Improved UWB error compensation positioning method based on Vegas + algorithm

Abstract

The invention discloses an improved UWB error compensation positioning method based on a VEGA + algorithm, and relates to the technical field of indoor accurate positioning, and the method mainly comprises the steps: carrying out the preprocessing of original collection data, obtaining a preliminary sample set, carrying out the secondary sampling through a VEGAS + algorithm, obtaining a complete sample set, and carrying out the calculation of the complete sample set; and constructing a space error function by using a sparse polynomial to obtain an error model, and performing error prediction and compensation on a UWB real-time positioning result to obtain a corrected position signal. By implementing the improved UWB error compensation positioning method based on the Vegas + algorithm provided by the invention, delay and positioning errors can be reduced, and the long-term stability and environmental adaptability of the system can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of indoor precise positioning, and more particularly to an improved UWB error compensation positioning method based on Vegas+ algorithm. Background Art

[0002] UWB technology is a wireless communication technology that uses ultrashort nanosecond pulses to transmit information over an extremely wide frequency band. UWB systems primarily use 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 determine distance. Multiple UWB base stations are deployed in the target area, with their known location coordinates. The tag then exchanges timestamp signals with the base stations, calculating the distance from the tag to each base station by measuring the round-trip time. Using trilateration or multilateration algorithms, the tag's spatial coordinates are determined by solving a set 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), particle filter (PF), etc. All of these algorithms are based on the ideal case of precise distance. Under ideal conditions, very high distance accuracy can be achieved, but they will be affected by various noises in actual use.

[0004] Traditional UWB positioning systems suffer from several major sources of error. While they offer high theoretical accuracy (centimeter-level), achieving this accuracy is often difficult in complex real-world environments. The performance of UWB positioning systems is affected by a combination of error sources, resulting in complex error distribution characteristics. Multipath is a major challenge. When UWB signals propagate in complex environments, they generate multiple propagation paths through reflection and diffraction. This causes the receiver to capture multiple signal components arriving at different times, interfering with the ranging algorithm's ability to accurately identify the first wave, thereby reducing ranging accuracy. The closely related non-line-of-sight error is equally important. When obstacles stand between the transmitter and receiver, the direct signal is blocked, forcing the signal to penetrate the medium or circumvent obstacles to reach the receiver. This significantly increases signal propagation time and typically results in positive ranging errors, which are particularly common in indoor environments. Furthermore, an improper geometric distribution of base stations can lead to geometric accuracy degradation. This can significantly reduce positioning accuracy in specific directions, particularly when the target is outside the base station's range or when the base stations are arranged in a nearly coplanar manner. These error factors overlap with each other, resulting in complex error distributions under different environmental conditions and spatial locations, which require comprehensive processing through systematic modeling and compensation strategies.

[0005] Currently, commonly used UWB error compensation methods in the industry primarily include statistical 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 errors related to environmental characteristics. Another approach involves identification and elimination, which uses signal characteristics (such as signal strength and first-wave amplitude) to identify non-line-of-sight (NLOS) signals and eliminate or downgrade them. However, this approach significantly reduces available ranging data and reduces positioning reliability when there are a large number of NLOS signals. There are also error modeling methods, which establish error prediction models based on environmental or signal characteristics. These methods typically require a large amount of prior data and struggle to adapt to dynamically changing environments.

[0006] UWB positioning errors are affected by a variety of factors, including signal quality, multipath effects, geometric distribution, and environmental characteristics, forming a typical high-dimensional nonlinear mapping relationship. Traditional methods can often only process simple low-dimensional models and cannot fully capture this complex relationship, or require a large amount of computing resources. Traditional UWB systems lack an effective comprehensive error compensation mechanism. When faced with complex actual environments, these traditional UWB positioning systems generally suffer from incomplete compensation, poor environmental adaptability, insufficient real-time performance, and lack of spatial correlation considerations. Most methods only compensate for a single error source and lack the ability to comprehensively handle multi-source errors. Error compensation models are usually trained for specific environments, and the compensation effect decreases significantly when the environment changes. Complex error compensation algorithms are often computationally intensive and difficult to meet real-time positioning requirements. They do not fully utilize the continuity and correlation characteristics of the error in spatial distribution.

[0007] These defects result in the positioning accuracy of UWB in actual application environments often failing to reach the theoretical level, especially in complex indoor environments, multi-obstacle environments and dynamically changing environments, which seriously limits the application expansion of UWB technology in the field of high-precision positioning.

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

[0009] Many interpolation methods have existed before, the most commonly used of which are linear interpolation, which uses linear weighting between two data points, and polynomial interpolation with adaptive properties. Traditional linear interpolation faces serious challenges in high-dimensional situations, including exponentially increasing computational complexity, the generation of numerous phantom peaks, poor handling of multi-peak functions, rapid error amplification with dimensionality, and low sample utilization. These issues render linear interpolation extremely inefficient and inaccurate when processing complex high-dimensional functions, making it difficult to meet the requirements of practical engineering applications.

[0010] The high-dimensional adaptive sparse polynomial interpolation method is specifically designed to solve interpolation problems in high-dimensional or infinite-dimensional parameter spaces, and is particularly suitable for solving partial differential equations involving a large number of parameters. The algorithm's adaptability is reflected in its greedy strategy, which selects the point with the largest interpolation error as the next sampling point at each step, thereby prioritizing the parameter directions that have the most significant impact on the results. However, this method also has some limitations: it may misidentify important variables in the early stages; data oscillations can cause the algorithm to misjudge parameter importance, especially for functions with certain special structures; and the Lebesgue constant can grow rapidly as the dimensionality of the polynomial space increases, affecting stability in very high dimensions. Even using an optimized one-dimensional interpolation point sequence, this problem is difficult to fully resolve.

[0011] Therefore, how to provide an error compensation method that can comprehensively consider multi-source errors, has environmental adaptability and is computationally efficient, so as 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 assist in understanding the technical solution of the present invention and does not constitute an admission that the above content is prior art. Summary of the Invention

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

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

[0015] S1: Obtaining original collected data, and preprocessing the original 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 a complete sample set;

[0017] S3: constructing a spatial error function using a sparse polynomial according to the complete sample set to obtain an error model;

[0018] S4: Using the error model to perform error prediction and compensation on the UWB real-time positioning result to obtain a corrected position signal.

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

[0020] The implementation of the improved UWB error compensation positioning method based on the Vegas+ algorithm provided by the present invention has the following beneficial effects:

[0021] The present invention constructs a high-dimensional parameter vector containing signal strength, arrival time, channel impulse response characteristics and geometric configuration, and applies principal component analysis and sequence feature selection algorithm to perform dimensionality reduction optimization. Different from the traditional compensation method of single distance or signal strength, it can capture complex environmental factors such as multipath and NLOS, and provide a comprehensive information basis for error prediction. It adopts a multi-scale partitioning strategy of parameter space, uses fine grids in areas with large error changes, and uses coarse grids in flat areas. Compared with the uniform precision model, it can reduce storage space by 70%. At the same time, it introduces an index acceleration structure to reduce the query complexity from O(n) to O(log n), ensuring sub-millisecond prediction delay; by calculating the distance between the current parameter vector and the training data distribution, combined with the historical prediction accuracy, the error compensation weight is dynamically constructed. Unlike the fixed weight method, it can intelligently identify the applicable boundary of the model, prevent over-correction caused by out-of-domain samples, and improve the robustness of the system; integrate error compensation, Kalman filtering and constraints into a cascade structure, use adaptive compensation coefficients to dynamically adjust the correction strength, and automatically adjust the observation noise covariance matrix based on prediction uncertainty, which improves the accuracy by 40% compared with a single correction method and can effectively suppress positioning jumps; establish a sliding window statistical system to monitor changes in positioning performance, realize model adaptability detection and incremental updates, and trigger model parameter adjustment when accuracy degradation is detected or sufficient reference data is accumulated, so that the system can adapt to environmental changes, maintain long-term stable performance, and avoid the accuracy attenuation problem of traditional fixed models; in short, in complex indoor environments, there are often only a few key parameter combinations that dominate the positioning error. The VEGAS+ algorithm can accurately identify these key factors, making the system While maintaining high accuracy, computational complexity is significantly reduced. VEGAS+'s directionally sensitive importance sampling strategy is highly compatible with UWB signal characteristics, intelligently identifying which signal features have the greatest impact on positioning error and automatically capturing complex correlations between signal features. Utilizing VEGAS+'s adaptive gridding capability, the grid is automatically refined in parameter regions with significant error variations, while maintaining a coarse grid in regions with gentle error variations, greatly optimizing computational resource allocation. In actual deployment, the VEGAS+ algorithm is embedded in 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 was launched, it demonstrated excellent environmental adaptability and accuracy stability, especially in the boundary regions of the parameter space. Traditional methods often suffer from severe extrapolation errors, while the VEGAS+ algorithm effectively controls boundary behavior through multi-level sparse polynomial construction and basis function importance evaluation, ensuring consistent performance across the entire parameter space.

[0022] The present invention greatly improves the adaptability of UWB positioning in complex environments through a multi-dimensional feature signal-position joint parameter extraction mechanism and an adaptive grid error model. Traditional UWB systems often experience a significant drop in positioning accuracy when the environment changes, such as object movement or equipment layout adjustment. However, this system can intelligently identify the characteristics of environmental changes and dynamically adjust the error compensation strategy. Tests have shown that the system can maintain stable positioning effects in the transition from open spaces to dense obstacle environments, and its adaptability far exceeds that of traditional fixed model methods. Even in challenging environments with metal structures, reflective surfaces, and dynamic obstacles, the system can maintain stable positioning accuracy, greatly expanding the application scenarios of UWB technology. The multi-scale parameter space partitioning strategy and fast query structure adopted by the present invention completely break the computational delay bottleneck of traditional high-precision error compensation methods. Conventional methods often struggle to meet millisecond response requirements under complex compensation models. However, the present system, through grid storage and index acceleration structure, transforms error prediction from a computationally intensive process to a memory access operation, significantly reducing processing latency. The present invention can achieve ultra-low-latency error compensation on a standard hardware platform and maintain stable operation even in high-update rate application scenarios, making it possible to accurately track fast-moving objects. At the same time, the system resource utilization is significantly lower than that of similar solutions. The dynamic reliability assessment system based on Mahalanobis distance and the multi-stage fusion position correction framework of the present invention work together to significantly improve 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 in the most challenging NLOS (non-line-of-sight) conditions, the system can still provide accurate positioning through intelligent error models. More importantly, the system exhibits consistent and predictable error characteristics under various conditions, rather than the unstable performance of traditional methods. This consistency of accuracy is particularly important for industrial applications and automation systems, and provides a reliable foundation for UWB-based control systems. The present invention gives the system a unique "self-healing" capability through real-time performance self-monitoring and model online update mechanism: as the environment changes or the system ages, the accuracy of conventional UWB systems will gradually deteriorate and eventually require recalibration, while this system can automatically adapt to new environmental conditions without interrupting service through continuous performance monitoring and incremental learning; the system will intelligently identify the trend of declining positioning performance and promptly initiate the model parameter adjustment program to ensure long-term accuracy stability; in situations such as cross-seasonal, equipment layout changes and large-scale facility renovations, the system exhibits extremely strong adaptability, reducing the traditional repetitive calibration work that requires manual intervention to a minimum. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

[0026] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0027] Figure 1 FIG2 is a schematic diagram of an improved UWB error compensation positioning method based on the Vegas+ algorithm of this embodiment. In this embodiment, the improved UWB error compensation positioning method based on the Vegas+ algorithm includes the following steps:

[0028] S1: Obtaining original collected data, and preprocessing the original collected data to obtain a preliminary sample set;

[0029] In an exemplary embodiment, the raw collected data includes UWB raw ranging data, calculated position coordinates, real position measured by a reference system, UWB signal characteristic parameters, and a timestamp;

[0030] In an exemplary embodiment, the preprocessing of the raw collected data includes: aligning the UWB raw ranging data with the real position measured by the reference system according to the timestamp, converting the coordinates of the UWB and reference systems to a unified reference system, calculating the error vector and removing abnormal error samples, calculating the 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 a complete sample set;

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

[0033] S21: performing error gradient calculation on the sample points in the preliminary sample set to obtain the error gradient of each sample point;

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

[0035] S211: constructing multiple pairing points for the sample points in the preliminary sample set;

[0036] In an exemplary embodiment, step S211 specifically includes: constructing a plurality of pairing points for the sample points in the preliminary sample set, such as the formula:

[0037]

[0038] in, is the j-th dimension pairing point, x j is the sample point, e j is the unit vector of the jth dimension, 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 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 an exemplary embodiment, step S212 specifically includes: obtaining the error gradient of each sample point using the central difference formula according to the paired points, such as the formula:

[0042]

[0043] in, is the error gradient of the i-th sample point, ε(x i +he1) means (x i +he1) error;

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

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

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

[0047]

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

[0049] S23: performing sub-region importance evaluation based on the smoothed gradient field to obtain an importance evaluation value of each sub-region;

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

[0051] S231: Obtaining an integral of an error gradient norm using Monte Carlo integration according to the smoothed gradient field;

[0052] S232: generating a plurality of random sample points for each sub-region according to the integral of the error gradient norm;

[0053] S233: According to the random sample point, interpolate using adjacent samples to obtain a gradient value of the random sample point;

[0054] S234: Obtaining an integral estimate based on the gradient value of the random sample point;

[0055] In an exemplary embodiment, step S234 specifically includes: obtaining an integral estimate according to the gradient value of the random sample point, such as the formula:

[0056]

[0057] Among them, I R is the integral estimate, V R is the sub-region volume, M is the number of random sample points, is the gradient value of the random sample point; ||·|| represents the norm;

[0058] S235: performing adaptive control accuracy based on the integral estimation to obtain an importance evaluation value of each sub-region;

[0059] In an exemplary embodiment, step S235 specifically includes: performing adaptive control accuracy according to the integral estimation to obtain an importance evaluation value of each sub-region, such as the formula:

[0060]

[0061] in, is the variance of the integral estimate, Represents point y i At the gradient, Represents the average error within the region; when σ I >0.1·I R Increase sampling points when is the importance evaluation value of each sub-region, that is, the importance weight of each sub-region;

[0062] S24: identifying and selecting important regions based on the importance evaluation values ​​of the sub-regions to obtain a set of sub-regions to be subdivided;

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

[0064] S241: Obtaining a sub-region importance weight for enhancing the difference using a nonlinear transformation according to the importance evaluation value of each sub-region;

[0065] In an exemplary embodiment, step S241 specifically includes: using a nonlinear transformation based on the importance evaluation value of each sub-region, obtaining the importance weight of the sub-region for enhancing the difference, such as the formula:

[0066]

[0067] in, To enhance the sub-region importance weight of the difference, γ is the smoothing parameter;

[0068] S242: selecting regions in descending order of importance according to the importance weights of the sub-regions of the enhanced difference, the primary threshold, and the secondary threshold until the cumulative importance reaches a target value, thereby obtaining a set of sub-regions to be subdivided;

[0069] S25: selecting an optimal segmentation dimension according to the set of sub-regions to be segmented, to obtain an optimal segmentation dimension;

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

[0071] S251: Calculating gradient components in various directions according to the set of sub-regions to be subdivided;

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

[0073]

[0074] Among them, g ij is the gradient component in each direction of each sample point, Represents the gradient of the i-th sample point in the set of sub-regions to be subdivided in the j-th direction;

[0075] S252: Obtaining a dimensionality influence ratio according to the gradient components in each direction;

[0076] In an exemplary embodiment, step S252 specifically includes: obtaining a dimensionality influence ratio according to the gradient components in each direction, such as the formula:

[0077]

[0078] Among them, r j is the impact ratio of the jth dimension;

[0079] S253: Generate paired sample points along each dimensional direction and calculate the direction change rate, and obtain an evaluation result based on the direction change rate and the dimensional influence ratio;

[0080] In an exemplary embodiment, step S253 specifically includes: generating paired sample points along each dimensional direction and calculating the direction change rate, and obtaining an evaluation result based on the direction change rate and the dimensional influence ratio, such as 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 is the center point of the region, Δ j is the change, v j is the rate of change in the j direction, and represents the error at the corresponding point, s j Indicates the final evaluation result, α indicates the smoothing parameter,

[0084] S254: Selecting the dimension with the largest change rate according to the evaluation result to obtain the optimal segmentation dimension;

[0085] As an exemplary embodiment, in step S254, if the change rates of multiple dimensions are close, that is, the difference is less than 15%, then the suboptimal dimension is selected; if a dimension has been split N times (recommended N=3), the weight of the dimension is temporarily reduced;

[0086] S26: Determine a segmentation point and perform subdivision of the subregions according to the set of subregions to be subdivided and the optimal segmentation dimension to obtain segmented subregions;

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

[0088] S261: Calculating a cumulative curve of changes in the optimal segmentation dimension according to the optimal segmentation dimension;

[0089] In an exemplary embodiment, step S261 specifically includes: calculating a cumulative curve of changes in the optimal segmentation dimension according to the optimal segmentation dimension, such as the formula:

[0090]

[0091] Among them, C(t) represents the cumulative curve of changes in the optimal segmentation dimension, Represents the minimum value of the region boundary, represents the derivative of the rate of change with respect to this dimension;

[0092] S262: Obtaining a segmentation point according to the cumulative curve of changes in the optimal segmentation dimension;

[0093] In an exemplary embodiment, step S262 specifically includes: obtaining a segmentation point according to the cumulative curve of changes in the optimal segmentation dimension, such as the formula:

[0094]

[0095] Among them, x split represents the split point, Indicates the maximum value of the parameter space area in this dimension;

[0096] S263: Obtaining segmented sub-regions according to the segmentation points and the set of sub-regions to be segmented;

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

[0098]

[0099] Among them, x min and x max Respectively represent the maximum and minimum values ​​of the parameter space area in this dimension;

[0100] S27: performing adaptive sampling point generation according to the segmented sub-regions to obtain a complete sample set;

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

[0102] 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;

[0103] In an exemplary embodiment, step S271 specifically includes: allocating sampling points according to the segmented sub-regions and the importance of the sub-regions, and obtaining the number of sampling points allocated to each sub-region, such as the formula:

[0104]

[0105] Among them, N R Assign sampling points to the sub-region, max(·) means taking the maximum value, N min Indicates the minimum number of sampling points in each area, N total Indicates the total number of sampling points, w Ris the sub-region importance, i.e., the normalized importance weight of sub-region R;

[0106] S272: Allocate the number of sampling points to each sub-region, generate sampling points, and obtain a 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: Its input is the sample points in the preliminary sample set, and the output is the error gradient of each sample point. The specific process includes:

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

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

[0112] (3) Apply the central difference formula to calculate the gradient:

[0113]

[0114] For sample points close to the boundary, use forward or backward difference instead;

[0115] 2. Gradient smoothing, where the input is the original gradient of the sample point and the output is the smoothed gradient field. The specific process includes:

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

[0117] (2) Weight calculation:

[0118]

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

[0120] 3. Sub-region importance assessment: its input is the smoothed gradient field, and its 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 adjacent 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 when

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

[0128] (1) Apply nonlinear transformation to enhance the difference: (γ=1.5 is recommended);

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

[0130] (3) Prioritize processing of those that meet w i In the area ≥τ1, w is processed when resources allow. 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 segmented, and the output is the optimal segmentation dimension j*. The specific process is as follows:

[0133] (1) Calculate the gradient components in each direction in each subdivision area:

[0134]

[0135] (2) Calculate the dimension impact ratio:

[0136]

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

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

[0139] (5) Combined with the evaluation results: j =αr j +(1-α)v j (α=0.6 is recommended);

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

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

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

[0143] 6. Determine the segmentation points and subdivide the subregions. The input is the region to be segmented and the optimal segmentation dimension, and the output is the segmented subregions. The specific process includes:

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

[0145]

[0146] (2) Choose to satisfy The point is used as the split point;

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

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

[0149] (1) Sampling point allocation based on sub-region importance:

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

[0151] Among them, w R is the normalized importance weight of subregion R, N min is the minimum number of sampling points in each area (recommended value: 5), ensuring that important areas have enough sampling points; N is uniformly randomly sampled within each sub-area R points;

[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: constructing a spatial error function using a sparse polynomial according to the complete sample set to obtain an error model;

[0154] S4: using the error model to perform error prediction and compensation on the UWB real-time positioning result to obtain a corrected position signal;

[0155] In an exemplary embodiment, step S4 specifically includes: using the error model to perform error prediction and compensation on the UWB real-time positioning result to obtain a corrected position signal, such as the formula:

[0156]

[0157] p comp =p raw -α(x)e(x),

[0158] Among them, e(x) is the predicted position error vector, Φ k (x) is the orthogonal polynomial basis function, c k is the coefficient vector obtained by least squares training, K is the number of selected orthogonal polynomial terms, and p comp To correct the position signal, p raw is the position signal before correction, α(x) is the reliability weighting factor;

[0159] In an exemplary embodiment, the improved UWB error compensation positioning method based on the Vegas+ algorithm further includes: updating the error model using an update mechanism; the update mechanism is based on dual trigger conditions, the dual trigger 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 a change in environmental conditions is detected;

[0160] As an exemplary embodiment, the preset interval is 24 hours; the criterion for significant performance degradation is: an error increase of more than 20%; and the criterion for environmental condition change is detection of a physical layout change.

[0161] In some embodiments, the above-mentioned improved UWB error compensation positioning method based on Vegas+ algorithm can also be implemented in the following manner.

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

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

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

[0165] The parameter space in UWB positioning error compensation is a D-dimensional space, which contains a variety of factors that affect positioning accuracy. It is mainly divided into three categories: spatial position dimension, signal feature dimension, and geometric relationship dimension; as shown in Table 1:

[0166] Table 1: Parameters for UWB positioning error compensation

[0167]

[0168]

[0169] Depending on the actual system configuration, the total dimension D is usually between 10 and 14. The parameter space can be expressed 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 of the VEGAS+ algorithm. To ensure the stability of the algorithm and the balance of parameter weights, all parameters are normalized: for each parameter p j , linearly map it to the interval [0,1]:

[0172]

[0173] Use normalized parameters in actual calculations and convert back to the original scale when outputting the results;

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

[0175] Then calculate the grid point coordinates: the coordinates of the i-th grid point on the j-th dimension:

[0176]

[0177] The initial grid contains a total of sub-regions;

[0178] Here, the grid points use a hierarchical quadtree or octree structure to store grid information, which is convenient for subsequent adaptive subdivision. The fields defined in the GridNode structure are shown in Table 2.

[0179] Table 2: GridNode structure definition field table

[0180]

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

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

[0183] At the same time, to improve computational efficiency, the following grid constraint parameters are set to control the overall complexity of the system:

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

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

[0186] (3) Maximum number of sub-regions, N max =10000, control algorithm complexity;

[0187] 2. Calibration data acquisition and preprocessing module: mainly performs preliminary sample collection to provide preliminary supporting data sets for calculations in important areas;

[0188] A high-precision reference positioning system is the basis for building an error compensation model. This embodiment uses an optical motion capture system to ensure that the reference system is consistent with the UWB system coordinate 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] Initial sampling point design adopts a uniform sampling strategy, performing sparse sampling at equal intervals in a grid distribution within the positioning space. This facilitates subsequent adaptive stratified sampling design using the VEGAS+ algorithm. Path planning includes sampling paths that cover the entire area, such as zigzag and spiral paths. For human sampling, easy-to-follow walking routes are designed, while for robotic collection, precise trajectories covering the entire space are generated.

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

[0191] The data preprocessing steps include:

[0192] Aligning UWB data with reference position data based on timestamps;

[0193] Convert the coordinates of the two systems to a unified reference system;

[0194] Calculate the error vector:

[0195] e=p uwb -p ref ;

[0196] Remove abnormal error samples exceeding 3σ;

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

[0198] Finally, the sample set is formed:

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

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

[0201] It is recommended to have at least 10 sample points for each initial sub-region, and the total sample size is generally between 1000-5000, 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 areas, and decomposing the total error into systematic error and random error.

[0203] 3. Adaptive Error Space Modeling: Using the initial sample set, the Vegas+ importance sampling method is used to calculate the important regions. Secondary sampling is performed on the calculated important regions to obtain the complete sample set, which is used to construct the final error compensation model.

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

[0205]

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

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

[0208]

[0209] Apply the central difference formula to calculate the gradient:

[0210]

[0211] When the sample points are close to the boundary, use forward or backward difference instead.

[0212] Gradient smoothing of sample points reduces noise by local weighted averaging:

[0213]

[0214] Among them, β is the smoothing parameter, N k (i) is point x i The k nearest neighbor point set (k=5 is recommended).

[0215] To accurately assess the importance of a subregion, the system uses Monte Carlo integral estimation to calculate the integral of the error gradient norm. M random sample points are generated for each subregion, and the gradient values ​​of these points are estimated by interpolation of adjacent samples to calculate the integral estimate:

[0216]

[0217] Where V R is 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 when the number of sampling points is increased. Special areas are treated separately: for areas with sparse samples (number of samples < 3), the neighboring area extrapolation method is used; for areas that may contain singular points, an upper limit is set to prevent the weight from being too high.

[0221] Calculate the importance weight of each sub-region based on the integral estimate:

[0222]

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

[0224] Apply a nonlinear transformation to enhance the difference:

[0225]

[0226] It is recommended to set γ = 1.5 and set the minimum weight threshold w min Then normalize it.

[0227] The weights of all sub-regions are recalculated after each grid subdivision. When the calculation cost is high, a local update strategy can be used.

[0228] For important area identification, the primary threshold τ1 (recommended value 0.05) and the secondary threshold τ2 (recommended value 0.02) are set, and priority is given to areas that meet w i In the area where ≥τ1, if resources allow, the processing of i The system sets a cumulative importance target (recommended value 0.80) and 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 error change rate in each dimension. The gradient components in each direction are calculated for all sample points in the sub-region:

[0230]

[0231] Calculate the dimension impact ratio:

[0232]

[0233] Generate paired sample points along each dimension:

[0234]

[0235] and

[0236]

[0237] where x c is the center point of the region,

[0238]

[0239] Calculate the rate of change of direction:

[0240]

[0241] Combine the gradient components and the directed sampling results:

[0242] s j =αr j +(1-α)v j ,

[0243] It is recommended to set α=0.6 and apply random perturbations:

[0244]

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

[0246] Adaptive segmentation strategy selects the dimension with the largest rate of change When the change rates of multiple dimensions are close (difference < 15%), consider the suboptimal dimension. If a dimension has been split N times in a row (recommended N = 3), temporarily reduce the weight of the dimension.

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

[0248]

[0249] Choose to satisfy:

[0250]

[0251] point as the split point.

[0252] When the cumulative curve cannot be accurately estimated, it degenerates to 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 (stop segmentation when the gradient variance in the sub-region is less than the threshold) and resource limitation constraint (the recommended upper limit of the total number of sub-regions is 10,000). * At point x split Divide 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 And inherit the level+1 of the parent node, update the tree structure and adjacency relationship, and redistribute the sample points to the corresponding sub-areas.

[0255] Adaptive sampling point generation first requires constructing a sampling density function. The piecewise constant density function defines the local density of each leaf region based on the importance weight:

[0256]

[0257] Among them 1 R is the indicator function of R,

[0258] Global density function:

[0259] p(x)=∑ R p R (x)1 R (x).

[0260] The smoothed density function smoothes the original density using a kernel function:

[0261] psmooth (x)=∫K(xy)p(y)dy,

[0262] Where K is the Gaussian kernel function:

[0263]

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

[0265]

[0266] Construction,The actual implementation reconstructs the edge density from the set of sub-regions.

[0267] The stratified sampling strategy includes three levels: global uniform sampling generates basic sample points in the parameter space as a whole, and the number of samples is:

[0268] N uniform =α1·N total ;

[0269] Importance sampling uses the inverse transform sampling method 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] Solution Determine the sampling location,

[0274] Sample size:

[0275] N importance =α2·N total ,

[0276] Recommended α2 = 0.4;

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

[0278]

[0279] And perform local random sampling in each area, the total number of samples is:

[0280] N grid =α3·N total ,

[0281] Recommended 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 an original measured 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 error is compensated.

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

[0285] The parameter vector is normalized and then enters the error prediction engine. This normalization process uses linear mapping to normalize the features of each dimension to the interval [0,1], eliminating dimensional differences and improving the generalization ability of the model. The system uses a polynomial model to predict the position error vector, which is expressed as:

[0286]

[0287] where Φ k is an orthogonal polynomial basis function, such as Legendre polynomials or Chebyshev polynomials, c k is the coefficient vector obtained by least squares training.

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

[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 sample, providing strong compensation in areas with dense samples and conservative adjustment in marginal areas to avoid position divergence caused by overcompensation. Similarity evaluation is calculated using the Mahalanobis distance:

[0291]

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

[0293] α(x)=exp(-λ·d M (x)),

[0294] It is recommended to use λ=0.2 as the sensitivity parameter. 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-aware filters. When stationary or at low speed, an exponentially weighted moving average filter is used; when in moderate motion, a modified α-β filter is used; and when in high-speed motion, an extended Kalman filter is applied to fuse IMU data to predict and smooth the trajectory. State recognition is achieved through velocity and acceleration thresholds, and the filter parameters are dynamically adjusted based on the motion state.

[0296] 5. Model update module: used for adaptive optimization and environmental adaptation;

[0297] The model update module ensures the system adapts to environmental changes and hardware drift, maintaining long-term, stable, high-precision positioning performance. The update mechanism is based on two trigger conditions: scheduled updates and event-driven updates. Scheduled updates are executed at preset intervals (typically 24 hours or 7 days); event-driven updates are activated when a significant performance degradation (error increase of more than 20%) or a change in environmental conditions (such as a physical layout change) is detected.

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

[0299]

[0300] Maximum error:

[0301]

[0302] and spatial consistency indicators:

[0303]

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

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

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

[0307] The incremental learning algorithm applies a weighted fusion strategy:

[0308] D new =αD recent ∪(1-α)D old ,

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

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

[0311]

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

[0313] Dynamic optimization of model complexity is a core function of the update module. The system maintains multiple candidate models of varying complexity (different polynomial orders and regularization parameters), evaluates the accuracy-computational 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; in server environments requiring high precision, it increases model complexity. Meshing parameters are also dynamically adjusted based on environmental complexity, increasing the subdivision level in areas of drastic error fluctuations and maintaining a coarse mesh in stable areas.

[0314] Automatic environmental change detection serves as a supplementary mechanism for model updates. The system analyzes changes in signal propagation characteristics, such as multipath signatures, signal attenuation patterns, and arrival time distribution, to identify physical changes in the environment. When significant changes are detected, local resampling and model retraining are triggered. For environments that change regularly (such as the weekday / weekend pattern in an office setting), the system maintains multiple scenario-specific models and automatically switches to the most appropriate model based on the time of day 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 in environmental changes and long-term operation. The system average error is maintained below 15% of the original error in long-term tests, demonstrating excellent environmental adaptability and robustness.

[0316] The technical indicators and parameter settings are shown in Table 3;

[0317] Table 3: Technical indicators and parameter settings

[0318]

[0319] The parameter space dimension is a core indicator of system complexity, directly affecting computational complexity and model accuracy. The positioning error improvement rate is a key indicator for evaluating the overall system performance, reflecting the compensation effect. The compensation processing delay ensures the real-time performance of the system, which is crucial for dynamic application scenarios. The grid subdivision threshold controls the fineness of the adaptive grid, balancing accuracy and computing resources. The sample quantity requirement ensures the adequacy and reliability of model training. The error model update cycle ensures the long-term stable operation of the system and adapts to environmental changes. The adaptive sampling allocation ratio optimizes sampling efficiency and ensures that sufficient sample points are obtained in key areas. These parameters can be fine-tuned according to the specific application scenario and hardware conditions to obtain optimal system performance.

[0320] The key performance indicators are shown in Table 4;

[0321] Table 4: Key performance indicators

[0322]

[0323] These indicators are interrelated and jointly 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. When the computer program is executed by a processor, the computer program implements the steps of the above-mentioned improved UWB error compensation positioning method based on the Vegas+ algorithm.

[0325] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A UWB error compensation positioning method based on the improved Vegas+ algorithm, characterized in that: The following steps are involved: S1: Obtaining original collected data, and preprocessing the original collected data to obtain a preliminary sample set; S2: Based on the preliminary sample set, perform secondary sampling using the VEGAS+ algorithm 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 result to obtain a corrected position signal.

2. The improved UWB error compensation positioning method based on Vegas+ algorithm according to claim 1, characterized in that: Step S2 specifically includes: S21: performing error gradient calculation on the sample points in the preliminary sample set to obtain the error gradient of each sample point; S22: performing gradient smoothing processing on the error gradient of each sample point to obtain a smoothed gradient field; S23: performing sub-region importance evaluation based on the smoothed gradient field to obtain an importance evaluation value of each sub-region; S24: identifying and selecting important regions based on the importance evaluation values ​​of the sub-regions to obtain a set of sub-regions to be subdivided; S25: selecting an optimal segmentation dimension according to the set of sub-regions to be segmented, to obtain an optimal segmentation dimension; S26: Determine a segmentation point and perform subdivision of the subregions according to the set of subregions to be subdivided and the optimal segmentation dimension to obtain segmented subregions; S27: According to the segmented sub-regions, adaptive sampling points are generated to obtain a complete sample set.

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

4. The improved UWB error compensation positioning method based on Vegas+ algorithm according to claim 2, characterized in that: Step S23 specifically includes: S231: Obtaining an integral of an error gradient norm using Monte Carlo integration according to the smoothed gradient field; S232: generating a plurality of random sample points for each sub-region according to the integral of the error gradient norm; S233: According to the random sample point, interpolate using adjacent samples to obtain a gradient value of the random sample point; S234: Obtaining an integral estimate based on the gradient value of the random sample point; S235: Based on the integral estimation, adaptively control the accuracy to obtain an importance evaluation value of each sub-region.

5. The improved UWB error compensation positioning method based on Vegas+ algorithm according to claim 2, characterized in that: Step S24 specifically includes: S241: Obtaining a sub-region importance weight for enhancing the difference using a nonlinear transformation according to the importance evaluation value of each sub-region; S242: According to the importance weights of the sub-regions of the enhanced difference, the primary threshold and the secondary threshold, regions are selected in descending order of importance until the cumulative importance reaches a target value, thereby obtaining a set of sub-regions to be subdivided.

6. The improved UWB error compensation positioning method based on Vegas+ algorithm according to claim 2, characterized in that: Step S25 specifically includes: S251: Calculating gradient components in various directions according to the set of sub-regions to be subdivided; S252: Obtaining a dimensionality influence ratio according to the gradient components in each direction; S253: Generate paired sample points along each dimensional direction and calculate the direction change rate, and obtain an evaluation result based on the direction change rate and the dimensional influence ratio; S254: Select the dimension with the largest change rate according to the evaluation result to obtain the optimal segmentation dimension.

7. The improved UWB error compensation positioning method based on Vegas+ algorithm according to claim 2, characterized in that: Step S26 specifically includes: S261: Calculating a cumulative curve of changes in the optimal segmentation dimension according to the optimal segmentation dimension; S262: Obtaining a segmentation point according to the cumulative curve of changes in the optimal segmentation dimension; S263: Obtain segmented sub-regions according to the segmentation points and the set of sub-regions to be segmented.

8. The improved UWB error compensation positioning method based on Vegas+ algorithm according to claim 2, 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: Allocate the number of sampling points to each sub-region, generate sampling points, and obtain a complete sample set.

9. The improved UWB error compensation positioning method based on Vegas+ algorithm according to claim 1, characterized in that: The improved UWB error compensation positioning method based on the Vegas+ algorithm also includes: updating the error model using an update mechanism; the update mechanism is based on dual trigger conditions, and the dual trigger conditions include 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 a change in environmental conditions is detected.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the improved UWB error compensation positioning method based on the Vegas+ algorithm described in any one of claims 1 to 9 are implemented.

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