A method for optimizing a three-body orbit moon communication navigation constellation based on data preprocessing

Abstract

The application provides a three-body orbit moon communication navigation constellation optimization method based on data preprocessing, and steps are as follows: S1, determining the type of orbits and the range of amplitudes in the constellation; S2, preprocessing the related data of the satellites on the orbits used for evaluating the performance of the constellation, so as to obtain different orbit sets and databases used in optimization; S3, based on the orbit sets and databases obtained through preprocessing, an initial scheme of the constellation is designed; S4, on the basis of the current number of satellites, one satellite is reduced, and the intelligent optimization algorithm is used in each orbit set to count the corresponding orbit set; S5, step S4 is repeated until the constellation cannot meet the coverage requirements any more; S6, the navigation performance is further optimized for the navigation constellation; and S7, if the navigation performance of the finally obtained constellation is not ideal, the number of satellites is gradually increased, and then step S6 is repeated to continue optimizing the navigation performance until the navigation performance meets the requirements.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of constellation optimization design, and particularly relates to a three-body orbit moon constellation optimization method based on data preprocessing. BACKGROUND

[0002] With the increasing interest of human beings in moon exploration, more and more countries and space agencies have proposed their own exploration plans, which puts forward higher requirements for basic services such as moon communication and navigation. However, the existing ground facilities have poor coverage performance on the moon. For some special areas, such as the back of the moon, they cannot be directly covered. Moreover, the sharp increase in the number of space vehicles between the earth and the moon leads to a sharp increase in the amount of information generated, and the ground facilities are already difficult to meet the demand. The construction of a moon constellation can greatly alleviate the pressure on the ground facilities and effectively solve the above problems. Many space agencies have proposed moon constellations that can provide communication and navigation services. The constellation design will directly affect the function implementation and performance level of the entire system, and it needs to determine the number of satellites, the type and parameters of the orbit, the phase of the satellite and the cooperative working mode. Limited by cost and mission objectives, the number of satellites and the working mode are generally determined. Therefore, the design variables of the general constellation are the type and parameters of the orbit and the phase of the satellite on the orbit.

[0003] The optimization design of the constellation is a relatively complex optimization problem, and generally uses intelligent optimization algorithms for solution. However, due to the existence of three-body orbits in the earth-moon space, the design of the moon constellation is different from the traditional earth constellation composed of Kepler orbits. The rich types and properties of three-body orbits bring more choices and possibilities to constellation design, but also lead to a larger design space. Moreover, the grid point method for evaluating the performance of communication and navigation constellations also requires a large amount of calculation, which is unacceptable for intelligent optimization algorithms that consume a large amount of computing resources. Therefore, the optimization of constellations generally with three-body orbits only optimizes part of the parameters of the constellation, rather than simultaneously optimizing all parameters, which will result in missing many configurations with excellent performance. By preprocessing the data used for constellation performance evaluation, including limiting the orbit period, discretizing the orbit amplitude and generating an offline database, the method can effectively reduce the amount of calculation in constellation optimization, thereby realizing the simultaneous optimization of all parameters. And by optimizing the coverage performance first, the minimum number of satellites that can meet the basic coverage requirements of the communication and navigation constellation is obtained, as well as as many candidate constellation configurations as possible. Then, on the basis of meeting the requirements, the navigation performance of the constellation is further optimized. SUMMARY

[0004] Therefore, the application provides a three-body orbit moon communication and navigation constellation optimization method based on data preprocessing, which is used for optimizing constellation parameters based on specific task requirements of a moon communication or navigation constellation, so as to obtain a candidate constellation configuration with optimal performance.

[0005] To achieve the above object, the application provides a three-body orbit moon communication and navigation constellation optimization method based on data preprocessing, which specifically comprises the following steps:

[0006] S1: According to the specific task target of the moon communication and navigation constellation, the type and amplitude range of the orbit in the constellation are determined.

[0007] S2: The related data of the satellite on the orbit used for constellation performance evaluation are preprocessed, including limiting the orbit period, discretizing the orbit amplitude and generating an offline database, so as to obtain different orbit sets and databases used in optimization.

[0008] S3: Based on the orbit sets and databases obtained by preprocessing, an initial scheme of the constellation is designed by using a simulation-based comparative analysis method, and the initial scheme is used as the current number of satellites.

[0009] S4: On the basis of the current number of satellites, one satellite is reduced, and intelligent optimization algorithms are used in each orbit set to optimize the constellation parameters with the coverage performance of the constellation as the objective function, so as to find a configuration that can meet the coverage requirements and count the corresponding orbit set.

[0010] S5: Repeat step S4 until the satellite is reduced to the point where no configuration that can meet the coverage requirements can be found, that is, the minimum number of satellites required and the corresponding orbit set are obtained, and the constellation configuration that meets the requirements in these sets is obtained.

[0011] S6: For the navigation constellation, after the coverage performance of the constellation is optimized to completely meet the coverage requirements in each orbit set corresponding to the current number of satellites that can find a configuration that meets the coverage requirements, the navigation performance is further optimized.

[0012] S7: If the navigation performance of the finally obtained configuration is not ideal, step S6 can be repeated after gradually increasing the number of satellites to continue optimizing the navigation performance until it meets the requirements.

[0013] In a possible implementation manner, in the three-body orbit moon communication and navigation constellation optimization method based on data preprocessing provided by the application, step S1 specifically comprises:

[0014] The type and amplitude range of the orbit for constructing the constellation are determined according to the specific requirements of the task and the characteristics of the orbit. In order to realize the coverage of the lunar surface, the halo orbit near the L1, L2 point is selected to construct the lunar communication and navigation constellation. The types of orbits include halo orbits, planar and vertical Lyapunov orbits, and distant retrograde orbits (DRO). Among these orbits, the halo orbit has a large change in its geometric shape with the change of the amplitude, which leads to the change of its coverage characteristics on the lunar surface. Moreover, considering that the required orbit is near the moon, it is not conducive to communication if it is too far away, and it will also increase the maintenance cost. The halo orbit family is relatively close to the moon, so it can be included in the constellation design. The minimum value of its amplitude is very small, close to 0, and the maximum value is about 82863 km. Unlike halo orbits, the amplitude range of the planar and vertical Lyapunov orbit family is large, the minimum orbit amplitude also tends to 0, but the maximum can be tens of thousands of kilometers away from the moon. The excessive distance is not conducive to providing communication and navigation services to the lunar surface. Since the geometric shapes of these orbit families are similar and do not change greatly with the change of the amplitude, a part of the orbit with a small amplitude can be selected to participate in the constellation design. Here, the maximum value of the halo orbit amplitude is taken as the upper limit of the amplitude of other orbit families. In addition, the geometric shapes of different DROs are also similar, but as the amplitude increases, the increase in the coverage range of the lunar surface area will quickly tend to stagnate. It mainly covers the equatorial region, and the coverage of other areas cannot be solved by increasing the amplitude, but only by relying on other types of orbits. Moreover, when the DRO amplitude is the smallest, its orbit is near the moon. When its amplitude gradually increases, its orbit gradually moves away from the moon. During this process of gradually increasing the orbit amplitude, the distribution of the phase angle change speed of the satellite located on the orbit becomes more and more uneven, causing the relative phase between the satellites to be in a large change, which is not conducive to coverage. Therefore, the maximum value of the DRO amplitude can be set smaller than the maximum value of the halo orbit amplitude, and its specific range is set according to the periodical relationship between various orbits in the subsequent preprocessing.

[0015] In a possible implementation, in the above-mentioned three-body orbit lunar communication and navigation constellation optimization method based on data preprocessing provided by the application, step S2 specifically comprises:

[0016] Firstly, the period of the orbit is limited, that is, when selecting orbits for the same constellation, only orbits with the same period or a period ratio of m:n are selected. This is to compress the period of the constellation to reduce the time required for performance evaluation. Because if the periods of the orbits in the constellation are different or cannot form an integer ratio, the period of the entire constellation will become very large. To fully evaluate the performance of the constellation, a long simulation time is required. In addition, the determined period of the constellation is also beneficial for operation in formal operation after deployment, such as phase adjustment, which is a relatively common setting. If only orbits with the same period are considered in constellation design, it will result in that the orbit types with no intersection in the period range cannot be matched with each other. Moreover, among the orbit types with intersection in the period range, only the orbits with the same amplitude range can be matched with each other, which will also greatly limit the selection of orbits for the constellation. Therefore, in order to enable each orbit type to be matched with more types and amplitude ranges of orbits to form a constellation, the part that meets the integer ratio of m:n in each interval needs to be selected to form a new orbit interval, so as to enrich the selection of orbits for the constellation. Because for all selected orbit families, the amplitude has a unique correspondence with the orbit, and the amplitude is determined, the period of the orbit is determined, so the period range of all orbits can be determined according to the orbit amplitude range determined in S1. In addition, the method of setting the orbit interval according to the integer ratio of the period is also beneficial for adjusting the period range of the participating orbit types in the constellation design. For example, the period range of the DRO is set according to the period range of other orbit types. In order to ensure that the constellation of each period can select the DRO, the minimum value of the period is set as the minimum value of the period of other orbit families, and the maximum value meets the integer ratio with the maximum value of the period of other orbit families. Moreover, the integer ratio of the period is not necessarily limited to the given combination. For special orbit types, the period ratio can be set individually according to the needs. For example, the halo orbits of L1 and L2 are symmetrical about the moon, and they are located on the front and back of the moon, respectively. Orbits with similar amplitudes in them are often selected together to construct a moon constellation. In these two orbit families, the period range of the orbits with an amplitude of 0 to 60000 km is relatively small, and does not meet the existing integer ratio of the period. Therefore, they cannot be selected at the same time to form a constellation. A more unique period ratio value can be set for them, so that the orbits in the two orbit families in this amplitude range can select orbits with similar amplitudes. Finally, all orbit intervals of the same orbit type are integrated into a set.

[0017] Then, in order to reduce the number of orbits to be considered in constellation optimization, the orbits in each orbit set are discretized with fixed amplitude intervals. Because orbits with close amplitudes are also close in performance for three-body orbits, it is desirable to replace all orbits with a subset of them. And by discretizing the orbits, the number of orbits is limited, so the data of visibility and relative geometry of a satellite on an orbit with respect to the grid points on the lunar surface can be generated in advance for the optimization process. If the amplitudes of these orbits are continuous, all the orbit data cannot be generated in advance. So, the optimization of a constellation is only based on these discretized orbits. When discretizing the orbits in a set, first, the reference orbit family in each period interval needs to be determined. In the same period interval, the orbit family with the slowest period change with respect to amplitude is taken as the reference orbit family, that is, the orbit family with the largest amplitude range in the period interval. Then, a limited number of orbits can be selected from the reference orbit family with fixed amplitude intervals as needed. Finally, the periods of the selected reference orbits are taken as the standard to select the required orbits in other orbit families in the same set as candidate orbits.

[0018] Finally, according to the determined amplitudes of the orbits in each orbit set, the corresponding unique orbit can be obtained, and an offline database of satellite visibility and geometry on the orbit is generated for direct calling in optimization. Because in general constellation optimization and design, the visibility and geometry of a satellite on the same orbit need to be recalculated in each performance evaluation, but these data are actually exactly the same. So, if the required data can be preprocessed and prepared, and directly called in the optimization process, a large amount of repeated calculation can be omitted, thereby achieving the effect of accelerating the calculation. The orbit data in the database is numbered by [set number n set -constellation period number n T -orbit number n O ]. Among them, the set number represents the type of orbit. The period number is the number of different constellation periods, which corresponds to the orbits that can be used to form the constellation of the period. The orbit number represents the number of orbits that can be used to form the constellation of the period. When the set number is determined, the range of the period number can be determined. When the set and period numbers are determined, the range of the orbit number can be determined. Of course, to determine the initial state of the satellite in the constellation, the initial phase φ is also needed. The phase represents the position of the satellite on the orbit, which is the ratio of the time required to run from the initial position of the orbit to the position to the period of the orbit, and its range is [0, 1). Finally, the position of a satellite can be represented by [set number n set -constellation period number n T -orbit number n O -phase φ]. To form a constellation, a satellite needs to be selected from the orbits with the same set number and period number.

[0019] In a possible implementation, in the method for optimizing a three-body orbit moon communication navigation constellation based on data preprocessing provided by the application, step S3 specifically comprises:

[0020] Based on the obtained orbit set and the database, an initial scheme of the constellation is designed using a simulation-based comparative analysis method, and the initial scheme is taken as the current number of satellites.

[0021] Specifically, first, a constellation configuration scheme is selected within the existing orbit set range based on prior experience. According to the range of the moon target area to be served, an orbit type that has an advantage in covering the target area is selected, for example, a halo orbit family pointing south is selected for covering the south pole, and a DRO orbit family is selected for covering the equator.

[0022] Then, a set of orbits with these orbit families is selected, and orbits of the corresponding type are selected from the set. Different numbers of satellites are arranged on different orbits as design schemes. That is, when selecting, the orbit set number n set is first determined, and then a certain constellation period number n T is selected from the corresponding orbit. Advantageous partial orbits for covering the target area are selected from the corresponding orbit, and a certain number of satellites are arranged on these orbits as the constellation configuration scheme. In this process, different constellation periods, orbit combinations, numbers of satellites on each orbit, and phases of each satellite can be selected to obtain different constellation configuration schemes for subsequent selection and adjustment.

[0023] After that, the coverage performance of these schemes is simulated. For a communication constellation, the most important performance indicator is the coverage rate of the constellation to the target. For a navigation constellation, the coverage rate and the navigation accuracy are the most important performances, but meeting the coverage requirement is the basis for providing navigation services. A communication / navigation constellation needs to meet one / four-fold coverage of the target area, that is, at least one / four satellites are visible to the area. When calculating the coverage rate of the target area, a grid point method is generally used. This method is to discretize the target area into a limited number of grid points, then calculate the visibility of each grid point relative to the satellites in the constellation at each time step in the constellation period, and finally calculate the overall coverage rate of the constellation. There are different ways to measure coverage rate, and coverage time percentage (CTP) is one of them. For a communication / navigation constellation, the CTP of a certain grid point is the proportion of the time that the point is covered by at least one / four satellites to the entire simulation time. The CTP of the target area is the average of the CTPs of all grid points in the area. When the CTP of a constellation in a certain orbit set reaches 100%, it means that the area meets the complete one / four-fold coverage, that is, the coverage requirement of the communication / navigation constellation is met.

[0024] Finally, based on the results of the coverage performance simulation, the scheme with better performance or less number of satellites is selected. Then, the parameters of the obtained scheme are manually adjusted appropriately. The adjustment includes adjusting the number of satellites on each orbit and the phase of the satellites on the orbit in the constellation O . The adjustment is continuously performed according to the results of the performance simulation until it is difficult to improve the performance or reduce the number of satellites, and the scheme with the optimal coverage performance and the least number of satellites in the adjustment process is selected as the initial scheme, and the number of satellites is taken as the current number of satellites.

[0025] In a possible implementation, in the three-body orbit moon communication navigation constellation optimization method based on data preprocessing provided in the application, step S4 specifically includes:

[0026] On the basis of the current number of satellites, one satellite is reduced, and intelligent optimization algorithms are used in each orbit set to optimize the constellation parameters with the coverage performance of the constellation as the objective function, to find a constellation that can meet the coverage requirements, and to count the corresponding orbit set. The optimization problem performed in each set can be described as:

[0027]

[0028] wherein J is the objective function of optimization, x is the optimization variable vector, p is the fixed parameter vector, g and h are inequality and equality constraints, x LB and x UB are the upper and lower limits of the optimization variable. Because the performance indicators of the communication and navigation constellation are different, the corresponding objective functions are also different. For the communication constellation, the objective function J C is:

[0029]

[0030] wherein CTP 1-fold is the one-time coverage time proportion of the communication constellation on the target area. When the CTP 1-fold of the constellation in a certain orbit set is optimized to 100%, it indicates that the area meets the complete one-time coverage, that is, the task requirement of the communication constellation is met. At this time, the constellation configuration and the corresponding orbit set are recorded.

[0031] In the optimization problem, the fixed parameter vector p is:

[0032] p=(N,n set ) T (3)

[0033] wherein N is the number of satellites in the constellation, nset is the orbit set number. These two parameters are fixed in the optimization.

[0034] In this optimization problem, the optimization variable vector x is:

[0035] [n T ,n O1 ,n O2 ,φ2,...,n ON ,φ N ](4)

[0036] where n T is the constellation period number, [n O1 ,n O2 ,...,n ON ] is the orbit number of each satellite, and [φ2,...,φ N ] is the initial phase of the satellite on these orbits. Because the initial phase of the first satellite can be directly set to 0, there are only N-1 satellite phases, which can reduce a design variable. Because the constellation period number and the orbit number are integers, and the initial phase is a decimal number, this problem is a mixed integer optimization problem. Moreover, in the optimization, the range of the constellation period number is limited by the orbit set number, and the range of the orbit number is limited by the constellation period number and the orbit set number at the same time.

[0037] In addition, for a communication constellation, only one coverage of the target area is required. However, for a navigation constellation, four coverages of the target area are required, i.e., at least four satellites are visible. Therefore, when optimizing the coverage rate, the objective function J N of the navigation constellation is:

[0038]

[0039] where CTP 4-fold is the four-coverage time ratio of the navigation constellation to the target area, which is calculated in a similar way to the one-coverage time ratio of the communication constellation, i.e., by the grid point method, which is not described here.

[0040] Here, the genetic algorithm (GA) in the intelligent optimization algorithm is selected to optimize the problem, which is performed in different orbit sets. The genetic algorithm GA is a method of searching for an optimal solution by simulating the natural evolution process. First, the algorithm randomly generates an initial configuration solution set, and then the performance of the configurations is simulated respectively, and the target function value, i.e., CTP, is quickly obtained after processing by calling the satellite visibility data in the database. Then, configurations with better performance are selected from the solution set, and the next generation population, i.e., the configuration solution set, is obtained through the crossover and mutation operations of chromosomes similar to the biological population evolution process. Then, after repeated selection, crossover and mutation operations in generations, the optimized constellation configuration is obtained.

[0041] In a possible implementation, in the above-mentioned three-body orbit moon communication and navigation constellation optimization method based on data preprocessing provided by the application, step S5 specifically comprises:

[0042] The step S4 is repeated, the number of satellites is continuously reduced, and the coverage performance of the constellation is optimized in each orbit set to find a configuration that can meet the coverage requirement under the current number of satellites, and the corresponding orbit set is counted, until the number of satellites is reduced to all sets and no configuration can be found to realize complete coverage of the target area. The current number of satellites is increased by one, that is, the minimum number of satellites that can meet the coverage requirement is obtained, and the corresponding orbit set and constellation configuration at this time are recorded.

[0043] In a possible implementation, in the above-mentioned three-body orbit moon communication and navigation constellation optimization method based on data preprocessing provided by the application, step S6 specifically comprises:

[0044] For the communication constellation, the index for evaluating its performance is the coverage of the target, so the minimum number of satellites that can meet the coverage requirement is found, and the corresponding orbit set and constellation configuration at this time are recorded. For the navigation constellation, the most important performance index is not only the coverage of the target, but also the navigation accuracy. Therefore, on the basis of meeting the coverage requirement, the navigation accuracy of the constellation needs to be further optimized. The navigation accuracy of the constellation has many measurement indexes, and the method takes the widely used geometry dilution of precision (GDOP) as an example. The GDOP represents the navigation error caused by measurement error, and the smaller the value is, the better the navigation performance is. The calculation method of the GDOP corresponding to a grid point in the target area is as follows:

[0045]

[0046] Q=H T H -1 (7)

[0047]

[0048] where (x, y, z) is the position of the grid point, (xm, ym, zm) is the relative position of the mth satellite visible to the point, R m is the relative distance of the satellite. H is a matrix constructed by the relative geometry of the satellite and the point, and matrix Q can be obtained from H, which is a 4x4 square matrix, Q 11 , Q 22 , Q 33 , Q 44 are the elements on the diagonal of Q.

[0049] Because the navigation constellation needs to meet the requirement of fourfold coverage first, and then further optimize the navigation accuracy, the objective function J N optimized by the navigation constellation in each orbit set is a piecewise function:

[0050]

[0051] where GDOP mean is the average GDOP value of the target area. When the fourfold coverage of the constellation does not meet the requirement, the optimization objective of J N is to maximize CTP 4-fold . When the coverage requirement is met, the optimization objective is to further minimize the average value GDOP mean of GDOP. And when GDOP mean is too large, the constellation configuration exceeding 1000 is directly counted as 1000.

[0052] Similarly, based on the genetic algorithm GA, the optimization of the navigation constellation can be carried out in the confirmation that the orbit set meeting the coverage requirement can be found. The visibility and geometric position of the satellites in the database can be directly called during optimization, and the objective function value can be quickly obtained after processing, and the optimized constellation configuration is obtained accordingly.

[0053] In a possible implementation, in the above-mentioned three-body orbit moon communication navigation constellation optimization method based on data preprocessing provided by the application, step S7 specifically comprises:

[0054] After the optimization of the navigation performance of the constellation in step S6, if it is found that the average GDOP value of the obtained constellation is relatively poor and cannot meet the navigation requirement, the number of satellites can be further increased on the basis of the current number of satellites, and then step S6 is repeated to continue optimizing the navigation performance of the constellation until it can meet the navigation accuracy requirement. The navigation accuracy requirement can be set according to the needs, and generally it is set to be not greater than a certain value. Then, among the results corresponding to the number of satellites, the orbit set and the constellation configuration meeting the navigation requirement are counted.

[0055] The advantages and beneficial effects of the present application are as follows:

[0056] 1. The three-body orbit moon communication and navigation constellation optimization method based on data preprocessing disclosed in the present application avoids repeated data calculation by preprocessing data used for communication and navigation performance evaluation, greatly improving the calculation speed.

[0057] 2. The three-body orbit moon communication and navigation constellation optimization method based on data preprocessing disclosed in the present application gradually reduces the number of satellites and optimizes the coverage performance of the constellation based on the initial scheme obtained by the simulation-based comparative analysis method, to obtain the minimum number of satellites that can meet the basic coverage requirements of the communication and navigation constellation, and the navigation performance of the constellation can be further optimized on this basis to obtain the constellation configuration that meets the communication and navigation requirements with the minimum number of satellites. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 The three-body orbit moon communication and navigation constellation optimization method based on data preprocessing disclosed in the present application;

[0059] Figure 2 The type and amplitude range diagram for moon communication and navigation constellation design;

[0060] Figure 3 The orbit period interval diagram;

[0061] Figure 4 The orbit period interval diagram (interval 3 to 5);

[0062] Figure 5 The orbit period interval diagram (interval 8 to 12);

[0063] Figure 6-1 The orbit image in orbit set 1;

[0064] Figure 6-2 The orbit image in orbit set 2;

[0065] Figure 6-3 The orbit image in orbit set 3;

[0066] Figure 6-4 The orbit image in orbit set 4;

[0067] Figure 6-5 The orbit image in orbit set 5;

[0068] Figure 6-6 The orbit image in orbit set 6;

[0069] Figure 6-7 is the track image in track set 7;

[0070] Figure 6-8 is the track image in track set 8;

[0071] Figure 6-9 is the track image in track set 9;

[0072] Figure 6-10 is the track image in track set 10;

[0073] Figure 6-11 is the track image in track set 11;

[0074] Figure 6-12 is the track image in track set 12;

[0075] Figure 6-13 is the track image in track set 13;

[0076] Figure 6-14 is the track image in track set 14;

[0077] Figure 6-15 is the track image in track set 15;

[0078] Figure 6-16 is the track image in track set 16;

[0079] Figure 6-17 is the track image in track set 17;

[0080] Figure 6-18 is the track image in track set 18;

[0081] Figure 6-19 is the track image in track set 19;

[0082] Figure 6-20 is the track image in track set 20;

[0083] Figure 6-21 is the track image in track set 21;

[0084] Figure 6-22 is the track image in track set 22;

[0085] Figure 6-23 is the track image in track set 23;

[0086] Figure 6-24 is the track image in track set 24;

[0087] Figure 6-25 is the track image in track set 25;

[0088] Figure 6-26 Orbit image for orbit set 26;

[0089] Figure 6-27 Orbit image for orbit set 27;

[0090] Figure 6-28 Orbit image for orbit set 28;

[0091] Figure 7 Initial constellation plan for global communications constellation;

[0092] Figure 8-1 Global communications constellation configuration 1 to meet coverage requirements; Figure 8-2 Global communications constellation configuration 2 to meet coverage requirements; Figure 8-3 Global communications constellation configuration 3 to meet coverage requirements; Figure 8-4 Global communications constellation configuration 4 to meet coverage requirements; Figure 8-5 Global communications constellation configuration 5 to meet coverage requirements;

[0093] Figure 8-6 Global communications constellation configuration 6 to meet coverage requirements;

[0094] Figure 8-7 Global communications constellation configuration 7 to meet coverage requirements;

[0095] Figure 9 Initial constellation plan for global navigation constellation;

[0096] Figure 10-1 Global navigation constellation configuration 1 to meet coverage requirements;

[0097] Figure 10-2 Global navigation constellation configuration 2 to meet coverage requirements;

[0098] Figure 10-3 Global navigation constellation configuration 3 to meet coverage requirements;

[0099] Figure 11-1 Global navigation constellation configuration 1 after navigation performance optimization;

[0100] Figure 11-2 Global navigation constellation configuration 2 after navigation performance optimization;

[0101] Figure 11-3 Global navigation constellation configuration 3 after navigation performance optimization;

[0102] Figure 12 Initial constellation plan for combined navigation and communications constellation;

[0103] Figure 13 Combined navigation and communications constellation (7 satellites) after navigation performance optimization;

[0104] Figure 14-1 Hybrid constellation configuration 1 (8 satellites) for coverage requirement;

[0105] Figure 14-2 Hybrid constellation configuration 2 (8 satellites) for coverage requirement;

[0106] Figure 14-3 Hybrid constellation configuration 3 (8 satellites) for coverage requirement;

[0107] Figure 14-4 Hybrid constellation configuration 4 (8 satellites) for coverage requirement;

[0108] Figure 14-5 Hybrid constellation configuration 5 (8 satellites) for coverage requirement;

[0109] Figure 14-6 Hybrid constellation configuration 6 (8 satellites) for coverage requirement;

[0110] Figure 14-7 Hybrid constellation configuration 7 (8 satellites) for coverage requirement;

[0111] Figure 14-8 Hybrid constellation configuration 8 (8 satellites) for coverage requirement;

[0112] Figure 14-9 Hybrid constellation configuration 9 (8 satellites) for coverage requirement;

[0113] Figure 14-10 Hybrid constellation configuration 10 (8 satellites) for coverage requirement;

[0114] Figure 14-11 Hybrid constellation configuration 11 (8 satellites) for coverage requirement;

[0115] Figure 14-12 Hybrid constellation configuration 12 (8 satellites) for coverage requirement;

[0116] Figure 15-1 Hybrid constellation configuration 1 (8 satellites) for navigation performance optimization;

[0117] Figure 15-2 Hybrid constellation configuration 2 (8 satellites) for navigation performance optimization;

[0118] Figure 15-3 Hybrid constellation configuration 3 (8 satellites) for navigation performance optimization. DETAILED DESCRIPTION

[0119] The technical solutions in the embodiments of the present application will be clearly and completely described with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only exemplary and are not intended to limit the present application.

[0120] The present application provides a flow chart of a three-body orbit moon communication and navigation constellation optimization method based on data preprocessing, as shown in Figure 1 , comprising the following steps:

[0121] S1: According to the specific mission objectives of the moon communication and navigation constellation, determine the type and amplitude range of the orbits in the constellation;

[0122] The step S1 specifically comprises:

[0123] According to the specific requirements of the task and the characteristics of the orbit, determine the type and amplitude range of the orbit used to construct the constellation. In order to realize the coverage of the moon surface, the three-body orbits near the L1 and L2 points are selected to construct the moon communication and navigation constellation. The types of orbits include halo orbits, planar and vertical Lyapunov orbits, and DRO. Among these orbits, the halo orbit family is included in the constellation design, and the planar and vertical Lyapunov orbit family takes the maximum value of the halo orbit amplitude as the upper limit of the orbit amplitude. The amplitude range of the DRO orbit family can be smaller than other types of orbits, which is specifically set according to the period relationship between various orbits in the following preprocessing. The final orbit type and amplitude range are shown in Figure 2 . In Figure 2 , the green curve is the northward halo orbit of L1,2, the blue curve is the southward halo orbit of L1,2, the cyan is the planar Lyapunov orbit of L1,2, the magenta is the vertical Lyapunov orbit of L1,2, and the red is the DRO orbit. The origin of the figure is the position of the moon, the x-axis is the direction of the line connecting the earth and the moon, the z-axis is the direction of the earth-moon orbit, and the y-axis is right-handed with the x and z axes. The orbits corresponding to the L1 and L2 points in the figure are located on the front and back of the moon respectively, and the DRO orbit is located on the earth-moon plane. The amplitudes of halo and vertical Lyapunov orbits are the maximum absolute values of their orbits in the z direction, the amplitude of planar Lyapunov orbit is the maximum absolute value of its orbit in the y direction, and the amplitude of DRO orbit is the distance from its x-axis intersection position to the moon.

[0124] S2: Preprocess the relevant data of the satellites on the orbits used for constellation performance evaluation, including limiting the orbit period, discretizing the orbit amplitude, and generating an offline database, thereby obtaining different orbit sets and databases used in optimization;

[0125] The step S2 specifically comprises:

[0126] First, the period of the orbit is limited, i.e. when choosing orbits for the same constellation, only orbits with the same period or a period ratio of m:n are chosen. If the constraint of the same period is followed, the period range of all the orbit types chosen in this paper can be divided into 13 intervals according to the type of the orbit, and the type of the orbit contained in each interval is different, as shown in Figure 3 In the legend, "planar" and "vertical" refer to planar and vertical Lyapunov orbits respectively. Because the halo orbits of L1 increase first and then decrease with the increase of the amplitude, there is no unique correspondence between them. Therefore, in Figure 3 , the halo orbits of L1 are divided into two parts, one part increases with the increase of the amplitude, marked as L1-halo+, and the other part decreases with the increase of the amplitude, marked as L1-halo-. This is equivalent to artificially dividing the halo orbits of L1 into two families of orbits, so that a certain period only corresponds to one orbit. It should be noted that the halo orbits of L1 and L2 actually correspond to two symmetric orbit families in the north and south, and only one is plotted in the figure, but in fact there are two families of orbits that can be chosen in constellation design. In addition, because the period range of some intervals in Figure 3 is small, it is not convenient to label, only part of the interval is labeled. In the two red boxes in the figure, they correspond to intervals 3 to 5 and intervals 8 to 12 respectively, which are as shown in Figure 4 and Figure 5 .

[0127] If only the orbits with the same period are considered, only the orbits from the 13 intervals need to be selected. But this selection method will result in the orbits of different types with no intersection in the period range, which cannot be matched to form constellations, such as the halo orbits of L1 and the vertical Lyapunov orbits of L2. Moreover, it will result in only the orbits with the same period range in different orbit types that can be matched, which will also greatly limit the selection of orbits for constellations. Especially for some corresponding orbit types, such as the planar or vertical Lyapunov orbits of L1, 2, their period ranges have obvious differences. Many orbits with the same period in two orbit families cannot provide orbits with similar amplitudes, which is not conducive to the construction of constellations with symmetric properties about the moon. Therefore, in order to enable each orbit type to be matched with more types and amplitude ranges of orbits to form constellations, the part that satisfies the period integer ratio of m:n needs to be selected from each interval to form a new orbit interval, so as to enrich the selection of orbits for constellations. After verification, the period ratio values of 1:2, 2:3, 3:4, 2:5, and 4:5 can meet the needs of providing different types and amplitude ranges of orbits for most corresponding orbit types, which can greatly enrich the types of orbit matching in constellations. In addition, setting the orbit interval according to the period integer ratio can also adjust the period range of some orbit types participating in the constellation design. For example, the period range of the DRO is set according to the period range of other orbit types. In order to ensure that each period constellation can select a DRO, the minimum value of its period is selected as the minimum value of the halo orbit of L2, and the maximum value can be selected as 0.8 times the maximum value of the vertical Lyapunov orbit of L2 (i.e., the ratio is 4:5). In this way, the DRO can be matched with all other types of orbits. Other orbit types can also be adjusted according to the needs by similar methods.

[0128] It should be noted that the integer ratio of periods is not limited to the above combinations. For special orbit types, a unique period ratio can be set for them as needed. For example, the halo orbits of L1 and L2 are symmetric about the Moon, and are located on the front and back of the Moon, respectively. Orbits with similar amplitudes in these two families are often selected together to form a lunar constellation. In these two families, the orbits with amplitudes from 0 to 60,000 km have a small period range, and do not satisfy the existing integer period ratio, so they cannot be selected at the same time to form a constellation. A more unique period ratio can be set for them, so that orbits in these two families with amplitudes in this range can be selected with orbits with similar amplitudes. However, as the numerator or denominator of the ratio increases, the period of the constellation also increases. Therefore, through experiments, it is found that it is more appropriate to select 5:6, 6:7, 9:11, and 11:13 as the ratio to separately handle these two parts of the orbits, as long as the period of the constellation is not too large. If it is necessary to enable specific ranges of other specific orbit types to be selected at the same time to form a constellation, a similar method can be used to set a unique period ratio for them.

[0129] After the period of the orbit is limited, all orbit intervals of the same orbit type are integrated into a set. Finally, 28 fixed and limited sets are formed, which contain different orbit types. When the period of the constellation is determined, a certain number of orbits can be selected from the set to form a constellation.

[0130] Then, in order to reduce the number of orbits that need to be considered in the optimization of the constellation, the orbits in each orbit set are discretized at fixed amplitude intervals, and the optimization of the constellation is only based on these discretized orbits. When discretizing the orbits of a set, the reference orbit family in each period interval needs to be determined first. In the same period interval, the amplitude is used as the standard for measuring the geometric characteristics of the orbit, and the orbit family with the slowest period change relative to the amplitude is used as the reference orbit family, i.e., the orbit family with the largest amplitude change range in the period interval. Then, a limited number of orbits can be selected from the reference orbit family at fixed amplitude intervals as needed. Finally, the periods of the selected reference orbits are used as the standard to select the required orbits in other orbit families in the same set as candidate orbits. According to the period limitation mentioned above, the selected orbits should be divided into two categories. One category is to select orbits with the same period as the reference orbit according to the original period of the reference orbit. The other category is orbits with a period ratio of m:n to the period of the reference orbit. For example, the period of the reference orbit is T, and the period of the selected orbit is nT / m. The period of the selected orbit is determined by the period of the reference orbit, and the period of the reference orbit is determined by the period of the reference orbit. Figure 4For example, interval 2 in FIG. 6, the ratio of the period of the partial orbit of interval 1 to that of interval 2 is 4:5. And the orbit types of interval 2 also include those of interval 1, so these orbits are in the same set. At this time, the halo orbit of L1 in interval 2 has the largest range of amplitude variation, so it is taken as the reference orbit family, and a limited number of reference orbits are taken from it at fixed amplitude intervals. Then, according to the periods of these orbits, orbits of the same period or satisfying the period ratio are taken from other orbit families. That is, first, orbits of the same period are taken from the halo orbits of DRO and L2 in interval 2, and then orbits of 4 / 5 of the period are taken from interval 1 or 2. Note that although the reference orbits of the former and the latter have the same amplitude, the constellation periods formed by them are different, and need to be distinguished in the database. After discretization, orbits with a fixed number of orbit sets can be obtained, as shown in FIG. 6. Figure 6-1 to Figure 6-28 As mentioned in S2, the halo orbit of L1 is divided into two families of L1-halo+ and L1-halo-, so there are a total of 11 types of orbits: DRO, north L1-halo+, south L1-halo+, north L1-halo-, south L1-halo-, north L2-halo, south L2-halo, planar L1-Lyapunov, planar L2-Lyapunov, vertical L1-Lyapunov, and vertical L2-Lyapunov. The following are the orbit types in each set in FIG. 6: Figure 6-1 to Figure 6-28

[0131] Figure 6-1 : DRO, north L2-halo, south L2-halo;

[0132] Figure 6-2 : DRO, north L1-halo-, south L1-halo-, north L2-halo, south L2-halo;

[0133] Figure 6-3 : DRO, north L1-halo-, south L1-halo-, north L2-halo, south L2-halo, planar L1-Lyapunov;

[0134] Figure 6-4 : DRO, north L1-halo+, south L1-halo+, north L1-halo-, south L1-halo-, north L2-halo, south L2-halo, planar L1-Lyapunov;

[0135] Figure 6-5 ​: DRO, North L2-halo, South L2-halo, Planar L1-Lyapunov, Vertical L1-Lyapunov;

[0136] Figure 6-6 : DRO, North L2-halo, South L2-halo, Planar L1-Lyapunov, Vertical L1-Lyapunov;

[0137] Figure 6-7 : North L2-halo, South L2-halo, Planar L1-Lyapunov, Vertical L1-Lyapunov;

[0138] Figure 6-8 : North L2-halo, South L2-halo, Planar L1-Lyapunov, Planar L2-Lyapunov, Vertical L1-Lyapunov;

[0139] Figure 6-9 : Planar L1-Lyapunov, Planar L2-Lyapunov, Vertical L1-Lyapunov;

[0140] Figure 6-10 : Planar L1-Lyapunov, Planar L2-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0141] Figure 6-11 : Planar L2-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0142] Figure 6-12 : Planar L2-Lyapunov, Vertical L2-Lyapunov;

[0143] Figure 6-13 : Vertical L2-Lyapunov;

[0144] Figure 6-14 : DRO, North L2-halo, South L2-halo, Planar L1-Lyapunov, Planar L2-Lyapunov, Vertical L1-Lyapunov;

[0145] Figure 6-15 : DRO, North L2-halo, South L2-halo, Planar L1-Lyapunov, Planar L2-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0146] Figure 6-16 : DRO, North L2-halo, South L2-halo, Planar L2-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0147] Figure 6-17 : DRO, North L2-halo, South L2-halo, Planar L2-Lyapunov, Vertical L2-Lyapunov;

[0148] Figure 6-18 : DRO, North L2-halo, South L2-halo, Vertical L2-Lyapunov;

[0149] Figure 6-19 : DRO, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Planar L1-Lyapunov, Planar L2-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0150] Figure 6-20 : DRO, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Planar L1-Lyapunov, Planar L2-Lyapunov, Vertical L2-Lyapunov;

[0151] Figure 6-21 : DRO, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Vertical L2-Lyapunov;

[0152] Figure 6-22 : DRO, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Planar L1-Lyapunov, Vertical L1-Lyapunov;

[0153] Figure 6-23 : DRO, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Planar L1-Lyapunov, Planar L2-Lyapunov, Vertical L1-Lyapunov;

[0154] Figure 6-24: DRO, North L1-halo+, South L1-halo+, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Plane L1-Lyapunov, Plane L2-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0155] Figure 6-25 : DRO, North L1-halo+, South L1-halo+, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Plane L1-Lyapunov, Plane L2-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0156] Figure 6-26 : DRO, North L1-halo+, South L1-halo+, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Plane L1-Lyapunov, Plane L2-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0157] Figure 6-27 : DRO, North L1-halo+, South L1-halo+, North L1-halo-, South L1-halo-, North L2-halo, South L2-halo, Plane L1-Lyapunov, Plane L2-Lyapunov, Vertical L1-Lyapunov;

[0158] Figure 6-28 : DRO, North L2-halo, South L2-halo, Plane L1-Lyapunov, Vertical L1-Lyapunov, Vertical L2-Lyapunov;

[0159] Finally, according to the determined amplitude of the orbit in each orbit set, the unique corresponding orbit can be obtained, and an offline satellite visibility and geometric position database located on the orbit is generated for direct calling during optimization. Because in general constellation optimization and design, the visibility and geometric position of the satellite on the same orbit need to be recalculated in each performance evaluation, but these data are actually completely the same. Therefore, if the required data can be preprocessed and prepared, it can be directly called during optimization, which can save a lot of repeated calculations and speed up the calculation. The orbit data in the database is arranged according to [set number n set -Constellation period number n T -Orbit number n OThe orbit number indicates the number of the orbit in the constellation that can be used to form the constellation of the period. When the set number is determined, the range of the period number can be determined. When the set and period numbers are determined, the range of the orbit number can be determined. Of course, to determine the initial state of the satellite in the constellation, the initial phase φ is also needed. The phase indicates the position of the satellite on the orbit, which is the ratio of the time needed to run from the initial position of the orbit to the position to the period of the orbit, and the range is [0, 1). Finally, the position of a satellite can be represented by [set number n set -constellation period number n T -orbit number n O -phase φ]. To form a constellation, satellites need to be selected from orbits with the same set number and period number.

[0160] Through large-scale numerical verification, the performance of the constellation composed of various types of orbits is evaluated, and it is found that when the coverage performance is calculated by calling the database, the speed is 141.89 times that of the general method. When calculating the GDOP, the speed is 1.56 times that of the general method. At this point, the offline database that can be directly called in optimization to greatly reduce the amount of calculation has been constructed through preprocessing.

[0161] S3: Based on the orbit set and the database obtained through preprocessing, an initial scheme of the constellation is designed using a simulation-based comparative analysis method, and the number of satellites at present is taken as the initial scheme.

[0162] The step S3 specifically includes:

[0163] Based on the orbit set and the database obtained through preprocessing, an initial scheme of the constellation is designed using a simulation-based comparative analysis method, and the number of satellites at present is taken as the initial scheme.

[0164] The specific measures are as follows: first, in the range of the existing orbit set, the configuration scheme of the constellation is selected through prior experience. According to the range of the lunar target area that needs to be served, the orbit type that has an advantage in covering the target area is selected, such as the halo orbit family facing south for covering the South Pole, and the DRO orbit family for covering the equator.

[0165] Then, the set with these orbit families is selected, and the orbits corresponding to the types are selected in the set, and different numbers of satellites are set on different orbits as the design scheme. That is, when selecting, the orbit set number n set is first determined, and then a constellation period number n TIn the corresponding orbit, the part of the orbit which is more advantageous to cover the target area is selected, and a certain number of satellites are arranged in these orbits as constellation configuration schemes. In this process, different constellation periods, orbit combinations, the number of satellites in each orbit, and the phase of each satellite can be selected to obtain different constellation configuration schemes for subsequent selection and adjustment.

[0166] After that, the coverage performance of these schemes is simulated. For a communication constellation, the most important performance indicator is the coverage rate of the constellation to the target; for a navigation constellation, coverage rate and navigation accuracy are the most important performances, but meeting the coverage requirement is the basis for providing navigation services. The communication / navigation constellation needs to meet the one / four-fold coverage of the target area, that is, at least one / four satellites are visible to the area. When calculating the coverage rate of the target area, the grid point method is generally used. This method is to discretize the target area into a limited number of grid points, then calculate the visibility of each grid point relative to the satellites in the constellation at each time step in the constellation period, and finally count the overall coverage rate of the constellation. There are different ways to measure coverage rate, and coverage time percentage (CTP) is one of them. For a communication / navigation constellation, the CTP of a certain grid point is the proportion of the time that the point is covered by at least one / four satellites to the entire simulation time. The CTP of the target area is the average of the CTPs of all grid points in the area. When the CTP of a constellation in a certain orbit set reaches 100%, it means that the area meets the complete one / four-fold coverage, that is, it meets the coverage requirements of the communication / navigation constellation.

[0167] Finally, based on the results of the coverage performance simulation, the scheme with better performance or fewer satellites is selected. Then, the parameters of the obtained scheme are manually adjusted as appropriate. The adjustment includes adjusting the orbit number n O in the configuration, or adjusting the number of satellites in each orbit and the phase of the satellite in the orbit. After adjustment, the results with better performance or fewer satellites are continuously selected according to the results of performance simulation until it is difficult to improve performance or reduce the number of satellites, and the scheme with the best coverage performance in the adjustment process is selected, and the number of satellites is the least as the initial scheme, and the number is the current number of satellites.

[0168] S4: Based on the current number of satellites, one satellite is reduced, and in each orbit set, an intelligent optimization algorithm is used to optimize the constellation parameters with the coverage performance of the constellation as the objective function to find a configuration that meets the coverage requirements, and the corresponding orbit set is counted;

[0169] The step S4 specifically includes:

[0170] On the basis of the current number of satellites, one satellite is reduced, and intelligent optimization algorithms are used in each orbit set to optimize constellation parameters with the coverage performance of the constellation as the objective function, to find a configuration that can meet the coverage requirements, and to count the corresponding orbit set. The optimization problem in each set can be described as:

[0171]

[0172] where J is the objective function of optimization, x is the optimization variable vector, p is the fixed parameter vector, g and h are inequality and equality constraints, x LB and x UB are the upper and lower limits of the optimization variable. Because the performance indicators of communication and navigation constellations are different, their corresponding objective functions are also different. For a communication constellation, its objective function J C is:

[0173]

[0174] where CTP 1-fold is the one-time coverage time ratio of the communication constellation to the target area, which is generally calculated using the grid point method. This method is to discretize the target area into a finite number of grid points, then calculate the visibility of each grid point relative to the satellites in the constellation at each time step in the constellation period, and finally count the overall coverage performance of the constellation. The CTP of a certain grid point is the proportion of the time that the point is covered by at least one satellite to the entire simulation time. The CTP of the target area is the average of the CTPs of all grid points in the area. When the CTP 1-fold of the constellation in a certain orbit set is optimized to 100%, it means that the area meets the requirement of complete one-time coverage, i.e. the mission requirements of the communication constellation are met. At this time, record the constellation configuration and the corresponding orbit set.

[0175] In this optimization problem, the fixed parameter vector p is:

[0176] p=(N,n set ) T (3)

[0177] where N is the number of satellites in the constellation, and n set is the orbit set number. These two parameters are fixed in the optimization.

[0178] In this optimization problem, the optimization variable vector x is:

[0179] [n T ,n O1 ,n O2 ,φ2,...,n ON ,φ N ](4)

[0180] where n T is the constellation period number, [n O1 ,n O2 ,...,n ON ] is the orbit number of each satellite, and [φ2,...,φ N ] is the initial phase of the satellites on these orbits. Since the initial phase of the first satellite can be directly set to 0, there are only N-1 satellite phases, which can reduce one design variable. Since the constellation period number and the orbit number are integers, and the initial phase is a decimal number, the problem is a mixed integer optimization problem. Moreover, in the optimization, the range of the constellation period number is limited by the orbit set number, and the range of the orbit number is limited by both the constellation period number and the orbit set number.

[0181] In addition, for a communication constellation, only one-fold coverage of the target area is required. However, for a navigation constellation, four-fold coverage of the target area is required, i.e., at least four satellites are visible to it. Therefore, when optimizing the coverage rate, the objective function J N of the navigation constellation is:

[0182]

[0183] where CTP 4-fold is the four-fold coverage time ratio of the navigation constellation to the target area, which is calculated in a similar way to the one-fold coverage time ratio of the communication constellation, i.e., by the grid point method, which is not repeated here.

[0184] Here, the genetic algorithm (GA) in the intelligent optimization algorithm is selected to optimize the problem, which is performed in different orbit sets. Genetic algorithm GA is a method of searching for the optimal solution by simulating the natural evolution process. First, the algorithm randomly generates an initial set of configurations, then simulates the performance of these configurations respectively, and quickly obtains the objective function value CTP after processing by calling the visibility data of the satellites in the database. Then, select configurations with better performance from the solution set, and obtain the next generation population, i.e., the configuration solution set, through the crossover and mutation operations of chromosomes similar to the biological population evolution process. After repeated selection, crossover and mutation operations in each generation, the optimized constellation configuration is obtained.

[0185] S5: Repeat S4 until the number of satellites is reduced to the minimum number of satellites required to find a configuration that meets the coverage requirements, i.e., the minimum number of satellites required and the corresponding orbit set that meet the requirements are obtained, and the constellation configuration in these sets that meet the requirements is obtained.

[0186] The step S5 specifically includes:

[0187] Step S4 is repeated, the number of satellites is constantly reduced, and the coverage performance of the constellation is optimized in each orbit set to find a configuration that can meet the coverage requirement under the current number of satellites, and the corresponding orbit set is counted, until the number of satellites is reduced to all sets cannot find a configuration that meets the coverage requirement. Add one to the current number of satellites, that is, the minimum number of satellites that can meet the coverage requirement, and record the corresponding orbit set and constellation configuration at this time.

[0188] S6: For the navigation constellation, in each orbit set corresponding to the current number of satellites that can find a configuration that meets the coverage requirement, after optimizing the coverage performance of the constellation to completely meet the coverage requirement, further optimize the navigation performance;

[0189] The step S6 specifically includes:

[0190] For the communication constellation, the index for evaluating its performance is the coverage of the target, so the minimum number of satellites that can meet the coverage requirement is found, and the corresponding orbit set and constellation configuration at this time are recorded. For the navigation constellation, the most important performance index is not only the coverage of the target, but also the navigation accuracy. Therefore, on the basis of meeting the coverage requirement, the navigation accuracy of the constellation needs to be further optimized. There are many indexes for measuring the navigation accuracy of the constellation, and the geometric dilution of precision GDOP is taken as an index which is widely used in this method. The GDOP represents the navigation error caused by measurement error, and the smaller the value is, the better the navigation performance is. The calculation method of the GDOP corresponding to a grid point in the target area is as follows:

[0191]

[0192] Q = H T H -1 (7)

[0193]

[0194] Where (x, y, z) is the position of the grid point, (xm, ym, zm) is the relative position of the mth satellite visible to the point, R m is the relative distance of the satellite. H is a matrix constructed by the relative geometric relationship between the satellite and the point, and the matrix Q can be obtained from H. Q 11 , Q 22 , Q 33 , Q 44 are the elements on the diagonal of Q.

[0195] Because the navigation constellation needs to meet the fourfold coverage requirement first, and then further optimize the navigation accuracy, the objective function J N optimized in each orbit set is a piecewise function:

[0196]

[0197] where GDOP mean is the average GDOP value of the target area. When the fourfold coverage of the constellation does not meet the requirement, the optimization objective of J N is to maximize CTP 4-fold . When the coverage requirement is met, the optimization objective is to further minimize the average GDOP value GDOP mean . And GDOP mean is too large, the constellation configuration exceeding 1000 is directly counted as 1000.

[0198] Similarly, based on the genetic algorithm GA, the optimization of the navigation constellation can be carried out in the confirmation that the orbit set meeting the coverage requirement can be found. The visibility and geometric position of the satellites in the database can be directly called during the optimization, and the objective function value can be quickly obtained after processing, and the optimized constellation configuration is obtained.

[0199] S7: If the navigation performance of the finally obtained configuration is not ideal, the number of satellites can be gradually increased to repeat S6 to continue optimizing the navigation performance until it meets the needs.

[0200] The step S7 specifically includes:

[0201] After the optimization of the navigation performance of the constellation in step S6, if it is found that the average GDOP value of the obtained constellation is relatively poor and cannot meet the navigation needs, the number of satellites can be further increased on the basis of the current number of satellites, and then step S6 is repeated to continue optimizing the navigation performance of the constellation until it can meet the accuracy of the navigation needs. The navigation accuracy requirement can be set according to the needs, and generally it is set to be not greater than a certain value, which is set to 10 here. Then, in the results corresponding to the number of satellites, the orbit set and the constellation configuration meeting the navigation needs are counted.

[0202] The effectiveness of the method proposed in the application will be described below by taking the global communication, global navigation and hybrid constellation of communication and navigation as solving examples.

[0203] First, the global communication constellation. Using the simulation-based comparative analysis method, the initial scheme as shown in Figure 7 can be obtained, which has a total of 7 satellites. On this basis, the number of satellites is gradually reduced, and the coverage performance of the constellation is optimized in each orbit set to obtain the minimum number of satellites that can meet the coverage requirement as 5. At this time, a total of 8 orbit sets can find a configuration that meets the coverage requirement. After induction and arrangement, there are 7 configurations as shown in Figure 8-1 to Figure 8-7 , and the orbit composition and satellite number distribution are as follows:

[0204] Configuration 1 : DRO (1), south L1 -halo + (1), north L2-halo (2), south L2-halo (1);

[0205] Configuration 2: north L2-halo (2), south L2-halo (2), planar L1 -Lyapunov (1);

[0206] Configuration 3: north L2-halo (2), south L2-halo (1), vertical L1 -Lyapunov (2);

[0207] Configuration 4: north L2-halo (1), south L2-halo (2), vertical L1 -Lyapunov (2);

[0208] Configuration 5: planar L2-Lyapunov (1), north L2-halo (2), south L1 -halo + (2);

[0209] Configuration 6: vertical L2-Lyapunov (1), north L2-halo (1), south L1 -halo + (3);

[0210] Configuration 7: vertical L2-Lyapunov (2), north L2-halo (1), south L1 -halo + (2);

[0211] Then the global navigation constellation. Using the simulation-based comparative analysis method, the initial scheme as shown in Figure 9 can be obtained, which has 16 satellites in total. On this basis, the number of satellites is gradually reduced, and the coverage performance of the constellation in each orbit set is optimized, and the minimum number of satellites that can meet the coverage requirements is 15. At this time, a total of 3 orbit sets can find a configuration that meets the coverage requirements. After induction and arrangement, there are 3 configurations as shown in Figure 10-1 to Figure 10-3 , and the orbit composition and satellite number distribution are as follows:

[0212] Configuration 1 : DRO (4), north L2-halo (2), south L2-halo (2), north L2-halo (1), south L2-halo (2), planar L1 -Lyapunov (1), vertical L1 -Lyapunov (3);

[0213] Configuration 2: north L2-halo (4), south L2-halo (4), planar L1 -Lyapunov (2), vertical L1 -Lyapunov (5);

[0214] Configuration 3: DRO (3), North L2-halo (4), South L2-halo (4), North L1-halo+ (2), South L1-halo+ (2);

[0215] After further GDOP optimization in the 3 sets, the results are shown in Figure 11-1 to Figure 11-3 The orbital configuration and satellite number distribution of the optimized configurations are the same as in Figure 10-1 to Figure 10-3 except for the phase distribution of the satellites. The optimized 3 configurations can all provide the required navigation accuracy for the lunar surface, with average GDOP values of 3.135, 5.972, and 3.132, respectively.

[0216] Because the lunar constellation can provide communication and navigation services for the same or different regions simultaneously in addition to providing services for a certain region alone, i.e., as a hybrid constellation, in some phased deployment strategies of global navigation constellations, the first phase is to provide communication services for the South Pole, the second phase is to provide navigation services for the South Pole while providing communication services for the world, and the third phase is to provide navigation services for the world. Therefore, we also take the hybrid constellation that provides navigation services for the South Pole and communication services for the world as a design goal.

[0217] Using the simulation-based comparative analysis method, the initial scheme shown in Figure 12 is obtained, which has 10 satellites in common. On this basis, the number of satellites is gradually reduced, and the coverage performance of the constellation is optimized in each orbital set, and the minimum number of satellites that can meet the coverage requirements is 7. However, at this time, only one orbital set can find a configuration that meets the requirements. After further GDOP optimization in the set, the configuration obtained is shown in Figure 13 Although this configuration can achieve complete coverage, even after optimization, its GDOP value is still very poor (greater than 100). Therefore, the number of satellites is increased to 8, and optimization is continued. After optimization of the coverage rate, a total of 15 orbital sets can find configurations that meet the coverage requirements. After induction and arrangement, a total of 12 different configurations shown in Figure 14-1 to Figure 14-12 are obtained, and the orbital configuration and satellite number distribution are as follows:

[0218] Configuration 1: DRO (1), North L2-halo (1), South L2-halo (4), South L1-halo+ (2);

[0219] Configuration 2: South L2-halo (3), South L2-halo (1), North L1-halo- (1), South L1-halo- (1), South L1-halo+ (2);

[0220] Configuration 3: North L2-halo (2), South L2-halo (5), Vertical L1-Lyapunov (1);

[0221] Configuration 4: North L2-halo (2), South L2-halo (4), Vertical L1-Lyapunov (2);

[0222] Configuration 5: North L2-halo (1), South L2-halo (4), Vertical L1-Lyapunov (2), Vertical L2-Lyapunov (1);

[0223] Configuration 6: North L2-halo (2), South L2-halo (2), South L1-halo+ (4);

[0224] Configuration 7: DRO (1), North L2-halo (1), South L2-halo (1), North L1-halo- (1), South L1-halo- (4);

[0225] Configuration 8: DRO (1), North L2-halo (1), South L2-halo (3), North L1-halo- (1), South L1-halo- (2);

[0226] Configuration 9: North L2-halo (2), South L2-halo (3), South L1-halo+ (3);

[0227] Configuration 10: South L2-halo (6), North L1-halo+ (2);

[0228] Configuration 11: North L2-halo (1), South L2-halo (5), South L1-halo+ (2);

[0229] Configuration 12: South L2-halo (7), Vertical L1-Lyapunov (1);

[0230] After further GDOP optimization in the 15 orbit sets, the GDOP average of the optimization results in 6 sets is below 10, and there are three types of configurations after summarizing. One type of configuration in each of the first two sets has slightly poor performance; one type of configuration in the last 4 sets has good performance. The three types of configurations are shown in Table 1, and the orbit composition and satellite number distribution are as follows: Figure 15-1 to Figure 15-3

[0231] ​Configuration 1: south L2-halo (2), south L2-halo (1), north L1-halo-(2), south L1-halo-(3);

[0232] Configuration 2: north L2-halo (1), south L2-halo (4), vertical L2-Lyapunov (1), vertical L2-Lyapunov (2);

[0233] Configuration 3: north L2-halo (1), south L2-halo (3), south L1-halo+(4);

[0234] The average GDOP values of the three types of configurations are 8.509, 8.598 and 4.989 respectively, all of which can meet the global communication requirements while providing the required navigation accuracy for the South Pole.

[0235] The algorithm effectively reduces the calculation amount of the constellation composed of three-body orbits in the optimization process by preprocessing the data used for performance evaluation of the communication navigation constellation, successfully overcomes the problem that all parameters of the constellation, i.e., the orbit type, orbit amplitude and phase of the satellite, cannot be optimized simultaneously in the existing research, so that the method can obtain more candidate constellation configurations than the general method. In addition, by gradually reducing the number of satellites and optimizing the coverage performance of the constellation based on the initial scheme obtained by the simulation-based comparative analysis method, the minimum number of satellites that meets the basic coverage requirements of the constellation can be obtained, and the navigation performance of the constellation can be further optimized on this basis to obtain a constellation configuration that meets the communication and navigation requirements with the smallest number of satellites, which reduces the cost of the constellation while ensuring the performance of the constellation.

[0236] In summary, the method proposed in the application has the advantages of extremely fast calculation speed and more candidate configurations obtained in the optimization design of the lunar communication navigation constellation composed of three-body orbits, has good engineering application value, and has a good popularization prospect.

[0237] The basic principles and implementation steps of the application are demonstrated above, and the effectiveness and practicality of the method proposed in the application are verified by examples. Obviously, those skilled in the art can make various modifications and variations to the application without departing from the spirit and scope of the application. Thus, if these modifications and variations of the application fall within the scope of the claims of the application and their equivalent technologies, the application also intends to include these modifications and variations.

Claims

1. A method for optimizing a constellation of communication and navigation satellites for a three-body orbiting moon based on data preprocessing, characterized in that, The method comprises the following steps: S1: according to the specific task target of the lunar communication and navigation constellation, the type and amplitude range of the orbit in the constellation are determined; S2: the relevant data of the satellite on the orbit for constellation performance evaluation are preprocessed, including limiting the orbit period, discretizing the orbit amplitude, and generating an offline satellite visibility and geometric position database, so as to obtain different orbit sets and databases used in optimization; S3: based on the orbit sets and databases obtained by preprocessing, an initial scheme of the constellation is designed using a simulation-based comparative analysis method, and the initial scheme is used as the current number of satellites; S4: on the basis of the current number of satellites, one satellite is reduced, and intelligent optimization algorithms are used in each orbit set to optimize the constellation parameters with the coverage performance of the constellation as the objective function, to find a configuration that can meet the coverage requirements, and to count the corresponding orbit set; S5: repeat step S4 until the satellite is reduced to the minimum number of satellites required to find a configuration that meets the coverage requirements, that is, the minimum number of satellites required and the corresponding orbit set are obtained, and the constellation configuration that meets the requirements in the set is obtained; S6: for the navigation constellation, in each orbit set corresponding to the current number of satellites that meets the coverage requirements, after optimizing the coverage performance of the constellation to completely meet the coverage requirements, the navigation performance is further optimized; S7: if the navigation performance of the final configuration is not ideal, gradually increase the number of satellites and repeat step S6 to continue optimizing the navigation performance until it meets the requirements.

2. The method of claim 1, wherein the method is based on data preprocessing of a three-body orbit lunar communication navigation constellation optimization. Step S1 specifically comprises: In order to realize the coverage of the lunar surface, three-body orbits near L1 and L2 points are selected to construct the lunar communication and navigation constellation; the types of orbits include halo orbits, planar and vertical Lyapunov orbits, and distant retrograde orbits DRO; The maximum value of the halo orbit amplitude is taken as the upper limit of the amplitudes of other orbit families; the maximum value of the DRO amplitude is set to be smaller than the maximum value of the halo orbit amplitude, and the specific range is set according to the period relationship between various orbits in preprocessing.

3. The method of claim 1, wherein the method is based on data preprocessing of a three-body orbit lunar communication navigation constellation optimization. Step S2 specifically comprises: First, the period of the orbit is limited, that is, when selecting orbits for the same constellation, only orbits with the same period or a period in the ratio of m:n are selected; the period range of the DRO is set according to the period range of other orbit types; in order to ensure that the constellation of each period can select the DRO, the minimum value of the period is set to be the minimum value of the period of other orbit families, and the maximum value of the period satisfies the integer ratio with the maximum value of the period of other orbit families; Then, in order to reduce the number of orbits to be considered in constellation optimization, the orbits in each orbit set are discretized with fixed amplitude intervals; when discretizing the orbits in a certain set, the reference orbit family in each period interval needs to be determined; in the same period interval, taking the orbit family with the slowest period change relative to amplitude as the reference orbit family, that is, the orbit family with the largest amplitude change range in the period interval; a limited number of orbits are selected from the reference orbit family with fixed amplitude intervals; the periods of the selected reference orbits are used as the standard to select the required orbits in other orbit families in the same set as candidate orbits; Finally, the unique corresponding orbit is obtained according to the amplitude of the orbit in the determined orbit set, and an offline database of satellite visibility and geometric position on the orbit is generated for direct calling during optimization; the orbit data in the database is numbered by [set number n set - constellation period number n T - orbit number n O ]; wherein the set number represents the type of orbit; the period number is the number of different constellation periods, which is used to constitute the orbit of the constellation; the orbit number represents the number of orbits that can be used to constitute the constellation of the period; when the set number is determined, the range of the period number can be determined; when the set and the period number are determined, the range of the orbit number can be determined; to determine the initial state of the satellite in the constellation, the initial phase φ is also needed; the phase represents the position of the satellite on the orbit, which is the ratio of the time required to run from the initial position of the orbit to the position to the orbit period, and its range is [0, 1); finally, the position of a satellite is represented by [set number n set - constellation period number n T - orbit number n O - phase φ]; to constitute a constellation, satellites need to be selected from orbits with the same set number and period number.

4. The method of claim 1, wherein the method is based on data preprocessing of a three-body orbit lunar communication navigation constellation optimization. Step S3 specifically includes: First, in the range of the existing orbit set, the configuration scheme of the constellation is selected by prior experience; according to the range of the target area to be served, the orbit type with an advantage in covering the target area is selected; Then, a set of these orbital families is selected, and in these sets, the orbital families corresponding to the selected categories are selected, and different numbers of satellites are arranged in different orbits as design schemes; that is, when selecting, the orbital set number n is first determined set Then, from a certain constellation period number n T In the corresponding orbits, the partial orbits that are beneficial to the coverage of the target area are selected, and a certain number of satellites are arranged in these orbits as constellation configuration schemes; in this process, different constellation periods, orbital combinations, numbers of satellites on each orbit, and phases of each satellite are selected to obtain different constellation configuration schemes for subsequent selection and adjustment; Then, the coverage performance of these schemes is simulated; the communication / navigation constellation needs to meet one / four-fold coverage of the target area, that is, at least one / four satellites are visible to the area; when calculating the coverage rate of the target area, the grid point method is used; this method is to discretize the target area into a limited number of grid points, then calculate the visibility of each grid point relative to the satellites in the constellation at each time step in the period of the constellation, and finally calculate the overall coverage rate of the constellation; for the communication / navigation constellation, the CTP of a certain grid point is the proportion of the time that the point is covered by at least one / four satellites to the entire simulation time; and the CTP of the target area is the average of the CTPs of all grid points in the area; when the CTP of the constellation in a certain orbit set reaches 100%, it means that the area meets the complete one / four-fold coverage, that is, the coverage requirement of the communication / navigation constellation is met; Finally, based on the results of the coverage performance simulation, the scheme with better performance or less satellites is selected; the parameters of the obtained scheme are adjusted; the adjustment includes adjusting the orbit number n O in the configuration, or adjusting the number of satellites on each orbit and the phase of the satellites on the orbit; after the adjustment, the results with better performance or less satellites are constantly selected according to the results of the performance simulation until it is difficult to improve the performance or reduce the number of satellites, and the scheme with the optimal coverage performance in the adjustment process is selected, and the number of satellites is the least as the initial scheme, and the number is the current number of satellites.

5. The method of claim 1, wherein the method is based on data preprocessing of a three-body orbit lunar communication navigation constellation optimization. Step S4 specifically includes: On the basis of the current number of satellites, one satellite is reduced, and intelligent optimization algorithms are used in each orbit set to optimize the constellation parameters with the coverage performance of the constellation as the objective function, to find a configuration that can meet the coverage requirements, and to count the corresponding orbit set; the optimization problem in each set is described as: where J is the objective function to be optimized, x is the vector of optimization variables, p is the vector of fixed parameters, g and h are inequality and equality constraints, respectively, x LB and x UB are the upper and lower bounds of the optimization variables; since the performance metrics of the communication and navigation constellations are different, the corresponding objective functions are also different; for the communication constellation, the objective function J C is: Among them, CTP 1-fold The percentage of time a communication constellation provides coverage of a target area; when the CTP of a constellation in a certain orbital set... 1-fold When the coverage is optimized to 100%, it means that the area meets the requirements of a complete first layer of coverage, that is, the mission requirements of the communication constellation are met; at this time, the constellation configuration and the corresponding set of orbits are recorded.

6. The method of claim 5, wherein the method is based on data preprocessing of a three-body orbit lunar communication navigation constellation optimization. In this optimization problem, the fixed parameter vector p is: p = (N, n set ) T (3) where N is the number of satellites in the constellation, n set is the orbit set number; these two parameters are fixed in the optimization.

7. The method of claim 5, wherein the method is based on data preprocessing of a three-body orbit lunar communication navigation constellation optimization. In this optimization problem, the optimization variable vector x is: [n T ,n O1 ,n O2 ,φ2,...,n ON ,φ N ](4) where n T is the constellation period number, [n O1 ,n O2 ,...,n ON ] is the orbit number of each satellite, and [φ2,...,φ N ] is the initial phase of the satellites on these orbits; because the initial phase of the first satellite is directly set to 0, there are only N-1 satellite phases, which reduces one design variable; because the constellation period number and the orbit number are integers, the initial phase is a decimal number.

8. The method for optimizing constellation of three-body orbit moon communication navigation satellites based on data preprocessing according to claim 5 or 6, characterized in that: For communication constellation, only one-coverage to the target area is required; but for navigation constellation, four-coverage to the target area is required, i.e. at least four satellites are visible to the target area; so the objective function J N for navigation constellation is: wherein CTP 4-fold is the four-fold coverage time proportion of the target area by the constellation of navigation stars.

9. The method of claim 8, wherein the method is based on data preprocessing of a three-body orbit lunar communication navigation constellation optimization. Step S6 specifically includes: The navigation accuracy of the constellation adopts the geometric dilution of precision factor GDOP, which represents the navigation error caused by measurement error, and the smaller the value, the better the navigation performance; the calculation method of the GDOP corresponding to a certain grid point in the target area is as follows: Q = H T H -1 (7) Where (x,y,z) is the position of the grid point, (x m ,y m ,z m R is the relative position of the m-th visible satellite to this point. m H is the relative distance to the satellite; H is a matrix constructed from the relative geometric relationship between the satellite and the point, and matrix Q is obtained from H, which is a 4×4 square matrix. 11 Q 22 Q 33 Q 44 It is an element on the diagonal of Q; Because the navigation constellation needs to meet the requirement of fourfold coverage first, and then further optimize the navigation accuracy, the objective function J N optimized by the navigation constellation in each orbit set is a piecewise function: Among them, GDOP mean J represents the average GDOP value of the target area; when the constellation's quadruple coverage does not meet the requirements, J... N The optimization objective is to maximize CTP. 4-fold When the coverage requirement is met, the optimization objective is to further minimize the average GDOP. mean And GDOP mean Constellation configurations that are too large, exceeding 1000, are directly counted as 1000; Similarly, based on the genetic algorithm GA, the optimization of the navigation constellation is carried out in the orbit set that can meet the coverage requirements; during optimization, the visibility and geometric position of the satellites in the database are directly called, and after processing, the objective function value is quickly obtained, and the optimized constellation configuration is obtained.

10. The method of claim 9, wherein the method is based on data preprocessing of a three-body orbit lunar communication navigation constellation optimization. Step S7 specifically includes: After the optimization of the navigation performance of the constellation in step S6, if the average GDOP value of the obtained constellation is found to be unable to meet the navigation requirement, the number of satellites is further increased on the basis of the current number of satellites, and then step S6 is repeated to continue optimizing the navigation performance of the constellation until it can meet the accuracy of the navigation requirement; the navigation accuracy requirement is set according to the self needs; and then among the results corresponding to the number of satellites, the orbit set and the constellation configuration that can meet the navigation requirement are counted.

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