Method and system for TT&C station deployment based on double-layer planning model

Abstract

The application relates to a TT&C station deployment method and system based on a double-layer planning model. The TT&C station deployment method based on the double-layer planning model comprises the following steps: discretely generating a plurality of alternative TT&C stations in a preset station distribution area and according to a satellite elevation angle threshold; based on ephemeris data of a target satellite, calculating a visible time window between each alternative TT&C station and the target satellite, and generating a visible arc segment set; and based on a genetic algorithm, iteratively selecting M TT&C stations from the alternative TT&C stations as a station combination, wherein M is a preset station distribution quantity. The TT&C station deployment method and system based on the double-layer planning model can generate alternative stations at grid points by discretely distributing a station distribution area, and can convert a station distribution problem into a permutation and combination problem of selecting stations. A nested genetic algorithm is applied to complete specific selection of the stations.

Description

Technical Field

[0001] This invention belongs to the field of dual-layer optimized station deployment technology, specifically involving a method and system for deploying telemetry and control stations based on a dual-layer planning model. Background Technology

[0002] The optimized deployment of ground tracking and control stations is one of the core technologies in the field of aerospace tracking and control. Its core task is to rationally select the geographical locations of ground stations while meeting the requirements for continuous tracking and data relay of multiple spacecraft (such as low-Earth orbit satellite constellations) in a specific airspace, in order to achieve the best overall tracking performance with the fewest number of stations, while ensuring the reliability and economy of the system.

[0003] An ideal ground station deployment scheme requires a comprehensive consideration of multiple factors: First, it must ensure optimal coverage of the mission airspace, guaranteeing the visibility of the target satellite and its ability to track continuously; second, it needs to consider load balancing of ground equipment to avoid overloading individual stations; third, it should effectively avoid resource redundancy caused by multiple stations tracking the same satellite simultaneously, while also preventing resource conflicts caused by the same station being assigned to track multiple satellites at the same time. Furthermore, factors such as the geographical constraints of the deployment area and the dynamic characteristics of specific satellite orbits further increase the complexity of the problem. From a computational perspective, this problem is a combinatorial optimization problem requiring searching a vast solution space, belonging to the NP-hard category, and its solution is exceptionally complex.

[0004] Currently, existing technical solutions in this field mainly have the following limitations: First, there is insufficient utilization and optimization of visible time windows (visible arcs). Many existing methods, while calculating satellite-to-ground visibility based on satellite ephemeris during planning, often only reach a qualitative analysis or simple screening level, failing to deeply explore and optimize the combined value of all potential visible arcs. The lack of effective overall scheduling capabilities for short-lived, intermittently occurring visible windows results in the incomplete development and utilization of valuable tracking resources. Second, the handling of resource conflicts and redundancy is overly simplistic and lacks precise quantitative models. Existing technologies can typically identify simple conflicts or redundancies between pairs of arc segments, but for complex scenarios such as "multi-satellite conflicts" (multiple satellites visible from a single station within a given timeframe) and "multi-station redundancy" (multiple stations tracking the same satellite simultaneously), there is a lack of effective mathematical descriptions and modeling tools. Most solutions only perform qualitative avoidance or post-event checks, rather than treating these as core constraints and objectives in the optimization model beforehand. This means that the final solution may face a higher risk of conflict during actual operation or fail to fully utilize the reliability improvements and relay tracking opportunities brought by redundancy. Third, the operational feasibility of the optimization models is weak. In pursuit of theoretical completeness, existing methods often construct multi-objective optimization functions that include multiple conflicting, redundant, overlapping, and duration objectives. While such models are comprehensive, they are often overly complex, inefficient in solving problems, and difficult to apply to practical engineering scenarios involving large-scale satellite constellations. How to transform complex multi-objective, multi-constraint problems into single-objective problems that can be solved efficiently, while ensuring the quality of the solution, is a pain point that existing technologies have not adequately addressed.

[0005] In summary, existing technologies have not yet provided a solution for the problem of optimized deployment of ground stations that can efficiently and quantitatively coordinate and track benefits, resource conflicts and redundancy, and is applicable to large-scale engineering calculations. Therefore, there is an urgent need in this field for a new method to overcome the above-mentioned shortcomings. Summary of the Invention

[0006] The purpose of this invention is to provide a simple and rationally designed telemetry and control station deployment method and system based on a two-layer planning model in order to solve the above problems.

[0007] The present invention achieves the above objectives through the following technical solutions: The first aspect of the present invention provides a method for deploying telemetry and control stations based on a two-layer programming model, the method comprising: Based on the preset deployment area and satellite elevation angle threshold, multiple alternative telemetry and control stations are generated discretized within the deployment area; Based on the ephemeris data of the target satellite, the visible time window between each of the candidate telemetry and control stations and the target satellite is calculated, and a set of visible arc segments is generated; Based on the genetic algorithm, M telemetry and control stations are iteratively selected from the candidate telemetry and control stations as a station combination, where M is the preset number of stations; For each of the aforementioned site combinations, the following inner-layer optimization process is performed: Select a subset of visible arc segments generated by all telemetry and control stations in the site combination from the set of visible arc segments; Construct a conflict matrix and a redundancy matrix for the subset of visible arc segments; the conflict matrix is ​​used to identify the temporal conflict relationship between different visible arc segments of the same tracking and control station; the redundancy matrix is ​​used to identify the temporal redundancy relationship between visible arc segments of different tracking and control stations for the same satellite. Based on the conflict matrix and redundancy matrix, a fitness function is constructed to evaluate the subset of visible arc segments; the fitness function includes at least a penalty term for conflict and a reward term for redundancy. Based on the genetic algorithm, a scheduling scheme for the arc segment that optimizes the fitness function is searched in the subset of visible arc segments; The optimal fitness value obtained is used as the evaluation value of the current site combination; Repeat the inner optimization process of the above site combination until the outer genetic algorithm iteration ends, and output the site combination with the best evaluation value as the final telemetry and control station deployment scheme.

[0008] As a further optimization of the present invention, if two visible arc segments satisfy the following conditions: they correspond to the same telemetry and control station, correspond to different satellites, and their time windows overlap, then they are marked as conflict in the conflict matrix; If two visible arc segments satisfy the following conditions: they correspond to the same satellite, they correspond to different telemetry and control stations, and their time windows overlap, then they are marked as redundant in the redundancy matrix.

[0009] As a further optimization of the present invention, the fitness function F is expressed as: F = k1f1+k2f2+k3f3+k4f4+k5G, where f1 is the total duration of the selected arc segment; f2 is the number of redundant arc segments; f3 is the number of selected arc segments; f4 is the number of non-repeating satellites in the selected arc segment; G is the penalty function for arc segment conflicts; k1 to k5 are weight coefficients, and the sum of the weight values ​​k1, k2, k3, k4, and k5 is 1.

[0010] As a further optimization of the present invention, the conflict matrix and the redundancy matrix are reduced in order: if the row and column corresponding to a certain visible arc segment in the conflict matrix and the redundancy matrix are both zero, then the visible arc segment is removed from the current optimization process.

[0011] As a further optimization of the present invention, a telemetry and control station conflict group is generated based on the conflict matrix to describe the complex conflict relationship between multiple visible arc segments. Based on the redundancy matrix, a satellite redundancy group is generated to describe the complex redundancy relationships among multiple visible arc segments; The calculation of the fitness function depends on the collision group of the telemetry and control station and the satellite redundancy group.

[0012] As a further optimization of the present invention, the surface coverage radius of a single site is calculated based on the minimum operating elevation angle and orbital altitude of the satellite; Based on the coverage radius, a regular hexagonal seamless coverage model is used to perform discretization positioning of the stations within the station deployment area.

[0013] As a further optimization of the present invention, the visible surface coverage circle and its radius of the satellite at a given altitude are calculated by the calculation station. ; In the formula The angle is the geocentric angle between the satellite's nadir point B and the observation point P, where r is the satellite's radial distance and its value is the Earth's radius R. e Satellite altitude H, E is the satellite elevation angle, and the geocentric angle is the angle between the satellite and the Earth's center. The radius of the visible coverage circle of the satellite is twice the maximum observable arc of the satellite. The radius of the visible coverage circle of the Earth's surface corresponding to the station is... .

[0014] As a further optimization of the present invention, the angular distance between any two stations is set to... The corresponding surface distance is The area of ​​the overlapping zone of the land cover between adjacent sites accounts for 6%, and each site has 6 adjacent sites.

[0015] A second aspect of the present invention provides a telemetry and control station deployment system based on a two-layer programming model, comprising: One or more processors; The computer-readable storage medium is coupled to the processor and stores program instructions thereon; The program instructions can be executed by the processor to cause the system to perform the methods described above.

[0016] The beneficial effects of this invention are as follows: This invention, by constructing conflict and redundancy matrices, achieves for the first time a precise and quantitative description of complex scenarios involving "multi-satellite conflicts" and "multi-station redundancy." Furthermore, by constructing conflict and redundancy groups, it provides a structured tool for the inner-layer optimization algorithm to quickly determine the effectiveness of solutions. This overcomes the shortcomings of existing technologies that rely heavily on qualitative analysis and post-event checks, enabling the final deployment scheme to theoretically avoid resource conflicts and proactively utilize redundant resources for relay tracking, thereby improving the reliability and practicality of the scheme. This invention employs a two-layer optimization model combining an outer layer (site selection) and an inner layer (scheduling), decomposing the complex NP-hard problem into two relatively independent yet collaboratively optimized sub-problems. By reducing the order of the conflict / redundancy matrix before the inner layer optimization, a large number of conflict-free and non-redundant arc segments are removed, effectively reducing the decision space of the inner layer optimization problem. Furthermore, by designing a reasonable genetic algorithm encoding method, fitness function, and genetic operators, the algorithm can efficiently search within a huge combinatorial solution space, thereby obtaining high-quality feasible solutions within an acceptable computational time, solving the problem of solution difficulties caused by the complexity of existing methods. The fitness function of this invention comprehensively considers multiple key performance indicators such as total arc duration, redundancy, total number of arcs, and number of satellites, and allows users to flexibly adjust the optimization focus according to actual task requirements through weighting coefficients. The final output not only provides the optimal combination of site geographical locations but also includes a corresponding detailed optimal arc scheduling scheme. This provides users with a comprehensive deployment solution that combines high tracking efficiency, high resource utilization, and high system reliability, enhancing the method's decision support capabilities. The method framework of this invention is independent of specific satellite constellations or deployment area shapes. The described two-layer optimization structure, matrix-based conflict / redundancy description method, and genetic algorithm-based solution strategy are applicable to various aerospace telemetry and control scenarios and other similar deployment requirements. By adjusting input parameters (such as satellite ephemeris, elevation constraints, deployment area, number of stations m, etc.) and objective function weights, it can quickly adapt to different mission requirements, demonstrating the method's good versatility and scalability. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the deployment method of telemetry and control stations based on a two-layer planning model according to the present invention. Figure 2 This is a schematic diagram of the visible coverage area between the satellite and the ground according to the present invention; Figure 3 This is a schematic diagram of the overlapping coverage circles of adjacent sites according to the present invention; Figure 4 This is a schematic diagram of the relationship between the two sites in this invention; Figure 5 This is the timing diagram of arc segment conflict (redundancy) of the present invention; Figure 6 This is a schematic diagram of a single-station multi-satellite conflict arc segment of the present invention. Detailed Implementation

[0018] The present application will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are only used to further illustrate the present application and should not be construed as limiting the scope of protection of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application based on the above application content.

[0019] Example 1 This embodiment proposes a telemetry and control station deployment method based on a two-layer planning model to address resource conflicts and redundancy, overcoming three shortcomings of existing methods in the background art. This invention models the station deployment process as a discrete optimization problem. The station deployment area is discrete, and a satellite-to-ground visibility coverage model is applied to ensure the candidate stations guarantee mission airspace coverage effectiveness. Based on specific satellite ephemeris data, visible arc segments are generated, focusing on resource conflicts and redundancy. A two-layer optimization approach is applied; by optimizing the arc segments, station optimization is achieved, realizing optimized station deployment for specific satellites and specific deployment areas.

[0020] This method involves a two-layer optimization process. The outer layer is the process of selecting m sites from n candidate sites. The process of combinatorial optimization; the inner layer is the process of selecting the combination of arc segments that satisfy the optimal fitness value from the arc segments belonging to the given m telemetry and control stations. Let the number of arc segments be k, then it is... The optimization process involves a nested genetic algorithm. The technical characteristic of this "two-layer optimization" is that the outer layer selects m sites from n candidate sites using a genetic algorithm, while the inner layer optimizes the arc segment combinations based on the selected sites. The objective function of the inner layer needs to consider factors such as the number of satellites, the number of arc segments, arc segment conflicts, the total duration of arc segments, and resource redundancy (relay capability), involving multiple objectives and constraints, thus constituting a multi-objective optimization problem. To facilitate computation, multiple objectives and constraints can be transformed into a single objective function using weighting coefficients and penalty functions. The objective function of the outer layer can be the same as that of the inner layer. For different site combinations in the outer layer, the inner layer provides the arc segment combination that optimizes the objective function for each site combination. The site combination corresponding to the optimal objective value among all arc segment combinations is the optimal site placement result. The nested genetic algorithm is used to solve the optimal site placement problem. The inner layer genes use 0-1 encoding to represent two states: arc tracking or non-tracking. The chromosome length is k (the number of arc segments), and the solution space size is 2^k. k -1; The outer genes are encoded using natural numbers, with the encoded value being the site number. The chromosome length is the number of selected sites m, and the solution space size is . Design appropriate crossover and mutation operators so that the generated chromosome can cover all candidate sites in the solution space.

[0021] Specifically, in this embodiment, the present invention provides a two-layer optimized site deployment method that considers resource conflicts and redundancy, including: S1, Given a discrete deployment area, generate n candidate sites; S2, based on the given satellite ephemeris, performs satellite-to-ground visibility prediction and generates effective visible arc segments; S3, the process of selecting m sites (outer genetic algorithm); S4, for the selected m stations, generate a matrix of the number of collisions and redundancy ratios of the telemetry and control stations, as well as other relevant indicators, based on the effective visible arc segments contained therein; S5, Determine the objective optimization function; S6, Search for the optimal combination of visible arc segments that optimizes the objective function (inner genetic algorithm). Step S1 further includes: S101, the circle of visible ground cover and its radius for a given altitude satellite at a given station are calculated using the following formula: ; like Figure 2 In the formula The angle is the geocentric angle between the satellite's nadir point B and the observation point P, where r is the satellite's radial distance and its value is the Earth's radius R. e Add satellite altitude H, where E is the satellite elevation angle (elevation angle) and the geocentric angle. The radius of the visible coverage circle of the satellite is twice the maximum observable arc of the satellite. The radius of the visible coverage circle of the Earth's surface corresponding to the station is... .

[0022] S102, the angular distance (geocentric angle) between any two stations (centers) is set as... The corresponding surface distance is The area of ​​the overlapping zone of the land cover between adjacent sites accounts for 6%, and each site has 6 adjacent sites. Figure 3 A schematic diagram of 7 stations is provided. The 7 black circles represent the ground cover circles of the 7 stations, and the vertices and center point of the regular hexagons represent the coordinates of the 7 stations. Assume the given station deployment area is... Figure 3 The area indicated by the red circle is covered by a network of stations deployed at the center and around the circumference of the circle, achieving full coverage of the deployment area. Furthermore, the visible coverage area expands outwards from the given deployment area. Satellites whose nadir points fall within this area (within the black circle) are observable. In this station configuration, there is only double coverage between stations, and the coverage ratio is relatively small.

[0023] S103. If the deployment area is an irregular shape, prioritize deploying stations along the boundary line and at the geometric center. Deploying appropriate stations along the boundary line can expand the visible coverage area outward from the given deployment area. Corner. The principle for station deployment in other areas should be to minimize the overlap between stations and ensure full coverage of the deployment area.

[0024] S104, Given the latitude and longitude coordinates of a station within the station layout area, its distance from another station, and its azimuth, as follows: Figure 4As shown, the azimuth angle between the two points is α (the angle between the line connecting the two points and the due north direction, which is 0 degrees), and the distance between the two points is d. The latitude and longitude of station 1 (long1, lat1) can be used to calculate the latitude and longitude of another station (long2, lat2) using the following formula. Based on this, the coordinates of all candidate stations within the station layout area can be calculated.

[0025] long2 = long1 + d×sinɑ / [R e *cos(lat1)×2π / 360]; lat2 = lat1 + d × cosɑ / (R) e *2π / 360); Step S2 further includes: Given candidate sites generated by S1, and the given satellite ephemeris, elevation angle, and satellite-to-ground interaction distance, construct a set A of all valid visible arcs for all satellites within a given scenario time period. For any arc 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.

[0026] In step S3, the process of selecting m stations is as follows: The process of selecting m sites from n candidate sites belongs to... The permutation and combination problem can be solved using a genetic algorithm. Genes are encoded using natural numbers, with the encoded value being the site index. The chromosome length is the number of selected sites, *m*. The fitness value of each individual is passed in by the inner layer of the genetic algorithm. By designing suitable crossover and mutation operators and selecting appropriate crossover and mutation probabilities, the generated chromosomes exhibit diversity and can search for all candidate sites in the solution space.

[0027] Step S4 further includes: S401, from the set of valid visible arc segments A generated in S2, select the arc segment set SW corresponding to the given m stations, which is the arc segment set corresponding to a certain individual of the genetic algorithm in S3. Let the number of arc segments be k. The arc segments are arranged in ascending order of their start time; S402, construct a k×k dimensional conflict number matrix. cft_n ij Indicates visible arc segment vp i and VP j Is there a conflict? When vp i— sa=vp j— sa and vpi— s≠vp j— If at time s , Then cft_n ij =1 indicates a conflict, meaning there is overlap in the tracking times of two satellites by the same telemetry and control station (resource); otherwise, =0 indicates no conflict.

[0028] S403, construct a k×k dimensional redundancy matrix. rdu_n ij Indicates visible arc segment vp i and VP j Is there redundancy? When vp i— sa≠vp j— sa and vp i— s=vp j— If at time s , Then rdu_n ij =1 indicates redundancy, meaning there is overlap in the tracking time of the same satellite between two tracking stations; otherwise, it is 0, indicating no redundancy. Redundancy can represent relay tracking of the same satellite by different tracking stations.

[0029] S404, a reduction in the order of the conflict and redundancy matrices.

[0030] 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 resource conflict (redundancy) with other arc segments. Since the inner genetic algorithm considers the scheduling of conflicting arc segments, conflict-free and non-redundant arc segments do not need to participate in the scheduling, and the chromosome length is also reduced accordingly. This operation can reduce the computational scale of the problem.

[0031] S405, constructing a conflict group for telemetry and control stations.

[0032] The conflict number matrix can describe "two-star conflict" but not "multi-star conflict". Constructing a conflict group of telemetry and control stations that includes "multi-star conflict" can simplify the judgment process of feasible solution of non-conflict arc segment combination in the inner layer genetic algorithm and improve the performance of inner layer optimization iteration.

[0033] Resource conflicts occur between different arcs of the same station, and conflict groups can be constructed for each station in turn.

[0034] Single-site collision group generation process: Step 1: Establish a conflict group .

[0035] Step 2: Select the collision number matrix for the station from the collision number matrix, which consists of the arc segments corresponding to the station.

[0036] Step 3: Add the corresponding order identity matrix to the collision number matrix to generate a new collision number matrix.

[0037] Step 4: Search sequentially for the largest all-ones matrix in the collision number matrix. For each matrix, form a collision arc set by assigning corresponding arc segment numbers. Add these collision arc sets sequentially to CC.

[0038] In step 4, the process of finding all-one square matrices and generating conflict groups is described as follows: Let the order of the conflict number matrix be N. Obviously, the order of the smallest all-one square matrix is ​​2, that is, the smallest conflict is a 2-star conflict.

[0039] ① In the collision number matrix at position (i, i), find the number of consecutive 1s to the right (down) from that position in row (column), and record this number N. i That is, a square matrix Matrn consisting entirely of 1s. i The order of the arc is used to index the corresponding arc segment information and generate a conflict arc segment set SW. i .

[0040] ② i changes sequentially from 1 to N-1, generating a set of record counts {N1, N2, ..., N}. N-1}, the set of all-one square matrices {MatrN1, MatrN2, ..., MatrN} N-1}, the set of conflict arcs {SW1, SW2, ..., SW} N-1}

[0041] ③ Compare adjacent square matrices Matrn sequentially i and MatrN i+1 order N i and N i+1 If N i+1 >=N i SW set of conflict arcs i+1 Add it to CC, that is, CC = CC + SW i+1 The first set of conflicting arc segments is directly added to the conflict set, CC = CC + SW1.

[0042] S406, construct a satellite redundancy group.

[0043] The redundancy matrix can describe "two-station redundancy" but not "multi-station redundancy". Constructing a satellite redundancy group that includes "multi-station redundancy" can simplify the calculation process of multi-station relay in the feasible solution of conflict-free arc combination in the inner-layer genetic algorithm.

[0044] Resource redundancy occurs between different arc segments of the same satellite, and redundancy groups can be constructed for each satellite in turn.

[0045] The process of generating a single-satellite redundancy group is the same as the process of generating a single-station collision group in S405.

[0046] In step S5, the objective optimization function is determined, and the process is as follows: The constraints are that there are no conflicts among the selected arc segment combinations (a certain individual solution), and the objective function is to maximize the total duration of the selected arc segment combinations, increase the number of redundant arc segments (allowing for multi-station relay), increase the number of arc segments, and involve a large number of satellites. In this model, the decision variable is the effective visible arc segment, and the arc segment set after the S404 operation constitutes the decision space.

[0047] The mathematical models for each objective function are as follows: Sum the durations of the arc segments; The number of redundant arc segments; Number of arc segments, g i The inner-layer genetic algorithm corresponds to the chromosomes and genes. A set of non-repeating satellites within an arc segment, with a set length equal to the number of satellites. F = [max(f1),max(f2),max(f3),max(f4)], represents a multi-objective function; st , represents the constraint function; Considering both the objective function and constraints, the constraints are transformed into penalty functions.

[0048] The objective function is F = k1f1+k2f2+k3f3+k4f4+k5G, where the weights k1, k2, k3, k4, and k5 sum to 1.

[0049] In step S6, the search for the optimal combination of visible arc segments that optimizes the objective function (inner layer genetic algorithm) is as follows: The number of combinations of k arc segments is Each combination corresponds to a solution, which is a combinatorial optimization problem that can be solved using a genetic algorithm. Genes are encoded using 0-1, and chromosomes are represented as C=(g1,g2,...g...). k ), where the length is the number of arc segments k, g i A value of 1 indicates that the arc segment is vp. i Tracking, 0 indicates no tracking. The fitness value for each individual is determined according to S7.

[0050] In step S7, the fitness calculation process of the inner-layer genetic algorithm is as follows: S701, chromosome decoding, mapping to obtain the set of selected arc segment numbers in an individual; S702, arc segments are classified according to telemetry and control stations, and arc segments of the same telemetry and control station form a subset of arc segment numbers; S703. The set of arc segment numbers of the same telemetry and control station is intersected with each "multi-satellite conflict" set in the conflict group corresponding to the station. If there is a dimension greater than or equal to 2, it indicates that there is a conflict between the arc segments. This individual is an infeasible solution. The penalty function G is a random number from 0 to 1. The other objective function values ​​(f1 to f4) are set to 0. The fitness value is F=K5G. The calculation ends.

[0051] S704, after all arc segments intersect, the dimension is less than 2, indicating that there is no conflict between arc segments in this individual, which is an optional solution, and the penalty function G is a large number a; S705, under feasible solutions, calculate the number of arc segments f3, the total duration of the arc segments (converted to hours) f1, and the number of different satellites f4 corresponding to the solution in sequence; S706, in the feasible solution, the arc segments are classified by satellite. The arc segment number of the same satellite is sequentially intersected with each "multi-station redundancy" set in the redundancy group corresponding to that satellite. The dimension of the intersection is f2. S706, the sum of the above values ​​with coefficient weights is the fit of the feasible solution.

[0052] In this method, a large fitness value indicates an excellent solution, while a fitness value less than 1 indicates an infeasible solution.

[0053] Example 2 In a more specific embodiment, the steps corresponding to Embodiment 1 are performed as follows: The scenario in this embodiment is as follows: Given the latitude and longitude of the center point of the station deployment area (34... 。 N,108 。 E), the deployment area is a circle with a radius of 800km; 1000 Leo orbit satellites, with an altitude of 500km and an elevation angle of 60°. º The forecast period for the visible arc segment is from 05:49:38 on May 30, 2025 to 05:49:38 on May 31, 2025, with 6 stations deployed. The objective is to optimize the arc segment combinations corresponding to each station, ensuring a longer total duration, more redundant arc segments (allowing for multi-station relay), a larger number of arc segments, and a greater number of satellites involved. The constraint is that there are no conflicts between the selected arc segment combinations for the optimized stations.

[0054] The specific steps are as follows: S1, given a discrete deployment area, generates candidate sites: The radius of the satellite's visible coverage circle at an altitude of 500km was calculated to be r=264km. The first station was located at the center of the deployment area (34km). 。 N,108 。 E), assuming a regular hexagonal configuration, calculate the coordinates of the six surrounding stations with a radius of [missing information]. With a radius of r = 457 km, the coordinates of 6 stations are calculated using formula S104. The coordinates of the remaining stations are then calculated sequentially outwards. When the distance between a station and the first station is greater than the radius of the station deployment area, stations are deployed at intervals along the circumference of the deployment area. Assume n candidate stations are generated.

[0055] S2, based on the given satellite ephemeris, performs satellite-to-ground visibility prediction and generates effective visible arc segments: Using specialized forecasting software, calculations were performed on n stations and 1000 satellites at an elevation angle of 60 degrees. º The visible arc between 05:49:38 on 2025-05-30 and 05:49:38 on 2025-05-31.

[0056] S3, the process of selecting m sites (outer genetic algorithm): Choose 6 sites from n candidate sites (n>6). The set of candidate sites is SA=(sa1,sa2,...,sa3) n The problem involves selecting 6 individuals from a set of 6 (a permutation and combination problem). The gene encoding value is the site number, and the chromosome length is 6. The fitness value of each individual is passed in by the inner-layer genetic algorithm. The mutation operator has a relatively high probability of 0.5, which can generate new solutions with significant changes.

[0057] S4, for the selected m stations, generate a matrix of tracking station collision count, redundancy ratio (number), and other relevant indicators based on the included valid visible arc segments: Let the selected 6 stations be (sa2, sa5, sa8, sa...). 15 ,sa 17 ,sa 23 From the set of valid visible arc segments generated by S2, the corresponding arc segment set is selected according to the information of 6 stations, and the arc segments are arranged in ascending order of start time; Construct the conflict number matrix and redundancy number matrix using methods S402 and S403, and then reduce the order of the matrices using method S404. Figure 5 Given a time series diagram of multiple arc segment conflicts (redundancy) for a given time period, the conflict and redundancy number matrices corresponding to the 10 arc segments in the diagram and the reduced-order matrices are as follows. For ease of explanation, the conflict and redundancy number matrices are merged. Elements with a value of 1 in the matrix indicate that two arc segments have a conflict, and elements with a value of 2 indicate that two arc segments have redundancy. Arc segments 1 and 10 are removed after the order reduction.

[0058]

[0059] Construct a collision group for the telemetry and control station according to the S405 method.

[0060] Figure 6The arc segment time series diagram for a single-station multi-satellite conflict is given. The matrix changes during the conflict group establishment process corresponding to this example are as follows. According to the S405 algorithm, the final all-one square matrix is ​​marked with a blue box. The arc segment numbers corresponding to the first all-one square matrix are 2, 3, and 4, and the arc segment numbers corresponding to the second all-one square matrix are 4 and 5. Therefore, the conflict group of this telemetry and control station contains two conflict arc segment sets: a 3-satellite conflict set {2, 3, 4} and a 2-satellite conflict set {4, 5}. The conflict group can be represented as {{2, 3, 4}, {4, 5}}.

[0061] Similarly, a satellite redundancy group is constructed.

[0062] S5, Determine the objective optimization function; The objective function is F = k1f1+k2f2+k3f3+k4f4+k5G, where k1, k2, k3, k4, and k5 have the same weight, which is 1 / 5.

[0063] S6, Search for the optimal combination of visible arc segments that optimizes the objective function; The combination of visible arc segments corresponding to the maximum fitness value is selected as the optimal solution; the combination of arc segments corresponding to a fitness value less than 1 is an infeasible solution. The combination of telemetry and control stations corresponding to this optimal solution is the optimal solution in a certain iteration of the outer genetic algorithm. The outer GA iteration ends after a given number of iterations, obtaining the combination of telemetry and control stations corresponding to the optimal fitness value, which is the optimal station combination.

[0064] S7, inner layer genetic algorithm calculates individual fitness; repeat the inner layer optimization process of the above site combination until the outer layer genetic algorithm iteration ends, and output the site combination with the best evaluation value as the final telemetry and control station deployment scheme.

[0065] This iterative process ensures that the outer algorithm evolves progressively and selects high-performance station combinations. For each candidate scheme in each generation of the population, its performance is precisely evaluated through inner-layer optimization. Through repeated iterations, the algorithm ultimately outputs the station combination with the highest evaluation value found throughout the search process. This combination represents the optimal telemetry and control station deployment scheme that achieves the longest total tracking time, the most redundant relay opportunities, the most tracking arcs, and the most satellites while satisfying all constraints. Those skilled in the art, based on the above description, can clearly understand the algorithm's loop mechanism, termination conditions, and output rules, and can implement this invention accordingly.

[0066] This invention transforms the station deployment problem into a permutation and combination problem of selecting stations by generating candidate stations at grid points in a discrete deployment area. A nested genetic algorithm is applied to complete the specific selection of stations. By constructing a conflict and redundancy matrix of arc segments, conflict groups and redundancy groups are generated, which can intuitively describe "multi-satellite conflict," "multi-station redundancy," and "multi-station relay." The conflict groups, redundancy groups, matrix order reduction, and normalized single-objective fitness function simplify the calculation of the objective function. Based on this invention, domain-specific objective functions can be designed to construct station deployment methods adapted to different needs.

[0067] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for deploying telemetry and control stations based on a two-level programming model, characterized in that, The method includes: Based on the preset deployment area and satellite elevation angle threshold, multiple alternative telemetry and control stations are generated discretized within the deployment area; Based on the ephemeris data of the target satellite, the visible time window between each of the candidate telemetry and control stations and the target satellite is calculated, and a set of visible arc segments is generated; Based on the genetic algorithm, M telemetry and control stations are iteratively selected from the candidate telemetry and control stations as a station combination, where M is the preset number of stations; For each of the aforementioned site combinations, the following inner-layer optimization process is performed: Select a subset of visible arc segments generated by all telemetry and control stations in the site combination from the set of visible arc segments; Construct a conflict matrix and a redundancy matrix for the subset of visible arc segments; the conflict matrix is ​​used to identify the temporal conflict relationship between different visible arc segments of the same tracking and control station; the redundancy matrix is ​​used to identify the temporal redundancy relationship between visible arc segments of different tracking and control stations for the same satellite. Based on the conflict matrix and redundancy matrix, a fitness function is constructed to evaluate the subset of visible arc segments; the fitness function includes at least a penalty term for conflict and a reward term for redundancy. Based on the genetic algorithm, a scheduling scheme for the arc segment that optimizes the fitness function is searched in the subset of visible arc segments; The optimal fitness value obtained is used as the evaluation value of the current site combination; Repeat the inner optimization process of the above site combination until the outer genetic algorithm iteration ends, and output the site combination with the best evaluation value as the final telemetry and control station deployment scheme; in, If two visible arc segments satisfy the following conditions: they correspond to the same telemetry and control station, they correspond to different satellites, and their time windows overlap, then they are marked as conflict in the conflict matrix. If two visible arc segments satisfy the following conditions: they correspond to the same satellite, they correspond to different telemetry and control stations, and their time windows overlap, then they are marked as redundant in the redundancy matrix. The fitness function F is expressed as: F = k1f1+k2f2+k3f3+k4f4+k5G, where f1 is the total duration of the selected arc segment; f2 is the number of redundant arc segments; f3 is the number of selected arc segments; f4 is the number of non-repeating satellites in the selected arc segment; G is the penalty function for arc segment conflicts; k1 to k5 are weight coefficients, and the sum of the weight values ​​k1, k2, k3, k4, and k5 is 1; The conflict matrix and redundancy matrix are reduced in order: if the row and column corresponding to a certain visible arc segment in the conflict matrix and redundancy matrix are both zero, then the visible arc segment is removed from the current optimization process.

2. The telemetry and control station deployment method based on a two-layer planning model according to claim 1, characterized in that: Calculate the surface coverage radius of a single site based on the satellite's minimum operating elevation angle and orbital altitude; Based on the coverage radius, a regular hexagonal seamless coverage model is used to perform discretization positioning of the stations within the station deployment area.

3. The telemetry and control station deployment method based on a two-layer planning model according to claim 2, characterized in that: Calculate the visible surface coverage circle and its radius of the satellite at a given altitude for the calculated station. ； In the formula The angle is the geocentric angle between the satellite's nadir point B and the observation point P, where r is the satellite's radial distance and its value is the Earth's radius R. e Satellite altitude H, E is the satellite elevation angle, and the geocentric angle is the angle between the satellite and the Earth's center. The radius of the visible coverage circle of the satellite is twice the maximum observable arc of the satellite. The radius of the visible coverage circle of the Earth's surface corresponding to the station is... .

4. The telemetry and control station deployment method based on a two-layer programming model according to claim 3, characterized in that: The angular distance between any two stations is set to The corresponding surface distance is The area of ​​the overlapping zone of the land cover between adjacent sites accounts for 6%, and each site has 6 adjacent sites.

5. A telemetry and control station deployment system based on a two-layer programming model, characterized in that: include: One or more processors; A computer-readable storage medium coupled to the processor, having program instructions stored thereon; The program instructions can be executed by the processor to cause the system to perform the method as described in any one of claims 1-4.

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