Indoor satellite flash positioning method and system for transformer substation based on NSGA-II optimized anchor point layout

Abstract

The invention discloses a substation indoor star flash positioning method and system for optimizing anchor layout based on NSGA-II, and the method comprises the steps: constructing an objective function through maximizing a coverage area, minimizing an average positioning error and minimizing the number of base stations, constructing constraint conditions through base station installation position constraints and coverage quality constraints, and solving an optimal base station layout scheme through employing a multi-objective optimization algorithm; and under the optimal base station layout scheme, a star-flash-based Chan-Kalman filtering algorithm is adopted to carry out real-time positioning on the motion trail of the indoor automatic guided vehicle of the transformer substation. The method can significantly improve the positioning precision and track stability of the indoor equipment of the transformer substation.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to the cross-application of wireless positioning technology and multi-objective optimization algorithms. More specifically, it relates to a substation indoor star-flash positioning method and system based on NSGA-II optimized anchor point layout. Background Technology

[0002] As a core hub of the power grid, substations are rapidly improving their level of intelligence. In this process, various digital and intelligent sensing devices, such as online monitoring, intelligent inspection, mobile operations, and video surveillance, are being widely deployed within the substations. These devices cover everything from "low-power, high-connectivity" sensor networks to "high-speed, high-bandwidth" video and mobile terminals, urgently requiring substation wireless networks to possess integrated communication support capabilities that combine broadband and narrowband bandwidth, offer flexible deployment, and ensure secure control.

[0003] However, existing substation wireless networks are often constructed using a combination of technologies such as LoRa, ZigBee, Bluetooth, WAPI, and Wi-Fi, resulting in numerous problems including inconsistent technical approaches, inadequate security mechanisms, insufficient independent controllability, and complex terminal access methods. This not only increases the complexity of system integration and operation and maintenance but also hinders the standardization, intelligentization, and reliability development of substation wireless communication networks.

[0004] Against this backdrop, StarFlash technology, as a new generation of short-range wireless communication standard, offers new possibilities for building efficient, reliable, and secure indoor wireless communication environments in substations, thanks to its advantages of low power consumption, high speed, low latency, and strong anti-interference capabilities. It is particularly suitable for mission-critical communication in the complex electromagnetic environment of substations. Meanwhile, positioning and trajectory tracking are core requirements for intelligent inspection and mobile operations; their accuracy and real-time performance are crucial to the efficiency and security of operational processes.

[0005] However, the performance of the StarScan positioning system is highly dependent on the spatial layout of its base stations. Inappropriate base station deployment can lead to increased positioning errors, more blind spots, and negatively impact the overall system performance.

[0006] To address this issue, there is an urgent need for a method that can adaptively optimize base station layout for complex environments, thereby improving the accuracy and robustness of the Starflash positioning system.

[0007] To address the aforementioned issues, there is an urgent need for a method and system for precise positioning of mobile devices in substation environments. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a substation indoor star-flash positioning method and system based on NSGA-II optimized anchor point layout.

[0009] The present invention adopts the following technical solution.

[0010] In a first aspect, this invention relates to a substation indoor starburst positioning method based on NSGA-II optimized anchor point layout, characterized in that the method includes the following steps: A substation indoor star-flash positioning method based on NSGA-II optimized anchor point layout, characterized in that the method includes the following steps: The objective function is constructed to maximize the coverage area, minimize the average positioning error, and minimize the number of base stations. The constraint conditions are constructed using base station installation location constraints and coverage quality constraints. The base station installation location constraints include physical space limitations, height limitations, and distance limitations. The coverage quality constraints include minimum coverage rate and redundancy requirements. Based on the constraints, a total penalty term is constructed, and a multi-objective optimization algorithm is used to solve for the optimal base station layout scheme. During the multi-objective optimization process, the fitness is calculated by combining the objective function value and the total penalty term, thus obtaining the optimal base station layout scheme. Under the optimal base station layout scheme, the Chan-Kalman filtering algorithm based on star flash is used to locate the movement trajectory of the AGV indoor automated guided vehicle in the substation in real time.

[0011] More preferably, the construction of the objective function to maximize the coverage area, minimize the average positioning error, and minimize the number of base stations includes: The objective function is:

[0012] In the formula, , , As weight, , ,and Within a given working area, there are M test points, and the true coordinates of each test point are... The coordinates calculated by the positioning algorithm are , Number of base stations; , , These are the normalized values ​​for coverage area, average positioning error, and number of base stations, respectively.

[0013] More preferably, when a test point n is not within the effective coverage area of ​​any base station, the penalty value for minimum coverage is... β4 is the violation threshold; otherwise, ; If a test point n is covered by fewer than imin base stations, then the penalty value for redundancy requirement is... nmin is the minimum required redundancy, in is the number of base stations actually covering the test point n, and β5 is an adjustment factor; otherwise, .

[0014] More preferably, the physical space constraint refers to the penalty value if base station i is located in an area where it cannot be installed. The adjustment coefficient β1 is a positive number, indicating a violation; otherwise, ; The height limit refers to the penalty value if the height of base station i is lower than hmin or higher than hmax. Where htarget is the target height and β2 is an adjustment coefficient; otherwise, ; The distance constraint refers to the penalty value for each pair of base stations i and j if the distance between them is less than dmin or greater than dmax. Where dij is the actual distance between base stations i and j, dtarget is the desired distance, and β3 is an adjustment coefficient; otherwise, .

[0015] More preferably, the total penalty term Ptotal is defined as the sum of all individual penalty terms:

[0016] in, The penalty value is for physical space constraints. The penalty value is a height restriction. The penalty value is the distance limit. The penalty value for minimum coverage. This is the penalty value for redundancy.

[0017] More preferably, in the optimal base station layout scheme, a total of N ≥ 4 star-flash base stations with known coordinates are deployed, and the three-dimensional coordinates of the i-th star-flash base station are marked as follows: , ; The AGV equipped with the Star Flash tag communicates wirelessly with multiple Star Flash base stations in known locations in the vicinity; the signal arrival time difference is calculated based on the return response signal obtained from the wireless communication, and the time difference is converted into pseudorange difference; Using pseudo-distance difference, the Chan filtering algorithm is used to calculate the estimated position and estimation error covariance matrix of the AGV vehicle through a two-step weighted least squares method; The estimated position and estimation error covariance matrix obtained by the Chan filtering algorithm are used as inputs to the Kalman filtering algorithm to update the target state transition equation and target observation equation in the Kalman filtering algorithm, thus obtaining the final AGV position.

[0018] More preferably, auxiliary variables and linearized equations are constructed, and the initial position of the AGV is solved using the least squares method; an error covariance matrix is ​​constructed, and a weighted matrix is ​​constructed using the error covariance matrix; using the weighted matrix, the initial position of the AGV is further optimized using the weighted least squares method to obtain the estimated position of the AGV and the estimated error covariance matrix. The estimated position of the AGV is used as the state variable of the Kalman filtering algorithm, and the estimated error covariance matrix is ​​used as the process noise matrix. The Kalman filtering algorithm is divided into two stages: prediction and update. In the prediction stage, the state variable prediction equation and the error covariance prediction equation are obtained, the process noise matrix and the observation noise matrix are adjusted, and the state variable prediction equation and the error covariance prediction equation are updated by combining the Kalman filter gain to obtain the final AGV position.

[0019] This invention also proposes an indoor star-flash positioning system for substations based on NSGA-II optimized anchor point layout, including a layout module and a positioning module: The layout module constructs objective functions to maximize coverage area, minimize average positioning error, and minimize the number of base stations, and constructs constraint conditions based on base station installation location constraints and coverage quality constraints. It then uses a multi-objective optimization algorithm to solve for the optimal base station layout scheme. Under the optimal base station layout scheme, the positioning module uses a Chan-Kalman filtering algorithm based on star flash to perform real-time positioning of the movement trajectory of the indoor automated guided vehicle in the substation.

[0020] The present invention also proposes a terminal, including a processor and a storage medium: The storage medium is used to store instructions; The processor is used to perform the steps of the above method according to the instructions.

[0021] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0022] The beneficial effects of this invention are that, compared with the prior art, the substation indoor star-flash positioning method and system based on NSGA-II optimized anchor point layout in this invention, combined with the NSGA-II (non-dominated sorting genetic algorithm) multi-objective optimization algorithm, takes positioning accuracy, coverage, system cost and other optimization objectives as optimization goals, and optimizes the spatial layout of anchor points through intelligent algorithms, which can significantly improve the positioning performance of the substation indoor star-flash system, and provide strong support for personnel trajectory prediction in substation scenarios, thereby providing key technical guarantees for building a unified, safe and efficient wireless communication and intelligent sensing platform.

[0023] The beneficial effects of the present invention also include: 1. With the rapid development of the Internet of Things (IoT) and smart manufacturing, the demand for unmanned systems that can adapt to complex environmental changes and possess high flexibility and intelligence is increasing. Combining advanced positioning technologies (such as StarFlash), optimization algorithms (such as NSGA-II), and positioning algorithms (such as Kalman filtering) to build an integrated solution can not only significantly improve the positioning accuracy and driving stability of mobile devices, but also promote the automation level of the entire production process and drive technological innovation and development in related industries.

[0024] 2. The star-flash positioning and Kalman filter positioning optimization technology based on NSGA-II optimized anchor point layout aims to solve the problems of substation indoor positioning technology such as suboptimal base station layout, inaccurate positioning, and unstable trajectory. It has important theoretical value and broad application prospects. Attached Figure Description

[0025] Figure 1 This invention relates to a substation indoor star-flash positioning method based on NSGA-II optimized anchor point layout; Figure 2 This is a schematic diagram of the substation indoor star-flash positioning method based on NSGA-II optimized anchor point layout according to the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer and more accurate, the technical solutions of this invention are described in detail below through several specific embodiments. The embodiments used in this invention are merely illustrative and are not intended to limit the scope of this invention.

[0027] The technical solution of the present invention is as follows: This invention proposes a substation indoor starburst positioning method based on NSGA-II optimized anchor point layout, comprising the following steps: The objective function is constructed to maximize the coverage area, minimize the average positioning error, and minimize the number of base stations. The constraint conditions are constructed using base station installation location constraints and coverage quality constraints. The base station installation location constraints include physical space limitations, height limitations, and distance limitations. The coverage quality constraints include minimum coverage rate and redundancy requirements. The objective function constructed to maximize coverage area, minimize average positioning error, and minimize the number of base stations includes: The objective function is:

[0028] In the formula, , , As weight, , ,and Within a given working area, there are M test points, and the true coordinates of each test point are... The coordinates calculated by the positioning algorithm are , Number of base stations; , , These are the normalized values ​​for coverage area, average positioning error, and number of base stations, respectively.

[0029] When a test point n is not within the effective coverage area of ​​any base station, the penalty value for minimum coverage is... β4 is the violation threshold; otherwise, ; If a test point n is covered by fewer than imin base stations, then the penalty value for redundancy requirement is... nmin is the minimum required redundancy, in is the number of base stations actually covering the test point n, and β5 is an adjustment factor; otherwise, .

[0030] Physical space constraints refer to the penalty value if base station i is located in an area where it cannot be installed. The adjustment coefficient β1 is a positive number, indicating a violation; otherwise, ; The height limit refers to the penalty value if the height of base station i is lower than hmin or higher than hmax. Where htarget is the target height and β2 is an adjustment coefficient; otherwise, ; The distance constraint refers to the penalty value for each pair of base stations i and j if the distance between them is less than dmin or greater than dmax. Where dij is the actual distance between base stations i and j, dtarget is the desired distance, and β3 is an adjustment coefficient; otherwise, .

[0031] Based on the constraints, a total penalty term is constructed, and a multi-objective optimization algorithm is used to solve for the optimal base station layout scheme. During the multi-objective optimization process, the fitness is calculated by combining the objective function value and the total penalty term, thus obtaining the optimal base station layout scheme. The total penalty term Ptotal is defined as the sum of all individual penalty terms:

[0032] in, The penalty value is for physical space constraints. The penalty value is a height restriction. The penalty value is the distance limit. The penalty value for minimum coverage. This is the penalty value for redundancy.

[0033] Under the optimal base station layout scheme, the Chan-Kalman filtering algorithm based on star flash is used to locate the movement trajectory of the AGV indoor automated guided vehicle in the substation in real time.

[0034] In the optimal base station layout scheme, suppose a total of N ≥ 4 star-flash base stations with known coordinates are deployed. The three-dimensional coordinates of the i-th star-flash base station are plotted. , ; The AGV equipped with the Star Flash tag communicates wirelessly with multiple Star Flash base stations in known locations in the vicinity; the signal arrival time difference is calculated based on the return response signal obtained from the wireless communication, and the time difference is converted into pseudorange difference; Using pseudo-distance difference, the Chan filtering algorithm is used to calculate the estimated position and estimation error covariance matrix of the AGV vehicle through a two-step weighted least squares method; The estimated position and estimation error covariance matrix obtained by the Chan filtering algorithm are used as inputs to the Kalman filtering algorithm to update the target state transition equation and target observation equation in the Kalman filtering algorithm, thus obtaining the final AGV position.

[0035] Construct auxiliary variables and linearized equations, and use the least squares method to solve for the initial position of the AGV; construct the error covariance matrix, and use the error covariance matrix to construct a weighted matrix; use the weighted matrix and the weighted least squares method to further optimize the initial position of the AGV, and obtain the estimated position and the estimated error covariance matrix of the AGV. The estimated position of the AGV is used as the state variable of the Kalman filtering algorithm, and the estimated error covariance matrix is ​​used as the process noise matrix. The Kalman filtering algorithm is divided into two stages: prediction and update. In the prediction stage, the state variable prediction equation and the error covariance prediction equation are obtained, the process noise matrix and the observation noise matrix are adjusted, and the state variable prediction equation and the error covariance prediction equation are updated by combining the Kalman filter gain to obtain the final AGV position.

[0036] This invention also proposes an indoor star-flash positioning system for substations based on NSGA-II optimized anchor point layout, including a layout module and a positioning module: The layout module constructs objective functions to maximize coverage area, minimize average positioning error, and minimize the number of base stations, and constructs constraint conditions based on base station installation location constraints and coverage quality constraints. It then uses a multi-objective optimization algorithm to solve for the optimal base station layout scheme. Under the optimal base station layout scheme, the positioning module uses a Chan-Kalman filtering algorithm based on star flash to perform real-time positioning of the movement trajectory of the indoor automated guided vehicle in the substation.

[0037] The present invention also proposes a terminal, including a processor and a storage medium: The storage medium is used to store instructions; The processor is used to perform the steps of the above method according to the instructions.

[0038] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0039] The first aspect of this invention relates to a substation indoor starburst positioning method based on NSGA-II optimized anchor point layout, such as... Figure 2 As shown, the method includes the following steps: Step 1: Construct objective functions to maximize coverage area, minimize average positioning error, and minimize the number of base stations. Construct constraint conditions with base station installation location constraints and coverage quality constraints. Use a multi-objective optimization algorithm to solve for the optimal base station layout scheme.

[0040] Step 1 uses NSGA-II to optimize the layout of the Starlight base stations. This algorithm can simultaneously consider multiple objective functions, such as maximizing the coverage area, minimizing the average positioning error, and balancing the relationship between the number of base stations and positioning performance, to find a set of approximate optimal solutions.

[0041] The objective function is constructed to maximize coverage area, minimize average positioning error, and minimize the number of base stations, including: The objective function is:

[0042] In the formula, , , As weight; ; ,and Within a given working area, there are M test points, and the true coordinates of each test point are... The coordinates calculated by the positioning algorithm are ; Number of base stations; , , These are the normalized values ​​for coverage area, average positioning error, and number of base stations, respectively.

[0043] Specifically, the weights are set based on the application scenario. In the substation safety monitoring scenario, , , The values ​​are set to 0.3, 0.5, and 0.2 respectively (accuracy priority); for personnel positioning scenarios, they are set to 0.5, 0.3, and 0.2 respectively (coverage priority); and for resource-constrained scenarios, they are set to 0.3, 0.3, and 0.4 respectively (efficiency priority). The basis for these settings is... + + =1, , , ∈[0.2, 0.6]; primary objective weight ≥ 0.3, secondary objective weight ≥ 0.2.

[0044] For a stroboscopic base station, its coverage area can be approximated as a circular region, centered at the base station location, with a radius depending on the maximum effective transmission distance R of the stroboscopic signal (usually determined by hardware characteristics and environmental conditions). Assuming each base station has the same coverage radius, the coverage area Ai of the i-th base station can be expressed using the formula for the area of ​​a circle:

[0045] However, in practical applications, due to factors such as building structure and obstacles, the actual coverage area of ​​a base station may not be a perfect circle, but rather a more complex shape. Therefore, accurately calculating the coverage area may require consideration of specific environmental maps and signal attenuation models.

[0046] Ideally, the total coverage area Attotal of the entire system is the union of the coverage areas of all individual base stations. However, if the coverage areas of multiple base stations overlap, directly adding them together will lead to an overestimation of the actual coverage area. Therefore, the correct approach is to calculate the area of ​​the union of these circles.

[0047] In practice, a grid method is used for calculation, which involves dividing the working area into many small square or rectangular grids, and then checking whether each grid is covered by at least one base station; if so, the grid is considered part of the total coverage area. The objective function can then be directly defined as maximizing the proportion of the number of covered grids to the total number of grids in the area.

[0048] Positioning error typically refers to the difference between the calculated position and the actual position. In stroboscopic systems, common positioning methods include polygonal measurement or time difference of arrival. These methods rely on accurate distance measurement, but due to complex signal propagation paths, multipath effects, and non-line-of-sight propagation, the actual measured distance may deviate, leading to positioning error.

[0049] Suppose there are M test points within a given working area, and the true coordinates of each test point are... The coordinates calculated by the positioning algorithm are Therefore, the positioning error of the i-th test point can be defined as the Euclidean distance:

[0050] Average positioning error across the entire working area This can be obtained by averaging the error values ​​of all test points:

[0051] The objective function here is The goal is to find a base station layout scheme that minimizes the average positioning error of all test points under that layout.

[0052] Minimizing the number of base stations is used as an objective function of NSGA-II primarily to reduce the number of base stations as much as possible while meeting positioning accuracy and coverage requirements. This helps reduce costs, simplify deployment, and potentially reduce system complexity and maintenance costs.

[0053] Treating the number of base stations N as an independent objective function, while ensuring that other objectives (such as maximizing coverage area and minimizing average positioning error) are satisfied, .

[0054] In practical applications, since the importance of each objective varies, weighting factors are introduced to adjust the relative importance of each objective. For example, coverage area, positioning error, and the number of base stations can be assigned corresponding weighting coefficients. , , This makes the overall objective function take the form of a weighted sum.

[0055] The constraints are constructed based on base station installation location constraints and coverage quality constraints, including: for each base station i, a penalty function Pi is defined, which returns a positive value when the base station location violates a constraint; if the base station location meets all constraints, it returns 0; the base station location includes physical space constraints. Height restrictions and distance restrictions .

[0056] The constraints are constructed based on base station installation location constraints and coverage quality constraints, including: coverage quality constraints such as minimum coverage rate and redundancy requirements; if a test point n is not within the effective coverage area of ​​any base station, the penalty value for the minimum coverage rate is... β4 is the violation threshold; otherwise, If a test point n is covered by fewer than imin base stations, the penalty value is... nmin is the minimum required redundancy, in is the number of base stations actually covering the test point n, and β5 is an adjustment factor; otherwise, .

[0057] The violation threshold β4 is typically set to be 10-100 times the order of magnitude of the objective function value. The violation threshold β4 is used to penalize base station deployments that do not meet the minimum coverage constraint. Its value should generally be a large positive number to ensure a strong penalty for solutions that violate the constraint, thereby guiding the optimization process towards a solution that meets the coverage requirements. Therefore, the violation threshold β4 ranges from 100 to 1000 to ensure that the severity of the coverage constraint is fully reflected; the specific value is set according to the actual situation.

[0058] The adjustment factor β5 is used as a penalty for redundancy requirements, aiming to penalize base station configurations that fail to meet the minimum redundancy requirements. The value of β5 should be set according to the severity of the impact of insufficient redundancy. If insufficient redundancy significantly affects system reliability, a larger β5 value can be chosen; otherwise, a moderately smaller β5 value can be selected. Generally, the value of β5 should be large enough to incentivize the optimization algorithm to meet the redundancy requirements, but it should not be too large to avoid over-constraining the optimization of other objectives. The adjustment factor β5 is smaller than the violation threshold β4 because redundancy violations are slightly less severe than complete lack of coverage. The adjustment factor β5 is 0.5 to 0.8 times the violation threshold β4, with a setting range between 50 and 500, depending on the specific circumstances.

[0059] When using multi-objective optimization algorithms such as NSGA-II, handling constraints with penalty terms is an effective method. This method allows us to impose additional costs or penalties on constraint violations without completely eliminating infeasible solutions, thereby guiding the optimization process towards a solution that satisfies all constraints. The total penalty term for base station installation location constraints can be the sum of penalty values ​​for all base stations.

[0060] Physical space constraints: Base stations cannot be placed in locations where installation is impossible, such as inside walls or behind other obstacles. If base station i is located in an uninstallable area, a penalty value is applied. Where the adjustment coefficient β1 is a large positive number, it indicates a severe violation. Otherwise, .

[0061] Specifically, the adjustment coefficient β1 is the largest among all penalty coefficients because the physical constraint is a hard constraint. β1 is a penalty term coefficient used for physical space constraints, penalizing base stations located in uninstallable areas. The value of β1 should be large enough to ensure that base stations in uninstallable areas are not placed in the final solution. Generally, β1 should be a significantly large positive number to strictly avoid placing base stations in uninstallable areas during optimization and to prevent the solution space from being affected by invalid solutions. Therefore, the adjustment coefficient β1 ranges from 1000 to 10000, ensuring that solutions that violate the physical constraint are almost impossible to select. The specific calculation formula is β1 = 10 × max(β2, β3, β4, β5).

[0062] Height limit: If the height of base station i is lower than hmin or higher than hmax, the penalty value is... Where htarget is the target height (which can be hmin or hmax, depending on which is closer), and β2 is an adjustment coefficient used to control the importance of height deviation. Otherwise, .

[0063] Specifically, considering the high sensitivity of the substation environment, the adjustment coefficient β2 is determined based on the degree of impact of altitude deviation. If the altitude deviation of the base station has a significant impact on system performance, β2 should be set to a larger value; if the altitude deviation has a smaller impact on the system, a smaller value can be set. β2 can be adjusted according to the degree of impact of altitude restrictions on positioning accuracy or signal coverage. Therefore, the range of β2 is 10~100.

[0064] Distance constraint: For each pair of base stations i and j, if the distance between them is less than dmin or greater than dmax, the penalty value is... , where dij is the actual distance between base stations i and j, dtarget is the desired distance (which can be dmin or dmax, depending on which is closer), and β3 is an adjustment coefficient. Otherwise, .

[0065] Specifically, distance constraints are generally more lenient than height constraints, hence β3 < β2. The adjustment factor β3 is the adjustment coefficient for the distance constraint between base stations. The value of this coefficient typically depends on the impact of the desired distance between base stations on coverage quality, network capacity, etc. Therefore, β3 is set in the range of 10 to 50.

[0066] Coverage quality constraints play a crucial role in base station layout optimization, ensuring that every point within the entire working area is effectively covered by the signal of at least one base station. For substation indoor positioning systems based on star-flash technology, good coverage quality is fundamental to achieving accurate positioning. This involves two main constraints: minimum coverage rate and redundancy requirements.

[0067] Minimum coverage: Ensures that every point within the entire working area can receive a valid signal from at least one base station. If a test point i is outside the valid coverage area of ​​any base station, the penalty value is... Where the adjustment coefficient β4 is a large positive number, it indicates a severe violation. Otherwise, .

[0068] Specifically, the adjustment coefficient β4 is the adjustment coefficient for the minimum coverage constraint, used to penalize base station layouts that do not cover the test points. The value of the adjustment coefficient β4 should ensure a strong penalty for non-compliant solutions, making the optimization algorithm tend to meet the minimum coverage requirement. Therefore, the value of the adjustment coefficient β4 ranges from 500 to 2000, which is 50-200% of the expected value of the objective function, and the specific value should be set according to the actual situation.

[0069] Redundancy requirement: Critical areas need to be covered by two or more base stations to improve reliability. For each critical test point i, if it is covered by fewer than nmin base stations (nmin is the minimum required redundancy), the penalty value is [value missing]. Where ni is the actual number of base stations covering the test point, and β5 is an adjustment coefficient used to control the importance of insufficient redundancy. Otherwise, .

[0070] Specifically, the adjustment factor β5 is the adjustment factor for redundancy requirements, typically used to control the penalty for insufficient redundancy. The value of β5 should be adjusted based on the impact of redundancy on system reliability. To ensure the importance of redundancy constraints without exceeding coverage constraints, the value of β5 is set to a range of 20~200, specifically calculated as β5=base_penalty×(nmin—ni)², where the base penalty term base_penalty is set to a range of 10~50.

[0071] For the entire layout scheme, the total penalty term Ptotal can be defined as the sum of all individual penalty terms:

[0072] Step 2: Under the optimal base station layout scheme, the Chan-Kalman filtering algorithm based on star flash is used to locate the movement trajectory of the indoor automated guided vehicle in the substation in real time.

[0073] NSGA-II is a widely used multi-objective optimization algorithm suitable for solving problems involving multiple conflicting objectives, such as base station layout optimization. Based on the defined constraints and objective function, the following are the steps to implement these settings within the NSGA-II framework.

[0074] (1) Initialize the population First, an initial population needs to be generated, with each individual representing a possible base station layout scheme. Each individual can be represented by a vector, where each element represents the location of a base station or other relevant parameters. These location or parameter values ​​are randomly generated during initialization.

[0075] (2) Fitness assessment For each individual, calculate its corresponding objective function value and the degree of constraint violation (reflected by a penalty term). Specifically: Objective function: Calculate the performance of each individual based on the defined objective function.

[0076] Constraint handling: Cost and resource constraints are incorporated into fitness through penalty terms.

[0077] The resulting fitness function is,

[0078] Where is the weight coefficient of the total penalty term.

[0079] (3) Quick Non-Dominated Sort A fast non-dominated sort is performed on the current population, which involves dividing the individuals in the population into different tiers, where all individuals within each tier are not dominant to each other. This process helps to distinguish solutions of different quality levels.

[0080] (4) Calculate the crowding distance To maintain population diversity, individuals within the same non-dominated layer are further ranked according to crowding distance. Crowding distance reflects the distance an individual is from other individuals in its layer; a greater distance indicates a more unique individual.

[0081] (5) Selection, crossover and mutation Selection: Individuals are selected for the next generation based on non-dominant ranking and crowding distance. A binary tournament selection strategy is typically used, prioritizing individuals with higher rankings and larger crowding distances.

[0082] Crossover: Generates new offspring through crossover operations. Common methods include single-point crossover, two-point crossover, or multi-point crossover.

[0083] Mutation: Performing mutation operations on certain individuals with a certain probability, such as fine-tuning the location of base stations or adjusting power settings, in order to explore a wider solution space.

[0084] (6) Merge parent generation and child generation The newly generated offspring are merged with the parent generation to form a new and larger population.

[0085] (7) Repeat steps 3 to 6. The process continues until a termination condition is met, such as reaching the predetermined maximum number of iterations, or the objective function value reaching the predetermined optimal range or satisfying a certain threshold, or satisfying all constraints and the total value of the penalty term being small.

[0086] (8) Output results.

[0087] Finally, a set of Pareto optimal solutions is selected from the final population as an approximate solution to the problem. These solutions represent the best trade-offs among the various objectives.

[0088] In a preferred embodiment, the NSGA-II algorithm with a population size of 100 is used, with the crossover operator SBX, a probability of 0.9, and a distribution index η of 15; the mutation operator PM, a probability of 0.3, and a distribution index η of 20 is used.

[0089] Starflash technology is a short-range wireless communication and positioning solution. It can provide high-precision, low-latency positioning services, and its short-range wireless communication perfectly meets the basic requirements of indoor positioning. The positioning technology of this invention uses a starflash-based Chan-Kalman filtering algorithm to perform real-time positioning of the movement trajectory of an indoor automated guided vehicle (AGV) in a substation.

[0090] Based on the optimized deployment of the StarShine base stations, the AGV is equipped with a StarShine tag module to wirelessly communicate with multiple known StarShine base stations in the vicinity. The specific process includes the following: (1) Data collection Signal synchronization and interaction: The base station periodically sends synchronization signals or probe frames; after receiving the signal, the star-flash tag on the AGV returns a response signal according to the protocol; the system records the signal transmission timestamps between each base station and the tag, which are used to calculate the time difference of arrival (TDOA) or time of flight (ToF).

[0091] Multi-dimensional information collection: The system acquires signal arrival time difference, signal strength, and possible angle information (AOA / AOD) as input parameters for the positioning algorithm. Simultaneously, it collects data from other sensors on the AGV, such as acceleration and angular velocity provided by the inertial measurement unit (IMU) and speed feedback from the encoder, for subsequent fusion processing.

[0092] (2) Data preprocessing Due to issues such as multipath propagation, non-line-of-sight (NLOS) interference, and signal attenuation in the indoor environment of substations, the raw data collected usually contains noise and outliers. Therefore, necessary preprocessing operations are required to improve data quality.

[0093] Denoising and outlier removal: High-frequency noise was removed from the collected TDOA / RSSI data using sliding window filtering or median filtering; outliers that significantly deviated from the normal range were identified and removed using statistical analysis methods.

[0094] NLOS error correction: An environment-modeling-based NLOS detection algorithm is used to determine whether the current ranging is affected by non-line-of-sight propagation. If NLOS is detected, a correction model is used to compensate for the ranging results or reduce the weight of the base station data in the positioning calculation.

[0095] Data standardization and time alignment: Unifying data from different sensors to the same time base ensures consistency in subsequent fusion processing; normalizing or standardizing the units of various types of data facilitates the fusion of multi-source information.

[0096] Data caching and transmission: Preprocessed data is temporarily stored in a local buffer and uploaded to the central processing unit or edge computing node at a fixed frequency or by event triggering; it supports data packet tagging (including timestamps, device IDs, etc.) for subsequent state estimation and trajectory prediction.

[0097] (3) Output results After the above data acquisition and preprocessing process, the system outputs a set of structured, high-quality datasets that can be used for positioning calculations. These datasets include: valid TDOA / ToF / RSSI / AOA measurements between the AGV and each base station at each time point; auxiliary sensor data such as IMU and encoder data; and data validity identification and confidence assessment results.

[0098] Under the optimal base station layout scheme, a Chan-Kalman filtering algorithm based on star-flash is used to perform real-time positioning of the movement trajectory of the AGV indoor automated guided vehicle. This includes: after optimizing the deployment of star-flash base stations, the AGV is equipped with a star-flash tag module to communicate wirelessly with multiple known star-flash base stations in the vicinity; the base stations periodically send synchronization signals or probe frames; after receiving the signals, the star-flash tags on the AGV return response signals according to the protocol; the system records the signal transmission timestamps between each base station and the tag to calculate the signal arrival time difference; the arrival time difference is converted into pseudorange, auxiliary variables are constructed, and the estimated position and estimation error covariance matrix of the AGV are solved.

[0099] Suppose that the system deploys N ≥ 4 star-flash base stations with known coordinates, whose spatial coordinates are as follows:

[0100] The time difference between the signals received by the star-flash tags installed on the AGV and the signals transmitted by each base station can be converted into the following form of pseudorange difference:

[0101] in, The three-dimensional coordinates of the AGV's current position. Denotes the Euclidean norm. This represents the pseudorange difference corresponding to the signal arrival time difference between the i-th base station and the first base station.

[0102] Since the above equations are nonlinear and the solution is relatively complex, the Chan algorithm achieves efficient estimation of the target position through a two-step weighted least squares method, which is suitable for three-dimensional spatial modeling. Therefore, the Chan algorithm is introduced to transform it into a linear least squares problem for solution.

[0103] First, construct the auxiliary variables and linearize the equation. Let the distance difference... Define auxiliary variables:

[0104] Squaring the original TDOA equation and rearranging it to obtain a linear form, we get the linearized equation:

[0105] Where A is a coefficient matrix composed of base station coordinates, and b is the distance difference. A vector composed of the squares of . In one embodiment,

[0106]

[0107]

[0108] in, This represents the square of the distance from the i-th AGV to the origin.

[0109] Ignoring the effects of noise, a preliminary solution is obtained using the ordinary least squares method:

[0110] This allows us to obtain a preliminary location estimate.

[0111] Considering the influence of measurement error, an error covariance matrix C is constructed, and a weighting matrix W=C is introduced. 1. Further optimization results using weighted least squares:

[0112] The weight matrix is ​​a positive definite symmetric q×q matrix, which ultimately yields a more accurate AGV 3D position estimate:

[0113] and its estimated error covariance matrix:

[0114]

[0115] and , It is a positive definite symmetric matrix eigenvalues, It is a unitary matrix.

[0116] Kalman filtering has significant advantages in determining the position of AGVs, gradually approximating the true position through iterative parameter optimization and reducing prediction errors. However, this algorithm still faces some challenges in application: it is extremely sensitive to the selection of initial values; if the initial position estimate deviates significantly from the actual position, it will lead to subsequent positioning offsets and error accumulation. Furthermore, since Kalman filtering is a continuous optimization process, the covariance matrix of the previous moment directly affects the positioning information of subsequent moments. During AGV operation, especially under complex working conditions and in variable indoor environments, signal instability and external interference may cause the covariance matrix to fail to accurately reflect the current position information, leading to accumulated errors and affecting the overall accuracy and reliability of the filtering algorithm in real-time AGV positioning.

[0117] To address the aforementioned issues, an adaptive Kalman filter algorithm is considered to reduce prediction error and improve prediction accuracy. The target state transition equation and target observation equation for the Kalman filter are as follows:

[0118]

[0119] in, These are the state variables, state transition matrix, system noise variables, measurement variables, measurement transition matrix, and noise variables during the measurement process. The results of the Chan algorithm are then used. As the input to the Kalman filter, i.e. In one embodiment, it is also possible to... As process noise matrix .

[0120] The core process of Kalman filtering consists of two stages: prediction and update. The prediction stage mainly includes two steps: state prediction and error covariance prediction. This stage works by inferring the target's current motion state based on the target's motion state at the previous moment. The process noise matrix and the observation noise matrix are denoted as follows: and The state variable prediction equation and the error covariance prediction equation are as follows:

[0121]

[0122] To improve the filter's adaptability to changing environments, the process noise matrix and observation noise matrix are adaptively adjusted. The specific formula is as follows:

[0123]

[0124] in, For the observation noise matrix, The process noise matrix is... For observation output, For prediction error, Smoothing factor ( Control the weights, and combine them with the Kalman filter gain formula:

[0125] At this point, the state transition equation and the target observation equation are updated as follows:

[0126]

[0127] in, This is the optimal estimate for the Kalman filter. Indicates the Kalman filter gain. The magnitude of this value reflects the importance of observational and predictive information in the state estimation at the current moment. (Kalman filter optimal estimate) It contains the location and status information of the AGV.

[0128] A second aspect of this invention relates to a substation indoor star-flash positioning system based on NSGA-II optimized anchor point layout. The system is implemented using the method described in the first aspect of this invention. The system includes a layout module and a positioning module. The layout module constructs objective functions to maximize coverage area, minimize average positioning error, and minimize the number of base stations, and constructs constraint conditions based on base station installation location constraints and coverage quality constraints. A multi-objective optimization algorithm is used to solve for the optimal base station layout scheme. Under the optimal base station layout scheme, the positioning module uses a star-flash-based Chan-Kalman filtering algorithm to perform real-time positioning of the movement trajectory of the substation indoor automated guided vehicle.

[0129] A third aspect of the present invention relates to a terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to perform the steps of the method described in the first aspect of the present invention.

[0130] A fourth aspect of the present invention relates to a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method described in the first aspect of the present invention.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions of the present invention still include content that can be modified or equivalently replaced in the specific implementation of the present invention. Any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A substation indoor starburst positioning method based on NSGA-II optimized anchor point layout, characterized in that, The method includes the following steps: The objective function is constructed to maximize the coverage area, minimize the average positioning error, and minimize the number of base stations. The constraint conditions are constructed using base station installation location constraints and coverage quality constraints. The base station installation location constraints include physical space limitations, height limitations, and distance limitations. The coverage quality constraints include minimum coverage rate and redundancy requirements. Based on the constraints, a total penalty term is constructed, and a multi-objective optimization algorithm is used to solve for the optimal base station layout scheme. During the multi-objective optimization process, the fitness is calculated by combining the objective function value and the total penalty term, thus obtaining the optimal base station layout scheme. Under the optimal base station layout scheme, the Chan-Kalman filtering algorithm based on star flash is used to locate the movement trajectory of the AGV indoor automated guided vehicle in the substation in real time.

2. The substation indoor starburst positioning method based on NSGA-II optimized anchor point layout according to claim 1, characterized in that: The objective function constructed to maximize coverage area, minimize average positioning error, and minimize the number of base stations includes: The objective function is: In the formula, , , As weight, ， ,and Within a given working area, there are M test points, and the true coordinates of each test point are... The coordinates calculated by the positioning algorithm are , Number of base stations; , , These are the normalized values ​​for coverage area, average positioning error, and number of base stations, respectively.

3. The substation indoor starburst positioning method based on NSGA-II optimized anchor point layout according to claim 1, characterized in that: When a test point n is not within the effective coverage area of ​​any base station, the penalty value for minimum coverage is... β4 is the violation threshold; otherwise, ; If a test point n is covered by fewer than imin base stations, then the penalty value for redundancy requirement is... nmin is the minimum required redundancy, in is the number of base stations actually covering the test point n, and β5 is an adjustment factor; otherwise, .

4. The substation indoor starburst positioning method based on NSGA-II optimized anchor point layout according to claim 1, characterized in that: Physical space constraints refer to the penalty value if base station i is located in an area where it cannot be installed. The adjustment coefficient β1 is a positive number, indicating a violation; otherwise, ; The height limit refers to the penalty value if the height of base station i is lower than hmin or higher than hmax. Where htarget is the target height and β2 is an adjustment coefficient; otherwise, ; The distance constraint refers to the penalty value for each pair of base stations i and j if the distance between them is less than dmin or greater than dmax. , where dij is the actual distance between base stations i and j, dtarget is the expected distance, and β3 is an adjustment coefficient; otherwise, .

5. The substation indoor starburst positioning method based on NSGA-II optimized anchor point layout according to claim 1, characterized in that: The total penalty term Ptotal is defined as the sum of all individual penalty terms: in, The penalty value is for physical space constraints. The penalty value is a height restriction. The penalty value is the distance limit. The penalty value for minimum coverage. This is the penalty value for redundancy.

6. The substation indoor starburst positioning method based on NSGA-II optimized anchor point layout according to claim 1, characterized in that: In the optimal base station layout scheme, suppose a total of N ≥ 4 star-flash base stations with known coordinates are deployed. The three-dimensional coordinates of the i-th star-flash base station are plotted. , ; The AGV equipped with the Star Flash tag communicates wirelessly with multiple Star Flash base stations in known locations in the vicinity; the signal arrival time difference is calculated based on the return response signal obtained from the wireless communication, and the time difference is converted into pseudorange difference; Using pseudo-distance difference, the Chan filtering algorithm is used to calculate the estimated position and estimation error covariance matrix of the AGV vehicle through a two-step weighted least squares method; The estimated position and estimation error covariance matrix obtained by the Chan filtering algorithm are used as inputs to the Kalman filtering algorithm to update the target state transition equation and target observation equation in the Kalman filtering algorithm, thus obtaining the final AGV position.

7. The substation indoor star-flash positioning method based on NSGA-II optimized anchor point layout according to claim 6, characterized in that: Construct auxiliary variables and linearized equations, and use the least squares method to solve for the initial position of the AGV; construct the error covariance matrix, and use the error covariance matrix to construct a weighted matrix; use the weighted matrix and the weighted least squares method to further optimize the initial position of the AGV, and obtain the estimated position and the estimated error covariance matrix of the AGV. The estimated position of the AGV is used as the state variable of the Kalman filtering algorithm, and the estimated error covariance matrix is ​​used as the process noise matrix. The Kalman filtering algorithm is divided into two stages: prediction and update. In the prediction stage, the state variable prediction equation and the error covariance prediction equation are obtained, the process noise matrix and the observation noise matrix are adjusted, and the state variable prediction equation and the error covariance prediction equation are updated by combining the Kalman filter gain to obtain the final AGV position.

8. A substation indoor star-flash positioning system based on NSGA-II optimized anchor point layout using the method described in any one of claims 1-7, comprising a layout module and a positioning module, characterized in that: The layout module constructs objective functions to maximize coverage area, minimize average positioning error, and minimize the number of base stations, constructs constraint conditions with base station installation location constraints and coverage quality constraints, and uses a multi-objective optimization algorithm to solve for the optimal base station layout scheme. Under the optimal base station layout scheme, the positioning module uses a Chan-Kalman filtering algorithm based on star flash to perform real-time positioning of the movement trajectory of the indoor automated guided vehicle in the substation.

9. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-7.

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