Wireless positioning base station deployment method in complex terrain environment

Abstract

The application discloses a wireless positioning base station deployment method in a complex terrain environment, and relates to the technical field of wireless positioning and network optimization, and comprises the following steps: acquiring three-dimensional terrain data and a mobile path and discretizing the three-dimensional terrain data and the mobile path into key points; constructing a signal transmission model containing terrain shielding loss and a multi-target optimization model; solving by using a multi-population differential evolution algorithm; screening a feasible region based on a physical connection state in iteration; adaptively selecting a mutation mode according to base station density; taking a mobile node meeting a precision threshold value as a dynamic auxiliary anchor point and correcting a target function by fusing historical data through a time sequence sliding window; and outputting a deployment scheme after precision and fault tolerance checking of the scheme. The application improves the convergence speed, positioning precision and system fault tolerance of base station deployment in a complex terrain.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning and network optimization technology, specifically relating to a method for deploying wireless positioning base stations in complex terrain environments. Background Technology

[0002] In wireless positioning systems operating in complex terrain environments, the geometric distribution of base stations directly determines the positioning accuracy of mobile nodes and the reliability of the system. Existing technologies typically employ heuristic algorithms or convex optimization methods for base station site selection. However, in scenarios with severe mountain obstruction and dramatic terrain undulations, signal transmission exhibits highly nonlinear and discontinuous characteristics. Traditional optimization algorithms often treat the search space as a continuous feasible region, ignoring the physical connectivity constraints caused by terrain obstruction. This leads to a large number of iterative calculations falling into invalid regions, resulting in slow convergence and a tendency to get trapped in local optima. Furthermore, existing deployment schemes largely rely on static reference networks composed of fixed base stations. With limited deployment costs, the distribution of fixed nodes is sparse. If individual base stations fail or are affected by environmental interference, the lack of dynamic compensation mechanisms makes it difficult to maintain high-precision continuous positioning services. Therefore, there is an urgent need for a base station deployment method that can adapt to the physical characteristics of complex terrain and balance optimization efficiency with system fault tolerance. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention aims to provide a method for deploying wireless positioning base stations in complex terrain environments, enabling rapid optimization of base station deployment schemes and highly robust positioning coverage.

[0004] This invention provides a method for deploying wireless positioning base stations in complex terrain environments, comprising:

[0005] Acquire three-dimensional terrain data of the target area and the preset movement path of the mobile node, and discretize the preset movement path into multiple path key points;

[0006] Based on the three-dimensional terrain data, a signal transmission model including terrain occlusion loss is constructed, and a multi-objective optimization model is constructed with the objectives of minimizing the positioning error of the key points of the path, minimizing the number of base stations deployed, and maximizing the network fault tolerance rate.

[0007] Multiple group differential evolution algorithms are used to solve the multi-objective optimization model to obtain the base station deployment scheme. In the iterative solution process, feasible regions are filtered based on the physical connectivity between candidate base station locations and key points of the path. Differential mutation modes are adaptively selected according to the base station distribution density in local areas. Mobile nodes that meet the positioning accuracy threshold are used as dynamic auxiliary anchor points. The historical observation data of the dynamic auxiliary anchor points are time-weighted and fused through a time sliding window to correct the objective function of the multi-objective optimization model.

[0008] The positioning accuracy and fault tolerance of the base station deployment scheme are verified. If the verification passes, the final base station deployment scheme is output.

[0009] The expression for the signal transmission model is: ;in, For the first The base station and the first Total path loss between nodes The reference path loss at the reference distance, This is the path loss index. For the first The base station and the first Horizontal distance between nodes This is the terrain occlusion attenuation coefficient. The height or relative elevation difference of the mountain acts as a barrier. This refers to the shadow fading margin or random disturbance term.

[0010] The mathematical expression of the multi-objective optimization model is: ;in, This represents the total number of key points along the path. For the number of base stations deployed, For network fault tolerance;

[0011] Sub-cost function corresponding to a single path key point The expression is: ;in, For the first The coordinate location parameters of each base station, In order to be with the first A set of fixed base stations directly connected to key points along a path. In order to be with the first The set of adjacent path key points directly connected to each path key point In order to be with the first A set of dynamic auxiliary anchor points that directly connect key points along a path. To measure the noise variance, This is the weighted residual term based on the measurement noise.

[0012] The method of solving the multi-objective optimization model using a multi-group differential evolution algorithm includes: if there are poles near the proposed deployment area of ​​the base station, generating positive initial individuals and corresponding negative individuals within a preset range around the poles; selecting the individual with the best fitness from the positive initial individuals and the negative individuals as the initial population; adaptively adjusting the population size according to the degree of terrain obstruction and signal loss intensity: in areas with severe obstruction and high signal loss, splitting a single population into multiple sub-populations; and merging adjacent redundant populations in open, unobstructed areas.

[0013] The feasible region filtering based on the physical connectivity status of candidate base station locations and key points along the path, and the adaptive selection of differential mutation modes based on the base station distribution density in local areas, includes: First stage: Pre-calculating the effective communication coverage range of each individual, generating a feasible region mask, and selecting mutation parents only from valid individuals whose feasible region masks satisfy preset connectivity conditions; Second stage: Adaptively selecting mutation modes based on regional base station density: In densely populated base station areas, a first mutation mode is used for mutation, the formula for which is: In sparse base station blind areas, a second mutation mode guided by dynamic anchor points is used for mutation. The formula for the second mutation mode is: ;in, The mutated individual; It is the kth mutated parent generation; It is the p-th mutated parent generation; It is the q-th mutated parent generation; The adaptive scaling factor is initially set to 0.9 and decreases linearly to 0.4 with each iteration. It is the best individual in the current population; The coordinates of the centroid of the dynamic anchor point set at the current moment.

[0014] The iterative solution process also includes: performing a binomial crossover operation on the mutated individual and the parent individual to generate a test individual; performing adaptive terrain anchoring correction on the test individual: if the test individual is located in an undeployable area, then anchoring it to the nearest point on the boundary of the nearest feasible area; if the test individual cannot meet the connectivity requirements with at least two of the path key points, then calculating its movement step size in the direction of optimal connectivity and gradually adjusting it until the connectivity constraints are met.

[0015] The step of performing time-series weighted fusion of historical observation data of the dynamic auxiliary anchor points through a time sliding window to correct the objective function of the multi-objective optimization model includes: dynamic auxiliary anchor point admission determination: only moving nodes with positioning errors less than or equal to a preset error threshold are used as dynamic auxiliary anchor points, constructing a set of dynamic auxiliary anchor points; time-series weight allocation: weights are assigned to each historical moment within the time sliding window using an exponential decay weight formula, the formula being: ;in, For a moment The weighting coefficients, For the current moment, The time decay coefficient, The sliding window length is used for calculation of the centroid of the time-series fusion dynamic auxiliary anchor point. Based on the weights and the coordinates of the dynamic auxiliary anchor points at each historical moment, the centroid of the time-series fusion dynamic auxiliary anchor point is calculated. The collaborative residual correction term is obtained by fusing the joint residuals of the fixed base station and the time-series fusion dynamic auxiliary anchor point and correcting the original sub-cost function.

[0016] The positioning accuracy and fault tolerance verification of the base station deployment scheme includes: determining the final base station location using an elite selection strategy and population midpoint augmentation optimization; calculating the normalized root mean square error through Monte Carlo simulation to evaluate positioning accuracy; and executing a base station fault tolerance reconstruction mechanism: if a base station fault is detected, a local scheme reconstruction is automatically triggered, a temporary positioning network is formed by combining surrounding normal base stations with dynamic auxiliary anchor points of time-series fusion, and the weights of the temporary positioning network are optimized in real time, and the equivalent coverage weights of surrounding base stations are fine-tuned.

[0017] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the wireless positioning base station deployment method in complex terrain environments as described above.

[0018] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the wireless positioning base station deployment method in complex terrain environments as described above.

[0019] This invention discloses a method for deploying wireless positioning base stations in complex terrain environments. By transforming terrain physical connectivity constraints into feasible region masks and embedding them into the mutation stage of a differential evolution algorithm, it fundamentally eliminates a large number of invalid searches caused by ignoring occlusion in traditional algorithms in complex terrain, significantly improving the optimization convergence speed. By constructing a collaborative optimization mechanism based on the fusion of mobile node temporal observations, it uses historical data of mobile nodes that meet the accuracy threshold as dynamic auxiliary anchor points and corrects the objective function with exponential decay weights, effectively suppressing instantaneous noise interference and supplementing the spatial observation information of sparse fixed base stations, thereby significantly improving positioning accuracy and geometric configuration stability with limited deployment costs. Furthermore, through a base station fault-tolerant reconfiguration mechanism, a temporary cooperative network of surrounding base stations and dynamic anchor points is automatically activated when fixed nodes fail, realizing the dynamic self-healing of the positioning system and solving the industry problem of easy interruption of UAV inspection positioning services in complex scenarios such as remote mountainous areas. Attached Figure Description

[0020] Figure 1 This is a flowchart of a wireless positioning base station deployment method in complex terrain environments according to an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0022] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0023] like Figure 1 As shown, this embodiment provides a method for deploying wireless positioning base stations in complex terrain environments. This method achieves rapid optimization of base station deployment schemes and highly robust coverage by deeply embedding terrain physical constraints and spatiotemporal information of mobile nodes into an optimization algorithm. Specifically, the method includes the following steps:

[0024] Step S100: Obtain the three-dimensional terrain data of the target area and the preset movement path of the moving node, and discretize the preset movement path into multiple path key points.

[0025] Specifically, 3D terrain data typically originates from digital elevation models (DEMs) or lidar point clouds, containing geometric information such as mountain height, vegetation distribution, and surface undulations. The preset movement path refers to the expected flight trajectory of a mobile node (such as an inspection drone) during operation. Path discretization is not simply mathematically spaced sampling, but rather a physical spatial mapping combined with 3D terrain features. For example, in areas with drastic terrain changes, high risk of line-of-sight obstruction, or small turning radii, the sampling density is appropriately increased; in flat and open areas, the sampling density is reduced. Each key point on the path not only represents a spatial coordinate but also is associated with environmental attributes such as terrain elevation and the distribution of surrounding obstacles, serving as a physical reference anchor point for subsequent signal coverage calculations and positioning accuracy assessments. This terrain-bound discretization method ensures that the optimized model accurately reflects the positioning needs in complex environments, avoiding coverage blind spots caused by sampling distortion.

[0026] Step S200: Construct a signal transmission model that includes terrain occlusion loss based on three-dimensional terrain data, and construct a multi-objective optimization model with the objectives of minimizing the positioning error of key points on the path, minimizing the number of base stations deployed, and maximizing the network fault tolerance rate.

[0027] Specifically, the signal transmission model serves as a physical bridge connecting the geographical environment and communication performance. Unlike the free-space model, this model explicitly introduces a terrain occlusion factor, converting geometric parameters such as mountain height differences and relative azimuth angles into signal attenuation, thereby accurately quantifying the link quality between any candidate base station location and key points on the path. Based on this, a multi-objective optimization model comprises three mutually constraining physical objectives: minimizing positioning error to ensure navigation safety and operational accuracy of mobile nodes throughout the entire path; minimizing the number of base stations deployed to control the overall cost of hardware procurement, installation, and subsequent maintenance; and maximizing network fault tolerance to ensure that the system can still maintain basic positioning service capabilities when individual base stations fail due to power outages, malfunctions, or extreme weather. These three objectives often conflict in complex terrains. For example, reducing the number of base stations may lead to deterioration of local geometry, increasing errors, while improving fault tolerance usually requires redundant deployment. Therefore, this model essentially seeks a Pareto optimal solution set that satisfies engineering constraints, rather than a single numerical solution.

[0028] Step S300: The multi-group differential evolution algorithm is used to solve the multi-objective optimization model to obtain the base station deployment scheme. In the iterative solution process, the feasible region is screened based on the physical connectivity of the candidate base station locations and key points of the path. The differential mutation mode is adaptively selected according to the base station distribution density in the local area. Mobile nodes that meet the positioning accuracy threshold are used as dynamic auxiliary anchors. The historical observation data of the dynamic auxiliary anchors are time-weighted and fused through a time sliding window to correct the objective function of the multi-objective optimization model.

[0029] This is the core element that distinguishes this invention from traditional optimization methods, integrating physical environment perception and dynamic data utilization into every step of the algorithm iteration. First, the feasible region screening mechanism acts as a "physical filter" for the algorithm. After each new candidate base station location is generated, the system immediately determines, based on 3D terrain data, whether there is line-of-sight connectivity between the location and key points on the relevant path. If the location is completely obscured by mountains, preventing the establishment of an effective link, the candidate location is directly marked as invalid and removed from the search space, no longer participating in subsequent fitness evaluations. This mechanism fundamentally eliminates the invalid searches performed by traditional algorithms in infeasible regions, significantly improving convergence efficiency. Second, the density-adaptive mutation mode acts as an "intelligent navigator" for the algorithm. The system monitors the distribution density of base stations in a local area in real time: in densely populated areas, a mutation strategy emphasizing global exploration is adopted to avoid getting trapped in local optima and maintain population diversity; in sparsely populated blind areas, a mutation strategy emphasizing local development is switched, and the centroid information of dynamic auxiliary anchor points is used to guide the search direction, accelerating the filling of coverage gaps. Finally, the dynamic auxiliary anchor point temporal fusion mechanism acts as a "virtual enhancer" for the system. During the iteration process, mobile nodes whose positioning accuracy already meets a preset threshold are identified as dynamic auxiliary anchor points. The system does not directly use their instantaneous observations, but instead uses a time-sliding window to weightedly fuse their historical trajectory data, suppressing random noise interference and generating a high-confidence virtual reference source. The observation residuals of this virtual reference source are incorporated into the objective function for collaborative correction, effectively supplementing spatial observation constraints without increasing the number of physical base stations, thus mitigating the geometric configuration defects caused by the sparsity of fixed base stations.

[0030] Step S400: Perform positioning accuracy and fault tolerance verification on the base station deployment scheme. In response to the verification passing, output the final base station deployment scheme.

[0031] Specifically, the verification process constitutes a closed-loop verification from algorithm optimization to engineering implementation. Positioning accuracy verification typically employs methods such as Monte Carlo simulation, calculating the normalized root mean square error of each key point along the entire path, considering measurement noise, clock skew, and terrain disturbances, to ensure it meets operational safety thresholds. Fault tolerance verification simulates scenarios of random failure of one or more base stations, assessing whether the remaining network can still maintain minimum positioning coverage. Only when both verifications pass does the system output the final deployment scheme, including the three-dimensional coordinates of base stations, the number of deployments, antenna orientation, and fault tolerance configuration parameters. If the verification fails, the system automatically feeds back to step S300, adjusting optimization weights or constraints and iterating again until a feasible solution that meets all engineering indicators is obtained. This closed-loop mechanism ensures that the output scheme is not only mathematically optimal but also physically reliable and engineering-implementable.

[0032] It should be understood that although this embodiment uses a drone inspection scenario as an example, the method is also applicable to other scenarios such as mobile robot positioning in complex terrain and communication networking for emergency rescue in the wild. As long as the problem of positioning base station deployment of mobile nodes in unstructured environments is involved, the technical approach of this invention can be adopted.

[0033] In some embodiments, the expression for the signal transmission model is: .in, For the first The base station and the first Total path loss between nodes The reference path loss at the reference distance, This is the path loss index. For the first The base station and the first Horizontal distance between nodes This is the terrain occlusion attenuation coefficient. The height or relative elevation difference of the mountain acts as a barrier. This represents the shadow fading margin or random interference term. Specifically, this signal transmission model is not a general free-space propagation model, but a specialized model with physical modifications for complex terrain environments. In unstructured environments such as mountains or canyons, signal propagation is affected not only by distance but also by the severe modulation caused by terrain undulations. The formula... This term represents the quantitative characterization of terrain shading loss. Among them, Calculated using three-dimensional terrain data, it represents the maximum protrusion height or effective obstruction thickness relative to the line of sight on the profile of the connection between the base station and the node. This reflects the additional signal attenuation intensity per unit height of obstruction under specific geological and vegetation conditions. For example, in densely forested canyon areas, The value can be set to 0.05dB / m to 0.08dB / m, but can be appropriately reduced in mountainous areas with exposed rock. As a path loss index, it is also dynamically assigned values ​​based on local environmental characteristics, such as 3.0 in open areas, 3.5 in densely vegetated areas, and 4.0 in deep canyons. This parameterized modeling approach allows the algorithm to accurately distinguish between "line-of-sight connectivity" and "non-line-of-sight occlusion" states, providing quantitative physical criteria for subsequent feasible region selection, rather than relying solely on simple geometric distance thresholds. It should be understood that although this embodiment provides specific parameter value examples, in practical applications, these parameters can be calibrated through field surveys or channel measurement data to adapt to different geographical environments.

[0034] Furthermore, the mathematical expression for the multi-objective optimization model is: .in, This represents the total number of key points on the path. For the number of base stations deployed, Network fault tolerance. Sub-cost function corresponding to a single path critical point. The expression is: .in, For the first The coordinate location parameters of each base station, In order to be with the first A set of fixed base stations directly connected to key points along a path. In order to be with the first The set of adjacent path key points directly connected to each path key point In order to be with the first A set of dynamic auxiliary anchor points that directly connect key points along a path. To measure the noise variance, This is the weighted residual term based on measurement noise.

[0035] This multi-objective optimization model constructs the core evaluation system for the base station deployment problem. There are inherent physical constraints among the three optimization objectives: reducing the number of base stations. This often weakens the geometric structure, leading to increased positioning errors; while pursuing high network fault tolerance... Typically, this requires adding redundant nodes, which contradicts the goal of minimizing costs. Therefore, this model aims to find a set of Pareto optimal solutions that maximize resource utilization efficiency while meeting basic positioning accuracy and safety redundancy requirements.

[0036] In the sub-cost function In its design, this invention employs a joint evaluation mechanism based on information fusion. This represents the absolute positional constraints provided by static infrastructure and serves as the benchmark for positioning solutions; set Path continuity constraints are introduced, and the relative positional relationships between adjacent key points are used to smooth the trajectory and suppress single-point abrupt noise; set This incorporates mobile nodes that meet the accuracy threshold as dynamic auxiliary anchor points, utilizing their spatiotemporal redundancy information to fill coverage blind spots of fixed base stations. The union of these three sets essentially constructs a multi-source heterogeneous observation network of "fixed + adjacent + dynamic". (The formula...) The term, acting as a confidence weight, ensures that high-quality observational data dominates the optimization process, while high-noise data is automatically suppressed. Weighted residual term. This comprehensively reflects the actual contribution of each observation link to positioning accuracy under the current base station layout.

[0037] Specifically, the weighted residual term Express it using the following formula: .

[0038] It is important to emphasize that the aforementioned signal transmission model and multi-objective optimization model together form the basis for the fitness evaluation of the subsequent differential evolution algorithm. For each candidate base station location generated during the algorithm's iteration process, its corresponding path loss and offspring value must be calculated using the aforementioned formulas, thereby guiding the mutation and selection direction of the population. This modeling approach, which deeply couples physical environment characteristics with optimization objectives, effectively avoids the infeasibility problem caused by terrain simplification in traditional methods, ensuring the consistency between the final output base station deployment scheme in theoretical calculations and engineering practice.

[0039] In some embodiments, the process of solving the multi-objective optimization model using a multi-population differential evolution algorithm includes specific population initialization and adaptive control strategies. Specifically, if there are poles near the area where the base station is to be deployed, positive initial individuals are generated within a preset range around the poles, and corresponding negative individuals are generated simultaneously. The individual with the best fitness is selected from the positive initial individuals and the negative individuals as the initial population.

[0040] This initialization strategy fully utilizes existing physical infrastructure information in complex terrain environments. In scenarios such as overhead line inspection in mountainous areas, power poles are not only support points for power facilities but also often advantageous locations for communication signal transmission, as they are usually located at higher elevations or with relatively open views. Therefore, introducing the pole locations as prior knowledge into population initialization can significantly improve the engineering feasibility of the initial solution. Specifically, the system first identifies the three-dimensional coordinates of all available power poles within the deployment area and delineates a sampling sphere centered on each power pole with a radius equal to one-third of the base station's maximum communication range. Within this sphere, positive initial individuals are randomly generated. Simultaneously, to prevent the algorithm from prematurely converging to local optima near the power poles and ignoring potentially better non-power pole locations (such as isolated mountaintops or artificial platforms), this invention introduces a reverse learning mechanism. The generation of reverse individuals follows the principle of central symmetry, and its calculation formula is as follows: ,in For positive individuals in the first Dimensional coordinates Pre-determine the location of a certain number (e.g., 3) of base towers near this tower. The mean coordinates of the dimensions. Through this symmetrical mapping, the reverse individuals actually explore the search space on the other side of the tower cluster center as the symmetrical point, effectively increasing the diversity coverage of the population. Subsequently, the system calculates the fitness values ​​of the forward and reverse individuals (i.e., the comprehensive evaluation value based on the aforementioned signal transmission model and multi-objective optimization model), and selects the individuals with the best fitness to form the initial population. This dual mechanism of "physical constraint guidance + reverse exploration supplementation" ensures that the initial scheme does not deviate from the actual engineering situation and avoids the slow convergence problem caused by blind random initialization. Furthermore, during the iterative solution process, the system also adaptively adjusts the population size according to the degree of regional terrain occlusion and signal loss intensity: in areas with severe occlusion and high signal loss, a single population is split into multiple sub-populations; in open and unobstructed areas, adjacent redundant populations are merged.

[0041] This adaptive control mechanism aims to address the computational resource misallocation problem caused by the non-uniform distribution of the search space in complex terrain environments. In areas with dramatic terrain undulations, dense vegetation, or deep canyons, signal propagation exhibits high nonlinearity, and the feasible region is often fragmented into multiple discrete, narrow segments. In such cases, maintaining a single large-scale population for searching can easily lead to the neglect of these small feasible segments due to homogeneous competition among individuals, or repeated crossing of the feasible region boundary due to an excessively large global search step size. Therefore, when the system detects that the average path loss in a certain area exceeds a preset high-loss threshold (e.g., 120dB), or the terrain elevation standard deviation exceeds a preset complex terrain threshold (e.g., 200m), the area is determined to be a severely occluded region, and the single population originally responsible for that area is split into two or more independent subpopulations. Each subpopulation has independent mutation parameters and a search centroid, enabling refined mining within its own local feasible region, thereby significantly improving the probability of capturing narrow feasible regions. Conversely, in open areas with flat terrain and unobstructed views, signal coverage is continuous and feasible domain connectivity is strong. Too many subpopulations would waste computational resources. In such cases, the system merges multiple adjacent subpopulations with high overlap in their search ranges into a single unified population. By increasing the population size, it enhances global exploration capabilities and accelerates convergence towards the optimal solution. It should be understood that the aforementioned high-loss threshold and complex terrain threshold are not fixed and can be calibrated or dynamically adjusted based on the overall environmental characteristics of the target area in practical applications. For example, in areas with poor overall signal conditions, the threshold for triggering splitting can be appropriately increased to avoid excessive population fragmentation; while in critical road sections where positioning accuracy is extremely high, the threshold can be lowered to achieve higher search resolution. Through this dynamic resource allocation strategy, this invention achieves the optimal balance between computational efficiency and optimization accuracy, ensuring that the optimal base station deployment scheme that meets engineering requirements is obtained within a limited computation time.

[0042] In some embodiments, feasible regions are filtered based on the physical connectivity of candidate base station locations and key path points, and differential mutation modes are adaptively selected according to the base station distribution density in local areas. This mechanism constitutes the core search engine for solving the multi-objective optimization model of this invention. By mapping terrain physical constraints and network topology states to the mutation operator of the evolutionary algorithm in real time, it solves the problem of low efficiency of traditional differential evolutionary algorithms in blindly searching in complex discontinuous search spaces.

[0043] Specifically, the adaptive mutation process is executed in two tightly coupled stages. The first stage is feasible region pre-screening, which involves pre-calculating the effective communication coverage of each individual, generating a feasible region mask, and selecting mutation parents only from valid individuals whose feasible region masks satisfy preset connectivity conditions. In this embodiment, the feasible region mask is essentially a binary physical connectivity discrimination matrix. After generating candidate base station coordinates in each iteration, the system immediately calls 3D terrain data to perform line-of-sight propagation detection. If a candidate individual has an unobstructed line-of-sight link with at least two path key points, its mask value is set to 1, marking it as a valid individual; conversely, if it is completely obstructed by mountains, preventing the establishment of the geometric configuration required for positioning, the mask value is set to 0. Only individuals with a mask value of 1 are eligible to be selected into the mutation parent set. This hard filtering mechanism is equivalent to building a physical firewall within the algorithm, forcing the search process to always stay on effective manifolds with engineering feasibility, fundamentally eliminating the computational waste of fitness evaluation in invalid areas blocked by mountains, and significantly improving the effective search efficiency of the algorithm compared to traditional methods.

[0044] The second stage involves density-adaptive mode switching, which adaptively selects a mutation mode based on the regional base station density: in densely populated areas, the first mutation mode is used; in sparsely populated blind areas, a second mutation mode guided by dynamic anchor points is used. The regional base station density is quantified by calculating the number of base stations or their average spacing within a preset neighborhood of the current candidate location. For example, when the average spacing between base stations in the neighborhood is less than 300 meters, it is considered a dense area; when the average spacing is greater than or equal to 300 meters, it is considered a sparse blind area. This threshold is typically set to about half the maximum communication radius of the base station to accurately reflect the degree of coverage overlap.

[0045] In densely populated base station areas, due to the good connectivity of the feasible region and high signal coverage redundancy, the main challenge in optimization is to avoid getting trapped in local optima while maintaining solution diversity. Therefore, the first mutation mode preferably adopts the classic DE / rand / 1 strategy, which randomly selects three different valid individuals for difference operations. This strategy has strong global exploration capabilities, enabling extensive sampling within a continuous feasible region and preventing the population from prematurely converging to a suboptimal tower cluster location.

[0046] Conversely, in sparsely populated dead zones, fixed base stations have weak geometric configurations, making positioning accuracy extremely sensitive to base station location, and the feasible region often exhibits fragmented characteristics. In this case, the second mutation mode uses the following formula for dynamically anchor-guided mutation: ;in, The adaptive scaling factor is initially set to 0.9 and decreases linearly to 0.4 with each iteration. It is the best individual in the current population; Let be the centroid coordinates of the current set of dynamic anchor points. In this formula, It plays a crucial guiding role as a "virtual lighthouse." Because sparse areas lack sufficient fixed base stations to provide strong geometric constraints, the algorithm is prone to losing its search direction. Dynamic auxiliary anchor points, on the other hand, are mobile nodes whose own positioning errors already meet the high-precision threshold; their temporally fused centroid coordinates represent the most reliable spatial reference benchmark in that area at the current moment. The mutation vector no longer relies solely on the differential information between fixed base stations but also incorporates a traction component pointing towards the centroid of the dynamic anchor point. This means that newly generated candidate base station locations are actively pulled towards the area with the highest observation quality from mobile nodes, thereby quickly filling coverage gaps and improving positioning geometric accuracy. Simultaneously, the adaptive scaling factor... The linear decrease in the number of iterations (e.g., from 0.9 to 0.4) allows the algorithm to perform large-step directional exploration in the early stages using dynamic anchor points, and then fine-tune around the optimal solution in the later stages, achieving a dynamic balance between exploration and development. It should be understood that although this embodiment uses 300 meters as an example of the switching threshold between dense and sparse areas, in practical applications, this threshold can be adaptively adjusted according to the base station communication radius, terrain complexity, and positioning accuracy requirements. For example, in ultra-long-distance communication scenarios, this threshold can be appropriately increased.

[0047] In some embodiments, the iterative solution process further includes: performing a binomial crossover operation on the mutated individual and its parent individual to generate a test individual; and performing adaptive terrain anchoring correction on the test individual. This step constitutes a key safety valve for the algorithm's mapping from the mathematical search space to the physical engineering space. Specifically, the binomial crossover operation is a standard step in differential evolution algorithms used to recombine genetic information. A preset crossover probability (e.g., 0.9) controls the inheritance ratio of genes in each dimension between the mutated individual and its parent individual, aiming to maintain population diversity and prevent premature convergence. However, in complex terrain environments, test individuals generated solely through crossover operations are highly likely to fall into physically infeasible or communicatively ineffective areas. Therefore, this invention introduces an adaptive terrain anchoring correction mechanism as a mandatory constraint repair method to ensure that all candidate base station locations entering the fitness evaluation stage are feasible for engineering implementation.

[0048] It is particularly important to emphasize that this adaptive terrain anchoring correction mechanism is fundamentally different from the penalty function method commonly used in traditional optimization algorithms. The penalty function method typically reduces the probability of selection by imposing a large penalty on out-of-bounds or rule-breaking individuals, but it does not change the coordinates of the individuals themselves. This leads to a significant waste of computational resources on evaluating invalid solutions, and it is prone to causing algorithmic stagnation when the constraint boundaries are steep. In contrast, the anchoring correction of this invention is an active geometric repair strategy that directly "pulls" rule-breaking individuals back into the feasible region or makes them satisfy the constraints, thereby ensuring the effectiveness of each iteration's evaluation and significantly improving the algorithm's optimization efficiency under strong constraints.

[0049] This adaptive terrain anchoring correction mechanism comprises two parallel or sequential processing branches, each addressing different violation types. The first branch addresses spatial deployment constraints: if the test individual is located in an undeployable area, it is anchored to the nearest point on the boundary of the nearest feasible area. Undeployable areas refer to restricted zones pre-defined by the 3D geographic information system, such as steep slopes, deep valleys, water bodies, basic farmland, or areas occupied by existing buildings. When the 3D coordinates of a test individual fall into such areas, the system does not discard the individual directly but calculates the geometric projection of that coordinate point to the boundary of the nearest feasible area. In practice, this projection can be based on the shortest line projection using Euclidean distance or a geodesic projection considering terrain undulations. By forcibly moving the individual to the nearest feasible point on the boundary, deployment violations are eliminated while preserving the search direction information carried by the original individual to the greatest extent possible, avoiding the loss of effective search momentum due to random resets. It should be understood that although this embodiment describes the preferred method of projecting to the nearest point on the boundary, in other embodiments, alternative strategies such as projecting to the centroid of the region or moving along a specific safety corridor may be adopted according to actual engineering needs, as long as the corrected position can meet the physical deployment safety requirements.

[0050] The second branch addresses communication connectivity constraints: if an experimental individual cannot meet the connectivity requirements with at least two path key points, its movement step size towards the optimal connectivity direction is calculated and gradually adjusted until the connectivity constraints are met. In wireless positioning systems, for a mobile node to achieve two-dimensional or three-dimensional positioning, it must simultaneously establish line-of-sight links with at least two (usually three or more) known base stations. If an experimental individual is located in a deployable area, but the number of visible path key points is insufficient due to mountain obstruction, then that location cannot provide effective positioning services. In this case, the system initiates a connectivity repair process. First, a local line-of-sight field or connectivity gradient map is constructed based on three-dimensional terrain data to identify the spatial direction that can increase the number of visible key points, i.e., the "optimal connectivity direction." Subsequently, the algorithm drives the experimental individual to move along this direction with an adaptive step size. The step size is usually related to the number of currently missing connectivity links and terrain roughness: a larger step size is used when there are many missing links or the terrain is flat to quickly approach the feasible area; the step size is automatically reduced for a fine search when approaching a critical state or when the terrain is complex. This gradual adjustment strategy avoids crossing narrow line-of-sight channels or falling into new blind spots due to excessively large single movement spans. Through this mechanism, the algorithm can transform candidate solutions that are "positionally valid but functionally ineffective" into truly effective solutions with positioning capabilities, further enhancing the practicality and reliability of the final output solution.

[0051] In some embodiments, historical observation data of dynamic auxiliary anchor points are time-weightedly fused using a time sliding window to correct the objective function of the multi-objective optimization model. This mechanism is a key means of improving the robustness of the positioning system under the condition of limited fixed base station resources. Its core idea is to transform mobile nodes that meet specific accuracy conditions into high-confidence virtual reference sources and suppress instantaneous observation noise through time-series filtering, thereby dynamically compensating for the deficiencies of the fixed base station's geometric configuration. Specifically, this fusion process includes the following four closely linked steps.

[0052] The first step is the dynamic auxiliary anchor point admission determination: only mobile nodes with positioning errors less than or equal to a preset error threshold are used as dynamic auxiliary anchor points, constructing a dynamic auxiliary anchor point set. Specifically, not all mobile nodes can directly participate in optimization correction; they must undergo rigorous quality screening. In this embodiment, the preset error threshold is preferably set to 3 meters. This value has a clear physical meaning: in complex terrain wireless positioning scenarios, 3 meters is usually the watershed between "high-precision reliable state" and "low-precision drift state." When the real-time positioning error of a mobile node exceeds this threshold, it indicates that it may be in an area with severe multipath effects or satellite signal obstruction. If it is included in the optimization system at this time, it will introduce systematic bias, causing the base station deployment scheme to converge in the wrong direction. Therefore, the admission determination mechanism acts as a "quality valve" of the system, ensuring that only those mobile nodes with sufficiently accurate positions are qualified to become the reference source for auxiliary optimization. It should be understood that 3 meters is only a preferred example. In practical applications, this threshold can be adaptively adjusted according to the sensor accuracy of the mobile node, the safety margin of the operation, and the level of environmental interference. For example, it can be tightened to 1 meter in high-precision surveying scenarios, while it can be relaxed to 5 meters in emergency search and rescue scenarios.

[0053] The second step is time-series weight allocation: An exponentially decaying weighting formula is used to assign weights to each historical moment within the time sliding window. The formula is expressed as: .in, For a moment The weighting coefficients, For the current moment, The time decay coefficient, The value represents the sliding window length. This formula is designed to reflect the "nearer, larger; farther, smaller" principle of temporal correlation, meaning that observations closer to the current time are assigned a higher degree of confidence. Parameters and Together, they determine the system's memory characteristics and response sensitivity to historical information. The data span for fusion is defined, for example, a value of 5 or 6, which means that the system comprehensively considers the state of the most recent 5 to 6 moments. This is sufficient to cover the short-range motion trajectory of the mobile node at a typical inspection speed and to provide a sufficient sample size to smooth out random noise. This controls the rate of weight decay, for example, by taking a value between 2.0 and 2.5. When When the weights are large, the weights of historical data decay slowly, and the system exhibits strong smoothness, making it suitable for scenarios where moving nodes move in uniform linear motion; when When the weights are smaller, the weights are quickly concentrated on the latest moment, making the system more sensitive to maneuvering changes and suitable for scenarios with frequent turns or speed changes. Through this parameterized weight allocation, the algorithm can achieve the best balance between suppressing measurement noise and tracking dynamic changes, avoiding the lag effect caused by simple arithmetic averaging or the jitter risk caused by single-point values.

[0054] The third step is the calculation of the centroid of the time-series fusion dynamic auxiliary anchor point: based on the weights and the coordinates of the dynamic auxiliary anchor points at each historical time, the centroid of the time-series fusion dynamic auxiliary anchor point is calculated. Specifically, the system takes the coordinates of all qualified dynamic auxiliary anchor points within the sliding window, and performs a weighted average according to the time-series weights calculated above, to obtain a comprehensive centroid coordinate. This centroid no longer represents the physical position at a single moment, but rather the "statistically expected position" of the moving node over a recent period. Compared to the original observation point, this centroid effectively filters out high-frequency position jumps caused by factors such as receiver thermal noise and instantaneous multipath reflections, forming an extremely stable virtual reference point. In subsequent optimization iterations, this centroid will be treated as a fixed anchor point with known precise coordinates, thereby significantly enhancing the geometric constraint strength of the local area without increasing the cost of physical hardware.

[0055] Specifically, the integrated centroid coordinates Calculate using the following formula: ;in Let be the coordinates of the c-th dynamic anchor point at time t;

[0056] The fourth step is collaborative residual correction: The joint residuals of fixed base stations and time-series fusion dynamic auxiliary anchors are fused to correct the original sub-cost function, resulting in a collaborative residual correction term. Specifically, the system uses the stable centroids calculated above... Substituting the corresponding observation data into the signal transmission model, the theoretical residuals between the model and the candidate base station locations are calculated. Combined with the residual information from the fixed base station, a cooperative residual correction term is generated. This correction term is directly added to the original sub-cost function. In this process, a new evaluation objective is formed. The physical essence of this operation is to use the spatiotemporal redundancy information of mobile nodes to "fill" the rank deficiency or weak observation dimension in the observation equation of fixed base stations. Especially in blind spots where the line of sight of fixed base stations is obstructed, such as canyons and dense forests, dynamic auxiliary anchor points can often provide the only effective observation link. By explicitly embedding this high-quality information into the optimization objective function, the algorithm can perceive coverage gaps and accuracy weaknesses that cannot be detected by fixed base stations alone, thereby driving the base station deployment scheme to actively tilt or adjust towards these areas, ultimately achieving uniformity of positioning accuracy and improvement of robustness across the entire network. It should be understood that this correction is not a simple numerical superposition, but a deep fusion based on the physical model, ensuring semantic consistency between dynamic information and static infrastructure at the optimization level.

[0057] Specifically, the cooperative residual correction term Calculate using the following formula: ;

[0058] In some embodiments, the process of verifying the positioning accuracy and fault tolerance of the base station deployment scheme includes: determining the final base station location using an elite selection strategy and population midpoint enhancement optimization. Specifically, the elite selection strategy is used throughout the entire iteration process to ensure that the fitness value of the best individual in each generation of the population remains monotonically constant, thereby ensuring the stability of the algorithm's convergence. However, in complex terrain environments, due to the high non-convexity and multimodal characteristics of the search space, even if the algorithm converges, a single best individual may still deviate from the theoretical global extreme point due to minor perturbations from numerical calculation accuracy or local noise. Therefore, this embodiment introduces population midpoint enhancement optimization as a post-processing step. When the algorithm terminates after reaching the preset maximum number of iterations, the system does not directly output the coordinates of the currently recorded global best individual, but instead calculates the arithmetic mean of the coordinates of all surviving individuals in the subpopulation corresponding to the base station. The physical mechanism of this operation is that, at the end of the evolution, effective individuals have formed a tight spatial cluster in the high-fitness region, and their distribution centroid is often closer to the true probability expectation center than any discrete individual. Through this statistical averaging of collective intelligence, single-point random errors can be effectively filtered out, making the final determined base station deployment coordinates more robust and geometrically stable at the engineering implementation level.

[0059] Specifically, the formula for the elite selection strategy is: ;in, This is the dynamic anchor point collaborative residual correction term.

[0060] Specifically, the formula for the population midpoint enhancement optimization is as follows: Where L is the population size and G is the maximum number of iterations. This refers to the l-th individual in the population corresponding to the n-th base station.

[0061] Furthermore, this embodiment calculates the normalized root mean square error (NRMSE) using Monte Carlo simulation to evaluate positioning accuracy. Specifically, given the nonlinearity of signal propagation in complex terrain and the randomness of environmental noise, a single deterministic calculation cannot fully characterize the actual performance of the system. Therefore, the system constructs a probabilistic model incorporating multidimensional random variables such as measurement noise, clock skew, and terrain occlusion disturbances, and executes large-scale (e.g., more than 1000) independent repeated Monte Carlo experiments. In each experiment, based on the aforementioned determined base station location and signal transmission model, the positioning calculation process of the mobile node at each key point along the entire path is simulated, and the deviation between the current location and the actual location is statistically estimated. The formula for calculating the normalized root mean square error (NRMSE) is: ;in, For the number of Monte Carlo simulations, This represents the total number of key points on the path. For the first In the simulation, the first The true location of each key point This corresponds to the estimated location. This indicator eliminates the influence of absolute distance dimensions and can objectively reflect the relative positioning level under different terrain complexities and base station configurations. Only when the NRMSE is lower than a preset safety threshold (e.g., 5 meters) is the solution judged to be accurate enough. This statistically based evaluation method, compared with the traditional geometrical factor of precision (GDOP) analysis, can more realistically reflect the system reliability boundary under complex physical environments.

[0062] More importantly, this embodiment also implements a base station fault-tolerant reconstruction mechanism: if a base station fault is detected, a local scheme reconstruction is automatically triggered. A temporary positioning network is formed by combining surrounding normal base stations with dynamic auxiliary anchor points fused by time series, and the weights of the temporary positioning network are optimized in real time, with fine-tuning of the equivalent coverage weights of surrounding base stations. This mechanism extends the scope of protection of this invention from the static "deployment planning stage" to the dynamic "system operation and maintenance stage," solving the pain point of base station failure leading to network-wide paralysis or requiring long-term global replanning in the prior art. Specifically, when the system detects that a base station has failed due to power outage, hardware damage, or link interruption, it does not start the time-consuming global optimization algorithm to solve again, but immediately activates the local self-healing protocol. First, the system automatically identifies the set of adjacent normal base stations within the coverage area of ​​the faulty base station and uses them as the static skeleton of the temporary positioning network. Second, the system calls the dynamic auxiliary anchor point time series fusion module established in the aforementioned embodiment to filter out mobile nodes that are currently located in the fault area and whose positioning accuracy meets the admission threshold, and uses them as virtual replacement nodes. Since the spatiotemporal trajectories of these mobile nodes are continuous, their historical fusion data can effectively fill the geometric observation gaps left by the faulty base station. Subsequently, based on real-time observation residuals, the system dynamically adjusts the fusion weights of each node in the temporary network (including surrounding fixed base stations and dynamic auxiliary anchors) using lightweight online optimization algorithms such as gradient descent or recursive least squares. For example, the weights of normal base stations near the edge of the fault area are appropriately increased, and high-confidence dynamic anchors are given greater influence. This allows for the restoration of local positioning service capabilities through soft parameter reconstruction without altering the physical topology. It should be understood that the computational complexity of this local reconstruction is far lower than that of global replanning, and its response time can typically be controlled within one second, ensuring the continuity and security of positioning services for mobile nodes traversing fault areas. Furthermore, although this embodiment uses a single base station failure as an example, this mechanism is also applicable to scenarios with concurrent failures or performance degradation of multiple base stations. As long as the remaining resources and the combination of dynamic anchors can meet the minimum geometric observability conditions, basic emergency positioning functions can be maintained.

[0063] This embodiment provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the wireless positioning base station deployment method in complex terrain environments as described in any of the foregoing embodiments.

[0064] Specifically, this electronic device constitutes the physical carrier of the technical solution of this invention at the product end. The processor can be a hardware entity with data processing and control capabilities, such as a central processing unit, digital signal processor, application-specific integrated circuit (ASIC), or field-programmable gate array (FPGA). In the application scenario of this invention, the processor is configured to execute program instructions stored in memory to complete a series of operations, including acquiring 3D terrain data, constructing a signal transmission model, performing multi-population differential evolution iterative solutions, and fault tolerance verification. For example, when performing computationally intensive steps such as population adaptive splitting and fusion or dynamic anchor point time-series weighted fusion, the processor can accelerate the process through multi-threaded parallel processing or vector operations to meet the timeliness requirements of real-time deployment planning or online reconstruction. The memory is used to persistently or temporarily store the program code, 3D geographic information data, historical observation sequences of mobile nodes, and population state information during the iteration process required to implement the above methods. It should be understood that although this embodiment uses a general computer architecture as an example, in other embodiments, the electronic device can also be a dedicated computing module integrated into a UAV ground control station, edge computing gateway, or cloud server, as long as it has the hardware capability to execute the aforementioned method steps. This combination of hardware and software transforms abstract optimization algorithms into practically deployable engineering products, providing clear physical objects for subsequent technology rights protection and infringement comparison.

[0065] In addition, this embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the wireless positioning base station deployment method in complex terrain environments as described in any of the foregoing embodiments.

[0066] Specifically, a computer-readable storage medium refers to any tangible medium capable of containing, storing, communicating, propagating, or transmitting a program for use by or in conjunction with an instruction execution system, apparatus, or device. In this invention, the sequence of program instructions stored on this medium corresponds one-to-one with the steps of the base station deployment method described in the foregoing embodiments. When these instructions are loaded into a processor and executed, they drive the hardware entity to reproduce the complete technical flow of this invention. Specific forms of this storage medium include, but are not limited to, random access memory, read-only memory, erasable programmable read-only memory, flash memory, hard disk drive, solid-state drive, optical disk, magnetic tape, or cloud storage services. For example, in remote mountainous inspection operations, a program containing the method of this invention can be pre-installed on the solid-state drive of a portable industrial control computer, or updated to the flash memory of the onboard computing unit via a wireless network before the drone takes off. This layout, which uses the storage medium as the object of protection, ensures that even if the infringement only manifests as the sale, distribution, or download of software without involving the manufacture of specific hardware devices, the rights holder can still assert rights based on the storage medium, thereby constructing a comprehensive three-dimensional protection system covering methods, devices, and media.

[0067] To further verify the effectiveness and superiority of the technical solution of this invention in practical engineering, this embodiment takes the inspection scenario of a 110kV overhead line in a remote mountainous area as an example for detailed explanation. The line is 25km long, with terrain mainly consisting of mountains and valleys, an elevation difference of 800m, and a vegetation coverage of approximately 70%. There are multiple areas with severe satellite signal obstruction, making it a typical test field for verifying the deployment method of wireless positioning base stations in complex terrain. In this scenario, the drone inspection operation requires a normal positioning error of no more than 5m, the number of base stations deployed is limited to no more than 30 due to maintenance costs, and the system must have uninterrupted positioning capability even under single base station failure.

[0068] Based on the aforementioned scenario characteristics, the system parameters are set as follows: the region of interest is set to a rectangular area of ​​25km × 2.5km; the inspection path is discretized into 500 key points at 50m intervals; the maximum communication range R of the base station is set to 600m, the transmit power to 23dBm, and the receive sensitivity to -105dBm. Regarding the signal transmission model, the baseline path loss L0 is set to 40dB, the path loss exponent γ is set to 3.4, the terrain occlusion attenuation coefficient η is set to 0.06dB / m, and the shadow fading standard deviation σ is set to 4.5dB. These parameters accurately characterize the signal propagation characteristics in this mixed environment of dense forest and canyon in the mountainous area. In terms of algorithm configuration, the population size L is set to 12, the maximum number of iterations G is set to 40, the initial scaling factor α is set to 0.95 and decreases linearly with iteration, and the crossover probability pC is set to 0.85. In particular, considering the characteristics of the UAV inspection speed and strong trajectory continuity in this scenario, the time-series sliding window length W is preferably set to 6, and the time decay coefficient τ is set to 2.5. This parameter combination can suppress instantaneous measurement noise while retaining sufficient trajectory dynamic information, avoiding insufficient smoothing due to an excessively short window or hysteresis error introduced by an excessively long window.

[0069] During algorithm execution, the adaptive mechanisms described in the aforementioned embodiments were fully validated. In the initial stage, the system generated a mixed initial population including the areas surrounding towers and open areas on mountaintops for 35 base station locations to be optimized. As iterations progressed, the population adaptive control mechanism identified nine areas with severe obstruction from dense forests in canyons and automatically triggered population splitting, enhancing local search accuracy; simultaneously, population fusion was performed in ten open areas, reducing redundant computation. From the convergence process, the average positioning error decreased to 8.2m in the 12th iteration, to 4.2m in the 28th iteration, and stably converged to 3.2m by the end of the 40th iteration, without falling into local optima or diverging, demonstrating the efficient optimization capability of the terrain-aware two-stage differential mutation operator in discontinuous search spaces. The final output base station deployment scheme included 27 base stations, saving 3 from the budget limit. Nineteen base stations were deployed on the tops of existing towers, making full use of existing infrastructure; eight base stations were deployed in open areas on mountaintops, effectively filling coverage blind spots between towers. All 500 key points along the inspection route are directly connected to at least two base stations or dynamic auxiliary anchor points, achieving full coverage without blind spots.

[0070] To quantitatively evaluate the technical advantages of this invention, it was compared with the Multi-Population Differential Evolutionary Algorithm (MPDE), Semidefinite Programming Algorithm (SDP), Uniform Layout Method, and Least Squares Method (LLS). The test results are shown in Table 1.

[0071] Table 1 Comparison of Test Results

[0072] Test results show that, in terms of positioning accuracy, the normalized root mean square error of the proposed solution is 3.2m, significantly better than MPDE's 3.8m, SDP's 4.9m, LLS's 5.4m, and the uniform arrangement method's 7.6m. This is mainly due to the dynamic enhancement effect of the dynamic auxiliary anchor point temporal fusion mechanism on the geometric configuration. Regarding computational efficiency, the proposed solution runs in 11.2s on a standard computer, approximately 11% faster than MPDE and over 92% faster than SDP, verifying the effectiveness of feasible region screening and population adaptive control in eliminating invalid searches. In terms of deployment cost, the proposed solution requires only 27 base stations to meet the requirements, while the uniform arrangement method requires 38, SDP requires 32, and LLS requires 41. Even compared to MPDE (26 base stations), which has the fewest base stations, the proposed solution reduces the positioning error by 15.8% with only one additional base station, and increases the base station fault tolerance rate from 87% to 92%, demonstrating superior overall cost-effectiveness.

[0073] Furthermore, this embodiment specifically conducted a simulation test on the base station fault-tolerant reconstruction mechanism. After randomly selecting two base stations in the system to simulate a power outage, the fault-tolerant reconstruction mechanism automatically completed the local scheme reconstruction within 0.85 seconds. During this period, the system constructed a temporary positioning network by calling surrounding normal base stations and time-series fusion dynamic auxiliary anchor points, and optimized the fusion weights in real time. The test results show that even under the extreme condition of simultaneous failure of two base stations, the overall positioning coverage rate remained at 100%, with no positioning interruptions or accuracy exceeding limits. This result strongly demonstrates that the local self-healing mechanism based on dynamic anchor point collaboration proposed in this invention can effectively address the equipment reliability challenges in unattended environments in remote mountainous areas, ensuring the continuous safety of UAV inspection operations. It should be understood that the above specific parameters and test results are only illustrative examples. In practical applications, those skilled in the art can adaptively adjust the parameters in this embodiment according to the terrain complexity of the specific route, the performance indicators of the UAV, and the specifications of the communication equipment, without departing from the protection scope of this invention.

[0074] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for deploying wireless positioning base stations in complex terrain environments, characterized in that, include: Acquire three-dimensional terrain data of the target area and the preset movement path of the mobile node, and discretize the preset movement path into multiple path key points; Based on the three-dimensional terrain data, a signal transmission model including terrain occlusion loss is constructed, and a multi-objective optimization model is constructed with the objectives of minimizing the positioning error of the key points of the path, minimizing the number of base stations deployed, and maximizing the network fault tolerance rate. Multiple group differential evolution algorithms are used to solve the multi-objective optimization model to obtain the base station deployment scheme. In the iterative solution process, feasible regions are filtered based on the physical connectivity between candidate base station locations and key points of the path. Differential mutation modes are adaptively selected according to the base station distribution density in local areas. Mobile nodes that meet the positioning accuracy threshold are used as dynamic auxiliary anchor points. The historical observation data of the dynamic auxiliary anchor points are time-weighted and fused through a time sliding window to correct the objective function of the multi-objective optimization model. The positioning accuracy and fault tolerance of the base station deployment scheme are verified. If the verification passes, the final base station deployment scheme is output.

2. The method for deploying wireless positioning base stations in complex terrain environments according to claim 1, characterized in that, The expression for the signal transmission model is: ;in, For the first The base station and the first Total path loss between nodes The reference path loss at the reference distance, This is the path loss index. For the first The base station and the first Horizontal distance between nodes This is the terrain occlusion attenuation coefficient. The height or relative elevation difference of the mountain acts as a barrier. This refers to the shadow fading margin or random disturbance term.

3. The method for deploying wireless positioning base stations in complex terrain environments according to claim 1, characterized in that, The mathematical expression of the multi-objective optimization model is: ;in, This represents the total number of key points along the path. For the number of base stations deployed, For network fault tolerance; Sub-cost function corresponding to a single path key point The expression is: ;in, For the first The coordinate location parameters of each base station, In order to be with the first A set of fixed base stations directly connected to key points along a path. In order to be with the first The set of adjacent path key points directly connected to each path key point In order to be with the first A set of dynamic auxiliary anchor points that directly connect key points along a path. To measure the noise variance, This is the weighted residual term based on the measurement noise.

4. The method for deploying wireless positioning base stations in complex terrain environments according to claim 1, characterized in that, The method of solving the multi-objective optimization model using multiple group difference evolution algorithms includes: If there are poles or towers near the area where the base station is to be deployed, then a positive initial individual is generated within a preset range around the poles or towers, and a corresponding reverse individual is generated at the same time. The individual with the best fitness is selected from the positive initial individual and the reverse individual as the initial population. Population size is adaptively adjusted based on the degree of occlusion and signal loss intensity in the region: in areas with severe occlusion and high signal loss, a single population is split into multiple subpopulations; in open and unobstructed areas, adjacent redundant populations are merged.

5. The method for deploying wireless positioning base stations in complex terrain environments according to claim 1, characterized in that, The feasible region filtering based on the physical connectivity between candidate base station locations and key points along the path, and the adaptive selection of differential mutation modes based on the base station distribution density in local areas, includes: Phase 1: Pre-calculate the effective communication coverage of each individual, generate a feasible domain mask, and select the variant parent only from the effective individuals whose feasible domain mask satisfies the preset connectivity conditions; Phase Two: Adaptively Selecting the Variation Mode Based on Regional Base Station Density: In areas with dense base stations, the first mutation mode is used for mutation. In sparse base station blind areas, a second mutation mode guided by dynamic anchor points is used for mutation. The formula for the second mutation mode is: ;in, For the mutated individual; The adaptive scaling factor is initially set to 0.9 and decreases linearly to 0.4 with each iteration. It is the best individual in the current population; The coordinates of the centroid of the dynamic anchor point set at the current moment.

6. The method for deploying wireless positioning base stations in complex terrain environments according to claim 1, characterized in that, The iterative solution process also includes: A binomial crossover operation was performed between the mutant individuals and their parent individuals to generate experimental individuals; Adaptive terrain anchoring correction is performed on the test individual: if the test individual is located in an undeployable area, it is anchored to the nearest point on the boundary of the nearest feasible area; if the test individual cannot meet the connectivity requirements with at least two of the path key points, its movement step size in the direction of optimal connectivity is calculated and gradually adjusted until the connectivity constraints are met.

7. The method for deploying wireless positioning base stations in complex terrain environments according to claim 1, characterized in that, The step of performing time-series weighted fusion of historical observation data of the dynamic auxiliary anchor points through a time sliding window to correct the objective function of the multi-objective optimization model includes: Dynamic auxiliary anchor point admission determination: Only moving nodes with positioning errors less than or equal to a preset error threshold are used as the dynamic auxiliary anchor points, and a set of dynamic auxiliary anchor points is constructed. Time-series weight allocation: Weights are assigned to each historical moment within the time sliding window using an exponentially decaying weight formula, the formula being: ,in, For a moment The weighting coefficients are T, τ, and W, where T is the current time, τ is the time decay coefficient, and W is the sliding window length. Calculation of the centroid of the dynamic auxiliary anchor point for time-series fusion: Based on the weights and the coordinates of the dynamic auxiliary anchor points at each historical moment, calculate the centroid of the dynamic auxiliary anchor point for time-series fusion. Collaborative residual correction: The joint residuals of the fixed base station and the time-series fusion dynamic auxiliary anchor point are fused to correct the original sub-cost function, resulting in a collaborative residual correction term.

8. The method for deploying wireless positioning base stations in complex terrain environments according to claim 1, characterized in that, The step of verifying the positioning accuracy and fault tolerance of the base station deployment scheme includes: The final base station location was determined by employing an elite selection strategy and population midpoint enhancement optimization. The normalized root mean square error was calculated using Monte Carlo simulation to evaluate positioning accuracy. Implement a base station fault tolerance and reconstruction mechanism: If a base station fault is detected, a local scheme reconstruction is automatically triggered. A temporary positioning network is formed by combining surrounding normal base stations with dynamic auxiliary anchor points of time-series fusion, and the weight of the temporary positioning network is optimized in real time, and the equivalent coverage weight of surrounding base stations is fine-tuned.

9. An electronic device, characterized in that, The system includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the wireless positioning base station deployment method in complex terrain environments as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, It stores a computer program, which, when executed by a processor, implements the wireless positioning base station deployment method in complex terrain environments as described in any one of claims 1 to 8.

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