Three-body orbit lunar communication navigation constellation optimization method based on data preprocessing

Abstract

The invention provides a three-body orbit lunar communication navigation constellation optimization method based on data preprocessing. The three-body orbit lunar communication navigation constellation optimization method comprises the following steps: S1, determining the type and amplitude range of an orbit in a constellation; s2, preprocessing related data of satellites on orbits for constellation performance evaluation to obtain different orbit sets and databases used in optimization; s3, designing and obtaining an initial scheme of the constellation based on the track set obtained through preprocessing and a database; s4, on the basis of the current number of satellites, reducing one satellite, and in each orbit set, performing statistics on the corresponding orbit set by using an intelligent optimization algorithm; s5, the step S4 is repeated until the number of satellites is reduced, and the configuration meeting the coverage requirement cannot be found any more; s6, further optimizing the navigation performance for the navigation constellation; and S7, if the navigation performance of the finally obtained configuration is not ideal enough, gradually increasing the number of satellites, then repeating the step S6, and continuing to optimize the navigation performance until the navigation performance meets the requirement.

Description

Technical Field

[0001] The present invention belongs to the technical field of constellation optimization design, and in particular relates to a three-body orbit lunar constellation optimization method based on data preprocessing. Background Art

[0002] As human beings' interest in lunar exploration increases, more and more countries and space agencies have proposed their own exploration plans, which puts higher requirements on basic services such as lunar communications and navigation. However, the existing ground facilities have poor coverage of the moon. For some special areas, such as the back of the moon, it cannot be directly covered. Moreover, the substantial increase in spacecraft in the cis-lunar space has led to a sharp increase in the amount of information generated, and ground facilities have been difficult to meet the demand. Building a lunar constellation can greatly alleviate the pressure on ground facilities and effectively solve the above problems. Many space agencies have proposed lunar constellations that can provide communication and navigation services. The constellation design will directly affect the functional realization and performance level of the entire system. It needs to determine the number of satellites, orbit type and parameters, satellite phases, and collaborative working modes. Limited by cost and mission objectives, the number of satellites and working modes are generally determined. Therefore, the design variables of the general constellation are the orbit type and parameters, as well as the phase of the satellite in orbit.

[0003] The optimal design of the constellation is a relatively complex optimization problem, which is generally solved by intelligent optimization algorithms. However, due to the existence of three-body orbits in the Earth-Moon space, the design of the lunar constellation is different from the traditional Earth constellation composed of Keplerian orbits. The rich types and properties of three-body orbits bring more choices and possibilities to the constellation design, but also lead to a larger design space. In addition, the grid point method for evaluating the performance of the communication and navigation constellation also requires a large amount of calculation, which is unacceptable for the intelligent optimization algorithm that consumes a lot of computing resources. Therefore, the optimization of constellations with three-body orbits generally only optimizes some parameters of the constellation, rather than optimizing all parameters at the same time, which will result in missing many configurations with excellent performance. By preprocessing the data used for constellation performance evaluation, including limiting the orbital period, discretizing the orbital amplitude and generating an offline database, this method can effectively reduce the amount of calculation in constellation optimization, thereby realizing the simultaneous optimization of all parameters. And first, by optimizing the coverage performance, the minimum number of satellites that can meet the basic coverage requirements of the communication and navigation constellation, as well as as many candidate constellation configurations as possible, are obtained. Then, on the basis of meeting the requirements, the navigation performance of the constellation is further optimized. Summary of the invention

[0004] In view of this, the present invention proposes a three-body orbit lunar communication and navigation constellation optimization method based on data preprocessing, which is used to optimize the constellation parameters on the basis of known specific mission requirements of the lunar communication or navigation constellation to obtain a candidate constellation configuration with optimal performance.

[0005] To achieve the above object, the present invention proposes a three-body orbit lunar communication and navigation constellation optimization method based on data preprocessing, which specifically includes the following steps:

[0006] S1: Determine the types and amplitude ranges of orbits in the constellation based on the specific mission objectives of the lunar communications and navigation constellation;

[0007] S2: Preprocessing the data of satellites in orbit for constellation performance evaluation, including limiting orbit period, discretizing orbit amplitude and generating offline database, thereby obtaining different orbit sets and databases used in optimization;

[0008] S3: Based on the orbit set and database obtained by preprocessing, the initial plan of the constellation is designed using the simulation-based comparative analysis method, and this is used as the current number of satellites;

[0009] S4: Based on the current number of satellites, one satellite is reduced, and in each orbital 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 can meet the coverage requirements, and the corresponding orbital set is counted;

[0010] S5: Repeat step S4 until the number of satellites is reduced to the point where no configuration that meets the coverage requirement can be found, that is, the minimum number of satellites and corresponding orbital sets required, as well as constellation configurations that meet the requirements in these sets, are obtained;

[0011] S6: For the navigation constellation, in each orbital set corresponding to the current number of satellites that can find a configuration that meets the coverage requirements, after optimizing the constellation coverage performance until the coverage requirements are fully met, further optimize the navigation performance;

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

[0013] 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 present invention, step S1 specifically includes:

[0014] The type and amplitude range of the orbit used to build the constellation are determined according to the specific needs of the mission and the characteristics of the orbit. In order to achieve coverage of the lunar surface, this method selects a three-body orbit near the L1 and L2 points to build a lunar communication and navigation constellation. The types of orbits include halo orbits, planar and vertical Lyapunov orbits, and distantretrograde orbits (DRO). Among these orbits, the geometry of the halo orbit will change significantly with the change of amplitude, resulting in changes in its coverage characteristics for the lunar surface. In addition, considering that an orbit near the moon is required, a distance that is too far is not conducive to communication and will also increase maintenance costs. The halo orbit family is relatively close to the moon, so it can be included in the constellation design as a whole. The minimum amplitude is very small, approaching 0, and the maximum is about 82,863 kilometers. Unlike the halo orbit, the amplitude range of the planar and vertical Lyapunov orbit family is very large, and the minimum orbit amplitude is also approaching 0, but the maximum can be hundreds of thousands of kilometers away from the moon. Too large a distance is not conducive to providing communication and navigation services on the lunar surface. Since the geometric shapes of these orbital families are similar and do not change significantly with the amplitude change, some orbits with smaller amplitudes can be selected to participate in the constellation design. Here, the maximum amplitude of the halo orbit is used as the upper limit of the amplitude of other orbital families. In addition, the geometric shapes of different DROs are also similar, but as the amplitude increases, the increase in their coverage of the lunar surface area will quickly stagnate. It mainly covers the equatorial region, and the coverage of other areas cannot be solved by increasing the amplitude, and can only rely on other types of orbits. Moreover, when the amplitude of the DRO is the smallest, its orbit is near the moon. When its amplitude gradually increases, its orbit gradually moves away from the moon. In the process of gradually increasing the amplitude of this orbit, the speed of the change of the phase angle of the satellite on it will become more and more unevenly distributed throughout the orbit, resulting in a relatively large change in the relative phase between satellites, which is not conducive to coverage. Therefore, the maximum amplitude of the DRO can be set smaller than the maximum amplitude of the halo orbit, and its specific range is set according to the periodic relationship between various orbits in the subsequent preprocessing.

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

[0016] First, limit the orbital period, 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. This is to compress the period of the constellation to reduce the time required for performance evaluation. Because if the orbital periods within 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 constellation period is also conducive to operations in the formal operation after deployment, such as phase adjustment, which is a more common setting. If only orbits with the same period are considered in constellation design, it will lead to the inability to match orbital types with no intersection in the period range. Moreover, among the orbital types with an intersection in the period range, only orbits with the same amplitude range of the period can be matched with each other, which will greatly limit the orbital selection of the constellation. Therefore, in order to enable each orbital type to be matched with orbits of more types and amplitude ranges to form a constellation, it is necessary to select the part that satisfies the period integer ratio of m:n from each interval to form a new orbital interval to enrich the orbital selection of the constellation. Because for all selected orbital families, the amplitude and the orbit have a unique correspondence, and the orbital period is determined when the amplitude is determined, so the orbital amplitude range determined in S1 can determine the period range of all orbits. In addition, the method of setting the orbital interval according to the integer ratio of the period is also conducive to adjusting the period range of some orbital types participating in the constellation design. For example, the period range of DRO is set according to the period range of other orbital types. In order to ensure that DRO can be selected for each period of the constellation, the minimum value of its period is set to the minimum value of the period of other orbital families, and the maximum value satisfies the integer ratio with the maximum value of the period of other orbital families. Moreover, the integer ratio of the period is not necessarily limited to a given combination. For special orbital types, the period ratio can be set separately as needed. For example, the halo orbits of L1 and L2 are symmetrical about the moon, located on the front and back of the moon respectively, and the orbits with similar amplitudes are often selected together to construct the lunar constellation. In these two orbital families, the period range corresponding to the orbits within the amplitude of 0 to 60,000 km is small, and they just do not meet the existing integer ratio of the period, so they cannot be selected at the same time to form a constellation. A more unique period ratio can be set for it, so that the orbits in the two orbital families in this amplitude range can choose orbits with amplitudes closer to their own. Finally, all orbital intervals with the same orbital type are integrated into one set.

[0017] Then, in order to reduce the number of orbits to be considered in constellation optimization, the orbits in each orbital set are discretized with fixed amplitude intervals. Because for three-body orbits, orbits with similar amplitudes are also similar in performance. Therefore, it is desirable to replace all orbits with some orbits. And by discretizing the number of orbits to be limited, the visibility and relative geometric position data of the satellites on the orbit relative to the grid points on the lunar surface can be generated in advance for use in the optimization process. If the amplitudes of these orbits are continuous, it is impossible to generate all the orbital data in advance. Therefore, the optimization of the constellation is only based on these discretized orbits. When discretizing the orbits of a set, it is first necessary to determine the reference orbital family in each period interval. In the same period interval, the amplitude is used as the standard to measure the geometric characteristics of the orbit, and the orbital family with the slowest change in period relative to the amplitude is the reference orbital family, that is, the orbital family with the largest amplitude change range in the period interval. Then, a limited number of orbits can be selected from the reference orbital family at fixed amplitude intervals as needed. Finally, based on the period of the selected reference orbits, the required orbits are selected as candidate orbits from other orbital families in the same set.

[0018] Finally, it is necessary to obtain the unique corresponding orbit based on the amplitude of the orbit in each orbital set, and thereby generate an offline database of the satellite visibility and geometric position on the orbit for direct call during optimization. Because in general constellation optimization and design, the visibility and geometric position of satellites on the same orbit need to be recalculated in each performance evaluation, but these data are actually exactly the same. Therefore, if the required data can be pre-processed and prepared, and directly called during the optimization process, a large amount of repeated calculations can be omitted, thereby achieving the effect of accelerating the calculation. The orbital data in the database are sorted by [set number n set - Constellation period number n T - Track number n O ] are numbered. The set number indicates the type of orbit. The period number is the number of different constellation periods, corresponding to the orbits that can be used to form the constellation of the period. The orbit number indicates the number of the orbit in the constellation that can be used to form 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 required. The phase indicates the position of the satellite in orbit, which is the ratio of the time required to move from the initial position of the orbit to that position to the orbit period, and its range is [0, 1). Finally, the position of a satellite can be obtained by [set number n set - Constellation period number n T - Track number n O To form a constellation, satellites need to be selected from orbits with the same set number and period number.

[0019] In a possible implementation, in the above-mentioned three-body orbit lunar communication navigation constellation optimization method based on data preprocessing provided by the present invention, step S3 specifically includes:

[0020] Based on the orbital set and database obtained through preprocessing, the initial plan of the constellation is designed using a simulation-based comparative analysis method, and this is used as the current number of satellites.

[0021] The specific measures are as follows: First, within the existing orbital set, select the constellation configuration scheme through prior experience. According to the range of the lunar target area to be served, select the orbit type that has an advantage in covering it, such as choosing the south-facing halo orbit family for covering the South Pole and choosing the DRO orbit family for covering the equator.

[0022] Then, we select sets with these orbital families, select corresponding types of orbits in these sets, and set different numbers of satellites on different orbits as design solutions. That is, we first determine the orbital set number n when selecting. set , then from a constellation period number n T Among the corresponding orbits, select some orbits that are more favorable for covering the target area, and place a certain number of satellites on these orbits as constellation configuration schemes. In this process, different constellation periods, orbit combinations, the number of satellites on each orbit, and the phase φ of each satellite can be selected to obtain different constellation configuration schemes for subsequent selection and adjustment.

[0023] Afterwards, the coverage performance of these schemes is simulated. For communication constellations, the most important performance indicator is the coverage rate of the constellation over the target; for navigation constellations, coverage rate and navigation accuracy are both the most important performance, but meeting the coverage requirements is the basis for providing navigation services. The communication / navigation constellation needs to meet the single / quadruple 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 discretizes the target area into a finite number of grid points, and then calculates the visibility of each grid point relative to the satellites in the constellation at each time step within the constellation cycle, and finally calculates 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 communication / navigation constellations, the CTP of a 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 value of the CTP of all grid points in the area. When the CTP of the constellation in a certain orbital set reaches 100%, it means that the area meets the complete single / quadruple 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 solution with better performance or fewer satellites is selected. Then, the parameters of the obtained solution are manually adjusted appropriately. The adjustment includes adjusting the orbit number n in the configuration. O Adjustments are made, or the number of satellites on each orbit and the phase of the satellites on the orbit are adjusted. After the adjustment, the results with better performance or fewer satellites are continuously selected according to the results of the performance simulation until it is difficult to improve the performance or reduce the number of satellites. The solution with the best coverage performance during the adjustment process and the one with the least number of satellites is selected as the initial solution, and this number is used as the current number of satellites.

[0025] In a possible implementation, in the above-mentioned three-body orbit lunar communication navigation constellation optimization method based on data preprocessing provided by the present invention, step S4 specifically includes:

[0026] Based on the current number of satellites, one satellite is reduced, and in each orbital 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 can meet the coverage requirements, and to count the corresponding orbital sets. The optimization problem in each set can be described as:

[0027]

[0028] where J is the objective function to be optimized, x is the optimization variable vector, p is the fixed parameter vector, g and h are inequality and equality constraints, and x is LB With x UB are the upper and lower limits of the optimization variables. Because the performance indicators of communication and navigation constellations are different, their corresponding objective functions are also different. For the communication constellation, its objective function J C for:

[0029]

[0030] Among them, CTP 1-fold is the time proportion of the communication constellation covering the target area. 1-fold When it is optimized to 100%, it means that the area meets the complete first-layer coverage, that is, it meets the mission requirements of the communication constellation. At this time, the constellation configuration and the corresponding orbit set are recorded.

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

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

[0033] Where N is the number of satellites in the constellation, nset is the track 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] Among them, n T is the constellation period number, [n O1 ,n O2 ,...,n ON ] is the orbit number of each satellite, [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 one design variable. Because the constellation period number and the orbit number are integers, and the initial phase is a decimal, 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 both the constellation period number and the orbit set number.

[0037] In addition, for the communication constellation, only one layer of coverage of the target area is required. However, for the navigation constellation, four layers of coverage of the target area must be met, that is, at least four satellites are visible to it. Therefore, when optimizing the coverage rate, the objective function J of the navigation constellation is N for:

[0038]

[0039] Among them, CTP 4-fold It is the proportion of the time of the quadruple coverage of the target area by the navigation constellation. Its calculation method is similar to the proportion of the time of the single coverage of the communication constellation, and is also calculated by the grid point method, so it will not be repeated here.

[0040] Here, the genetic algorithm (GA) in the intelligent optimization algorithm is selected to optimize the problem, which is carried out in different orbital sets. The 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 configuration solution set, and then simulates the performance of these configurations respectively. By calling the visibility data of the satellite in the database, the objective function value, i.e. CTP, is quickly obtained after processing. Then, a configuration with better performance is selected from the solution set, and the next generation of population, i.e., the configuration solution set, is obtained through crossover and mutation operations similar to the chromosomes in the evolution of biological populations. Then, after repeated selection, crossover and mutation operations from generation to generation, the optimized constellation configuration is obtained.

[0041] In a possible implementation, in the above-mentioned three-body orbit lunar communication navigation constellation optimization method based on data preprocessing provided by the present invention, step S5 specifically includes:

[0042] Repeat step S4, continuously reduce the number of satellites, optimize the coverage performance of the constellation in each orbital set, find the configuration that can meet the coverage requirements under the current number of satellites, and count the corresponding orbital sets until the number of satellites is reduced to all sets and no configuration that can fully cover the target area can be found. Add one to the current number of satellites to get the minimum number of satellites that can meet the coverage requirements, and record the corresponding orbital set and constellation configuration at this time.

[0043] In a possible implementation, in the above-mentioned three-body orbit lunar communication navigation constellation optimization method based on data preprocessing provided by the present invention, step S6 specifically includes:

[0044] For communication constellations, the indicator for evaluating their performance is the coverage of the target, so it is sufficient to find the minimum number of satellites that can meet the coverage requirements and record the corresponding orbital set and constellation configuration at this time. For navigation constellations, in addition to the coverage of the target, the most important performance indicators are navigation accuracy. Therefore, it is necessary to further optimize the navigation accuracy of the constellation on the basis of meeting the coverage requirements. There are many measurement indicators for the navigation accuracy of the constellation. This method takes the more widely used geometric dilution of precision (Geometry Dilution of Precision, GDOP), which characterizes the navigation error caused by measurement error. The smaller the value, the better the navigation performance. The calculation method of 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, and 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. The matrix Q can be obtained from H, which is a 4×4 square matrix. 11 , Q 22 , Q 33 , Q 44 are the elements on the diagonal of Q.

[0049] Because the navigation constellation needs to meet the requirements of quadruple coverage before further optimizing the navigation accuracy, the objective function J optimized in each orbital set is N is a piecewise function:

[0050]

[0051] Among them, GDOP mean is the average GDOP value of the target area. When the quadruple coverage of the constellation does not meet the requirements, J N The optimization goal is to maximize CTP 4-fold When the coverage requirement is met, the optimization goal is to further minimize the average GDOP GDOP mean . And GDOP mean If the constellation configuration is too large and exceeds 1000, it will be counted as 1000 directly.

[0052] Similarly, based on the genetic algorithm GA, the optimization of the navigation constellation can be carried out after confirming that a set of orbits that meet the coverage requirements can be found. During the optimization, the visibility and geometric position of the satellites in the database can be directly called, and the objective function value can be quickly obtained after processing, thereby obtaining the optimized constellation configuration.

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

[0054] After optimizing the navigation performance of the constellation in step S6, if it is found that the average GDOP value of the constellation is relatively poor and cannot meet the navigation requirements, satellites can be further added based on 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 required for navigation. The navigation accuracy requirement can be set according to its own needs, and is generally set to no more than a certain value. Then, in the results of the corresponding number of satellites, the orbital set and constellation configuration that can meet the navigation requirements are counted.

[0055] Advantages and beneficial effects of the present invention:

[0056] 1. The three-body orbit lunar communication and navigation constellation optimization method based on data preprocessing disclosed in the present invention avoids repeated data calculations by preprocessing the data used for communication and navigation performance evaluation, greatly improving the calculation speed. This solves the problem that all constellation parameters, namely the orbit type, orbit amplitude and phase of the satellite, cannot be optimized at the same time in the optimization problem of the constellation composed of three-body orbits, so that this method can obtain more candidate constellation configurations than general methods.

[0057] 2. The three-body orbit lunar communication and navigation constellation optimization method based on data preprocessing disclosed in the present invention obtains the minimum number of satellites that can meet the basic coverage requirements of the communication and navigation constellation by gradually reducing the number of satellites and optimizing the coverage performance of the constellation on the basis of an initial plan obtained by a simulation-based comparative analysis method. 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 and requires the minimum number of satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A three-body orbit lunar communication and navigation constellation optimization method based on data preprocessing disclosed by the present invention;

[0059] Figure 2 Schematic diagram of the types and amplitude ranges designed for use in lunar communications and navigation constellations;

[0060] Figure 3 is the orbital period interval diagram;

[0061] Figure 4 is the orbital period interval diagram (intervals 3 to 5);

[0062] Figure 5 This is the orbital period interval diagram (interval 8 to 12);

[0063] Figure 6-1 is the track image in track set 1;

[0064] Figure 6-2 is the track image in track set 2;

[0065] Figure 6-3 is the track image in track set 3;

[0066] Figure 6-4 is the track image in track set 4;

[0067] Figure 6-5 is the track image in track set 5;

[0068] Figure 6-6 is the orbital image in orbital set 6;

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

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

[0071] Figure 6-9 is the orbital image in orbital 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 orbital image in orbital set 12;

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

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

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

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

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

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

[0081] Figure 6-19 is the orbital image in orbital 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 a track image in track set 22;

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

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

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

[0088] Figure 6-26 is the track image in track set 26;

[0089] Figure 6-27 is the orbital image in orbital set 27;

[0090] Figure 6-28 is the orbital image in orbital set 28;

[0091] Figure 7 This is the initial plan diagram for the global communication constellation;

[0092] Figure 8-1 To meet the global communication constellation configuration required for coverage1; Figure 8-2 To meet the coverage requirements of global communications constellation configuration 2; Figure 8-3 To meet the coverage requirements of global communications constellation configuration 3; Figure 8-4 To meet the coverage requirements of global communications constellation configuration 4; Figure 8-5 Global communications constellation configuration to meet coverage requirements 5;

[0093] Figure 8-6 To meet the coverage requirements of global communication constellation configuration 6;

[0094] Figure 8-7 Global communications constellation configuration to meet coverage requirements7;

[0095] Fig. 9 This is the initial plan diagram for the global navigation constellation;

[0096] Figure 10-1 To meet the global navigation constellation configuration required for coverage1;

[0097] Figure 10-2 To meet the coverage requirements of global navigation constellation configuration 2;

[0098] Figure 10-3 To meet the coverage requirements of global navigation constellation configuration 3;

[0099] Figure 11-1 A global navigation constellation configuration optimized for navigation performance1;

[0100] Figure 11-2 Global navigation constellation configuration 2 optimized for navigation performance;

[0101] Figure 11-3 Global navigation constellation configuration 3 optimized for navigation performance;

[0102] Fig.12 This is the initial scheme diagram of the hybrid constellation;

[0103] Fig.13 A hybrid navigation and communication constellation (7 satellites) optimized for navigation performance;

[0104] Figure 14-1 To meet the coverage requirements of the hybrid constellation configuration 1 (8 satellites);

[0105] Figure 14-2 To meet the coverage requirements, the hybrid constellation configuration 2 (8 satellites) is used;

[0106] Figure 14-3 To meet the coverage requirements, the hybrid constellation configuration 3 (8 satellites) is used;

[0107] Figure 14-4 To meet the coverage requirements, the hybrid constellation configuration 4 (8 satellites) is used;

[0108] Figure 14-5 To meet the coverage requirements, the hybrid constellation configuration 5 (8 satellites) is used;

[0109] Figure 14-6 To meet the coverage requirements, the hybrid constellation configuration 6 (8 satellites) is used;

[0110] Figure 14-7 To meet the coverage requirements, the hybrid constellation configuration 7 (8 satellites) is used;

[0111] Figure 14-8 To meet the coverage requirements, the hybrid constellation configuration 8 (8 satellites) is used;

[0112] Figure 14-9 To meet the coverage requirements, the hybrid constellation configuration 9 (8 satellites) is used;

[0113] Figure 14-10 To meet the coverage requirements, the hybrid constellation configuration 10 (8 satellites) is used;

[0114] Figure 14-11 To meet the coverage requirements, the hybrid constellation configuration 11 (8 satellites) is used;

[0115] Figure 14-12 To meet the coverage requirements, the hybrid constellation configuration 12 (8 satellites) is used;

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

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

[0118] Figure 15-3 This is the navigation performance-optimized hybrid constellation configuration 3 (8 satellites). DETAILED DESCRIPTION

[0119] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only for illustration and are not intended to limit the present invention.

[0120] The present invention provides a flow chart of a method for optimizing a three-body orbit lunar communication and navigation constellation based on data preprocessing, such as Figure 1 As shown, the following steps are included:

[0121] S1: Determine the types and amplitude ranges of orbits in the constellation based on the specific mission objectives of the lunar communications and navigation constellation;

[0122] The step S1 specifically includes:

[0123] The type and amplitude range of the orbit used to build the constellation are determined based on the specific needs of the mission and the characteristics of the orbit. In order to achieve coverage of the lunar surface, this method selects a three-body orbit near the L1 and L2 points to build a lunar 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 fully incorporated into the constellation design, and the planar and vertical Lyapunov orbit families use 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 that of other types of orbits, and it is specifically set according to the periodic relationship between various orbits in the subsequent preprocessing. The final orbit type and amplitude range are as follows Figure 2 As shown. Figure 2 In the figure, the green curve is the northward halo orbit of L1 and 2, the blue curve is the southward halo orbit of L1 and 2, the cyan is the plane Lyapunov orbit of L1 and 2, the magenta is the vertical Lyapunov orbit of L1 and 2, and the red is the DRO orbit. The origin in 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 revolution axis, and the y-axis forms a right-hand rule with the x-axis and the z-axis. The orbits corresponding to points L1 and L2 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 amplitude of the Halo and vertical Lyapunov orbits is the maximum absolute value of their orbits in the z direction, the amplitude of the plane Lyapunov orbit is the maximum absolute value of their orbits in the y direction, and the amplitude of the DRO orbit is the distance from the intersection with the x-axis to the moon.

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

[0125] The step S2 specifically includes:

[0126] First, the orbital period is restricted, 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. If the period is the same, the period range of all orbital types selected in this paper can be divided into 13 intervals according to the type of orbit, and each interval contains different types of orbits, such as Figure 3 As shown in the figure, "planar" and "vertical" refer to the planar and vertical Lyapunov orbits, respectively. Because the period of the L1 halo orbit increases first and then decreases as the amplitude increases, there is no unique correspondence between the two. Therefore, in Figure 3 In the figure, the L1 halo orbit is divided into two parts. One part increases with the increase of amplitude, marked as L1-halo+; the other part decreases with the increase of amplitude, marked as L1-halo-. This is equivalent to artificially dividing the L1 halo orbit into two families of orbits, so that a certain period corresponds to only one orbit. It should be noted that the L1 and L2 halo orbits actually correspond to two symmetrical north-south orbital families. Only one is drawn in the figure, but in fact there are two families of orbits to choose from in constellation design. In addition, because Figure 3 The period range of some intervals in the middle is too small to be marked, so only some of them are marked. The two red boxes in the figure correspond to intervals 3 to 5 and intervals 8 to 12, respectively. Figure 4 and Figure 5 shown.

[0127] If we only consider orbits with the same period, we only need to choose from the orbital sets corresponding to these 13 intervals. However, these selection methods will result in that orbital types with no intersection in period ranges cannot be matched with each other to construct constellations, such as the halo orbit of L1 and the vertical Lyapunov orbit of L2. Moreover, among different orbital types, only orbits with the same amplitude range of period can be matched with each other, which will greatly limit the orbital selection of constellations. In particular, some corresponding orbital types, such as the planar or vertical Lyapunov orbits of L1 and 2, have significantly different period ranges. Many parts of the two orbital families with the same period cannot provide orbits with relatively close amplitudes, which is not conducive to the construction of constellations with symmetric characteristics about the moon. Therefore, in order to enable each orbital type to be matched with orbits of more types and amplitude ranges to form a constellation, it is necessary to select parts from each interval that satisfy the period integer ratio of m:n to form a new orbital interval to enrich the orbital selection of the constellation. After verification, the period ratios of 1:2, 2:3, 3:4, 2:5, and 4:5 can meet the needs of providing orbits of different types and amplitude ranges for most corresponding orbit types, which can greatly enrich the types of orbit combinations in the constellation. In addition, by setting the orbit interval according to the period integer ratio, the period range of some orbit types participating in the constellation design can also be adjusted. For example, the period range of DRO is set according to the period range of other orbit types. In order to ensure that DRO can be selected for constellations of each period, we choose the minimum value of its period as the minimum value of L2's halo, and the maximum value can be selected as 0.8 times the maximum value of L2's vertical Lyapunov (that is, the ratio is 4:5). In this way, DRO can be matched with all other types of orbits. Other types of orbits can also adjust their period ranges as needed in a similar way.

[0128] It should be noted that the integer ratio of the period is not necessarily limited to the above combination. For special orbit types, the period ratio can be set separately as needed. For example, the halo orbits of L1 and L2 are symmetrical about the moon, located on the front and back of the moon respectively. Among them, orbits with similar amplitudes are often selected together to construct lunar constellations. In these two orbital families, the period range corresponding to the orbits within the amplitude of 0 to 60,000 km is small, and they just do not satisfy the existing period integer ratio, so they cannot be selected at the same time to form a constellation. A more unique period ratio can be set for it, so that the orbits in the two orbital families in this amplitude range can choose orbits with amplitudes closer to themselves. However, as the numerator or denominator of the ratio increases, the constellation period will also increase. Therefore, it has been verified that when the constellation period is not too large, it is more appropriate to select 5:6, 6:7, 9:11, 11:13 as the ratio to process these two parts of the orbit separately. If it is necessary to enable specific ranges of other specific orbital types to be selected at the same time to construct a constellation, a similar method can also be used to set a unique period ratio for them.

[0129] After the orbital period is limited, all orbital intervals with the same orbital type are integrated into one set. Finally, 28 fixed, finite sets are formed, each containing a different type of orbit. And when the period of the constellation is determined, a certain orbit can be selected from this set to construct the constellation.

[0130] Then, in order to reduce the number of orbits that need to be considered in constellation optimization, the orbits in each orbital set are discretized with fixed amplitude intervals, and the constellation optimization is performed only on the basis of these discretized orbits. When discretizing the orbits of a set, it is first necessary to determine the reference orbital family in each period interval. In the same period interval, the amplitude is used as the standard to measure the geometric characteristics of the orbit, and the orbital family with the slowest change in period relative to the amplitude is the reference orbital family, that is, the orbital family with the largest amplitude change range in the period interval. Then, a limited number of orbits can be selected from the reference orbital family at fixed amplitude intervals as needed. Finally, based on the period of the selected reference orbits, the required orbits are selected from other orbital families in the same set as candidate orbits. According to the period restrictions mentioned above, the selected orbits should be divided into two categories. One is to select orbits with the same period as the original period of the reference orbit. The other is orbits with a period in the ratio of m:n to the reference orbit. Figure 4Taking interval 2 in as an example, the ratio of the period of some orbits in intervals 1 and 2 is 4:5. And the orbit types of interval 2 itself also include interval 1, so these orbits are in the same set. At this time, the amplitude variation range of the halo orbit of L1 in interval 2 is the largest, so it is used as the reference orbit family, and a limited number of reference orbits are taken from it according to a fixed amplitude interval. Then, according to the periods of these orbits, orbits with the same period or that satisfy the period ratio are taken from other orbit families. That is, first take orbits with the same period from the DRO of interval 2 and the halo orbit of L2, and then take orbits with a period of 4 / 5 from interval 1 or 2. Note that although the amplitudes of the reference orbits of the former and the latter are the same, the constellation periods they constitute are different and need to be distinguished in the database. After discretization, orbits with a fixed number of orbital sets can be obtained, as shown in the following example. Figure 6-1 to Figure 6-28 As shown. As mentioned in S2, L1's halo orbits are divided into two families of orbits, L1-halo+ and L1-halo-, so there are a total of 11 types of orbits: DRO, northbound L1-halo+, southbound L1-halo+, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, planar L1-Lyapunov, planar L2-Lyapunov, vertical L1-Lyapunov and vertical L2-Lyapunov. The following are Figure 6-1 to Figure 6-28 The types of tracks in each set:

[0131] Figure 6-1 : DRO, northbound L2-halo, southbound L2-halo;

[0132] Figure 6-2 : DRO, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo;

[0133] Figure 6-3 : DRO, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, plane L1-Lyapunov;

[0134] Figure 6-4 : DRO, northbound L1-halo+, southbound L1-halo+, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, plane L1-Lyapunov;

[0135] Figure 6-5: DRO, northbound L1-halo+, southbound L1-halo+, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, plane L1-Lyapunov, vertical L1-Lyapunov;

[0136] Figure 6-6 : DRO, northward L2-halo, southward L2-halo, plane L1-Lyapunov, vertical L1-Lyapunov;

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

[0138] Figure 6-8 : Northward L2-halo, Southward 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, plane L1-Lyapunov, plane 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, northbound L2-halo, southbound L2-halo, plane L2-Lyapunov, vertical L1-Lyapunov, vertical L2-Lyapunov;

[0147] Figure 6-17 : DRO, northbound L2-halo, southbound L2-halo, planar L2-Lyapunov, vertical L2-Lyapunov;

[0148] Figure 6-18 : DRO, northbound L2-halo, southbound L2-halo, vertical L2-Lyapunov;

[0149] Figure 6-19 : DRO, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, plane L1-Lyapunov, plane L2-Lyapunov, vertical L1-Lyapunov, vertical L2-Lyapunov;

[0150] Figure 6-20 : DRO, northward L1-halo-, southward L1-halo-, northward L2-halo, southward L2-halo, plane L1-Lyapunov, plane L2-Lyapunov, vertical L2-Lyapunov;

[0151] Figure 6-21 : DRO, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, vertical L2-Lyapunov;

[0152] Figure 6-22 : DRO, northward L1-halo-, southward L1-halo-, northward L2-halo, southward L2-halo, plane L1-Lyapunov, vertical L1-Lyapunov;

[0153] Figure 6-23 : DRO, northward L1-halo-, southward L1-halo-, northward L2-halo, southward L2-halo, plane L1-Lyapunov, plane L2-Lyapunov, vertical L1-Lyapunov;

[0154] Figure 6-24: DRO, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, plane L1-Lyapunov, plane L2-Lyapunov, vertical L1-Lyapunov, vertical L2-Lyapunov;

[0155] Figure 6-25 : DRO, northward L1-halo-, southward L1-halo-, northward L2-halo, southward L2-halo, plane L1-Lyapunov, vertical L2-Lyapunov;

[0156] Figure 6-26 : DRO, northbound L1-halo+, southbound L1-halo+, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, plane L1-Lyapunov, plane L2-Lyapunov, vertical L1-Lyapunov, vertical L2-Lyapunov;

[0157] Figure 6-27 : DRO, northbound L1-halo+, southbound L1-halo+, northbound L1-halo-, southbound L1-halo-, northbound L2-halo, southbound L2-halo, plane L1-Lyapunov, plane L2-Lyapunov, vertical L1-Lyapunov;

[0158] Figure 6-28 : DRO, northbound L2-halo, southbound L2-halo, plane L1-Lyapunov, vertical L1-Lyapunov, vertical L2-Lyapunov;

[0159] Finally, it is necessary to obtain the unique corresponding orbit based on the amplitude of the orbit in each orbital set, and thereby generate an offline database of the satellite visibility and geometric position on the orbit for direct call during optimization. Because in general constellation optimization and design, the visibility and geometric position of satellites on the same orbit need to be recalculated in each performance evaluation, but these data are actually exactly the same. Therefore, if the required data can be pre-processed and prepared, and directly called during the optimization process, a large amount of repeated calculations can be omitted, thereby achieving the effect of accelerating the calculation. The orbital data in the database are sorted by [set number n set - Constellation period number n T - Track number n O] are numbered. The set number indicates the type of orbit. The period number is the number of different constellation periods, corresponding to the orbits that can be used to form the constellation of the period. The orbit number indicates the number of the orbit in the constellation that can be used to form 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 required. The phase indicates the position of the satellite in orbit, which is the ratio of the time required to move from the initial position of the orbit to that position to the orbit period, and its range is [0, 1). Finally, the position of a satellite can be obtained by [set number n set - Constellation period number n T - Track number n O To form a constellation, satellites need to be selected from orbits with the same set number and period number.

[0160] After large-scale numerical verification, the performance of constellations composed of various types of orbits was evaluated, and it was found that when the coverage performance was calculated by calling the database, the speed was 141.89 times that of the general method. When calculating GDOP, the speed was 1.56 times that of the general method. So far, after preprocessing, the offline database that can be directly called in optimization to greatly reduce the amount of calculation has been built.

[0161] S3: Based on the orbit set and database obtained by preprocessing, the initial plan of the constellation is designed using the simulation-based comparative analysis method, and this is used as the current number of satellites;

[0162] The step S3 specifically includes:

[0163] Based on the orbital set and database obtained through preprocessing, the initial plan of the constellation is designed using a simulation-based comparative analysis method, and this is used as the current number of satellites.

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

[0165] Then, we select sets with these orbital families, select corresponding types of orbits in these sets, and set different numbers of satellites on different orbits as design solutions. That is, we first determine the orbital set number n when selecting. set , then from a constellation period number n TAmong the corresponding orbits, select some orbits that are more favorable for covering the target area, and place a certain number of satellites on these orbits as constellation configuration schemes. In this process, different constellation periods, orbit combinations, the number of satellites on each orbit, and the phase φ of each satellite can be selected to obtain different constellation configuration schemes for subsequent selection and adjustment.

[0166] Afterwards, the coverage performance of these schemes is simulated. For communication constellations, the most important performance indicator is the coverage rate of the constellation over the target; for navigation constellations, coverage rate and navigation accuracy are both the most important performance, but meeting the coverage requirements is the basis for providing navigation services. The communication / navigation constellation needs to meet the single / quadruple 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 discretizes the target area into a finite number of grid points, and then calculates the visibility of each grid point relative to the satellites in the constellation at each time step within the constellation cycle, and finally calculates 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 communication / navigation constellations, the CTP of a 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 value of the CTP of all grid points in the area. When the CTP of the constellation in a certain orbital set reaches 100%, it means that the area meets the complete single / quadruple coverage, that is, the coverage requirement of the communication / navigation constellation is met.

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

[0168] S4: Based on the current number of satellites, one satellite is reduced, and in each orbital 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 can meet the coverage requirements, and the corresponding orbital set is counted;

[0169] The step S4 specifically includes:

[0170] Based on the current number of satellites, one satellite is reduced, and in each orbital 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 can meet the coverage requirements, and to count the corresponding orbital sets. The optimization problem in each set can be described as:

[0171]

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

[0173]

[0174] Among them, CTP 1-fold It is the proportion of the time that the communication constellation covers the target area. The grid point method is generally used for calculation. This method discretizes the target area into a finite number of grid points, and then calculates the visibility of each grid point relative to the satellites in the constellation at each time step within the constellation cycle, and finally calculates the overall coverage performance of the constellation. The CTP of a 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 CTP of all grid points in the area. When the CTP of the constellation in a certain orbital set 1-fold When it is optimized to 100%, it means that the area meets the complete first-layer coverage, that is, it meets the mission requirements of the communication constellation. At this time, the constellation configuration and the corresponding orbit set are recorded.

[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, n set is the track 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] Among them, n T is the constellation period number, [n O1 ,n O2 ,...,n ON ] is the orbit number of each satellite, [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 one design variable. Because the constellation period number and the orbit number are integers, and the initial phase is a decimal, 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 both the constellation period number and the orbit set number.

[0181] In addition, for the communication constellation, only one layer of coverage of the target area is required. However, for the navigation constellation, four layers of coverage of the target area must be met, that is, at least four satellites are visible to it. Therefore, when optimizing the coverage rate, the objective function J of the navigation constellation is N for:

[0182]

[0183] Among them, CTP 4-fold It is the proportion of the time of the quadruple coverage of the target area by the navigation constellation. Its calculation method is similar to the proportion of the time of the single coverage of the communication constellation, and is also calculated by the grid point method, so it will not be repeated here.

[0184] Here, the genetic algorithm (GA) in the intelligent optimization algorithm is selected to optimize the problem, which is carried out in different orbital sets. The 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 configuration solution set, and then simulates the performance of these configurations respectively. By calling the visibility data of the satellite in the database, the objective function value, i.e. CTP, is quickly obtained after processing. Then, a configuration with better performance is selected from the solution set, and the next generation of population, i.e., the configuration solution set, is obtained through crossover and mutation operations similar to the chromosomes in the evolution of biological populations. Then, after repeated selection, crossover and mutation operations from generation to generation, the optimized constellation configuration is obtained.

[0185] S5: Repeat S4 until the number of satellites is reduced to the point where no configuration that meets the coverage requirements can be found, that is, the minimum number of satellites and the corresponding orbital sets required, as well as the constellation configurations that meet the requirements in these sets, are obtained;

[0186] The step S5 specifically includes:

[0187] Repeat step S4, continuously reduce the number of satellites, optimize the coverage performance of the constellation in each orbital set, find the configuration that can meet the coverage requirements under the current number of satellites, and count the corresponding orbital sets until the number of satellites is reduced to a point where no configuration that meets the coverage requirements can be found in all sets. Add one to the current number of satellites to obtain the minimum number of satellites that can meet the coverage requirements, and record the corresponding orbital set and constellation configuration at this time.

[0188] S6: For the navigation constellation, in each orbital set corresponding to the current number of satellites that can find a configuration that meets the coverage requirements, after optimizing the constellation coverage performance until the coverage requirements are fully met, further optimize the navigation performance;

[0189] The step S6 specifically includes:

[0190] For communication constellations, the indicator for evaluating their performance is the coverage of the target, so it is sufficient to find the minimum number of satellites that can meet the coverage requirements and record the corresponding orbital set and constellation configuration at this time. For navigation constellations, in addition to the coverage of the target, the most important performance indicators are navigation accuracy. Therefore, it is necessary to further optimize the navigation accuracy of the constellation on the basis of meeting the coverage requirements. There are many measurement indicators for the navigation accuracy of the constellation. This method takes the more widely used geometric precision dilution factor GDOP, which characterizes the navigation error caused by measurement error. The smaller the value, the better the navigation performance. The calculation method of 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, and 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. The matrix Q can be obtained from H, which is a 4×4 square matrix. 11 , Q 22 , Q 33 , Q 44 are the elements on the diagonal of Q.

[0195] Because the navigation constellation needs to meet the requirements of quadruple coverage before further optimizing the navigation accuracy, the objective function J optimized in each orbital set is N is a piecewise function:

[0196]

[0197] Among them, GDOP mean is the average GDOP value of the target area. When the quadruple coverage of the constellation does not meet the requirements, J N The optimization goal is to maximize CTP 4-fold When the coverage requirement is met, the optimization goal is to further minimize the average GDOP GDOP mean . And GDOP mean If the constellation configuration is too large and exceeds 1000, it will be counted as 1000 directly.

[0198] Similarly, based on the genetic algorithm GA, the optimization of the navigation constellation can be carried out after confirming that a set of orbits that meet the coverage requirements can be found. During the optimization, the visibility and geometric position of the satellites in the database can be directly called, and the objective function value can be quickly obtained after processing, thereby obtaining the optimized constellation configuration.

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

[0200] The step S7 specifically includes:

[0201] After optimizing 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 requirements, satellites can be further added based on 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 required for navigation. The navigation accuracy requirement can be set according to its own needs, and is generally set to no more than a certain value, which is set to 10 here. Then, in the results of the corresponding number of satellites, the orbital set and constellation configuration that can meet the navigation needs are counted.

[0202] The effectiveness of the method proposed in the present invention is illustrated below by taking global communication, global navigation and communication-navigation hybrid constellation as solution examples.

[0203] The first is the global communication constellation. Using the simulation-based comparative analysis method, we can get the following Figure 7 The initial solution shown in Figure 1 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 orbital set, and the minimum number of satellites that can meet the coverage requirements is 5. At this time, there are a total of 8 orbital sets that can find a configuration that meets the coverage requirements. After induction and arrangement, Figure 8-1 to Figure 8-7 The orbital composition and satellite number distribution of the 7 configurations shown in the figure are as follows:

[0204] Configuration 1: DRO (1 satellite), southbound L1-halo+ (1 satellite), northbound L2-halo (2 satellites), southbound L2-halo (1 satellite);

[0205] Configuration 2: Northward L2-halo (2 satellites), Southward L2-halo (2 satellites), Planar L1-Lyapunov (1 satellite);

[0206] Configuration 3: Northward L2-halo (2 satellites), southward L2-halo (1 satellite), vertical L1-Lyapunov (2 satellites);

[0207] Configuration 4: northward L2-halo (1 satellite), southward L2-halo (2 satellites), vertical L1-Lyapunov (2 satellites);

[0208] Configuration 5: Planar L2-Lyapunov (1 satellite), northward L2-halo (2 satellites), southward L1-halo+ (2 satellites);

[0209] Configuration 6: vertical L2-Lyapunov (1 satellite), northward L2-halo (1 satellite), southward L1-halo+ (3 satellites);

[0210] Configuration 7: vertical L2-Lyapunov (2 satellites), northward L2-halo (1 satellite), southward L1-halo+ (2 satellites);

[0211] Then there is the global navigation constellation. Using a simulation-based comparative analysis approach, we can get the following: Fig. 9 The initial solution shown in Figure 1 has 16 satellites. 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 15. At this time, there are a total of 3 orbital sets that can find configurations that meet the coverage requirements. After induction and arrangement, Figure 10-1 to Figure 10-3 The orbital composition and satellite number distribution of the three configurations shown in the figure are as follows:

[0212] Configuration 1: DRO (4 satellites), northbound L2-halo (2 satellites), southbound L2-halo (2 satellites), northbound L2-halo (1 satellite), southbound L2-halo (2 satellites), planar L1-Lyapunov (1 satellite), vertical L1-Lyapunov (3 satellites);

[0213] Configuration 2: Northward L2-halo (4 satellites), Southward L2-halo (4 satellites), Planar L1-Lyapunov (2 satellites), Vertical L1-Lyapunov (5 satellites);

[0214] Configuration 3: DRO (3 satellites), northbound L2-halo (4 satellites), southbound L2-halo (4 satellites), northbound L1-halo+ (2 satellites), southbound L1-halo+ (2 satellites);

[0215] After further GDOP optimization in these three sets, the results are as follows Figure 11-1 to Figure 11-3 The orbital composition and satellite number distribution of the optimized configuration are shown in Figure 10-1 to Figure 10-3 The three optimized configurations can provide navigation accuracy that meets the requirements for the lunar surface, and their average GDOP values ​​are 3.135, 5.972, and 3.132 respectively.

[0216] Because in addition to providing services for a certain area, the lunar constellation may also need to provide communication and navigation services for the same or different areas at the same time, that is, as a hybrid communication and navigation constellation. For example, in the phased deployment strategy of some global navigation constellations, the first phase is to provide communication services for Antarctica, the second phase is to provide navigation services for Antarctica and communication services for the world at the same time, and the third phase is to provide navigation services for the world. Therefore, we will also take the hybrid constellation that provides navigation services for Antarctica and communication services for the world at the same time as the design goal.

[0217] Using the simulation-based comparative analysis method, we can obtain Fig.12 The initial solution shown in Figure 1 has a total of 10 satellites. Based on this, 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 of this set, the configuration obtained is as follows Fig.13 As shown in Figure 1. Although this configuration can achieve full coverage, its GDOP value is still poor (greater than 100) even after optimization. Therefore, the number of satellites is increased to 8 and the optimization is continued. After optimizing the coverage rate, a total of 15 orbital sets can find configurations that meet the coverage requirements. After summarizing and sorting, there are a total of Figure 14-1 to Figure 14-12 The orbital composition and satellite number distribution of the 12 different configurations shown in the figure are as follows:

[0218] Configuration 1: DRO (1 satellite), northbound L2-halo (1 satellite), southbound L2-halo (4 satellites), southbound L1-halo+ (2 satellites);

[0219] Configuration 2: Southbound L2-halo (3 satellites), Southbound L2-halo (1 satellite), Northbound L1-halo- (1 satellite), Southbound L1-halo- (1 satellite), Southbound L1-halo+ (2 satellites);

[0220] Configuration 3: Northward L2-halo (2 satellites), southward L2-halo (5 satellites), vertical L1-Lyapunov (1 satellite);

[0221] Configuration 4: Northward L2-halo (2 satellites), southward L2-halo (4 satellites), vertical L1-Lyapunov (2 satellites);

[0222] Configuration 5: Northward L2-halo (1 satellite), southward L2-halo (4 satellites), vertical L1-Lyapunov (2 satellites), vertical L2-Lyapunov (1 satellite);

[0223] Configuration 6: Northbound L2-halo (2 satellites), Southbound L2-halo (2 satellites), Southbound L1-halo+ (4 satellites);

[0224] Configuration 7: DRO (1 satellite), northbound L2-halo (1 satellite), southbound L2-halo (1 satellite), northbound L1-halo- (1 satellite), southbound L1-halo- (4 satellites);

[0225] Configuration 8: DRO (1 satellite), northbound L2-halo (1 satellite), southbound L2-halo (3 satellites), northbound L1-halo- (1 satellite), southbound L1-halo- (2 satellites);

[0226] Configuration 9: Northbound L2-halo (2 satellites), Southbound L2-halo (3 satellites), Southbound L1-halo+ (3 satellites);

[0227] Configuration 10: Southbound L2-halo (6 satellites), Northbound L1-halo+ (2 satellites);

[0228] Configuration 11: Northbound L2-halo (1 satellite), Southbound L2-halo (5 satellites), Southbound L1-halo+ (2 satellites);

[0229] Configuration 12: southward L2-halo (7 satellites), vertical L1-Lyapunov (1 satellite);

[0230] After further GDOP optimization in these 15 orbital sets, the average GDOP of the optimization results in 6 sets was below 10. After summarization, there were three types of configurations. The first two sets each had one type of configuration with slightly poor performance; the last four sets had one type of configuration with better performance. These three types of configurations are as follows: Figure 15-1 to Figure 15-3 As shown in the figure, its orbital composition and satellite number distribution are as follows:

[0231] Configuration 1: Southbound L2-halo (2 satellites), Southbound L2-halo (1 satellite), Northbound L1-halo- (2 satellites), Southbound L1-halo- (3 satellites);

[0232] Configuration 2: Northward L2-halo (1 satellite), Southward L2-halo (4 satellites), Vertical L2-Lyapunov (1 satellite), Vertical L2-Lyapunov (2 satellites);

[0233] Configuration 3: Northbound L2-halo (1 satellite), southbound L2-halo (3 satellites), southbound L1-halo+ (4 satellites);

[0234] The average GDOP values ​​of these three configurations are 8.509, 8.598 and 4.989 respectively, all of which can provide satisfactory navigation accuracy for Antarctica while meeting global communication needs.

[0235] This algorithm effectively reduces the amount of calculation in the optimization process of the constellation composed of three orbits by preprocessing the data used for communication and navigation constellation performance evaluation, and successfully overcomes the problem that all parameters of the constellation in existing studies, namely the orbit type, orbit amplitude and phase of the satellite, cannot be optimized at the same time, so that this method can obtain more candidate constellation configurations than general methods. In addition, by gradually reducing the number of satellites and optimizing the coverage performance of the constellation based on the initial solution 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 minimum number of satellites, while ensuring the constellation performance and reducing the constellation cost.

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

[0237] The above shows the basic principle and implementation steps of the present invention, and verifies the effectiveness and practicality of the method proposed in the invention with examples. Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for optimizing a three-body orbit lunar communication and navigation constellation based on data preprocessing, characterized in that: The following steps are involved: S1: Determine the types and amplitude ranges of orbits in the constellation based on the specific mission objectives of the lunar communications and navigation constellation; S2: Preprocessing the data of satellites in orbit for constellation performance evaluation, including limiting orbit period, discretizing orbit amplitude and generating offline database, thereby obtaining different orbit sets and databases used in optimization; S3: Based on the orbit set and database obtained by preprocessing, the initial plan of the constellation is designed using the simulation-based comparative analysis method, and this is used as the current number of satellites; S4: Based on the current number of satellites, one satellite is reduced, and in each orbital 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 can meet the coverage requirements, and the corresponding orbital set is counted; S5: Repeat step S4 until the number of satellites is reduced to the point where no configuration that meets the coverage requirement can be found, that is, the minimum number of satellites and corresponding orbital sets required, as well as constellation configurations that meet the requirements in these sets, are obtained; S6: For the navigation constellation, in each orbit set that meets the coverage requirement configuration corresponding to the current number of satellites, after optimizing the constellation coverage performance until the coverage requirement is fully met, further optimize the navigation performance; S7: If the navigation performance of the configuration finally obtained 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 for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 1, characterized in that: Step S1 specifically includes: In order to achieve coverage of the lunar surface, a three-body orbit near the L1 and L2 points is selected to build a lunar communication and navigation constellation; the types of orbits include halo orbits, planar and vertical Lyapunov orbits, and long-range retrograde orbits DRO; The maximum value of the halo orbit amplitude is used as the upper limit of the amplitudes of other orbital families; the maximum amplitude of DRO is set smaller than the maximum amplitude of the halo orbit, and the specific range is set according to the periodic relationship between various orbits in the preprocessing.

3. The method for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 1, characterized in that: Step S2 specifically includes: First, the orbital period is restricted, 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 DRO is set according to the period range of other orbital types; in order to ensure that DRO can be selected for constellations of each period, the minimum value of its period is set to the minimum value of the period of other orbital families, and the maximum value is set to the maximum value of the period of other orbital families to meet an integer ratio; Then, in order to reduce the number of orbits that need to be considered in constellation optimization, the orbits in each orbital set are discretized with fixed amplitude intervals; when discretizing the orbits of a set, it is necessary to determine the reference orbital family in each period interval; in the same period interval, the amplitude is used as the standard for measuring the geometric characteristics of the orbit, and the orbital family with the slowest period change relative to the amplitude is used as the reference orbital family, that is, the orbital family with the largest amplitude change range in the period interval; a limited number of orbits are selected from the reference orbital family with fixed amplitude intervals; the required orbits are selected from other orbital families in the same set as candidate orbits based on the period of the selected reference orbits; Finally, it is necessary to obtain the unique corresponding orbit according to the amplitude of the orbit in each orbit set, and generate an offline database of satellite visibility and geometric position on the orbit for direct call during optimization; the orbit data in the database is sorted by [set number n set - Constellation period number n T - Track number n O ] are numbered; the set number indicates the type of orbit; the period number is the number of different constellation periods, corresponding to the orbits that constitute the period constellation; the orbit number indicates the number of the orbit in the constellation that can be used to constitute 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; to determine the initial state of the satellite in the constellation, the initial phase φ is also required; the phase indicates the position of the satellite in the orbit, which is the ratio of the time required to move from the initial position of the orbit to that position to the orbit period, and its range is [0, 1); finally, the position of a satellite is given by [set number n set - Constellation period number n T - Track number n O -phase φ]; to form a constellation, it is necessary to select satellites from orbits with the same set number and period number.

4. The method for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 1, characterized in that: Step S3 specifically includes: First, within the existing orbital set, the constellation configuration is selected based on prior experience. Based on the range of the lunar target area to be served, the orbit type with the best coverage is selected. Then, select a set with these orbital families, select the corresponding type of orbits in these sets, and set different numbers of satellites on different orbits as a design scheme; that is, when selecting, first determine the orbital set number n set , then from a constellation period number n T Among the corresponding orbits, select some orbits that are beneficial to the coverage of the target area, and place a certain number of satellites on these orbits as constellation configuration schemes; in this process, select different constellation periods, orbit combinations, the number of satellites on each orbit, and the phase φ of each satellite to obtain different constellation configuration schemes for subsequent selection and adjustment; Afterwards, the coverage performance of these schemes is simulated; the communication / navigation constellation needs to meet the single / quadruple coverage of the target area, that is, at least one / four satellites are visible to the area; and when calculating the coverage rate of the target area, the grid point method is used; this method discretizes the target area into a finite number of grid points, and then calculates the visibility of each grid point relative to the satellites in the constellation at each time step within the constellation cycle, and finally calculates the overall coverage rate of the constellation; for the communication / navigation constellation, the CTP of a 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 value of the CTP of all grid points in the area; when the CTP of the constellation in a certain orbital set reaches 100%, it means that the area meets the complete single / quadruple 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 fewer satellites is selected; the parameters of the obtained scheme are adjusted; the adjustment includes the orbit number n in the configuration O Adjustments are made to 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 fewer satellites are continuously 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 solution with the least number of satellites in the solution with the best coverage performance during the adjustment process is selected as the initial solution, and this number is used as the current number of satellites.

5. The method for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 1, characterized in that: Step S4 specifically includes: Based on the current number of satellites, one satellite is reduced, and in each orbital 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 can meet the coverage requirements, and to count the corresponding orbital sets; the optimization problem in each set is described as: where J is the objective function to be optimized, x is the optimization variable vector, p is the fixed parameter vector, g and h are inequality and equality constraints, and x is LB With x UB are the upper and lower limits of the optimization variables; because the performance indicators of communication and navigation constellations are different, their corresponding objective functions are also different; for the communication constellation, its objective function J C for: Among them, CTP 1-fold is the proportion of the time that the communication constellation covers the target area; when the CTP of the constellation in a certain orbital set 1-fold When it is optimized to 100%, it means that the area meets the complete first-layer coverage, that is, it meets the mission requirements of the communication constellation; at this time, the constellation configuration and the corresponding orbit set are recorded.

6. The method for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 5, characterized in that: 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 track set number; these two parameters are fixed during the optimization.

7. The method for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 5, characterized in that: In this optimization problem, the optimization variable vector x is: [n T ,n O1 ,n O2 ,φ2,...,n ON ,f N ](4) Among them, n T is the constellation period number, [n O1 ,n O2 ,...,n ON ] is the orbit number of each satellite, [φ2,...,φ N ] is the initial phase of the satellite in 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.

8. The method for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 5 or 6, characterized in that: For the communication constellation, only one layer of coverage of the target area is required; but for the navigation constellation, four layers of coverage of the target area must be met, that is, at least four satellites are visible to it; so when optimizing the coverage, the objective function J of the navigation constellation is N for: Among them, CTP 4-fold It is the proportion of time of quadruple coverage of the target area by the navigation constellation.

9. The method for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 1, characterized in that: Step S6 specifically includes: The navigation accuracy of the constellation uses the geometric dilution of precision factor GDOP, which characterizes the navigation error caused by the measurement error. The smaller the value, the better the navigation performance. The calculation method of the GDOP corresponding to a 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, (xm, ym, zm) is the relative position of the mth satellite visible to the point, and R m is the relative distance of the satellite; H is the matrix constructed by the relative geometric relationship between the satellite and the point. The matrix Q is obtained from H, which is a 4×4 square matrix. 11 , Q 22 , Q 33 , Q 44 are the elements on the diagonal of Q; Because the navigation constellation needs to meet the requirements of quadruple coverage before further optimizing the navigation accuracy, the objective function J optimized in each orbital set is N is a piecewise function: Among them, GDOP mean is the average GDOP value of the target area; when the quadruple coverage of the constellation does not meet the requirements, J N The optimization goal is to maximize CTP 4-fold ; When the coverage requirement is met, the optimization goal is to further minimize the average GDOP GDOP mean ; and GDOP mean Too large, constellation configurations exceeding 1000 are directly counted as 1000; Similarly, based on the genetic algorithm GA, the optimization of the navigation constellation is carried out after confirming that a set of orbits that meets the coverage requirements can be found; during optimization, the visibility and geometric position of the satellites in the database are directly called, and the objective function value is quickly obtained after processing, thereby obtaining the optimized constellation configuration.

10. The method for optimizing the three-body orbit lunar communication and navigation constellation based on data preprocessing according to claim 9, characterized in that: Step S7 specifically includes: After optimizing the navigation performance of the constellation in step S6, if it is found that the average GDOP value of the constellation cannot meet the navigation requirements, further increase the number of satellites based on the current number of satellites, and then repeat step S6 to continue optimizing the navigation performance of the constellation until it can meet the required navigation accuracy; the navigation accuracy requirement is set according to its own needs; then, in the results of the corresponding number of satellites, the orbital set and constellation configuration that can meet the navigation requirements are counted.

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