A space object monitoring satellite constellation configuration optimization system and method

Abstract

The application discloses a space target monitoring satellite constellation configuration optimization system and method, and the system comprises the following modules: a constraint modeling and configuration module, which uniformly models detection constraints and observation constraints in a space target monitoring process and constructs an observable judgment model; a monitoring performance evaluation index module, which constructs multiple monitoring performance evaluation indexes; a multi-target parallel optimization module based on a determinant point process, which, based on a non-dominated sorting genetic algorithm, models the diversity of a non-dominated solution set by introducing a determinant point process, selects the individual quality and the diversity of the solution set by maximizing the determinant of a subset of a kernel matrix, and completes efficient screening by using a greedy approximation inference method; and a constellation configuration optimization solving module, which takes the monitoring performance evaluation indexes as optimization targets, constructs a multi-target optimization problem, calls the multi-target parallel optimization module based on the determinant point process to perform joint optimization, and obtains an optimal or approximately optimal constellation configuration scheme under multiple constraint conditions.

Description

Technical Field

[0001] This invention belongs to the field of aerospace, specifically relating to a system and method for optimizing the configuration of a space target surveillance satellite constellation. Background Technology

[0002] In recent years, with the rapid development of space activities, the number of spacecraft and space debris in orbit has been increasing, making the low Earth orbit (LEO) space environment increasingly complex and crowded, and the risk of collisions between space targets has continued to rise. Currently, the number of space debris with a diameter greater than 10 cm has reached tens of thousands, the number of debris with a scale of 1 cm to 10 cm has reached millions, and the number of tiny debris smaller than 1 cm has reached hundreds of millions, making the space environment safety situation increasingly severe. To ensure the safe operation of spacecraft in orbit, continuous, stable, and high-precision monitoring and tracking of LEO space targets is required. Therefore, LEO space target surveillance has become one of the important research directions in the field of space situational awareness. In practical mission requirements, space target surveillance not only requires the ability to detect targets but also to achieve accurate observation and real-time status updates, thus placing higher demands on performance such as coverage, revisit time, and effective observation duration. To meet these performance requirements, a constellation of LEO space target surveillance satellites is typically constructed to achieve high coverage, short revisit time, and long effective surveillance duration. However, low-Earth orbit (LEO) space target surveillance missions are constrained by various factors, including sensor performance, spatial geometry, illumination conditions, and target motion characteristics. As a result, the satellite constellation configuration and surveillance performance indicators exhibit a highly nonlinear and strongly coupled relationship, making the constellation configuration optimization problem characterized by multiple constraints, high dimensionality, and high complexity. Existing research typically constructs multiple surveillance performance indicators based on target distribution characteristics, combines them into a single objective function using a weighted approach, and then uses Monte Carlo methods or genetic algorithms to search for and optimize the constellation configuration. While the aforementioned methods can yield feasible constellation schemes to some extent, they still have significant shortcomings: Firstly, the modeling of detection and observation constraints is not systematic enough, lacking a unified and clear mathematical expression for key constraints such as Earth's shadow occlusion, relative angular velocity, and observation angle. This may lead to deviations between the optimization results and actual monitoring scenarios, and observation constraints are usually introduced in the form of fixed conditions, lacking a flexible configuration mechanism. Secondly, the fixed-weight single-objective weighting method relies on empirical settings, making it difficult to balance the relationships between multiple performance indicators. Furthermore, when conducting random or heuristic searches in a large-scale parameter space, the computational complexity is high, limiting optimization efficiency and making it difficult to meet the engineering practicality and real-time requirements of complex monitoring tasks. Therefore, there is an urgent need for a method and system that can uniformly model and flexibly configure the various detection and observation constraints involved in the monitoring of low-Earth orbit targets, and combine an efficient multi-objective optimization mechanism to achieve constellation configuration optimization. Summary of the Invention

[0003] To address the problems in existing space surveillance constellation design methods, such as unsystematic and inconsistent modeling and expression of detection and observation constraints, lack of multi-index coordination and flexible configuration mechanisms for surveillance performance evaluation, and low efficiency in constellation configuration optimization under complex constraints and multi-target coupling conditions, this invention aims to overcome the shortcomings of existing technologies and proposes a space target surveillance satellite constellation configuration optimization system and method.

[0004] In view of this, the present invention provides a space target surveillance satellite constellation configuration optimization system, comprising: The constraint modeling and configuration module is used to uniformly model the detection constraints and observation constraints in the process of space target monitoring, and configure various constraints according to mission requirements to build an observability determination model to determine the observability of space targets at a given time and within a time interval. The monitoring performance evaluation index module is used to build various monitoring performance evaluation indexes and supports the configuration and selection of monitoring performance evaluation indexes according to different task requirements. A multi-objective parallel optimization module based on determinant point processes is used to model the diversity of non-dominated solution sets based on non-dominated sorting genetic algorithms. It achieves joint optimization selection of individual quality and solution set diversity by maximizing the determinant of the kernel matrix subset, and uses a greedy approximate inference method to efficiently screen a fixed-size solution set. The constellation configuration optimization solution module is used to construct a multi-objective optimization problem of constellation configuration with monitoring performance evaluation index as the optimization objective. It calls the multi-objective parallel optimization module based on determinant point process to jointly optimize constellation orbital parameters and configuration schemes to obtain the optimal or near-optimal constellation configuration scheme that satisfies multiple constraints. As an improvement to the above system, the detection constraint and observation constraint are used to determine whether the spatial target meets the effective observation conditions at a given time, wherein; The detection constraints are used to describe the limitations of the sensor's own performance on the detectability of the target, including: sensor operating distance constraints, field of view constraints, and observable arc length constraints; The observation constraints are used to describe the impact of spatial geometric relationships, lighting conditions, and target motion characteristics on observation feasibility; including: Earth occlusion constraints, Earth shadow constraints, Sun and Moon exclusion angle constraints, relative angular velocity constraints, and observation angle constraints.

[0005] As an improvement to the above system, the construction process of the observable decision model includes: By defining an instantaneous constraint set and an instantaneous observability sequence, and by determining the continuous observable interval based on the observable arc length constraint, a complete observability determination model for the target within the monitoring time window is constructed.

[0006] As an improvement to the above system, the monitoring performance evaluation index module constructs various monitoring performance evaluation indices, including: Effective correlation coverage is used to measure the effective coverage capability of an observation constellation for space targets that can be used for target correlation and continuous tracking. The total constellation time utilization rate reflects the overall observation time investment and resource utilization level of the observed constellation within the simulated time; and The overall average revisit interval is used to reflect the level of the observation constellation's ability to conduct continuous and stable surveillance of space targets; Wherein, the effective association coverage Satisfy the following formula:

[0007] in, Represents the set of spatial targets Total quantity For the goal The number of observable arc segments, Indicate target The One observable arc segment Representing the target The The start time of the first observable arc segment and the first The end time of each observable arc segment Indicates the first The observable arc segment and the first The time interval between each observable arc segment As an indicator function, when the target The number of observable arc segments is no less than two, and there exists a first arc segment. The observable arc segment and the first The time interval between each observable arc segment is no greater than a given threshold. When the association condition is met, the indicator function is 1; otherwise, it is 0. The total time utilization rate of the constellation Satisfy the following formula:

[0008] in, To monitor the length of the time window, For the goal observable arc segment set One of the observable arc segments, This indicates the length of the arc segment; The total average revisit interval Satisfy the following formula:

[0009] in, This represents the set of targets with at least two observable arc segments. Number of spatial targets Representing the target The The start time of the first observable arc segment and the first The end time of each observable arc segment Indicates the first The observable arc segment and the first The time interval between observable arc segments.

[0010] As an improvement to the aforementioned system, the constellation configuration optimization solution module uses the monitoring performance evaluation index as the optimization objective to obtain a set of candidate optimization objectives for constellation configuration optimization. for:

[0011] in, Represents the constellation configuration parameter vector. , and These correspond to the effective association coverage rate, total constellation time utilization rate, and total average revisit interval, respectively. From the target set Select at least two objectives to construct a constellation configuration multi-objective optimization problem, satisfying the following equation:

[0012] in, This represents the set of functions whose optimization objective is to maximize. Let represent the set of functions whose optimization objective is to minimize. and These represent the number of elements in each of the two sets.

[0013] As an improvement to the above system, the processing procedure of the constellation configuration optimization solution module includes: Acquire orbital data of the space target to be monitored, the orbital data including at least orbital altitude, inclination, and right ascension of the ascending node; filter the target orbital altitudes according to the mission scenario requirements to construct a target set within a specified altitude range; Taking into account the distribution of space targets at orbital altitude, inclination, and right ascension of the ascending node, the target set is subjected to distribution-preserving sampling to ensure the representativeness of the distribution; The constellation configuration scheme is represented as a set of adjustable constellation configuration parameter vectors that describe the orbital layout and structural form of the constellation. ,in, These are the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and angle of apogee. For the number of orbital surfaces, The number of satellites in each orbital plane, Phase factor ; and Together they determine the size of the constellation and satisfy , Total number of satellites; Based on the multi-objective optimization problem of constellation configuration, a multi-objective parallel optimization module based on determinant point process is invoked to jointly optimize the constellation orbital parameters and configuration schemes, so as to obtain the optimal or near-optimal constellation configuration schemes that satisfy multiple constraints.

[0014] As an improvement to the above system, the processing procedure of the multi-objective parallel optimization module based on the determinant point process includes: Step A1: Initialize the population individuals, with each individual corresponding to a set of design parameters to describe the scheme of the surveillance constellation configuration to be optimized; Step A2: Divide the current population into several subsets and calculate the multi-objective function value of each individual in parallel using a multi-process approach; Step A3: Generate a set of offspring individuals based on selection, crossover, and mutation operations; Step A4: Merge the parent individuals with the offspring individuals to form a joint population; Step A5: Perform non-dominated sorting on the joint population based on the multi-objective function values ​​to obtain multiple non-dominated layers; Step A6: Perform diversity selection based on determinant point processes; Step A7: Form a new generation of population from the selected individuals, return to step A2, and proceed to the next iteration until the termination condition is met.

[0015] As an improvement to the above system, the processing procedure of step A6 specifically includes: Sub-step A6.1: Based on the similarity relationship between individuals in the candidate solution set and the corresponding individual quality weights, construct the kernel matrix of the determinant point process. The kernel matrix simultaneously encodes individual quality information and the diversity relationship between individuals. Sub-step A6.2: Based on the constructed kernel matrix, a greedy approximate inference method is used to select a predetermined number of individuals from the candidate solution set, so that the probability of high-quality individuals being selected is greater, while the probability of highly similar individuals being selected at the same time is suppressed.

[0016] As an improvement to the above system, the system also includes a result output and visualization module, which is used to output and visualize the constellation configuration scheme and its corresponding performance indicators.

[0017] On the other hand, the present invention provides a method for optimizing the configuration of a space target surveillance satellite constellation. According to the above system implementation, the method includes: The constraint modeling and configuration module performs unified modeling of detection constraints and observation constraints in the process of space target monitoring, and configures various constraints according to mission requirements to build an observability determination model to determine the observability of space targets at a given time and within a given time interval. The monitoring performance evaluation index module constructs a variety of monitoring performance evaluation indexes and supports the configuration and selection of monitoring performance evaluation indexes according to different task requirements; The constellation configuration optimization solution module uses the monitoring performance evaluation index as the optimization objective, constructs a multi-objective optimization problem of constellation configuration, and calls the multi-objective parallel optimization module based on the determinant point process. The multi-objective parallel optimization module based on the determinant point process is based on the non-dominated sorting genetic algorithm. It introduces the determinant point process to model the diversity of the non-dominated solution set. It achieves joint optimization selection of individual quality and solution set diversity by maximizing the determinant of the kernel matrix subset. It also uses a greedy approximate inference method to complete the efficient screening of a fixed-size solution set. The constellation configuration optimization solution module performs joint optimization of constellation orbital parameters and configuration schemes to obtain the optimal or near-optimal constellation configuration schemes that satisfy multiple constraints.

[0018] Compared with the prior art, the advantages of the present invention are: 1. A complete system architecture covering constraint modeling, constellation configuration optimization, performance evaluation and result visualization was constructed, realizing modular decoupling and closed-loop linkage of constraint determination, optimization solution and performance feedback, and improving the overall system collaboration and engineering scalability; 2. Within the non-dominated sorting framework, instead of the traditional crowding distance-based sorting mechanism, a determinant point process (DPP) is introduced. k Individual selection significantly enhances the diversity of solution sets while ensuring solution quality, making the Pareto front distribution more balanced and stable. 3. Construct a multi-dimensional performance index system for surveillance tasks, and embed indicators such as effective correlation coverage, time utilization and revisit interval into the optimization closed loop to achieve "performance-driven" constellation configuration design and auxiliary decision support. Attached Figure Description

[0019] Figure 1 This is a flowchart of the space target surveillance satellite constellation configuration optimization system; Figure 2 This is a flowchart of a multi-objective parallel optimization module based on a matrix point process; Figure 3It outputs the constellation configuration parameters and monitoring performance indicators; Figure 4 It is a 3D scene visualization of a space target monitoring constellation; Figure 5 This is a cutting-edge graphic display from Pareto. Detailed Implementation

[0020] To achieve the above objectives, the technical solution proposed in this application includes the following functional modules, such as... Figure 1 As shown: 1. Constraint Modeling and Configuration Module: This module provides a unified model for the detection and observation constraints involved in the monitoring of space targets, and allows for flexible configuration of various constraints according to different mission requirements, thereby determining the observability of space targets at a given moment and within a given time interval. Among these constraints, detection constraints are limited by the capabilities of the sensors themselves, while observation constraints are limited by environmental factors during system operation.

[0021] 2. Multi-objective parallel optimization module based on determinant point process: Based on non-dominated sorting, a quality-aware determinant point process model is introduced to probabilistically model the candidate solution set. By maximizing the determinant of the subset of the kernel matrix, the joint optimization selection of individual quality and solution set diversity is achieved. A greedy approximate inference method is used to complete the efficient screening of a fixed-size solution set, so as to improve the distribution uniformity and stability of the non-dominated solution set in the multi-objective parallel optimization process. 3. Surveillance performance evaluation index module: Based on the target observability determination results, a variety of surveillance performance evaluation indexes are constructed to reflect the space target surveillance capability, and the monitoring performance evaluation indexes can be configured and selected according to different surveillance mission requirements, so as to quantitatively evaluate the surveillance performance of different constellation configuration schemes. 4. Constellation Configuration Optimization Solution Module: Taking the monitoring performance evaluation index as the optimization objective, and combining the constraint modeling and configuration module and the multi-objective parallel optimization module based on the determinant point process, the constellation orbit parameters and configuration scheme are jointly optimized and solved to obtain the optimal or near-optimal constellation configuration scheme that satisfies multiple constraints. 5. Results Output and Visualization Module: Outputs and visualizes the optimized constellation configuration parameters and their corresponding monitoring performance evaluation results to assist users in analyzing, comparing, and making decisions on different constellation configuration schemes.

[0022] In the above technical solution, the constellation configuration optimization problem can be defined as follows: under the given set of space targets, monitoring time window and monitoring satellite orbital parameter constraints, by constructing an observability determination model that includes detection constraints and observation constraints, the mapping relationship between constellation configuration parameters and monitoring performance evaluation indicators is established, and on this basis, the constellation configuration scheme that satisfies the constraints and has the best monitoring performance is solved.

[0023] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0024] Example 1 Embodiment 1 of the present invention provides a space target surveillance satellite constellation configuration optimization system, including a constraint modeling and configuration module, a multi-objective parallel optimization module based on a matrix point process, a surveillance performance evaluation index module, a constellation configuration optimization solution module, and a result output and visualization module.

[0025] The following is a detailed introduction to each module: I. Constraint Modeling and Configuration Module To comprehensively describe the observability of space targets relative to surveillance satellites, this invention constructs a constraint modeling and configuration module. This module defines three detection constraints and five observation constraints to determine whether a space target meets the conditions for effective observation at a given time. The detection constraints describe the limitations imposed by sensor performance on target observability; the observation constraints describe the impact of spatial geometry, illumination conditions, and target motion characteristics on observation feasibility. All constraints are uniformly represented as decision conditions or inequality constraint functions and can be flexibly selected and combined according to different surveillance mission requirements. The constraint determination results serve as the basic input for subsequent surveillance performance evaluation and satellite constellation configuration optimization.

[0026] The specific definitions of the above eight constraints are given below: 1) Detection constraints Sensor operating distance constraints Sensor range constraint refers to the limitation imposed by the detection sensitivity and resolution of optical sensors, meaning that the target can only operate within a certain range when the relative distance between the space target and the monitoring satellite, i.e., the magnitude of the position vector of the space target relative to the monitoring satellite, is within a certain range. Not exceeding the sensor's maximum effective detection range Only then can the target be successfully detected. (This is represented as...)

[0027] 2) Detection constraints Field of view constraints In this embodiment, each satellite carries two optical sensors, which are installed perpendicular to the satellite's velocity direction, with azimuth angles of ±90° and elevation angles of 0°. Field of view constraint refers to the requirement that the space target must be within the sensor's field of view, i.e., the horizontal and vertical deviation angles of the target relative to the sensor's line of sight. Not exceeding the sensor's maximum field of view limits in both the horizontal and vertical directions. 。 is represented as

[0028] 3) Detection constraints Observable arc length constraint The observable arc length constraint refers to the requirement that a space target must continuously meet detection conditions within a time period (start time) due to limitations imposed by sensor imaging, integration time, and target motion characteristics. End time Maintain observable status, and the duration of continuous observation is not less than a given threshold. Only then can an effective observation arc segment be formed. This is represented as...

[0029] 4) Observation constraints Earth occlusion constraint The Earth and its near-Earth atmosphere are considered as a single, opaque obstruction. If the line of sight between the monitoring satellite and a space target passes through this equivalent obstruction, the observation is considered infeasible. Let the Earth's radius be... The thickness of the near-Earth atmosphere is The position vector of the space target relative to the surveillance satellite is The position vector of the monitoring satellite relative to the Earth's center is This constraint is equivalent to " and The included angle The critical line of sight for surveillance satellite observations is greater than The included angle ", indicating as

[0030] Because the cos function is Monotonically decreasing, this constraint can be further simplified to

[0031] Using the definition of vector dot product ,therefore It can be represented as

[0032] Due to the included angle satisfy According to the Pythagorean theorem, we can obtain

[0033] Therefore, this constraint can be represented by a vector as follows:

[0034] 5) Observational constraints Ground shadow constraint When a space target is located within the Earth's conical umbra, its reflected light signal is significantly reduced due to the lack of solar illumination, making optical surveillance difficult to implement effectively. Therefore, the target is determined to be unobservable at that moment. This invention employs a conical umbra, and this constraint can be defined as the angle between the Earth and the Sun at the target point. It needs to be greater than the Earth's apparent radius angle. With the apparent radius angle of the sun The difference. This constraint can be expressed as...

[0035] Let the position vector of the space target relative to the Earth's center be... The position vector of the sun relative to the Earth's center is Earth's radius is The radius of the sun is Then the position vector of the sun relative to the target is .

[0036] According to the definition of the dot product, the angle between the sun and the earth at the target point satisfies... The apparent radius angle of the Earth satisfies The apparent radius angle of the sun satisfies Therefore, this constraint can be represented using a vector.

[0037] 6) Observational constraints Excluding angular constraints of the sun and moon Because solar radiation intensity is extremely high, when the sun approaches or enters the sensor's field of view, it can cause detector saturation or even pose a potential risk. Therefore, it is necessary to set a solar exclusion angle constraint. Although the moon's brightness is lower than the sun's, it still acts as a strong background light source, significantly reducing the target's signal-to-noise ratio. Therefore, lunar exclusion angle constraints need to be set. .

[0038] Assume the directions of the sun and moon for the monitoring satellite are respectively... The line of sight for monitoring satellites to observe space targets is Then the angle between the line of sight and the direction of the sun. Need to be greater than The angle between the direction of the moon and the direction of the moon Need to be greater than , can be represented as

[0039] According to the definition of the vector dot product, , Because the cos function is It is monotonically decreasing, therefore the two conditions can be expressed as follows:

[0040] 7) Observational constraints Relative angular velocity constraint Considering the limitations of optical sensor exposure time and tracking capability, the line-of-sight angular velocity between the monitoring satellite and the target is... It should not exceed the maximum angular velocity allowed by the sensor. .

[0041] Let the velocity of the spatial target be... The speed of the monitored satellite's movement is Then the velocity of the space target relative to the surveillance satellite can be expressed as:

[0042] because ,in, This represents the line-of-sight angular velocity of a space target relative to a monitoring satellite. Both sides are simultaneously... Cross product, we get

[0043] Using vector identities , can be obtained

[0044] Due to the direction of angular velocity Perpendicular to and The plane of rotation constituted, therefore Position vector of the space target relative to the surveillance satellite Perpendicular, therefore we can obtain Therefore, the relative angular velocity between the surveillance satellite and the space target can be expressed as:

[0045] Therefore, this constraint can be expressed as

[0046] 8) Observational constraints Observation angle constraints To ensure that the space target has sufficient reflected light intensity and imaging contrast, the angle between the target-monitoring satellite direction and the target-sun direction should be within a preset range to avoid the adverse effects of too small or too large angles on the target's observability.

[0047] Let the line of sight for the surveillance satellite to observe space targets be... The position vector of the sun relative to the target is The observation angle is The range of observation angles is This constraint can be expressed as:

[0048] According to the definition of the vector dot product, Because the cos function is It is monotonically decreasing, therefore the constraint can be expressed as

[0049] Due to the constraint of the observable arc length This constraint relies on the continuity determination of the time series and cannot be used to determine the instantaneous observability at a single moment; therefore, it is not included in the instantaneous constraint set. The instantaneous constraint set is defined as follows:

[0050] For any constraint Its instantaneous decision function is defined as:

[0051] At a given moment Space targets Compared to surveillance satellites The instantaneous observable function is defined as:

[0052] in, Indicates the corresponding constraint terms Enable or disable? When it is activated, The value indicates that the constraint is not enabled. When any enabled constraint is not satisfied, the instantaneous observable decision function takes the value of 0.

[0053] During the monitoring time window Within this framework, discrete time series data are used to determine observability.

[0054] in, Represents the first in a discrete time series At a certain point in time, The time interval between two points in time. This represents the number of equal divisions within the monitoring time window. It defines the instantaneous observability sequence. This represents the instantaneous observable state of the target over time within the entire monitoring window. .

[0055] Observable arc length constraint This is used to determine whether a target has formed a continuously observable interval that meets the minimum duration requirement, based on an instantaneous observable time series. It can be represented as...

[0056] The above interval For a continuous observable time arc, two conditions must be met: First, for the interval... Observability at all points in time Both are 1; secondly, the interval The corresponding arc length is not less than the threshold. By calculating all unique ones This allows us to obtain all observable arc segments within the monitoring time window. 1. II. Multi-objective parallel optimization module based on determinant point process A multi-objective parallel optimization module based on determinant point processes, grounded in the NSGA-II framework of the non-dominated sorting genetic algorithm, introduces determinant point processes to model and select diversity in the non-dominated solution set. Figure 2 As shown, the specific steps include: Step A1: Population Initialization. Initialize the population individuals, with each individual corresponding to a set of design parameters used to describe the scheme of the surveillance constellation configuration to be optimized.

[0058] Step A2: Parallel objective function evaluation. The current population is divided into several subsets, and simulation is performed using a multi-process approach, calculating the multi-objective function value for each individual.

[0059] Step A3: Generate offspring individuals. Generate a set of offspring individuals based on selection, crossover, and mutation operations.

[0060] Step A4: Merge parent and offspring. Merge parent individuals with offspring individuals to form a joint population.

[0061] Step A5: Non-dominated sorting. The joint population is non-dominated based on the multi-objective function values, resulting in multiple non-dominated layers.

[0062] Step A6: Diversity selection based on determinant-based point processes. Individuals are sequentially added to the new generation population according to the non-dominated layer order. When the number of individuals in a certain non-dominated layer exceeds the remaining available slots, the individuals in the current non-dominated layer are used as the candidate solution set, and the following sub-steps are executed: Sub-step A6.1: Based on the similarity relationship between individuals in the candidate solution set and the corresponding individual quality weights, construct the kernel matrix of the determinant point process. The kernel matrix simultaneously encodes individual quality information and the diversity relationship between individuals. Sub-step A6.2: Based on the constructed kernel matrix, a determinant point process sampling algorithm is used to select a predetermined number of individuals from the candidate solution set, so that the probability of high-quality individuals being selected is greater, while the probability of highly similar individuals being selected at the same time is suppressed.

[0063] Step A7: Generate the next generation population. The selected individuals are grouped into a new generation population. Return to step A2 to begin the next iteration, until the termination condition is met.

[0064] The Determinant Point Process (DPP) is a probabilistic model used to describe the repulsive relationships between elements in a set, suitable for selecting a subset of elements that are significantly different from each other in a candidate set. However, in multi-objective optimization scenarios, if only diversity is considered while the quality of individual elements is ignored, some low-quality solutions may be retained.

[0065] Therefore, this invention introduces individual quality weights into the determinant process to construct a "quality-aware" determinant process model, so that the solution set selection process takes into account both the quality of individual solutions and the overall diversity of the solution set.

[0066] Let the candidate solution set be For each individual in the candidate solution set Its characteristics are represented as ,in Represents an individual No. The values ​​of the objective function are defined, and the corresponding individual quality weights are defined. The range of values ​​satisfies This is used to describe the overall merits and demerits of an individual under multiple objective function values, and its mapping function can be expressed as:

[0067] in, Represents an individual Normalized features It is a mapping function for multi-objective function values, which can be constructed by weighted summation of multi-objective function values ​​or by sorting multi-objective levels.

[0068] To describe the diversity relationships among candidate solutions, we define any two candidate solutions... and The similarity function is The similarity function is used to measure the similarity between two individuals in the parameter space. The more similar the two individuals, the larger the corresponding function value. The similarity function is constructed based on the Euclidean distance between candidate solutions in the normalized objective space. It maps the distance to a similarity value using a Gaussian kernel function, thus describing the distribution differences of different candidate solutions in the multi-objective space, and is expressed as:

[0069] The similarity function is a positive definite kernel function. Wherein, For the scale parameter, satisfying It is used to adjust the similarity decay rate.

[0070] Based on the aforementioned individual quality weights and similarity functions, a determinant-based point process kernel matrix for "quality perception" is constructed. ,and It is a positive semi-definite matrix. Each element in the matrix is ​​defined as...

[0071] The corresponding matrix form is

[0072] in, This is a diagonal matrix of individual quality weights. This is a similarity matrix composed of similarity functions. Because... It is a non-negative diagonal matrix, and It is a positive semi-definite matrix, therefore It is also a positive semi-definite matrix. In this construction method, the kernel matrix simultaneously encodes the quality level of an individual and the similarity and repulsion relationships between individuals.

[0073] During the determinant point process, any candidate subset The probability of being selected is defined as

[0074] The above probability definition satisfies

[0075] in, The kernel matrix represents subsets The submatrix formed by the corresponding rows and columns, It is the identity matrix. This is a normalization factor used to ensure that the sum of the selection probabilities of all candidate subsets is 1, thus forming a valid probability distribution. When subsets When the subset contains high-quality and diverse individuals, the determinant value is large; while when the subset contains high-quality and diverse individuals, the determinant value is large. When the quality of individuals is low or they are highly similar, the determinant value is small. Therefore, subsets with high-quality individuals and greater differences among them have a higher probability of being selected.

[0076] In the multi-objective optimization process, to ensure a fixed size for the next generation population, this invention employs a fixed-size determinant point process model, selecting a specified number of points from the candidate solution set. k individuals, that is k -DPP. Then subset The probability of being selected is defined as

[0077] However, due to k - The precise sampling computation of DPP is computationally complex and difficult to implement in engineering. Therefore, a greedy approximation algorithm is used to solve the determinant maximization problem. The specific steps are as follows: Step B1: Initialize the selected subset. .

[0078] Step B2: Iteratively select candidate individuals. In the... In the next iteration For all candidate solutions that were not selected into the subset ,in" " represents the set difference symbol, indicating the difference between candidate sets. Remove selected subsets The remaining elements are then calculated, and their determinant gain after being added to the current subset is also calculated.

[0079] Step B3: Maximum Gain Criterion Selection. Select the candidate solution that maximizes the determinant gain. and update subsets ,in satisfy

[0080] Step B4: Termination condition. When the size of the subset reaches a certain number. k When the iteration ends, output the final set of selected individuals. This is the result of selection in this generation of the population.

[0081] By employing the greedy approximation strategy described above, we can effectively approximate the objective of maximizing a fixed-size determinant while maintaining low computational complexity, thereby achieving joint optimization selection of individual quality and diversity in the candidate solution set.

[0082] III. Introduction to the Monitoring Performance Evaluation Indicators Module The surveillance performance evaluation index module is used to construct various surveillance performance evaluation indices based on target observability determination results, given a constellation configuration and surveillance time window. These indices can be configured and selected according to different surveillance mission requirements, thereby quantitatively evaluating the constellation's space target surveillance capabilities and providing an evaluation basis for subsequent constellation configuration optimization. The surveillance performance evaluation indices include effective correlation coverage, total constellation time utilization, and total average revisit interval, described in detail below: 1) Indicator 1: Effective Association Coverage Rate During the monitoring time window Internally, regarding space targets If there are at least two independent observable arc segments, and the time interval between two adjacent observable arc segments is not greater than a given threshold. If so, it is considered that the target has formed a valid correlation observation record within the simulation time.

[0083] Effective correlation coverage is defined as the proportion of the number of targets that meet the above conditions to the total number of targets. It is used to measure the effective coverage capability of the observation constellation for space targets that can be used for target correlation and continuous tracking.

[0084] Let the set of spatial targets be ,Target The set of observable arc segments is

[0085] in, Representing the target The The start and end times of each observable arc segment are given. The effective correlation coverage is then defined as...

[0086] in, This represents the total number of space targets. For the goal The number of observable arc segments, Indicate target The One observable arc segment Representing the target The The start time of the first observable arc segment and the first The end time of each observable arc segment Indicates the first The observable arc segment and the first The time interval between each observable arc segment This is an indicator function; its value is 1 when the condition is true and 0 when the condition is false. Therefore, the condition in an indicator function represents: the target... When the number of observable arc segments is not less than two, there exists a first arc segment. The observable arc segment and the first The time interval between each observable arc segment is no greater than a given threshold. .

[0087] 2) Indicator Two: Total Time Utilization Rate by Constellation The total constellation time utilization rate describes the proportion of time that the observation constellation spends effectively observing all targets within the monitoring time window, reflecting the overall observation time investment and resource utilization level of the observation constellation during the simulation time.

[0088] Set space target The set of observable arc segments is The monitoring time window length is The total time utilization rate of a constellation is defined as:

[0089] in, For space targets The set of observable arc segments is One of the observable arc segments, This indicates the length of the arc segment.

[0090] 3) Indicator 3: Overall average revisit interval The total average revisit interval is used to measure the temporal continuity of repeated observations of space targets by an observation constellation. It reflects the level of the observation constellation's ability to conduct continuous and stable surveillance of space targets. The smaller the value, the more frequent the revisits and the better the continuity.

[0091] For a target that is observed at least twice within the simulation time, calculate the average revisit interval between two adjacent observable arcs and take the average for all targets that meet the condition.

[0092] Suppose that satisfies The target set is The total average revisit interval is defined as:

[0093] in, This indicates the number of spatial targets with at least two observable arc segments. Representing the target The The start time of the first observable arc segment and the first The end time of each observable arc segment Indicates the first The observable arc segment and the first The time interval between observable arc segments.

[0094] IV. Introduction to the Constellation Configuration Optimization Solution Module The constellation configuration optimization module is used to jointly optimize constellation orbital parameters and configuration schemes based on existing constraints and performance evaluation metrics. This module uses monitored performance evaluation metrics as the optimization objective and searches for constellation configuration schemes that meet mission requirements through optimization algorithms.

[0095] 1) Acquisition of space target data In this embodiment, this module obtains the orbital data of space targets from the public space target database Space-Track. The target orbital information is given in two-row root (TLE) format, including parameters such as orbital altitude, inclination, and right ascension of the ascending node. Based on the mission scenario requirements, the target orbital altitudes are first filtered to construct a target set within a specified altitude range.

[0096] 2) Distribution-preserving target sampling Due to the large number of targets, directly using all targets would drastically increase the computational load. Therefore, this module samples the target set. During sampling, the distribution of targets at orbital altitude, inclination, and right ascension of the ascending node is comprehensively considered. By partitioning the parameter space and selecting samples according to the proportion of targets within each partition, the sampled target subset maintains consistency with the original target set in overall distribution. This reduces the computational scale while ensuring the representativeness of the target distribution.

[0097] 3) Representation of constellation configuration parameters This module represents constellation configuration schemes as a set of adjustable constellation configuration parameter vectors. This describes the orbital layout and structural form of a constellation. The parameters include: Orbital elements of Walker constellation seed satellites: semi-major axis eccentricity track inclination Right ascension of ascending node perigee argument , near point angle ; Number of orbital surfaces ; Number of satellites in each orbital plane ; Phase factor .

[0098] in, , , These represent the ranges of values ​​for the semi-major axis, eccentricity, and orbital inclination, respectively; while the number of orbital surfaces... and the number of satellites in each orbital plane Both are positive integers, and they jointly determine the size of the constellation, satisfying the condition that... , This represents the total number of satellites.

[0099] 4) Optimize target construction and multi-target optimization settings In the process of constellation configuration optimization, the advantages and disadvantages of different constellation schemes in terms of surveillance effectiveness are usually reflected in multiple aspects, and it is difficult to comprehensively reflect the overall surveillance capability of the constellation using only a single performance index. For example, using only the number of targets covered or the coverage ratio as the optimization objective can increase the scale of observable targets, but it may lead to discrete target observation time and insufficient repeat observation capability; while focusing only on temporal continuity or revisit performance may sacrifice the effective achievement of overall target coverage. Therefore, it is necessary to comprehensively consider multiple surveillance performance evaluation indicators, construct a multi-objective optimization problem, and conduct a comprehensive evaluation and optimization of constellation configurations.

[0100] Based on the monitoring performance evaluation index module, the candidate optimization objective set for constellation configuration optimization is constructed as follows:

[0101] in, Represents the constellation configuration parameter vector. , and These correspond to the effective association coverage rate, total constellation time utilization rate, and total average revisit interval, respectively. For specific definitions, please refer to the monitoring performance evaluation index module.

[0102] Among the above optimization objectives, and The optimization objective is to maximize, The optimization objective is to minimize, i.e. In the process of constructing a multi-objective optimization problem, starting from the set of objectives... Select at least two objectives to form a constellation configuration multi-objective optimization problem, the general form of which can be expressed as:

[0103] in, This represents the set of functions whose optimization objective is to maximize. Let represent the set of functions whose optimization objective is to minimize. and These represent the number of elements in each of the two sets.

[0104] In practical applications, two or three of these metrics can be selected to form an optimization target set based on specific task requirements. For example, in task scenarios that emphasize continuous target tracking capabilities, a focus can be placed on joint optimization. and In task scenarios that emphasize resource utilization efficiency, joint optimization is possible. and .

[0105] By introducing multi-objective optimization, trade-offs can be made between different monitoring performance indicators, and a set of constellation configuration schemes that are representative in each indicator can be output, providing a more comprehensive reference for subsequent constellation design and engineering decisions.

[0106] 5) Constellation configuration optimization solution process The constellation configuration optimization solution process, based on constraint modeling, monitoring performance evaluation index construction, and optimization objective setting, completes the overall optimization of constellation configuration schemes through a multi-objective parallel algorithm. This process generates, evaluates, and optimizes constellation configuration schemes through the sequential invocation and collaborative operation of multiple functional modules. The optimization solution process includes the following steps: Step C1: Optimize scene initialization Based on the requirements of the surveillance mission, set basic parameters such as the surveillance time window, target orbital altitude range, and constellation size to complete the initial configuration of the optimized scenario.

[0107] Step C2: Target set generation Under initialization conditions, a set of spatial targets for optimization calculations is generated and imported, serving as a unified input for subsequent constellation configuration performance evaluation and visibility analysis.

[0108] Step C3: Constructing a multi-objective optimization problem Based on the monitoring performance evaluation index module, select no fewer than two indices from the index set, construct a constellation configuration multi-objective optimization problem, and clarify the optimization direction of each optimization objective.

[0109] Step C4: Optimize parameters and algorithm configuration A multi-objective parallel optimization module based on a matrix point process is enabled, and relevant parameters of the optimization algorithm are set. At the same time, feasible region constraints of constellation configuration parameters are set in the algorithm as the basis for determining the generation and updating of configuration schemes.

[0110] Step C5: Configuration Simulation and Performance Evaluation During the optimization algorithm iteration process, the constraint modeling and configuration module is called to perform orbit configuration simulation and visibility analysis on the current constellation configuration scheme, and the monitoring performance evaluation index module is further called to calculate the corresponding objective function value.

[0111] Step C6: Iterative optimization of configuration scheme Based on the relevant parameters in the optimization module set in step C4 and the calculation method of the multi-objective function value in step C5, the optimization algorithm in the multi-objective parallel optimization module based on the determinant point process is used to select and update the constellation configuration scheme, and gradually search for a constellation configuration scheme with better performance.

[0112] Step C7: Solution set output Once the preset termination condition is met, the constellation configuration optimization process ends, outputting a multi-objective optimization solution set that satisfies the constraints, i.e., the Pareto front solution set under multi-objective conditions. Each solution corresponds to a set of non-dominated constellation configuration schemes. For each constellation configuration scheme, the following information is output: a) Constellation configuration parameter information This includes orbital parameters such as the number of orbital planes, the number of satellites per orbital plane, phase factors, and constellation orbital altitude and inclination, which are used to fully describe the constellation configuration scheme. b) Surveillance performance evaluation index values ​​corresponding to constellations Output the index values ​​of the constellation configuration under each optimization objective, including effective association coverage, total constellation time utilization, and total average revisit interval, to reflect the differences of different constellation configurations in various dimensions.

[0113] c) Pareto front solution set structure information Identify the relative positions of each constellation configuration scheme in a multi-objective space to provide a basis for subsequent scheme selection and comparative analysis.

[0114] V. Introduction to the Results Output and Visualization Module The results output and visualization module is used to structure, numerically output, and visualize the near-optimal constellation schemes output by the constellation configuration optimization solution module, so as to support comparative analysis and engineering decision-making for different configuration schemes.

[0115] 1) Constellation configuration parameter output For each candidate constellation configuration scheme obtained through optimization, the system outputs its complete orbital parameters and configuration information. The parameters are output in the form of a structured table, with each satellite corresponding to one row of records, which can be easily exported to CSV, Excel or database formats for subsequent simulation verification or engineering implementation.

[0116] 2) Monitor performance index results output Based on the calculation results of the monitoring performance evaluation index module, the corresponding performance index values ​​are output for each constellation configuration scheme. The performance differences of different constellation configuration schemes are presented in the form of a comparison table.

[0117] 3) Three-dimensional scene visualization of space target monitoring constellation To present the constellation configuration and its monitoring effect more intuitively, this module uses the optimized constellation orbit parameters to construct a 3D simulation scene. The 3D view and timeline animation functions can dynamically display the satellite's trajectory, the target's visible range, and the coverage process. It can also generate access reports and statistical reports to verify the correctness of the optimization results and the engineering feasibility.

[0118] 4) Graphical analysis and comparative display Building upon numerical output, this module further provides graphical display capabilities, including multi-target Pareto front distribution maps (two-dimensional or three-dimensional), observation frequency distribution maps for each target, and statistical curves of observation time intervals. This visualization method enables intuitive comparisons of different constellation configurations in terms of coverage capability, resource utilization efficiency, and continuous monitoring performance.

[0119] Example 2 Embodiment 2 of the present invention proposes a space target surveillance satellite constellation configuration optimization system, which includes five functional modules: constraint modeling and configuration module, multi-objective parallel optimization module based on matrix point process, surveillance performance evaluation index module, constellation configuration optimization solution module, and result output and visualization module.

[0120] The constellation configuration optimization solution module is the main module. Its function is to call the constraint modeling and configuration module, the multi-objective parallel optimization module based on the determinant point process, and the monitoring performance evaluation index module to solve for the optimal or near-optimal constellation configuration information. This information will be passed to the result output and visualization module to achieve a clear display of the constellation configuration.

[0121] The specific implementation of the constellation configuration optimization solution module is as follows: 1. Acquisition of Space Target Data In this embodiment, orbital data of space targets are obtained from the publicly available space target database Space-Track, and the target orbital altitude filtering range is set in this scenario to construct a target set within this altitude range.

[0122] 2. Distribution-preserving target sampling Because there are a large number of targets in this altitude range, the target set is sampled. After comprehensively considering the target's orbital altitude, inclination, and distribution at the right ascension of the ascending node, an appropriate number of targets are selected as a target subset. This subset maintains the same overall distribution as the original target set, reducing the computational scale and ensuring the representativeness of the target distribution.

[0123] 3. Representation of constellation configuration parameters The constellation configuration scheme is represented as a set of adjustable constellation configuration parameter vectors, used to represent the encoding of individuals in the algorithm, expressed as follows: The meanings of each parameter are as follows: Orbital elements of Walker constellation seed satellites: semi-major axis eccentricity track inclination Right ascension of ascending node perigee argument , near point angle ; Number of orbital surfaces ; Number of satellites in each orbital plane ; Phase factor .

[0124] Among them, among them, , , These represent the ranges of values ​​for the semi-major axis, eccentricity, and orbital inclination, respectively; the number of orbital surfaces. and the number of satellites in each orbital plane Both are positive integers, and they jointly determine the size of the constellation, satisfying the condition that... , This represents the total number of satellites.

[0125] 4. Optimize target setting and multi-target optimization settings Taking into account the three indicators proposed in the monitoring performance evaluation module: effective correlation coverage Total time utilization rate of constellations and total average revisit interval The candidate optimization objective set for constellation configuration optimization is constructed as follows:

[0126] in, This represents the constellation configuration parameter vector.

[0127] Among the above optimization objectives, and The optimization objective is to maximize, The optimization objective is to minimize, i.e. In the process of constructing a multi-objective optimization problem, starting from the set of objectives... Select at least two objectives to form a constellation configuration multi-objective optimization problem, the general form of which can be expressed as:

[0128] in, This represents the set of functions whose optimization objective is to maximize. Let represent the set of functions whose optimization objective is to minimize. and These represent the number of elements in each of the two sets.

[0129] 5. Solving Constellation Configuration Optimization Constellation configuration optimization is based on constraint modeling, monitoring performance evaluation index construction, and optimization objective setting. It utilizes a multi-objective parallel algorithm to achieve overall optimization of constellation configuration schemes. This process generates, evaluates, and optimizes constellation configuration schemes through the sequential invocation and collaborative operation of multiple functional modules. The solution process follows these steps: Step C1: Optimize scene initialization Set monitoring time window The timeframe is from 06:14:00 on July 1, 2025 to 06:14:00 on July 2, 2025, with a duration of 24 hours and a time step of 10 seconds. The target orbital altitude range is set to 600-800 km, the target subset size is 100, and the constellation scale is also specified. Complete the initial configuration for optimizing the scenario.

[0130] Step C2: Target set generation Under initialization conditions, a set of spatial targets for optimization calculations is generated and imported, serving as a unified input for subsequent constellation configuration performance evaluation and visibility analysis.

[0131] Step C3: Constructing a multi-objective optimization problem Based on the monitoring performance evaluation index module, all three indices are selected from the index set to construct a constellation configuration multi-objective optimization problem, and the optimization direction of each optimization objective is clarified.

[0132] Step C4: Optimize parameters and algorithm configuration Set the relevant parameters of the optimization algorithm in the multi-objective parallel optimization module based on the determinant point process: Population size 50; Maximum number of iterations: 10; Crossover probability 0.9; The mutation probability is 0.3; Number of parallel processes: 5.

[0133] Meanwhile, the feasible region constraint of the constellation configuration parameters is set in the algorithm as the criterion for determining the generation and updating of configuration schemes: semi-long shaft ; Eccentricity ; track inclination .

[0134] Step C5: Configuration Simulation and Performance Evaluation During the optimization algorithm iteration process, for the constellation configuration scheme in the current population, the constraint modeling and configuration module is invoked to perform orbit configuration simulation and visibility analysis. The constraints that the monitoring satellite and the target must satisfy are as follows: Detection constraints Sensor operating distance constraints Set the maximum effective detection distance of the sensor to This constraint can be expressed as

[0135] Detection constraints Field of view constraints Set the maximum field of view of the sensor in both the horizontal and vertical directions to [limit]. , This constraint can be expressed as

[0136] Detection constraints Observable arc length constraint Set a threshold for the continuous observation time of a space target. The starting time of a certain detection arc segment is The end time is This constraint can be expressed as

[0137] Observational constraints Earth occlusion constraint Set near-Earth atmospheric thickness This constraint can be expressed as

[0138] Observational constraints Ground shadow constraint This constraint can be expressed as

[0139] Observational constraints Excluding angular constraints of the sun and moon Set solar exclusion angle constraint Moon Exclusion Angular Constraint This constraint can be expressed as

[0140] Observational constraints Relative angular velocity constraint Set the maximum angular velocity allowed by the sensor between the surveillance satellite and the target. This constraint can be expressed as

[0141] Observational constraints Observation angle constraints Set the observation angle range to This constraint can be expressed as

[0142] Due to the constraint of the observable arc length This constraint relies on the continuity determination of the time series and cannot be used to determine the instantaneous observability at a single moment; therefore, it is not included in the instantaneous constraint set. The instantaneous constraint set is defined as follows:

[0143] For any constraint Its instantaneous decision function is defined as:

[0144] At a given moment Space targets Compared to surveillance satellites The instantaneous observable function is defined as:

[0145] in, Indicates the corresponding constraint terms Enable or disable? When it is activated, The value indicates that the constraint is not enabled. When any enabled constraint is not satisfied, the instantaneous observable decision function takes the value of 0.

[0146] During the monitoring time window Within this framework, discrete time series data are used to determine observability.

[0147] in, Represents the first in a discrete time series At a certain point in time, The time interval between two points in time. This represents the number of equal divisions within the monitoring time window. It defines the instantaneous observability sequence. This represents the instantaneous observable state of the target over time within the entire monitoring window. .

[0148] Observable arc length constraint This is used to determine whether a target has formed a continuously observable interval that meets the minimum duration requirement, based on an instantaneous observable time series. It can be represented as...

[0149] The above interval For a continuous observable time arc, two conditions must be met: First, for the interval... Observability at all points in time Both are 1; secondly, the interval The corresponding arc length is not less than the threshold. By calculating all unique ones This allows us to obtain all observable arc segments within the monitoring time window.

[0150] After obtaining all observable arc segments, the monitoring performance evaluation index module is further invoked to calculate the corresponding objective function value: Indicator 1: Effective Association Coverage During the monitoring time window Internally, regarding space targets If there are at least two independent observable arc segments, and the time interval between two adjacent observable arc segments is not greater than a given threshold. If the target is considered to have formed an effective correlation observation record within the simulation time, the effective correlation coverage rate is defined as the proportion of the number of targets that meet the above conditions to the total number of targets.

[0151] Let the set of spatial targets be ,Target The set of observable arc segments is

[0152] in, Representing the target The The start and end times of each observable arc segment are given. The effective correlation coverage rate is...

[0153] in, This represents the total number of space targets. For the goal The number of observable arc segments, Indicate target The One observable arc segment Representing the target The The start time of the first observable arc segment and the first The end time of each observable arc segment Indicates the first The observable arc segment and the first The time interval between each observable arc segment This is an indicator function; its value is 1 when the condition is true and 0 when the condition is false. Therefore, the condition in an indicator function represents: the target... When the number of observable arc segments is not less than two, there exists a first arc segment. The observable arc segment and the first The time interval between each observable arc segment is no greater than a given threshold. .

[0154] Indicator 2: Total Time Utilization Rate by Zodiac Sign Set space target The set of observable arc segments is Monitoring time window The length is 1 day, that is The total time utilization rate for constellations is:

[0155] in, For space targets The set of observable arc segments is One of the observable arc segments, This indicates the length of the arc segment.

[0156] Indicator 3: Overall Average Revisit Interval For a target that is observed at least twice within the simulation time, calculate the average revisit interval between two adjacent observable arcs and take the average for all targets that meet the condition.

[0157] Suppose that satisfies The target set is The overall average revisit interval is:

[0158] in, This indicates the number of spatial targets with at least two observable arc segments. Representing the target The The start time of the first observable arc segment and the first The end time of each observable arc segment Indicates the first The observable arc segment and the first The time interval between observable arc segments.

[0159] Step C6: Iterative optimization of configuration scheme Based on the relevant parameters set in the optimization module in step C4 and the calculation method of the multi-objective function value in step C5, the optimization algorithm in the multi-objective parallel optimization module based on the determinant point process is used to select and update constellation configuration schemes, gradually searching for constellation configuration schemes with better performance. The specific steps are as follows: Step A1: Population initialization; Initialize the population of individuals, with each individual corresponding to a set of design parameters to describe the configuration of the surveillance constellation to be optimized.

[0160] Step A2: Parallel evaluation of the objective function; The current population is divided into several subsets, and simulation is performed using a multi-process approach. The multi-objective function value of each individual is calculated.

[0161] Step A3: Generate offspring individuals; A set of offspring individuals is generated based on selection, crossover, and mutation operations.

[0162] Step A4: Merge the parent generation and the child generation; Parents and offspring are merged to form a joint population.

[0163] Step A5: Non-dominated sorting; Multiple non-dominated layers are obtained by performing non-dominated sorting on the joint population based on the multi-objective function value.

[0164] Step A6: Diversity selection based on determinant point processes; Individuals are added to the new generation population sequentially according to the non-dominated layer order. When the number of individuals in a certain non-dominated layer exceeds the remaining available slots... k When this happens, individuals in the current non-dominated layer are used as candidate solutions. Perform the following sub-steps: Sub-step A6.1: Each individual The features are represented as The corresponding individual quality weight , A mapping function for the values ​​of multiple objective functions. The range of values ​​satisfies .

[0165] Using Gaussian kernel function Describe two candidate solutions and similarity, Scale parameter settings .

[0166] Construct a determinant-based point process kernel matrix based on individual quality weights and similarity. The calculation method for each element in the matrix is ​​as follows: .

[0167] Sub-step A6.2: Establish a mechanism to select a specified number of solutions from the candidate solution set. k individual k -DPP problem, subset The probability of being selected is defined as The determinant maximization problem is solved using a greedy approximation algorithm. The specific steps are as follows: Step B1: Initialize the selected subset. .

[0168] Step B2: Iteratively select candidate individuals. In the... In the next iteration For all candidate solutions that were not selected into the subset Calculate the determinant gain after adding it to the current subset. Step B3: Maximum Gain Criterion Selection. Select the candidate solution that maximizes the determinant gain. and update subsets ,in satisfy .

[0169] Step B4: Termination condition. When the size of the subset reaches a certain number. k When the iteration ends, output the final set of selected individuals. This is the result of selection in this generation of the population.

[0170] Step A7: Generate the next generation population.

[0171] The selected individuals are grouped into a new generation of population, and the process returns to step A2 to enter the next iteration until the termination condition is met.

[0172] Step C7: Solution set output Once the preset termination condition is met, the constellation configuration optimization process ends, outputting a multi-objective optimization solution set that satisfies the constraints, i.e., the Pareto front solution set under multi-objective conditions. Each solution corresponds to a set of non-dominated constellation configuration schemes. For each constellation configuration scheme, the following information is output: constellation configuration parameter information, the corresponding monitoring performance evaluation index value of the constellation, and the Pareto front solution set structure information.

[0173] The information output from the constellation configuration optimization solution module is fed into the results output and visualization module. This module structures, quantifies, and visualizes the near-optimal constellation scheme to support comparative analysis and engineering decision-making for different configurations. Specific outputs include: constellation configuration parameters and monitoring performance index results. Figure 3 As shown, the 3D scene visualization of the space target surveillance constellation is as follows: Figure 4 As shown, graphical analysis and comparison are presented as follows: Figure 5 As shown.

[0174] Example 3 Embodiment 3 of the present invention proposes a method for optimizing the configuration of a space target surveillance satellite constellation. Based on the above system implementation, the method includes: The constraint modeling and configuration module performs unified modeling of detection constraints and observation constraints in the process of space target monitoring, and configures various constraints according to mission requirements to build an observability determination model to determine the observability of space targets at a given time and within a given time interval. The monitoring performance evaluation index module constructs a variety of monitoring performance evaluation indexes and supports the configuration and selection of monitoring performance evaluation indexes according to different task requirements; The constellation configuration optimization solution module uses the monitoring performance evaluation index as the optimization objective, constructs a multi-objective optimization problem of constellation configuration, and calls the multi-objective parallel optimization module based on the determinant point process. The multi-objective parallel optimization module based on the determinant point process is based on the non-dominated sorting genetic algorithm. It introduces the determinant point process to model the diversity of the non-dominated solution set. It achieves joint optimization selection of individual quality and solution set diversity by maximizing the determinant of the kernel matrix subset. It also uses a greedy approximate inference method to complete the efficient screening of a fixed-size solution set. The constellation configuration optimization solution module performs joint optimization of constellation orbital parameters and configuration schemes to obtain the optimal or near-optimal constellation configuration schemes that satisfy multiple constraints.

[0175] It is worth noting that in the embodiments of the above system, the modules included are divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional module are only for easy differentiation and are not used to limit the scope of protection of the present invention.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A space target surveillance satellite constellation configuration optimization system, characterized in that, include: The constraint modeling and configuration module is used to uniformly model the detection constraints and observation constraints in the process of space target monitoring, and configure various constraints according to mission requirements to build an observability determination model to determine the observability of space targets at a given time and within a time interval. The monitoring performance evaluation index module is used to build various monitoring performance evaluation indexes and supports the configuration and selection of monitoring performance evaluation indexes according to different task requirements. A multi-objective parallel optimization module based on determinant point process is used to model the diversity of non-dominated solution sets by introducing a determinant point process based on non-dominated sorting genetic algorithm. It achieves joint optimization selection of individual quality and solution set diversity by maximizing the determinant of the subset of the kernel matrix, and completes efficient screening of fixed-size solution sets by using a greedy approximate inference method. and The constellation configuration optimization solution module is used to construct a multi-objective optimization problem of constellation configuration with monitoring performance evaluation index as the optimization objective. It calls the multi-objective parallel optimization module based on determinant point process to jointly optimize constellation orbital parameters and configuration schemes to obtain the optimal or near-optimal constellation configuration scheme that satisfies multiple constraints. The monitoring performance evaluation index module constructs various monitoring performance evaluation indices, including: Effective correlation coverage is used to measure the effective coverage capability of an observation constellation for space targets that can be used for target correlation and continuous tracking. The total constellation time utilization rate reflects the overall observation time investment and resource utilization level of the observed constellation within the simulated time; and The overall average revisit interval is used to reflect the level of the observation constellation's ability to conduct continuous and stable surveillance of space targets; Wherein, the effective association coverage Satisfy the following formula: in, Represents the set of spatial targets Total quantity For the goal The number of observable arc segments, Indicate target The One observable arc segment Representing the target The The start time of the first observable arc segment and the first The end time of each observable arc segment Indicates the first The observable arc segment and the first The time interval between each observable arc segment As an indicator function, when the target The number of observable arc segments is no less than two, and there exists a first arc segment. The observable arc segment and the first The time interval between each observable arc segment is no greater than a given threshold. When the association condition is met, the indicator function is 1; otherwise, it is 0. The total time utilization rate of the constellation Satisfy the following formula: in, To monitor the length of the time window, For the goal observable arc segment set One of the observable arc segments, This indicates the length of the arc segment; The total average revisit interval Satisfy the following formula: in, This represents the set of targets with at least two observable arc segments. Number of spatial targets Representing the target The The start time of the first observable arc segment and the first The end time of each observable arc segment Indicates the first The observable arc segment and the first The time interval between observable arc segments.

2. The space target surveillance satellite constellation configuration optimization system according to claim 1, characterized in that, The detection constraints and observation constraints are used to determine whether a spatial target meets the effective observation conditions at a given time, wherein; The detection constraints are used to describe the limitations of the sensor's own performance on the detectability of the target, including: sensor operating distance constraints, field of view constraints, and observable arc length constraints; The observation constraints are used to describe the impact of spatial geometric relationships, lighting conditions, and target motion characteristics on observation feasibility; including: Earth occlusion constraints, Earth shadow constraints, Sun and Moon exclusion angle constraints, relative angular velocity constraints, and observation angle constraints.

3. The space target surveillance satellite constellation configuration optimization system according to claim 2, characterized in that, The construction process of the observable decision model includes: By defining an instantaneous constraint set and an instantaneous observability sequence, and by determining the continuous observable interval based on the observable arc length constraint, a complete observability determination model for the target within the monitoring time window is constructed.

4. The space target surveillance satellite constellation configuration optimization system according to claim 1, characterized in that, The constellation configuration optimization solution module uses the monitoring performance evaluation index as the optimization objective to obtain a set of candidate optimization objectives for constellation configuration optimization. for: in, Represents the constellation configuration parameter vector. , and These correspond to the effective association coverage rate, total constellation time utilization rate, and total average revisit interval, respectively. From the target set Select at least two objectives to construct a constellation configuration multi-objective optimization problem, satisfying the following equation: in, This represents the set of functions whose optimization objective is to maximize. Let represent the set of functions whose optimization objective is to minimize. and These represent the number of elements in each of the two sets.

5. The space target surveillance satellite constellation configuration optimization system according to claim 4, characterized in that, The processing steps of the constellation configuration optimization solution module include: Acquire orbital data of the space target to be monitored, the orbital data including at least orbital altitude, inclination, and right ascension of the ascending node; filter the target orbital altitudes according to the mission scenario requirements to construct a target set within a specified altitude range; Taking into account the distribution of space targets at orbital altitude, inclination, and right ascension of the ascending node, the target set is subjected to distribution-preserving sampling to ensure the representativeness of the distribution; The constellation configuration scheme is represented as a set of adjustable constellation configuration parameter vectors that describe the orbital layout and structural form of the constellation. ,in, These are the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and angle of apogee. For the number of orbital surfaces, The number of satellites in each orbital plane, Phase factor ; and Together they determine the size of the constellation and satisfy , Total number of satellites; Based on the multi-objective optimization problem of constellation configuration, a multi-objective parallel optimization module based on determinant point process is invoked to jointly optimize the constellation orbital parameters and configuration schemes, so as to obtain the optimal or near-optimal constellation configuration schemes that satisfy multiple constraints.

6. The space target surveillance satellite constellation configuration optimization system according to claim 1, characterized in that, The processing steps of the multi-objective parallel optimization module based on the determinant point process include: Step A1: Initialize the population individuals, with each individual corresponding to a set of design parameters to describe the scheme of the surveillance constellation configuration to be optimized; Step A2: Divide the current population into several subsets and calculate the multi-objective function value of each individual in parallel using a multi-process approach; Step A3: Generate a set of offspring individuals based on selection, crossover, and mutation operations; Step A4: Merge the parent individuals with the offspring individuals to form a joint population; Step A5: Perform non-dominated sorting on the joint population based on the multi-objective function values ​​to obtain multiple non-dominated layers; Step A6: Perform diversity selection based on determinant point processes; Step A7: Form a new generation of population from the selected individuals, return to step A2, and proceed to the next iteration until the termination condition is met.

7. The space target surveillance satellite constellation configuration optimization system according to claim 6, characterized in that, The processing procedure of step A6 specifically includes: Sub-step A6.1: Based on the similarity relationship between individuals in the candidate solution set and the corresponding individual quality weights, construct the kernel matrix of the determinant point process. The kernel matrix simultaneously encodes individual quality information and the diversity relationship between individuals. Sub-step A6.2: Based on the constructed kernel matrix, a greedy approximate inference method is used to select a predetermined number of individuals from the candidate solution set, so that the probability of high-quality individuals being selected is greater, while the probability of highly similar individuals being selected at the same time is suppressed.

8. The space target surveillance satellite constellation configuration optimization system according to claim 1, characterized in that, The system also includes a result output and visualization module, which is used to output and visualize the constellation configuration scheme and its corresponding performance indicators.

9. A method for optimizing the configuration of a space target surveillance satellite constellation, implemented according to any one of claims 1-8, the method comprising: The constraint modeling and configuration module performs unified modeling of detection constraints and observation constraints in the process of space target monitoring, and configures various constraints according to mission requirements to build an observability determination model to determine the observability of space targets at a given time and within a given time interval. The monitoring performance evaluation index module constructs a variety of monitoring performance evaluation indexes and supports the configuration and selection of monitoring performance evaluation indexes according to different task requirements; The constellation configuration optimization solution module uses the monitoring performance evaluation index as the optimization objective, constructs a multi-objective optimization problem of constellation configuration, and calls the multi-objective parallel optimization module based on the determinant point process. The multi-objective parallel optimization module based on the determinant point process is based on the non-dominated sorting genetic algorithm. It introduces the determinant point process to model the diversity of the non-dominated solution set. It achieves joint optimization selection of individual quality and solution set diversity by maximizing the determinant of the kernel matrix subset. It also uses a greedy approximate inference method to complete the efficient screening of a fixed-size solution set. The constellation configuration optimization solution module performs joint optimization of constellation orbital parameters and configuration schemes to obtain the optimal or near-optimal constellation configuration schemes that satisfy multiple constraints.

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