A pseudolite base station layout optimization method suitable for urban lifeline monitoring

Abstract

This invention proposes a pseudo-satellite base station layout optimization method suitable for urban lifeline monitoring, belonging to the field of deformation monitoring. The method determines the urban lifeline areas to be monitored based on existing city maps and analysis of relevant GNSS signal strength and positioning accuracy. It also analyzes system measurement errors in positioning scenarios to determine the constraints on base station layout, using GDOP (Geostationary Descent Point)... w Evaluation metrics were established, and a mathematical model of the base station geometric layout was built in the positioning area. The Monte Carlo algorithm was used to solve the mathematical optimization model with Cramérault lower bound (CRLB) constraints, thus initially determining the current optimal layout of base stations in the positioning area. These models were then used as superior individuals in a population, and an improved genetic algorithm was used to obtain the optimal base station layout. This invention makes the deployment of pseudo-satellite base stations in urban environments more flexible and accurate, improving base station signal coverage and quality, system positioning accuracy, and enhancing the efficiency of urban lifeline monitoring.

Description

Technical Field

[0001] This invention relates to a method for optimizing the layout of pseudo-satellite base stations in urban environments, belonging to the fields of radio navigation and positioning technology and deformation monitoring, and is applicable to large-scale urban spaces. Background Technology

[0002] With the acceleration of urbanization, the safety monitoring of urban lifelines is receiving increasing attention. Urban lifeline projects are critical infrastructures distributed in a network within a space, characterized by their engineering nature, concealment, coupling, and long-term service. They have strong public attributes, a wide impact, and can generate significant chain reactions under natural disasters and safety accidents. At the same time, ground and building settlement also pose various hidden dangers. Currently, urban lifeline projects, influenced by multiple factors, may enter a period of high accident incidence. For large-scale and structurally complex urban lifeline projects, their construction and service environments are becoming increasingly demanding, the difficulty of supervision is continuously increasing, and the requirements for their functions and performance are becoming increasingly stringent.

[0003] GNSS can periodically observe urban subsidence and proactively identify potential facility risks caused by it. However, in urban environments, buildings and other obstacles can cause multipath effects on GNSS signals, namely signal reflection and refraction. This can lead to positioning errors and instability, thus affecting the accuracy and reliability of monitoring. Furthermore, tall buildings and narrow streets can obstruct GNSS receiver antennas, affecting signal reception and positioning accuracy. Considering the inherently limited positioning accuracy of GNSS systems, especially in urban canyons and densely populated areas with high-rise buildings, single-use GNSS may not be sufficient for urban lifeline monitoring applications requiring high-precision positioning.

[0004] Using pseudosatellites can provide more stable and reliable positioning services, overcoming the limitations of GNSS in urban environments. By deploying base stations on the ground or rooftops and enhancing signal transmission, pseudosatellites can compensate for the deficiencies of GNSS signals in urban environments, providing more accurate and reliable positioning services. Therefore, a well-planned layout of pseudosatellite base stations can expand communication coverage, provide emergency communication, support mobile communication needs, provide high-speed communication services, and also support services such as the Internet of Things and smart cities. However, research on optimizing pseudosatellite base station layouts in urban environments is limited. Simple pseudosatellite system base station layouts can no longer meet the demands for high-precision and stable positioning services, thus failing to reduce deployment costs and advance urban lifeline infrastructure projects. Finding a pseudosatellite base station layout scheme that simultaneously satisfies both coverage effectiveness and efficiency is crucial. Furthermore, while overly compact pseudosatellite base station deployments can improve positioning accuracy to some extent, they also result in excessively high costs, hindering widespread adoption.

[0005] Based on a summary and analysis of existing research, this paper proposes a pseudo-satellite base station layout optimization method combining the Monte Carlo algorithm and an improved genetic algorithm. This method not only improves the reliability of pseudo-satellite base station layout in urban environments but also reduces computational complexity and workload, thereby increasing operational efficiency. Simultaneously, it enhances the regional coverage capability of pseudo-satellite base stations to a certain extent. Compared to traditional genetic algorithms, the improved genetic algorithm exhibits faster convergence speed, higher search accuracy, and lower computational cost. Furthermore, it can optimize problems under multiple constraints, thus improving the solution efficiency and quality of the pseudo-satellite base station layout optimization problem. This makes the deployment of pseudo-satellite base stations in urban environments more flexible and accurate, improving base station signal coverage and system positioning accuracy, and ultimately enhancing the reliability of pseudo-satellite base station layout in urban environments. Summary of the Invention

[0006] Technical Issues: In most urban environments, GNSS signals often fail to provide effective coverage, sometimes even failing to reach the designated areas. Using traditional pseudosatellite base station deployments does not significantly improve positioning accuracy or urban lifeline safety monitoring. Existing research often fails to simultaneously meet the requirements of both coverage effectiveness and efficiency in pseudosatellite base station deployments, thus failing to effectively solve practical problems. Consequently, it cannot adequately support traditional networks and advance urban lifeline safety monitoring. Simple pseudosatellite system base station deployments are no longer sufficient to meet the demands of high-precision, stable positioning services and other functionalities.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: a method for optimizing the layout of pseudo-satellite base stations in an urban environment, the method comprising the following steps:

[0008] S1: Determine the urban lifeline areas that need to be monitored based on existing city maps and analysis of relevant GNSS signal strength and positioning accuracy, while also referring to urban planning and development plans;

[0009] S2: Through system measurement error analysis in urban environment positioning scenarios, GDOP was used. w Develop evaluation metrics and establish a mathematical model for the geometric layout of base stations.

[0010] S3: Solve mathematical optimization models with Cramer-Rao lower bound (CRLB) constraints using the Monte Carlo algorithm.

[0011] S4: By constructing a penalty function, it is transformed into an unconstrained optimization problem.

[0012] S5: Then, it is solved as an excellent individual in the population.

[0013] S6: The optimal base station layout is obtained by using a genetic algorithm based on the mountaineering method, thereby optimizing the layout of pseudo-satellite base stations in urban environments.

[0014] Specifically, S1 identifies the urban lifeline areas requiring monitoring. Based on the urban lifeline network topology and existing urban maps, GNSS signal strength analysis and positioning accuracy assessment are conducted. Simultaneously, considering important infrastructure and key equipment in urban planning and development, risk assessment and priority determination are performed to determine signal coverage and the number of pseudo-satellite base stations. To differentiate the errors between pseudo-satellite systems and GNSS in urban environments, GDOP is used. w This serves as a standard for evaluating the layout of pseudo-satellite base stations, thereby highlighting the rationality and advantages / disadvantages of such layouts.

[0015] Specifically, in S2, a mathematical model of the base station's geometric layout is established through system measurement error analysis in urban environment positioning scenarios, using GDOP. w As a standard for measuring the layout of system base stations, based on the four system base station locations LS1(x1,y1,z1), LS2(x2,y2,z2), LS3(x3,y3,z3) and LS4(x4,y4,z4) as custom variables of the base station layout model, we can obtain Equation (1).

[0016]

[0017] The purpose of the base station layout optimization model is to find the optimal solution (X,Y,Z) for the unknown vector (X,Y,Z). i ,Y i Z i This is the optimal location for the base station. In this environment, when GDOP... w The smaller the value, the more reasonable the layout of pseudo-satellite base stations. The objective function in this positioning scenario is Equation (2).

[0018]

[0019] Specifically, S3 uses the Monte Carlo algorithm to solve mathematical optimization models with Cramerlow lower bound (CRLB) constraints, and GDOP is used in this environment. w When determining the location, its lower bound of Clamello is:

[0020] CRLB = a 2 (R H S -1 R) -1 (3)

[0021] Where R is the coefficient matrix between the base station coordinates (X,Y,Z), i=1,2,...,n and the positioning target coordinates (x,y), and S is the positioning system GDOP. w The covariance matrix of the measurement error, where a is the propagation speed of the positioning signal in the air, and S is specifically represented as follows:

[0022]

[0023] Where, d n Based on the pseudorange between different base station layouts, the unbiased estimator closest to the lower bound is selected as the best unbiased estimator through CRLB, and the next step of the Monte Carlo algorithm is carried out under the Cramerlow lower bound constraint.

[0024] In S4, within the positioning area, the probability distribution of the Monte Carlo algorithm is set to a uniform distribution. Random values ​​based on this probability distribution are then generated by computer, with a defined range for each value. New random values ​​are continuously generated using a recursive formula, and multiple samples are taken within the range. The objective function established by the base station layout model of the positioning area is used, with the Cramerlow lower bound as one of the evaluation criteria. The selected random numbers that meet the constraints are substituted into the objective function to solve the problem. Then, each calculation result is compared to obtain the optimal location for the base station layout in the positioning area. For constrained optimization problems, a penalty function is constructed to transform them into unconstrained optimization problems.

[0025] U(X,Y,Z,γ)=f(X,Y,X)+γu(X,Y,Z) (5)

[0026] Where γ is the penalty factor, and u(X,Y,Z) is the penalty term, expressed by equation (6) as follows:

[0027]

[0028] Among them l i (X,Y,Z) and r i (X, Y, Z) represent the inequality constraints and equality constraints in equation (6), respectively. Solve the unconstrained optimization problem by following these steps:

[0029] A chooses the initial point (X0, Y0, Z0), assuming the penalty factor γ is positive, and the termination condition is that μ is also positive, the value of which depends on the established model. Let m start from 1.

[0030] B with (X) m-1 ,Y m-1 Z m-1 Starting with point , we solve the unconstrained optimization problem: min{f(X,Y,Z)+γ} m u(X,Y,Z)}, obtain the optimal solution (X) under the current loop. m ,Y m Z m ),

[0031] C if γ m u(X m,Y m Z m )≥CRLB, while u(X) m ,Y m Z m If μ ≤ μ, then the iteration terminates and the optimal solution is obtained.

[0032] D Update γ m+1 >γ m m = m + 1, then return to step B to continue the iteration.

[0033] After the loop ends, the initial optimal base station layout coordinates can be obtained.

[0034] Among them, the improved genetic algorithm based on the mountain climbing method in S6 obtains the optimal base station layout method as follows:

[0035] A sets the current optimal solution obtained by the Monte Carlo algorithm that satisfies the conditions as a subpopulation consisting of excellent individuals, GOPe.

[0036] B then calculates the threshold R using equation (7): where D represents the distance between the i-th individual and the optimal individual, N represents the number of individuals in the population, i is a positive integer, iterating from 1 to N-1, and c is a constant, with c = 0.3 selected. The threshold R selected in this way can be adaptively adjusted according to the distance changes between individuals in each generation.

[0037]

[0038] C takes the best individual as the current individual, adaptively updates it, and updates its fitness function. Centering on the best individual, it searches backwards for individuals whose Euclidean distance is greater than a threshold R. If a search is successful, that individual is added to the Group of Populations (GOP), and the current individual is replaced by that individual.

[0039] This process continues until the last individual is found. In this way, a sub-elite population can be obtained near the extreme values ​​of different excellent individuals. Assume the number of individuals in GOPo is K, as shown in equation (8):

[0040] GOPo={S1,S2,…,S K} (8)

[0041] D. Assume the number of individuals in the GOP is L, and GOP = {S1', S2', ..., S...} L '}, select the i-th individual S from the elite population GOPo i With the j-th individual S in GOPe j 'Calculate the vector difference to obtain the chromosome difference vector V' ij , as in equation (9).

[0042]

[0043] Where n represents the number of base stations, i = 1, 2, ..., K, j = 1, 2, ..., Q, before proceeding to the next step, X ij Each component retains only its symbol to ensure its distinction from other components. Furthermore, each component must have a unique symbol to indicate the direction of ascent it represents. This ensures that each component is represented correctly and can be correctly converted to other components. For example, V ij = [+2,0,-3,+1,…], where the vector represents individual S. i direction of climbing

[0044] E through S i The difference vector V between them ij To determine the new chromosome W i First, regarding S i The sequence is sorted out, and duplicate sequences that do not meet the conditions are deleted. Then, according to the calculation method of equation (10), S is calculated. i Adjustments were made, replacing any repetitive sequences that did not meet the criteria; finally, the new chromosome W was... i With the known S i Combine them.

[0045] W i =S i +V ij •overall•step (10)

[0046] Where, overall represents the total range vector of each component of the chromosome, with each chromosome being a vector; step represents the step size factor; when calculating fitness, if the fitness of the new chromosome is higher than that of the original chromosome, it is replaced, using W. i Replace S i Otherwise S i It remains unchanged.

[0047] Let G let j = j + 1. If j ≤ Q, repeat step CE.

[0048] Let H = i + 1. If i ≤ K, repeat steps DE.

[0049] This method generates pseudo-satellite base station layout coordinates, is applicable to various urban positioning scenarios, and can more quickly solve for pseudo-satellite base station layout schemes. This achieves greater flexibility and accuracy in pseudo-satellite base station layout, improves base station signal coverage and system positioning accuracy, and enhances the efficiency of combining GNSS and pseudo-satellite systems for urban lifeline monitoring.

[0050] Compared to existing technologies, the advantages of this invention are as follows: This invention determines the urban lifeline areas requiring monitoring based on existing city maps and analysis of relevant GNSS signal strength and positioning accuracy; and through system measurement error analysis in urban environmental positioning scenarios, it uses GDOP... w This paper establishes evaluation metrics and a mathematical model for the geometric layout of base stations. Based on summarizing and analyzing existing research, a pseudo-satellite base station layout optimization method combining Monte Carlo algorithm and improved genetic algorithm is proposed. This method not only improves the reliability of pseudo-satellite base station layout in urban environments but also reduces computational complexity and workload, thus improving operational efficiency. Simultaneously, it enhances the regional coverage capability of pseudo-satellite base stations to a certain extent. Compared to traditional genetic algorithms, the improved genetic algorithm using the mountain climbing method achieves faster convergence speed, higher search accuracy, and lower computational load in obtaining the optimal pseudo-satellite base station layout. Furthermore, it can optimize problems under multiple constraints, thereby improving the solution efficiency and quality of the pseudo-satellite base station layout optimization problem. This makes the construction of pseudo-satellite base station layouts in urban environments more flexible and accurate, improving base station signal coverage and system positioning accuracy, and ultimately enhancing the reliability of pseudo-satellite base station layouts in urban environments. Attached Figure Description

[0051] Figure 1 and Figure 2 This is a schematic diagram of the simulation results for an example.

[0052] Figure 3 This is a schematic diagram of the overall process of the present invention. Detailed Implementation

[0053] To enhance understanding of the present invention, the following detailed description of the solution is provided in conjunction with the accompanying drawings and embodiments.

[0054] Example: This invention enables more flexible and accurate deployment of pseudo-satellite base stations in urban environments, and can improve base station signal coverage and system positioning accuracy.

[0055] Technical solution: The method of the present invention to solve the above-mentioned technical problems is achieved through the following technical solution:

[0056] S1: Based on the urban lifeline network topology, starting with existing urban maps, we analyze GNSS signal strength and assess positioning accuracy. Simultaneously, referencing important infrastructure and key equipment in urban planning and development, we conduct risk assessments and prioritize signal coverage and the number of pseudo-satellite base stations. To highlight the differences between pseudo-satellite systems and GNSS errors in urban environments, and to emphasize the advantages and disadvantages of pseudo-satellite base station deployment, we adopt GDOP (Geometric Positioning Optimization). w As a standard for measuring the quality of pseudo-satellite base station deployment, GDOP is one such standard. w It is the covariance matrix D of the observation error vector.η With some changes, since the pseudoranges of different pseudosatellites no longer follow the same normal distribution, D... η The diagonal elements are no longer consistent. Suppose that at this time D η The form is:

[0057]

[0058] Among them, GDOP w This represents the variance of the pseudorange measurement error of the receiver for pseudosatellites. Specifically, GDOP w It is used to measure the quality of pseudo-satellite base station layout and reflects the sensitivity of the receiver to pseudo-satellite measurement errors at different locations.

[0059] in This reflects the receiver's sensitivity to pseudo-satellite measurement errors at different locations, specifically the variance of the pseudorange measurement error of pseudo-satellite i, where i is a positive integer with a maximum value not exceeding N. If we assume the variance of the master station's error is... Then let matrix D η Represented as:

[0060]

[0061] In this matrix, the i-th element of the diagonal matrix W represents the ratio of the pseudorange error variance of the corresponding pseudosatellite to the pseudorange error variance of the master station. This ratio depends only on the distance from the pseudosatellite base station to the receiver. When the distances between the receiver and each pseudosatellite base station are unequal, this ratio will change accordingly, affecting the variance of the observation error. Since they are no longer the same, smaller weights should be assigned to the observation equations with larger errors during the solution process to reduce the impact of larger errors on positioning accuracy. Based on this idea, a weight matrix P is multiplied on both sides of the error equation, and the original error equation will become the form.

[0062] PV = PHdX + Pη

[0063] Since larger elements in matrix W indicate a larger variance in pseudorange measurement error, a weight matrix can be introduced, therefore P = W. -1 This involves adjusting the coefficients of each equation in the error equation set. By adjusting the weights, the weights of observation equations with large pseudorange errors can be reduced, thereby altering the impact of each pseudosatellite's pseudorange error on the accuracy of the positioning results.

[0064] Error variance of the main station Substituting the weight matrix P, it cannot be obtained by using the least squares method:

[0065]

[0066] Among them, H wIt is the position matrix in a ground-based pseudo-satellite positioning system, G w Given the weighting coefficient matrix, and based on the concept of precision factor, the weighted geometrical precision factor (GDOP) applicable to ground-based pseudosatellite positioning systems can be similarly derived from the weighting coefficient matrix. w :

[0067]

[0068] where d w11 d w22 d w33 d w44 It is G w The diagonal elements of a matrix.

[0069] S2: Through system measurement error analysis in urban environmental positioning scenarios, based on historical data and risk assessment, areas in the city with high accident and disaster risks are identified. The coordinates of the base station location are set as the independent variable, and the minimum average GDOP in the positioning scenario is determined. w Using the base station locations as the dependent variable, and then determining the constraints of the base station layout, a mathematical model of the base station geometric layout is established. Based on the four system base station locations LS1(x1,y1,z1), LS2(x2,y2,z2), LS3(x3,y3,z3), and LS4(x4,y4,z4) as the control variables of the base station layout model, we can obtain:

[0070]

[0071] The optimization model for base station layout is to find the optimal solution (X,Y,Z) for the unknown vector (X,Y,Z). i ,Y i Z i This represents the optimal location of the base station, if the GDOP in the positioning scenario... w The smaller the value, the more reasonable the base station layout is in this positioning scenario. The objective function for this positioning scenario is:

[0072]

[0073] Select a reasonable base station location within the positioning area to minimize the number of base stations in the positioning area, and find an optimal solution that meets the conditions at each base station location. That is, maximize the coverage area of ​​the pseudo-satellite base station signal under certain constraints to achieve the expected goal.

[0074] The positioning area in the pseudosatellite positioning system is divided into several regions, and a base station location is selected within each region. For example, if a region has 5 base stations, with 4 of them located in different locations, it is divided into four sub-regions. The reasonable pseudosatellite coverage area can then be obtained based on the objective function.

[0075] S3: Using the Cramero lower bound as a constraint, the Cramero lower bound represents a definite lower limit for a parameter estimator. For any unbiased estimator, if its variance has a lower bound, then the unbiased estimator can only approximate its value at infinity in its vicinity. Therefore, we can use this model to perform optimal theoretical positioning performance analysis on the positioning system. When using GDOPw to trade off positioning accuracy in the positioning system, its Cramero lower bound is:

[0076] CRLB = a 2 (R H S -1 R) -1

[0077] Where R is the coefficient matrix between the base station coordinates (X,Y,Z), i=1,2,...,n and the positioning target coordinates (x,y), and S is the positioning system GDOP. w The covariance matrix of the measurement error, where a is the propagation speed of the positioning signal in the air, and S is specifically represented as follows:

[0078]

[0079] Where, d n Based on the pseudorange between different base station layouts, the best unbiased estimator is selected using Cramerlow Lower Bound (CRLB) by using pseudorange data between different base stations. The CRLB lower bound can serve as an indicator of the rationality of the base station layout. The criterion is that within the positioning area, each target lies on the mean of its CRLB trajectory across all base stations. The next step, the Monte Carlo algorithm, is then performed using the Cramerlow lower bound constraint.

[0080] S4: Using the Monte Carlo algorithm to address the complexity and diverse constraints of real-world problems in urban environments. Since the objective function established by the Monte Carlo algorithm contains numerous discontinuous and uncertain factors, within the positioning area, the probability distribution of the Monte Carlo algorithm is set to a uniform distribution. Random values ​​from this probability distribution are then generated by computer, with a defined range for the random values. New random values ​​are continuously generated using a recursive formula, and multiple samplings are performed within the range. The objective function is established using the base station layout model of the positioning area, with the Cramerlow lower bound as one of the evaluation criteria. The selected random numbers that meet the constraints are substituted into the objective function to solve the problem. Then, each calculation result is compared to obtain the optimal location for the base station layout in the positioning area. For constrained optimization problems, a penalty function is constructed to transform them into unconstrained optimization problems.

[0081] U(X,Y,Z,γ)=γu(X,Y,Z)+f(X,Y,Z) (5)

[0082] Where u(X,Y,Z) is the penalty term, expressed by equation (6) as follows:

[0083]

[0084] Among them l i (X,Y,Z) and r i (X, Y, Z) represent the inequality constraints and equality constraints in equation (6), respectively. Solve the unconstrained optimization problem by following these steps:

[0085] A selects an initial point (X0, Y0, Z0), assumes the penalty factor γ is positive, and the termination condition is that μ is also positive, which depends on the established model. Assume m starts from 1.

[0086] B with (X) m-1 ,Y m-1 Z m-1 Starting with point , we solve the unconstrained optimization problem: min{f(X,Y,Z)+γ} m u(X,Y,Z)}, obtain the optimal solution (X) under the current loop. m ,Y m Z m ).

[0087] C if γ m u(X m ,Y m Z m )≥CRLB, while u(X) m ,Y m Z m If μ ≤ μ, then the iteration terminates and the optimal solution is obtained.

[0088] D Update γ m+1 >γ m , m = m + 1, then return to step B to continue iterating.

[0089] After the loop ends, the initial optimal base station layout coordinates can be obtained.

[0090] S5: First, determine the parameters of the genetic algorithm. In this optimization problem, the goal is to optimize the layout of pseudo-satellite base stations, i.e., optimize the coordinates of the pseudo-satellite base stations. Based on the characteristics of the coordinates, we choose to use real-number encoding to represent the chromosome vectors of individuals. Assume the coordinates of the base stations are S... i (x i ,y i ,z i ), where N is the number of base stations, then the chromosome vector C of an individual can be represented in the following form:

[0091] C = [S1,S2,…,S] N ]

[0092] =[x1,y1,z1,x2,y2,z2,…,x N ,y N ,z N ]

[0093] In each chromosome, three adjacent gene loci correspond to the X, Y, and Z coordinates of a pseudosatellite base station. In the genetic algorithm, each chromosome C represents a pseudosatellite base station deployment scheme. Throughout the entire population, all chromosomes represent a base station deployment scheme in the same way. By analyzing the chromosomes, the coordinates of each pseudosatellite base station can be visually observed. At this point, no encoding / decoding process is needed. If the coordinates of a certain dimension of some base stations are already determined, then the chromosome variable corresponding to that dimension is omitted. During the encoding process, it is only necessary to clarify the correspondence between each gene locus in each chromosome and the actual meaning of the problem to be solved.

[0094] The optimal solution obtained by the Monte Carlo algorithm that meets the conditions is set as a subpopulation POPt composed of excellent individuals. The individuals in the population are sorted from high to low fitness, and the individuals with the best fitness are grouped into a subpopulation POP.

[0095] S6: The steps of the genetic algorithm based on the mountain climbing method are as follows:

[0096] A sets the current optimal solution obtained by the Monte Carlo algorithm that satisfies the conditions as a subpopulation consisting of excellent individuals, GOPe.

[0097] B then calculates the threshold R using the following formula: where D represents the distance from the i-th individual to the optimal individual, N represents the number of individuals in the population, i is a positive integer, iterating from 1 to N-1, and c is a constant, with c = 0.3 selected. The threshold R selected in this way can be adaptively adjusted according to the changes in distance between individuals in each generation.

[0098]

[0099] C takes the best individual as the current individual, adaptively updates it, and updates its fitness function. Centering on the best individual, it searches backwards for individuals whose Euclidean distance is greater than a threshold R. If a search is successful, that individual is added to the Group of Populations (GOP), and the current individual is replaced by that individual.

[0100] This process continues until the last individual is found. In this way, a sub-elite population can be obtained that is near different optimal individuals, i.e., extreme values. Assuming the number of individuals in GOPo is K, it is as follows:

[0101] GOPo={S1,S2,…,S K}

[0102] D. Assume the number of individuals in the GOP is L, and GOP = {S1', S2', ..., S...} L '}, select the i-th individual S from the elite population GOPo i With the j-th individual S in the GOP j 'Calculate the vector difference to obtain the chromosome difference vector V' ij , as shown in the following formula.

[0103] V ij =[S i -S j ′]

[0104] =[x i1 -x j1' ,y i1 -y j1' ,z i1 -z j1' ,…,x in -x jn' ,y in -y jn' ,z in -z jn' ,]

[0105] Where n represents the number of base stations, i = 1, 2, ..., K, j = 1, 2, ..., L. Before proceeding to the next step, X ijEach component retains only its symbol to ensure its distinction from other components. Furthermore, each component must have a unique symbol to indicate the direction of ascent it represents. This ensures that each component is represented correctly and can be correctly converted to other components. For example, V ij = [+2,0,-3,+1,…], where the vector represents individual S. i direction of climbing

[0106] E through S i The difference vector V between them ij To determine the new chromosome W i First, regarding S i The process involves sorting the data, deleting duplicate sequences that do not meet the criteria, and then calculating S according to the following formula. i Adjustments were made, replacing any repetitive sequences that did not meet the criteria; finally, the new chromosome W was... i With the known S i Combine them.

[0107] W i =S i +V ij ·overall·step

[0108] Here, `overall` represents the total range vector of each component of the chromosome, with each chromosome representing a vector, and `step` represents the step size factor. When calculating fitness, if the fitness of the new chromosome is higher than that of the original chromosome, it is replaced, using W. i Replace S i Otherwise S i It remains unchanged.

[0109] Let F = j + 1. If j ≤ L, repeat step CE.

[0110] Let G = i + 1. If i ≤ K, repeat steps DE.

[0111] The core of the improved climbing strategy lies in subtracting the difference between high-quality and low-quality individuals. This process allows the algorithm to utilize the genetic information of both previously obtained high-quality individuals and those with average fitness, improving the utilization rate of population base information. Simultaneously, since a vector V is randomly generated during the climbing process... ij So, in calculating V ij V needs to be generated multiple times. ij And determine vector W i However, if each random trial requires a new vector, the computational load will increase significantly.

[0112] Figure 1 and Figure 2Simulation results show that the pseudo-satellite base station layouts generated by the method proposed in this invention can effectively improve signal coverage and reduce the weighted average GDOP. w Its value can adapt to different urban positioning environments and solve the base station layout scheme more quickly, making the pseudo-satellite base station layout and construction more flexible and accurate, and improving the base station signal coverage and system positioning accuracy.

[0113] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the specific embodiments described above. The specific embodiments and descriptions in the specification are merely for further illustrating the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the claims and their equivalents.

[0114] The above embodiments of the present invention are merely examples for clearly illustrating the present invention. Those skilled in the art should understand that the above description is not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for optimizing the layout of pseudo-satellite base stations in an urban environment, characterized in that: The method includes the following steps: S1: Determine the urban lifeline areas that need to be monitored based on existing city maps and analysis of relevant GNSS signal strength and positioning accuracy, while also referring to urban planning and development plans; S2: By analyzing the system measurement error in urban positioning scenarios, using GDOPw as the evaluation index, a mathematical model of the base station geometric layout is established. S3: Solve mathematical optimization models with Cramer-Rao lower bound (CRLB) constraints using the Monte Carlo algorithm. S4: By constructing a penalty function, it is transformed into an unconstrained optimization problem. S5: Then solve it as an excellent individual in the population. S6: The optimal base station layout is obtained by using a genetic algorithm based on the mountaineering method, thereby optimizing the layout of pseudo-satellite base stations in urban environments; Among them, the improved genetic algorithm based on the mountain climbing method in S6 obtains the optimal base station layout method as follows: A: Set the current optimal solution obtained by the Monte Carlo algorithm that satisfies the conditions as the subpopulation of excellent individuals. e B: Then calculate the threshold B using equation (7): where D i This represents the distance from the i-th individual to the optimal individual. This represents the number of individuals in the group, where i is a positive integer, iterating from 1 to... , As a constant, select =0.3, so the threshold B is chosen to adaptively adjust according to the changes in distance between individuals in each generation. (7) C: Take the best individual as the current individual, adaptively update it, and update its fitness function. Centered on the best individual, search backwards for individuals whose Euclidean distance to it is greater than the threshold B. If the search is successful, add that individual to the population. And replace the current individual with that individual. This process continues until the last individual is found. In this way, a sub-elite population can be obtained that is near different optimal individuals, i.e., extreme values. ,set up The number of individuals is As in equation (8): D: Assumption The number of individuals is From elite groups o Choose the first individual and The Middle individual Perform vector difference to obtain chromosome difference vector. As shown in equation (9), (9) in Represents the number of base stations. Before proceeding to the next step, Each component retains only its symbol to ensure its distinction from other components. Each component must have a unique symbol to indicate the direction of ascent it represents. This ensures that each component is correctly represented and can be correctly converted to other components. E through Difference vectors between To determine new chromosomes First of all, regarding The sequence is sorted out, and duplicate sequences that do not meet the conditions are deleted. Then, according to the calculation method of equation (10), the sequence is... Adjustments were made, replacing any repetitive sequences that did not meet the criteria; finally, the new chromosome was... With known Combined, (10) in, This represents the total range vector of each component of a chromosome, with each chromosome having its own vector. `step` represents the step size factor. When calculating fitness, if the fitness of the new chromosome is higher than that of the original chromosome, it is replaced. Alternative ;otherwise remain unchanged. G: Order ,like Repeat step CE. H: Order ,like Repeat steps DE.

2. The method for optimizing the layout of pseudo-satellite base stations in an urban environment according to claim 1, characterized in that: S1 identifies the urban lifeline areas requiring monitoring, specifically as follows: Based on the urban lifeline network topology, starting with existing urban maps, GNSS signal strength analysis and positioning accuracy assessment are conducted. Simultaneously, referencing important infrastructure and key equipment in urban planning and development plans, risk assessments and priority determinations are made to determine signal coverage and the number of pseudo-satellite base stations. To differentiate the errors between pseudo-satellite systems and GNSS in urban environments, GDOPw is used as a standard for measuring pseudo-satellite base station layout, thereby highlighting the rationality and advantages / disadvantages of pseudo-satellite base station layout. Specifically, GDOPw... w This represents the weighted combination index of the error variance corresponding to the receiver in pseudorange measurements of each pseudosatellite.

3. The method for optimizing the layout of pseudo-satellite base stations in an urban environment according to claim 1, characterized in that: In S2, a mathematical model of the geometric layout of base stations is established through system measurement error analysis in urban environment positioning scenarios. GDOPw is used as the standard for measuring the system base station layout, based on the locations of the four system base stations. As a custom variable in the base station layout model, we can obtain equation (1); (1) The purpose of the base station layout optimization model is to solve for the unknown vector ( The optimal solution The optimal location for the base station is the location of the base station. In this environment, the smaller the GDOPw value, the more reasonable the pseudo-satellite base station layout is. The objective function in this positioning scenario is Equation (2). (2)。 4. The method for optimizing the layout of pseudo-satellite base stations in an urban environment according to claim 1, characterized in that: In S3, the Monte Carlo algorithm is used to solve a mathematical optimization model with Cramer-Rao lower bound (CRLB) constraints. When using GDOPw for localization in this environment, the Cramer-Rao lower bound is: Where R is the coefficient matrix between the base station coordinates (X, Y, Z) and the positioning target coordinates (x, y). It is the covariance matrix of the measurement error of the positioning system GDOPw. To determine the speed at which a location signal travels through the air. pass The unbiased estimator closest to the lower bound is selected as the best unbiased estimator, and the next step of the Monte Carlo algorithm is carried out under the Cramero lower bound constraint.

5. The method for optimizing the layout of pseudo-satellite base stations in an urban environment according to claim 3, characterized in that: In S4, within the positioning area, the probability distribution of the Monte Carlo algorithm is set to a uniform distribution. Random values ​​based on this probability distribution are then generated by computer, with a defined range for each value. New random values ​​are continuously generated using a recursive formula, and multiple samples are taken within the range. The objective function established by the base station layout model of the positioning area is used, with the Cramerlow lower bound as one of the evaluation criteria. The selected random numbers that meet the constraints are substituted into the objective function to solve the problem. Then, each calculation result is compared to obtain the optimal location for the base station layout in the positioning area. For constrained optimization problems, a penalty function is constructed to transform them into unconstrained optimization problems. (5) in, It is a penalty item. It is the penalty factor, expressed by equation (6) as follows: (6) in and Express the inequality constraints and equality constraints in equation (6) respectively, and solve the unconstrained optimization problem according to the following steps: A: Select initial point Set a penalty factor The termination condition is It is also a positive number, depending on the model established. Let's assume... start, B: With Starting from the first point, solve the unconstrained optimization problem: To obtain the optimal solution in the current loop. , C: If ,at the same time If the iteration terminates, the optimal solution is obtained. D: Update Then return to step B and continue the iteration. After the loop ends, the initial optimal base station layout coordinates can be obtained.

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