Optimization method and system for photometric multi-station intersection positioning station arrangement

Abstract

This invention provides a method and system for optimizing the layout of optical multi-station intersection positioning. The method includes: constructing a geometric factor (GDOP) model reflecting the amplification of positioning error by the measurement error of a spatial target under the station layout; constructing a multi-constraint station layout optimization model based on the minimum GDOP model, the maximum total coverage of the monitoring range, and the strongest robustness index of the multi-station system, combined with constraint functions constructed from terrain-allowed deployment area constraints, measurement pitch angle constraints, line-of-sight terrain constraints, and station spacing baseline constraints; and constructing an improved NSGA-II genetic algorithm for solving the multi-constraint station layout optimization model, using the improved NSGA-II genetic algorithm to solve for the position of each station. This achieves global optimal station layout search, realizes intelligent optimization of the station layout scheme, and improves the accuracy of optical intersection positioning and the robustness of the system.

Description

Technical Field

[0001] This invention relates to the field of station layout, specifically to an optimized method and system for optical multi-station intersection positioning. Background Technology

[0002] Optical theodolites, as crucial equipment for space target tracking and measurement, achieve target tracking and positioning by measuring the relative azimuth and relative pitch angles. Since single-station optical equipment can only acquire angle information and cannot directly determine target distance, multi-station intersection positioning is typically employed in practical applications. This involves jointly calculating the target's three-dimensional coordinates using angle measurements from multiple stations. The accuracy of multi-station intersection positioning depends not only on the measurement accuracy of each station but also closely on the spatial geometry between them. An inappropriate station layout can lead to an excessively large Geometric Dilution of Precision (GDOP), significantly amplifying measurement errors during the intersection process. Under the same measurement accuracy conditions, the GDOP can differ by several times or even tens of times depending on the station layout, affecting the overall system performance. For intersection positioning, Yan et al. laid the foundation for simplified solution strategies for different numbers of stations using trilateration positioning methods. Kartal et al. simulated different observation geometries, revealing the spatial distribution patterns of GDOP. In the field of station deployment optimization, Zhang Zhengchao et al. systematically analyzed the positioning accuracy characteristics under different deployment modes by comparing typical geometric topologies such as T-type and Y-type. In recent years, intelligent optimization algorithms have provided new approaches to solving complex station deployment optimization problems. Zhang Jun et al. attempted to use a genetic algorithm to construct a cross-sectional measurement station deployment model, verifying the effectiveness of heuristic algorithms in handling nonlinear station deployment constraints.

[0003] Existing technologies have the following problems: 1. They mostly use minimizing a single GDOP as the optimization objective, ignoring practical engineering needs such as coverage and system robustness; 2. They do not adequately consider constraints such as terrain occlusion, effective observation elevation angle, and baseline distance in complex environments; 3. Most solutions focus on empirical station deployment in specific scenarios, lacking a systematic optimization method that can adapt to different terrains and resource configurations, and traditional optimization algorithms are prone to getting trapped in local optima when facing large-scale search spaces. Summary of the Invention

[0004] This invention provides a method and system for optimizing the deployment of optical measurement multi-station intersection positioning, which can solve the above-mentioned technical problems in the prior art.

[0005] To achieve the above objectives, in one aspect, embodiments of the present invention provide a method for optimizing the deployment of optical measurement multi-station intersection positioning, comprising:

[0006] A multi-station optical tracking and positioning model is constructed, which uses multiple stations to perform optical tracking and measurement of space targets; a geometric factor (GDOP) model is constructed, which reflects the amplification of positioning error by the measurement error of space targets under the station layout.

[0007] Based on the minimum geometric factor GDOP model, the maximum total coverage of the monitoring range, and the strongest robustness index of the multi-station system, a constraint function is constructed by combining the terrain-allowed deployment area constraint, measurement elevation angle constraint, line-of-sight terrain visibility constraint, and station spacing baseline constraint. The layout of multiple stations is then constructed into a multi-constraint station layout optimization model. The parameters of the improved NSGA-II genetic algorithm are defined, and an improved NSGA-II genetic algorithm is constructed based on the parameters of the improved NSGA-II genetic algorithm to solve the multi-constraint station layout optimization model.

[0008] The improved NSGA-II genetic algorithm was used to solve for the location of each station.

[0009] On the other hand, embodiments of the present invention provide an optical measurement multi-station intersection positioning and site optimization system, comprising:

[0010] The geometric factor GDOP model building unit is used to construct an optical multi-station intersection positioning model that uses multiple stations to perform optical tracking measurements on space targets; and to construct a geometric factor GDOP model that reflects the amplification of positioning error by the measurement error of space targets under the station layout.

[0011] The genetic algorithm construction unit is used to construct a multi-constraint station layout optimization model based on the constraints of the geometric factor GDOP model (minimum, maximum total coverage of monitoring range, and strongest robustness index of multi-station system), combined with the constraints of terrain-allowed deployment area, measurement pitch angle, line-of-sight terrain visibility, and station spacing baseline. The parameters of the improved NSGA-II genetic algorithm are defined, and an improved NSGA-II genetic algorithm for solving the multi-constraint station layout optimization model is constructed based on the parameters of the improved NSGA-II genetic algorithm.

[0012] The solution unit is used to solve for the location of each station using the improved NSGA-II genetic algorithm.

[0013] Thirdly, embodiments of the present invention provide a computer-readable storage medium storing one or more programs, which, when executed by a computer device, cause the computer device to perform the aforementioned optical measurement multi-station intersection positioning optimization method.

[0014] Fourthly, embodiments of the present invention provide a computer device, comprising:

[0015] A processor; and a memory configured to store computer-executable instructions, which, when executed, cause the processor to perform the aforementioned optical measurement multi-station intersection positioning optimization method.

[0016] The above technical solution has the following beneficial effects: In optical tracking and measurement of space targets, the spatial layout of the stations directly affects the accuracy of optical rendezvous positioning and the robustness of the system. For the station layout optimization problem of the optical multi-station rendezvous positioning system, a multi-constraint optimization problem is constructed that considers positioning accuracy (Geometric Difference of Precision, GDOP), coverage capability, and system robustness. A station layout optimization model is constructed that includes multiple constraints from practical engineering, such as terrain occlusion, baseline length constraints, and minimum elevation angle, making the model closer to engineering reality. Based on this, the NSGA-II algorithm is specifically improved, namely, the implementation strategy of the genetic algorithm is improved by introducing a fitness function with a penalty term, adopting adaptive crossover and mutation probabilities, and an elite retention strategy to form an improved standard non-dominated sorting genetic algorithm (NSGA-II), effectively balancing the algorithm's global search capability and local convergence speed. By maintaining population diversity through non-dominated sorting and crowding mechanisms to solve complex nonlinear optimization problems, the search for the globally optimal station layout scheme is realized, achieving intelligent optimization of the station layout scheme. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of an optical measurement multi-station intersection positioning optimization system according to an embodiment of the present invention. Figure 2 This is a logical structure diagram of an optical measurement multi-station intersection positioning and deployment optimization system according to an embodiment of the present invention; Figure 3 This is an embodiment of the present invention showing the station layout and target trajectory of a regular polygonal measuring station; Figure 4 These are schematic diagrams of three terrain scenarios according to embodiments of the present invention, wherein (a) is flat terrain, (b) is single-peak terrain, and (c) is complex terrain; Figure 5 The results of station layout optimization in a flat terrain scene with 6 regular polygons according to the present invention are shown in (a) and (b) respectively. Figure 6 This is the performance index convergence process in a 6-station regular polygon flat terrain scenario according to an embodiment of the present invention; Figure 7 The above are the station layout optimization results under the 6-station regular polygonal single-peak terrain scenario of the present invention, where (a) is a comparison of station layout before and after optimization, and (b) is a comparison of GDOP before and after optimization. Figure 8 This is the performance index convergence process under a 6-station regular polygonal single-peak terrain scenario according to an embodiment of the present invention; Figure 9 The following are the station layout optimization results under a complex terrain scenario with 6 regular polygons in this embodiment of the invention. Among them, (a) is a comparison of station layout before and after optimization, and (b) is a comparison of GDOP before and after optimization. Figure 10 This is the performance index convergence process in a complex terrain scenario with 6 regular polygons in this embodiment of the invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] like Figure 1 As shown, in conjunction with embodiments of the present invention, a method for optimizing the deployment of optical measurement multi-station intersection positioning is provided, including:

[0021] S101: Construct an optical measurement multi-station intersection positioning model that uses multiple stations to perform optical tracking measurements on space targets; construct a geometric factor GDOP model that reflects the amplification of positioning error by the measurement error of space targets under the station layout.

[0022] S102: Based on the geometric factor GDOP model, the layout of multiple stations is constructed into a multi-constraint station layout optimization model; the parameters of the improved NSGA-II genetic algorithm are defined, and an improved NSGA-II genetic algorithm for solving the multi-constraint station layout optimization model is constructed based on the parameters of the improved NSGA-II genetic algorithm.

[0023] S103: The improved NSGA-II genetic algorithm is used to solve for the location of each station.

[0024] like Figure 2 As shown, in conjunction with embodiments of the present invention, a multi-station optical measurement intersection positioning optimization system is provided, comprising:

[0025] The geometric factor GDOP model construction unit 21 is used to construct an optical multi-station intersection positioning model that uses multiple stations to perform optical tracking measurements on space targets; and to construct a geometric factor GDOP model that reflects the amplification of positioning error by the measurement error of space targets under the station layout.

[0026] Genetic algorithm construction unit 22 is used to construct a multi-constraint station layout optimization model based on the constraint function constructed by combining the constraints of terrain-allowed deployment area, measurement pitch angle, line-of-sight terrain, and station spacing baseline, based on the minimum geometric factor GDOP model, the maximum total coverage of the monitoring range, and the strongest robustness index of the multi-station system. The parameters of the improved NSGA-II genetic algorithm are defined, and an improved NSGA-II genetic algorithm for solving the multi-constraint station layout optimization model is constructed based on the parameters of the improved NSGA-II genetic algorithm.

[0027] Solver 23 is used to solve for the location of each station using the improved NSGA-II genetic algorithm.

[0028] In conjunction with embodiments of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores one or more programs, which, when executed by a computer device, cause the computer device to perform the aforementioned optical measurement multi-station intersection positioning optimization method.

[0029] In conjunction with embodiments of the present invention, a computer device is provided, comprising:

[0030] A processor; and a memory configured to store computer-executable instructions, which, when executed, cause the processor to perform the aforementioned optical measurement multi-station intersection positioning optimization method.

[0031] The technical solutions of the present invention will be described in detail below with reference to specific application examples. For technical details not described in the implementation process, please refer to the relevant descriptions above.

[0032] In optical tracking and measurement of space targets, the spatial layout of stations directly affects the accuracy of optical rendezvous and positioning and the robustness of the system. To address the station layout optimization problem of optical multi-station rendezvous and positioning systems, a multi-constraint optimization problem was constructed, balancing positioning accuracy (Geometric Difference of Precision, GDOP), coverage capability, and system robustness. A station layout optimization model was built, incorporating practical engineering constraints such as terrain occlusion, baseline length constraints, and minimum elevation angle, making the model more closely reflect engineering realities. Based on this, the NSGA-II algorithm was specifically improved by refining the implementation strategy of the genetic algorithm, introducing a fitness function with a penalty term, and employing adaptive crossover and mutation probabilities as well as an elite retention strategy, forming an improved standard non-dominated sorting genetic algorithm (NSGA-II). This effectively balances the algorithm's global search capability and local convergence speed. By maintaining population diversity through non-dominated sorting and crowding mechanisms, complex nonlinear optimization problems are solved, achieving global optimal station layout search and realizing intelligent optimization of station layout schemes.

[0033] I. Principles of the GDOP Intersection Model

[0034] (I) In S101, an optical measurement multi-station rendezvous and positioning model is constructed, which uses multiple stations to perform optical tracking measurements on space targets. Specifically, this includes:

[0035] Survey station The measurement data is for the azimuth angle. And measuring pitch angle The corresponding angle measurement accuracy is and The coordinates of the station under the launch system are , Indicates site , For the total number of stations, there are ( ( ) Several monitoring stations need to be optimized for station layout. Indicates the sequence number of the measurement data. Where n is the total number of time-series observation samples. Since subsequent calculations are performed point-by-point, the stations... The measurement data sequence, i.e., the measurement azimuth angle Sequence and measurement of pitch angle Sequence using and express.

[0036] Station Observing space targets in the launch system axis, axis, Direction cosine along the axis Transformation matrix from measurement frame to emission frame calculate:

[0037] (1)

[0038] in, The transformation matrix from the measurement frame to the transmission frame is... , , The forms are as follows:

[0039] (2)

[0040] in, , , These are the roll angle, pitch angle, and yaw angle, respectively, caused by the space target's own attitude deflection.

[0041] Assume the space target is relative to the station Relative azimuth and relative elevation angles under the launch system and for:

[0042] , (3)

[0043] Among them, relative azimuth angle Projecting spatial targets onto Vectors on the plane Angle between axes; relative pitch angle For space targets and Angle between two planes.

[0044] Define the direction cosine change coefficient matrix for the measurement and launch systems. , and monitoring station observation error covariance matrix for:

[0045] , (4)

[0046] (5)

[0047] In equations (4) and (5), the subscripts This matrix represents the coefficient matrix used to describe the mapping relationship between the measurement frame and the transmission frame. Indicates the first One monitoring station.

[0048] Station Weight matrix in the measurement system for:

[0049] (6)

[0050] Construct the total weight matrix for all stations :

[0051] (7)

[0052] After the calculation is completed, the first two stations ( =1, Calculate the initial value of the least squares difference based on the observed data (=2). The calculation process is shown below:

[0053] definition:

[0054] (8)

[0055] This represents the cosine value of the angle between the lines of sight of the two observation stations. This represents the projection of the inter-station baseline vector onto the line of sight at station 1. This represents the projection of the inter-station baseline vector onto the line of sight at station 2;

[0056] Calculate the two stations ( =1, =2) Estimated distance to space target and They are respectively:

[0057] , (9)

[0058] This represents the estimated distance from station 1 to the space target. This represents the estimated distance from station 2 to the space target;

[0059] Least squares difference initial value for:

[0060] , , (10)

[0061] Indicates the first Estimated distances from each station to the target;

[0062] Let the current number be... The target position for the next iteration is Calculate the geometric relationship between each station and the space target:

[0063] , , (11)

[0064] No. Horizontal distance from each station to the space target and slant distance for:

[0065] , (12)

[0066] Calculate the relative azimuth and relative elevation angles and Theoretical observations:

[0067] , (13)

[0068] like Then update .

[0069] Construct relative azimuth and relative elevation angles and Observation residual vector :

[0070] (14)

[0071] in, , , .

[0072] First-order partial derivative coefficient matrix The elements are:

[0073] (15)

[0074] in, , , .

[0075] For participating in the intersection calculation The observation residual vector composed of individual stations, , Given by the formula; relative azimuth angle For the target location The partial derivative vector, Relative pitch angle For the target location The vector of partial derivatives;

[0076] The solution is obtained using the weighted least squares method, with the initial value of the target position being... Coordinates are At that time, the calculation of the first... The coordinate correction for the next iteration is:

[0077] (16)

[0078] like ,Pick .

[0079] Otherwise Repeat the above calculation process until... ,Pick .

[0080] The accuracy matrix of the above least-squares intersection positioning is:

[0081] (17)

[0082] The above technical solution is also a specific embodiment of the geometric factor GDOP model construction unit 21.

[0083] (ii) In S101, a geometric factor GDOP model is constructed to reflect the amplification of positioning error by measurement error of space target under the station layout, including:

[0084] The geometric factor GDOP reflects the degree to which measurement errors amplify positioning errors under a given station layout; the larger the geometric factor GDOP, the greater the positioning error. Specifically, the geometric factor GDOP can be calculated from the error of the positioning equation.

[0085] The root mean square error of the location is defined as:

[0086] (18)

[0087] Based on the weighted least squares estimation iterative formula constructed by formula (16), the covariance matrix of the position solution is given by formula (17), and then the root mean square error formula (18) is obtained. Based on formulas (16)-(18), the geometric factor GDOP is defined as:

[0088] (19)

[0089] in, This represents the average variance of the angle measurement.

[0090] The above technical solution is also a specific embodiment of the geometric factor GDOP model construction unit 21.

[0091] II. Optimization Solution of Site Layout Based on Genetic Algorithm

[0092] (I) Multi-constraint site layout optimization model

[0093] In S102, based on the minimum geometric factor GDOP model, the maximum total coverage of the monitoring range, and the strongest robustness index of the multi-station system, a constraint function is constructed by combining the constraints of terrain-allowed deployment area, measurement elevation angle, line-of-sight terrain visibility, and station spacing baseline constraints. This constructs a multi-constraint station layout optimization model, including:

[0094] To address the problem of multi-site collaborative deployment under complex constraints, it is necessary to establish a multi-constraint optimization model to find the optimal deployment scheme that balances positioning accuracy, coverage capability, and system robustness.

[0095] 1. Coverage capability evaluation

[0096] To quantify the effective detection range (coverage capability) of the monitoring station network, the monitoring range is divided into... There are 1 grid point, denoted as _ . Introducing a terrain visibility discrimination function. When grid points With grid points When the line of sight between them is higher than the elevation of the surrounding terrain ,otherwise Definition of the first The first station for the first Effective observed state variables of each grid point This effective observed state variable Both the measurement elevation angle constraint and the terrain line-of-sight constraint must be satisfied simultaneously:

[0097] (20)

[0098] Among them, the measurement pitch angle limitation It can avoid significant atmospheric refraction errors and ground clutter interference at low elevation angles.

[0099] Define the total coverage function of the monitoring network over the monitoring range as follows:

[0100] (twenty one)

[0101] in, This is an indicator function.

[0102] 2. System robustness evaluation

[0103] Considering the potential for single-station optical measurement equipment failure, communication link interruption, or data anomalies in actual measurements, it is necessary to evaluate the performance retention capability of a multi-station system when a certain station is missing. Define robustness evaluation indicators for multi-station systems. The mean of the relative rate of change of the system's geometric factor GDOP before and after the station failure:

[0104] (twenty two)

[0105] in, The geometric factor is the system's normal operating condition. To remove the first Geometric factors after each station. Robustness evaluation index of multi-station systems. The closer the value is to 1, the smaller the impact of station failure on the overall positioning accuracy of the system, and the stronger the system's fault tolerance.

[0106] 3. Multi-constraint optimization model

[0107] Based on the mean values ​​of the geometric factor GDOP corresponding to formula (19), the coverage function corresponding to formula (21), and the relative change rate of the geometric factor GDOP corresponding to formula (22), a multi-station layout multi-constraint optimization mathematical model is established. Let the first... The position vector of the transmitter system of each station is The mathematical model for multi-site layout and multi-constraint optimization is expressed as follows: .

[0108] The optimization constraint function aims to minimize GDOP, maximize the total coverage of the monitoring range, and maximize the robustness of the multi-station system. The constraint function is defined as follows:

[0109] ,st (twenty three)

[0110] The meanings of the constraints in equation (23) are as follows:

[0111] 1. Terrain-permissible deployment area constraints: station coordinates Must be located in an area where the terrain allows for deployment. Inside, and the station elevation It shall not be lower than the local ground elevation. ;

[0112] 2. Measurement elevation angle constraints and line-of-sight constraints: Ensure that the station meets the minimum elevation angle limit for spatial targets and that the line of sight is not obstructed by terrain;

[0113] 3. Quantity constraint: Total number of stations No more than the system's maximum capacity ;

[0114] 4. Baseline Constraints Between Stations: Based on the effective tracking distance (baseline length) of the optical measuring equipment within the stations and the communication synchronization requirements, the distance between stations must be within [specific range]. Within the range, and with terrain visibility constraints maintained between stations to meet group communication synchronization requirements.

[0115] The above technical solution is also a specific embodiment of the genetic algorithm construction unit 22.

[0116] (II) Genetic Algorithm

[0117] The multi-station, multi-constraint station layout optimization problem exhibits significant mathematical complexity: 1. There are numerous optimization constraints, and the three indicators of GDOP, coverage, and robustness must be considered simultaneously; 2. There is a complex nonlinear mapping relationship between GDOP and the spatial location of the stations; 3. The multi-station configuration scheme corresponds to a high-dimensional continuous decision space, resulting in a large problem scale; 4. The multi-constraint model involves multiple factors such as terrain shading, measurement elevation angle, and baseline length; 5. The constraint function has a large number of local extrema within the feasible region, exhibiting typical multimodal characteristics.

[0118] The aforementioned characteristics make this station placement optimization problem difficult to solve effectively using traditional gradient descent methods: 1. Traditional methods struggle to handle multi-constrained non-convex optimization problems; 2. They are highly sensitive to initial values ​​and easily get trapped in local optima. Genetic algorithms, on the other hand, are a global random search method that simulates natural selection and genetic mechanisms. They have advantages such as not relying on gradient information, having no special requirements for the form of constraint functions, and being naturally adaptable to multi-constrained optimization. This invention, based on the standard Nondominated Sorting Genetic Algorithm II (NSGA-II), improves the algorithm for the station placement optimization problem and solves the optimization problem.

[0119] In S102, the parameters of the improved NSGA-II genetic algorithm are defined, including:

[0120] 1. Chromosome vector. The decision variable for each station is determined by its three-dimensional coordinates in the emission frame. Indicates. All. The coordinates of each station are arranged sequentially to form a chromosome vector. :

[0121] (twenty four)

[0122] Chromosome dimensions are Each component of the chromosome takes its value within the terrain-permitted deployment area of ​​the corresponding station, corresponding to the [missing information]. Spatial location of each station Consistent with the definition in formula (23).

[0123] 2. Fitness function. Use the optimization constraint function in formula (23). , , Constructing a multi-constraint fitness function:

[0124] (25)

[0125] To handle the multiple constraints in formula (23), an adaptive penalty term is introduced for each component of the optimization constraint function:

[0126] (26)

[0127] in, For the first The dynamic penalty factor of an optimization constraint function. The constraint violation degree is the cumulative value of all constraint violations:

[0128] (27)

[0129] In the formula, For the first The violation of an optimization constraint function. When When the solution fully satisfies the constraints, the penalty term degenerates to 0, and the multi-constraint fitness function degenerates to the original optimization constraint function. When the constraints are violated, the dynamic penalty factor increases dynamically with the degree of violation, thereby ensuring the feasibility of the solution while avoiding excessive narrowing of the effective search space.

[0130] 3. Non-dominated ranking and crowding calculation

[0131] Multi-constraint fitness functions provide penalized evaluation vectors for multi-constraint problems, but ensuring both solution quality and diversity during population evolution requires the introduction of non-dominated ordering and crowding mechanisms. Non-dominated ordering determines the priority level of solutions, while crowding calculation maintains the uniformity of solution distribution within the same level.

[0132] (1) Non-dominated sorting. In the genetic algorithm system, "solution" and "individual" are equivalent concepts, both corresponding to a complete placement scheme. For any two individuals in the population... and If the following conditions are met simultaneously:

[0133] (28)

[0134] Then it is called Dominate , recorded as .

[0135] The population is hierarchically classified according to dominance relationships, and all dissociations not dominated by any individual constitute the first Pareto front. Remove from the population The above process is then repeated to obtain the second frontier. This process is repeated until all individuals in the population have completed the stratification. The closer they are... The better the overall performance of the solution, the higher its retention priority in the selection operation.

[0136] (2) Crowding distance. To maintain the uniformity of solution distribution on the same Pareto front, the crowding distance is calculated for individuals within the same rank. All individuals within that rank are then grouped according to their rank. The constraint function values ​​are sorted in ascending order, individual Under constraints The directional congestion distance component is defined as the ratio of the difference between the constraint values ​​of its left and right adjacent individuals to the range of that constraint value:

[0137] (29)

[0138] Summing the components along the directions of the three optimization constraint functions yields the individual... Total congestion distance:

[0139] (30)

[0140] Individuals located at the ends of the sorting sequence, i.e., the extreme points of each constraint, have a crowding distance set to positive infinity to ensure that they are preferentially retained during selection. The larger the crowding distance, the more sparse and isolated the solution is in the constraint space, and the higher its selection priority within the same Pareto level. This avoids excessive population aggregation in the local region of the frontier and ensures a globally uniform coverage of the Pareto front.

[0141] 4. Genetic operators.

[0142] Genetic operators are applied to chromosome vectors The real components of the corresponding formula (24) include the selection operator, crossover operator, and mutation operator. The calculation process uses the parent population and the offspring population. The parent population is the output of the selection operator and the input of the crossover and mutation operators, serving as a guiding mechanism for the direction of population evolution. Through the approach of "selection (choosing the best among the best) - crossover (information recombination) - mutation (introducing randomness)," it is ensured that the station layout scheme can approach the Pareto optimal front that balances GDOP, coverage, and robustness in each generation of evolution. The offspring population is calculated based on the parent population and merged with the original parent population to expand the total number of station configuration schemes in the search space, realizing the iterative evolution of the station layout scheme in the search space and ensuring that the population evolves towards a higher-performance Pareto front. The execution steps and mathematical expressions of each genetic operator are given below.

[0143] (1) Selection operator: This operator selects individuals of higher quality from the current population as parents to generate the next generation.

[0144] Two individuals are randomly selected from the population each time. , The winner is determined and added to the parent set according to the following rules:

[0145] If the two have different non-dominant ranking levels, retain the one with the lower ranking; the lower the ranking, the closer they are. The better the overall performance; if the two have the same non-dominated ranking level, the total congestion distance is retained. Larger solutions, with greater total crowding distances, indicate greater isolation within the constraint space, which helps maintain population diversity. Repeat the above process until a solution is selected. Each parent individual.

[0146] (2) Crossover operator: This operator uses a simulated binary crossover calculation method to recombine the information of two parent individuals to generate a new child individual.

[0147] Let the two parent chromosomes be... , The first chromosome Dimensional components ,remember , The corresponding number Dimensional component values , Set the crossover probability. Determine whether to perform crossover on this dimension component. The larger the value, the more significant the difference between offspring and parents. Each dimension has [number of components]. The probability of performing crossover is [not specified]. If the crossover value is 0.3, then each component in each dimension has a 30% probability of performing a crossover and a 70% probability of not performing one. If a crossover is performed in that dimension, the corresponding offspring component is generated according to the following steps. , :

[0148] The first step is to generate uniformly random numbers. , ( It is a mathematical symbol, read as "follows a distribution of...". This represents a standard uniform distribution, meaning the values ​​range from 0 to 1, and each number has an equal probability of appearing; the overall meaning is: generate a random number that follows a uniform distribution from 0 to 1. Calculate the expansion factor :

[0149] (31)

[0150] Used to control the distance between offspring and parents: Offspring are distributed between their parents. Offspring are distributed outside of their parents. The distribution index is used to control the distribution shape of the expansion factor β. The larger, The more concentrated the offspring are around 1, the more they tend to resemble their parents; The smaller, The more dispersed the distribution of offspring, the further away they are from their parents.

[0151] The second step is based on the expansion factor. Generate offspring components:

[0152] , (32)

[0153] All chromosomes Repeat the above operations on the dimensional components to obtain two complete offspring chromosomes. , .

[0154] (3) Mutation operator: This operator uses a polynomial mutation calculation method to introduce random perturbation in the local area of ​​the offspring chromosome to maintain population diversity and avoid premature convergence of the algorithm.

[0155] offspring chromosomes or The dimensional components, with mutation probability Determine whether to perform mutation on this dimension; if so, let the component to be mutated be... Its allowed value range is The mutated component value is:

[0156] (33)

[0157] Among them, the disturbance quantity Given by the following multinomial distribution:

[0158] , (34)

[0159] in, (Same meaning as above) represents a uniformly random number. The distribution index is the variation index. The larger the disturbance, the greater the amount of disturbance. The more concentrated the disturbance is around 0, the more refined it is. The smaller the value, the smaller the disturbance. The more dispersed the distribution, the greater the magnitude of variation. (Probability of variation) To ensure that, on average, exactly one component of each chromosome mutates, the perturbation strength and the problem dimension are considered. Matching.

[0160] The above technical solution is also a specific embodiment of the genetic algorithm construction unit 22.

[0161] In S102, an improved NSGA-II genetic algorithm for solving multi-constraint site layout optimization models is constructed based on the parameters of the improved NSGA-II genetic algorithm, including:

[0162] Based on the above algorithm parameter definitions, a complete iterative solution process for the improved NSGA-II is presented. The algorithm starts with a randomly initialized population, drives the population to evolve generation by generation through genetic operators, and ensures the intergenerational continuation of high-quality solutions through an elite preservation mechanism, eventually converging to the Pareto optimal front. The specific steps are as follows.

[0163] 1. Initialization.

[0164] The size of the random generation is initial population The coordinates of each station are within the terrain-permitted deployment area. Uniform sampling within the population, and removal of individuals that do not satisfy the basic constraints of formula (23) to ensure the basic feasibility of the initial population. Calculate the multi-constraint fitness function for all individuals. Perform non-dominated sorting and crowding distance initialization.

[0165] 2. Genetic evolution.

[0166] In the Generation, by selecting operators based on the current population The parent set is generated, and the size is generated by the crossover operator (31)-(32) and the mutation operator (33)-(34). offspring population And calculate its multi-constraint fitness function. Merge the parent and child generations into a single scale. temporary population :

[0167] (35)

[0168] For temporary populations Perform non-dominated sorting to obtain the hierarchical front sequence. ; calculate and assign the congestion distance within each front edge according to formula (28)-formula (29).

[0169] 3. Environment selection.

[0170] Based on the principles of prioritizing non-dominant ranking levels and crowding distance within the same ranking level, from temporary populations... Selected from Individuals constitute the next generation population. The complete Pareto front is then incorporated sequentially. The process continues until the remaining capacity is insufficient to accommodate a complete Pareto front, resulting in a truncated front. For truncated fronts that cannot be fully accommodated, selection is performed in descending order of crowding distance to ensure a uniform distribution of the population within the constrained space. Furthermore, an elite retention ratio is set. ,Will Center front Each elite individual was directly retained until This ensures that excellent solutions are not lost due to random operations.

[0171] 4. Termination Condition. Repeat the above genetic evolution and environmental selection process until the number of iterations reaches a preset maximum value. When the time is up, the algorithm terminates and outputs the first Pareto front in the final population. This serves as the Pareto optimal solution set. To facilitate process monitoring, the evolution of the current optimal GDOP, coverage, and robustness metrics is recorded every 20 generations.

[0172] The above technical solution is also a specific embodiment of the genetic algorithm construction unit 22.

[0173] S103: The steps for solving the location of each station using the improved NSGA-II genetic algorithm are as follows:

[0174] After the algorithm terminates, it will return a Pareto front consisting of a set of non-dominated solutions. Each solution emphasizes one aspect of each of the three constraints, and there is no absolute superiority or inferiority among them. However, engineering practice requires a unique station layout scheme, therefore it is necessary to consider... The optimal compromise solution with the best overall performance is selected. This decision is made using the ideal point method, which uses the ideal optimal value of each constraint as a reference to objectively quantify the overall difference between each candidate solution and the optimal state, thus avoiding the uncertainty caused by subjective setting of weighting coefficients.

[0175] The ideal point is defined as the first Pareto front of each constraint function. The reference vector formed by obtaining the optimal values ​​above:

[0176] (36)

[0177] Since the three optimization constraint functions have different dimensions and orders of magnitude, the distance needs to be normalized. The first Pareto front is then calculated. Each solution Normalized Euclidean distance to the ideal point:

[0178] (37)

[0179] in, Represents the ideal optimal target vector. The first Pareto front indicates the Pareto front. There are 10 candidate solutions; and The first The optimization constraint function is at the first Pareto front. The maximum and minimum values ​​are used to eliminate the influence of dimensional differences. The final selection... The minimum solution is taken as a compromise:

[0180] (38)

[0181] This solution is the optimal complete station deployment scheme selected from the Pareto front, and it also provides the three-dimensional coordinates of all m stations. This solution is closest to the ideal point in the normalized optimization constraint function space, comprehensively considering GDOP accuracy, coverage, and system robustness, and can be used as the final station deployment scheme output.

[0182] The above technical solution is also a specific embodiment of the solving unit 23.

[0183] In summary, this invention makes targeted improvements to the traditional NSGA-II algorithm: First, an adaptive penalty function is introduced, employing a dynamic penalty factor for constraint violations to ensure solution feasibility while avoiding excessive narrowing of the search space; Second, an adaptive mutation rate and weight strategy are introduced, enabling the algorithm to automatically balance the proportion of global search and local exploitation at different evolutionary stages, effectively alleviating premature convergence and maintaining search stability; Third, feasible region-guided repair is performed to ensure population feasibility while avoiding excessive narrowing of the search space by the penalty function; Fourth, an elite retention strategy is adopted, retaining the best individuals from each generation. Fifth, trajectory weights are allocated to avoid interference from low-elevation observation conditions on the evaluation of the optimization target. Sixth, the uniform distribution of the Pareto front is maintained through crowding distance calculation to preserve population diversity. Seventh, decision variables are encoded with real numbers to directly represent station coordinates, avoiding the accuracy loss problem in binary encoding schemes.

[0184] III. Simulation Experiment

[0185] (a) Simulation Scenarios

[0186] (I-1) Ballistic trajectory parameters

[0187] A standard ballistic trajectory is used as the target motion model to comprehensively evaluate the positioning performance of different station deployment schemes in typical application scenarios. The target motion follows the ballistic equations:

[0188] ,

[0189] in, The trajectory is set to gravitational acceleration, and the other trajectory parameters are shown in Table 1. The trajectory is parabolic in shape and has typical characteristics of wide range and high maneuverability.

[0190] Table 1 Ballistic trajectory parameter configuration

[0191]

[0192] (I-2) Station Parameters

[0193] The station parameters are divided into Table 2, General Constraints for Stations, and Table 3, Geometric Scheme Parameters for Station Layout.

[0194] Table 2 General Constraint Configuration for Observation Stations

[0195]

[0196] Table 3 Parameter Configuration for Site Layout Geometric Scheme

[0197]

[0198] The station layout schemes in Table 3 are selected based on the practical engineering requirements of optical measurement. The measurement process requires at least 3 and at most 10 stations to participate in the calculation, ensuring the solvability of the target location and avoiding computational redundancy. All five schemes are used as initial station layout inputs for the improved NSGA-II algorithm, and the performance comparison before and after optimization is used to quantify the algorithm's improvement effect. Taking a 6-station regular polygon layout as an example, the initial station layout and target trajectory are as follows: Figure 3 As shown.

[0199] (I-3) Terrain Scene

[0200] To examine the algorithm's adaptability under different terrain conditions, three types of terrain models were defined:

[0201] 1. Flat terrain. All stations have an elevation of zero, serving as an ideal reference benchmark:

[0202] .

[0203] 2. Single-peak terrain. A Gaussian-shaped peak, approximately 1500m high, exists in the center of the region; the placement of monitoring stations must avoid areas with obstruction.

[0204] .

[0205] 3. Complex terrain. A Gaussian mixture model was used to simulate the superposition of multiple peaks, with multiple peak-valley structures distributed within the observation area. The terrain was complex and the line-of-sight obstruction conditions were more severe. The height, position, and width parameters of each peak in the terrain function were fixed using random seeds to ensure experimental repeatability.

[0206] ,

[0207] In the formula, For the first The center of the height of each mountain peak; The horizontal coordinates of the mountain peak's center; and Control the mountain peaks separately and The directional range of expansion. The three terrain scenarios used in the simulation experiment are as follows: Figure 4 As shown:

[0208] (I-4) Algorithm Parameters

[0209] An improved NSGA-II algorithm is used to solve the optical multi-station intersection positioning optimization problem. The basic parameter configuration of the algorithm is shown in Table 4.

[0210] Table 4 Basic parameter configuration of NSGA-II algorithm

[0211]

[0212] The following improvements were made to the NSGA-II algorithm to enhance its convergence and search efficiency in complex site deployment scenarios:

[0213] 1. Adaptive mutation rate strategy. The actual mutation probability is dynamically adjusted as the iteration progresses:

[0214] ,

[0215] in Let be the current iteration number. This strategy enables the algorithm to automatically balance the proportion of global search and local exploration at different evolutionary stages, effectively mitigating the problem of premature convergence.

[0216] 2. Adaptive Weighting Strategy. Let the base weights be... These correspond to three optimization objectives: GDOP (Gross Diversity Optimization), coverage, and robustness. In the early stages of optimization, the focus is on coverage to expand the search range; in the middle stages, balanced optimization is performed; and in the later stages, the focus shifts to GDOP accuracy. When population diversity falls below a set threshold, the weight adjustment is automatically halved to maintain search stability and prevent Pareto front degradation caused by sudden weight mutations.

[0217] 3. Feasibility-guided repair. When offspring individuals generated by genetic operators violate baseline constraints, causing station spacing to be out of range... Within the set range, iterative push-pull operations are performed using the maximum number of repair rounds to adjust overlapping or excessively distant stations to a feasible distance. This strategy ensures population feasibility while avoiding excessive narrowing of the search space by the penalty function.

[0218] 4. Elite Local Search. Every 20 generations, the top 5 elite individuals in the Pareto front are searched for optimal solutions in both positive and negative directions for each decision variable, using weighted fitness. To improve the basis, accelerate the approximation of the Pareto front to the true optimal surface, and significantly improve the quality of the solution.

[0219] 5. Trajectory Weighting. The last 30% of sampling points on the ballistic trajectory are assigned double the weight, while the remaining points have a weight of 1.

[0220] ,

[0221] This strategy focuses the optimization process on the positioning accuracy of the reentry phase, which meets the accuracy requirements for key ballistic segments in engineering practice and avoids interference from low elevation angle observation conditions on the evaluation of the optimization target.

[0222] For easy reference, all the improved NSGA-II algorithm parameters are summarized in Table 5.

[0223] Table 5. New parameter configurations for the improved NSGA-II algorithm

[0224]

[0225] (II) Optimization Results of Site Layout

[0226] The improved NSGA-II algorithm will be demonstrated in various geometric deployment scenarios, its effectiveness in optical multi-station deployment optimization will be quantitatively verified, and the optimization results of different deployment configurations under various terrain constraints will be shown.

[0227] (II-1) 3-station T-shaped scene

[0228] Table 6 shows a comparison of the site deployment performance and algorithm optimization results in a 3-site T-shaped scenario:

[0229] Table 6. Comparison of station deployment performance before and after optimization in a 3-station T-shaped scenario.

[0230]

[0231] (II-2) Y-shaped scenario with 4 stations

[0232] Table 7 shows a comparison of the deployment performance and algorithm optimization results for a 4-station Y-shaped scenario:

[0233] Table 7 Comparison of station deployment performance before and after optimization in a 4-station Y-shaped scenario

[0234]

[0235] (II-3) 6-station regular polygon scene

[0236] Table 8 shows the performance comparison of station placement and algorithm optimization in a 6-station regular polygon scene. Figure 5 Figure 10 As shown:

[0237] Table 8. Comparison of station deployment performance before and after optimization in a 6-station regular polygon scene.

[0238]

[0239] (II-4) 8-station diamond-shaped scene

[0240] Table 9 shows the performance comparison of station deployment and algorithm optimization in an 8-station diamond-shaped scenario:

[0241] Table 9 Comparison of station layout performance before and after optimization in 8-station diamond-shaped scenario

[0242]

[0243] (II-5) 10 random scenarios

[0244] Table 10 shows the performance comparison of station deployment and algorithm optimization in a random 10-station scenario:

[0245] Table 10 Comparison of station deployment performance before and after optimization in a random 10-station scenario

[0246]

[0247] To address the challenge of station placement optimization in optical multi-station intersection positioning, a global optimization method based on a genetic algorithm is proposed. With geometrical precision factor (GDOP), observation coverage, and system robustness as multiple objectives, and incorporating practical factors such as terrain occlusion, baseline length constraints, and minimum elevation angle, a comprehensive optimization model with multiple constraints is constructed, making the model more closely reflect engineering realities. The implementation strategy of the genetic algorithm is improved by introducing a fitness function with a penalty term and employing adaptive crossover and mutation probabilities, as well as an elite retention strategy, effectively balancing the algorithm's global search capability and local convergence speed. Extensive simulation verification is conducted. Comparative experiments under different terrain and station numbers demonstrate that the improved NSGA-II algorithm exhibits fast convergence speed, high solution quality, and insensitivity to the initial population, demonstrating good robustness.

[0248] In the above detailed description, various features are combined together in a single embodiment to simplify this disclosure. This approach to disclosure should not be construed as reflecting an intention that embodiments of the claimed subject matter require more features than are explicitly stated in each claim. Rather, as reflected in the appended claims, the invention is presented with fewer features than all of the features of the single disclosed embodiment. Therefore, the appended claims are hereby explicitly incorporated into the detailed description, wherein each claim stands alone as a preferred embodiment of the invention.

[0249] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing station arrangement in light measurement multi-station intersection positioning, characterized in that, include: Construct an optical measurement multi-station intersection positioning model that uses multiple stations to perform optical tracking and measurement of space targets; A geometric factor GDOP model is constructed to reflect the amplification of positioning error by measurement error of space targets under the station layout. Based on the minimum geometric factor GDOP model, the maximum total coverage of the monitoring range, and the strongest robustness index of the multi-station system, a constraint function is constructed by combining the terrain-allowed deployment area constraint, measurement elevation angle constraint, line-of-sight terrain visibility constraint, and station spacing baseline constraint. The layout of multiple stations is then constructed into a multi-constraint station layout optimization model. The parameters of the improved NSGA-II genetic algorithm are defined, and an improved NSGA-II genetic algorithm is constructed based on the parameters of the improved NSGA-II genetic algorithm to solve the multi-constraint station layout optimization model. The improved NSGA-II genetic algorithm was used to solve for the location of each station.

2. The method of claim 1, wherein: A multi-station optical measurement rendezvous and positioning model is constructed, employing multiple stations to perform optical tracking measurements on space targets, including: Survey station The measurement data is for the azimuth angle. And measuring pitch angle The corresponding angle measurement accuracy is and The coordinates of the station under the launch system are , Indicates site , For the total number of stations, there are One testing station needs to be optimized in terms of its layout. , Indicates the sequence number of the measurement data. , where n is the number of time-series observation samples; the station Measurement azimuth Sequence and measurement of pitch angle The sequences are respectively represented as and express; Station Observing space targets under the launch system axis, axis, Direction cosine along the axis Transformation matrix from measurement frame to emission frame calculate: （1） in, Let be the transformation matrix from the measurement frame to the transmission frame. , , The formats are as follows: （2） in, , and These are the roll angle, pitch angle, and yaw angle generated by the space target's own attitude deflection, respectively. Assume the space target is relative to the station The relative azimuth and relative elevation angles under the launch system are: and for: , （3） Among them, relative azimuth angle Projecting spatial targets onto Vectors on the plane Angle between axes; relative pitch angle For space targets and Angle between planes; Define the direction cosine change coefficient matrix for the measurement and launch systems. , and monitoring station observation error covariance matrix for: , （4） （5） In equations (4) and (5), the subscripts This matrix represents the coefficient matrix used to describe the mapping relationship between the measurement frame and the transmission frame; Station Weight matrix in the measurement system for: （6） Construct the total weight matrix for all stations : （7） Using the first two stations =1 and Calculate the initial value of the least squares difference from the observed data of =2. Specifically, this includes: definition: （8） This represents the cosine value of the angle between the lines of sight of the two observation stations. This represents the projection of the inter-station baseline vector onto the line of sight at station 1. This represents the projection of the inter-station baseline vector onto the line of sight at station 2; Calculate two stations =1 and =2, estimated distance to the space target: , （9） This represents the estimated distance from station 1 to the target. This represents the estimated distance from station 2 to the space target; Least squares difference initial value for: , , （10） Indicates the first Estimated distances from each station to the space target; Let the current number be... The target position for the next iteration is Calculate the geometric relationship between each station and the space target: , , （11） No. Horizontal distance from each station to the space target and slant distance for: , （12） Calculate the relative azimuth and relative elevation angles and Theoretical observations: , （13） like Then update ; Construct relative azimuth and relative elevation angles and Observation residual vector : （14） in, , , ; First-order partial derivative coefficient matrix The elements are: （15） in, , , ; For participating in the intersection calculation The observation residual vector composed of individual stations, , Given by the formula; relative azimuth angle For the target location The partial derivative vector, Relative pitch angle For the target location The vector of partial derivatives; The solution is obtained using the weighted least squares method, with the initial value of the target position being... Coordinates are At that time, the calculation of the first... The coordinate correction for the next iteration is: （16） like ,Pick ; Otherwise Repeat the above calculation process until... ,Pick ; The accuracy matrix of the above least-squares intersection positioning is: （17）。 3. The optical multi-station intersection positioning optimization method according to claim 2, characterized in that, A geometric factor (GDOP) model is constructed to reflect the amplification of positioning error by measurement error of space targets under the station layout, including: Define the root mean square error of positioning as: （18） Based on the weighted least squares estimation iterative formula constructed by formula (16), the covariance matrix of the position solution is given by formula (17), and then the root mean square error formula (18) is obtained. Based on formulas (16)-(18), the geometric factor GDOP is defined as: （19） in, This represents the average variance of the angle measurement.

4. The optical multi-station intersection positioning optimization method according to claim 3, characterized in that, Based on the minimum geometric factor GDOP model, the maximum total coverage of the monitoring range, and the strongest robustness index of the multi-station system, and combining the constraint functions constructed by the terrain-allowed deployment area constraint, measurement elevation angle constraint, line-of-sight terrain visibility constraint, and station spacing baseline constraint, a multi-constraint station layout optimization model is constructed for the layout of multiple stations, including: Divide the monitoring scope into The coverage capability of a network of quantized monitoring stations at each grid point is denoted as . Introducing a terrain visibility discrimination function When grid points With grid points When the line of sight between them is higher than the elevation of the surrounding terrain ,otherwise ; Define the first The first station for the first Effective observed state variables of each grid point This effective observed state variable Both the measurement elevation angle constraint and the terrain line-of-sight constraint must be satisfied simultaneously: （20） Among them, the measurement pitch angle limitation Used to avoid significant atmospheric refraction errors and ground clutter interference at low elevation angles; Define the total coverage function of the monitoring network over the monitoring range as follows: （21） in, For indicator functions; Based on anomalies encountered in actual measurements, such as single-station equipment failure, communication link interruption, or data anomalies, this study evaluates the performance retention capability of a multi-station system when a certain station is missing and defines robustness evaluation indicators for the multi-station system. The mean of the relative rate of change of the system's geometric factor GDOP before and after the station failure: （22） in, The geometric factor is the system's normal operating condition. To remove the first Geometric factors after individual stations; robustness evaluation indicators for multi-station systems The closer the value is to 1, the smaller the impact of station failure on the overall positioning accuracy of the system; Let the first The position vector of the transmitter system of each station is Based on the mean values ​​of the geometric factor GDOP corresponding to formula (19), the total coverage function corresponding to formula (21), and the relative change rate of the geometric factor GDOP corresponding to formula (22), a multi-station layout multi-constraint optimization mathematical model is established, which is expressed as follows: ; The optimization constraint function aims to minimize GDOP, maximize the total coverage of the monitoring range, and maximize the robustness of the multi-station system. The constraint function is defined as follows: ,s.t. (23) The constraints in equation (23) are as follows: Terrain-permissible deployment area constraints refer to the coordinates of the survey station. Must be located in an area where the terrain allows for deployment. Inside, and the station elevation It shall not be lower than the local ground elevation. ; Measurement elevation angle constraints and line-of-sight terrain constraints refer to ensuring that the station meets the minimum elevation angle limit for spatial targets. And the view is unobstructed by terrain; The quantity constraint refers to the total number of stations. No more than the system's maximum capacity ; Inter-station baseline constraints refer to the requirement that the distance between stations must be within a certain range, based on the baseline length of the optical measurement equipment within each station and the communication synchronization requirements. Within the range, and the terrain line-of-sight constraints between stations must be maintained to meet communication synchronization requirements.

5. The optical multi-station intersection positioning optimization method according to claim 4, characterized in that, Define the parameters of the improved NSGA-II genetic algorithm, including: The decision variables for each station are its three-dimensional coordinates in the launch frame. Indicates; will all The coordinates of each station are arranged sequentially to form a chromosome vector. : （24） Chromosome dimensions are Each component of the chromosome takes its value within the terrain-permitted deployment area of ​​the corresponding station, corresponding to the [missing information]. Spatial location of each station Consistent with the definition in formula (23); The optimization function in formula (23) is used. , , Constructing a multi-constraint fitness function: （25） To handle the multiple constraints in formula (23), an adaptive penalty term is introduced for each component of the optimization constraint function: （26） in, For the first The dynamic penalty factor of an optimization constraint function. The constraint violation degree is the cumulative value of all constraint violations: （27） In the formula, For the first The violation of an optimization constraint function; when When the solution fully satisfies the constraints, the penalty term degenerates to 0, and the multi-constraint fitness function degenerates to the original optimization constraint function; when the constraints are violated, the dynamic penalty factor increases dynamically with the degree of violation. By introducing non-dominated sorting and crowding mechanisms, the quality and diversity of solutions are balanced during population evolution, where: In the genetic algorithm system, an individual refers to a solution. In non-dominated sorting, for any two individuals in the population... and If the following conditions are met simultaneously: （28） Then it is called Dominate , recorded as This forms a non-dominated sort, which is then used to determine the priority level of the solutions. The population is hierarchically classified according to the dominance relationship of non-dominated ranking, and all solutions not dominated by any individual constitute the first Pareto front. Remove from the population The above process is then repeated to obtain the second frontier. This process is repeated until all individuals in the population have completed the classification; the closer they are... The better the solution, the higher its retention priority in the selection operation; Crowding distances are calculated for individuals within the same rank to maintain uniformity of solution distribution on the same Pareto front; all individuals within the same rank are then grouped according to their rank. The constraint function values ​​are sorted in ascending order, individual Under constraints The directional congestion distance component is defined as the ratio of the difference between the constraint values ​​of its left and right adjacent individuals to the range of that constraint value: （29） Summing the components along the directions of the three optimization constraint functions yields the individual... Total congestion distance: （30） Individuals located at both ends of the sorting sequence, i.e., the extreme points of each constraint, have a crowding distance set to positive infinity to ensure that they are preferentially retained during selection; the larger the crowding distance, the more sparse and isolated the solution is in the constraint space, and the higher the selection priority within the same Pareto level. Genetic operators are applied to chromosome vectors The real components of the corresponding formula (24) include the selection operator, crossover operator, and mutation operator, where: The selection operator selects high-quality individuals from the current population as parents to generate the next generation; each time, two individuals are randomly selected from the population. , The winner is determined and added to the parent set according to the following rules: If the two have different non-dominant ranking levels, retain the one with the lower ranking; the lower the ranking, the closer they are. The better the overall performance; if the two have the same non-dominated ranking level, the total congestion distance is retained. Larger solutions, with greater total crowding distances, indicate greater isolation within the target space, which helps maintain population diversity; this process continues until a solution is selected. One parent generation individual; Let the two parent chromosomes be... , The first chromosome Dimensional components ,remember , The corresponding number Dimensional component values , ; Set the crossover probability using the crossover operator. Decision No. Whether to perform crossover on the dimensional components The larger the parent, the more significant the difference between the offspring and the parent; if we consider the first generation... If cross-components are performed, the two parent components will generate corresponding child components according to the following steps. , : The first step is to generate uniformly random numbers. Calculate the expansion factor : （31） Used to control the distance between offspring and parents: Offspring are distributed between their parents. The offspring are distributed outside the parent generation; The distribution index is used to control the distribution shape of the expansion factor β. The larger, The more concentrated the offspring are around 1, the more they tend to resemble their parents; The smaller, The more dispersed the distribution, the further the offspring are from their parents; The second step is based on the expansion factor. Generate offspring components: , （32） All chromosomes Repeat the above operations on the dimensional component to obtain two new daughter chromosomes. , ; offspring chromosomes or The dimensional components, with mutation probability Decision on the first Does the component to be mutated need to be mutated? If so, let the component to be mutated be... Its allowed value range is The mutated component value is: （33） Among them, the mutation operator uses perturbation amount This indicates that the disturbance amount Represented as: , （34） in, Uniformly random numbers, The distribution index is the variation index. The larger the disturbance, the greater the amount of disturbance. The more concentrated the disturbance is around 0, the more refined it is. The smaller the value, the smaller the disturbance. The more dispersed the distribution, the greater the amplitude of variation; the probability of variation To ensure that, on average, exactly one component of each chromosome mutates, the perturbation strength and the problem dimension are considered. Matching.

6. The optical multi-station intersection positioning optimization method according to claim 5, characterized in that, An improved NSGA-II genetic algorithm for solving multi-constraint site layout optimization models is constructed based on the parameters of the improved NSGA-II genetic algorithm, including: Based on the parameters of the genetic algorithm, starting with a randomly initialized population, the population is driven to evolve generation by generation through genetic operators, and the elite retention mechanism is used to ensure the intergenerational continuation of high-quality solutions. Finally, it converges to the Pareto optimal front, thus obtaining the genetic algorithm for solving the multi-constraint station layout optimization model.

7. The optical multi-station intersection positioning optimization method according to claim 1, characterized in that, Based on genetic algorithm parameters, starting with a randomly initialized population, the population evolves generation by generation through genetic operators, and an elite retention mechanism ensures the intergenerational continuation of high-quality solutions, ultimately converging to the Pareto optimal front. This yields a genetic algorithm for solving multi-constraint site optimization models, including: Initialization settings, specifically including: The size of the random generation is initial population The coordinates of each station are within the deployment area permitted by the terrain. Uniform sampling is performed within the population, and individuals that do not meet the constraints of formula (23) are removed to form the initial population. Calculate the multi-constraint fitness function for all individuals. Perform non-dominated sorting initialization and crowding distance initialization; Setting up genetic evolution specifically includes: In the Generation, by selecting operators based on the current population The parent set is generated, and the scale is generated by formulas (31) and (32) corresponding to the crossover operator, and formulas (33)-(34) corresponding to the mutation operator. offspring population It also calculates the multi-constraint fitness function and merges the parent and child generations into a single scale. temporary population : （35） For temporary populations Perform non-dominated sorting to obtain the hierarchical front sequence. ;Calculate and assign the congestion distance within each frontal line according to formula (28)-formula (29); The environment settings include: Based on the principles of prioritizing non-dominant ranking levels and crowding distance within the same ranking level, from temporary populations... Selected from Individuals constitute the next generation population. ; sequentially incorporate the complete Pareto front The process continues until the remaining capacity is insufficient to accommodate a complete Pareto front, resulting in a truncated front. For truncated fronts, selection is performed in descending order of crowding distance to ensure a uniform distribution of the population within the constrained space. Furthermore, an elite retention ratio is set. ,Will Center front Each elite individual was directly retained until ; Set termination conditions, specifically including: Repeated genetic evolution and environmental selection, when the number of iterations reaches a preset maximum value. At this point, the genetic algorithm terminates, outputting the first Pareto front in the final population. As the Pareto optimal solution set.

8. The optical multi-station intersection positioning optimization method according to claim 1, characterized in that, The improved NSGA-II genetic algorithm was used to determine the location of each station, including: The ideal point is defined as the first Pareto front of each constraint function. The reference vector formed by obtaining the optimal values ​​above: （36） Since the three optimization constraint functions have different dimensions and orders of magnitude, the distance needs to be normalized; the first Pareto front needs to be calculated. Each solution Normalized Euclidean distance to the ideal point: （37） in, Represents the ideal optimal target vector. The first Pareto front indicates the Pareto front. There are 10 candidate solutions; and The first The optimization constraint function is at the first Pareto front. The maximum and minimum values ​​are used to eliminate the influence of dimensional differences; finally, the maximum and minimum values ​​are selected. The minimum solution is taken as a compromise: （38） To be closest to the ideal point in the normalized optimization constraint function space, The three-dimensional coordinates of all m stations are included as the final station layout scheme.

9. A multi-station intersection positioning and site optimization system for optical measurement, characterized in that, include: The geometric factor GDOP model building unit is used to construct an optical multi-station intersection positioning model that uses multiple stations to perform optical tracking measurements on space targets; and to construct a geometric factor GDOP model that reflects the amplification of positioning error by the measurement error of space targets under the station layout. The genetic algorithm construction unit is used to construct a multi-constraint station layout optimization model based on the constraints of the geometric factor GDOP model (minimum, maximum total coverage of monitoring range, and strongest robustness index of multi-station system), combined with the constraints of terrain-allowed deployment area, measurement pitch angle, line-of-sight terrain visibility, and station spacing baseline. The parameters of the improved NSGA-II genetic algorithm are defined, and an improved NSGA-II genetic algorithm for solving the multi-constraint station layout optimization model is constructed based on the parameters of the improved NSGA-II genetic algorithm. The solution unit is used to solve for the location of each station using the improved NSGA-II genetic algorithm.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores one or more programs, which, when executed by a computer device, cause the computer device to perform the optical measurement multi-station intersection positioning optimization method according to any one of claims 1-7.

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