Particle Swarm Optimization Method for Indoor Pseudolite Base Station Layout Optimization Based on Minimum GDOP Configuration

Abstract

The present invention specifically discloses a method for optimizing the layout of indoor pseudolite base stations based on the minimum GDOP configuration, which relates to the technical field of indoor positioning. The method includes: S1. Defining the scenario and the number of base stations, setting the population size, and initializing the population based on minimizing the geometric dilution of precision GDOP; S2. Collecting the number of visible satellites and horizontal dilution of precision data, calculating the objective function value, storing the non-dominated solutions according to the Pareto dominance relationship, and determining the initial optimal position of the particle swarm; S3. Updating the inertia weight using a piecewise adaptive linear decreasing strategy, and updating the particle velocity and position; S4. Recalculating the particle objective function value, updating the individual and global optimal positions, and updating the external archive; S5. Checking whether the termination condition is satisfied, and if not, continuing the iteration; S6. Outputting the finally obtained non-dominated solution set. This method effectively improves the performance of the indoor pseudolite positioning system and provides a new way for optimizing the layout of base stations.

Description

Technical Field

[0001] The present invention relates to the technical field of indoor positioning, in particular to a method for optimizing the layout of indoor pseudolite base stations based on the minimum GDOP configuration for a particle swarm. Background Art

[0002] In an indoor shielding environment, positioning faces many challenges. Among the existing positioning technologies based on external positioning base stations, although the pseudolite positioning technology has advantages such as indoor-outdoor compatibility, high precision, high reliability, and flexible deployment, in practical applications, its performance is affected by various factors, and the geometric layout of the base stations is a key factor determining the accuracy of positioning solution.

[0003] Currently, in the research on optimizing the layout of indoor pseudolite base stations, various methods have been proposed. For example, the method based on the NSGA-II algorithm does not consider complex factors such as electromagnetic interference and the difficulty of base station installation in the actual environment; the method based on the weighted horizontal dilution of precision (WHDOP) is limited by the multipath effect in a complex indoor environment and does not fully consider layout optimization in a dynamic scenario; the research based on multi-objective particle swarm optimization (MOPSO) is only based on simulation experiments and does not consider practical factors such as the pseudolite ranging ability in actual deployment; the generalized center-guided firefly algorithm enhanced by K-means (KGFA) does not consider practical factors such as the multipath effect and non-line-of-sight reception in the propagation of pseudolite signals and has not been verified by actual deployment; the method for the layout of a spatial pseudolite system based on GDOP geometry has not been verified by an actual system and does not explore the optimization strategy when multiple unmanned aerial vehicles cooperate to serve a larger area.

[0004] Meanwhile, most existing studies only use DOP (dilution of precision) as the optimization objective function, but DOP has limitations in the indoor positioning scenario and is difficult to be used as a decisive evaluation criterion for optimizing the layout of pseudolite base stations. When the traditional MOPSO algorithm is used to handle the problem of optimizing the layout of indoor pseudolite base stations, the particle positions are randomly initialized, resulting in an uneven distribution of the initial solutions, being far from the Pareto front, increasing the number of iterations required for convergence, and reducing the algorithm efficiency and optimization accuracy. Therefore, a new method is needed to solve these problems and improve the performance of the indoor pseudolite positioning system. Summary of the Invention

[0005] The object of the present invention is to propose a method for optimizing the layout of indoor pseudolite base stations based on the minimum GDOP configuration for a particle swarm, so as to improve the usability and positioning accuracy of the indoor pseudolite positioning system, solve the deficiencies of existing methods in practical applications, overcome the defects of the initialization strategy and the inertia weight adjustment strategy of the traditional MOPSO algorithm, and achieve more efficient and accurate optimization of the layout of indoor pseudolite base stations.

[0006] To achieve the above object, the present invention proposes a method for optimizing the layout of indoor pseudolite base stations based on the minimum GDOP configuration, and the steps are as follows:

[0007] Step S1: Define the restricted area and the reliable area for the deployment of pseudolite base stations in the indoor shielding environment, determine the number of base stations and initialize the algorithm, and set the population size of the particle swarm algorithm; initialize the population based on minimizing the Geometric Dilution of Precision (GDOP), and at the same time initialize the learning factor, inertia weight, particle velocity, and related parameters of the external archive size;

[0008] Step S2: Set sampling points in the indoor scenario, collect the number of visible satellites NVPS and Horizontal Dilution of Precision (HDOP) data, perform data processing through minimization and normalization to obtain evaluation indicators, and calculate the multi-objective function value in combination with the indoor pseudolite base station layout constraints; screen non-dominated solutions according to the Pareto dominance relationship and store them in the external archive to construct an initial archive, and at the same time determine the optimal position of the initial individuals in the particle swarm and the optimal position of the group;

[0009] Step S3: Update the inertia weight using a piecewise adaptive linear decreasing strategy, and update the velocity and position of the particles according to the updated inertia weight;

[0010] Step S4: Recalculate the multi-objective function value of each particle, and update its individual optimal position and the optimal position of the group according to the multi-objective function value; at the same time, update the external archive according to the latest non-dominated solutions;

[0011] Step S5: Check and determine whether the preset termination condition is met. If the termination condition is not met, return to Step S3 to continue the iterative calculation. If the termination condition is met, enter Step S6;

[0012] Step S6: After meeting the termination condition, output the finally obtained non-dominated solution set.

[0013] Preferably, in Step S1, initializing the particles in the population based on minimizing the Geometric Dilution of Precision (GDOP) includes setting the positions of some particles as the vertex coordinates of the optimal configuration for minimum GDOP two-dimensional ranging single-point positioning, and randomly distributing the remaining particles in the feasible region.

[0014] Preferably, the calculation formula for the vertex coordinates of the optimal configuration for minimum GDOP two-dimensional ranging single-point positioning is as follows:

[0015] ;

[0016] where, , are the coordinates and coordinates of the base station y respectively, is the optimal configuration radius, is the initial rotation angle, is the number of pseudo-satellite base stations.

[0017] Preferably, in step S2, the optimization objective function based on NVPS is to maximize the average NVPS of all sampling points in the scene. Taking the negative value converts it into a minimization problem, and the formula is as follows:

[0018] ;

[0019] where, is the NVPS optimization objective function, is the number of sampling points selected in the scene, t is the number of iterations, is the th number of visible satellites of the sampling point;

[0020] The optimization objective function based on HDOP is to minimize the average HDOP of all sampling points in the scene, and the calculation formula is as follows:

[0021] Assume that the position of the th pseudo-satellite base station is , the position of the receiver is , and the vector from the base station to the receiver is:

[0022] ;

[0023] where, is the difference between the coordinates of the base station r and the receiver , is the difference between the coordinates of the base station r and the receiver y , is the difference between the coordinates of the base station r and the receiver z ;

[0024] The modulus of the vector is:

[0025] ;

[0026] The direction cosines , , are respectively:

[0027] ;

[0028] where, is the The direction cosine of the th pseudo-satellite base station in the is the th pseudo-satellite base station in the direction; is the th pseudo-satellite base station in the direction;

[0029] In a two-dimensional plane, the geometric matrix is a matrix, and the formula is as follows:

[0030] ;

[0031] where is the U th pseudo-satellite base station in the direction; is the U th pseudo-satellite base station in the direction;

[0032] The matrix is:

[0033] ;

[0034] The calculated HDOP formula is:

[0035] ;

[0036] where is the element in the inverse matrix corresponding to the direction; is the element in the inverse matrix corresponding to the direction;

[0037] Based on the HDOP, the optimization objective function is to minimize the average HDOP of all sampling points in the scene, and the formula is as follows:

[0038] ;

[0039] where is the HDOP optimization objective function, is the horizontal dilution of precision of the th sampling point;

[0040] Normalize the NVPS optimization objective function and the HDOP optimization objective function, and the formula is as follows:

[0041] ;

[0042] Among them, is the normalized NVPS optimization objective function, is the normalized HDOP optimization objective function, , are respectively the minimum and maximum values; , are respectively the minimum and maximum values.

[0043] Preferably, the indoor pseudolite base station layout constraint conditions are as follows:

[0044] The indoor pseudolite base station realizes two-dimensional high-precision positioning based on the TDOA algorithm. In the regional range, the number of base stations is:

[0045] ;

[0046] Among them, is the total number of base stations in all deployment areas;

[0047] When performing base station layout, each base station must be laid out within the specified area. For the th base station, its coordinates must satisfy:

[0048] ;

[0049] Among them, , are respectively the minimum and maximum values of the coordinates of the pseudolite base station in the actual deployment area; , are respectively the y minimum and maximum values of the coordinates of the pseudolite base station in the actual deployment area; , are respectively the z minimum and maximum values of the coordinates of the pseudolite base station in the actual deployment area;

[0050] According to the fixed structures in the actual environment, the base station restricted scenarios are divided into restricted areas. The coordinate range of the th restricted area is:

[0051] ;

[0052] Among them, , are respectively the th restricted area's minimum and maximum values of the coordinates, , are respectively the minimum and maximum values of the coordinates of the y th restricted area, , are respectively the minimum and maximum values of the coordinates of the z th restricted area.

[0053] The set of all restricted areas is:

[0054] ;

[0055] Among them, is the th restricted area; when the base station is deployed in the actual environment, it must meet the following constraints. Each base station cannot be deployed in the restricted area. For the th base station , its coordinates must satisfy:

[0056] ;

[0057] Based on the NVPS, HDOP evaluation indicators and the indoor pseudolite base station layout constraints, calculate the multi-objective function value. The formula is as follows:

[0058] ;

[0059] Among them, is the multi-objective function value.

[0060] Preferably, in step S3, the formula for calculating the inertial weight of the piecewise adaptive linear decreasing strategy is:

[0061] ;

[0062] ;

[0063] Among them, is the maximum value of the inertial weight, is the minimum value of the inertial weight, is the difference between the maximum weight and the minimum weight; is the initial slope, is the later slope; is the iteration turning point, ; is the maximum number of iterations, is the inertial weight of the t th iteration, is the inertial weight of the th iteration.

[0064] Preferably, in step S3, the velocity and position update formulas of the particles are as follows:

[0065] ;

[0066] where represents the velocity of the particle in the -th iteration in the -dimensional space; represents the velocity of the particle in the -dimensional space; , are uniformly distributed random numbers between regions ; , are learning factors; is the individual optimal position of the particle in the -th iteration in the -dimensional space; is the position of the particle in the -th iteration in the -dimensional space; is the global optimal position of the particle in the -th iteration in the -dimensional space; is the position of the particle in the -th iteration in the -dimensional space.

[0067] Therefore, the present invention proposes a particle swarm indoor pseudolite base station layout optimization method based on the minimum GDOP configuration, and its beneficial effects are as follows:

[0068] (1) Through the initialization strategy based on the minimum GDOP configuration, making full use of the geometric characteristics of the scenario, high-quality and uniformly distributed initial solutions are generated, effectively meeting the geometric constraints of the base stations. Compared with the traditional random initialization method, the convergence speed of the algorithm and the performance of the final solution are significantly improved.

[0069] (2) Adopting the hybrid initialization strategy of "optimal configuration guidance + random sampling", taking into account both the convergence speed and the global exploration ability, avoiding the algorithm falling into local optima, and enhancing the robustness of the algorithm.

[0070] (3) The piecewise adaptive linear decreasing strategy inertia weight update method can dynamically adjust the inertia weight decreasing rate according to different stages of the optimization process, achieving a better balance between global exploration and local development, overcoming the defects of traditional fixed inertia weight and linear decreasing inertia weight adjustment strategies, and improving the optimization accuracy of the algorithm.

[0071] (4) By establishing a multi-objective optimization layout model of indoor pseudolite base stations including NVPS and HDOP, and using the optimization method of the present invention to solve it, the best balance can be achieved between improving system availability and enhancing positioning accuracy, effectively improving the performance of the indoor pseudolite positioning system.

[0072] The technical solution of the present invention will be further described in detail below with reference to the drawings and embodiments. Description of the Drawings

[0073] Figure 1 It is a flowchart of the particle swarm indoor pseudolite base station layout optimization method based on the minimum GDOP configuration of the present invention;

[0074] Figure 2 It is a schematic diagram of the comparison of inertia weights between the piecewise adaptive linear decreasing strategy and the traditional inertia weight adjustment strategy of the present invention. Specific Embodiments

[0075] To make the technical solution, advantages and objectives of the present invention clearer, the technical solution of the embodiments of the present invention will be described clearly and completely below. The described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0076] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meaning understood by those of ordinary skill in the art to which the present invention belongs.

[0077] Embodiment 1

[0078] As Figure 1 shown, it is a flowchart of the particle swarm indoor pseudolite base station layout optimization method based on the minimum GDOP configuration of the present invention, and the specific steps are as follows:

[0079] S1. Initialization settings.

[0080] First, clarify the restricted area and reliable area for the deployment of pseudolite base stations in the indoor shielding environment, determine the number of base stations and initialize the algorithm, and set the population size of the particle swarm algorithm; initialize the population based on minimizing the geometric dilution of precision GDOP, and at the same time initialize relevant parameters such as learning factors, inertia weights, particle velocities, and external archive sizes;

[0081] Among them, initializing the particles in the population based on minimizing the geometric dilution of precision GDOP includes setting the positions of some particles as the vertex coordinates of the optimal configuration of the minimum GDOP two-dimensional ranging single-point positioning, and the remaining particles are randomly distributed in the feasible region; the calculation formula for the vertex coordinates of the optimal configuration of the minimum GDOP two-dimensional ranging single-point positioning is as follows:

[0082] ;

[0083] Among them, , are the coordinates and coordinates of the base station y respectively, is the radius of the optimal configuration, is the initial rotation angle, is the number of pseudolite base stations.

[0084] The present invention adopts a hybrid initialization strategy of "optimal configuration guidance + random sampling", in which 50% of the particles are accurately initialized through analytical solutions, and the remaining 50% are randomly distributed within the feasible region to balance the convergence speed and global exploration ability.

[0085] S2. Calculation of the objective function and construction of the initial archive.

[0086] Set sampling points in the indoor scenario, collect the data of the number of visible satellites NVPS and the horizontal dilution of precision HDOP, perform data processing through minimization and normalization to obtain evaluation indicators, and calculate the multi-objective function values in combination with the layout constraints of indoor pseudolite base stations; screen the non-dominated solutions according to the Pareto dominance relationship and store them in the external archive to construct the initial archive, and at the same time determine the optimal positions of the initial individuals and the optimal position of the population in the particle swarm;

[0087] The optimization objective function based on NVPS is to maximize the average NVPS of all sampling points in the scenario, and take the negative value to convert it into a minimization problem. The formula is as follows:

[0088] ;

[0089] Among them, is the NVPS optimization objective function, is the number of sampling points selected in the scenario, t is the number of iterations, is the th number of visible satellites of the sampling point;

[0090] The optimization objective function based on HDOP is to minimize the average HDOP of all sampling points in the scenario. The calculation formula is as follows:

[0091] Assume that the position of the th pseudo-satellite base station is , and the position of the receiver is . The vector from the base station to the receiver is:

[0092] ;

[0093] where is the difference in the coordinates between the base station r and the receiver , is the difference in the coordinates between the base station r and the receiver y , is the difference in the coordinates between the base station r and the receiver z ;

[0094] The magnitude of the vector is:

[0095] ;

[0096] The direction cosines , , are respectively:

[0097] ;

[0098] where is the direction cosine of the th pseudo-satellite base station in the direction; is the direction cosine of the th pseudo-satellite base station in the direction; is the direction cosine of the th pseudo-satellite base station in the direction;

[0099] In a two-dimensional plane, the geometric matrix is a matrix, and the formula is as follows:

[0100] ;

[0101] where is the direction cosine of the U th pseudo-satellite base station in the direction; is the U th pseudo-satellite base station in the Direction cosines of the direction;

[0102] Matrix is:

[0103] ;

[0104] The HDOP calculation formula is obtained as:

[0105] ;

[0106] Among them, is the element corresponding to the direction in the inverse matrix; is the element corresponding to the direction in the inverse matrix.

[0107] Based on the HDOP, the optimization objective function is to minimize the average HDOP of all sampling points in the scene. The formula is as follows:

[0108] ;

[0109] Among them, is the HDOP optimization objective function, is the horizontal dilution of precision factor of the th sampling point;

[0110] Normalize the NVPS optimization objective function and the HDOP optimization objective function. The formula is as follows:

[0111] ;

[0112] Among them, is the normalized NVPS optimization objective function, is the normalized HDOP optimization objective function, , are respectively 's minimum and maximum values; , are respectively 's minimum and maximum values; After normalization, the value ranges of all indicators are [0,1].

[0113] The layout constraints of the indoor pseudolite base station are as follows:

[0114] The indoor pseudolite base station realizes two-dimensional high-precision positioning based on the TDOA algorithm. In the regional range, the number of base stations is:

[0115] ;

[0116] Among them, is the total number of base stations in all deployment areas;

[0117] When arranging the base stations, each base station must be arranged within the specified area. For the th base station, its coordinates must satisfy:

[0118] ;

[0119] where, and are respectively the minimum and maximum values of the coordinates of the pseudolite base station in the actual deployment area; and are respectively the minimum and maximum values of the y coordinates of the pseudolite base station in the actual deployment area; and are respectively the minimum and maximum values of the z coordinates of the pseudolite base station in the actual deployment area;

[0120] According to the fixed structures in the actual environment, the base station restricted scenarios are divided into restricted areas. The coordinate range of the th restricted area is:

[0121] ;

[0122] where, and are respectively the minimum and maximum values of the coordinates of the th restricted area, and are respectively the minimum and maximum values of the coordinates of the y th restricted area, and are respectively the minimum and maximum values of the coordinates of the z th restricted area.

[0123] The set of all restricted areas is:

[0124] ;

[0125] where, is the th restricted area; The base stations in the actual environment deployment must meet the following constraints. Each base station cannot be deployed in the restricted area. For the th base station , its coordinates must satisfy:

[0126] ;

[0127] Calculate the multi-objective function value based on the NVPS, HDOP evaluation indicators and the layout constraints of the indoor pseudolite base station. The formula is as follows:

[0128] ;

[0129] Among them, is the multi-objective function value. The present invention adopts a multi-objective optimization algorithm. On the premise of meeting the system constraints, by minimizing the objective function , solve the Pareto optimal solution set to achieve the optimal trade-off between the system availability (maximizing NVPS) and the positioning accuracy (minimizing HDOP) of the indoor pseudolite base station.

[0130] S3. Update the particle velocity and position.

[0131] Adopt a piecewise adaptive linear decreasing strategy to update the inertia weight, and update the particle velocity and position according to the updated inertia weight; this strategy can flexibly adjust the inertia weight according to the actual situation in the search process, effectively avoiding the problem that the traditional fixed inertia weight easily leads to the algorithm falling into a local optimum.

[0132] The traditional MOPSO algorithm adopts a fixed inertia weight, and this static parameter setting easily leads to the algorithm falling into a local optimal solution. Among the parameters of the MOPSO algorithm, the adjustment of the inertia weight has the most significant impact on the algorithm performance. The current mainstream inertia weight adjustment strategy adopts a linear decreasing method:

[0133] ;

[0134] Among them, and are the maximum and minimum values of the inertia weight respectively; is the current iteration number, is the maximum iteration number.

[0135] In view of the limitations of the linear decreasing inertia weight adjustment strategy, the present invention proposes a piecewise adaptive linear decreasing inertia weight adjustment strategy. The calculation formula is:

[0136] ;

[0137] ;

[0138] Among them, is the maximum value of the inertia weight, is the minimum value of the inertia weight, is the difference between the maximum weight and the minimum weight; is the initial slope, is the later slope; is the iterative turning point; is the maximum number of iterations, is the t inertia weight of the th iteration, is the inertia weight of the

[0139] According to the stability analysis of the Lyapunov function, when the iterative process reaches 30% of the total duration, the system state variables satisfy:

[0140] ;

[0141] At this time, switching the search strategy can ensure the asymptotic stability of the convergence process. Therefore, the present invention adopts as the turning point of the exploration-exploitation stage.

[0142] As Figure 2 shown, in the piecewise adaptive linear decreasing strategy, the inertia factor has a piecewise linear relationship with time, and the turning point is set at t = 30. The piecewise adaptive linear decreasing strategy adopts a large slope to quickly decline in the initial iteration stage ( ), which is beneficial to quickly locate the potential optimal region; in the later iteration stage ( ), it turns to a small slope for gentle decline, which can not only ensure the convergence accuracy but also avoid falling into local optima. In contrast, the linear decreasing strategy maintains a constant change rate throughout the iterative process. Although it is simple to implement, it lacks the ability to adaptively adjust different stages of the optimization process. By comparison, the piecewise adaptive strategy achieves a better balance between global exploration and local exploitation by dynamically adjusting the decline rate.

[0143] The velocity and position update formulas of the particle are as follows:

[0144] ;

[0145] where, represents the velocity of particle in the th iteration in the -dimensional space; represents the velocity of particle in the th iteration in the -dimensional space; is the inertia factor; , are the uniform random numbers between regions ; , are the learning factors; is the particle The individual optimal position in the -dimensional space in the th iteration; is the position of particle in the -dimensional space in the th iteration; is the global optimal position of the swarm in the -dimensional space in the th iteration; is the position of particle in the th iteration in the -dimensional space.

[0146] S4. Update of individual and global optimal positions and update of archive.

[0147] In each iteration process, recalculate the multi-objective function values of each particle, and update its individual optimal position and the global optimal position of the swarm according to the multi-objective function values. At the same time, update the external archive according to the latest non-dominated solution situation to ensure that the current optimal non-dominated solution set is always saved in it.

[0148] S5. Judgment of termination condition.

[0149] Check whether the preset termination condition is reached. If the termination condition is not satisfied, increase the iteration count by 1 and return to S3 for continued iteration; once the termination condition is satisfied, enter the final step S6. This process ensures that the algorithm can stop in time when the expected optimization effect is achieved, avoiding unnecessary waste of computing resources.

[0150] S6. Result output.

[0151] When the termination condition is satisfied, output the finally obtained non-dominated solution set, marking the end of the algorithm. These non-dominated solution sets represent the optimized pseudo-satellite base station layout positions for the indoor shielding environment considering system availability and positioning accuracy, providing a scientific basis for practical applications.

[0152] It should be noted that the content not elaborated in detail in the present invention is all prior art and is well-known to those skilled in the art.

[0153] Therefore, the present invention provides a particle swarm optimization method for indoor pseudo-satellite base station layout based on the minimum GDOP configuration, which improves the availability and positioning accuracy of the indoor pseudo-satellite positioning system, overcomes the defects of the initialization strategy and the inertia weight adjustment strategy of the traditional MOPSO algorithm, and realizes more efficient and accurate indoor pseudo-satellite base station layout optimization.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing the layout of indoor pseudolite base stations based on the minimum GDOP configuration, characterized in that It includes the following steps: Step S1: Identify the restricted areas and feasible regions for the deployment of pseudolite base stations in indoor shielding environments, determine the number of base stations and initialize the algorithm, and set the population size of the particle swarm algorithm; Initialize the population based on minimizing the geometric dilution of precision GDOP, and at the same time initialize the learning factor, inertia weight, particle velocity, and related parameters of the external archive size; Among them, initializing the particles in the population based on minimizing the geometric dilution of precision GDOP includes setting the positions of some particles as the vertex coordinates of the optimal configuration of two-dimensional ranging single-point positioning with the minimum GDOP, and the remaining particles are randomly distributed in the feasible region; Step S2: Set sampling points in the indoor scenario and collect the number of visible satellites NVPS and horizontal dilution of precision HDOP data; The optimization objective function based on NVPS is to maximize the average NVPS of all sampling points in the scenario, and take the negative value to convert it into a minimization problem; The optimization objective function based on HDOP is to minimize the average HDOP of all sampling points in the scenario; Normalize the NVPS optimization objective function and the HDOP optimization objective function; Calculate the multi-objective function value based on the NVPS, HDOP evaluation indicators, and indoor pseudolite base station layout constraints. The formula is as follows: ； Among them, is the multi-objective function value, is the NVPS optimization objective function after normalization, is the HDOP optimization objective function after normalization; Select non-dominated solutions according to the Pareto dominance relationship and store them in the external archive to construct the initial archive. At the same time, determine the optimal positions of the initial individuals in the particle swarm and the optimal position of the group; Step S3: Update the inertia weight using a piecewise adaptive linear decreasing strategy, and update the velocity and position of the particles according to the updated inertia weight; Step S4: Recalculate the multi-objective function value of each particle, and update its individual optimal position and the optimal position of the group according to the multi-objective function value; At the same time, update the external archive according to the latest non-dominated solutions; Step S5: Check and determine whether the preset termination condition is met. If the termination condition is not met, return to Step S3 to continue the iterative calculation. If the termination condition is met, enter Step S6; Step S6: After meeting the termination condition, output the finally obtained non-dominated solution set.

2. The method for optimizing the layout of indoor pseudolite base stations based on the minimum GDOP configuration according to claim 1, characterized in that The calculation formula for the vertex coordinates of the optimal configuration of two-dimensional ranging single-point positioning with the minimum GDOP is as follows: ； Among them, , are the coordinates and coordinates of the base station respectively, is the optimal configuration radius, is the initial rotation angle, and is the number of pseudolite base stations.

3. The particle swarm indoor pseudolite base station layout optimization method based on the minimum GDOP configuration according to claim 1, wherein In Step S2, the optimization objective function based on NVPS is to maximize the average NVPS of all sampling points in the scenario, and take the negative value to convert it into a minimization problem. The formula is as follows: ； Among them, is the NVPS optimization objective function, is the number of sampling points selected within the scenario, is the number of iterations, is the number of visible satellites at the th sampling point; The optimization objective function based on HDOP is to minimize the average HDOP of all sampling points in the scenario. The calculation formula is as follows: Assume that the th pseudolite base station location is , the receiver location is , and the vector from the base station to the receiver is: ； Among them, is the base station and the receiver 's difference in coordinates, is the base station and the receiver 's difference in coordinates, is the base station and the receiver 's difference in coordinates; Magnitude of a vector is as follows: ； Direction cosine , , are respectively: ； in, It is Pseudo-satellite base stations Direction cosines of direction; It is Pseudo-satellite base stations Direction cosines of direction; It is Pseudo-satellite base stations Direction cosines of direction; In a two-dimensional plane, the geometric matrix is a matrix, and the formula is as follows: ； Among them, is the direction cosine of the U th pseudo-satellite base station in the direction; is the direction cosine of the U th pseudo-satellite base station in the direction. Matrix is as follows: ； The derived HDOP calculation formula is: ； Among them, is the element in the inverse matrix corresponding to direction; is the element in the inverse matrix corresponding to direction. The optimization objective function based on HDOP is to minimize the average HDOP of all sampling points in the scenario. The formula is as follows: ； Among them, is the HDOP optimization objective function, is the horizontal dilution of precision of the nth sampling point; Normalize the NVPS optimization objective function and the HDOP optimization objective function. The formula is as follows: ； Among them, is the normalized NVPS optimization objective function, is the normalized HDOP optimization objective function, , are respectively the minimum and maximum values of , are respectively the minimum and maximum values of 4. The method for optimizing the layout of the indoor pseudolite base station based on the minimum GDOP configuration according to claim 3, characterized in that The indoor pseudolite base station layout constraints are as follows: The indoor pseudolite base station realizes two-dimensional high-precision positioning based on the TDOA algorithm. Within the regional scope, the number of base stations is as follows: ； Among them, is the total number of base stations in all deployment areas; When performing base station layout, each base station must be located within the specified area. For the th base station, its coordinates must satisfy: ； Among them, and are respectively the minimum and maximum values of the x coordinates of the pseudolite base station in the actual deployment area; and are respectively the minimum and maximum values of the y coordinates of the pseudolite base station in the actual deployment area; and are respectively the minimum and maximum values of the z coordinates of the pseudolite base station in the actual deployment area; Divide the base station restricted scenario into restricted areas. The coordinate range of the th restricted area is: ； Among them, , are respectively the minimum and maximum values of the coordinates of the -th restricted area, and are respectively the minimum and maximum values of the coordinates of the -th restricted area, are respectively the minimum and maximum values of the coordinates of the -th restricted area; The set of all restricted areas is: ； Among them, is the th restricted area; when the base stations are deployed in the actual environment, the following constraint conditions are satisfied. Each base station cannot be deployed in the restricted area. For the th base station , its coordinates must satisfy: 。 5. The method for optimizing the layout of indoor pseudolite base stations based on the minimum GDOP configuration according to claim 1, wherein In Step S3, the calculation formula for the inertia weight of the piecewise adaptive linear decreasing strategy is: ； ； Among them, is the maximum value of the inertia weight, is the minimum value of the inertia weight, is the difference between the maximum weight and the minimum weight; is the initial slope, is the later slope; is the iteration turning point, ; is the maximum number of iterations, is the inertia weight of the th iteration, is the inertia weight of the th iteration.

6. The method for optimizing the layout of indoor pseudolite base stations based on the minimum GDOP configuration according to claim 1, wherein In Step S3, the update formulas for the velocity and position of the particles are as follows: ； Among them, represents the velocity of the particle at the -th iteration in the -dimensional space; represents the velocity of the particle at the -th iteration in the -dimensional space; is the inertia weight; and are uniformly distributed random numbers between ; and are the learning factors; is the individual optimal position of the particle at the -th iteration in the -dimensional space; is the position of the particle at the -th iteration in the -dimensional space; is the global optimal position of the particle at the -th iteration in the -dimensional space; is the position of the particle at the -th iteration in the -dimensional space.

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