Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the exemplary embodiments below are not intended to represent all implementations consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the disclosure, as detailed in the appended claims.

Aiming at the defects of the existing regression orbit design method, the invention provides a simple strict regression orbit design method, which combines an analytical method and a numerical method to design a strict regression orbit parameter meeting the input condition constraint. The design method of the present invention can be described as follows:

the input parameters are given orbit inclination angle, regression days, regression total turns and the like, firstly, an orbit design analysis method is utilized, earth oblateness perturbation items J2 and J3 are considered, iterative correction calculation is carried out, and a group of rough regression orbit flat-root numbers are designed

Then, performing flat transient conversion to convert the number into the transient orbit number; then, the orbit is recurred by using a numerical method, and the semimajor axis a in the transient root parameter is subjected to₀Carrying out iterative correction to reduce the longitude deviation of the satellite subsatellite point locus after a regression period to obtain a regression orbit root optimization initial value sigma_osc(a₁，e₁，i1，Ω₁，ω₁，M₁) (ii) a Finally, converting the regression position error and the weighted speed error of the strict regression orbit into a nonlinear equation set problem of the initial parameters and the regression period of the orbit, and solving an initial value sigma by adopting a nonlinear equation set solving tool minpack_oscThe parameters of each orbit and the regression period in the process are optimized and improved in a small range, and a strict regression orbit parameter sigma with higher regression precision can be obtained^*(a^*，e^*，i^*，Ω^*，ω^*，M^*) The method steps of the present invention are described in detail below.

Fig. 2 and 3 are flowcharts illustrating a method for obtaining strict regression trajectory parameters according to an exemplary embodiment, and as shown in fig. 2 and 3, the method includes the following steps S101-S104:

in step S101, an orbit analysis method is adopted, and the earth oblateness perturbation item J is considered₂And J₃To obtain a set of rough regression trajectory flat roots

a₀Is a semi-major axis; e.g. of the type₀Is the eccentricity; i.e. i₀Is the track inclination angle; omega₀Is the original ascension crossing point right ascension channel, omega₀Is the argument of the near place; m₀Is a flat proximal angle;

input parameters may be acquired before step S101 is performed, the input parameters including:

days of regression N_dayReturn to the total number of turns N_citInitial epoch t₀Eccentricity e₀Argument of near place omega₀The inclination angle of the track is i₀(if the task requires a sun synchronous orbit, the inclination angle needs to be determined by semimajor axis calculation at first), and the earth oblateness perturbation term J₂、J₃Constant of global gravity μ = G · M_eEquator mean radius of the earth R_e. When the task requirement is a near-circular orbit, let the eccentricity e₀=0, argument of perigee ω₀Can be any value; when the task requires non-circular orbit, e₀And ω₀A given value is taken.

Calculating the initial value a of the semimajor axis₀：

Further, if the task requirement is that the sun synchronously returns to the orbit, the orbit inclination angle i needs to be determined first₀(ii) a If the mission requires a non-sun synchronous orbit, i.e. the determined orbit inclination angle i is known₀Then the semimajor axis initial value can be directly calculated iteratively.

In one embodiment, the method further comprises:

acquiring an orbit inclination angle i according to the following formula according to the characteristics of the sun synchronous orbit₀：

Wherein, the semi-major axis a'₀The initial estimate is given by the following formula:

wherein T is the satellite orbit period.

In one embodiment, an orbit resolution method is employed, taking into account the earth's ellipticity perturbation term J₂And J₃To obtain the rough regression orbit number

The method comprises the following substeps:

a1, calculating a semi-major axis a by using a constraint relation between a satellite orbit intersection point period and a fixed star period parameter through the following iterative formula_k+1：

Using normalized unit calculation, i.e.

Setting an initial value a of iterative computation_k＝1；；

When | a_k+1-a_kWhen | < 0.00000001, the iteration is finished to obtain a_k+1；

A2, performing denormalization calculation according to the following formula;

a′₀＝a_k+1·R_e (6)

a3, correcting a 'according to the following formula according to the relation between the semi-major axis and the ground track'₀：

a₀＝a′₀+Δa (7)；

Wherein the content of the first and second substances,

n is the track angular velocity:

wherein, N_dayThe number of days of regression; n is a radical of hydrogen_cirThe number of regression total turns is; mu is an earth gravity constant; r_eIs the average radius of the equator of the earth; e.g. of the type₀Is the eccentricity; i.e. i₀Is the track inclination angle; omega₀Is the argument of the perigee.

Calculating the eccentricity ratio:

further, if the task request is a circular orbit or the eccentricity is not specified, the eccentricity e is calculated by using the frozen orbit characteristic and the following formula₀This eccentricity may be referred to as the frozen eccentricity; if the task requires the specification of eccentricity e₀This step is skipped.

The frozen orbit is a stable equilibrium solution of a kinetic equation, the long-term variation terms of the eccentricity and the perigee argument are zero, and once the orbit is adjusted to be close to the nominal value of the orbit, the subsequent arch wire oscillates in a small range without active control. According to the characteristic of the frozen orbit, the stability of the satellite orbit arch line in the orbit plane can be realized, and the consistency of the orbit height during the satellite point revisit can be ensured.

At this time, the method further includes:

the frozen eccentricity is calculated according to the following iterative formula:

wherein e is_nThe initial value of (b) can be arbitrarily selected within the range of (0, 0.002);

when | e_n+1-e_n|＜10^-7The iteration is finished to obtain the eccentricity e₀。

Obtaining kernels of frozen orbit parametersThe center is the calculated freezing eccentricity and the argument omega of the perigee is₀Eccentricity e =90 ° as an example_nThe initial value can be arbitrarily selected in the range of (0, 0.002), and the iterative calculation formula of freezing eccentricity is shown as (12).

Flat transient conversion:

in step S102, an instantaneous orbit number corresponding to the rough regression orbit number is obtained by using a calculation function of the flat transient conversion;

through the steps, a is determined₀，e₀，i₀，ω₀Initial rising point right ascension omega₀Flat near point angle M₀Can be arbitrarily specified. Thus, the rough regression orbit number is obtained

The set of orbital elements is the average element and needs to be converted to the instantaneous element before proceeding to the next numerical integration extrapolation calculation.

In one embodiment, the obtaining of the instantaneous orbit number corresponding to the rough regression orbit number by using the flat transient conversion calculation function includes:

obtaining the instantaneous orbit number corresponding to the rough regression orbit number by the following formula:

wherein Mean2Osc (σ) is a calculation function of the flat transient conversion; a is a₀Is a semi-major axis; e.g. of the type₀Is the eccentricity; i.e. i₀Is the track inclination angle; omega₀Is the original right ascension point right ascension, omega₀Is a perigee argument; m₀Is a flat proximal angle.

Wherein Mean2Osc (σ) is a calculation function of a normal functional flat-transient transformation in the field, and is not described herein again.

Correcting the semimajor axis, and calculating a regression period:

in step S1+3, recursion of the orbit by using a numerical method is utilized, and iterative correction is carried out on the semimajor axis in the parameter of the instantaneous orbit root number to obtain an initial value for optimizing the regression orbit root numberσ_osc0(a₁，e₁，i₁，Ω₁，ω₁，M₁)；

The orbit parameters obtained by the algorithm calculation are all J in the earth non-spherical gravity perturbation term only considered₂、J₃And in order to meet the high-precision regression orbit characteristic, a high-precision numerical integration method is required to be adopted to integrate the perturbation acceleration item of the high-order earth gravity field to obtain a regression orbit parameter with higher precision. The numerical integration orbit extrapolation algorithm in the step considers the 30 × 30 order earth non-spherical gravity perturbation term, the orbit extrapolation algorithm is represented by Ephem, the satellite position and velocity conversion is represented by Convert, and the functions are common function functions in the field and are not repeated herein.

Specifically, a numerical method is used for recursion of the orbit, and the semimajor axis in the parameters of the instantaneous orbit number is subjected to iterative correction to obtain an initial regression orbit number optimization value sigma_osc0(a₁，e₁，i₁，Ω₁，ω₁，M₁) The method comprises the following steps:

starting epoch time t₀Instantaneous orbital radical of time σ_oscConverting the position speed into the position speed under the J2000 inertial coordinate system, and calculating the longitude Lon of the subsatellite point in the earth-fixed coordinate system ECEF₀；

Using a₀The regression cycle is calculated according to the following formula:

in order to ensure the calculation precision and the convergence of the subsequent iterative calculation, the calculation regression period should be combined with the actual extrapolation verification of a numerical integration method, and the flat root phase amplitude angle at the starting moment is compared

And extrapolating the number of regression turns N_cirSatellite behind circle

To determine the actual regression cycle, the comparison threshold may be empirically set to an amplitude value of 1 second of operation of the LEO satellite, i.e. about 0.06 °.

Using numerical integration to integrate sigma_oscExtrapolation prediction of a regression period T_regressAcquiring the position and the speed of the satellite in the J2000 inertial system at the end time of the period, and calculating the longitude Lon of the point under the satellite in the earth-fixed coordinate system ECEF_TThen, there are:

ΔLon＝Lon_T-Lon₀ (17)

according to the rotation angular rate omega of the earth_eAnd further has the characteristics of that,

according to the relationship between the satellite orbit period and the semimajor axis, improving the initial value of the semimajor axis of the regression orbit parameter by adopting a numerical iteration method of the following formula:

substituting the new orbit parameter semimajor axis as an initial value into a formula (16) corresponding to the regression period, and repeating the steps until the absolute value of delta T_orbit|＜ΔT_epsWherein, Δ T_epsIs the convergence threshold of the iterative process described above.

Empirically, the LEO strictly regresses the iterative correction of the orbit to converge on the threshold value DeltaT_epsGenerally, it may be taken to be 0.02s.

At this time, for the design of the sun synchronous regression orbit, since the semimajor axis is corrected and adjusted in a large range, it is necessary to adjust the semimajor axis according to the new semimajor axis a₀Re-correcting and calculating the track inclination i by the formula (1)₀。

After the iteration is finished, acquiring the orbit parameter sigma obtained by the iteration_oscThe regression period is T_regress。

Optimizing and improving strict regression orbit parameters:

in step S104, adoptUsing a nonlinear equation set to carry out small-range optimization improvement on each orbit parameter and regression period in the regression orbit root number optimization initial value so as to obtain a strict regression orbit parameter sigma with higher regression precision^*(a^*，e^*，i^*，Ω^*，ω^*，M^*)。

The track parameters generated by the algorithm have better regression characteristics, and in order to obtain high-precision strict regression track parameters, a nonlinear problem solving tool kit minpack is adopted in the step, so that the initial values of the track parameters are further improved and optimized. minpack is a functional toolkit for solving a nonlinear system of equations using a Jacobian matrix, where solving for an exact regression trajectory can improve the speed of the optimal solution. The method comprises the following specific steps:

according to the earth gravity field data model file, selecting a higher order earth gravity field perturbation model order (for example, the highest order earth gravity field perturbation model order as much as possible, such as 90 × 90 order), and according to the initial orbit parameter (t)₀，σ_osc) Calculating the position and the speed of the satellite under the earth-fixed coordinate system ECEF at the initial moment by using the coordinate conversion function, and recording as (r)₀，v₀)；

Recursion of satellite orbit by a regression period T_regressCalculating the position speed at the end of the regression period, calculating the position speed of the satellite in the earth-fixed coordinate system ECEF at the initial moment by using the coordinate transfer function, and recording as (r)_f，v_f)；

Calculating the position error and the speed error of the start-stop moment of the next regression period of the earth-fixed coordinate system ECEF:

taking the process as a nonlinear equation set to be solved of the minpack algorithm:

{Δr_x，Δr_y，Δr_z，1000·Δv_x，1000·Δv_y，1000·Δv_z}＝F(σ_osc，T_regress)≈0；

due to a small speed error, the position error is quickly diverged under the action of time accumulation, and the precision requirement of strict regression cannot be met. The speed error is multiplied by 1000 as an amplification factor, which is similar to a constraint penalty factor when an optimization target is constructed in an intelligent optimization algorithm.

According to the search solving variation range of each track parameter in the Minpack algorithm, a group of track initial roots and a corresponding strict regression period are obtained by utilizing the solving capability of a nonlinear equation set of the Minpack algorithm, so that the regression revisiting precision of the reference track under the earth-fixed system can meet the following formula:

the search solving variation range setting for each track parameter in the Minpack algorithm is shown in table 1.

TABLE 1 optimal adjustment Range in the targeting Algorithm

Parameter(s)

Δa

Δe

Δi

ΔΩ

Δω

ΔM

ΔTregress

Range

±500m

±0.0002

0°

0°

±0.5°

±1.5°

±2s

The implementation process is described in detail by the following embodiments.

1. The following input parameters are obtained:

initial epoch time t ₀12 in 2022, 4-month, 18-day, beijing.

Ascent point right ascension omega₀Peace proximal angle M₀The design process is not influenced, and the design process can be arbitrarily specified. Both are set to 0 here.

Other parameters are fixed constant terms, and the universal standard value in the field is adopted.

2. Calculating the initial value of the semimajor axis

Calculating to obtain a semi-major axis initial value a according to the iterative algorithm in the step 2₀＝6938016.696m

3. Calculating freezing eccentricity

Obtaining the frozen eccentricity e₀＝0.001068497。

4. Flat transient conversion

The plain root obtained by the above steps is:

after the flat transient transformation, the transient root is obtained as follows:

5. correcting semimajor axis, calculating regression period

Selecting the perturbation order of the earth gravity field as 30 multiplied by 30, and correcting the semimajor axis by using a numerical integration method to obtain the semimajor axis a of the transient root₀=6928656.468m, the convergence condition is satisfied in the first iteration, so the semi-major axis is unchanged. At this time, the regression cycle of the regression trajectory is: t is_regress＝86379s；

The regression position error under the geosynthetic system is:

6. solving strict regression orbit parameters

Substituting the orbit parameters and the accurate regression period obtained in the last step into a minpack algorithm module, selecting the perturbation order of the earth gravity field as 70 multiplied by 70, and obtaining the final strict regression orbit parameters after iterative optimization:

the initial transient parameters of the orbit are as follows:

the regression cycle was: t is_regress＝86379s；

The regression error under the earth's fixation is:

referring to fig. 3, it can be seen that the regression error of the strict regression orbit parameter is greatly reduced, and the regression error can be completely used as a reference orbit parameter for maintaining and controlling the corresponding pipeline radius, so as to complete a high-precision revisit task similar to the SAR remote sensing satellite earth observation.

The analytical method and numerical method combined optimization design method provided by the disclosure simplifies theoretical formula derivation in the conventional regression orbit design process, adopts a simple analytical method to iteratively calculate initial values, and further improves the initial values of the orbit parameters by recursion of the orbit by using a high-precision numerical method, thereby combining the advantages of the two modes. In addition, the regression position error and the weighted speed error of the strict regression orbit are converted into the problem of the nonlinear equation set of the initial parameters and the regression period of the orbit, and the problem is solved by adopting a mature nonlinear equation set solving tool minpack, so that the optimal design of the parameters of the strict regression orbit can be completed quickly. Due to the adoption of the progressive design and optimization method, the calculation process is simple and easy to understand, the solving efficiency is high, the calculation time is short, and a large amount of time can be saved for the design and analysis stage of the strict regression orbit.

Based on the method for obtaining the strict regression trajectory parameter described in the embodiment corresponding to fig. 1, the following is an embodiment of the apparatus of the present disclosure, and may be used to implement the embodiment of the method of the present disclosure.

The embodiment of the present disclosure provides an apparatus for obtaining a strict regression orbit parameter, as shown in fig. 4, including:

a first obtaining module 11, configured to adopt an orbit analysis method and consider an earth oblateness perturbation term J₂And J₃To obtain a set of rough regression orbit flat roots

A is a₀Is a semi-major axis; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the omega₀Is the original ascension crossing point, the omega₀Is the argument of the near place; the M is₀Is a flat proximal angle;

the second obtaining module 12 is configured to obtain an instantaneous orbit root corresponding to the rough regression orbit root by using a calculation function of flat-to-transient conversion;

a third obtaining module 13, configured to iteratively correct the semimajor axis in the parameter of the instantaneous orbit root by using a numerical method to recur the orbit, so as to obtain an initial value σ for optimizing the regression orbit root_osc(a₁，e₁，i₁，Ω₁，ω₁，M₁)；

A fourth obtaining module 14, configured to perform a small-range optimization and improvement on each orbit parameter and regression cycle in the regression orbit root optimization initial value by using a nonlinear equation set to obtain a strict regression orbit parameter σ with higher regression accuracy^*(a^*，e^*，i^*，Ω^*，ω^*，M^*)。

In one embodiment, the first obtaining module is specifically configured to:

according to the constraint relation between the satellite orbit intersection point period and the fixed star period parameter, the semimajor axis a is calculated according to the following iterative formula_k+1：

Wherein, a normalization unit is adopted

Calculating and iteratively calculating an initial value a_k＝1，

When | a_k+1-a_kWhen the absolute value is less than 0.00000001, the iteration is finished to obtain the semimajor axis a_k+1；

According to formula a'₀＝a_k+1·R_ePerforming a denormalization calculation;

according to the relation between the semi-major axis and the ground track, correcting the a 'by adopting the formula'₀：

a₀＝a′₀+Δa；

Wherein the content of the first and second substances,

wherein, the N is_dayThe number of days of regression; said N is_cirThe number of regression total turns; μ is an earth gravity constant; the R is_eIs the average radius of the equator of the earth; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the omega₀Is the argument of the perigee.

In one embodiment, the first obtaining module is specifically configured to:

obtaining the track inclination angle i according to the following formula₀：

Wherein, the semi-major axis a'₀The initial estimate is given by the following formula:

wherein T is the satellite orbit period.

In one embodiment, the first obtaining module is specifically configured to:

calculating the eccentricity according to the frozen track characteristic and the following iterative formula:

wherein, said e_nThe initial value of (2) belongs to (0, 0.002);

when | e_n+1-e_n|＜10^-7The iteration is finished to obtain the eccentricity e₀。

In an embodiment, the second obtaining module is specifically configured to:

obtaining the instantaneous orbit number corresponding to the rough regression orbit number through the following formula:

wherein the Mean2Osc (σ) is a computational function of a flat transient; a is a₀Is a semi-major axis; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the omega₀Is the original ascension crossing point, the omega₀Is a perigee argument; the M is₀Is a flat proximal angle.

In one embodiment, the third obtaining module is specifically configured to:

starting epoch time t₀Instantaneous orbital radical of time σ_oscConverting the position speed into the position speed under the J2000 inertial coordinate system, and calculating the longitude Lon of the subsatellite point in the earth-fixed coordinate system ECEF₀；

The regression period was calculated according to the following formula:

using numerical integration to integrate the sigma_oscExtrapolation prediction of a regression cycle T_regressAcquiring the satellite at the end of the cycleThe position and the speed under the J2000 inertial system are calculated, and the longitude Lon of the point under the satellite in the earth-fixed coordinate system ECEF is calculated_T；

According to the relationship between the satellite orbit period and the semimajor axis, improving the initial value of the semimajor axis of the regression orbit parameter by adopting a numerical iteration method of the following formula:

wherein the content of the first and second substances,

ΔLon＝Lon_T-Lon₀(ii) a The ω is_eIs the earth rotation angular rate;

substituting the new orbit parameter semimajor axis as an initial value into a formula corresponding to the regression period, and repeating the steps until the absolute value delta T is obtained_orbit|＜ΔT_epsWherein, the Δ T_epsIteratively correcting a convergence threshold for a strict regression trajectory of the LEO;

after the iteration is finished, acquiring an orbit parameter sigma obtained by the iteration_oscThe regression period is T_regress。

In one embodiment, the fourth obtaining module is specifically configured to:

according to the earth gravity field data model file, selecting a high-order earth gravity field perturbation model order according to the initial orbit parameter (t)₀，σ_osc) Calculating the position velocity of the satellite under the earth-fixed coordinate system ECEF at the initial moment by using the coordinate conversion function, and recording as (r)₀，v₀)；

Recursion of satellite orbit by a regression period T_regressCalculating the position and speed at the end of the regression period, and calculating the position and speed of the satellite under the earth-fixed coordinate system ECEF at the initial moment by using the coordinate conversion function, and recording as (r)_f，v_f)；

Calculating the position error and the speed error of the start-stop moment of the next regression period of the earth-fixed coordinate system ECEF:

Δr＝|r_f-r₀|

Δv＝|v_f-v_f|；

taking the process as a nonlinear equation set to be solved of the minpack algorithm:

{Δr_x，Δr_y，Δr_z，1000·Δv_x，1000·Δv_y，1000·Δv_z}＝F(σ_osc，T_regress)≈0；

due to a small speed error, the position error is quickly diverged under the action of time accumulation, and the precision requirement of strict regression cannot be met. The speed error is multiplied by 1000 as an amplification factor, which is similar to a constraint penalty factor when an optimization target is constructed in an intelligent optimization algorithm.

According to the search solving variation range of each track parameter in the Minpack algorithm, a group of track initial roots and a corresponding strict regression period are obtained by utilizing the solving capability of a nonlinear equation set of the Minpack algorithm, so that the regression revisiting precision of the reference track under the earth-fixed system can meet the following formula:

based on the method for obtaining the strict regression track parameter described in the embodiment corresponding to fig. 1, an embodiment of the present disclosure further provides a computer-readable storage medium, for example, the non-transitory computer-readable storage medium may be a Read Only Memory (ROM), a Random Access Memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, and the like. The storage medium stores computer instructions for executing the method for obtaining the strict regression trajectory parameters described in the embodiment corresponding to fig. 1, which is not described herein again.

Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.

It will be understood that the present disclosure is not limited to the precise arrangements that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.

Claims (10)

1. A method for obtaining strict regression orbit parameters is characterized by comprising the following steps:

adopting an orbit analysis method, and considering an earth oblateness perturbation item J₂And J₃Obtaining a group of rough regression orbit flat roots;

acquiring an instantaneous orbit root corresponding to the rough regression orbit root by adopting a calculation function of flat-to-instantaneous conversion;

recursion of the orbit by using a numerical method, and iterative correction of a semimajor axis in the parameters of the instantaneous orbit number to obtain an initial regression orbit number optimization value;

and carrying out small-range optimization improvement on each orbit parameter and regression period in the regression orbit root number optimization initial value by adopting a nonlinear equation set so as to obtain a strict regression orbit parameter with higher regression precision.

2. The method according to claim 1, wherein the orbit analysis method is adopted, and the earth oblateness perturbation term J is considered₂And J₃To obtain the rough regression orbit number, including:

calculating the semimajor axis a according to the constraint relation between the satellite orbit intersection point period and the fixed star period parameter and the following iterative formula_k+1：

Wherein, adoptNormalized unit

Calculating and iteratively calculating an initial value a_k＝1，

δ＝[(-12-22e₀ ²)+(16+29e₀ ²)·sin²i₀+(16-20sin²i₀)·e₀cosω₀-(12-15sin²i₀)·e₀ ²cos2ω₀]；

When | a_k+1-a_kWhen the absolute value is less than 0.00000001, the iteration is finished to obtain the semi-long axis a_k+1；

According to the formula a₀′＝a_k+1·R_ePerforming a denormalization calculation;

according to the relation between the semi-major axis and the ground track, correcting the a 'by adopting the formula'₀：

a₀＝a′₀+Δa；

Wherein, the first and the second end of the pipe are connected with each other,

wherein, the N is_dayThe number of days of regression; said N is_cirThe number of regression total turns is; the muIs the constant of the earth's gravity; the R is_eIs the average radius of the equator of the earth; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the omega₀Is the argument of the perigee.

3. The method of claim 2, further comprising:

obtaining the track inclination angle i according to the following formula₀：

Wherein, the semi-major axis a'₀The initial estimate is given by the following formula:

wherein T is the satellite orbit period.

4. The method of claim 1, further comprising:

calculating the eccentricity according to the frozen track characteristic and the following iterative formula:

wherein, said e_nThe initial value of (2) belongs to (0, 0.002);

when | e_n+1-e_n|＜10^-7The iteration is finished to obtain the eccentricity e₀。

5. The method according to claim 1, wherein the obtaining the instantaneous orbit number corresponding to the rough regression orbit number by the flat transient transformation calculation function comprises:

obtaining the instantaneous orbit number corresponding to the rough regression orbit number by the following formula:

wherein the Mean2Osc (σ) is a calculation function of the flat transient conversion; a is a₀Is a semi-major axis; said e₀Is the eccentricity; i is described₀Is the track inclination angle; the omega₀Is the original ascension crossing point, the omega₀Is the argument of the near place; the M is₀Is a flat proximal angle.

6. The method of claim 1, wherein the iteratively modifying the semimajor axis in the parameter of the instantaneous orbit root by using a numerical method to recur the orbit to obtain an initial value for optimizing the regression orbit root comprises:

starting epoch time t₀Instantaneous orbital radical of time σ_oscConverting the position speed into the position speed under the J2000 inertial coordinate system, and calculating the longitude Lon of the subsatellite point in the earth-fixed coordinate system ECEF₀；

The regression period was calculated according to the following formula:

using numerical integration method to integrate the sigma_oscExtrapolation prediction of a regression cycle T_regressAcquiring the position and the speed of the satellite under the J2000 inertial system at the end moment of the period, and calculating the position and the speed in the earth-fixed coordinate systemSustanship point longitude Lon in ECEF_T；

According to the relationship between the satellite orbit period and the semimajor axis, improving the initial value of the semimajor axis of the regression orbit parameter by adopting a numerical iteration method of the following formula:

wherein the content of the first and second substances,

ΔLon＝Lon_T-Lon₀(ii) a The ω is_eIs the earth rotation angular rate;

substituting the new orbit parameter semimajor axis as an initial value into a formula corresponding to the regression period, and repeating the steps until the absolute value of delta T_orbit|＜ΔT_epsWherein, the Δ T_epsIteratively correcting a convergence threshold for a strict regression trajectory of the LEO;

after the iteration is finished, acquiring the orbit parameter sigma obtained by the iteration_oscThe regression period is T_regress。

7. The method according to claim 1, wherein the performing a short-range optimization improvement on each orbit parameter and regression cycle in the regression orbit root number optimization initial value by using a nonlinear equation set to obtain a strict regression orbit parameter with higher regression accuracy comprises:

according to the earth gravity field data model file, selecting a high-order perturbation model order of the earth gravity field according to the initial orbit parameter (t)₀，σ_osc) Calculating the position and the speed of the satellite under the earth-fixed coordinate system ECEF at the initial moment by using the coordinate conversion function, and recording as (r)₀，v₀)；

Recursion of satellite orbit by a regression period T_regressCalculating the position and speed at the end of the regression period, and calculating the position and speed of the satellite under the earth-fixed coordinate system ECEF at the initial moment by using the coordinate conversion function, and recording as (r)_f，v_f)；

Calculating the position error and the speed error of the start-stop moment of the next regression cycle of the earth-fixed coordinate system ECEF:

Δr＝|r_f-r₀|

Δv＝|v_f-v_f|；

taking the process as a nonlinear equation set to be solved of the minpack algorithm:

{Δr_x，Δr_y，Δr_z，1000·Δv_x，1000·Δv_y，1000·Δv_z}＝F(σ_osc，T_regress)≈0；

due to a small speed error, the position error is quickly diverged under the action of time accumulation, and the precision requirement of strict regression cannot be met. The speed error is multiplied by 1000 as an amplification factor, which is similar to a constraint penalty factor when an optimization target is constructed in an intelligent optimization algorithm.

According to the search solving variation range of each track parameter in the Minpack algorithm, a group of track initial roots and a corresponding strict regression period are obtained by utilizing the solving capability of a nonlinear equation set of the Minpack algorithm, so that the regression revisiting precision of the reference track under the earth-fixed system can meet the following formula:

8. an apparatus for obtaining a strict regression orbit parameter, comprising:

a first acquisition module for adopting an orbit analysis method and considering an earth oblateness perturbation item J₂And J₃To obtain a set of rough regression trajectory flat roots;

the second acquisition module is used for acquiring the instantaneous orbit number corresponding to the rough regression orbit number by adopting a calculation function of flat-transient conversion;

the third acquisition module is used for recursion of the orbit by using a numerical method, and carrying out iterative correction on the semimajor axis in the parameter of the instantaneous orbit root to obtain an initial value for optimizing the regression orbit root;

and the fourth acquisition module is used for performing small-range optimization improvement on each orbit parameter and the regression period in the regression orbit root number optimization initial value by adopting a nonlinear equation set so as to obtain a strict regression orbit parameter with higher regression precision.

9. An apparatus for obtaining a strict regression orbit parameter, comprising:

a processor;

a memory for storing processor-executable instructions;

wherein the processor is configured to:

an orbit analysis method is adopted, and an earth oblateness perturbation item J is considered₂And J₃Obtaining a group of rough regression orbit flat roots;

acquiring an instantaneous orbit root corresponding to the rough regression orbit root by adopting a calculation function of flat-to-instantaneous conversion;

recursion of the orbit by using a numerical method, and iterative correction of a semimajor axis in the parameters of the instantaneous orbit number to obtain an initial regression orbit number optimization value;

and carrying out small-range optimization improvement on each orbit parameter and regression period in the regression orbit root number optimization initial value by adopting a nonlinear equation set so as to obtain a strict regression orbit parameter with higher regression precision.

10. A computer-readable storage medium having computer instructions stored thereon, which when executed by a processor implement the method of any one of claims 1 to 7.

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