Multi-station relay aerospace mission planning method

Abstract

The invention relates to the technical field of spaceflight measurement and control, in particular to a multi-station relay spaceflight mission planning method, and solves the problems that an existing technical bureau is limited to two / three-station relay, arc section redundancy lacks quantitative analysis, and the optimization speed is low. The method comprises the following steps: 1, determining a continuous tracking demand for more than or equal to 3 hours in an execution period of 7 days, and generating a satellite-ground visible time window; 2, constructing a redundant time / ratio matrix and reducing the order, and establishing a multi-station relay constraint model; 3, repairing an infeasible solution; 4, establishing a multi-objective function (minimizing the sum of redundancy ratios, the number of arc segments, repeated stations, maximizing the duration and unifying the measurement standard); and 5, solving by using a target hierarchy method, and simulating annealing optimization in combination with multi-dimensional coding. According to the method, arc segment redundancy is quantitatively described, an infeasible solution is repaired, multi-station cooperative scheduling is achieved, and optimization efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of aerospace telemetry and control technology, specifically a multi-station relay aerospace mission planning method. Background Technology

[0002] Multi-site relay tracking in space missions achieves full coverage of the target's flight trajectory by scheduling different stations in different time periods. This process requires not only continuous tracking of the target satellite but also load balancing of ground equipment to avoid resource redundancy during multiple coverage operations, while also considering the proportion of overlapping segments. The interplay of multiple factors makes the mission optimization problem extremely complex. With its large system scale and numerous possible combinations, it falls under the category of a complex large-scale combinatorial optimization problem, i.e., an NP-hard problem.

[0003] Existing multi-station relay tracking technologies have three significant shortcomings: First, most technologies only consider two-station or three-station relays, which is insufficient to meet the needs of complex space missions for multi-station collaborative scheduling; second, the description of arc overlap is mostly qualitative analysis, lacking precise quantitative analysis methods, resulting in insufficient scientificity and rationality of scheduling schemes; and third, less attention is paid to improving optimization speed, making it difficult to quickly obtain the optimal scheduling scheme when facing large-scale arc combinations, thus affecting the execution efficiency of space missions.

[0004] To overcome the aforementioned shortcomings of existing technologies, this invention proposes a multi-station relay space mission planning method. By quantitatively describing the redundancy relationship between arc segments and optimizing the algorithm process, it achieves efficient optimization of multi-station relay scheduling. Summary of the Invention

[0005] To address the problems in existing technologies, this invention provides a multi-station relay space mission planning method. It quantitatively describes the redundancy between two arc segments by defining redundancy time and redundancy ratio indices, and introduces a redundancy matrix to quantitatively describe the redundancy relationships between multiple arc segments. The redundancy matrix facilitates the construction of constraint models and objective functions. Repairing infeasible solutions improves population quality and increases optimization speed. For multi-objective ranking, a goal hierarchy method is applied to solve the optimization problem of multiple objectives. By encoding arc segments with multi-dimensional chromosomes, simulated annealing is applied to optimize the multi-station relay scheduling model.

[0006] The technical solution adopted by this invention to solve its technical problem is: a multi-station relay space mission planning method, comprising the following steps:

[0007] S1, gives the execution period and duration required for the space mission, wherein the execution period and duration are a combination of arc segments that can be continuously tracked for h hours within a given d days;

[0008] S2, during the execution period, performs satellite-to-ground visibility prediction based on the given satellite ephemeris and station locations, generating an effective visibility time window; and generates scene time information, starting at time T. sce_start End time T sce_end =T sce_start +d; During the execution period, based on the minimum elevation angle, perform satellite-to-ground visibility prediction for the given satellite ephemeris and station location, and generate a set of effective visible time windows A. Any time window vp within A... i =(sa,s,ts,te), where sa, s, ts, and te represent arc segment vp respectively. i The corresponding ground station number, satellite number, arc start time, and end time;

[0009] S3, Establish the constraint condition model;

[0010] S4, Infeasible solution repair process;

[0011] S5, Establish a multi-objective function model;

[0012] S6, the objective-level method for solving the problem;

[0013] S7. Simulated annealing method is used to optimize the multi-station relay scheduling model.

[0014] Specifically, step S3 includes the following sub-steps:

[0015] S301, Sort the set of visible time windows A generated in S2 in ascending order of their start times, and let the number of time windows be n;

[0016] S302 defines two time window redundancy: time window vp corresponding to two stations and one satellite. i and VP j When VP i— sa≠vp j— sa and vp i— s=vp j— If there is a time overlap between two windows, then the time window vp i and VP j There is redundancy in two windows;

[0017] S303 defines the redundancy-related parameters for two time windows:

[0018] Define arc length vpl i =vp i _te-vp i _ts, vpl j =vp j _te-vp j _ts;

[0019] Define rdu_tij ,rdu_t ji This represents two time windows (vp). i， vp j The length of the overlapping portion of time, obviously rdu_t ij =rdu_t ji =min(vp i _te , vp j _te)-max(vp i _ts , vp j _ts);

[0020] Define rdu_r ij ,rdu_r ji The redundancy ratio, rdu_r, is the ratio of the overlap length of two time windows to the length of each individual time window. ij =rdu_t ij / vpl i ,rdu_r ji =rdu_t ji / vpl j ;

[0021] In relay tracking, the redundancy ratio of each time window is between (0,1) and the value is small, while the overlapping period rdu_t is greater than the device switching time;

[0022] S304, establish a time window redundancy ratio matrix and a redundancy time matrix. The redundancy ratio matrix is ​​a square matrix with all diagonal elements being 0. The i-th row (column) in the matrix represents the i-th time window. Summing each row of the matrix yields the sum of the redundancy ratios of the corresponding time window and other visible windows.

[0023] S305, Redundant Matrix Reduction: If the row and column elements corresponding to arc segment i in the matrix are both 0, then delete that row and column, and decrease the matrix order by 1. Let the number of arc segments after reduction be k.

[0024] S306, Establish a multi-station relay constraint model: a set of arc segments ordered by start time, and adjacent arc segments vp h VP j VP k Between two arc segments, if there is only one arc segment, the length of the arc segment is greater than or equal to h; if there are two arc segments, the two arc segments overlap, and the effective length of the arc segment (the overlapping part is calculated once) is greater than or equal to h; if there are multiple arc segments, between any three adjacent arc segments, the middle arc segment overlaps with the preceding and following arc segments respectively, the preceding and following arc segments do not overlap, and the length of the arc segment meets the requirements.

[0025] Specifically, the repair process for infeasible solutions in step S4 includes:

[0026] S401, traverse the arc segments in the chromosome whose state is 1;

[0027] S402, for two adjacent arc segments with a value of 1, if the redundancy ratio is 0, if these two arc segments are adjacent, then set the gene value of the arc segment with the shorter time to 0; if there are other arc segments with a value of 0 between these two arc segments, then select an arc segment that has redundancy with both of these arc segments and set that arc segment to 1.

[0028] S403, if there is a redundancy ratio of 1, then set the arc segment to 0;

[0029] S404, For arc segments with a redundancy ratio greater than 1, if other arc segments that are redundant with this arc segment are all 1 in the chromosome, then this arc segment is set to 0.

[0030] Specifically, the multi-objective function model established in step S5 includes:

[0031] S501, Objective function 1: Minimize the redundancy ratio of adjacent arc segments in the arc segment combination, which is divided by the number of arc segments f3 for easier comparison;

[0032] S502, Objective function 2: The total relay time is the longest, which is the time of the end of the last arc minus the time of the start of the first arc, or the time of each arc minus the sum of the overlapping time of adjacent arcs;

[0033] S503, Objective function 3: Minimize the number of arc segments, expressed by summing the coded values;

[0034] S504, Objective function 4: Minimize the number of repeated stations in multi-station relay tracking, represented by the length of the set of non-repeating stations in the arc segment;

[0035] S505, Unified metric for multi-objective functions: Convert f2 and f4 into finding the minimum value. Take the reciprocal of f2 and multiply it by the relay tracking time h, and it is still called f2. Take the reciprocal of f4 and multiply it by the number of arcs f3, and it is still called f4. The multi-objective function is converted to F=[min(f1),min(f2),min(f3),min(f4)].

[0036] Specifically, step S6, the objective-level method solution process, includes:

[0037] S601, with f1 as the single objective, find the set of arc segments with the minimum redundancy ratio of adjacent arc segments in the arc segment combination, denoted as strategy C1;

[0038] S602, with f2 as the single objective, find the set of arc segments with the longest total duration of the arc segment combination, denoted as strategy C2;

[0039] S603, in strategy C1+C2 ， Find C3 with f2 as the single objective;

[0040] S604, with f3 as the single objective, find the set of arc segments with fewer arc segments in the arc segment combination, denoted as strategy C4;

[0041] S605, in strategy C3+C4 ， Find C5 with f3 as the single objective;

[0042] S606, with f4 as the single objective, find the set of arc segments with fewer repeated stations in the arc segment combination, denoted as strategy C6;

[0043] S607, in strategy C5+C6, with f4 as the single objective, C7 is the optimal solution in the sense of objective hierarchy.

[0044] Specifically, step S7, which applies simulated annealing to optimize the multi-station relay scheduling model, includes:

[0045] S701, the design variables adopt binary encoding form. The number of all visible arc segments (the arc segments corresponding to the matrix after the redundancy matrix is ​​reduced in order) is the number of bits in the binary encoding. When the arc segment is selected, the encoding is set to 1, and when it is not selected, it is set to 0.

[0046] S702, Multidimensional Coding: Extends one-dimensional gene coding to multidimensional, including arc segment number, arc segment information, arc segment state, arc segment redundancy ratio vector, arc segment redundancy time vector, etc. The chromosome dimension is the same as the number of arc segments k after the reduction.

[0047] S703 sets simulated annealing parameters such as population size, number of iterations, initial temperature, attenuation factor, and acceptance criterion probability;

[0048] S704, run the simulated annealing process: repair infeasible solutions that do not meet the constraints, calculate the fitness value using the objective layering method, and iterate to find the optimal solution.

[0049] Specifically, the minimum elevation angle in step S2 is 30º, and in step S1, d=7 and h≥3.

[0050] Specifically, in step S304, the redundant time matrix is ​​a symmetric matrix with initial values ​​of 0 for each element. The given time window is traversed, and the intersection operation is performed between any time window and the other time windows. If the intersection is not empty, the length of the time window of the intersection arc segment is filled in at the corresponding position. If the intersection is empty, 0 is filled in.

[0051] Specifically, in step S304, the redundancy ratio matrix is ​​generated based on the redundancy time matrix, and the corresponding position of the matrix is ​​divided by the length of the corresponding satellite-to-ground visible time window.

[0052] The beneficial effects of this invention are:

[0053] By introducing redundancy time, redundancy ratio index and redundancy matrix, a quantitative description of the redundancy relationship between arc segments is realized, which intuitively and clearly reflects the overlap between arc segments, and provides a solid foundation for the construction of constraint model and objective function;

[0054] The addition of an infeasible solution repair process effectively improves population quality, increases optimization speed, and solves the problems of few feasible solutions and low optimization efficiency in existing technologies.

[0055] The objective hierarchy method is used to solve the multi-objective optimization problem. By optimizing multiple objectives in a hierarchical manner, the compromise and coordination between objectives are achieved. The optimal arc segment combination can be obtained to meet the requirements of multiple objectives such as small overlap between arc segments, few arc segments, few required stations, many different equipment, and long relay time.

[0056] By encoding arc segments in multiple dimensions and combining them with an improved simulated annealing algorithm, a highly efficient optimization of the multi-station relay scheduling model is achieved. This model is suitable for multi-station relay tracking scenarios and can be used to construct multi-station relay aerospace mission planning methods that meet different needs. It overcomes the shortcomings of existing technologies that are mostly limited to two-station and three-station relays. Attached Figure Description

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] Figure 1 A system flowchart of a multi-station relay space mission planning method provided by the present invention;

[0059] Figure 2 The diagram above illustrates the two-segment index representation of a multi-station relay space mission planning method provided by this invention. "Time (view periods)" means: a time axis with "satellite-station visible time period" as the core, used to intuitively show the distribution, overlap, and relay order of different arc segments in time;

[0060] Figure 3 This is a schematic diagram of the redundancy of two stations in a multi-station relay space mission planning method provided by the present invention. The time axes are defined as follows: Figure 2 ;

[0061] Figure 4 This is a schematic diagram of multi-station relay and multi-station redundancy in a space mission planning method provided by the present invention. The time axes are defined as follows: Figure 2 . Detailed Implementation

[0062] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0063] like Figures 1-4As shown, the multi-station relay space mission planning method of the present invention includes:

[0064] S1 specifies the required execution period and duration for the space mission;

[0065] S2, during the execution period, performs satellite-to-ground visibility prediction based on the given satellite ephemeris and station location, and generates an effective visibility time window;

[0066] S3, Establish the constraint condition model;

[0067] S4, Infeasible solution repair process;

[0068] S5, Establish a multi-objective function model;

[0069] S6, the objective-level method for solving the problem;

[0070] S7. Simulated annealing method is used to optimize the multi-station relay scheduling model.

[0071] Step S1 includes:

[0072] The execution period and duration required for a space mission can be described as a combination of arc segments that can be continuously tracked for h hours within a given d days.

[0073] Step S2 further includes:

[0074] Generate scene time information, starting at time T. sce_start End time T sce_end =T sce_start +d; During the execution period, based on the minimum elevation angle, perform satellite-to-ground visibility prediction for the given satellite ephemeris and station location, and generate a set of effective visible time windows A. Any time window vp within A... i =(sa,s,ts,te), where sa, s, ts, and te represent arc segment vp respectively. i The corresponding ground station number, satellite number, arc start time, and end time.

[0075] In step S3, the process is as follows:

[0076] The overlap of time windows between two arc segments is a prerequisite for relay tracking between them. The overlap of time windows in the constraint model can be described by the following method:

[0077] S301, S2 generates a set of visible time windows A. Let the number of time windows be n, and let the time windows be arranged in ascending order of their start times.

[0078] S302 defines two time window redundancy. The time window VP corresponds to two stations and one satellite. i and VP jIf there is time overlap between two windows, then the time window VP i and VP j There is two window redundancy, that is, when vp i— sa≠vp j— sa and vp i— s=vp j— If at time s Then there is redundancy in two time windows;

[0079] S303 defines the redundancy correlation parameters for two time windows.

[0080] Figure 2 China VPL i vpl j rdu_t ij rdu_t ji These represent time windows (vp) i and VP j The length of the overlap between the two time windows, and the length of the time between them.

[0081] vpl i =vp i _te-vp i _ts;

[0082] vpl j =vp j _te-vp j _ts;

[0083] rdu_t ij =rdu_t ji =min(vp i _te , vp j _te)-max(vp i _ts , vp j _ts);

[0084] The time window redundancy ratio is defined as the ratio of the overlapping time length to the visible window time length.

[0085] rdu_r ij =rdu_t ij / vpl i

[0086] rdu_r ji =rdu_t ji / vpl j

[0087] This indicator reflects the magnitude of the conflict's impact on the time window; the larger the indicator value, the greater the impact of the conflict on the time window.

[0088] The greater the influence of the mouth.

[0089] ;

[0090] The value ranges from 0 to 1. When both values ​​are 0, it means that the two time windows do not overlap, that is, there is no redundancy and relay tracking is not possible. When both values ​​are 1, it means that the two time windows completely overlap. When only one value is 1, it means that the arc segment is included. Other values ​​indicate that the two time windows overlap.

[0091] In relay tracking, the redundancy ratio of each time window should be between (0,1) and the value should be small so that the overlapping time of the tracking arc is short, so as to avoid wasting resources. At the same time, the overlapping period rdu_t should be greater than the device switching time.

[0092] S304, Establish the time window redundancy matrix.

[0093] Two-window redundancy is the foundation for available time window redundancy analysis. However, when analyzing the overall redundancy of each resource, the aforementioned resource redundancy indicators cannot provide an intuitive comparison of redundancy between resources. Therefore, the concept of several types of redundancy matrices is proposed, given a time window number of n.

[0094] Constructing the time window redundancy ratio matrix

[0095] ;

[0096] In the matrix, the i-th row (column) represents the i-th time window (segment). Although there is time overlap between the time window and itself, this overlap is not considered redundant, and the redundancy ratio is recorded as 0. Therefore, the time window redundancy ratio matrix is ​​a square matrix with all diagonal elements being 0. Similar to the time window redundancy ratio matrix, a redundant time matrix can also be given, which is used in the objective optimization process.

[0097] Constructing a time window redundancy time matrix

[0098] ;

[0099] Summing each row of the above matrix yields the redundancy ratio between the corresponding time window and all other visible windows in the set. This metric effectively measures the redundancy level between time windows and can serve as a reference factor during scheduling. If the sum of the redundancy ratios for time window i is greater than 1, it indicates that this arc segment overlaps with multiple other arc segments (multi-station redundancy). Figure 3 medium time window VP i2 As shown.

[0100] S305, Redundancy matrix order reduction.

[0101] If the row and column elements corresponding to arc segment i in the matrix are both 0, then that row and column are deleted from the matrix, and the matrix order is reduced by 1. The fact that the row and column elements corresponding to arc segment i are both 0 indicates that arc segment i has no redundancy (no time overlap) with other arc segments. There should be redundancy between arc segments in relay tracking; arc segments without redundancy do not need to participate in scheduling. This operation can reduce the computational scale of subsequent combinatorial problems. Let the number of arc segments after order reduction be k.

[0102] S306, Establish a multi-station relay constraint model.

[0103] The constraint model can be represented as a set of arc segments ordered by their start time. Adjacent arc segments vp h VP j VP k Between them, if SW has only one arc segment, then the length of that arc segment is greater than or equal to h; if there are two arc segments, then the two arc segments overlap, and the effective length of the arc segments (the overlapping part is counted once) is greater than or equal to h; if there are multiple arc segments, then between any three adjacent arc segments, the middle arc segment overlaps with the preceding and following arc segments respectively, the preceding and following arc segments do not overlap, and the arc segment length meets the requirements, such as... Figure 4 The model can be represented as follows:

[0104] ;

[0105] The specific steps for repairing infeasible solutions in step S4 are as follows.

[0106] In the multi-station relay scheduling model problem, the existence of two-station redundancy between adjacent arc segments is a hard constraint. Violating this constraint renders the scheduling strategy infeasible. When the number of visible arc segments is large, the probability of constraint violation increases sharply in combinations of visible arc segments. In this case, the random crossover and mutation operations can easily result in some arc segments having no redundancy or multiple stations having simultaneous redundancy, leading to very few feasible solutions. The following method can be used to repair infeasible solutions and transform them into feasible solutions.

[0107] S401, traverse the arc segments in the chromosome whose state is 1;

[0108] S402, for two adjacent arc segments with a value of 1, if the redundancy ratio is 0, if these two arc segments are adjacent, then set the gene value of the arc segment with the shorter time to 0; if there are other arc segments with a value of 0 between these two arc segments, then select an arc segment that has redundancy with both of these arc segments and set that arc segment to 1.

[0109] S403, if there is a redundancy ratio of 1, then set the arc segment to 0;

[0110] S404, the arc redundancy ratio is greater than 1. If there are other arcs that are redundant with this arc, they are all 1 in the chromosome, and this arc is set to 0.

[0111] In step S5, the process is as follows:

[0112] In the set of arc segment combinations that satisfy the constraints, find the arc segment combination that makes the objective function optimal. The stations corresponding to each arc segment in this arc segment combination are the optimal station combination for the multi-station relay of this task.

[0113] The objective function can be described as having a small overlap between arc segments, a small number of arc segments, a small number of required stations, a large number of different devices, and a long relay time. It is a multi-objective optimization problem, and a set of Pareto optimal solutions can be obtained by using the objective hierarchical method.

[0114] The mathematical models for each objective function are established below.

[0115] S501, Objective function 1 is established.

[0116] The overlap between arc segments is small, meaning that for any adjacent arc segment vp i VP j， Minimum overlap time

[0117] ;

[0118] f1 requires minimizing the redundancy ratio of each adjacent arc segment, which is a multi-objective optimization problem. It simplifies to minimizing the sum of the redundancy ratios of adjacent arc segments in a given combination. For easier comparison, this can be divided by the number of arc segments, f3.

[0119] ;

[0120] S502, Objective function 2 is established.

[0121] The total relay time, or the total time of the arc segment combination, is the sum of the end time of the last arc segment and the start time of the first arc segment. It can also be described as the duration of each arc segment minus the overlapping period of adjacent arc segments.

[0122] Sum the durations of the arc segments.

[0123] S503, Objective function 3 is established.

[0124] The number of arcs can be represented by the sum of their encoded values. The number of stations is related to the number of arcs; fewer arcs mean fewer stations.

[0125] ,

[0126] S504, Objective function 4 is established.

[0127] Multi-station relay tracking involves multiple devices, meaning there are few overlapping stations between multiple arc segments.

[0128] A set of non-repeating stations in an arc segment, with a length equal to the number of stations.

[0129] S505, Multi-objective function representation

[0130] The multi-objective function can be expressed as,

[0131] F=[min(f1),max(f2),min(f3),max(f4)],

[0132] To standardize the metrics for each objective, we first transform f2 and f4 into finding their minimum values. We take the reciprocal of f2 and multiply it by the relay tracking time h, still denoted as f2. Similarly, we take the reciprocal of f4 and multiply it by the number of arc segments f3, still denoted as f4. The multi-objective function is then transformed into…

[0133] F=[min(f1),min(f2),min(f3),min(f4)].

[0134] In step S6, the process is as follows:

[0135] In most multi-objective optimization problems, the performance of each objective is contradictory. Each objective can reach its optimum independently, but it is generally not possible for multiple objectives to reach their optimum simultaneously. A change in the performance of one objective may degrade the performance of other objectives. Therefore, we can only compromise and coordinate the objectives to achieve the optimum as much as possible.

[0136] The optimal solution is found by applying the objective hierarchy method.

[0137] The four objective functions constructed in S5 are sorted according to their existing numbers. Based on the optimal solution of each objective function, the optimal solution of the next objective function is calculated, and the optimal solution of the last objective function is taken as the global optimal solution.

[0138] S601, with f1 as the single objective, find the set of arc segments with the minimum redundancy ratio of adjacent arc segments in the arc segment combination, denoted as strategy C1;

[0139] S602, with f2 as the single objective, find the set of arc segments with the longest total duration of the arc segment combination, denoted as strategy C2;

[0140] S603, in strategy C1+C2 ， Find C3 with f2 as the single objective;

[0141] S604, with f3 as the single objective, find the set of arc segments with fewer arc segments in the arc segment combination, denoted as strategy C4;

[0142] S605, in strategy C3+C4 ， Find C5 with f3 as the single objective;

[0143] S606, with f4 as the single objective, find the set of arc segments with fewer repeated stations in the arc segment combination, denoted as strategy C6;

[0144] S607, in strategy C5+C6, with f4 as the single objective, find C7, which is the optimal solution in the sense of objective hierarchy;

[0145] The objective hierarchy method yields the best satisfaction for the objective function ranked first, and the satisfaction decreases as the objective function is ranked lower.

[0146] In step S7, the process is as follows:

[0147] The number of combinations of k redundant arc segments is Each combination corresponds to a solution, which is a combinatorial optimization problem that can be solved using the simulated annealing algorithm.

[0148] S701, Design Variable

[0149] The multi-station relay scheduling model uses the selection of all visible arc segments within a certain time range as the design variable. It is a discrete design variable, and the variable is in binary encoding form. The number of all visible arc segments (which can be a set of redundant arc segments, i.e., the arc segments corresponding to the reduced-order matrix of the redundancy matrix) is the number of bits in the binary encoding. When an arc segment is selected, the arc segment code is set to 1; when the arc segment is not selected, the code is set to 0. Mathematically, this is expressed as... , ;

[0150] S702, multidimensional encoding

[0151] To facilitate querying and retrieving arc segment-related information in actual calculations, the one-dimensional gene encoding is extended to a multi-dimensional encoding in the encoding implementation, including arc segment number, arc segment information, arc segment state (i.e., X), arc segment redundancy ratio vector, arc segment redundancy time vector, etc. The chromosome dimension is the same as the X dimension k.

[0152] S703, Simulated Annealing Parameter Settings

[0153] Set the population size, number of iterations, initial temperature, decay factor, and acceptance criterion probability, etc.

[0154] S704, simulating the annealing process.

[0155] Infeasible solutions that do not meet the constraints are repaired, the objective hierarchical method is used to calculate the fitness value, and the optimal solution is obtained through iterative iteration.

[0156] The scenario in this embodiment is as follows:

[0157] Table 1. Given satellite ephemeris:

[0158]

[0159] Table 2. Information on 10 given sites:

[0160]

[0161] The specific steps are as follows:

[0162] S1, scenario start time 2025-07-01 00:00:00, simulation period 7 days, multi-station relay duration not less than 3 hours.

[0163] S2, based on the given satellite ephemeris and station information, performs satellite-to-ground visibility prediction and generates effective visible arc segments.

[0164] Using professional forecasting software, the visible arc between 10 stations and 1 satellite at an elevation angle of 30º was calculated from July 1, 2025 to July 8, 2025.

[0165] S3, Establish the constraint condition model.

[0166] S301, the visible arc segments between the satellite and the ground are arranged in ascending order of their start times;

[0167] S302, S303, and S304 are used to construct redundancy ratio and redundancy time matrices.

[0168] Based on the above definition, if the number of visible time windows between the satellite and the ground is n, then an n*n redundancy ratio and redundancy time matrix is ​​generated, with the initial values ​​of the matrix elements being 0. The given time windows are traversed, and for any given time window, the intersection operation is performed with the other time windows. If the intersection is not empty, the length of the intersection arc time window is calculated, and the corresponding position in the redundancy time matrix is ​​filled with the value of that time window length. If the intersection is empty, the corresponding position in the redundancy time matrix is ​​filled with 0, generating a redundancy time matrix, which is a symmetric matrix. The redundancy ratio matrix is ​​generated by dividing the corresponding position in the generated redundancy time matrix by the length of the corresponding visible time window between the satellite and the ground.

[0169] S305, Redundant matrix order reduction

[0170] Remove rows and columns with all rows and columns equal to 0 from the redundancy ratio and redundancy time matrices. There is redundancy between the arc segments corresponding to the reduced-order matrix. Let the number of reduced-order arc segments be k. There may be a solution that satisfies the requirements among the combinations of these arc segments.

[0171] S306, Establish a multi-station relay constraint model.

[0172] S4, the infeasible solution repair process, involves changing the state values ​​of arc segments in the chromosome to create redundancy between adjacent arc segments.

[0173] S5, construct the objective function according to the claims.

[0174] S6. Apply the objective hierarchy method to find the optimal solution.

[0175] S7. Simulated annealing method is used to optimize the multi-station relay scheduling model.

[0176] This invention transforms the multi-station relay problem into a permutation and combination problem of selecting arc segments by using discrete space-to-ground visible time windows. By introducing redundant time and redundancy ratio matrices, the relationships between arc segments are intuitively described, and a constraint model and objective function are constructed. In the process of optimizing the multi-station relay scheduling model using simulated annealing algorithm, multi-dimensional parameter encoding, repair of infeasible solutions that do not meet the constraints, and calculation of the fitness value using a hierarchical objective method are employed. Iterative iteration is then used to find the optimal arc segment combination that satisfies the objectives of low overlap between arc segments, few arc segments, few required stations, many different devices, and long relay duration. Based on this invention, a domain-specific objective function can be designed to construct a space mission planning method for multi-station relays that adapts to different needs.

[0177] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of protection claimed by the present invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A multi-station relay space mission planning method, characterized in that, Includes the following steps: S1, gives the execution period and duration required for the space mission, wherein the execution period and duration are a combination of arc segments that can be continuously tracked for h hours within a given d days; S2, during the execution period, performs satellite-to-ground visibility prediction based on the given satellite ephemeris and station location, and generates an effective visibility time window; Generate scene time information, starting at time T. sce_start End time T sce_end =T sce_start +d; During the execution period, based on the minimum elevation angle, perform satellite-to-ground visibility prediction for the given satellite ephemeris and station location, and generate a set of effective visible time windows A. Any time window vp within A... i =(sa,s,ts,te), where sa, s, ts, and te represent arc segment vp respectively. i The corresponding ground station number, satellite number, arc start time, and end time; S3, Establish the constraint condition model; S4, Infeasible solution repair process; S5, Establish a multi-objective function model; S6, the objective-level solution process; S7. Simulated annealing method is used to optimize the multi-station relay scheduling model.

2. The multi-station relay space mission planning method according to claim 1, characterized in that: Step S3 specifically includes the following sub-steps: S301, Sort the set of visible time windows A generated in S2 in ascending order of their start times, and let the number of time windows be n; S302 defines two time window redundancy: time window vp corresponding to two stations and one satellite. i and VP j When VP i— sa≠vp j— sa and vp i— s=vp j— If there is a time overlap between two windows, then the time window vp i and VP j There is redundancy in two windows; S303 defines the redundancy-related parameters for two time windows: Define arc length vpl i =vp i _te-vp i _ts, vpl j =vp j _te-vp j _ts; Define rdu_t ij ,rdu_t ji This represents two time windows (vp). i， vp j The length of the overlapping portion of time, obviously rdu_t ij =rdu_t ji =min(vp i _te , vp j _te)-max(vp i _ts , vp j _ts); Define rdu_r ij ,rdu_r ji The redundancy ratio, rdu_r, is the ratio of the overlap length of two time windows to the length of each individual time window. ij =rdu_t ij / vpl i ,rdu_r ji =rdu_t ji / vpl j ; In relay tracking, the redundancy ratio of each time window is between (0,1) and the value is small, while the overlapping period rdu_t is greater than the device switching time; S304, establish a time window redundancy ratio matrix and a redundancy time matrix. The redundancy ratio matrix is ​​a square matrix with all diagonal elements being 0. The i-th row in the matrix represents the i-th time window. Summing each row of the matrix yields the sum of the redundancy ratios of the corresponding time window and other visible windows. S305, Redundant Matrix Reduction: If the row and column elements corresponding to arc segment i in the matrix are both 0, then delete that row and column, and decrease the matrix order by 1. Let the number of arc segments after reduction be k. S306, Establish a multi-station relay constraint model: a set of arc segments ordered by start time, and adjacent arc segments vp h VP j VP k Between two arc segments, if there is only one arc segment, the length of the arc segment is greater than or equal to h; if there are two arc segments, the two arc segments overlap, and the effective length of the arc segments is greater than or equal to h, where the overlapping part is calculated once; if there are multiple arc segments, between any three adjacent arc segments, the middle arc segment overlaps with the preceding and following arc segments respectively, the preceding and following arc segments do not overlap, and the arc segment length meets the requirements.

3. The multi-station relay space mission planning method according to claim 1, characterized in that: The repair process for infeasible solutions in step S4 specifically includes: S401, traverse the arc segments in the chromosome whose state is 1; S402, for two adjacent arc segments with a value of 1, if the redundancy ratio is 0, if these two arc segments are adjacent, then set the gene value of the arc segment with the shorter time to 0; if there are other arc segments with a value of 0 between these two arc segments, then select an arc segment that has redundancy with both of these arc segments and set that arc segment to 1. S403, if there is a redundancy ratio of 1, then set the arc segment to 0; S404, For arc segments with a redundancy ratio greater than 1, if other arc segments that are redundant with this arc segment are all 1 in the chromosome, then this arc segment is set to 0.

4. The multi-station relay space mission planning method according to claim 1, characterized in that: The multi-objective function model established in step S5 specifically includes: S501, Objective function f1: Minimize the redundancy ratio of adjacent arc segments in the arc segment combination, and divide by the number of arc segments f3 for easier comparison; S502, objective function f2: the longest total relay time is the sum of the end time of the last arc and the start time of the first arc, or the sum of the duration of each arc and the overlapping time of adjacent arcs. S503, objective function f3: minimize the number of arc segments, expressed as the sum of coded values; S504, Objective function f4: Minimize the number of repeated stations in multi-station relay tracking, represented by the length of the set of non-repeating stations in the arc segment; S505, Unified metric for multi-objective functions: Convert f2 and f4 into finding the minimum value. Take the reciprocal of f2 and multiply it by the relay tracking time h, and it is still called f2. Take the reciprocal of f4 and multiply it by the number of arcs f3, and it is still called f4. The multi-objective function is converted to F=[min(f1),min(f2),min(f3),min(f4)].

5. The multi-station relay space mission planning method according to claim 1, characterized in that: Step S6, the objective hierarchy method solution process, specifically includes: S601, with f1 as the single objective, find the set of arc segments with the minimum redundancy ratio of adjacent arc segments in the arc segment combination, denoted as strategy C1; S602, with f2 as the single objective, find the set of arc segments with the longest total duration of the arc segment combination, denoted as strategy C2; S603, in strategy C1+C2 ， Find C3 with f2 as the single objective; S604, with f3 as the single objective, find the set of arc segments with fewer arc segments in the arc segment combination, denoted as strategy C4; S605, in strategy C3+C4 ， Find C5 with f3 as the single objective; S606, with f4 as the single objective, find the set of arc segments with fewer repeated stations in the arc segment combination, denoted as strategy C6; S607, in strategy C5+C6, with f4 as the single objective, C7 is the optimal solution in the sense of objective hierarchy.

6. The multi-station relay space mission planning method according to claim 1, characterized in that: Step S7, applying simulated annealing to optimize the multi-station relay scheduling model, specifically includes: S701, the design variables adopt binary encoding form. The number of all visible arc segments is the number of bits in the binary encoding. When the arc segment is selected, the encoding is set to 1, and when it is not selected, it is set to 0. S702, Multidimensional Coding: Extends one-dimensional gene coding to multidimensional, including arc segment number, arc segment information, arc segment state, arc segment redundancy ratio vector, and arc segment redundancy time vector. The chromosome dimension is the same as the number of arc segments k after the reduction. S703 sets the simulated annealing parameters, including population size, number of iterations, initial temperature, attenuation factor, and acceptance criterion probability. S704, run the simulated annealing process: repair infeasible solutions that do not meet the constraints, calculate the fitness value using the objective layering method, and iterate to find the optimal solution.

7. The multi-station relay space mission planning method according to claim 1, characterized in that: In step S2, the minimum elevation angle is 30º, and in step S1, d=7 and h≥3.

8. The multi-station relay space mission planning method according to claim 2, characterized in that: In step S304, the redundant time matrix is ​​a symmetric matrix with initial values ​​of 0 for each element. The given time window is traversed, and the intersection operation is performed between any time window and the other time windows. If the intersection is not empty, the length of the time window of the intersection arc segment is filled in at the corresponding position. If the intersection is empty, 0 is filled in.

9. The multi-station relay space mission planning method according to claim 2, characterized in that: In step S304, the redundancy ratio matrix is ​​generated based on the redundancy time matrix, and the corresponding position in the matrix is ​​divided by the length of the corresponding satellite-to-ground visible time window.

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