A method and system for optimizing the configuration of a space target monitoring constellation considering complex constraints

Abstract

This invention discloses a method and system for optimizing the configuration of a space target monitoring constellation considering complex constraints, belonging to the field of aerospace mission design and optimization technology. The method first constructs a discrete orbital mode library containing conditions satisfying the regressive orbital dynamic resonance condition; based on this library, it constructs a generalized hybrid design variable consisting of integer indices and real-number fine-tuning quantities; it establishes an optimization model with space volume coverage, maximum revisit time, and system construction cost as objectives, and illumination, dynamics, and maneuverability as constraints; it uses rapid orbital geometry analysis to coarsely screen invalid links; and finally, it uses an improved non-dominated sorting genetic algorithm for global optimization to obtain the Pareto optimal constellation configuration set. This invention achieves accurate evaluation of the coverage effectiveness of three-dimensional space targets, ensures the physical feasibility and long-term stability of the configuration scheme, and efficiently solves high-dimensional multi-objective optimization problems.

Description

Technical Field

[0001] This invention relates to the field of aerospace mission design and optimization technology, and in particular to a method and system for optimizing the configuration of a space target monitoring constellation that takes into account complex constraints. Background Technology

[0002] With the rapid development of aerospace technology and the increasing frequency of human space activities, the number of space debris and malfunctioning satellites is growing exponentially, posing a serious threat to high-value spacecraft in orbit. Establishing an all-weather, all-day, high-precision space target monitoring system to achieve continuous detection, precise orbit determination, and collision warning of space targets has become a core requirement for ensuring aerospace safety.

[0003] Traditional space target monitoring methods primarily rely on ground-based radar and ground-based optical telescopes. However, ground-based observations are not only limited by the Earth's curvature, resulting in limited coverage, but are also inevitably constrained by atmospheric turbulence, day-night cycles, and weather conditions, making continuous tracking of space targets difficult and limiting their ability to detect small, faint targets in high orbits. To overcome the limitations of ground-based methods, space-based space target monitoring has become a current research hotspot due to its advantages such as being unaffected by the atmosphere, flexible observation geometry, minimal background radiation interference, and closer proximity to the target. In space-based monitoring systems, the configuration design of the satellite constellation directly determines the system's space coverage capability, target revisit cycle, and overall performance.

[0004] Although some progress has been made in the research of space-based monitoring constellations, existing technologies still have the following major shortcomings in terms of configuration optimization design:

[0005] First, the dimensionality mismatch in observation models makes it difficult to accurately reflect the detection effectiveness of space targets. Existing constellation design methods largely follow the design theories of traditional Earth remote sensing or communication constellations, and their evaluation metrics are usually based on "two-dimensional spherical coverage," that is, using ground grid points to statistically determine coverage rate or revisit time. However, space target monitoring differs fundamentally from Earth observation: Earth observation focuses on static or low-speed targets on a two-dimensional sphere, while space target monitoring must deal with high-speed, non-cooperative targets moving in a three-dimensional spherical shell. Simply applying the two-dimensional grid point method of Earth observation is not only computationally inefficient but also ignores the three-dimensional distribution characteristics of space targets at different orbital altitudes. It cannot accurately describe the constellation's "volume coverage" capability for faint, fragmented targets in three-dimensional space, leading to uneven resource allocation and easily creating monitoring blind spots in key orbital regions.

[0006] Second, insufficient consideration of optical imaging constraints leads to significant discrepancies between system performance assessments and actual results. Space-based optical sensors are mostly passive imaging devices, heavily reliant on the target's reflection characteristics of sunlight. Existing optimization models largely calculate based solely on the visibility of the geometric line of sight, simplifying or ignoring key physical constraints such as the solar phase angle, solar repulsion angle, and atmospheric obstruction. In reality, target visibility varies drastically with the phase angle; even if the geometric line of sight passes through, if the target is in shadow or the phase angle is too large resulting in a faint magnitude, the sensor cannot effectively detect it. The simplified handling of these complex illumination coupling constraints in existing technologies leads to inflated theoretical coverage of the designed constellations, resulting in poor engineering practicality.

[0007] Third, the configuration is too simple and the optimization algorithm is inefficient, making it difficult to meet the needs of multiple tasks. The configuration optimization of a space target monitoring constellation is a typical high-dimensional, nonlinear, multi-objective coupled optimization problem. On the one hand, existing designs are mostly limited to a single configuration. When facing complex tasks such as comprehensive surveys and key regional tracking, a single configuration is difficult to maximize performance by combining high and low inclination angles. On the other hand, in the optimization process involving multiple design variables such as orbital altitude, inclination angle, right ascension of the ascending node, and phase factor, traditional analytical methods are difficult to handle complex perturbation environments. Conventional intelligent algorithms, when facing such large-scale parameter optimization, suffer from slow convergence speed and are prone to getting trapped in local optima, making it difficult to find the best balance between detection coverage, system response speed, and construction cost.

[0008] In summary, existing space target monitoring constellation design methods have significant shortcomings in terms of coverage models, physical constraint coupling, and optimization algorithm efficiency. There is an urgent need for a constellation configuration optimization method and system that can break through the traditional two-dimensional Earth coverage thinking, fully couple the three-dimensional spatial target distribution characteristics, complex optical imaging constraints and orbital dynamics conditions, and have efficient global optimization capabilities. Summary of the Invention

[0009] To achieve the above objectives, this invention provides a method for optimizing the configuration of a space target monitoring constellation considering complex constraints, comprising the following steps:

[0010] Construct a discrete orbital mode library containing orbital parameters that satisfy the regressive orbital dynamic resonance condition.

[0011] Based on the discrete track mode library, a generalized hybrid design variable is constructed, consisting of integer indices pointing to specific track conditions in the discrete track mode library and real-number fine-tuning quantities for local adjustments.

[0012] Construct a multi-dimensional performance evaluation index system that includes spatial volume coverage, maximum revisit time, and system construction cost, as well as a complex physical constraint system that includes illumination and imaging constraints, return orbit dynamics stability constraints, and tactical maneuverability constraints.

[0013] Based on orbital geometry, the constellation configurations corresponding to the generalized hybrid design variables are rapidly analyzed and coarsely screened to eliminate invalid observation links.

[0014] Using the multidimensional performance evaluation index system as the optimization objective, and under the condition of satisfying the complex physical constraints, an improved non-dominated sorting genetic algorithm is used to globally optimize the generalized mixed design variables to obtain the Pareto optimal solution set as the constellation configuration design scheme.

[0015] Preferably, the construction of the discrete orbital mode library containing orbital parameters that satisfy the regression orbital dynamic resonance condition specifically includes:

[0016] Establish second-order zone harmonic coefficients considering Earth's non-spherical perturbations The satellite orbital dynamics model of the project is used to calculate the average orbital angular velocity. and the long-term precession of the right ascension of the ascending node :

[0017]

[0018]

[0019] in, The gravitational constant of Earth, For the semi-major axis of the track, For eccentricity, For the track inclination angle, This is the radius of the Earth's equator.

[0020] Solving for the dynamic resonance condition of the regressive orbit requires satisfying a specific proportional relationship between the satellite's orbital period and the Earth's rotation period:

[0021]

[0022] in, For satellites in Total number of laps within a day The number of days in the regression period. The rate of change of the angle of approach. This is the Earth's rotational angular velocity.

[0023] Generate a hierarchical discrete orbital mode library, including:

[0024] For the all-day, all-area census task, a solar-synchronous orbit mode library is constructed that simultaneously satisfies the solar synchronization condition and the aforementioned regressive orbit dynamic resonance condition. The solar synchronization condition requires the right ascension precession rate of the ascending node. .

[0025] For high-frequency revisit missions in mid- and low-latitude regions, a low-inclination near-Earth circular orbit mode library that satisfies the dynamic resonance condition of the revisit orbit is constructed within a set orbit inclination range.

[0026] To support the stationing and patrol missions of high-value targets in the geosynchronous orbit zone, a high-orbit layer mode library containing nominal parameters of near-geosynchronous orbit or inclined geosynchronous orbit will be constructed.

[0027] Assign a unique integer index to each set of orbital parameters in the discrete orbital mode library. .

[0028] Preferably, the construction of a generalized hybrid design variable based on the discrete orbit mode library, consisting of integer indices pointing to specific orbit conditions in the discrete orbit mode library and real-number fine-tuning quantities for local adjustments, specifically involves:

[0029] Define decision variables ,in This represents the number of sub-constellations in a mixed constellation.

[0030] For the Individual zodiac signs, their decision variables Defined as: .

[0031] in, The integer index selected from the discrete orbital mode library represents a selected set of basic orbital parameters; An integer representing the number of orbital surfaces; An integer representing the number of satellites on each orbital plane; In the interval A continuous real-valued phase factor is used to adjust the relative phase relationship between satellites on adjacent orbital planes.

[0032] Preferably, in the multi-dimensional performance evaluation index system, the spatial volume coverage rate The calculation formula is:

[0033]

[0034] in, For the statistical period, The number of slices to divide the target monitoring space radially. For the first Weighting factor of layer slices, In order to simulate time No. The net coverage area after Boolean union operation of the effective fields of view of all satellites on the slice. The total volume of the target monitoring space.

[0035] Preferably, the spatial volume coverage is calculated using a slicing method and polygon clipping technology, specifically including the following sub-steps:

[0036] The target monitoring space is divided uniformly or non-uniformly along the radial direction of the Earth's core. A thin layer was obtained. A two-dimensional slice.

[0037] For each simulation time point and each slice The sensor field of view of each satellite in the constellation is calculated in the slice. A two-dimensional projected polygon on the plane.

[0038] Using polygon clipping algorithms from computer graphics, at the same time... slices of the same layer Perform a Boolean union operation on the two-dimensional projected polygons of all satellites to obtain the net coverage polygon on the slice at that moment.

[0039] Calculate the area of ​​the net covered polygon, denoted as . .

[0040] For all simulation moments to and all slice layers to According to the spatial volume coverage The calculation formula is used to perform integration and summation to obtain the final spatial volume coverage.

[0041] Preferably, in the multidimensional performance evaluation index system, the maximum revisit time The calculation formula is:

[0042]

[0043] in, This refers to all discrete slice units of the target monitoring space or a pre-defined set of key monitoring areas. For unit The maximum time interval between two consecutive valid observations within a statistical period.

[0044] The system construction cost The calculation formula is:

[0045]

[0046] in, For integer index The weighting coefficients for single-satellite development costs are determined by the corresponding orbital altitude and satellite platform type. To make the first The total launch cost required to deploy each sub-constellation into orbit.

[0047] Preferably, the rapid analytical coarse screening of the constellation configuration corresponding to the generalized hybrid design variables based on orbital geometry, eliminating invalid observation links, specifically involves:

[0048] Based on the satellite orbital elements decoded from the generalized hybrid design variables, the relative geometric relationship between the mission satellite and the target space unit on the orbital plane is calculated.

[0049] Based on the relative geometry of the orbital plane, the rendezvous distance of the possible observation links between the mission satellite and the target space unit at the closest distance is quickly calculated, as well as the theoretical maximum dwell time of the possible observation links.

[0050] Observation links whose rendezvous distance is greater than the preset maximum effective detection distance are marked as invalid, and / or observation links whose theoretical maximum dwell time is less than the preset minimum effective imaging time are marked as invalid.

[0051] Preferably, the improved non-dominated sorting genetic algorithm is used to globally optimize the generalized mixed design variables. The improved non-dominated sorting genetic algorithm introduces an adaptive crossover operator, which dynamically adjusts the crossover probability based on the relationship between individual fitness and the average fitness of the population. The specific adjustment strategy is as follows:

[0052] Let the maximum fitness in the population be... The average fitness is The greater fitness of the two parent individuals to be crossovered is The algorithm presets the initial crossover probability as follows: Then adaptive crossover probability Calculate using the following formula:

[0053]

[0054] Preferably, the step of using an improved non-dominated sorting genetic algorithm to globally optimize the generalized mixed design variables further includes implementing a truncation strategy for on-demand computation, specifically:

[0055] After performing non-dominated sorting in each generation of evolution, the individuals in the population are divided into multiple non-dominated levels.

[0056] The parent and offspring populations are merged, and individuals are added to the new population layer by layer, starting from the first non-dominant level.

[0057] Adding all individuals from a non-dominant hierarchy will cause the total number of individuals in the new population to exceed the preset population size limit. Only then is the crowding distance of all individuals within that level calculated.

[0058] Individuals within this level are sorted according to the crowding distance, and individuals are selected in sequence to be added to the new population until the new population size reaches a certain level. .

[0059] Preferably, the step of using an improved non-dominated sorting genetic algorithm to globally optimize the generalized hybrid design variables further includes a differential evolution operation for the hybrid encoding:

[0060] For decision variables Integer index in It employs a discrete uniform crossover operator, which directly swaps the parent individuals of two individuals with a preset probability. Value, and for Perform a mutation operation, which includes randomly reselecting an index in the discrete orbital mode library, or selecting another index within the neighborhood of the orbital parameters corresponding to the current index.

[0061] For decision variables Integer variables in and Mutation is performed using an integer polynomial mutation operator to ensure that the mutated product... and It remains an integer and satisfies the preset size constraints. .

[0062] For decision variables continuous real variables It employs simulated binary crossover operators and polynomial mutation operators for operation.

[0063] Accordingly, embodiments of the present invention also provide a space target monitoring constellation configuration optimization system considering complex constraints, used to implement the method described in any one of the embodiments of the present invention, including:

[0064] The basic database and variable construction module is used to store and manage a discrete orbital mode library containing orbital parameters that satisfy the regression orbital dynamic resonance condition, and to call data from the discrete orbital mode library according to the task constraints input by the user to construct a generalized hybrid design variable population containing integer indices and real number fine-tuning quantities.

[0065] A two-tiered performance evaluation calculation module is used to accurately calculate the multi-dimensional performance indicators of constellation configuration schemes. The two-tiered performance evaluation calculation module includes an analytical coarse screening unit and a slice fine calculation unit. The analytical coarse screening unit quickly solves and eliminates invalid observation links based on orbital geometry. The slice fine calculation unit uses the slicing method and polygon clipping technology to perform volume fine calculation on the effective observation links and outputs the spatial volume coverage, maximum revisit time and system construction cost.

[0066] The intelligent evolutionary optimization module, built upon an improved non-dominated sorting genetic algorithm framework, drives the iterative evolution of the generalized hybrid design variable population. The module incorporates an adaptive evolutionary engine and a constraint loader. The adaptive evolutionary engine dynamically adjusts genetic operation parameters based on the population fitness distribution. The constraint loader automatically applies illumination and imaging constraints, regression trajectory dynamics stability constraints, and tactical maneuverability constraints during the evolutionary process, and eliminates solutions that do not meet these constraints.

[0067] The decision support and visualization module is used to receive the Pareto optimal solution set output by the intelligent evolution optimization module and perform visualization display and scheme analysis. The visualization display includes drawing a three-dimensional Pareto front surface, dynamic deduction of three-dimensional constellation configuration, and generation of heat map of coverage blind zone.

[0068] The basic database and variable construction module, the two-level performance evaluation and calculation module, the intelligent evolution optimization module, and the decision support and visualization module are connected and work together through a data bus.

[0069] The beneficial effects of this invention are:

[0070] 1. Existing constellation optimization methods mostly rely on two-dimensional grid point coverage models from Earth observation, which cannot accurately assess the detection capability of high-speed moving targets distributed in a three-dimensional spherical shell space, easily leading to monitoring blind spots. This invention constructs a two-level evaluation model combining "analytical geometric coarse screening" and "slice polygon trimming volume precise calculation," and for the first time uses "spatial volume coverage" as the core optimization index. This method first slices the target space radially, then uses computer graphics technology to perform Boolean union operations on the multi-star field of view on each slice, and finally calculates the net coverage volume accurately through integration. This fundamentally changes the evaluation dimension, enabling optimization design to directly target the three-dimensional distribution characteristics of non-cooperative targets such as space debris, thereby significantly improving the constellation's true detection probability and cataloging completeness for faint, small-sized space targets, and solving the problem of a serious disconnect between the evaluation results and actual performance of traditional methods.

[0071] 2. Existing technologies optimize in a continuous parameter space, which easily produces "pseudo-optimal solutions" with high theoretical performance but inconsistent with orbital dynamics (such as failing to meet regression conditions or rapidly diverging under perturbation). Engineering implementation requires significant fuel consumption to maintain the configuration, resulting in high costs. This invention pre-constructs a discrete orbital mode library containing parameters satisfying specific resonance conditions (such as sun-synchronous and regressive orbits) and converts optimization variables into combinations of integer indices to this library and local fine-tuning quantities. The search space is strictly limited to the range of "physical feasibility" and "mission applicability," ensuring that each constellation configuration found by the algorithm possesses inherent long-term orbital stability and mission compliance. Therefore, the design results can maintain performance without relying on complex active control, greatly reducing the fuel load of the satellite platform and on-orbit maintenance costs, thus achieving a balance between engineering implementation and economic efficiency for high-performance constellations.

[0072] 3. Optimization of space target monitoring constellations involves a mixture of discrete variables (orbit type, number of satellites) and continuous variables (phase), target conflicts (coverage, revisit, cost), and complex constraints (illuminance, dynamics, safety). Traditional optimization algorithms are prone to getting trapped in local optima or experiencing slow convergence. This invention designs an "integer-real number" differentiated encoding and evolutionary strategy for the mixed variables and improves the NSGA-II algorithm by introducing an adaptive crossover operator and an on-demand truncation strategy. The adaptive operator can dynamically balance global exploration and local development based on the population state; the on-demand truncation strategy significantly reduces unnecessary computational overhead. This enables the algorithm to efficiently and robustly perform global optimization in a vast solution space, quickly converging to a well-distributed Pareto optimal front. This provides users with a series of candidate solutions that achieve optimal trade-offs in multiple key dimensions such as coverage, response speed, and construction cost, providing a solid foundation for scientific decision-making. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in this invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0074] Figure 1 This is a flowchart of the steps of the method of the present invention.

[0075] Figure 2 A technical flowchart for optimizing the configuration of a space target monitoring constellation considering complex constraints. Detailed Implementation

[0076] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0077] Please see Figures 1-2 This invention provides a method for optimizing the configuration of a space target monitoring constellation considering complex constraints. First, a discrete orbital mode library is constructed, which pre-stores multiple sets of orbital parameters that satisfy the regression orbital dynamic resonance condition, ensuring the stability of the orbits during long-term operation. Second, based on this mode library, a generalized hybrid design variable is defined. This variable consists of an integer index pointing to a specific orbital parameter in the library and a real-valued fine-tuning amount for fine adjustment.

[0078] Subsequently, a multi-dimensional performance evaluation index system was established, specifically including three optimization objectives: space volume coverage, maximum revisit time, and system construction cost. A complex physical constraint system was also constructed, encompassing illumination imaging, dynamic stability, and maneuverability constraints. Next, rapid analytical calculations were performed based on the orbital geometry between the satellite and the target to initially screen and eliminate invalid observation links.

[0079] Then, for the selected effective links, the spatial volume coverage of the system is accurately calculated by slicing the three-dimensional space and combining it with polygon Boolean union operations from computer graphics. Finally, with the performance index as the objective, and under the premise of satisfying all constraints, an improved non-dominated sorting genetic algorithm is used to perform a global search and optimization of the mixed design variables, outputting a set of Pareto optimal solutions as the final constellation configuration design scheme. This method, by integrating a discretized modality library and mixed variable encoding, constrains the search space within the engineering feasible range, and simultaneously solves the three core problems of configuration feasibility, coverage evaluation accuracy, and optimization solution efficiency by utilizing an accurate three-dimensional volume evaluation model and an efficient multi-objective optimization algorithm.

[0080] In one possible implementation, firstly, a satellite orbital dynamics model is established, which focuses on the second-order zonal harmonic coefficients that have the greatest impact on the perturbation of Earth's non-spherical gravitational force, and is used to calculate the long-term variation of the orbital elements. Secondly, the regression orbital resonance condition is solved. This condition is a mathematical relationship that describes a specific integer proportional relationship that must be satisfied between the satellite's orbital period and the Earth's rotation period to ensure the periodic repetition of the satellite's nadir trajectory.

[0081] Based on this, three hierarchical sub-modal libraries are generated: the first is a sun-synchronous orbit modal library, where orbital parameters simultaneously satisfy the sun-synchronous condition and the aforementioned regression resonance condition, suitable for global surveys; the second is a low-inclination near-Earth circular orbit modal library, where orbits satisfy the regression condition within a set inclination range, suitable for revisiting mid- and low-latitude regions; and the third is a high-orbit modal library, containing nominal parameters of geosynchronous orbits and their variants, suitable for high-orbit target surveillance. All calculated orbital parameter sets are stored and assigned unique integer indices. This implementation transforms the continuous infinite search space of the optimization problem into a finite, engineering-compliant selection problem by pre-calculating and discretizing the storage of physically feasible orbital "genes," fundamentally eliminating the possibility of generating dynamically unstable or mission-mismatched configurations, and ensuring the direct implementability of the optimization results.

[0082] In one possible implementation, the generalized hybrid design variable is a vector used to describe a hybrid constellation configuration that may contain multiple sub-constellations. For each sub-constellation, a quadruple is used to represent it: the first element is an integer index that directly points to a specific orbital parameter record in the discrete orbital mode library, thus determining the basic orbital type and altitude of the sub-constellation; the second element is an integer representing the number of orbital planes; the third element is an integer representing the number of satellites in each orbital plane; and the fourth element is a continuous real number ranging from zero to the number of orbital planes minus one, called the phase factor, used to precisely adjust the relative positions of satellites in different orbital planes.

[0083] The decision variables for the entire constellation are vectors composed of the quadruples corresponding to all sub-constellations arranged sequentially. This hybrid encoding method of "integer index selection framework + real number fine-tuning of local parameters" cleverly integrates discrete configuration selection with continuous phase optimization, enabling the optimization algorithm to perform efficient searches at both the macro-configuration layout and micro-phase adjustment levels. It is a key technical means to handle this type of heterogeneous hybrid constellation design problem.

[0084] In one possible implementation, the spatial volume coverage is calculated using a slicing method and polygon clipping techniques, with the specific steps as follows:

[0085] First, the three-dimensional spatial region to be monitored (such as a spherical shell space) is divided radially into multiple thin layers, each of which is regarded as a two-dimensional curved surface.

[0086] Secondly, within the set statistical period, for each discrete time point and each layer of two-dimensional surface, the sensor fields of view of all satellites in the constellation are projected onto the surface to form multiple two-dimensional projection polygons; the polygon clipping library function is called to perform Boolean union operation on these polygons to automatically remove overlapping parts and calculate the net coverage area of ​​the layer at that time.

[0087] Finally, by iterating through all time points and all layers, the net coverage area is summed or weighted (different layers can be assigned different weights according to their importance), and then divided by the total volume of the target space to obtain the average spatial volume coverage. This method transforms the complex three-dimensional spatial coverage calculation into a series of geometric operations on a two-dimensional plane, significantly reducing computational complexity and time overhead while ensuring computational accuracy.

[0088] The maximum revisit time is defined as the maximum time interval between two consecutive observations by the constellation of all preset key monitoring units or discrete grid units in the target space within the entire statistical period. The system construction cost model is simplified to the sum of two parts: the first part is the development cost of all satellites, obtained by multiplying the number of satellites by a single-satellite cost coefficient determined by their orbital type; the second part is the launch and deployment cost, which is related to the number of orbital planes and orbital altitude. This indicator system comprehensively quantifies the constellation's coverage capability, response speed, and economic efficiency, providing a precise benchmark for multi-objective trade-offs.

[0089] In one possible implementation, this rapid screening step is performed before detailed performance simulations of each candidate constellation scheme are required. The principle is based on a rapid estimation of the orbital spatial geometry between the satellites and potential target points. For each satellite-target pair, the algorithm quickly calculates the shortest possible spatial distance between them during operation, i.e., the rendezvous distance. Simultaneously, it estimates the maximum duration for which the target may enter the satellite's sensor field of view, i.e., the dwell time.

[0090] Two preset thresholds are used: maximum effective detection distance and minimum effective imaging time. If the calculated rendezvous distance is greater than the maximum effective detection distance, it indicates that the target is consistently too far to be detected; if the estimated dwell time is less than the minimum effective imaging time, it indicates that even if the target is visible, effective image data cannot be obtained. Observation links that meet either of these conditions are immediately marked as invalid and ignored in subsequent precise calculations. This step utilizes simple geometric analytical operations to filter out most obviously invalid observation opportunities within milliseconds, avoiding sending these links into subsequent computationally intensive illumination judgment and precise coverage calculations, thereby improving the overall simulation evaluation efficiency by more than an order of magnitude.

[0091] In one possible implementation, the improved non-dominated sorting genetic algorithm introduces an adaptive crossover operator. During the algorithm's evolution, the crossover probability is not fixed but dynamically adjusted based on the fitness of the two parent individuals involved in the crossover operation. The specific rules are as follows: First, obtain the maximum and average fitness values ​​in the current population. When the fitness value of the better parent individual has reached or exceeded the maximum fitness value of the population, the crossover probability is set to zero, i.e., no crossover occurs, to absolutely protect the current optimal gene structure.

[0092] When the better fitness value is between the average fitness and the maximum fitness, the crossover probability decreases proportionally to the difference between it and the maximum fitness, providing gentle protection for better individuals. When the better fitness value is below the average fitness, a preset baseline crossover probability is used to encourage sufficient crossover exploration of individuals with average performance. This adaptive mechanism allows the algorithm to actively explore the global population in the early stages of evolution or when population diversity is insufficient, while shifting to refined local exploration when approaching the optimal solution region. This effectively balances the breadth and depth of the search, improving the ability and speed of convergence to the global Pareto front.

[0093] In one possible implementation, the improved non-dominated sorting genetic algorithm employs a truncation strategy based on on-demand computation. When each generation completes the selection operation to form a new population, the parent and offspring populations need to be merged, and selection is performed based on non-dominated sorting and crowding distance. Traditional methods require calculating crowding distance for all individuals, resulting in high computational costs. This strategy optimizes this by first performing a fast non-dominated sort on the merged population, dividing individuals into different levels of non-dominated layers. Then, starting from the optimal first layer, individuals from each layer are added to the new population layer by layer.

[0094] When processing a certain layer, if adding all individuals from that layer would cause the new population size to exceed a preset limit, then truncation is necessary. In this case, only individuals within that layer are calculated for their crowding distance within the target space. Crowding distance measures the local distribution density of an individual at its front edge; a larger distance indicates a sparser distribution around the individual. Subsequently, individuals in that layer are sorted from largest to smallest based on their crowding distance, prioritizing the retention of sparsely distributed individuals until the new population slots are filled. For layers already determined to be fully retained, there is no need to calculate their crowding distance. This strategy significantly reduces the number of time-consuming calculations for crowding distance, substantially improving the algorithm's efficiency in high-dimensional target spaces.

[0095] In one possible implementation, the improved non-dominated sorting genetic algorithm performs differentiated evolutionary operations on different components of the mixed design variables. For the integer index variable representing orbit type selection, a discrete uniform crossover operator is used, which directly swaps the index values ​​of two parent individuals with a certain probability, since the index itself has no continuous numerical meaning; the mutation operation includes random reselection within the entire modality library, or selecting a new index from the set of neighboring parameters of the orbit corresponding to the current index. For the integer variables representing the number of satellites and orbital planes, a specially designed integer polynomial mutation operator is used to ensure that the new value after mutation is still an integer and automatically satisfies the preset size constraints.

[0096] For continuous real-valued phase factors, standard analog binary crossover and polynomial mutation operators are used for fine-tuning. These genetic operators, "tailor-made" for different types of variables, respect their respective data characteristics and physical meanings. Operations on discrete variables ensure effective jumps between pre-defined feasible modes; operations on integer variables maintain integer feasibility of solutions; and operations on real-valued variables achieve smooth parameter optimization. The collaborative work of multiple operators enables the algorithm to efficiently handle mixed variable spaces, which is key to successfully solving such complex design problems.

[0097] Accordingly, embodiments of the present invention also provide a space target monitoring constellation configuration optimization system considering complex constraints, used to implement the method described in any one of the embodiments of the present invention, including:

[0098] The basic database and variable construction module is used to store and manage a discrete orbital mode library containing orbital parameters that satisfy the regression orbital dynamic resonance condition, and to call data from the discrete orbital mode library according to the task constraints input by the user to construct a generalized hybrid design variable population containing integer indices and real number fine-tuning quantities.

[0099] A two-tiered performance evaluation calculation module is used to accurately calculate the multi-dimensional performance indicators of constellation configuration schemes. The two-tiered performance evaluation calculation module includes an analytical coarse screening unit and a slice fine calculation unit. The analytical coarse screening unit quickly solves and eliminates invalid observation links based on orbital geometry. The slice fine calculation unit uses the slicing method and polygon clipping technology to perform volume fine calculation on the effective observation links and outputs the spatial volume coverage, maximum revisit time and system construction cost.

[0100] The intelligent evolutionary optimization module, built upon an improved non-dominated sorting genetic algorithm framework, drives the iterative evolution of the generalized hybrid design variable population. The module incorporates an adaptive evolutionary engine and a constraint loader. The adaptive evolutionary engine dynamically adjusts genetic operation parameters based on the population fitness distribution. The constraint loader automatically applies illumination and imaging constraints, regression trajectory dynamics stability constraints, and tactical maneuverability constraints during the evolutionary process, and eliminates solutions that do not meet these constraints.

[0101] The decision support and visualization module is used to receive the Pareto optimal solution set output by the intelligent evolution optimization module and perform visualization display and scheme analysis. The visualization display includes drawing a three-dimensional Pareto front surface, dynamic deduction of three-dimensional constellation configuration, and generation of heat map of coverage blind zone.

[0102] The basic database and variable construction module, the two-level performance evaluation and calculation module, the intelligent evolution optimization module, and the decision support and visualization module are connected and work together through a data bus.

[0103] Example

[0104] This embodiment addresses the urgent need for current space situational awareness by designing a space-based optical monitoring constellation to achieve continuous monitoring of space targets in Earth orbit. Specific tasks include: (1) conducting all-weather, comprehensive surveys and cataloging of space debris in low Earth orbit (LEO) at altitudes between 500 km and 1500 km; (2) providing high-frequency revisits for on-orbit spacecraft in specific regions (e.g., 30°N to 50°N, 70°E to 130°E) for collision warning and status monitoring; and (3) conducting close-range detailed surveys and patrols of high-value communication satellites and suspicious targets in geosynchronous orbit (GEO, approximately 35786 km altitude). This is a typical multi-target, multi-constraint, heterogeneous hybrid constellation design problem.

[0105] Step 1: Construct a discrete orbital mode library.

[0106] First, to address the problem that continuous optimization easily leads to dynamically infeasible solutions, a physically feasible discrete orbit mode library is established in advance.

[0107] Establish an orbital dynamics model, focusing on the most influential factors in the Earth's non-spherical gravitational perturbations. Item. In the model, the Earth's gravitational constant. Earth's equatorial radius Earth's second-order zone harmonic coefficient The average angular velocity of the satellite Precession of the right ascension of the ascending node Calculated using the following formula:

[0108]

[0109]

[0110] In this embodiment, all orbits are assumed to be near-circular orbits with an eccentricity of [missing information]. It is approximately 0.

[0111] Next, the regressor orbital dynamic resonance condition is calculated to ensure the periodicity of the constellation's Earth coverage. The regressor condition requires that the satellite's orbital period and the Earth's rotation period satisfy a specific proportional relationship:

[0112]

[0113] in, This is the Earth's rotational angular velocity. Approximately equal to . and These are coprime positive integers. This embodiment sets... The value ranges from 1 to 5 days. The approximate altitude is determined based on the target orbital height.

[0114] Based on the above model and conditions, the following three sub-modal libraries are generated:

[0115] Sun-Synchronous Orbit Modal Library (SSO Modal Library): Designed for all-day survey missions. Requires orbits to simultaneously meet sun-synchronous conditions. And regression conditions. For example, setting the regression period. Heavens, number of laps By combining the formulas for solar synchronous inclination and regression, the semi-major axis of the orbit can be calculated. (Corresponding altitude approximately 700km), Inclination Traversing different and Combined, a series of discrete SSO orbital parameters are generated.

[0116] Low-inclination near-Earth circular orbit mode library (LEO mode library): designed for high-frequency revisits in mid-to-low latitudes. Inclination angle can be set. exist to Between, with For each fixed interval. Selecting the regression period Okay, let's substitute the values ​​into the regression formula and solve for the corresponding semi-major axis. For example, when , , When, it can be solved (Altitude approximately 765km).

[0117] High Orbit Modality Library (GEO Modality Library): Targeted at the GEO zone. Directly selects the nominal parameters of standard geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO). For example, the semi-major axis of the GEO orbit. ,inclination ; IGSO orbital semi-major axis ,inclination At the same time, the concept of a "drift track" is introduced, which is achieved by fine-tuning the semi-major axis (e.g., This allows the satellite to drift slowly within the GEO zone, enabling scanning surveillance.

[0118] Finally, all the calculated orbital parameter sets (including) The nominal value is stored in the database, and a unique integer index is assigned to each set of parameters. .For example, The SSO orbit represents an altitude of 700km and an inclination of 98.2°. The LEO orbit represents an altitude of 765km and an inclination angle of 30°. Represents the standard GEO orbit.

[0119] Step 2: Establish a multi-objective hybrid optimization model.

[0120] Based on the modal library from step one, define the decision variables, objective, and constraints of the optimization problem.

[0121] Define decision variables This indicates that this embodiment considers a hybrid constellation containing three sub-constellations.

[0122] For the Each zodiac sign has the following variables: .in:

[0123] : Integer, select an index from the modality library in step one. For example, Select from the SSO modality library. Select from the LEO modal library. Select from the GEO modal library.

[0124] : Integer, number of orbital planes, range of values ​​is .

[0125] : Integer, the number of satellites per orbital plane, with a range of values ​​of 100. .

[0126] : Real number, phase factor, range of values ​​is .

[0127] The multidimensional performance evaluation index system includes three minimization objectives (for consistency, maximizing coverage is transformed into minimizing its negative value):

[0128] 1. Minimize negative spatial volume coverage ( ):

[0129]

[0130] In this embodiment, the statistical period (1 day). The target monitoring space is defined as: a spherical shell layer with an altitude ranging from 500 km to 35786 km. This shell is divided radially into equal parts. Layer. Weighting factor Based on historical debris density settings, the weight of the low Earth orbit (500-1500km) layer is 2.0, the weight of the mid-Earth orbit layer is 1.0, and the weight of the GEO (around 35786km altitude) layer is 1.5. Calculations will be performed in subsequent steps. Let be the volume of the entire spherical shell.

[0131] 2. Minimize the maximum revisit time ( ):

[0132]

[0133] In this embodiment, It consists of two parts: one is the discretized grid units (coarse-grained) of the entire three-dimensional space; the other is a grid for a key region (30-50 degrees north latitude, 70-130 degrees east longitude, and 500-1500 km altitude). Obtained through simulation statistics.

[0134] 3. Minimize system construction costs ( ):

[0135]

[0136] The cost model is simplified as follows: Based on the orbital altitude setting, the cost weight for LEO (<2000km) satellites is 1.0, and the cost weight for GEO satellites is 5.0. Simplified to ,in The semi-major axis of the track (km). The coefficient represents the higher the orbit and the more deployment surfaces, the higher the launch cost.

[0137] Complex physical constraint systems include:

[0138] Illumination and Imaging Constraints: Target visibility requires the following conditions to be met simultaneously: (a) the mission satellite's line of sight to the target is not obstructed by Earth; (b) the angle (phase angle) between the sun, target, and satellite is less than [value missing]. (c) The angle between the sun, satellite, and target (solar repulsion angle) is greater than 100°. To avoid direct sunlight on the sensor, which could cause stray light interference or damage to the device.

[0139] Regression orbit dynamics stability constraints: Through the selection of the mode library in step one, the stability of the orbit is implicitly guaranteed. Long-term stability of orbital parameters under perturbation.

[0140] Tactical maneuverability constraints: Assuming each satellite has limited orbital maneuverability, the total velocity increment... Budget is .

[0141] Space collision safety constraints: The minimum distance between any two satellites within the constellation during simulation must be greater than [missing information]. .

[0142] Step 3: Rapid analytical coarse screening based on orbital geometry.

[0143] Before detailed simulation, for any candidate constellation scheme (a specific set of...) This involves rapid screening. For each mission satellite and each potential target point (or target orbit), the orbital geometry between them is calculated within the simulation time window. The minimum distance (rendezvous distance) near the intersection of their orbital planes is quickly calculated. If this minimum distance is greater than the preset maximum effective detection range... (Assuming the optical sensor resolution requirements are met), this observation link is deemed invalid, and no further precise calculations are needed. Simultaneously, the target's dwell time within the sensor's field of view is estimated; if it is less than the shortest effective imaging time... This is also considered invalid. This step can eliminate more than 80% of invalid calculations.

[0144] Step 4: Volume calculation based on slice polygon clipping.

[0145] For the effective links that pass through the coarse sieve, perform precise three-dimensional volume coverage calculations.

[0146] 1. Slicing: Dividing the target space spherical shell (500-35786km) radially into... A concentric spherical shell with thin layers.

[0147] 2. Projection and Boolean operations: For each simulation time step and each slice The field of view of the optical sensors of all satellites in the constellation (assuming a conical shape with a semi-cone angle of ) is... The slice is projected onto the sphere containing the slice and approximated as a polygon on a two-dimensional map projection (such as Mercator projection). Using the Voronoi Diagram algorithm and clipping algorithm from computer graphics, the union of these polygons on the two-dimensional plane is calculated.

[0148] 3. Area Calculation and Integration: Calculate the area of ​​the union polygon. Traverse all time steps and all layers ,according to The formula is used to perform a weighted summation and averaging to obtain the average spatial volume coverage of the constellation scheme over a day. Simultaneously, the data for each spatial grid cell is recorded during the simulation. The maximum interval between two consecutive accesses of a accessed time series is called the access time series. ,all The maximum value in is .

[0149] Step 5: Implement global optimization using the improved NSGA-II algorithm.

[0150] An improved non-dominated sorting genetic algorithm (NSGA-II) is used to solve the above three-objective optimization problem, with a population size of [missing information]. Maximum number of generations .

[0151] Initialization and Mixed Encoding: 100 individuals are randomly generated. Each individual is a... For example, an individual might be encoded as: , , .in For a specific SSO orbital, , , .

[0152] Adaptive crossover operation: setting the initial crossover probability When selecting two parent individuals for crossover, first calculate their normalized fitness in the current population (based on non-dominated hierarchy and crowding). If the fitness of the two individuals is larger... Higher than the average fitness of the population Then reduce the crossover probability according to the formula. To protect excellent models; if Below Then maintain or use a higher To promote exploration.

[0153]

[0154] Differential mutation operation:

[0155] Integer index : based on probability Perform mutation. The mutation method is: using... The probability randomly jumps to another index within its modality library (such as the SSO library); The probability is used to find the nearest index that meets the regression conditions within the orbital height neighborhood (e.g., ±50km) corresponding to the current index.

[0156] For integers Integer polynomial mutation is used to ensure that the mutated value remains unchanged. and Inside, and satisfy Scale constraints.

[0157] For real numbers The method employs simulated binary crossover (SBX) and polynomial mutation.

[0158] On-demand computation truncation strategy and elite retention: In each generation, the parent and offspring generations (a total of 200 individuals) are merged. A fast non-dominated sort is performed. Starting from the first non-dominated rank (Rank 1), individuals are added to the new population tier by tier. When adding individuals to a certain rank (e.g., Rank 3), if adding all individuals from that rank would cause the new population to exceed 100, then only at that moment is the crowding distance calculated for all individuals within that rank, and individuals with larger crowding distances are prioritized for retention until all 100 slots are filled. Simultaneously, Rank 1 individuals (elites) from the previous generation are unconditionally retained to ensure that the optimal solution is not lost.

[0159] Iteration and Output: The process of selection, crossover, mutation, evaluation, sorting, and truncation is repeated for 200 generations. Finally, the algorithm converges and outputs approximately 20-30 optimal compromise solutions on the first non-dominated front (Pareto front).

[0160] Step Six: Decision Making and Configuration Generation.

[0161] The decision-maker selects a solution from the Pareto optimal solution set. For example, selecting an equilibrium solution results in the following decoded constellation configuration:

[0162] Sub-constellation 1 (SSO Census Layer): (700km sun-synchronous return orbit). , , There are a total of 12 satellites.

[0163] Sub-constellation 2 (LEO revisit layer): (765km, 30° inclination return orbit). , , There are a total of 12 satellites.

[0164] Sub-constellation 3 (GEO patrol layer): (GEO drift orbit, period slightly longer than 24 hours). , , There are two satellites in total, drifting relative to each other in the east-west direction within the GEO zone.

[0165] This hybrid constellation comprises 26 stars. Based on the precisely decoded orbital elements, a complete constellation deployment and operational plan can be generated.

[0166] To verify the effectiveness of the method of the present invention, the following two comparative simulation methods were used for comparison:

[0167] Comparative Example 1 (Traditional Two-Dimensional Grid Point Method): This method employs a traditional approach widely used in Earth observation constellation design. It divides the Earth's surface into grid points according to latitude and longitude (e.g., 1° × 1°), considering only satellite coverage of ground points. Evaluation metrics include the time-averaged coverage rate of ground points and the maximum revisit time. The optimization algorithm uses a standard genetic algorithm (SGA) to search within a continuous space of orbital altitude, inclination, and right ascension parameters of the ascending node. This method completely ignores the detection characteristics of three-dimensional targets in space and illumination constraints.

[0168] Comparative Example 2 (Simplified 3D Coverage Model + Standard NSGA-II): This method considers 3D space but uses a simplified coverage model: the space is divided into 3D grids (e.g., longitude, latitude, altitude), and only the geometric line of sight between the grid center point and the satellite is determined, ignoring Earth occlusion and illumination constraints. Performance metrics are the observed grid percentage and average revisit time. The standard NSGA-II algorithm is used for optimization, without adaptive crossover or on-demand truncation strategies.

[0169] Under the same computing resources (CPU time limited to 72 hours) and the same task background, the method of the present invention, Comparative Example 1, and Comparative Example 2 were optimized. The performance of the optimal compromise solutions obtained by the three methods (the solutions with the closest total cost on the Pareto front of each method) was compared, and the results are shown in the table below:

[0170]

[0171] Results analysis:

[0172] 1. Coverage Effectiveness: The two-dimensional model in Comparative Example 1 is completely incapable of evaluating and optimizing the actual coverage capability for space targets. While the simplified three-dimensional model in Comparative Example 2 can evaluate the coverage, its calculation of 68.5% coverage rate will be significantly lower in reality (many targets will be invisible) because it ignores key illumination constraints (phase angle). The method of this invention, through precise volume calculation and constraint coupling, achieves an 85.2% coverage rate that is closer to engineering reality, with a simulated detection probability of up to 94% for LEO debris, and ensures the observability of GEO targets under good illumination conditions (phase angle satisfaction rate of 89%).

[0173] 2. Response Time: The constellation designed by the method of this invention has the shortest maximum revisit time for key areas (1.3 hours), which is significantly better than the comparative methods. This is due to the heterogeneous hybrid configuration (LEO revisit layer) and the accurate maximum revisit time. The guidance.

[0174] 3. Optimization of Efficiency and Quality: The improved NSGA-II algorithm (adaptive crossover, on-demand truncation) used in this invention converges faster (120 generations) and finds a solution with superior performance. The introduction of the discrete orbital mode library ensures that all generated schemes have long-term dynamic stability, avoiding the common problem in the comparison methods of "theoretically optimal but not feasible in engineering".

[0175] 4. Computational efficiency: The invention’s unique “analytical coarse screening” step reduces the single scheme evaluation time from 320 seconds in Comparative Example 2 to 85 seconds while ensuring accuracy, making it possible to complete high-dimensional multi-objective optimization within a limited time.

[0176] In summary, this embodiment fully demonstrates the entire process of the method of the present invention, from problem definition, model establishment, algorithm implementation to result verification. Through specific parameter settings, calculation steps, and comparative experiments, it is fully demonstrated that the present invention has significant advantages in terms of coverage effectiveness accuracy, optimization result feasibility, and algorithm running efficiency when solving the problem of optimizing the configuration of space target monitoring constellations considering complex constraints. It can provide a scientific and reliable design solution for engineering practice.

[0177] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0178] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the configuration of a space target monitoring constellation considering complex constraints, characterized in that, Includes the following steps: Construct a discrete orbital mode library containing orbital parameters that satisfy the regression orbital dynamic resonance condition; Based on the discrete track mode library, a generalized hybrid design variable is constructed, consisting of an integer index pointing to a preset track condition in the discrete track mode library and a real-number fine-tuning amount for local adjustment. Construct a multi-dimensional performance evaluation index system that includes space volume coverage, maximum revisit time, and system construction cost, as well as a complex physical constraint system that includes illumination and imaging constraints, return orbit dynamics stability constraints, and tactical maneuverability constraints. Wherein, the spatial volume coverage The calculation formula is: ； in, For the statistical period, The number of slices to divide the target monitoring space radially. For the first Weighting factor of layer slices, In order to simulate time No. The net coverage area after Boolean union operation of the effective fields of view of all satellites on the slice. The total volume of the target monitoring space; Based on orbital geometry, the constellation configurations corresponding to the generalized hybrid design variables are rapidly analyzed and coarsely screened to eliminate invalid observation links; Using the multidimensional performance evaluation index system as the optimization objective, and under the condition of satisfying the complex physical constraints, an improved non-dominated sorting genetic algorithm is used to globally optimize the generalized mixed design variables to obtain the Pareto optimal solution set as the constellation configuration design scheme. The construction of the discrete orbital mode library, which includes orbital parameters satisfying the regression orbital dynamic resonance condition, specifically includes: Establish second-order zone harmonic coefficients considering Earth's non-spherical perturbations The satellite orbital dynamics model of the project is used to calculate the average orbital angular velocity. and the long-term precession of the right ascension of the ascending node : ； ； in, The gravitational constant of Earth, For the semi-major axis of the track, For eccentricity, For the track inclination angle, The radius of the Earth's equator; Solve for the dynamic resonance condition of the regression orbit, which must satisfy a preset proportional relationship between the satellite's orbital period and the Earth's rotation period: ； in, For satellites in Total number of laps within a day The number of days in the regression period. The rate of change of the angle of approach. This is the Earth's rotational angular velocity; Generate a hierarchical discrete orbital mode library, including: For the all-day, all-area census task, a solar-synchronous orbit mode library is constructed that simultaneously satisfies the solar synchronization condition and the aforementioned regressive orbit dynamic resonance condition. The solar synchronization condition requires the right ascension precession rate of the ascending node. ; For high-frequency revisit missions in mid- and low-latitude regions, a low-inclination near-Earth circular orbit mode library that satisfies the dynamic resonance condition of the revisit orbit is constructed within a set orbit inclination range. To construct a high-orbit layer mode library containing nominal parameters of near-geosynchronous orbit or inclined geosynchronous orbit for stationing and patrolling missions targeting high-value targets in the geosynchronous orbit zone; Assign a unique integer index to each set of orbital parameters in the discrete orbital mode library. .

2. The method for optimizing the configuration of a space target monitoring constellation considering complex constraints according to claim 1, characterized in that, The generalized hybrid design variable, based on the discrete orbit mode library, is constructed by consisting of integer indices pointing to preset orbit conditions in the discrete orbit mode library and real-number fine-tuning quantities for local adjustments. Specifically: Define decision variables ,in The number of sub-constellations in a mixed constellation; For the Individual zodiac signs, their decision variables Defined as: ; in, The integer index selected from the discrete orbital mode library represents a selected set of basic orbital parameters; An integer representing the number of orbital surfaces; An integer representing the number of satellites on each orbital plane; In the interval A continuous real-valued phase factor is used to adjust the relative phase relationship between satellites on adjacent orbital planes.

3. The method for optimizing the configuration of a space target monitoring constellation considering complex constraints according to claim 2, characterized in that, The spatial volume coverage The volume calculation is performed using the slicing method and polygon clipping technique, and includes the following sub-steps: The target monitoring space is divided uniformly or non-uniformly along the radial direction of the Earth's core. A thin layer was obtained. A two-dimensional slice; For each simulation time point and each slice The sensor field of view of each satellite in the constellation is calculated in the slice. A two-dimensional projected polygon on the plane; Using polygon clipping algorithms from computer graphics, at the same time... slices of the same layer Perform a Boolean union operation on the two-dimensional projected polygons of all satellites to obtain the net coverage polygon on the slice at that moment. Calculate the area of ​​the net covered polygon, denoted as . ; For all simulation moments to and all slice layers to According to the spatial volume coverage The calculation formula is used to perform integration and summation to obtain the final spatial volume coverage.

4. The method for optimizing the configuration of a space target monitoring constellation considering complex constraints according to claim 2, characterized in that, In the aforementioned multidimensional performance evaluation index system, the maximum revisit time The calculation formula is: ； in, This refers to all discrete slice units of the target monitoring space or a pre-defined set of key monitoring areas. For unit The maximum time interval between two consecutive valid observations within a statistical period; The system construction cost The calculation formula is: ； in, For integer index The weighting coefficients for single-satellite development costs are determined by the corresponding orbital altitude and satellite platform type. To make the first The total launch cost required to deploy each sub-constellation into orbit.

5. The method for optimizing the configuration of a space target monitoring constellation considering complex constraints according to claim 1, characterized in that, The rapid analytical coarse screening of the constellation configuration corresponding to the generalized hybrid design variables based on orbital geometry, eliminating invalid observation links, specifically involves: Based on the satellite orbital elements decoded from the generalized hybrid design variables, the relative geometric relationship between the mission satellite and the target space unit on the orbital plane is calculated. Based on the relative geometric relationship of the orbital plane, the rendezvous distance of the possible observation links between the mission satellite and the target space unit at the closest distance is quickly calculated, as well as the theoretical maximum dwell time of the possible observation links; Observation links whose rendezvous distance is greater than the preset maximum effective detection distance are marked as invalid, and / or observation links whose theoretical maximum dwell time is less than the preset minimum effective imaging time are marked as invalid.

6. The method for optimizing the configuration of a space target monitoring constellation considering complex constraints according to claim 2, characterized in that, The improved non-dominated sorting genetic algorithm is used to globally optimize the generalized mixed design variables. This improved algorithm incorporates an adaptive crossover operator, which dynamically adjusts the crossover probability based on the relationship between individual fitness and the average fitness of the population. The specific adjustment strategy is as follows: Let the maximum fitness in the population be... The average fitness is The greater fitness of the two parent individuals to be crossovered is The algorithm presets the initial crossover probability as follows: Then adaptive crossover probability Calculate using the following formula: 。 7. The method for optimizing the configuration of a space target monitoring constellation considering complex constraints according to claim 6, characterized in that, The improved non-dominated sorting genetic algorithm for global optimization of the generalized mixed design variables also includes a truncation strategy for on-demand computation, specifically: After performing non-dominated sorting in each generation of evolution, the individuals in the population are divided into multiple non-dominated levels; The parent population is merged with the offspring population, and individuals are added to the new population layer by layer, starting from the first non-dominant level. Adding all individuals from a non-dominant hierarchy will cause the total number of individuals in the new population to exceed the preset population size limit. Only then is the crowding distance of all individuals within that level calculated; Individuals within this level are sorted according to the crowding distance, and individuals are selected in sequence to be added to the new population until the new population size reaches a certain level. .

8. The method for optimizing the configuration of a space target monitoring constellation considering complex constraints according to claim 2, characterized in that, The improved non-dominated sorting genetic algorithm for global optimization of the generalized hybrid design variables also includes a differential evolution operation for the hybrid encoding: For decision variables Integer index in It employs a discrete uniform crossover operator, which directly swaps the parent individuals of two individuals with a preset probability. Value; and for Perform a mutation operation, which includes randomly reselecting an index in the discrete orbital mode library, or selecting another index in the neighborhood of the orbital parameters corresponding to the current index; For decision variables Integer variables in and Mutation is performed using an integer polynomial mutation operator to ensure that the mutated product... and It remains an integer and satisfies the preset size constraints. ; For decision variables continuous real variables It employs simulated binary crossover operators and polynomial mutation operators for operation.

9. A space target monitoring constellation configuration optimization system considering complex constraints, for implementing the method as described in any one of claims 1 to 8, characterized in that, include: The basic database and variable construction module is used to store and manage a discrete orbital mode library containing orbital parameters that satisfy the regression orbital dynamic resonance condition, and to call data from the discrete orbital mode library according to the task constraints input by the user to construct a generalized mixed design variable population containing integer indices and real number fine-tuning quantities. A two-level performance evaluation calculation module is used to accurately calculate the multi-dimensional performance indicators of constellation configuration schemes. The two-level performance evaluation calculation module includes an analytical coarse screening unit and a slice fine calculation unit. The analytical coarse screening unit quickly solves and eliminates invalid observation links based on orbital geometry. The slice calculation unit uses the slicing method and polygon clipping technology to perform volume calculation on the effective observation link, and outputs the spatial volume coverage, maximum revisit time and system construction cost. The intelligent evolutionary optimization module, built upon an improved non-dominated sorting genetic algorithm framework, drives the iterative evolution of the generalized hybrid design variable population. The module incorporates an adaptive evolutionary engine and a constraint loader. The adaptive evolutionary engine dynamically adjusts genetic operation parameters based on the population fitness distribution. The constraint loader automatically applies illumination and imaging constraints, regression trajectory dynamics stability constraints, and tactical maneuverability constraints during the evolutionary process, and eliminates solutions that do not meet these constraints. The decision support and visualization module is used to receive the Pareto optimal solution set output by the intelligent evolution optimization module and perform visualization display and scheme analysis. The visualization display includes drawing a three-dimensional Pareto front surface, dynamic deduction of three-dimensional constellation configuration, and generation of heat map of coverage blind zone. The basic database and variable construction module, the two-level performance evaluation and calculation module, the intelligent evolution optimization module, and the decision support and visualization module are connected and work together through a data bus.

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