CN116776474A - Parallel self-adaptive calculation method and system for spacecraft orbit - Google Patents
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Abstract
The invention discloses a parallel self-adaptive calculation method and a system of spacecraft orbit, which adopt a plurality of parallel point matching iterative algorithms to respectively carry out iterative correction on the initial state of each point matching moment, and adopt different initial subinterval step sizes, and determine the step size of the next subinterval according to the relation between the convergence state and the iterative times of each point matching iterative algorithm; repeating the iterative process until the iterative correction of all subinterval states is completed, and obtaining a spacecraft orbit; according to the invention, the calculated step length is adjusted according to the convergence condition and the iteration times of the point matching iteration method under different calculation step lengths, so that the step length of a subinterval in the calculation process is always proper, the problem that the calculation precision or efficiency is reduced due to overlong or too short calculation step length of the point matching iteration method is avoided, and the advantage of large step length calculation of the point matching iteration method is fully exerted.
Description
Technical Field
The invention relates to the technical field of aerospace, in particular to a parallel self-adaptive calculation method and system for spacecraft orbits.
Background
In the aerospace field, many problems can be described by mathematical models of nonlinear very differential equations. Therefore, in many aerospace engineering tasks, the efficiency of solving nonlinear ordinary differential equations severely affects the performance of the task. In recent years, a nonlinear ordinary differential equation solving method combining a point matching method and an iteration method is widely applied to space engineering tasks such as orbit recursion and orbit transfer of a spacecraft. The point matching iterative method has higher calculation precision and faster calculation speed than the traditional finite difference method, but the calculation efficiency of the method is generally seriously affected by calculation parameters, and the method can be prevented from being low in calculation efficiency by selecting proper calculation parameters. However, the adaptive parameter selection strategies of the existing point matching iterative algorithm are designed aiming at the serial method, and the serial point matching iterative method has the problem that the calculation efficiency is reduced because the serial calculation nodes are insufficient and the calculation operation is queued for the calculation nodes.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a parallel self-adaptive calculation method and a system for spacecraft orbits, so as to improve the calculation efficiency of the spacecraft orbits.
The invention is realized by the following technical scheme:
the parallel adaptive calculation method for the spacecraft orbit is characterized by comprising the following steps of:
step 1, selecting the total calculation interval and the number M of the distribution points of the total interval of the spacecraft orbit, and setting the step length of an initial subinterval;
step 2, adopting a plurality of parallel point matching iterative algorithms to carry out iterative correction on the initial state of each point matching moment respectively, adopting different initial subinterval step sizes for each point matching iterative algorithm, and determining the step size of the next subinterval according to the relation between the convergence state and the iterative times of each point matching iterative algorithm;
and 3, repeating the step 2 according to the determined step length of the next subinterval until the iterative correction of the states of all subintervals is completed, so as to obtain the state correction value of each subinterval, and further obtain the spacecraft orbit.
Preferably, in step 2, a GPU is adopted to implement parallel operation of a plurality of point matching iterative algorithms, which is specifically as follows:
and distributing a plurality of mutually independent and parallel CUDA streams on the GPU, wherein each CUDA stream runs a point allocation iterative algorithm with different initial subinterval step sizes.
Preferably, the method for correcting the subinterval state by the point matching iterative algorithm is as follows:
rewriting a point matching iterative calculation method into an error iterative equation and an error iterative equation by adopting a linear operation function;
and carrying out iterative correction on the initial state of each point in the subinterval by combining the error iterative equation and the state iterative equation with a constant matrix until the state correction value reaches the preset precision, and obtaining the spacecraft orbit of the subinterval.
Preferably, the expression of the error iterative equation is as follows:
the state iteration equation is as follows:
wherein ,for the position and speed estimation value of the spacecraft after the nth iteration correction, < + >> and />Respectively-> and />A vector corresponding to the d-th dimensional state of (c).
Preferably, in the step 2, the step length of the next subinterval is determined according to the relation between the convergence state and the iteration number as follows;
the step length of the S point matching iterative algorithm is n respectively 1 ×dt,n 2 ×dt,……，n s-1 ×dt；
wherein ,1＝n1 ＜n 2 ＜…＜n s-1 ，S≥2；
Sequencing each point matching iterative algorithm according to the step length from small to large, and when the first C point matching iterative algorithms converge in sequencing, namely, C is more than 0 and less than or equal to S;
the iteration times of the iterative algorithm of each point are respectively obtained as I 1 ，I 2 ……，I C And reducing the step length of the next subinterval according to the iteration times.
Preferably, the step length of the next subinterval is calculated as follows:
when (when)When (1):
dt＝n m ×dt，
when (when)When (1):
dt＝dt/n m+1 ，
preferably, when all the point matching iterative algorithms are not converged, the step length of the current subinterval is shortened, and the modified step length is adopted to carry out iterative correction on the initial state of the current subinterval.
Preferably, the modified step size is as follows:
dt＝dt/n s-1 。
the system of the parallel adaptive calculation method of the spacecraft orbit comprises
The initialization module is used for selecting the total calculation interval and the number M of the distribution points of the total interval of the spacecraft orbit and setting the step length of the initial subinterval;
the parallel iteration module is used for carrying out iterative correction on the initial state of each point matching moment by adopting a plurality of parallel point matching iteration algorithms, and each point matching iteration algorithm adopts different initial subinterval step sizes, and the step size of the next subinterval is determined according to the relation between the convergence state and the iteration times of each point matching iteration algorithm;
and the orbit module is used for finishing iterative correction of all subintervals states according to the determined step length of the next subinterval and combining a plurality of parallel distribution point iterative algorithms, and outputting the spacecraft orbit.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention discloses a parallel self-adaptive calculation method of spacecraft orbit, which adopts a plurality of parallel point matching iterative algorithms to carry out iterative correction on the initial state of each point matching moment respectively, adopts different initial subinterval step sizes of each point matching iterative algorithm, determines the step size of the next subinterval according to the relation between the convergence state of each point matching iterative algorithm and the iterative times, and then repeats the process according to the determined step size to finish the calculation of the spacecraft orbit.
Drawings
FIG. 1 is a schematic diagram of an adaptive computing method for spacecraft orbit according to the present invention;
FIG. 2 is a flow chart of a method of adaptive calculation of spacecraft orbit according to the invention;
FIG. 3 is a graph of the results of spacecraft orbit calculations of the present invention;
FIG. 4 is a graph of acceleration ratio caused by the adaptive parallel computing method of the present invention.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings, which illustrate but do not limit the invention.
As shown in fig. 1 and 2, a parallel adaptive calculation method for spacecraft orbit includes the following steps:
step 1, selecting the total calculation interval and the number M of the distribution points of the total interval of the spacecraft orbit, and setting the step length of an initial subinterval;
the fixed number of the allocation points is selected empirically, the number of the allocation points of the GPU-based parallel computing method is generally taken as an integral multiple of 32, and the total calculation interval t is calculated 0 ,t f ]The method comprises the steps of dividing the method into a plurality of subintervals, and setting the step length of an initial subinterval to be dt, namely the length of the subinterval.
wherein ,t0 To calculate the start time of the interval t f To calculate the end time of the interval.
In the total calculation interval [ t ] 0 ,t f ]Within the range according to the formulaSelecting M CGL nodes, wherein tau m ＝-cos((m-1)π/(M-1)),m＝1,2,…,M。
Step 2, carrying out iterative correction on the initial state of each point matching moment by adopting a plurality of parallel point matching iterative algorithms, and determining the step length of the next subinterval by adopting different initial subinterval step lengths by adopting each point matching iterative algorithm according to the relation between the convergence state and the iterative times of each point matching iterative algorithm, wherein the steps are as follows:
s2.1, determining a linear operation function according to the number of the distribution points;
using general matrix multiplication in the cuBLAS libraryNormal matrix Q, P, H and required for generating normal matrix cublastDgemm, diagonal matrix multiplication sub-function cublastDdgmm and GPU kernel functionThese constant matrices can be pre-generated and stored at the GPU side for use;
the expression of chebyshev's base function differential normative Q is as follows:
wherein Φ (τ) = [ Φ ] 0 (τ),φ 1 (τ),...,φ N (τ)]A vector consisting of values at τ for n+1 Chebyshev basis functions;
the expression of chebyshev basis function integral norms P is as follows:
wherein ,φ0 (τ)＝1,φ 1 (τ)＝cos(arccost),...,φ N (τ)＝cos((N-1)arccost)；
If τ= ±1, then +.>
Chang Ya comparably matrix ignoring small reserved constants onlyThe expression of (2) is as follows:
wherein ,03M×3M All zero matrix of 3M×3M, I 3M×3M A 3m×3m identity matrix;
the expression of the constant matrix H, which relates only to the number of points, is as follows:
H＝PT-TP，T＝dig(τ 1 ,τ 2 ,…,τ M )
s2.2, determining the initial state of the initial subinterval according to the cold start schemeThe initial motion is uniform linear motion with the initial speed, the process is realized by using a GPU kernel function, and the initial state is obtained by using the kernel function>Is a first derivative of (a).
S2.3, rewriting the point matching iterative calculation method into an error iterative equation and an error iterative equation by adopting a linear operation function.
The error iteration equation is as follows:
the state iteration equation is as follows:
wherein ,for the position and speed estimation value of the spacecraft after the nth iteration correction, < + >> and />Respectively-> and />A vector corresponding to the d-th dimensional state of (c).
S2.4, distributing a plurality of mutually independent and parallel CUDA streams on the GPU, and setting different step sizes of initial subintervals for each CUDA stream.
S2.5, each CUDA stream iteratively corrects the initial state of each point matching moment in the subinterval by combining an error iteration equation and a state iteration equation according to the step length of each subinterval and a constant matrix;
according to Chebyshev basis function differential normal square matrix Q and Chebyshev basis function integral normal square matrix P, a Chang Ya comparability matrix with a small amount of reserved constant is ignoredAnd carrying out iterative correction on the states of each point matching moment in the initial subinterval by combining the constant matrix H related to the point matching and the initial state of the initial subinterval with a point matching iterative method until each CUDA flow completes iteration, and obtaining a state correction value of the initial subinterval.
S2.6, determining the step length of the next subinterval of each CUDA flow according to the convergence state and the iteration times of the point matching iterative algorithm of each CUDA flow.
Let S CUDA flows in total, the calculation step sizes are n respectively 1 ×dt,n 2 ×dt,……，n s-1 X dt, where 1=n 1 ＜n 2 ＜…＜n s-1 S is more than or equal to 2. Let some of the S CUDA streams and only the first C CUDA streams converge, 0.ltoreq.C.ltoreq.S. If c=0, let the step dt=dt/n s-1 . If C is not equal to 0, the iteration times corresponding to each CUDA flow are recorded as I respectively 1 ，I 2 ……，I C When (when)Let step dt=n m X dt, when->Let step dt=dt/n m+1, wherein ,/>
And step 3, repeating the steps S2.5-2.6 until all subintervals in the total calculation interval are converged.
Example 1
Two mutually independent CUDA streams are distributed on the GPU, CUDA stream 1 and CUDA stream 2 can run different parallel programs on the two CUDA streams at the same time, the two CUDA streams adopt different initial subinterval step sizes, and an iterative correction method is adopted for carrying out iterative correction on the initial state of each point allocation moment in the initial subinterval.
In this embodiment, a description is focused on a step length setting method for a next subinterval according to an iteration state of a current subinterval.
S2.4, using dt as the step size of the initial subinterval in CUDA stream 1, and using 2×dt as the step size of the initial subinterval in CUDA stream 2.
S2.5, each CUDA stream carries out iterative correction on the initial state of each point in the initial subinterval by combining an error iterative equation and a state iterative equation according to the step length of each initial subinterval and a constant matrix;
s2.6, determining the change condition of the step length of the next subinterval of each CUDA flow according to the convergence state and the iteration times of the point matching iteration algorithm of the CUDA flow 1 and the CUDA flow 2, wherein the change condition is specifically as follows:
determining whether the iteration result of the CUDA flow 2 with the largest step length is converged or not, and marking the converged result as a first judgment result;
if the first judgment result is yes, since the step length of the CUDA stream 1 is smaller than that of the CUDA stream 2, the CUDA stream 1 is necessarily converged, the calculation result of the CUDA stream 2 is recorded, ti=ti+2×dt is made to be the initial time of the subinterval, ti is increased to represent the iteration end of the current subinterval, calculation of the next subinterval is started, and the step length of the next subinterval is determined according to the first judgment result and the iteration times of the CUDA streams.
The iteration number of CUDA stream 1 is noted as: i 1 ；
The iteration number of CUDA stream 2 is noted as: i 2 ；
Judgment of I 2 Whether or not greater than 2 times I 1 The result is marked as a second judgment;
if the second judgment result is yes, making the step dt=dt/2 of the next subinterval;
if the result of the second judgment is negative, making the step dt=2×dt of the next subinterval;
if the CUDA flow 1 is calculated and converged and the CUDA flow 2 is calculated and not converged, recording the calculation result of the CUDA flow 1, doubling the step length, and then calculating the next section.
If neither CUDA stream 1 nor CUDA stream 2 converges, the step size is halved and then the calculation is performed again in this interval.
If the result of the first judgment is negative, judging whether the CUDA flow 1 calculation is converged, and marking the result as a third judgment;
if the result of the third judgment is yes, recording the calculation result of the CUDA flow 1, and enabling ti=ti+dt, and dt=dt/2;
if the result of the third judgment is negative, making the step dt=dt/2 of the next subinterval;
and step S3, repeating the steps S2.5-S2.6 to perform iterative computation on the next subinterval according to the step length obtained in the step S2 until the computation of all subintervals is completed, and obtaining the orbit of the spacecraft.
When the starting time ti of the next subinterval is equal to the ending time of the total calculation interval, the track calculation of the total calculation interval is completed.
Example 2
A parallel adaptive calculation method of spacecraft orbit comprises the following steps:
step 1, for the common orbit prediction problem of satellites, selecting a fixed number of distribution points M according to running hardware support, and iterating an accuracy error limit epsilon, and allowingMaximum iteration number, initial subinterval step dt and overall calculation interval t 0 ,t f ]Dividing the total calculation interval into a plurality of continuous subintervals, and determining the point distribution time t according to the selected fixed point distribution number m Constructing constant matrices Q, P, H and corresponding to the number of the coordination points
And 2, distributing two mutually independent CUDA streams, namely CUDA stream 1 and CUDA stream 2 on the GPU, carrying out iterative computation by taking dt as a computation step length and M as a number of points on the CUDA stream 1, and carrying out iterative computation by taking 2 times of dt as a computation step length and M as a number of points on the CUDA stream 2.
The specific calculation process is as follows:
generating initial states of initial subintervals using GPU-kernelsThe iterative computation is started from the initial state. Status value +.>Substitution into kernel function to calculate the first derivative of the current state +.>And utilize the formula +.>Andfrom the current state value +>And first derivative>Calculating the state value after the next iteration correction +.>
Is a 6M dimensional column vector.
The 1 st to M th elements of the vector correspond to the position estimation value of the spacecraft in the x-axis direction at each matching point, the M+1 st to 2M th elements of the vector correspond to the position estimation value of the spacecraft in the y-axis direction at each matching point, the 2M+1 st to 3M th elements of the vector correspond to the position estimation value of the spacecraft in the z-axis direction at each matching point, the 3M+1 st to 4M th elements of the vector correspond to the speed estimation value of the spacecraft in the x-axis direction at each matching point, the 4M+1 st to 5M th elements of the vector correspond to the speed estimation value of the spacecraft in the y-axis direction at each matching point, and the 5M+1 th to 6M th elements of the vector correspond to the speed estimation value of the spacecraft in the z-axis direction at each matching point.
In the same way, the processing method comprises the steps of,and is also a 6M dimensional column vector.
The 1 st to 3M th elements of the vector correspond to speed estimated values of the spacecraft in three directions at each coordination point, and the 3M+1 th to 6M th elements of the vector correspond to gravity field estimated values of the spacecraft in all directions at each coordination point.
According to the following formulaCalculating the second norm e of the difference vector of the state estimation values at each point of the spacecraft after the n+1th and n-th iterative correction, if e is larger than epsilon, performing the next iterative calculation until e is smaller than epsilon, and recording the calculation result ∈>And exiting the iterative computation; in the iterative calculation process, if the iteration times are not converged after being larger than the set maximum iteration times, the iterative calculation is not converged, and the iterative calculation is stopped.
And 3, in the iterative computation of each subinterval, judging and determining whether the step length of the next subinterval is doubled or halved according to the convergence condition of the CUDA flow 1 and the CUDA flow 2 and the number relation of the iteration times.
If the CUDA stream 1 and the CUDA stream 2 are converged in calculation, the calculation result of the CUDA stream 2 is recorded, and the step length of the next subinterval is determined by combining the iteration times of the CUDA stream 1 and the CUDA stream 2.
If the iteration number I of CUDA flow 2 is 2 Number of iterations I of CUDA flow 2 greater than 2 times 1 Let step dt=dt/2, whereas let step dt=2×dt.
If the CUDA flow 1 calculation converges and the CUDA flow 2 calculation does not converge, recording the calculation result of the CUDA flow 1, making the step dt=dt/2, and then performing calculation of the next section.
If neither CUDA stream 1 nor CUDA stream 2 converges, let step dt=dt/2, and re-iterate the calculation for the state of the current subinterval.
The parallel self-adaptive calculation method of the spacecraft orbit selects a fixed number of points M, and initially calculates a step dt and a total calculation interval; distributing CUDA flow 1 with dt as step length, and carrying out iterative computation by using a parallel point allocation iterative class method with 2 times of dt as step length by CUDA flow 2; judging whether the calculation step length is doubled or halved according to the number relation between the convergence condition of the CUDA flow 1 and the CUDA flow 2 and the iteration times; and determining whether to perform iterative computation of the next interval or not according to convergence conditions of the CUDA flow 1 and the CUDA flow 2 until the sub-interval is iterated. The feedback acceleration Picard iteration method based on the GPU is realized by using the GPU parallel acceleration technology, the current solution is continuously iterated and corrected to gradually approach the true solution, and the iterative computation is distributed to a large number of computation nodes on the GPU to accelerate computation, so that a high-efficiency and high-precision parallel computation method is provided for spacecraft orbit prediction.
Example 3
The kinetic equation of the low earth satellite orbit recursion problem under the 40-order EGM2008 earth gravitational field model is:
wherein r= [ x, y, z] T μ= 3986004.418 ×10 as a near earth satellite position vector 8 m 3 /s 2 The gravitational constant, r= |r|represents the distance between the earth center and the mass center of the near-earth satellite, a is the initial moment of orbit recursion, a is the perturbation term, and in the embodiment, 40-order EGM2008 earth gravitational field model perturbation is considered.
In this embodiment, the initial calculation conditions are shown in table 1, the calculation parameters are shown in table 2, the calculated orbit of the near-earth satellite is shown in fig. 3, and the calculation accuracy after adaptively optimizing the calculation parameters is shown in fig. 4.
Table 1 initial calculation conditions employed in example 3
Table 2 calculation parameters employed in example 3
| Spacecraft operation time t f /s | Number of distribution points | Iterative accuracy error limit epsilon/m | Maximum number of iterations |
| 8000 | 64 | 10 -6 | 80 |
The invention discloses a parallel self-adaptive calculation method of spacecraft orbit, which comprises the following steps: selecting a fixed number of allocation points M, and initially calculating a step dt and a total calculation interval; distributing CUDA flow 1 with dt as step length, and carrying out iterative computation by using a parallel point allocation iterative class method with 2 times of dt as step length by CUDA flow 2; judging whether the calculation step length is doubled or halved according to the number relation between the convergence condition of the CUDA flow 1 and the CUDA flow 2 and the iteration times; and determining whether to perform iterative computation of the next interval according to convergence conditions of the CUDA flow 1 and the CUDA flow 2 until each sub-interval in the total computation interval is subjected to iterative computation, and obtaining the orbit of the spacecraft.
According to the invention, different CUDA flows are used for iterative computation with different computation parameters, and the proper computation parameters of the point matching iterative method are determined according to the convergence of the computation of the different CUDA flows and the number relation of computation iteration times, so that a high-efficiency parallel computation method capable of adaptively selecting the computation parameters is provided for spacecraft orbit prediction.
In another embodiment, the invention also provides a system of the parallel adaptive calculation method of the spacecraft orbit, which comprises an initialization module, a parallel iteration module and an orbit module.
The initialization module is used for selecting the total calculation interval and the number M of the distribution points of the total interval of the spacecraft orbit and setting the step length of the initial subinterval;
the parallel iteration module is used for carrying out iterative correction on the initial state of each point matching moment by adopting a plurality of parallel point matching iteration algorithms, and each point matching iteration algorithm adopts different initial subinterval step sizes, and the step size of the next subinterval is determined according to the relation between the convergence state and the iteration times of each point matching iteration algorithm;
and the orbit module is used for finishing iterative correction of all subintervals states according to the determined step length of the next subinterval and combining a plurality of parallel distribution point iterative algorithms, and outputting the spacecraft orbit.
The above is only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by this, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (9)
1. The parallel adaptive calculation method for the spacecraft orbit is characterized by comprising the following steps of:
step 1, selecting the total calculation interval and the number M of the distribution points of the total interval of the spacecraft orbit, and setting the step length of an initial subinterval;
step 2, adopting a plurality of parallel point matching iterative algorithms to carry out iterative correction on the initial state of each point matching moment respectively, adopting different initial subinterval step sizes for each point matching iterative algorithm, and determining the step size of the next subinterval according to the relation between the convergence state and the iterative times of each point matching iterative algorithm;
and 3, repeating the step 2 according to the determined step length of the next subinterval until the iterative correction of the states of all subintervals is completed, so as to obtain the state correction value of each subinterval, and further obtain the spacecraft orbit.
2. The method for parallel adaptive computation of spacecraft orbit according to claim 1, wherein in step 2, GPU is adopted to implement parallel operation of a plurality of point matching iterative algorithms, specifically as follows:
and distributing a plurality of mutually independent and parallel CUDA streams on the GPU, wherein each CUDA stream runs a point allocation iterative algorithm with different initial subinterval step sizes.
3. The parallel adaptive computing method of spacecraft orbit according to claim 1, wherein the method for correcting the subinterval state by the fitting iterative algorithm is as follows:
rewriting a point matching iterative calculation method into an error iterative equation and an error iterative equation by adopting a linear operation function;
and carrying out iterative correction on the initial state of each point in the subinterval by combining the error iterative equation and the state iterative equation with a constant matrix until the state correction value reaches the preset precision, and obtaining the spacecraft orbit of the subinterval.
4. A method of parallel adaptive computation of spacecraft orbit according to claim 3, wherein the expression of the error iteration equation is as follows:
the state iteration equation is as follows:
wherein ,for the position and speed estimation value of the spacecraft after the nth iteration correction, < + >> and />Respectively-> and />A vector corresponding to the d-th dimensional state of (c).
5. The parallel adaptive computing method of spacecraft orbit according to claim 1, wherein the step 2 is a method for determining the step length of the next subinterval according to the relation between the convergence state and the iteration number, as follows;
the step length of the S point matching iterative algorithm is n respectively 1 ×dt,n 2 ×dt,……，n s-1 ×dt；
wherein ,1＝n1 ＜n 2 ＜…＜n s-1 ，S≥2；
Sequencing each point matching iterative algorithm according to the step length from small to large, and when the first C point matching iterative algorithms converge in sequencing, namely, C is more than 0 and less than or equal to S;
the iteration times of the iterative algorithm of each point are respectively obtained as I 1 ，I 2 ……，I C And reducing the step length of the next subinterval according to the iteration times.
6. The method for parallel adaptive calculation of spacecraft orbit according to claim 5, wherein the step size of the next subinterval is calculated as follows:
when (when)When (1):
dt＝n m ×dt，
when (when)When (1):
dt＝dt/n m+1 ，
7. the method of claim 5, wherein when all the point matching iterative algorithms are not converged, the step size of the current subinterval is shortened, and the modified step size is adopted to correct the initial state of the current subinterval again.
8. A method of parallel adaptive computation of spacecraft orbit according to claim 7, wherein said modified step size is as follows:
dt＝dt/n s-1 。
9. a system for performing the parallel adaptive computing method of a spacecraft orbit of any of claims 1-8, comprising
The initialization module is used for selecting the total calculation interval and the number M of the distribution points of the total interval of the spacecraft orbit and setting the step length of the initial subinterval;
the parallel iteration module is used for carrying out iterative correction on the initial state of each point matching moment by adopting a plurality of parallel point matching iteration algorithms, and each point matching iteration algorithm adopts different initial subinterval step sizes, and the step size of the next subinterval is determined according to the relation between the convergence state and the iteration times of each point matching iteration algorithm;
and the orbit module is used for finishing iterative correction of all subintervals states according to the determined step length of the next subinterval and combining a plurality of parallel distribution point iterative algorithms, and outputting the spacecraft orbit.
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