Particle swarm indoor pseudo satellite base station layout optimization method based on minimum GDOP configuration

Abstract

The invention specifically discloses a particle swarm indoor pseudo satellite base station layout optimization method based on a minimum GDOP configuration, and relates to the technical field of indoor positioning. The method comprises the following steps: S1, determining a scene and the number of base stations, setting a population scale, and initializing a population based on a minimum geometric accuracy factor GDOP; s2, collecting the number of visible satellites and horizontal precision factor data, calculating an objective function value, and storing a non-dominated solution and determining an initial optimal position of a particle swarm according to a Pareto dominating relationship; s3, adopting a segmented adaptive linear decline strategy to update the inertia weight, and updating the particle speed and position; s4, recalculating a particle objective function value, updating the optimal positions of the individuals and the group, and updating an external file; s5, checking whether a termination condition is met or not, and if not, continuing iteration; and S6, outputting a finally obtained non-dominated solution set. According to the method, the performance of the indoor pseudo satellite positioning system is effectively improved, and a new way is provided for base station layout optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of indoor positioning, in particular to an optimization method for the layout of indoor pseudolite base stations based on the minimum GDOP configuration of 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 calculation.

[0003] Currently, in the research on the optimization of the layout of indoor pseudolite base stations, many 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 the 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 ranging ability of pseudolites 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] At the same time, most existing studies only use the 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 the optimization of the layout of pseudolite base stations. When the traditional MOPSO algorithm is used to handle the optimization problem of 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 an optimization method for the layout of indoor pseudolite base stations based on the minimum GDOP configuration of 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 a 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: Step S1: Identify 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 relevant parameters of the external archive size; 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 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 position 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.

[0007] 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 of the minimum GDOP two-dimensional ranging single-point positioning, and randomly distributing the remaining particles in the feasible region.

[0008] Preferably, the calculation formula for the vertex coordinates of the optimal configuration of the minimum GDOP two-dimensional ranging single-point positioning is as follows: ; where, , 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.

[0009] Preferably, in step S2, the optimization objective function based on NVPS is to maximize the average NVPS of all sampling points in the scenario. Taking the negative value converts it into a minimization problem, and the formula is as follows: ; where, 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; The optimization objective function based on HDOP is to minimize the average HDOP of all sampling points in the scenario, and the calculation formula is as follows: 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: ; where, is the difference in the coordinates between base station r and receiver , is the difference in the coordinates between base station r and receiver y , is the difference in the coordinates between base station r and receiver z ; The modulus of the vector is: ; The direction cosines , , are respectively: ; 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; In the 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; The matrix is: ; The HDOP calculation formula is obtained as: ; Among them, is the element corresponding to the direction in the inverse matrix; is the element corresponding to the direction in the inverse matrix; 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: ; Among them, is the HDOP optimization objective function, is the horizontal dilution of precision of the th sampling point; The NVPS optimization objective function and the HDOP optimization objective function are normalized. The formula is as follows: ; 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.

[0010] Preferably, the layout constraint conditions of indoor pseudo-satellite base stations are as follows: The indoor pseudo-satellite base station realizes two-dimensional high-precision positioning based on the TDOA algorithm. In the regional range, the number of base stations is: ; Among them, is the total number of base stations in all deployment areas; When arranging the base stations, each base station must be arranged within the specified area. For the Pseudo-satellite base stations, whose coordinates must satisfy: ; where and are respectively the minimum and maximum values of the coordinates of the pseudo-satellite base stations in the actual deployment area; and are respectively the minimum and maximum values of the y coordinates of the pseudo-satellite base stations in the actual deployment area; and are respectively the minimum and maximum values of the z coordinates of the pseudo-satellite base stations in the actual deployment area; 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: ; 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.

[0011] The set of all restricted areas is: ; where is the th restricted area; The base stations in the actual environment deployment must satisfy the following constraints. Each base station cannot be deployed in the restricted areas. For the th pseudo-satellite base station , whose coordinates must satisfy: ; Based on the NVPS, HDOP evaluation metrics and the indoor pseudo-satellite base station layout constraints, calculate the multi-objective function value. The formula is as follows: ; where is the multi-objective function value.

[0012] Preferably, in step S3, the calculation formula of the inertia weight for the segmented adaptive linear decreasing strategy is: ; ; where 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 t th iteration's inertia weight, is the th iteration's inertia weight.

[0013] Preferably, in step S3, the update formulas for the velocity and position of the particle are as follows: ; where represents the velocity of particle in the th iteration in the th dimensional space; represents the velocity of particle in the th iteration in the th dimensional space; is the inertia factor; , are the uniform random numbers between regions ; , are the learning factors; is the individual optimal position of particle in the th iteration in the th dimensional space; is the position of particle in the th iteration in the th dimensional space; is the global optimal position of particle in the th iteration in the th dimensional space; is the position of particle in the th iteration in the th dimensional space.

[0014] 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: (1) Through the initialization strategy based on the minimum GDOP configuration, the geometric features of the scene are fully utilized to generate high-quality and evenly distributed initial solutions, effectively satisfying 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.

[0015] (2) The hybrid initialization strategy of "optimal configuration guidance + random sampling" is adopted, 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.

[0016] (3) The inertial weight update method of the segmented adaptive linear decreasing strategy can dynamically adjust the inertial 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 the traditional fixed inertial weight and linear decreasing inertial weight adjustment strategies, and improving the optimization accuracy of the algorithm.

[0017] (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, the best balance can be achieved between improving system availability and enhancing positioning accuracy, effectively improving the performance of the indoor pseudolite positioning system.

[0018] The technical solution of the present invention will be further described in detail below through the drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flowchart of the particle swarm indoor pseudolite base station layout optimization method based on the minimum GDOP configuration of the present invention; Figure 2 is a schematic diagram of the comparison of inertial weights between the segmented adaptive linear decreasing strategy and the traditional inertial weight adjustment strategy of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] In order 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 work shall fall within the protection scope of the present invention.

[0021] 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.

[0022] Embodiment 1 As Figure 1 shown, the following is the 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: S1. Initialization settings.

[0023] First, clarify 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; 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: ; Among them, , are the coordinates of the base station and coordinates respectively, y is the radius of the optimal configuration, is the initial rotation angle, is the number of pseudolite base stations. 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 the global exploration ability.

[0024] S2. Calculation of the objective function and construction of the initial archive.

[0025] 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 constraint conditions; 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 group in the particle swarm;

[0026] 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, and the formula is as follows: ; Among them, is the NVPS optimization objective function, ​is the number of sampling points selected within the scene, t is the number of iterations, is the number of visible satellites of the The optimization objective function based on HDOP is to minimize the average HDOP of all sampling points within the scene. The calculation formula is as follows: Assume that the position of the th pseudolite base station is , the position of the receiver is , and the vector from the base station to the receiver is: ; Among them, 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 ; The modulus of the vector is: ; The direction cosines , , are respectively: ; Among them, is the direction cosine of the th pseudolite base station in the direction; is the direction cosine of the th pseudolite base station in the direction; is the direction cosine of the th pseudolite base station in the direction; In the 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 pseudolite base station in the direction; is the U th pseudolite base station in the Direction cosines of the direction; Matrix is: ; The HDOP calculation formula is obtained as: ; where is the element in the inverse matrix corresponding to the direction; is the element in the inverse matrix corresponding to the direction.

[0027] 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: ; where is the HDOP optimization objective function, is the horizontal dilution of precision factor of the th sampling point; The NVPS optimization objective function and the HDOP optimization objective function are normalized. The formula is as follows: ; where 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].

[0028] The layout constraints of the indoor pseudolite base stations are as follows: The indoor pseudolite base stations achieve two-dimensional high-precision positioning based on the TDOA algorithm. In the regional range, the number of base stations is: ; where is the total number of base stations in all deployment areas; When arranging the base stations, each base station must be arranged within the specified area. For the th base station, its coordinates must satisfy: ; where 、 are respectively the The minimum and maximum values of the coordinates; and are respectively the minimum and maximum values of the coordinates of the pseudolite base station in the actual deployment area; y The minimum and maximum values of the coordinates; and are respectively the minimum and maximum values of the coordinates of the pseudolite base station in the actual deployment area; z The minimum and maximum values of the coordinates; 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: ; where and are respectively the minimum and maximum values of the th restricted area's coordinates, and are respectively the minimum and maximum values of the th restricted area's y coordinates, and are respectively the minimum and maximum values of the th restricted area's z coordinates.

[0029] The set of all restricted areas is: ; where is the th restricted area; The base station in the actual environmental deployment satisfies the following constraint conditions. Each base station cannot be deployed in the restricted area. For the th base station , its coordinates must satisfy: ; Based on the NVPS, HDOP evaluation metrics and the indoor pseudolite base station layout constraint conditions, calculate the multi-objective function value. The formula is as follows: ; where is the multi-objective function value. The present invention adopts a multi-objective optimization algorithm. On the premise of satisfying the system constraint conditions, 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.

[0030] S3. Update the particle velocity and position.

[0031] The inertial weight is updated by using a segmented adaptive linear decreasing strategy, and the velocity and position of the particle are updated according to the updated inertial weight. This strategy can flexibly adjust the inertial weight according to the actual situation in the search process, effectively avoiding the problem that the traditional fixed inertial weight easily leads the algorithm to fall into a local optimum.

[0032] The traditional MOPSO algorithm uses a fixed inertial weight, and this static parameter setting easily leads the algorithm to fall into a local optimal solution. Among the various parameters of the MOPSO algorithm, the adjustment of the inertial weight has the most significant impact on the algorithm performance. The current mainstream inertial weight adjustment strategy adopts a linear decreasing method: ; where, and are the maximum and minimum values of the inertial weight respectively; is the current iteration number, is the maximum iteration number.

[0033] In view of the limitations of the linear decreasing inertial weight adjustment strategy, the present invention proposes a segmented adaptive linear decreasing inertial weight adjustment strategy, and the calculation formula is: ; ; where, 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 iteration number, is the inertial weight at the t -th iteration, is the inertial weight at the -th iteration.

[0034] According to the Lyapunov function stability analysis, when the iteration process reaches 30% of the total duration, the system state variables satisfy: ; At this time, switching the search strategy can ensure the asymptotic stability of the convergence process. Therefore, the present invention uses as the turning point of the exploration-exploitation stage.

[0035] Such as Figure 2As 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. In the initial iteration stage of the piecewise adaptive linear decreasing strategy ( ), it adopts a large slope to decline rapidly, which is beneficial to quickly locate the potential optimal region; in the later iteration stage ( ), it then turns to a small slope to decline gently, which can not only ensure the convergence accuracy but also avoid falling into the local optimum. In contrast, the linear decreasing strategy maintains a constant change rate throughout the iteration process. Although it is simple to implement, it lacks the ability to adaptively adjust different stages of the optimization process. Through comparison, it can be seen that the piecewise adaptive strategy achieves a better balance between global exploration and local exploitation by dynamically adjusting the decline rate.

[0036] The velocity and position update formulas of the particle are as follows: ; Among them, 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 uniformly random numbers between regions ; , are learning factors; is the individual optimal position of particle in the -th iteration in the -dimensional space; is the position of particle in the -th iteration in the -dimensional space; is the global optimal position of particle in the -th iteration in the -dimensional space; is the position of particle in the -th iteration in the -dimensional space.

[0037] S4. Update of individual and global optimal positions and archive update.

[0038] In each iteration process, recalculate the multi-objective function values of each particle, and update its individual optimal position and the optimal position of the population 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 stored in it.

[0039] S5. Judgment of termination condition.

[0040] Check whether the preset termination condition is reached. If the termination condition is not met, increase the iteration count by 1 and return to S3 to continue the iteration; once the termination condition is met, 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.

[0041] S6. Result output.

[0042] After the termination condition is met, output the finally obtained non-dominated solution set, marking the end of the algorithm. These non-dominated solution sets represent the optimized layout positions of the pseudolite base stations for the indoor shielding environment considering the system availability and positioning accuracy, providing a scientific basis for practical applications.

[0043] 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.

[0044] Therefore, the present invention provides a particle swarm optimization method for indoor pseudolite base station layout based on the minimum GDOP configuration, which improves the availability and positioning accuracy of the indoor pseudolite positioning system, overcomes the defects of the initialization strategy and inertia weight adjustment strategy of the traditional MOPSO algorithm, and realizes more efficient and accurate indoor pseudolite base station layout optimization.

[0045] 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 or equivalently replace the technical solutions of the present invention, 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 particle swarm indoor pseudo-satellite base station layout optimization method based on minimum GDOP configuration, characterized in that: The following steps are involved: Step S1, clarify the restricted area and trusted area of ​​pseudo-satellite base station deployment in the indoor shielded environment, determine the number of base stations and initialize the algorithm, set the particle swarm algorithm population size; initialize the population based on minimizing the geometric precision factor GDOP, and initialize the learning factor, inertia weight, particle speed and external file size related parameters; Step S2, set sampling points in the indoor scene, collect visible satellite number NVPS and horizontal precision dilution HDOP data, obtain evaluation indicators through data processing by minimization and normalization, and calculate the multi-objective function value in combination with the indoor pseudo-satellite base station layout constraint conditions; select non-dominated solutions according to the Pareto dominance relationship, store them in an external archive, construct an initial archive, and determine the optimal position of the initial individual in the particle swarm and the optimal position of the group; Step S3, using a piecewise adaptive linear decreasing strategy to update the inertia weight, and updating the speed and position of the particle 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 solution; 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 iterative calculation. If the termination condition is met, enter step S6; Step S6: After the termination condition is met, the final non-dominated solution set is output.

2. The particle swarm indoor pseudo-satellite base station layout optimization method based on minimum GDOP configuration according to claim 1 is characterized in that: In step S1, the particles in the population are initialized based on minimizing the geometric precision factor GDOP, including setting the positions of some particles to 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 domain.

3. The particle swarm indoor pseudo-satellite base station layout optimization method based on minimum GDOP configuration according to claim 2 is characterized in that: The formula for calculating the vertex coordinates of the optimal configuration for single-point positioning with minimum GDOP two-dimensional ranging is as follows: ； in, , Base Station of Coordinates and y coordinate, is the optimal configuration radius, is the initial rotation angle, is the number of pseudo-satellite base stations.

4. The particle swarm indoor pseudo-satellite base station layout optimization method based on minimum GDOP configuration according to claim 1, characterized in that: In step S2, the optimization objective function based on NVPS is to maximize the average NVPS of all sampling points in the scene, and the negative value is converted into a minimization problem. The formula is as follows: ； in, Optimize the objective function for NVPS, is the number of sampling points selected in the scene, t is the number of iterations, It is The number of visible satellites at each sampling point; The optimization objective function based on HDOP is to minimize the average HDOP of all sampling points in the scene. The calculation formula is as follows: Assume The location of the pseudo-satellite base station is , the receiver location is , the vector from the base station to the receiver for: ； in, For base station and receiver r of The difference in coordinates, For base station and receiver r of y The difference in coordinates, For base station and receiver r of z Difference of coordinates; The magnitude of a vector for: ； Direction Cosines , , They are: ； 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 two dimensions, the geometric matrix is a Matrix, the formula is as follows: ； in, For the U Pseudo-satellite base stations Direction cosines of direction; It is U Pseudo-satellite base stations Direction cosines of direction; matrix for: ； The HDOP calculation formula is: ； in, is the inverse matrix with The element corresponding to the direction; is the inverse matrix with The element corresponding to the direction; The objective function of HDOP optimization is to minimize the average HDOP of all sampling points in the scene. The formula is as follows: ； in, Optimize the objective function for HDOP, It is Horizontal precision dilution factor for each sampling point; The NVPS optimization objective function and the HDOP optimization objective function are normalized, and the formula is as follows: ； in, is the normalized NVPS optimization objective function, is the normalized HDOP optimization objective function, , They are The minimum and maximum values ​​of , They are The minimum and maximum values ​​of .

5. The particle swarm indoor pseudo-satellite base station layout optimization method based on minimum GDOP configuration according to claim 4 is characterized in that: The layout constraints of indoor pseudo-satellite base stations are as follows: Indoor pseudo-satellite base stations achieve two-dimensional high-precision positioning based on TDOA algorithm. Within the area, the number of base stations for: ； in, is the total number of base stations in all deployment areas; When laying out base stations, each base station must be placed within a specified area. Base stations, their coordinates Must meet: ； in, , They are the pseudo-satellite base stations in the actual deployment area. Minimum and maximum values ​​of coordinates; , They are the pseudo-satellite base stations in the actual deployment area. y Minimum and maximum values ​​of coordinates; , They are the pseudo-satellite base stations in the actual deployment area. z Minimum and maximum values ​​of coordinates; Divide the base station restricted scenario into restricted area, The coordinate range of the restricted area is: ； in, , Respectively restricted area The minimum and maximum values ​​of the coordinates, , Respectively restricted area y The minimum and maximum values ​​of the coordinates, , Respectively restricted area z Minimum and maximum values ​​of coordinates; All restricted areas are collected as follows: ； in, For the restricted area; the base station meets the following constraints in the actual environment deployment: each base station cannot be deployed in a restricted area. Base Station , whose coordinates Must meet: ； The multi-objective function value is calculated based on the NVPS, HDOP evaluation indicators and the indoor pseudo-satellite base station layout constraints. The formula is as follows: ； in, is the value of the multi-objective function.

6. The particle swarm indoor pseudo-satellite base station layout optimization method based on minimum GDOP configuration according to claim 1, characterized in that: In step S3, the inertia weight calculation formula of the piecewise adaptive linear decreasing strategy is: ； ； in, 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 late slope; is the iterative turning point, ; is the maximum number of iterations, For the t The inertia weight of the iteration, For the The inertia weight for iteration .

7. The particle swarm indoor pseudo-satellite base station layout optimization method based on minimum GDOP configuration according to claim 1, characterized in that: In step S3, the particle velocity and position update formulas are as follows: ； in, Represents particles exist In the iteration Speed ​​in dimensional space; Represents particles exist In the iteration Speed ​​in dimensional space; is the inertia factor; , For Region A uniform random number between ; , is the learning factor; For particles No. In the iteration The optimal position of an individual in dimensional space; For particles No. In the iteration Position in dimensional space; For particles No. In the iteration The optimal position of the group in dimensional space; For particles No. In the iteration Position in dimensional space.

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