Low-cost UWB base station arrangement optimization method for deterministic positioning

Abstract

The invention provides a deterministic positioning-oriented low-cost UWB base station arrangement optimization method, which comprises the following steps of: (1) constructing a distance measurement model under LoS / NLoS mixed interference, deriving statistical characteristics of positioning errors based on a ToA positioning algorithm, and forming mathematical expression of an error confidence interval; and (2) solving the maximum value exceeded by the confidence interval according to a specific positioning requirement, and constructing an optimization problem of joint positioning precision, certainty and base station number. And (3) setting a change range of the number of base stations, generating a particle swarm of multiple dimensions, designing particle interaction rules of different dimensions, and iteratively updating and solving an optimal base station arrangement scheme. According to the method, the specific deterministic positioning requirement can be met, meanwhile, the number of arranged base stations is minimized, and the equipment cost is reduced.

Description

Technical Field

[0001] The invention relates to wireless communications and networks, and to a base station layout optimization technology oriented to deterministic positioning. Background Art

[0002] In recent years, with the development of location-based services (LBS), people need not only high-precision positioning, but also highly deterministic positioning technology. Ultra-wideband (UWB) positioning technology has the advantages of high ranging accuracy and strong anti-interference ability, and is a more suitable choice. Most existing studies optimize the layout of UWB base stations by minimizing the average positioning error, ignoring the performance degradation in a specific small area, which poses certain safety risks in intelligent and automated applications. Therefore, the optimization of base station deployment and the minimum number of deployed base stations for deterministic positioning requirements (such as 95% positioning error within 0.5 m) need to be studied, and have application value and prospects.

[0003] At present, the main problems in base station layout optimization are: 1) In complex scenarios, there are mixed line of sight / non line of sight (LoS / NLoS) interference areas. How to reasonably arrange base stations to avoid introducing NLoS interference during tag movement? 2) How to balance positioning certainty, accuracy and equipment cost to optimize base station deployment plans more comprehensively? 3) In actual applications, some areas have higher positioning performance requirements, while some areas have lower positioning performance requirements. How to reasonably adjust the base station deployment plan for the areas of interest to achieve efficient use of base stations. Summary of the invention

[0004] Based on the existing method of solving the tag position based on the time of arrival method, the present invention firstly derives the confidence interval of the positioning error, obtains the extreme point of the maximum confidence interval by derivative calculation, and reduces the calculation complexity of the traversed area; secondly, facing specific positioning requirements (such as 95% positioning error within 0.5 m), comprehensively considers factors such as positioning certainty, accuracy, number of base stations, and enhancement of the region of interest, constructs an enhanced positioning performance function, and more comprehensively measures the positioning performance of the base station deployment solution; finally, the transformed dimension particle swarm algorithm is used to search for the optimal base station layout solution to achieve specific positioning requirements, enhancement of the region of interest, and minimization of base station equipment costs.

[0005] Technical solution of the present invention: A low-cost UWB base station layout optimization method for deterministic positioning, the specific steps are as follows: Step 1. Mathematical expression of the confidence interval of positioning error Firstly, a ranging model under LoS / NLoS mixed interference is constructed, and the tag coordinates are solved based on the ToA method. Then, the statistical distribution characteristics of the ranging error vector and the positioning error are analyzed. Finally, the mathematical expression of the positioning error confidence interval is derived.

[0006] Step 2. Constructing positioning performance function The confidence interval deviation and the location of the extreme points of the standard deviation are analyzed, and the positioning certainty, accuracy, number of base stations and enhancement of the area of ​​interest are comprehensively considered to construct an improved positioning performance function.

[0007] Step 3. Find the optimal base station layout The transformed dimension particle swarm algorithm is used to search for the optimal base station layout plan; the transformed dimension particle swarm algorithm first initializes the particle swarm speed and state; in each iteration, according to the positioning performance function of step 2, the function value of each particle is calculated, and the individual optimal solution and the group optimal solution are obtained accordingly, and the optimal base station layout is searched to meet specific deterministic positioning requirements, while minimizing the number of deployed base stations and reducing equipment costs.

[0008] Beneficial Effects The present invention can be used to meet specific positioning requirements in a given area (such as 95% positioning error within 0.5 m), derive confidence intervals, positioning errors and positioning performance functions under different base station arrangements, and provide the minimum number of base stations and the optimal arrangement scheme required to meet specific positioning requirements, thereby realizing base station arrangement for deterministic positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 Flow chart of the method of the present invention; Figure 2 Schematic diagram of particle state update in different dimensions according to an embodiment of the present invention; Figure 3 Comparison chart of deterministic positioning performance of non-interested areas in embodiments of the present invention; Figure 4 Comparison chart of deterministic positioning performance of regions of interest according to embodiments of the present invention. DETAILED DESCRIPTION

[0010] The technical solution provided by the present application is further described below in conjunction with specific embodiments and accompanying drawings. The advantages and features of the present application will become more clear with the following description.

[0011] The low-cost UWB base station layout optimization method for deterministic positioning proposed in the present invention is suitable for the situation of a positioning system based on the ToA method, and can be applied to LoS ​​scenarios or LoS / NLoS mixed scenarios. For specified positioning requirements, the minimum number of base stations and layout solutions required are solved.

[0012] The deterministic positioning refers to ( ) Positioning error is within a given error range.

[0013] The present invention proposes an algorithm to derive the mathematical expression of the confidence interval and analyze the position of its extreme points, which effectively reduces the computational complexity; comprehensively considers the positioning certainty, positioning accuracy and the cost of UWB base station equipment, constructs a mathematical expression for enhanced positioning performance, measures the positioning performance more comprehensively and realizes the enhancement of the area of ​​interest; utilizes the particle swarm algorithm with transformed dimensions to search for the optimal base station layout to meet the characteristic deterministic positioning requirements, while minimizing the number of deployed base stations and reducing equipment costs.

[0014] A low-cost UWB base station layout optimization method for deterministic positioning, the specific steps are as follows: Figure 1 ) Step 1. Mathematical expression of the confidence interval of positioning error Firstly, a ranging model under LoS / NLoS mixed interference is constructed, and the tag coordinates are solved based on the ToA method. Then, the statistical distribution characteristics of the ranging error vector and the positioning error are analyzed. Finally, the mathematical expression of the positioning error confidence interval is derived.

[0015] The details are as follows: Step (11), in the positioning system coordinate system, The UWB base station communicates with the tag in turn, and the channel state during LoS and NLoS transmission is expressed as: Constructing the ranging model under LoS / NLoS mixed interference, The measured distance between a base station and a tag is expressed as: (1) in, Indicates The actual distance between the base station and the tag; represents the measurement error, which has a mean of 0 and a variance of The Gaussian distribution of ; represents the mean ranging error introduced by NLoS transmission; It represents the random error introduced by NLoS interference, which has a mean of 0 and a variance of The Gaussian distribution of Assuming that in the experimental area, the statistical characteristics of the ranging error All are known.

[0016] Specific steps for solving label coordinates and positioning errors: Step (12), construct the TOA positioning linear equation and solve the tag coordinates Step (121), assuming that the reference base station coordinates are known to be , the label position coordinates with positioning error are , construct the ToA positioning equation , where the observation matrix , the measurement vector without ranging error , measurement error vector Respectively expressed as: , , . Step (122), using the least squares method to solve the label coordinates , in, Represents the observation matrix The pseudo-inverse matrix of , the positioning error is .

[0017] Step (13), analyzing the statistical distribution characteristics of the measurement error vector .

[0018] Step (131), substitute formula (1) in step (11) into the error vector In . Step (132), since the error is much smaller than the distance between the label and the target, that is, , the error vector is approximately Gaussian distributed, denoted as ,in, , Represent the error vector The mean and variance of .

[0019] Step (133), according to the statistical characteristics of the ranging error, calculate the error vector mean The elements are: . Step (134), based on the statistical characteristics of the ranging error, calculate the error vector variance diagonal elements, off-diagonal elements ( )for: , . Step (14), deriving the statistical distribution characteristics of positioning error .

[0020] Specific steps to derive the mathematical expression of the confidence interval: Step (15), set The confidence interval of the positioning error is ,in According to the statistical distribution of positioning error in step (14), the upper and lower bounds of the confidence interval are derived as , , in, is the t-distribution (Student's distribution) in The value of .

[0021] Step 2. Constructing positioning performance function The confidence interval deviation and the location of the extreme points of the standard deviation are analyzed, and the positioning certainty, accuracy, number of base stations and enhancement of the area of ​​interest are comprehensively considered to construct an improved positioning performance function.

[0022] Specific steps for solving the extreme points of the maximum confidence interval: Step (21), analyze the confidence interval deviation Extreme point location.

[0023] Step (211), there is a deviation between the upper and lower bounds of the confidence interval in step (15) In the same base station combination, the observation matrix The pseudo-inverse matrix is ​​expanded as follows: , Substituting the above formula into , the deviations in the X, Y, and Z directions can be expressed as: , , .

[0024] Step (212), to simplify the calculation, select the base station that is all in LoS transmission as the first reference base station, that is .

[0025] Step (213), taking the deviation in the X direction as an example, taking the partial derivative of x, we can get . Let the derivative be equal to 0. When there are less than 3 base stations and the tag blocked, the extreme point can be directly solved as: . Similarly, Taking partial derivatives of y and z, we can get The extreme point position of : . In step (214), the positions of the deviation extreme value points in the Y and Z directions are similarly obtained as follows: . Step (215), confidence interval deviation The extreme value is , , Or obtained at the boundary of the base station area.

[0026] Step (22), analyze the confidence interval standard deviation Extreme point location.

[0027] Step (221), the matrix Taking the second-order partial derivative of x, we get , Similarly, the matrix The second-order derivatives with respect to x, y, and z are all positive definite.

[0028] Step (222), from this, we can get the confidence interval standard deviation The second-order derivatives with respect to x, y, and z are also positive definite. In the fixed base station combination area, The extreme values ​​are obtained at the base station area boundaries.

[0029] Step (23), combine the above possible extreme value positions and record them as set , including extreme points and the boundaries of the region.

[0030] The present invention reduces the problem of searching for the maximum confidence interval in the traversal area to the problem of searching for the maximum confidence interval in the set The maximum confidence interval is searched within the , which effectively reduces the complexity of the algorithm.

[0031] Specific steps to build positioning performance function: Step (24) is for specific deterministic positioning requirements, such as Positioning error in Within, recorded as , construct the confidence interval beyond the range function, expressed as The above function value changes as the label moves. The maximum value will be obtained.

[0032] Step (25), construct the positioning performance function.

[0033] Step (251), as the tag moves, it is necessary to meet the deterministic positioning requirements everywhere, such as 95% positioning error within 0.5 m. Therefore, we set the maximum confidence interval out of range as the optimization target, expressed as . Step (252), after reaching the specified deterministic positioning requirement, the positioning accuracy is fully considered, and the positioning mean square error is expressed as , and obtains the extreme value in the base station boundary area. Similarly, the maximum mean square error is set as the optimization target, expressed as . Step (253), comprehensively considering the positioning certainty, accuracy and number of base stations, constructing an improved positioning performance function , in, , , A weight is assigned to each optimization target. Increasing a certain weight will result in a higher certainty and accuracy index in the optimization result or a smaller number of base stations required.

[0034] Specific steps for enhancing the region of interest: Step (26), considering that in actual applications, different regions have different positioning performance requirements, they are divided into regions of interest (denoted as ROI) and regions of non-interest (non-ROI). Similarly, the boundaries of the ROI and non-ROI regions and the set of extreme points contained in them are divided separately, denoted as , .

[0035] Step (27), after introducing the region of interest, construct the enhanced positioning performance function in, , are ROI and non-ROI weights respectively, satisfying .

[0036] The present invention is aimed at specific positioning requirements ( ), comprehensively considering factors such as positioning performance, equipment cost and enhancement of the area of ​​interest, and constructing a mathematical description of enhanced positioning performance under different base station layout schemes ( ), which is a more comprehensive measure that helps to achieve a balance between positioning performance and economic factors.

[0037] Step 3. Find the optimal base station layout The particle swarm algorithm with transformed dimensions is used to search for the optimal base station layout solution.

[0038] Specifically, the three-dimensional coordinates of all base stations in a base station deployment scheme are taken as a particle; The particle dimension is the dimension of the set of position coordinates of all base stations in the particle; A particle swarm is a collection of particles including multiple dimensions (i.e., multiple numbers of base stations); The particle velocity represents the change in the base station coordinates between two iterations; The transformed dimension particle swarm algorithm first initializes the particle swarm speed and state; in each iteration, according to the positioning performance function of step (2), the function value of each particle is calculated, and the individual optimal solution and the group optimal solution are obtained accordingly, and the optimal base station layout is searched to meet the specific deterministic positioning requirements, while minimizing the number of deployed base stations and reducing equipment costs.

[0039] Step (31), algorithm initialization, including particle swarm velocity and state initialization.

[0040] In step (311), it is assumed that each particle represents a three-dimensional coordinate vector of a group of base stations, that is, a base station layout scheme, which is expressed as follows: . The number of base stations deployed for this base station deployment plan, then The particle dimensions are , and satisfies , .

[0041] The particle swarm contains particles of various dimensions, and particles of each dimension are initially generated. Then the total number of particles in the particle swarm is , ≤ .

[0042] Step (312), randomly generating particle states within the base station deployment area.

[0043] In the Particle No. At the iteration, the state vector is expressed as , , in, , etc. are the coordinates of the base station inside the particle.

[0044] Step (313), randomly generate particle speed, in the Particle No. At the iteration, the velocity vector is expressed as . Step (32), in each iteration, according to the enhanced positioning performance function of step (27), the function value of each particle is calculated, and each particle records all states and compares them to select the particle state with the smallest function value as the individual optimal solution, which is recorded as . From the individual optimal solutions of all particles, the particle state with the smallest function value is selected as the group optimal solution, denoted as . Step (33), set the interactive update rules of particles of different dimensions, such as Figure 2 .

[0045] Step (331), in the process of updating particles to individual optimal and group optimal, there may be three dimensions, namely , , , corresponding to the dimensions of the ith particle, the ith particle’s individual optimal solution, and the ith particle’s swarm optimal solution. At the iteration, the probabilities corresponding to the three dimensions are , , .

[0046] Step (332), generate a random number between 0 and 1 , like , then The dimension of the i-th particle in the iteration is The particle dimensions are consistent in the iterations, that is, ; like , then The dimension of the i-th particle in the iteration is The individual optimal solution of the i-th particle in the iteration is consistent, that is, ; like , then The dimension of the i-th particle in the iteration is The optimal solution of the particle swarm in the iteration is consistent, that is, .

[0047] Step (333), unify the dimensions of the vectors in steps (31)-(33), when the vector dimension is greater than When the vector dimension is less than When , refer to the initialization process of step (31), randomly generate high-dimensional information and supplement the vector. The particle speed, state, individual optimal solution, and group optimal solution after truncation or supplementation are expressed as , , , .

[0048] Specific steps for searching the optimal base station layout based on particle swarm: Step (34), in order to balance group learning and individual learning, the inertia weight factor that changes with the number of iterations is set to , which decreases with the number of iterations. The inertia weight factor of the iteration is expressed as: . in, is the range of weight variation. is the maximum number of iterations.

[0049] Step (35), particle swarm iterative update.

[0050] Step (351), using the vector of uniform dimension in step (33) , , , , update the particle velocity: , in, , is the learning factor, usually set to 2; , is a random number, subject to Evenly distributed.

[0051] Step (352), set the iterative update frequency , using the updated velocity vector, update the particle state: . Step (36), repeat steps (32) to (35) until convergence or the maximum number of iterations is reached. The group optimal solution corresponds to the optimal base station deployment plan, and the dimension of the group optimal solution corresponds to the minimum number of deployed base stations.

[0052] Simulation comparison experiment: The present invention takes the enhanced positioning performance function in step (27) as the optimization target, constructs a particle swarm containing particles of different dimensions, and uses a particle swarm algorithm with transformed dimensions to search for a given positioning requirement to obtain the minimum number of base stations and base station layout plan, thereby achieving joint optimization of the number of base stations and the layout plan.

[0053] Experimental results: Assume that the positioning requirement in the [X, Y] direction of the non-interest area is [1, 0.2]m @ 95%, and the positioning requirement in the [X, Y] direction of the interest area is [0.5, 0.1]m @ 95%. From recent related literature, typical base station layout schemes are selected, denoted as Uniform[1], WPDOP[2], GDOP[3], and MSE[4]. In the proposed algorithm, the optimal base station layouts obtained by searching before and after the interest area (step (253), step (27)) are denoted as PSO-VND and PSO-VND-ROI respectively. The positioning error is statistically analyzed, and the cumulative distribution functions of different base station layout schemes in the non-interest area and the interest area are as follows: Figure 3 , 4 shown.

[0054] In non-interest areas, such as Figure 3 As shown in the figure, the proposed PSO-VND and PSO-VND-ROI deployment schemes both meet the positioning requirements ([1.0, 0.2] m @ 95%), that is, more than 95% of the positioning errors are within [1, 0.2] m, while the other four schemes do not meet the requirements. In the X direction, compared with the Uniform, WPDOP, GDOP, and MSE base station deployment schemes, the proposed PSO-VND base station deployment has improved the cumulative error distribution index within the positioning requirements by 22.08%, 32.58%, 14.94%, and 11.21%, respectively.

[0055] In the region of interest, Figure 4 As shown in the figure, the proposed PSO-VND-ROI layout scheme can further meet higher positioning requirements ([0.5, 0.1] m @95%), that is, more than 95% of the positioning errors are within [0.5, 0.1] m, which is not met by the other five layout schemes. In the X direction, compared with the Uniform, WPDOP, GDOP, MSE, and PSO-VND base station layout schemes, the proposed PSO-VND-ROI base station layout has improved the cumulative error distribution index within the positioning requirements by 52.85%, 53.16%, 56.2%, 40.2%, and 27.01%, respectively.

[0056] In addition, facing the same deterministic positioning requirement ([1.0, 0.2] m @ 95%), Uniform, WPDOP, GDOP, MSE and the solutions proposed in the present invention require the deployment of 23, 23, 44, 12 and 8 base stations respectively. From the perspective of equipment cost, the cost of the proposed solutions is reduced by 65.22%, 65.22%, 81.81% and 50.0% respectively.

[0057] The above experiments prove the effectiveness of the proposed algorithm. For the given deterministic positioning requirements, the required positioning performance can be achieved with the minimum number of base stations, which has practical application value.

[0058] References: [1] W.-N. He, X.-L. Huang, Z. Xu, F. Hu, and S. Yu, “Robust localization for mobile targets along a narrow path with LoS / NLoSinterference,” IEEE Internet of Things Journal, vol. 11, no. 11, pp. 20 853–20 866, 2024. [2] B. Cao, S. Wang, S. Ge, F. Chen, and H. Zhang, “UWB anchor nodeoptimization deployment using MGWO for the coal mine working face end,” IEEETransactions on Instrumentation and Measurement, vol. 72, pp. 1–12, 2023. [3] L. Zhang, K. Jiao, W. He, and X. Wang, “Anchor deployment optimization for range-based indoor positioning systems in non-line-of-sightenvironment,” IEEE Sensors Journal, vol. 24, no. 15, pp. 24 405–24 420, 2024. [4] W.-N. He, X.-L. Huang, Z. Xu, F. Hu, and S. Yu, “Adaptive anchordeployment for diverse demands on localization precision,” IEEE Transactionson Vehicular Technology, vol. 73, no. 12, pp. 19 480–19 494, 2024.

Claims

1. A low-cost UWB base station layout optimization method for deterministic positioning, characterized in that: The following steps are involved: Step 1. Mathematical expression of the confidence interval of positioning error Firstly, a ranging model under LoS / NLoS mixed interference is constructed, and the tag coordinates are solved based on the ToA method. Then, the statistical distribution characteristics of the ranging error vector and the positioning error are analyzed. Finally, the mathematical expression of the positioning error confidence interval is derived. Step 2. Constructing positioning performance function Analyze the confidence interval deviation and the location of the extreme point of the standard deviation, comprehensively consider the positioning certainty, accuracy, number of base stations and enhancement of the area of ​​interest, and construct an improved positioning performance function; Step 3. Find the optimal base station layout The transformed dimension particle swarm algorithm is used to search for the optimal base station layout plan; the transformed dimension particle swarm algorithm first initializes the particle swarm speed and state; in each iteration, according to the positioning performance function of step 2, the function value of each particle is calculated, and the individual optimal solution and the group optimal solution are obtained accordingly, and the optimal base station layout is searched to meet the deterministic positioning requirements of the characteristics, while minimizing the number of deployed base stations and reducing equipment costs.

2. A low-cost UWB base station layout optimization method for deterministic positioning according to claim 1, characterized in that: Step 1 is as follows: Step (11), in the positioning system coordinate system, The UWB base stations communicate with the tags in turn, and the channel states during LoS and NLoS transmission are expressed as: Constructing the ranging model under LoS / NLoS mixed interference, The measured distance between a base station and a tag is expressed as: (1) in, Indicates The actual distance between the base station and the tag; represents the measurement error, which has a mean of 0 and a variance of The Gaussian distribution of ; represents the mean ranging error introduced by NLoS transmission; It represents the random error introduced by NLoS interference, which has a mean of 0 and a variance of The Gaussian distribution of ; Step (12), constructing the TOA positioning linear equation and solving the tag coordinates; Step (121), assuming that the reference base station coordinates are known to be , the label position coordinates with positioning error are , construct the ToA positioning equation , where the observation matrix , the measurement vector without ranging error , measurement error vector Respectively expressed as: , , . Step (122), using the least squares method to solve the label coordinates , in, Represents the observation matrix The pseudo-inverse matrix of , the positioning error is ; Step (13), analyzing the statistical distribution characteristics of the measurement error vector ; Step (131), substitute formula (1) in step (11) into the error vector In . Step (132), since the error is much smaller than the distance between the label and the target, that is, , the error vector is approximately Gaussian distributed, denoted as ,in, , Represent the error vector The mean and variance of Step (133), according to the statistical characteristics of the ranging error, calculate the error vector mean The elements are: . Step (134), based on the statistical characteristics of the ranging error, calculate the error vector variance diagonal elements, off-diagonal elements ( )for: , . Step (14), derive the statistical distribution characteristics of positioning error . Specific steps to derive the mathematical expression of the confidence interval: Step (15), set The confidence interval of the positioning error is ,in According to the statistical distribution of positioning error in step (14), the upper and lower bounds of the confidence interval are derived as , , in, is the t-distribution (Student's distribution) in The value of .

3. The low-cost UWB base station layout optimization method for deterministic positioning according to claim 1, characterized in that: Step 2 is as follows: Step (21), analyze the confidence interval deviation Extreme point location, confidence interval deviation The extreme value is , , Or obtain it at the boundary of the base station area, as follows: . . Step (22), analyze the confidence interval standard deviation The location of the extreme point, The extreme values ​​are obtained at the boundaries of the base station area; Step (23), combine the above possible extreme value positions and record them as set , including extreme points and the boundaries of the region; Step (24), for Deterministic positioning requirements, building confidence interval out-of-range functions The above function value changes as the label moves. The maximum value will be achieved; Step (25), constructing a positioning performance function, including: Considering positioning certainty, accuracy and number of base stations, an improved positioning performance function is constructed , in, , , A corresponding weight is given to each optimization target. Increasing a certain weight will make the corresponding certainty and accuracy index in the optimization result higher or the number of base stations required less; Step (26), considering that in practical applications, different regions have different positioning performance requirements, they are divided into regions of interest (ROI) and non-ROIs; similarly, the boundaries of the ROI and non-ROI regions and the set of extreme points contained therein are divided separately, denoted as , ; Step (27), after introducing the region of interest, construct the enhanced positioning performance function in, , are ROI and non-ROI weights respectively, satisfying .

4. The low-cost UWB base station layout optimization method for deterministic positioning according to claim 1, characterized in that: Step 3 is as follows: Step (31), algorithm initialization, including particle swarm velocity and state initialization; In step (311), each particle represents a three-dimensional coordinate vector of a group of base stations, which is expressed as follows: . The number of base stations deployed for this base station deployment plan, then The particle dimensions are , and satisfies , ; The particle swarm contains particles of various dimensions, and particles of each dimension are initially generated. Then the total number of particles in the particle swarm is , ≤ ; Step (312), randomly generating particle states within the base station deployment area; In the Particle No. At the iteration, the state vector is expressed as , , in, , etc. are the coordinates of the base station in the particle respectively; Step (313), randomly generate particle speed, in the Particle No. At the iteration, the velocity vector is expressed as . Step (32), in each iteration, according to the enhanced positioning performance function of step (27), the function value of each particle is calculated, and each particle records all states and compares them to select the particle state with the smallest function value as the individual optimal solution, which is recorded as . From the individual optimal solutions of all particles, the particle state with the smallest function value is selected as the group optimal solution, denoted as . Step (33), set the interactive update rules of particles of different dimensions Step (331), in the process of updating particles to individual optimal and group optimal, there may be three dimensions, namely , , , corresponding to the dimensions of the ith particle, the ith individual optimal solution of the ith particle, and the ith particle swarm optimal solution; set at the At the iteration, the probabilities corresponding to the three dimensions are , , ; Step (332), generate a random number between 0 and 1 , like , then The dimension of the i-th particle in the iteration is The particle dimensions are consistent in the iterations, that is, ; like , then The dimension of the i-th particle in the iteration is The individual optimal solution of the i-th particle in the iteration is consistent, that is, ; like , then The dimension of the i-th particle in the iteration is The optimal solution of the particle swarm in the iteration is consistent, that is, ; Step (333), unify the dimensions of the vectors in steps (31)-(33), when the vector dimension is greater than When the vector dimension is less than When , refer to the initialization process of step (31), randomly generate high-dimensional information and supplement the vector. The particle speed, state, individual optimal solution, and group optimal solution after truncation or supplementation are expressed as , , , ; Step (34), in order to balance group learning and individual learning, the inertia weight factor that changes with the number of iterations is set to , which decreases with the number of iterations. The inertia weight factor of the iteration is expressed as: . in, is the range of weight variation. is the maximum number of iterations; Step (35), particle swarm iterative update; Step (351), using the vector of uniform dimension in step (33) , , , , update the particle velocity: , in, , is the learning factor, usually set to 2; , is a random number, subject to Even distribution; Step (352), set the iterative update frequency , using the updated velocity vector, update the particle state: . Step (36), repeat steps (32) to (35) until convergence or the maximum number of iterations is reached. The group optimal solution corresponds to the optimal base station deployment plan, and the dimension of the group optimal solution corresponds to the minimum number of deployed base stations.

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