UWB error compensation positioning method based on Vegas+ algorithm improvement

Abstract

The application discloses an UWB error compensation positioning method based on Vegas+ algorithm improvement, relates to the technical field of indoor accurate positioning, and mainly comprises the following steps: obtaining a preliminary sample set by preprocessing original collected data, obtaining a complete sample set by using a VEGAS+ algorithm for secondary sampling, constructing a space error function by using a sparse polynomial to obtain an error model, and performing error prediction and compensation on UWB real-time positioning results to obtain a corrected position signal. The UWB error compensation positioning method based on Vegas+ algorithm improvement can reduce delay and positioning error, and improve long-term stability and environmental adaptability of the system.

Description

A UWB Error Compensation Positioning Method Based on the Vegas+ Algorithm Technical Field

[0001] This invention relates to the field of indoor precise positioning technology, and more specifically, to a UWB error compensation positioning method based on an improved Vegas+ algorithm. Background Technology

[0002] Ultra-wideband (UWB) technology is a wireless communication technology that uses nanosecond-level ultrashort pulses to transmit information over an extremely wide frequency band. UWB systems primarily employ time-of-flight (TOF) or two-way ranging (TWR) techniques to measure signal propagation time, which is then multiplied by the speed of light to obtain the distance. Multiple UWB base stations are deployed in the target area, and their location coordinates are known. Tags exchange timestamp signals with the base stations, and the distance from the tag to each base station is calculated by measuring the round-trip time. Trilateration or multilateral measurement algorithms are used to determine the tag's spatial coordinates by solving a system of nonlinear equations.

[0003] Commonly used algorithms for calculating position include Least Squares (LS), Weighted Least Squares (WLS), Kalman Filter (KF), Extended Kalman Filter (EKF), and Particle Filter (PF). All of these algorithms are based on the ideal condition of accurate distance, which can achieve high distance accuracy under ideal conditions. However, in actual use, they are affected by various noises.

[0004] Traditional UWB positioning systems suffer from several major sources of error. While UWB positioning systems boast high theoretical accuracy (centimeter-level), achieving this level of precision is often difficult in complex real-world environments. The performance of UWB positioning systems is influenced by a combination of error sources, resulting in complex error distribution characteristics. Multipath propagation is a major challenge. When UWB signals propagate in complex environments, multiple propagation paths are generated through reflection and diffraction, causing the receiver to capture multiple signal components arriving at different times. This interferes with the ranging algorithm's accurate identification of the first wave, thus reducing ranging accuracy. Closely related non-line-of-sight errors are equally significant. When obstacles exist between the transmitter and receiver, the direct signal is blocked, forcing the signal to penetrate the medium or detour around the obstacle to reach the receiver. This significantly prolongs signal propagation time, typically resulting in positive ranging bias, especially common in indoor environments. Furthermore, an unreasonable geometric distribution of base stations can lead to geometric accuracy degradation, particularly when the target is outside the base station distribution area or when the base stations are approximately coplanar, significantly reducing positioning accuracy in specific directions. These error factors overlap and produce complex error distributions that vary under different environmental conditions and spatial locations, requiring comprehensive processing through systematic modeling and compensation strategies.

[0005] Currently, commonly used UWB error compensation methods mainly include statistical characteristic-based filtering methods, such as Kalman filtering and particle filtering. These methods primarily target random errors and have limited effectiveness in compensating for systematic errors and environmentally related errors. Another approach is identification and elimination techniques, which identify and eliminate or downweight non-line-of-sight (NLOS) signals based on signal characteristics (such as signal strength and initial amplitude). However, this method significantly reduces usable ranging data and lowers positioning reliability when there are many NLOS signals. There are also error modeling methods: establishing error prediction models based on environmental or signal characteristics. These methods typically require a large amount of prior data and are difficult to adapt to dynamically changing environments.

[0006] UWB positioning errors are influenced by various factors, including signal quality, multipath effects, geometric distribution, and environmental characteristics, forming a typical high-dimensional nonlinear mapping relationship. Traditional methods often can only handle low-dimensional, simple models, failing to fully capture this complex relationship or requiring significant computational resources. Traditional UWB systems lack effective comprehensive error compensation mechanisms. When facing complex real-world environments, these systems generally suffer from incomplete compensation, poor environmental adaptability, insufficient real-time performance, and a lack of consideration for spatial correlation. Most methods only compensate for single error sources, lacking the ability to comprehensively handle multi-source errors. Error compensation models are typically trained for specific environments, and their compensation effectiveness decreases significantly with environmental changes. Complex error compensation algorithms are often computationally intensive, making it difficult to meet real-time positioning requirements, and they fail to fully utilize the continuity and correlation characteristics of error spatial distribution.

[0007] These shortcomings mean that the positioning accuracy of UWB in real-world applications often falls short of theoretical levels, especially in complex indoor environments, environments with multiple obstacles, and dynamically changing environments, which severely limits the application and expansion of UWB technology in the field of high-precision positioning.

[0008] Meanwhile, indoor positioning also involves high-dimensional interpolation problems in numerical optimization algorithms, especially methods for efficient and accurate interpolation of complex functions in high-dimensional parameter spaces. This technology is widely used in fields that require the construction of high-precision surrogate models or response surfaces, such as computer-aided engineering (CAE), multiphysics coupling analysis, machine learning, computer graphics, and optimization design.

[0009] Many interpolation methods already exist, the most common being linear interpolation, which uses linear weighting between two data points, and adaptive polynomial interpolation. Traditional linear interpolation faces serious challenges in high-dimensional cases, including exponential growth in computational complexity, the generation of numerous phantom peaks, poor handling of multi-peak functions, rapid error amplification with dimensionality, and low sample utilization. These problems make linear interpolation extremely inefficient and inaccurate when processing complex high-dimensional functions, making it difficult to meet the needs of practical engineering applications.

[0010] High-dimensional adaptive sparse polynomial interpolation methods are designed to solve interpolation problems in high-dimensional or infinite-dimensional parameter spaces, and are particularly suitable for solving partial differential equations involving a large number of parameters. The algorithm's adaptability is reflected in its greedy strategy, where each step selects the point with the largest interpolation error as the next sampling point, thus prioritizing the capture of parameter directions that have the most significant impact on the result. However, this method also has some limitations: it may misidentify important variables in the early stages; data oscillations can lead to misjudgments of parameter importance, especially for functions with certain special structures; and as the dimension of the polynomial space increases, the Lebesgue constant may grow rapidly, affecting stability in ultra-high-dimensional cases, a problem that is difficult to completely solve even using an optimized sequence of one-dimensional interpolation points.

[0011] Therefore, how to provide an error compensation method that can comprehensively consider multi-source errors, is environmentally adaptable, and computationally efficient, in order to improve the accuracy and reliability of UWB positioning systems in complex environments, is an urgent problem to be solved.

[0012] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0013] The purpose of this invention is to provide a UWB error compensation positioning method based on the Vegas+ algorithm, which can reduce latency and positioning error, and improve the long-term stability and environmental adaptability of the system.

[0014] This invention provides a UWB error compensation positioning method based on an improved Vegas+ algorithm, comprising the following steps:

[0015] S1: Obtain the raw collected data, preprocess the raw collected data to obtain a preliminary sample set;

[0016] S2: Based on the preliminary sample set, perform secondary sampling using the VEGAS+ algorithm to obtain the complete sample set;

[0017] S3: Based on the complete sample set, construct a spatial error function using sparse polynomials to obtain the error model;

[0018] S4: Use the error model to predict and compensate for errors in the UWB real-time positioning results to obtain a corrected position signal.

[0019] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described UWB error compensation positioning method based on the Vegas+ algorithm improvement.

[0020] Implementing the UWB error compensation positioning method based on the improved Vegas+ algorithm provided by this invention has the following beneficial effects:

[0021] This invention constructs a high-dimensional parameter vector incorporating signal strength, time of arrival, channel impulse response characteristics, and geometric configuration. Principal component analysis and sequence feature selection algorithms are applied for dimensionality reduction optimization. Unlike traditional compensation methods based solely on distance or signal strength, this approach captures complex environmental factors such as multipath propagation and NLOS, providing a comprehensive information foundation for error prediction. A multi-scale parameter space partitioning strategy is employed, using fine grids in regions of significant error variation and coarse grids in regions of relative smoothness. Compared to a uniform accuracy model, this reduces storage space by 70%. Furthermore, an indexing structure is introduced to accelerate query complexity, reducing it from O(n) to O(log n). To ensure sub-millisecond prediction latency, the algorithm calculates the distance between the current parameter vector and the training data distribution, and dynamically constructs error compensation weights based on historical prediction accuracy. Unlike fixed-weight methods, this approach intelligently identifies model applicability boundaries, prevents overcorrection caused by out-of-domain samples, and improves system robustness. Error compensation, Kalman filtering, and constraints are integrated into a cascaded structure, using adaptive compensation coefficients to dynamically adjust the correction intensity. Based on prediction uncertainty, the observation noise covariance matrix is ​​automatically adjusted, resulting in a 40% accuracy improvement compared to single correction methods, and effectively suppressing positioning jumps. A sliding window statistical system is established to monitor changes in positioning performance, enabling model adaptability detection and incremental updates. When accuracy degradation is detected or sufficient reference data is accumulated, model parameter adjustments are triggered, allowing the system to adapt to environmental changes, maintain long-term stable performance, and avoid the accuracy decay problem of traditional fixed models. In summary, in complex indoor environments, only a few key parameter combinations often dominate positioning errors. The VEGAS+ algorithm can accurately identify these key factors, enabling the system to adapt to environmental changes and maintain long-term stable performance. While maintaining high accuracy, it significantly reduces computational complexity. VEGAS+'s direction-sensitive importance sampling strategy is highly compatible with UWB signal characteristics, intelligently identifying which signal features have the greatest impact on positioning errors and automatically capturing complex correlations between signal features. Utilizing VEGAS+'s adaptive mesh generation capability, it automatically refines the mesh in parameter regions with significant error changes, while maintaining a coarse mesh in regions with gradual error changes, greatly optimizing the allocation of computational resources. In actual deployment, the VEGAS+ algorithm is embedded into the core module of the UWB real-time error compensation system, forming a complete processing flow of "multi-dimensional feature extraction → VEGAS+ high-dimensional interpolation → adaptive error compensation → position fusion output". After the system went online, it demonstrated good environmental adaptability and accuracy stability. Especially in the parameter space boundary region, traditional methods often exhibit severe extrapolation errors, while the VEGAS+ algorithm effectively controls boundary behavior and ensures consistent performance across the entire parameter space through multi-level sparse polynomial construction and basis function importance evaluation.

[0022] This invention significantly improves the adaptability of UWB positioning in complex environments through a multi-dimensional feature signal-position joint parameter extraction mechanism and an adaptive gridded error model. Traditional UWB systems often experience a significant decrease in positioning accuracy when the environment changes, such as object movement or equipment layout adjustments. However, this system can intelligently identify environmental change characteristics and dynamically adjust error compensation strategies. Tests show that the system maintains stable positioning performance during transitions from open spaces to environments with dense obstacles, demonstrating adaptability far exceeding that of traditional fixed-model methods. Even in extremely challenging environments with metallic structures, reflective surfaces, and dynamic obstacles, the system maintains stable positioning accuracy, greatly expanding the application scenarios of UWB technology. The multi-scale parameter space partitioning strategy and fast query structure employed in this invention completely break through the computational latency bottleneck of traditional high-precision error compensation methods. Conventional methods often struggle to meet millisecond-level response requirements under complex compensation models, while this system, through gridded storage and index acceleration structures, transforms error prediction from a computationally intensive process to a memory access operation, significantly reducing processing latency. This invention achieves ultra-low latency error compensation on standard hardware platforms, maintaining stable operation even in high-refresh-rate application scenarios, making it possible to accurately track fast-moving objects, while significantly reducing system resource consumption compared to similar solutions. The combined effect of the dynamic reliability assessment system based on Mahalanobis distance and the multi-stage fusion position correction framework significantly improves the system's positioning accuracy and stability. The sudden errors, positioning jumps, and multipath interference problems commonly faced by traditional UWB systems are effectively suppressed in this system. Even under the most challenging NLOS (non-line-of-sight) conditions, the system can still provide accurate positioning through an intelligent error model. More importantly, the system exhibits consistent and predictable error characteristics under various conditions, unlike the unstable performance of traditional methods. This consistency in accuracy is particularly important for industrial applications and automation systems, providing a reliable foundation for UWB-based control systems. This invention endows the system with a unique "self-healing" capability through real-time performance self-monitoring and online model update mechanisms: as the environment changes or the system ages, the accuracy of conventional UWB systems gradually deteriorates, eventually requiring recalibration. However, this system can automatically adapt to new environmental conditions without interrupting service through continuous performance monitoring and incremental learning. The system intelligently identifies trends in positioning performance degradation and promptly initiates model parameter adjustment procedures to ensure stable accuracy over long-term operation. In situations such as seasonal changes, equipment layout changes, and large-scale facility renovations, the system demonstrates strong adaptability, minimizing the repetitive calibration work that traditionally requires manual intervention. Attached Figure Description

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0024] Figure 1 is a flowchart of the UWB error compensation positioning method based on the Vegas+ algorithm improvement provided by the present invention;

[0025] Figure 2 is a schematic diagram of the UWB positioning error compensation system architecture provided by the present invention. Detailed Implementation

[0026] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0027] Figure 1 shows a schematic diagram of the UWB error compensation positioning method based on the Vegas+ algorithm improvement in this embodiment. In this embodiment, the UWB error compensation positioning method based on the Vegas+ algorithm improvement includes the following steps:

[0028] S1: Obtain the raw collected data, preprocess the raw collected data to obtain a preliminary sample set;

[0029] In one exemplary embodiment, the raw acquisition data includes raw UWB ranging data, calculated position coordinates, the actual position measured by the reference system, UWB signal characteristic parameters, and timestamps;

[0030] In one exemplary embodiment, the preprocessing of the raw acquired data includes: aligning the raw UWB ranging data with the actual position measured by the reference system according to the timestamp, transforming the coordinates of the UWB and the reference system to a unified reference system, calculating the error vector and removing abnormal error samples, calculating geometric relationship features and adding them to the parameter vector, and finally forming a preliminary sample set.

[0031] S2: Based on the preliminary sample set, perform secondary sampling using the VEGAS+ algorithm to obtain the complete sample set;

[0032] In one exemplary embodiment, step S2 specifically includes:

[0033] S21: Calculate the error gradient for each sample point in the preliminary sample set to obtain the error gradient for each sample point;

[0034] In one exemplary embodiment, step S21 specifically includes:

[0035] S211: Construct multiple paired points for the sample points in the preliminary sample set;

[0036] In one exemplary embodiment, step S211 specifically includes: constructing multiple paired points for the sample points in the preliminary sample set, as shown in the formula:

[0037]

[0038] in, Let x be the pairing point in the j-th dimension. j For sample points, e j It is the unit vector of dimension j, and h is the step size;

[0039] As an exemplary embodiment, in step S211, the step size is set to 0.5-1% of the range of each dimension, that is, h j =0.005~0.01· and These are the maximum and minimum values ​​of the j-th dimension, respectively;

[0040] S212: Based on the paired points, the error gradient of each sample point is obtained using the central difference formula;

[0041] In one exemplary embodiment, step S212 specifically includes: obtaining the error gradient of each sample point based on the paired points using the central difference formula, as shown in the formula:

[0042]

[0043] in, Let ε(x) be the error gradient of the i-th sample point. i +he1) represents (x i The error at +he1);

[0044] As an exemplary embodiment, in step S212, forward or backward difference is used for sample points near the boundary;

[0045] S22: Perform gradient smoothing on the error gradient of each sample point to obtain a smoothed gradient field;

[0046] In one exemplary embodiment, step S22 specifically includes: performing gradient smoothing on the error gradient of each sample point to obtain a smoothed gradient field, as shown in the formula:

[0047]

[0048] in, For the smoothed gradient field, w ij For the weight, N k (i) is point x i The set of k nearest neighbors, where β is the smoothing parameter;

[0049] S23: Based on the smoothed gradient field, perform sub-region importance assessment to obtain the importance assessment value of each sub-region;

[0050] In one exemplary embodiment, step S23 specifically includes:

[0051] S231: Based on the smoothed gradient field, the integral of the error gradient norm is obtained using Monte Carlo integration;

[0052] S232: Generate multiple random sample points for each sub-region based on the integral of the error gradient norm;

[0053] S233: Based on the random sample points, the gradient value of the random sample points is obtained by interpolation of neighboring samples;

[0054] S234: Obtain the integral estimate based on the gradient values ​​of the random sample points;

[0055] In one exemplary embodiment, step S234 specifically includes: obtaining an integral estimate based on the gradient values ​​of the random sample points, as shown in the formula:

[0056]

[0057] Among them, I R For integral estimation, V R Let M be the volume of the sub-region and M be the number of random sample points. The gradient value is the value of a random sample point; ||·|| represents the norm;

[0058] S235: Based on the integral estimation, perform adaptive control accuracy to obtain the importance assessment value of each sub-region;

[0059] In one exemplary embodiment, step S235 specifically includes: performing adaptive control accuracy based on the integral estimation to obtain the importance assessment value of each sub-region, as shown in the formula:

[0060]

[0061] in, Let Variance be the integral estimate. Representing point y i Gradient, This represents the average error within the region; when σ I >0.1·I R Increase sampling points as needed; This represents the importance assessment value for each sub-region, i.e., the importance weight of each sub-region.

[0062] S24: Based on the importance assessment values ​​of each sub-region, important regions are identified and selected to obtain a set of sub-regions to be further subdivided;

[0063] In one exemplary embodiment, step S24 specifically includes:

[0064] S241: Based on the importance evaluation values ​​of each sub-region, a nonlinear transformation is used to obtain the importance weights of the sub-regions that enhance the differences.

[0065] In one exemplary embodiment, step S241 specifically includes: based on the importance evaluation values ​​of each sub-region, using a nonlinear transformation, obtaining the sub-region importance weights that enhance the differences, as shown in the formula:

[0066]

[0067] in, To enhance the importance weight of sub-regions with differences, γ is a smoothing parameter;

[0068] S242: Based on the importance weights, primary thresholds, and secondary thresholds of the sub-regions with enhanced differences, select regions in descending order of importance until the cumulative importance reaches the target value, thereby obtaining a set of sub-regions to be subdivided.

[0069] S25: Based on the set of sub-regions to be subdivided, select the optimal segmentation dimension to obtain the optimal segmentation dimension;

[0070] In one exemplary embodiment, step S25 specifically includes:

[0071] S251: Calculate the gradient components in each direction based on the set of sub-regions to be subdivided;

[0072] In one exemplary embodiment, step S251 specifically includes: calculating the gradient components in each direction based on the set of sub-regions to be subdivided, as shown in the formula:

[0073]

[0074] Among them, g ij These are the gradient components in each direction for each sample point. This represents the gradient of the i-th sample point in the set of sub-regions to be subdivided with respect to the j-th direction;

[0075] S252: Based on the gradient components in each direction, obtain the dimensionality influence ratio;

[0076] In one exemplary embodiment, step S252 specifically includes: obtaining the dimensionality influence ratio based on the gradient components in each direction, as shown in the formula:

[0077]

[0078] Where, r j The influence ratio of the j-th dimension;

[0079] S253: Generate paired sample points along each dimension and calculate the direction change rate. Based on the direction change rate and the dimension influence ratio, obtain the evaluation result.

[0080] In one exemplary embodiment, step S253 specifically includes: generating paired sample points along each dimensional direction and calculating the directional change rate; and obtaining an evaluation result based on the directional change rate and the dimensional influence ratio, as shown in the formula:

[0081]

[0082] s j =αr j +(1-α)v j ,

[0083] in, and Generate paired sample points in different dimensional directions, x c As the center point of the region, Δ j v is the change. j Let j be the rate of change in the j-direction. and s represents the error at the corresponding point. j This represents the final evaluation result, where α represents the smoothing parameter.

[0084] S254: Based on the evaluation results, select the dimension with the largest rate of change to obtain the optimal segmentation dimension;

[0085] As an exemplary embodiment, in step S254, if the change rates of multiple dimensions are close, i.e., their differences are <15%, then the second-best dimension is selected; if a dimension has been continuously divided N times (N=3 is recommended), the weight of that dimension is temporarily reduced.

[0086] S26: Based on the set of sub-regions to be subdivided and the optimal segmentation dimension, determine the segmentation points and subdivide the sub-regions to obtain the segmented sub-regions;

[0087] In one exemplary embodiment, step S26 specifically includes:

[0088] S261: Calculate the cumulative change curve on the optimal segmentation dimension based on the optimal segmentation dimension;

[0089] In one exemplary embodiment, step S261 specifically includes: calculating the cumulative change curve on the optimal segmentation dimension based on the optimal segmentation dimension, as shown in the formula:

[0090]

[0091] Where C(t) represents the cumulative change curve along the optimal segmentation dimension. This represents the minimum value at the boundary of the region. This represents the derivative of the rate of change with respect to this dimension;

[0092] S262: Obtain the segmentation point based on the cumulative change curve on the optimal segmentation dimension;

[0093] In one exemplary embodiment, step S262 specifically includes: obtaining the segmentation point based on the cumulative change curve on the optimal segmentation dimension, as shown in the formula:

[0094]

[0095] Where, x split Indicates the dividing point. This represents the maximum value of the parameter space region in this dimension;

[0096] S263: Based on the segmentation points and the set of sub-regions to be subdivided, obtain the segmented sub-regions;

[0097] As an exemplary embodiment, in step S263, if the cumulative curve cannot be accurately estimated, midpoint segmentation is used, as shown in the formula:

[0098]

[0099] Where, x min and x max These represent the maximum and minimum values ​​of the parameter space region in this dimension, respectively;

[0100] S27: Based on the segmented sub-regions, adaptive sampling points are generated to obtain a complete sample set;

[0101] In one exemplary embodiment, step S27 specifically includes:

[0102] S271: Sampling points are allocated according to the segmented sub-regions and their importance to obtain the number of sampling points allocated to each sub-region;

[0103] In one exemplary embodiment, step S271 specifically includes: allocating sampling points according to the segmented sub-regions and their importance, to obtain the number of sampling points allocated to each sub-region, as shown in the formula:

[0104]

[0105] Where, N R Assign the number of sampling points to the sub-region, where max(·) represents taking the maximum value, N min N represents the minimum number of sampling points in each region. total w represents the total number of sampling points. R This represents the importance of the sub-region, specifically the normalized importance weight of the sub-region R.

[0106] S272: Based on the number of sampling points allocated to each sub-region, generate sampling points to obtain the complete sample set;

[0107] As an exemplary embodiment, in step S272, sampling point generation is performed: for each sub-region, a corresponding number of uniformly distributed random points are generated within its boundary; the sampling points of all sub-regions are merged to form a complete sample set;

[0108] As an exemplary embodiment, step S2 specifically includes the following steps:

[0109] 1. Error gradient calculation, the input of which is the sample points in the initial sample set, and the output is the error gradient of each sample point. The specific process includes:

[0110] (1) Construct D paired points for each sample point.

[0111] (2) Set the step size to 0.5-1% of the range of each dimension:

[0112] (3) Calculate the gradient using the central difference formula:

[0113]

[0114] For sample points near the boundary, use forward or backward differencing instead;

[0115] 2. Gradient smoothing, whose input is the original gradient of the sample points and whose output is the smoothed gradient field, includes the following steps:

[0116] (1) Reduce noise through local weighted averaging:

[0117] (2) Weight calculation:

[0118]

[0119] The parameters include the k-nearest neighbor set (k=5 recommended) and the smoothing parameter β;

[0120] 3. Sub-region importance assessment, the input of which is a smoothed gradient field, and the output is the importance assessment value of each sub-region. The specific process includes:

[0121] (1) Use Monte Carlo integral estimation to calculate the integral of the error gradient norm;

[0122] (2) Generate M random sample points for each sub-region (M=10D is recommended, where D is the dimension);

[0123] (3) Estimate the gradient values ​​of these points by interpolating from nearby samples;

[0124] (4) Calculate the integral estimate:

[0125]

[0126] (5) Adaptive control accuracy: Calculate the variance of the integral estimate. When σ I >0.1·I R Increase sampling points as needed;

[0127] 4. Important region identification and selection: The input is the importance assessment value of the sub-region, and the output is the set of sub-regions to be further subdivided. The specific process is as follows:

[0128] (1) Applying nonlinear transformations to enhance differences: (Recommended γ = 1.5);

[0129] (2) Set the primary threshold τ1 (0.05 recommended) and the secondary threshold τ2 (0.02 recommended);

[0130] (3) Prioritize processing those that satisfy w i In regions ≥τ1, process w when resources permit. i Regions ≥τ2

[0131] (4) Select regions in descending order of importance until the cumulative importance reaches the target value (recommended 0.80);

[0132] 5. Optimal segmentation dimension selection: The input is the sub-region to be subdivided, and the output is the optimal segmentation dimension j*. The specific process is as follows:

[0133] (1) Calculate the gradient components in each direction for each subdivided region:

[0134]

[0135] (2) Calculate the dimensional influence ratio:

[0136]

[0137] (3) Generate paired sample points along each dimension: and

[0138] (4) Calculate the rate of change of direction:

[0139] (5) Based on the evaluation results: s j =αr j +(1-α)v j (Recommended α = 0.6);

[0140] (6) Select the dimension with the largest rate of change: j = argmax s j ;

[0141] (7) If the rates of change of multiple dimensions are close (difference <15%), consider the second-best dimension;

[0142] (8) If a dimension has been continuously segmented N times (N=3 recommended), temporarily reduce the weight of that dimension;

[0143] 6. Segmentation point determination and sub-region subdivision: The inputs are the region to be subdivided and the optimal segmentation dimension, and the output is the segmented sub-regions. The specific process includes:

[0144] (1) Calculate the cumulative change curve on the optimal segmentation dimension j*:

[0145]

[0146] (2) Select the one that satisfies The point is used as the dividing point;

[0147] (3) If the cumulative curve cannot be accurately estimated, then use midpoint segmentation:

[0148] 7. Adaptive sampling point generation: Its input is the final sub-region division and its importance weights, and its output is a complete sample set adaptively distributed according to the error gradient characteristics. The specific process is as follows:

[0149] (1) Assign sampling points based on the importance of sub-regions:

[0150] First, set the total number of sampling points N. total (Determined based on computing resources), and then the number of sampling points is allocated to each sub-region:

[0151] Among them, w R N is the normalized importance weight of subregion R. minThis is the minimum number of sampling points per region (recommended value: 5), ensuring that important regions receive a sufficient number of sampling points; N is uniformly and randomly sampled within each sub-region. R One point;

[0152] (2) Perform sampling point generation: For each sub-region, generate a corresponding number of uniformly distributed random points within its boundary; merge the sampling points of all sub-regions to form the final sampling set.

[0153] S3: Based on the complete sample set, construct a spatial error function using sparse polynomials to obtain the error model;

[0154] S4: Use the error model to predict and compensate for errors in the real-time UWB positioning results to obtain a corrected position signal;

[0155] In one exemplary embodiment, step S4 specifically includes: using the error model to predict and compensate for errors in the UWB real-time positioning results to obtain a corrected position signal, as shown in the formula:

[0156]

[0157] p comp =p raw -α(x)e(x),

[0158] Where e(x) is the predicted position error vector, Φ k (x) are orthogonal polynomial basis functions, c k Let p be the coefficient vector obtained through training using the least squares method, K be the number of terms in the selected orthogonal polynomial, and p be the coefficient vector. comp To correct the position signal, p raw The position signal before correction is given, and α(x) is the reliability weighting factor.

[0159] In an exemplary embodiment, the UWB error compensation localization method based on the Vegas+ algorithm further includes: updating the error model using an update mechanism; the update mechanism is based on dual triggering conditions, the dual triggering conditions including timed updates and event-driven updates; the timed updates update the error model at preset intervals; the event-driven updates update the error model when a significant performance degradation or change in environmental conditions is detected.

[0160] As an exemplary embodiment, the preset interval is 24 hours; the standard for significant performance degradation is an increase in error exceeding 20%; the standard for change in environmental conditions is the detection of a change in physical layout.

[0161] In some embodiments, the UWB error compensation positioning method based on the Vegas+ algorithm improvement described above can also be implemented in the following ways.

[0162] Figure 2 shows the architecture of the UWB positioning error compensation system in this embodiment. It mainly includes the following five functional modules: 1. Data acquisition and preprocessing module: collects the actual location of the tag and the original UWB positioning results, and calculates the error vector; 2. Parameter space modeling module: based on VEGAS+ adaptive grid partitioning and importance sampling; 3. Error model construction module: constructs a spatial error function using sparse polynomials; 4. Real-time compensation module: performs error prediction and compensation on the real-time UWB positioning results; 5. Model update module: continuously optimizes the error model to improve system adaptability.

[0163] In this embodiment, the UWB error compensation positioning method based on the Vegas+ algorithm is implemented using the aforementioned UWB positioning error compensation system, and its algorithm flow is as follows:

[0164] 1. Detailed explanation of system initialization and parameter space definition:

[0165] The parameter space in UWB positioning error compensation is a D-dimensional space containing various factors that affect positioning accuracy, mainly divided into three categories: spatial location dimension, signal feature dimension, and geometric relationship dimension; as shown in Table 1:

[0166] Table 1: Parameters in UWB Positioning Error Compensation

[0167]

[0168]

[0169] Depending on the actual system configuration, the total dimension D is typically between 10 and 14. The parameter space can be represented as:

[0170]

[0171] The specific selection of each variable depends on the system configuration and actual application scenario, forming a complete high-dimensional parameter space for error modeling and compensation in the VEGAS+ algorithm. To ensure algorithm stability and parameter weight balance, all parameters are normalized: for each parameter p... j Linearly map it to the interval [0,1]:

[0172]

[0173] In actual calculations, normalization parameters are used, and the output results are then converted back to the original scale.

[0174] First, a uniform grid is generated, and each dimension j is divided into... Divide into equal parts, of which Related to the importance of this dimension, for example, for the spatial location dimension, the typical value N0 = 5; for the signal feature dimension, the typical value N0 = 3; and for the geometric relationship dimension, the typical value N0 = 4.

[0175] Then, the coordinates of the grid points are calculated: the coordinates of the i-th grid point in the j-th dimension are:

[0176]

[0177] The initial mesh contains a total of Sub-regions;

[0178] Here, the grid points are stored using a hierarchical quadtree or octree structure to facilitate subsequent adaptive subdivision. The fields of the GridNode structure definition are shown in Table 2.

[0179] Table 2: GridNode Structure Definition Fields Table

[0180]

[0181] Where D is the parameter space dimension, which is usually between 10 and 14 depending on the UWB system configuration.

[0182] During initialization, a root node is created first to represent the entire parameter space. Child nodes are then recursively constructed based on the initial partitioning, and the level of all initial leaf nodes is set to 0.

[0183] To improve computational efficiency, the following mesh constraint parameters are set to control the overall system complexity:

[0184] (1) Maximum subdivision level, L max =8, limiting the maximum depth of mesh subdivision;

[0185] (2) Minimum unit size, Δ min =0.01, to avoid over-segmentation;

[0186] (3) Maximum number of subregions, N max =10000, controlling the algorithm complexity;

[0187] 2. Calibration Data Acquisition and Preprocessing Module: This module primarily performs preliminary sample acquisition, providing initial support datasets for calculations in key areas.

[0188] A high-precision reference positioning system is the foundation for building the error compensation model. In this embodiment, an optical motion capture system is used to ensure that the coordinate system of the reference system is consistent with that of the UWB system. At the same time, hardware triggering or Network Time Protocol (NTP) is used to ensure precise time synchronization between the two systems. This synchronization method is sufficient to meet the needs of static or low-speed scenarios.

[0189] The initial sampling point design adopts a uniform sampling strategy, performing sparse sampling at equal intervals in a grid distribution within the positioning space to facilitate subsequent adaptive hierarchical sampling design using the VEGAS+ algorithm. Path planning includes sampling paths such as "Z"-shaped and spiral patterns covering the entire area. For personnel data collection, easily executable walking routes are designed, while for robot data collection, precise trajectories covering the entire space are generated.

[0190] The data acquisition content mainly includes raw UWB ranging data, calculated position coordinates, the actual position measured by the reference system, UWB signal characteristic parameters, and precise timestamps.

[0191] Data preprocessing steps include:

[0192] Align UWB data with reference location data based on timestamps;

[0193] Transform the coordinates of the two systems to a unified reference frame;

[0194] Calculate the error vector:

[0195] e = p uwb -p ref ;

[0196] Remove outlier error samples exceeding 3σ;

[0197] Calculate the geometric relationship features and add them to the parameter vector;

[0198] The final sample set is formed:

[0199] (x i ,ei)i=1 N ,

[0200] Where x i It is a D-dimensional parameter vector, e i It is a 3-dimensional error vector.

[0201] It is recommended to have at least 10 sample points in each initial sub-region, with the total number of samples generally between 1,000 and 5,000, depending on the space complexity.

[0202] The initial error assessment includes calculating the statistical characteristics of the error (mean, variance, maximum, minimum), generating an error histogram to test the distribution characteristics, calculating spatial correlation to identify error clustering regions, and decomposing the total error into two parts: systematic error and random error.

[0203] 3. Adaptive error space modeling: The Vegas+ importance sampling method is used to calculate the importance region using the initial sample set. Secondary sampling is performed on the calculated importance region to obtain the complete sample set. The complete sample set is used to build the final error compensation model.

[0204] The initial grid evaluation phase accurately assesses the error distribution characteristics within each sub-region. Finite difference gradient calculation constructs D paired points for each sample point:

[0205]

[0206] Where e j It is the unit vector of dimension j, and h is the step size;

[0207] Set to 0.5-1% of the range for each dimension, that is:

[0208]

[0209] Calculate the gradient using the central difference formula:

[0210]

[0211] When the sample point is close to the boundary, forward or backward difference is used instead.

[0212] Gradient smoothing at sample points reduces noise through local weighted averaging:

[0213]

[0214] Where β is the smoothing parameter, N k (i) is point x i The set of k nearest neighbors (k=5 is recommended).

[0215] To accurately assess the importance of sub-regions, the system uses Monte Carlo integral estimation to calculate the integral of the error gradient norm. For each sub-region, M random sample points are generated, and the gradient values ​​of these points are estimated through neighbor interpolation. The integral estimate is then calculated.

[0216]

[0217] Where V RFor the sub-region volume, M = 10D is recommended.

[0218] Adaptive integral precision control is achieved by calculating the variance of the integral estimate:

[0219]

[0220] When σ I >0.1·I R Increase the number of sampling points as needed. Treat special regions separately: use the neighbor extrapolation method for sparse regions (number of samples < 3); set an upper limit for regions that may contain singularities to prevent excessive weighting.

[0221] The importance weights of each sub-region are calculated based on integral estimation.

[0222]

[0223] Where N is the total number of sub-regions.

[0224] Applying nonlinear transformations to enhance differences:

[0225]

[0226] We recommend γ = 1.5 and set a minimum weight threshold w. min Then normalization was performed.

[0227] After each mesh subdivision, the weights of all sub-regions are recalculated. When the computational cost is high, a local update strategy can be adopted.

[0228] For important region identification, set a primary threshold τ1 (recommended value 0.05) and a secondary threshold τ2 (recommended value 0.02), and prioritize processing regions that meet the w criteria. i In regions ≥τ1, processes that satisfy w, provided resources allow. i Regions ≥τ2. The system sets a cumulative importance target (recommended value 0.80), selects regions in descending order of importance until the sum reaches the target value, forming a set of regions to be subdivided.

[0229] The optimal segmentation dimension is selected by accurately evaluating the rate of change of error in each dimension. The gradient components in each direction are calculated for all sample points within the sub-region.

[0230]

[0231] Calculate the dimensional impact ratio:

[0232]

[0233] Generate paired sample points along each dimension:

[0234]

[0235] and

[0236]

[0237] Where x c It is the regional center point.

[0238]

[0239] Calculate the rate of change of direction:

[0240]

[0241] Combining gradient components and directed sampling results:

[0242] s j =αr j +(1-α)v j ,

[0243] We recommend α = 0.6 and apply random perturbations:

[0244]

[0245] Where ξ is the perturbation coefficient (recommended value 0.1) to prevent the algorithm from being too deterministic.

[0246] The adaptive segmentation strategy selects the dimension with the largest rate of change. When the rates of change of multiple dimensions are close (difference <15%), consider the second-best dimension. If a dimension has been continuously segmented N times (N=3 recommended), temporarily reduce the weight of that dimension.

[0247] The split point is calculated by dimension j. * Cumulative curve of changes on:

[0248]

[0249] Choose the option that satisfies:

[0250]

[0251] The point is used as the dividing point.

[0252] When the cumulative curve cannot be accurately estimated, it degenerates into midpoint segmentation:

[0253]

[0254] The system sets intelligent termination conditions: sub-region volume constraint (recommended to be 0.1% of the initial region volume), gradient variance constraint (segmentation stops when the gradient variance within a sub-region is less than a threshold), and resource limit constraint (the recommended maximum number of sub-regions is 10,000). The subdivision operation divides the sub-regions along dimension j. * At point x split Divided into two sub-regions R L and R R Mark the parent node as a non-leaf node and create child node N. L and N R It inherits the parent node's level+1, updates the tree structure and adjacency relationships, and redistributes the sample points to the corresponding sub-regions.

[0255] Adaptive sampling point generation first requires constructing a sampling density function. A piecewise constant density function defines a local density for each leaf region based on importance weights:

[0256]

[0257] Among them 1 R It is an indicator function of R.

[0258] Global density function:

[0259] p(x)=∑ R p R (x)1 R (x).

[0260] The density smoothing function smooths the original density using a kernel function:

[0261] p smooth (x)=∫K(xy)p(y)dy,

[0262] Where K is the Gaussian kernel function:

[0263]

[0264] The edge density function calculates the edge density in each dimension:

[0265]

[0266] In practice, edge density is reconstructed from a set of sub-regions.

[0267] The hierarchical sampling strategy includes three levels: global uniform sampling generates basic sample points throughout the parameter space, with the number of samples being:

[0268] N uniform =α1·N total ;

[0269] Importance sampling uses inverse transform sampling to sample at the edge density, by calculating the cumulative distribution function:

[0270]

[0271] And generate uniform random numbers:

[0272] u~U(0,1),

[0273] Solve Determine the sampling location.

[0274] Sample size:

[0275] N importance =α2·N total ,

[0276] Recommended α2 = 0.4;

[0277] Grid-guided sampling assigns a number of sampling points to each leaf region:

[0278]

[0279] And local random sampling is performed in each region, with a total number of samples:

[0280] N grid =α3·N total ,

[0281] I recommend α3 = 0.5.

[0282] 4. Real-time compensation module: used for accurate prediction and dynamic correction;

[0283] After the error model is built, it is applied to the uWB positioning system. For a uWB positioning system, each time a raw measurement position signal is input, a corrected position signal is obtained after passing through the real-time error compensation module and the model calculation. First, the error is calculated, and then the input is compensated for the error.

[0284] The real-time compensation module enables instant correction of the raw UWB positioning results, eliminating system errors by applying the aforementioned error model. The compensation process obtains the raw positioning results p from the UWB system. raw =[x raw ,y raw ,zraw ] T At the beginning, signal characteristics (signal strength, first wave amplitude ratio, etc.) and geometric relationship parameters (base station distribution, geometric factors, etc.) of the current location are collected simultaneously to construct a complete parameter vector x.

[0285] The parameter vector, after normalization, enters the error prediction engine. This normalization process uses a linear mapping to standardize the features of each dimension to the [0,1] interval, eliminating dimensional differences and improving the model's generalization ability. The system uses a multinomial model to predict the position error vector, expressed as:

[0286]

[0287] Where Φ k For orthogonal polynomial basis functions, such as Legendre polynomials or Chebyshev polynomials, c k This is the coefficient vector obtained through training using the least squares method.

[0288] The polynomial model was chosen based on its excellent function approximation ability and computational efficiency, making it particularly suitable for capturing nonlinear error patterns present in UWB positioning systems. To improve computational efficiency, the system implemented the Clenshaw recursive algorithm, cleverly utilizing polynomial recursion to reduce the computational complexity from O(K) to O(K). 2 The computational complexity is reduced to O(K), significantly improving real-time processing capabilities and enabling the system to run efficiently on resource-constrained devices. This algorithm avoids redundant calculations of intermediate terms through reverse recursion, ensuring numerical stability even with high-order polynomials. After error prediction, an adaptive weighted correction method is used for compensation.

[0289] p comp =p raw -α(x)e(x),

[0290] The reliability weighting factor α(x) is dynamically adjusted based on the similarity between the current parameter point and the training samples. It provides strong compensation in densely populated regions and conservatively adjusts in peripheral regions to avoid positional divergence caused by overcompensation. Similarity is evaluated using Mahalanobis distance.

[0291]

[0292] Where μ and Σ are the mean vector and covariance matrix of the training samples, respectively, considering the correlation and distribution characteristics between the various dimensions of the parameters, and more accurately reflecting the data distribution in the feature space compared to the traditional Euclidean distance. The covariance matrix Σ is calculated using the training data and updated periodically to ensure the system can adapt to environmental changes. The reliability weighting factor is defined as:

[0293] α(x)=exp(-λ·d M (x)),

[0294] A sensitivity parameter of λ = 0.2 is recommended. The system also sets a minimum threshold (usually 0.3) to prevent insufficient compensation in extreme cases.

[0295] In continuous positioning scenarios, the system integrates motion state perception filters. For stationary or low-speed states, an exponentially weighted moving average filter is used; for medium-speed motion, an improved α-β filter is employed; and for high-speed motion, an extended Kalman filter is applied to fuse IMU data, predicting and smoothing the trajectory. State recognition is achieved through velocity and acceleration thresholds, and the filtering parameters are dynamically adjusted according to the motion state.

[0296] 5. Model Update Module: Used for adaptive optimization and environmental adaptation;

[0297] The model update module ensures the system can adapt to environmental changes and hardware characteristic drift, maintaining long-term stable high-precision positioning performance. The update mechanism is based on dual trigger conditions: timed updates and event-driven updates. Timed updates are executed at preset intervals (typically 24 hours or 7 days); event-driven updates are activated when a significant performance degradation is detected (error increase exceeds 20%) or changes in environmental conditions are detected (changes in physical layout are detected).

[0298] Performance monitoring employs a multi-metric evaluation strategy, including average positioning error:

[0299]

[0300] Maximum error:

[0301]

[0302] Spatial consistency index:

[0303]

[0304] That is, the ratio of the standard deviation of the error to the mean.

[0305] When any metric exceeds a preset threshold, the system triggers an update process. For scenarios where a high-precision reference position cannot be obtained, the system indirectly evaluates performance through historical model consistency checks and user feedback.

[0306] The dataset management adopts a hierarchical storage structure, which includes three levels: the basic dataset (initial training data), the incremental dataset (newly collected samples), and the forgotten dataset (historical samples).

[0307] Incremental learning algorithms apply weighted fusion strategies:

[0308] D new =αD recent ∪(1-α)D old ,

[0309] Where α is the weighting factor between the old and new data (typical value 0.5).

[0310] To prevent over-adaptation to short-term fluctuations, the system introduces a time decay weight:

[0311]

[0312] Where λ f This is the forgetting rate parameter, which can be adaptively adjusted according to the rate of environmental change.

[0313] Dynamic optimization of model complexity is the core function of the update module. The system maintains multiple candidate models with different complexities (different polynomial orders and regularization parameters), evaluates the accuracy-computation cost ratio of each model through cross-validation, and selects the optimal configuration. For edge devices with limited computing resources, the system automatically reduces model complexity; while in server environments requiring high accuracy, it increases model complexity. Mesh generation parameters are also dynamically adjusted according to environmental complexity, increasing the subdivision level in regions with drastic error changes and maintaining a coarse mesh in stable regions.

[0314] Automatic environmental change detection serves as an auxiliary mechanism for model updates. The system analyzes changes in signal propagation characteristics, such as multipath features, signal attenuation patterns, and time-of-arrival distribution, to identify physical changes in the environment. When significant changes are detected, local resampling and model retraining are triggered. For environments that change periodically (such as weekday / weekend patterns in an office setting), the system maintains multiple scene-specific models and automatically switches to the most suitable model based on time and sensor data.

[0315] Through this continuous self-improvement mechanism, the model update module ensures that the UWB positioning system maintains stable high-precision performance under environmental changes and long-term operation. The average system error remains below 15% of the original error in long-term testing, demonstrating excellent environmental adaptability and robustness.

[0316] The technical specifications and parameter settings are shown in Table 3.

[0317] Table 3: Technical Specifications and Parameter Settings

[0318]

[0319] The parameter space dimension is a core indicator of system complexity, directly affecting computational complexity and model accuracy. The localization error improvement rate is a key indicator for evaluating the overall system performance, reflecting the compensation effect. Compensation processing latency ensures system real-time performance, which is crucial for dynamic application scenarios. The mesh subdivision threshold controls the fineness of the adaptive mesh, balancing accuracy and computational resources. Sample quantity requirements ensure the sufficiency and reliability of model training. The error model update cycle ensures long-term stable operation and adaptability to environmental changes. The adaptive sampling allocation ratio optimizes sampling efficiency, ensuring sufficient sample points in key areas. These parameters can be fine-tuned according to specific application scenarios and hardware conditions to achieve optimal system performance.

[0320] Key performance indicators are shown in Table 4.

[0321] Table 4: Key Performance Indicators

[0322]

[0323] These indicators are interrelated and together determine the overall performance and application value of the UWB positioning error compensation system.

[0324] This embodiment provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the UWB error compensation positioning method based on the Vegas+ algorithm improvement described above.

[0325] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A UWB error compensation positioning method based on an improved Vegas+ algorithm, characterized in that, Includes the following steps: S1: Obtain the raw collected data, preprocess the raw collected data to obtain a preliminary sample set; S2: Based on the preliminary sample set, perform secondary sampling using the Vegas+ algorithm to obtain the complete sample set; Step S2 specifically includes: S21: Calculating the error gradient of the sample points in the preliminary sample set to obtain the error gradient of each sample point; S22: Smoothing the error gradient of each sample point to obtain a smoothed gradient field; S23: Evaluating the importance of sub-regions based on the smoothed gradient field to obtain an importance evaluation value for each sub-region; S24: Identifying and selecting important regions based on the importance evaluation values ​​of each sub-region to obtain a set of sub-regions to be subdivided; S25: Selecting the optimal segmentation dimension based on the set of sub-regions to be subdivided to obtain the optimal segmentation dimension; S26: Determining the segmentation points and subdividing the sub-regions based on the set of sub-regions to be subdivided and the optimal segmentation dimension to obtain the sub-regions after segmentation. The domain; step S26 specifically includes: calculating the cumulative change curve on the optimal segmentation dimension according to the optimal segmentation dimension; obtaining the segmentation point according to the cumulative change curve on the optimal segmentation dimension; obtaining the segmented sub-regions according to the segmentation point and the set of sub-regions to be subdivided; S27: generating adaptive sampling points according to the segmented sub-regions to obtain a complete sample set; S3: constructing a spatial error function using a sparse polynomial according to the complete sample set to obtain an error model; S4: using the error model to perform error prediction and compensation on the UWB real-time positioning results to obtain a corrected position signal; step S4 specifically includes: using the error model to perform error prediction and compensation on the UWB real-time positioning results to obtain a corrected position signal, as shown in the formula: ， ,in, To predict the position error vector, These are orthogonal polynomial basis functions. This is the coefficient vector obtained through training using the least squares method. The number of terms in the selected orthogonal polynomial. To correct the position signal, The position signal before correction. This is a reliability weighting factor.

2. The UWB error compensation positioning method based on the Vegas+ algorithm improvement according to claim 1, characterized in that, Step S21 specifically includes: S211: constructing multiple paired points for the sample points in the preliminary sample set; S212: obtaining the error gradient of each sample point based on the paired points using the central difference formula.

3. The UWB error compensation positioning method based on the Vegas+ algorithm improvement according to claim 1, characterized in that, Step S23 specifically includes: S231: Obtaining the integral of the error gradient norm using Monte Carlo integration based on the smoothed gradient field; S232: Generating multiple random sample points for each sub-region based on the integral of the error gradient norm; S233: Obtaining the gradient value of the random sample points using neighbor interpolation based on the random sample points; S234: Obtaining the integral estimate based on the gradient value of the random sample points; S235: Performing adaptive control accuracy based on the integral estimate to obtain the importance assessment value of each sub-region.

4. The UWB error compensation positioning method based on the Vegas+ algorithm improvement according to claim 1, characterized in that, Step S24 specifically includes: S241: Based on the importance evaluation value of each sub-region, use nonlinear transformation to obtain the importance weight of the sub-regions that enhance differences; S242: Based on the importance weight of the sub-regions that enhance differences, the primary threshold and the secondary threshold, select regions in descending order of importance until the cumulative importance reaches the target value, and obtain the set of sub-regions to be subdivided.

5. The UWB error compensation positioning method based on the Vegas+ algorithm improvement according to claim 1, characterized in that, Step S25 specifically includes: S251: Calculate the gradient components in each direction based on the set of sub-regions to be subdivided; S252: Obtain the dimensional influence ratio based on the gradient components in each direction; S253: Generate paired sample points along each dimensional direction and calculate the directional change rate, and obtain the evaluation result based on the directional change rate and the dimensional influence ratio; S254: Select the dimension with the largest change rate based on the evaluation result to obtain the optimal segmentation dimension.

6. The UWB error compensation positioning method based on the Vegas+ algorithm improvement according to claim 1, characterized in that, Step S27 specifically includes: S271: Allocating sampling points according to the segmented sub-regions and their importance to obtain the number of sampling points allocated to each sub-region; S272: Generating sampling points according to the number of sampling points allocated to each sub-region to obtain a complete sample set.

7. The UWB error compensation positioning method based on the Vegas+ algorithm improvement according to claim 1, characterized in that, The UWB error compensation localization method based on the Vegas+ algorithm further includes: updating the error model using an update mechanism; the update mechanism is based on dual triggering conditions, including timed updates and event-driven updates; the timed updates update the error model at preset intervals; the event-driven updates update the error model when a significant performance degradation or change in environmental conditions is detected.

8. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the UWB error compensation positioning method based on the Vegas+ algorithm as described in any one of claims 1-7.

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