A Low-Cost Indoor Positioning Method for 6G Based on Sparse CSI Fingerprint Database Completion

Abstract

This invention proposes a low-cost indoor positioning method for 6G based on sparse CSI fingerprint database completion. It constructs a sparse CSI fingerprint database modeling framework for low-cost 6G positioning, establishing spatial relationships between missing reference points and surrounding known reference points through distance-weighted neighborhood search, and combining a denoising autoencoder to map high-dimensional CSI fingerprints to low-dimensional latent space features. Under joint guidance, a conditional residual diffusion mechanism is used to recover the latent space representation corresponding to the missing reference point, and the CSI fingerprint of the missing location is reconstructed through a decoder. A low-cost positioning reference database is constructed based on the completed fingerprint database, and a unified positioning model is used to achieve position estimation and maintain positioning performance for the test sample. This invention can enhance the ability of the sparse fingerprint database to characterize the real spatial channel distribution while reducing the offline reference point acquisition density and fingerprint database construction cost, thus mitigating the positioning performance degradation problem caused by sparse sampling.

Description

Technical Field

[0001] This invention belongs to the field of wireless indoor positioning and intelligent signal processing technology, and relates to a 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion. Background Technology

[0002] With the development of next-generation mobile communication technologies, high-precision indoor positioning based on wireless signals has broad application prospects in scenarios such as smart buildings, industrial internet, smart warehousing, and mobile robots. Compared to satellite navigation systems, which are susceptible to obstruction and signal attenuation in indoor environments, indoor positioning methods based on wireless local area network (WLAN) signals can utilize existing communication infrastructure to achieve location awareness services with lower deployment costs. Among these methods, fingerprint positioning based on CSI (Content Separation and Ingress) has attracted widespread attention due to its strong environmental characterization capabilities, as it can reflect the effects of multipath propagation, obstruction, reflection, and fading. These methods typically construct a fingerprint database by collecting the mapping relationship between reference point locations and corresponding CSI fingerprints offline, and then perform location estimation online using the matching relationship between the sample to be located and the offline reference database. However, existing CSI fingerprint positioning methods usually rely on high-density reference point acquisition, resulting in high costs for building and updating the offline fingerprint database; under sparse sampling conditions, the spatial continuity and local topological relationships of fingerprints are easily disrupted, leading to degradation in positioning performance. Meanwhile, CSI fingerprints are characterized by high dimensionality, complex values, and strong coupling, making it difficult for traditional interpolation or general generation methods to simultaneously maintain spatial continuity, local structural consistency, and the ability to represent complex features. Therefore, how to recover CSI fingerprints at missing locations while maintaining indoor positioning performance, while reducing the reference point acquisition density and fingerprint database construction costs, has become a pressing technical problem in this field. Summary of the Invention

[0003] To address the aforementioned issues, this invention proposes a low-cost 6G indoor positioning method based on sparse CSI fingerprint database completion, targeting the degradation of fingerprint spatial distribution and decreased positioning performance caused by missing reference points under sparse sampling conditions. This invention establishes a sparse fingerprint spatial distribution model, constructs a location-feature dual-condition guidance mechanism, and combines distance-weighted neighborhood search, denoising autoencoder latent space representation, neighborhood latent variable priors, and conditional residual diffusion recovery mechanism to recover the CSI fingerprints corresponding to missing reference points. Furthermore, it constructs a completed low-cost positioning reference database, achieving indoor positioning performance maintenance under low-cost conditions. This method overcomes the shortcomings of existing technologies in sparse fingerprint spatial modeling, local structure recovery, and low-cost positioning performance maintenance. It can improve the ability of the sparse fingerprint database to characterize the real spatial channel distribution while reducing offline reference point acquisition density and fingerprint database construction costs, thereby achieving low-cost, high-precision indoor positioning.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] A low-cost 6G indoor positioning method based on sparse CSI fingerprint database completion, the method comprising the following steps:

[0006] Step 1: Obtain CSI fingerprint data and corresponding reference point location information under sparse sampling conditions, and construct a sparse CSI fingerprint database;

[0007] Step 2: Based on the sparse CSI fingerprint database, establish a sparse fingerprint spatial distribution model to characterize the differences in the spatial distribution of reference points under dense and sparse sampling conditions and the impact of missing reference points on the spatial continuity of fingerprints.

[0008] Step 3: Construct a location-feature dual-condition guided model, where the location condition is used to describe the geometric location constraints of the missing reference point and its neighborhood spatial relationship, and the feature condition is used to describe the local CSI structure information of the known reference points in the neighborhood, thus forming a joint condition constraint mechanism for missing CSI fingerprint recovery;

[0009] Step 4: Establish the spatial relationship between the missing target reference point and the known neighboring reference points based on distance-weighted neighborhood search. By calculating the spatial distance between the missing target reference point and each known reference point, determine the set of neighboring reference points and their corresponding spatial weights.

[0010] Step 5: Construct a CSI latent space representation model based on a denoising autoencoder, map the high-dimensional CSI fingerprint of known reference points to a low-dimensional latent space, and extract compact and robust latent variable representations;

[0011] Step 6: Based on the set of neighborhood reference points and their corresponding spatial weights, construct the prior latent variables and local statistical conditions of the target missing reference point, which are used to characterize the prior information of the local CSI structure around the target missing reference point.

[0012] Step 7: Under the joint guidance of location conditions, prior neighborhood latent variables, and local statistical conditions, recover the latent space representation corresponding to the missing target reference point based on the conditional residual diffusion mechanism;

[0013] Step 8: Decode and reconstruct the latent space representation of the recovered target missing reference point to obtain the CSI fingerprint at the missing location, and fuse the missing CSI fingerprint with the original sparse CSI fingerprint library to construct a complete low-cost localization reference library.

[0014] Step 9: Indoor positioning is achieved based on the completed low-cost positioning reference library. The location of the CSI sample to be positioned is estimated, thereby maintaining positioning performance while reducing the offline reference point collection density and fingerprint library construction cost.

[0015] Compared with existing technologies, the advantages of this invention are as follows: By establishing a sparse fingerprint spatial distribution model, this invention can effectively characterize the differences in the spatial distribution of reference points under dense and sparse sampling conditions, as well as the impact of missing reference points on the spatial continuity of fingerprints. Simultaneously, by constructing a position-feature dual-condition guidance mechanism, it jointly models the geometric position constraints of the target missing reference point with the neighborhood local CSI structure constraints, improving the spatial rationality and local structural authenticity of the missing CSI fingerprint recovery results. Furthermore, this invention employs a denoising autoencoder to map high-dimensional complex CSI fingerprints to a low-dimensional latent space, and combines neighborhood latent variable priors, local statistical conditions, and conditional residual expansion. The proposed mechanism enables stable recovery of missing reference point CSI fingerprints, improving upon the limitations of traditional interpolation and general generation methods in achieving spatial continuity, structural consistency, and complex-valued feature representation under sparse sampling conditions. Furthermore, by fusing the recovered missing CSI fingerprints with the original sparse fingerprint database, a complete low-cost positioning reference database is constructed. Combined with a positioning model, this database enables location estimation of samples to be located, mitigating the performance degradation problem under sparse sampling conditions. Thus, while reducing the offline reference point acquisition density and fingerprint database construction cost, it maintains indoor positioning performance under low-cost conditions, demonstrating significant application value and promising prospects for wider adoption. Attached Figure Description

[0016] Figure 1 This is a flowchart of the 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to the present invention;

[0017] Figure 2 This is a comparison of the cumulative distribution function of the localization error of different CSI fingerprint completion methods under the condition of 85% known points.

[0018] Figure 3 This is a comparison chart of the average positioning error before and after completion under different known point ratios. Detailed Implementation

[0019] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0020] like Figure 1 As shown, this invention proposes a low-cost 6G indoor positioning method based on sparse CSI fingerprint database completion. The method includes the following steps:

[0021] Step 1: Obtain CSI fingerprint data and corresponding reference point location information under sparse sampling conditions, and construct a sparse CSI fingerprint database;

[0022] Step 2: Based on the sparse CSI fingerprint database, establish a sparse fingerprint spatial distribution model to characterize the differences in the spatial distribution of reference points under dense and sparse sampling conditions and the impact of missing reference points on the spatial continuity of fingerprints.

[0023] Step 3: Construct a location-feature dual-condition guided model, where the location condition describes the geometric location constraints of the missing reference point and its neighborhood spatial relationship, and the feature condition describes the local CSI structure information of the known reference points in the neighborhood, thus forming a joint condition constraint mechanism for missing CSI fingerprint recovery;

[0024] Step 4: Establish the spatial relationship between the missing target reference point and the known neighboring reference points based on distance-weighted neighborhood search. By calculating the spatial distance between the missing target reference point and each known reference point, determine the set of neighboring reference points and their corresponding spatial weights.

[0025] Step 5: Construct a CSI latent space representation model based on a denoising autoencoder, map the high-dimensional CSI fingerprint of known reference points to a low-dimensional latent space, and extract compact and robust latent variable representations;

[0026] Step 6: Based on the set of neighborhood reference points and their corresponding spatial weights, construct the prior latent variables and local statistical conditions of the target missing reference point, which are used to characterize the prior information of the local CSI structure around the target missing reference point;

[0027] Step 7: Under the joint guidance of location conditions, prior neighborhood latent variables, and local statistical conditions, recover the latent space representation corresponding to the missing target reference point based on the conditional residual diffusion mechanism;

[0028] Step 8: Decode and reconstruct the latent space representation of the recovered target missing reference point to obtain the CSI fingerprint at the missing location, and fuse the missing CSI fingerprint with the original sparse CSI fingerprint library to construct a complete low-cost localization reference library.

[0029] Step 9: Indoor positioning is achieved based on the completed low-cost positioning reference library. The location of the CSI sample to be positioned is estimated, thereby maintaining positioning performance while reducing the offline reference point collection density and fingerprint library construction cost.

[0030] Furthermore, in step 2, a sparse fingerprint spatial distribution model is established.

[0031] Let the CSI fingerprint database under complete and dense sampling conditions within the target indoor area be represented as:

[0032]

[0033] in, Represents a complete and dense fingerprint database. Indicates the first Spatial coordinates of a reference point Indicates the first CSI fingerprints corresponding to each reference point This represents the complete set of reference point indices; this formula is used to describe the one-to-one mapping relationship between the locations of reference points within the target area and their corresponding CSI fingerprints.

[0034] Under sparse sampling conditions, only a portion of the observed reference points are retained to form a sparse fingerprint database, denoted as:

[0035]

[0036] in, This indicates that a sparse fingerprint database has been observed. Denotes the set of sampled reference point indices, and satisfies This formula indicates that the sparse fingerprint database retains only a portion of the observation samples from the complete dense fingerprint database.

[0037] Correspondingly, the set of missing reference points that are not sampled but actually exist in the complete dense fingerprint database is denoted as:

[0038]

[0039] in, Represents the set of missing reference points. Indicates the first The location coordinates of the missing reference point Indicates the first The true CSI fingerprint corresponding to each missing reference point Let represent the set of missing reference point indices, satisfying:

[0040]

[0041]

[0042] The above relationship indicates that the complete set of reference points consists of the set of observed reference points and the set of missing reference points, and there is no overlap between the two.

[0043] In step 2, by analyzing the complete dense fingerprint database Observed sparse fingerprint database and the set of missing reference points A unified model is used to characterize the differences in the spatial distribution of reference points under dense and sparse sampling conditions, as well as the impact of missing reference points on the spatial continuity of fingerprints.

[0044] Under dense sampling conditions, the spatial interval between adjacent reference points is small, and CSI fingerprints usually exhibit continuous evolution characteristics as their location changes. This can more completely characterize the fine-grained laws of signal propagation as its location changes in indoor scenes. Under sparse sampling conditions, the spatial interval between reference points increases, and the range of unobserved areas in the middle expands, causing the originally continuously distributed fingerprint samples to become discrete. This leads to a degradation of the fingerprint database in terms of spatial coverage integrity, local topological continuity, and expression of positional transition relationships.

[0045] The sparse fingerprint spatial distribution model is also used to characterize the impact mechanism of missing reference points on positioning performance. That is, when the reference points are changed from dense sampling to sparse sampling, the matching relationship between the online sample to be located and the offline reference points will rely more on discrete reference samples for approximate expression, which will lead to a decrease in location resolution, blurring of local discrimination boundaries and an increase in positioning error.

[0046] Using the sparse fingerprint spatial distribution model established in step 2, the CSI fingerprint recovery problem under low-cost sampling conditions can be uniformly expressed as: given the sparse fingerprint database... Under the condition of restoring the set of missing reference points The corresponding CSI fingerprint information is used to enhance the spatial continuity and local structural integrity of the fingerprint database, and to provide an offline reference basis for subsequent low-cost indoor positioning.

[0047] Furthermore, in step 3, a location-feature dual-condition guided model is constructed.

[0048] Set a missing reference point for the target. The spatial coordinates are:

[0049]

[0050] in, This indicates the location coordinates of the missing reference point for the target. and These represent the x-coordinate and y-coordinate of the missing reference point in the indoor plane coordinate system, respectively.

[0051] Let the missing reference point of the target be... The corresponding set of known reference points in the neighborhood is Then the CSI fingerprint set of known reference points in the neighborhood is represented as:

[0052]

[0053] in, Indicates that the target reference point is missing. The set of neighborhood features Indicates the th in the neighborhood CSI fingerprints corresponding to known reference points This represents the set of neighboring reference point indices for the missing reference point of the target.

[0054] In step 3, the CSI fingerprint recovery process for the missing target reference point is described as a conditional recovery process constrained by both location and feature conditions, and its expression is:

[0055]

[0056] in, Indicates positional conditions With characteristic conditions Under the joint constraints, the target lacks a reference point. Missing CSI fingerprint The distribution of conditions for recovery.

[0057] The location conditions are used to describe the geometric location constraints of the missing reference point in the overall fingerprint space and its spatial relationship with neighboring reference points; the feature conditions are used to describe the local CSI structure information corresponding to the known reference points around the missing reference point.

[0058] When only location conditions are used for recovery, although the spatial location prior of the missing reference point of the target can be provided, it is difficult to accurately constrain the structural evolution law of the high-dimensional CSI fingerprint in the local area, which can easily lead to the recovery result being too smooth. When only feature conditions are used for recovery, although the local structural information of the known reference points in the neighborhood can be used, it is difficult to guarantee the consistency between the recovery result and the spatial location of the missing reference point of the target.

[0059] By incorporating both location and feature conditions into the missing CSI fingerprint recovery process, the recovery results simultaneously satisfy the consistency of overall spatial distribution and the authenticity of local structure, providing a conditional constraint basis for subsequent establishment of spatial relationships based on distance-weighted neighborhood search and recovery of missing CSI fingerprints based on conditional residual diffusion mechanism.

[0060] Furthermore, in step 4, a spatial relationship is established between the missing reference point of the target and the known reference points in the neighborhood based on distance-weighted neighborhood search.

[0061] Let the complete set of reference points within the target indoor area be:

[0062]

[0063] in, Represents the complete set of reference points within the target indoor area. Indicates the first A reference point, This represents the total number of reference points.

[0064] Let the first The spatial coordinates of each reference point are:

[0065]

[0066] in, Indicates the first Spatial coordinates of a reference point and These represent the x-coordinate and y-coordinate of the reference point in the indoor plane coordinate system, respectively.

[0067] Under sparse sampling conditions, the set of observed reference points is denoted as . The set of missing reference points is denoted as For any target, a reference point is missing. Its spatial coordinates are represented as follows:

[0068]

[0069] in, Indicates that the target reference point is missing. Spatial location coordinates.

[0070] For the missing reference point of the target With any observed reference point The spatial proximity between two entities is defined by the Euclidean distance:

[0071]

[0072] in, Indicates the missing reference point coordinates of the target. With the Coordinates of the observed reference points The Euclidean distance between them This represents the L2 norm operation. This formula is used to measure the spatial proximity between the missing reference point of the target and each observed reference point.

[0073] According to the Euclidean distance From the set of observed reference points Selecting reference points for the target The nearest observed reference points in space constitute the set of neighborhood reference points corresponding to the missing reference point of the target:

[0074]

[0075] in, Indicates that the target reference point is missing. The set of neighborhood reference points; This means selecting the closest Euclidean distance after sorting by Euclidean distance in ascending order. One reference point; This is a neighborhood scale parameter used to control the modeling range of local spatial structures.

[0076] Establishing a set of neighborhood reference points Subsequently, to characterize the differences in the contribution of different neighboring reference points to the recovery of the missing target reference point, a weighting coefficient based on spatial distance is introduced to define the missing target reference point. neighborhood reference point The corresponding spatial weights are:

[0077]

[0078] in, Indicates the th neighborhood Spatial weights for recovering missing reference points from observed reference points. Indicates that the target reference point is missing. Compared with neighboring observed reference points The Euclidean distance between them Indicates that the target reference point is missing. With neighborhood set The Middle Observed reference points The Euclidean distance between them This represents a very small constant to prevent the denominator from being zero. Represents the set of neighboring reference points The formula normalizes and sums all reference points. It employs an inverse distance-squared weighting method, giving greater weight to neighboring reference points closer to the missing target reference point.

[0079] In step 4, a local spatial relationship is established between the missing target reference point and the observed neighboring reference points by performing a neighborhood search and calculating spatial weights. This local spatial relationship is used to characterize the spatial distribution structure of known reference points around the missing target reference point and serves as the basis for subsequently constructing neighborhood latent variable priors and local statistical conditions.

[0080] In practical implementation, KDTree can be used to organize the spatial coordinates of observed reference points, and the set of neighboring reference points corresponding to the missing reference point of the target can be retrieved under the condition of a given search radius or number of nearest neighbors. .

[0081] The spatial relationship model established in step 4 can explicitly characterize the local spatial constraints between the missing reference point of the target and the surrounding known reference points under sparse sampling conditions, providing a spatial prior basis for subsequent missing CSI fingerprint recovery.

[0082] Furthermore, in step 5, a CSI latent space representation model is constructed based on a denoising autoencoder.

[0083] Let the first The CSI fingerprint corresponding to each reference point is represented as follows:

[0084] in, Indicates the first CSI fingerprint matrix corresponding to each reference point This indicates that the CSI fingerprint is defined in the complex field. Indicates the number of subcarriers. This indicates the number of antennas. The CSI fingerprint matrix contains both frequency and spatial dimension information, and preserves the coupling relationship between amplitude and phase in the complex domain.

[0085] For the CSI fingerprint matrix Expand the real and imaginary parts separately and concatenate them to form real-valued eigenvectors. During the training phase, random perturbations are added to the real-valued feature vectors to obtain noisy inputs.

[0086]

[0087] in, This represents the noisy input after adding random perturbations. This represents the real-valued feature vector obtained by expanding and normalizing the original complex CSI fingerprint. Let represent the Gaussian perturbation term, and satisfy:

[0088]

[0089] in, This indicates that the mean is 0 and the covariance is... Gaussian noise distribution Indicates noise intensity. This represents the identity matrix. The noisy input is used to improve the robustness of the latent space characterization to measurement noise and local perturbations.

[0090] In step 5, via the encoder Mapping the noisy input to a low-dimensional latent space yields the first... The latent variables corresponding to each reference point are:

[0091]

[0092] in, Indicates the first The low-dimensional latent feature vectors corresponding to each reference point The parameter is The encoder mapping is used to compress high-dimensional CSI features into a low-dimensional latent space, thereby extracting key features related to the local propagation environment, spatial location changes, and fingerprint structure representation.

[0093] Correspondingly, through the decoder The latent variables are remapped back to the CSI real-valued feature space, and the expression is as follows:

[0094]

[0095] in, This represents the real-valued CSI feature vector reconstructed from latent space features. The parameter is The decoder is used to restore latent space features to the original CSI feature space.

[0096] The training objective of the denoising autoencoder is defined as follows:

[0097]

[0098] in, This represents the reconstruction loss of the denoising autoencoder. Indicates all The average reconstruction error of each training sample is summed. This represents the original real-valued CSI eigenvector. This represents the CSI feature vector reconstructed by the decoder. This represents the squared norm 2. The training objective is used to constrain the encoder-decoder network to retain as much of the main structural information of the original CSI fingerprint as possible while reducing dimensionality.

[0099] After completing the latent space mapping, for target missing reference points, the recovery object is transformed from the original high-dimensional CSI fingerprint matrix into a low-dimensional latent feature vector, represented as:

[0100]

[0101] in, This represents the latent space features corresponding to the missing reference point of the target. This indicates the location condition where the target lacks a reference point. This represents the characteristic conditions of known reference points within the neighborhood of the missing reference point. By transforming the missing reference point recovery problem into a low-dimensional latent space, the modeling difficulty of subsequent condition generation and diffusion recovery processes can be reduced.

[0102] Step 5 achieves the mapping from high-dimensional CSI fingerprint to low-dimensional latent space representation through a denoising autoencoder. This improves the robustness of latent space features to local noise disturbances while preserving the main structural information of the original CSI. It also provides a feature basis for the subsequent construction of neighborhood latent variable priors and the recovery of the latent space representation of missing reference points based on the conditional residual diffusion mechanism.

[0103] Furthermore, in step 6, the prior and local statistical conditions of the neighborhood latent variables of the target missing reference point are constructed based on the neighborhood reference point set and the corresponding spatial weights.

[0104] Set a missing reference point for the target. The corresponding set of neighborhood reference points is The first in the neighborhood The latent space characteristics corresponding to each observed reference point are represented as follows: Its corresponding spatial weight is Then the prior representation of the neighborhood latent variables of the missing reference point in the latent space is:

[0105]

[0106] in, This represents the neighborhood prior representation of the missing reference point of the target in the latent space. Indicates the first Spatial weights corresponding to each neighboring observed reference point Indicates the first Latent space characteristics of a neighboring observed reference point This represents the set of neighboring reference points corresponding to the missing reference point of the target. The prior latent variables in the neighborhood are obtained by weighted aggregation of the latent space features of the observed reference points in the neighborhood, and are used to describe the prior information of the local propagation structure around the missing reference point of the target.

[0107] After constructing the neighborhood latent variable prior, to characterize the dispersion of the neighborhood latent space features relative to the prior center, the local statistical condition corresponding to the target missing reference point is defined as follows:

[0108]

[0109] in, This indicates the local statistical conditions corresponding to the missing reference point for the target. Indicates the first Spatial weights corresponding to each neighboring observed reference point Indicates the first Latent space characteristics of a neighboring observed reference point This represents the latent variables prior in the neighborhood of the target's missing reference point. This represents a minimal constant to prevent numerical instability. The local statistical conditions are used to measure the dispersion of the latent space features in the neighborhood of the missing target reference point, reflecting the strength of local CSI structure changes.

[0110] In step 6, the location conditions of the missing reference point of the target are determined. Neighborhood latent variables prior and local statistical conditions Together, they serve as conditional information for reconstructing the latent space representation of subsequently missing reference points, where, This represents the positional condition obtained after normalizing the coordinates of the missing reference point of the target.

[0111] The neighborhood latent variable prior is used to characterize the local structural similarity between the missing target reference point and the surrounding observed reference points; the local statistical conditions are used to characterize the dispersion and uncertainty of the neighborhood latent space feature distribution. By simultaneously introducing the neighborhood latent variable prior and the local statistical conditions, the subsequent recovery process can rely on both the local structural center of the known neighboring reference points and the magnitude of local structural changes, thereby improving the accuracy and stability of missing CSI fingerprint recovery.

[0112] Under sparse sampling conditions, if the reconstruction is based solely on the location conditions of the missing reference point, it is difficult to accurately characterize the evolution of the local CSI structure around the missing reference point. Furthermore, if the reconstruction relies solely on the latent space characteristics of the observed neighboring reference points, it is difficult to guarantee the consistency between the reconstruction result and the geometric location of the missing reference point. By constructing the aforementioned prior latent variables and local statistical conditions for the neighborhood, and using them in conjunction with the location conditions, joint conditional constraints are provided for subsequent reconstruction of the latent space representation of the missing reference point based on the conditional residual diffusion mechanism.

[0113] The neighborhood latent variable priors and local statistical conditions constructed in step 6 can effectively characterize the central trend and discrete features of the local propagation structure around the missing reference point in the low-dimensional latent space, providing a feature prior basis for subsequent missing CSI fingerprint recovery.

[0114] Furthermore, in step 7, under the joint guidance of location conditions, prior neighborhood latent variables, and local statistical conditions, the latent space representation corresponding to the missing target reference point is recovered based on the conditional residual diffusion mechanism.

[0115] Let the true latent space corresponding to the missing reference point of the target be represented as: The prior representation of the neighborhood latent variables, constructed from the observed reference points in the neighborhood, is as follows: The true latent space residual of the missing reference point relative to the prior of the neighboring latent variables is defined as:

[0116]

[0117] in, This represents the true latent space residual of the target missing reference point relative to the prior of the neighboring latent variables. This represents the true latent space representation corresponding to the missing reference point of the target. This represents the prior representation of the latent variables in the neighborhood, constructed from observed reference points in the neighborhood. The true latent space residual is used to characterize the offset of the missing reference point of the target relative to the center of the local structure in the neighborhood.

[0118] During the forward diffusion process, the true latent space residual... By gradually adding Gaussian noise, we obtain the first... Noisy residual state at each time step Its probability expression is:

[0119]

[0120] in, Indicates the first step in the forward diffusion process. Noisy residual state at each time step Conditional distribution, Indicates a Gaussian distribution. This represents the cumulative retention coefficient obtained by multiplying the noise scheduling parameters. Represents the identity matrix.

[0121] The cumulative retention coefficient Defined as:

[0122]

[0123] in, Indicates the first The retention coefficients corresponding to each time step Indicates the first Noise scheduling parameters corresponding to each time step Indicates from step 1 to step 2. The cumulative retention factor of the step, Indicates the first The retention coefficients corresponding to each time step.

[0124] Therefore, the first The noisy residual state at each time step is represented as follows:

[0125]

[0126] in, Indicates the first The noisy residual state at each time step It represents standard Gaussian noise and satisfies:

[0127]

[0128] In the reverse recovery process, a conditional residual denoising network is constructed. Based on the noisy residual state at the current time step Time step Normalized position conditions Neighborhood latent variables prior and local statistical conditions The true latent space residual of the target missing reference point is expressed as:

[0129]

[0130] in, This represents the true latent space residual of the target predicted by the conditional residual denoising network. The parameter is Conditional residual denoising network, This represents the positional condition obtained after normalizing the coordinates of the missing reference point of the target. This represents the prior of the neighborhood latent variable. This indicates local statistical conditions.

[0131] Based on the predicted true latent space residual To recover the latent space representation corresponding to the missing reference point of the target:

[0132]

[0133] in, This represents the latent space representation of the missing reference point obtained from the recovery.

[0134] In step 7, the conditional residual diffusion model is optimized while simultaneously constraining the residual prediction error and the latent space recovery error; wherein, the residual prediction loss is defined as:

[0135]

[0136] in, This represents the residual prediction loss. This represents the true latent space residual obtained from network prediction. This represents the true latent space residual corresponding to the missing reference point of the target. This represents the square norm 2.

[0137] Latent space recovery loss is defined as:

[0138]

[0139] in, Indicates the loss of potential space recovery. This represents the latent space representation of the target missing reference point obtained from the recovery. This represents the true latent space representation corresponding to the missing reference point of the target.

[0140] The overall training objective of the conditional residual diffusion model is defined as follows:

[0141]

[0142] in, This represents the overall training objective of the conditional residual diffusion model. This represents the weighting coefficient used to balance the contributions of residual prediction loss and latent space recovery loss.

[0143] In step 7, the latent space recovery process of the missing target reference point is described as a residual recovery process based on the prior latent variables of the neighborhood. This allows the model to not directly generate a complete latent space representation, but to learn the correction amount of the missing target reference point relative to the local structure center of the neighborhood. This improves the stability and accuracy of the latent space recovery and provides latent space recovery results for subsequent decoding and reconstruction of the missing CSI fingerprint.

[0144] Furthermore, in step 8, the latent space representation of the recovered target missing reference point is decoded and reconstructed to obtain the CSI fingerprint at the missing location, and a complete low-cost localization reference library is constructed.

[0145] Let the latent space of the target missing reference point recovered in step 7 be represented as follows: Then through the decoder Mapping it back to the original CSI fingerprint space yields the reconstructed CSI fingerprint corresponding to the target missing reference point:

[0146]

[0147] in, This represents the real-valued CSI eigenvector of the target missing reference point reconstructed from the latent space recovery results. The parameter is decoder mapping, This represents the latent space representation of the missing reference point obtained from the recovery.

[0148] The real-valued CSI feature vector After inverse normalization, the real and imaginary parts are recombined to restore the complex CSI fingerprint matrix corresponding to the missing reference point, as shown below:

[0149]

[0150] in, This represents the complex CSI fingerprint matrix of the target missing reference points obtained from the final reconstruction. This represents a nonlinear decoding mapping from the latent space to the original CSI fingerprint space. The decoding process is used to convert the structural features recovered in the latent space back into a CSI representation that includes antenna dimension, subcarrier dimension, and complex amplitude and phase information.

[0151] Under sparse sampling conditions, when the number of effective neighboring reference points near the missing target reference point is insufficient, making it difficult to construct a stable neighborhood latent variable prior, a backtracking reconstruction strategy based on inverse distance weighting is used to obtain the CSI fingerprint of the missing target reference point, represented as:

[0152]

[0153] in, This indicates the target missing reference point CSI fingerprint obtained by reconstructing using a rollback strategy. Indicates the first CSI fingerprints of observed reference points in a neighborhood, This represents the inverse distance weights based on spatial distance normalization. This represents the set of neighboring reference points corresponding to the missing target reference point. The backoff reconstruction strategy is used to ensure that the CSI fingerprint of the missing reference point can be completed when there are insufficient valid neighboring reference points.

[0154] After reconstructing the CSI fingerprints for all missing reference points, the recovered set of missing CSI fingerprints is denoted as:

[0155]

[0156] in, This represents the recovered set of missing reference point CSI fingerprints. Indicates the first The location coordinates of the missing reference point Indicates the first The CSI fingerprint is obtained by recovering from the missing reference points.

[0157] The recovered missing reference point CSI fingerprint set Compared with the original sparse fingerprint database By merging these elements, a complete low-cost positioning reference library is constructed, represented as follows:

[0158]

[0159] in, This represents the completed low-cost positioning reference library. Represents the original sparse fingerprint database. This represents the set of missing reference point CSI fingerprints obtained through recovery.

[0160] In step 8, the latent space representation of the recovered target missing reference points is decoded and reconstructed, and the recovered missing CSI fingerprint is fused with the original sparse fingerprint library. This allows the completed low-cost positioning reference library to enhance its ability to characterize the real spatial channel distribution while maintaining a low reference point acquisition density, thereby providing a more complete offline reference basis for subsequent indoor positioning.

[0161] Furthermore, in step 9, indoor positioning is achieved based on the completed low-cost positioning reference library.

[0162] Let the completed low-cost positioning reference library constructed in step 8 be:

[0163]

[0164] in, This represents the completed low-cost positioning reference library. Represents the original sparse fingerprint database. This represents the recovered set of missing reference point CSI fingerprints. The completed low-cost positioning reference library is used as an offline reference basis for the indoor positioning phase.

[0165] Let the CSI sample to be located be represented as:

[0166]

[0167] in, This indicates the CSI samples to be located acquired online. This indicates that the CSI sample to be located is defined in the complex field. Indicates the number of subcarriers. Indicates the number of antennas.

[0168] In step 9, the CSI sample to be located is... Input the localization model, and combine it with the completed low-cost localization reference library. After completing the location estimation, the predicted location of the sample to be located is obtained:

[0169]

[0170] in, This indicates the predicted location of the CSI sample to be located. and These represent the x-coordinate and y-coordinate of the predicted location in the indoor plane coordinate system, respectively.

[0171] The positioning model employs an indoor positioning network based on complex-valued feature modeling and a spatial-frequency joint attention mechanism. This network is used to extract spatial domain features, frequency domain features, and their cross-domain correlation information from the CSI samples to be positioned, and to complete the location estimation based on the completed low-cost positioning reference library.

[0172] To characterize the supporting effect of the improved low-cost positioning reference library on positioning performance, let the true position coordinates of the sample to be positioned be:

[0173]

[0174] The positioning error of the sample to be located is defined as:

[0175]

[0176] in, This represents the positioning error of the sample to be located. This represents the actual location coordinates of the sample to be located. This represents the L2 norm operation. The positioning error is used to measure the performance preservation effect of the completed low-cost positioning reference library in location estimation.

[0177] In step 9, the location estimation of the CSI sample to be located is achieved by utilizing the completed low-cost positioning reference library. This enables the indoor positioning method to reduce the offline reference point acquisition density and fingerprint library construction cost while enhancing the offline reference library's ability to characterize the real spatial channel distribution. This alleviates the positioning performance degradation problem under sparse sampling conditions and maintains indoor positioning performance under low-cost conditions.

[0178] In step 9, the location of the CSI sample to be located is estimated by using the completed low-cost positioning reference library. This enables the indoor positioning method to reduce the offline reference point acquisition density and fingerprint library construction cost, while enhancing the offline reference library's ability to characterize the real spatial channel distribution. This alleviates the positioning performance degradation problem under sparse sampling conditions and maintains indoor positioning performance under low-cost conditions.

[0179] like Figure 2 As shown, under the condition of 85% known points, when comparing the proposed method with other completion methods such as image-to-image mapping based on conditional generative adversarial networks, conditional variational autoencoders, gradient-penalized conditional Wasserstein generative adversarial networks, deep conditional variational autoencoders, and conditional generative adversarial networks, the proposed method outperforms other methods in terms of the cumulative distribution function of localization error. This indicates that the constructed completed localization reference library can more effectively support subsequent localization tasks. Figure 3As shown, under different known point ratios, compared with the original sparse fingerprint database before completion, the fingerprint database completed using the method of this invention can further reduce the average positioning error, indicating that this invention can effectively alleviate the positioning performance degradation under sparse sampling conditions while reducing offline sampling costs.

[0180] It should be noted that the above description of the embodiments is only for the purpose of helping to understand the method and core idea of ​​this application. For those skilled in the art, several improvements and modifications can be made to this application without departing from the principle of this application, and these improvements and modifications are also within the protection scope of the claims of this application.

Claims

1. A low-cost 6G indoor positioning method based on sparse CSI fingerprint database completion, characterized in that, Includes the following steps: Step 1: Obtain CSI fingerprint data and corresponding reference point location information under sparse sampling conditions, and construct a sparse CSI fingerprint database; Step 2: Based on the sparse CSI fingerprint database, establish a sparse fingerprint spatial distribution model to characterize the differences in the spatial distribution of reference points under dense and sparse sampling conditions and the impact of missing reference points on the spatial continuity of fingerprints. Step 3: Construct a location-feature dual-condition guided model, where the location condition describes the geometric location constraints of the missing reference point and its neighborhood spatial relationship, and the feature condition describes the local CSI structure information of the known reference points in the neighborhood, thus forming a joint condition constraint mechanism for missing CSI fingerprint recovery; Step 4: Establish the spatial relationship between the missing target reference point and the known neighboring reference points based on distance-weighted neighborhood search. By calculating the spatial distance between the missing target reference point and each known reference point, determine the set of neighboring reference points and their corresponding spatial weights. Step 5: Construct a CSI latent space representation model based on a denoising autoencoder, map the high-dimensional CSI fingerprint of known reference points to a low-dimensional latent space, and extract compact and robust latent variable representations; Step 6: Based on the set of neighborhood reference points and their corresponding spatial weights, construct the prior latent variables and local statistical conditions of the target missing reference point, which are used to characterize the prior information of the local CSI structure around the target missing reference point; Step 7: Under the joint guidance of location conditions, prior neighborhood latent variables, and local statistical conditions, recover the latent space representation corresponding to the missing target reference point based on the conditional residual diffusion mechanism; Step 8: Decode and reconstruct the latent space representation of the recovered target missing reference point to obtain the CSI fingerprint at the missing location, and fuse the missing CSI fingerprint with the original sparse CSI fingerprint library to construct a complete low-cost localization reference library. Step 9: Indoor positioning is achieved based on the completed low-cost positioning reference library. The location of the CSI sample to be positioned is estimated, thereby maintaining positioning performance while reducing the offline reference point collection density and fingerprint library construction cost.

2. The 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to claim 1, characterized in that, In step 2, a sparse fingerprint spatial distribution model is established; Let the CSI fingerprint database under complete and dense sampling conditions within the target indoor area be represented as: ； in, Represents a complete and dense fingerprint database. Indicates the first Spatial coordinates of a reference point Indicates the first CSI fingerprint matrix corresponding to each reference point This represents the complete set of reference point indices; this formula is used to describe the one-to-one mapping relationship between the locations of reference points within the target area and their corresponding CSI fingerprints; Under sparse sampling conditions, only a portion of the observed reference points are retained to form a sparse fingerprint database, denoted as: ； in, This indicates that a sparse fingerprint database has been observed. Indicates the first Spatial coordinates of a reference point Indicates the first CSI fingerprints corresponding to each reference point Denotes the set of sampled reference point indices, and satisfies This formula shows that the sparse fingerprint database retains only a portion of the observed samples from the complete dense fingerprint database. Correspondingly, the set of missing reference points that are not sampled but actually exist in the complete dense fingerprint database is denoted as: ； in, Represents the set of missing reference points. Indicates the first The location coordinates of the missing reference point Indicates the first The true CSI fingerprint corresponding to each missing reference point Let represent the set of missing reference point indices, satisfying: ； ； The above relationship indicates that the complete set of reference points consists of the set of observed reference points and the set of missing reference points, and there is no overlap between the two.

3. The 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to claim 2, characterized in that, In step 3, a location-feature dual-condition guided model is constructed; Set a missing reference point for the target. The spatial coordinates are: ； in, This indicates the location coordinates of the missing reference point for the target. and These represent the x-coordinate and y-coordinate of the missing target reference point in the indoor plane coordinate system, respectively. Let the missing reference point of the target be... The corresponding set of known reference points in the neighborhood is Then the CSI fingerprint set of known reference points in the neighborhood is represented as: ； in, Indicates that the target reference point is missing. The set of neighborhood features Indicates the th in the neighborhood CSI fingerprints corresponding to known reference points This represents the set of neighboring reference point indices of the missing target reference point; The CSI fingerprint recovery process for missing target reference points can be described as a conditional recovery process constrained by both location and feature conditions, expressed as follows: ； in, Indicates positional conditions With characteristic conditions Under the joint constraints, the target lacks a reference point. Missing CSI fingerprint The distribution of conditions for recovery; The location conditions are used to describe the geometric location constraints of the missing reference point in the overall fingerprint space and its spatial relationship with neighboring reference points; the feature conditions are used to describe the local CSI structure information corresponding to the known reference points around the missing reference point.

4. The 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to claim 3, characterized in that, In step 4, a spatial relationship between the missing target reference point and the known neighboring reference points is established based on distance-weighted neighborhood search. Let the complete set of reference points within the target indoor area be: ； in, Represents the complete set of reference points within the target indoor area. Indicates the first A reference point, Indicates the total number of reference points; Let the first The spatial coordinates of each reference point are: ； in, Indicates the first Spatial coordinates of a reference point and These represent the x-coordinate and y-coordinate of the reference point in the indoor plane coordinate system, respectively. Under sparse sampling conditions, the set of observed reference points is denoted as . The set of missing reference points is denoted as For any target, a reference point is missing. Its spatial coordinates are represented as follows: ； in, Indicates that the target reference point is missing. Spatial location coordinates, and These represent the x-coordinate and y-coordinate of the reference point in the indoor plane coordinate system, respectively. For the missing reference point of the target With any observed reference point The spatial proximity between two entities is defined by the Euclidean distance: ； in, Indicates the coordinates of the missing reference point of the target. With the Coordinates of the observed reference points The Euclidean distance between them This represents the L2 norm operation; this formula is used to measure the spatial proximity between the missing reference point of the target and each observed reference point. According to the Euclidean distance From the set of observed reference points Selecting reference points for the target The nearest observed reference points in space constitute the set of neighborhood reference points corresponding to the missing reference point of the target: ； in, Indicates that the target reference point is missing. The set of neighborhood reference points; This means selecting the closest Euclidean distance after sorting by Euclidean distance in ascending order. One reference point; This is a neighborhood scale parameter used to control the modeling range of local spatial structures; Establishing a set of neighborhood reference points Subsequently, to characterize the differences in the contribution of different neighboring reference points to the recovery of the missing target reference point, a weighting coefficient based on spatial distance is introduced to define the missing target reference point. neighborhood reference point The corresponding spatial weights are: ； in, Indicates the th in the neighborhood Spatial weights for recovering missing reference points from observed reference points. Indicates that the target reference point is missing. Compared with neighboring observed reference points The Euclidean distance between them Indicates that the target reference point is missing. With neighborhood set The Middle Observed reference points The Euclidean distance between them This represents a very small constant to prevent the denominator from being zero. Represents the set of neighboring reference points The formula normalizes and sums all reference points; it uses an inverse distance squared weighting method to give greater weight to neighboring reference points that are closer to the missing reference point of the target.

5. The 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to claim 4, characterized in that, In step 5, a CSI latent space representation model is constructed based on a denoising autoencoder; Let the first The CSI fingerprint corresponding to each reference point is represented as follows: in, Indicates the first CSI fingerprint matrix corresponding to each reference point This indicates that the CSI fingerprint is defined in the complex field. Indicates the number of subcarriers. The number of antennas is indicated; the CSI fingerprint matrix contains both frequency and spatial dimension information, and retains the coupling relationship between amplitude and phase in the complex domain; For the CSI fingerprint matrix Expand the real and imaginary parts separately and concatenate them to form real-valued eigenvectors. During the training phase, random perturbations are added to the real-valued feature vectors to obtain noisy inputs. ； in, This represents the noisy input after adding random perturbations. This represents the real-valued feature vector obtained by expanding and normalizing the original complex CSI fingerprint. Let represent the Gaussian perturbation term, and satisfy: ； in, This indicates that the mean is 0 and the covariance is... Gaussian noise distribution Indicates noise intensity. The identity matrix is ​​represented; the noisy input is used to improve the robustness of the latent space characterization to measurement noise and local perturbations. via encoder Mapping the noisy input to a low-dimensional latent space yields the first... The latent variables corresponding to each reference point are: ； in, Indicates the first The low-dimensional latent feature vectors corresponding to each reference point The parameter is encoder mapping, This represents a noisy input after random perturbation; the encoder is used to compress high-dimensional CSI features into a low-dimensional latent space, thereby extracting the main features related to the local propagation environment, spatial location changes, and fingerprint structure expression. Correspondingly, through the decoder The latent variables are remapped back to the CSI real-valued feature space, and the expression is as follows: ； in, This represents the real-valued CSI feature vector reconstructed from latent space features. The parameter is The decoder mapping; the decoder is used to restore latent space features to the original CSI feature space; The training objective of the denoising autoencoder is defined as follows: ； in, This represents the reconstruction loss of the denoising autoencoder. Indicates all The average reconstruction error of each training sample is summed. This represents the original real-valued CSI eigenvector. This represents the CSI feature vector reconstructed by the decoder. The squared norm 2 is used to constrain the encoder-decoder network to retain as much of the main structural information of the original CSI fingerprint as possible while reducing dimensionality. After completing the latent space mapping, for target missing reference points, the recovery object is transformed from the original high-dimensional CSI fingerprint matrix into a low-dimensional latent feature vector, represented as: ； in, This represents the latent space features corresponding to the missing reference point of the target. This indicates the location condition where the target lacks a reference point. It represents the characteristic conditions of known reference points in the neighborhood of the missing reference point of the target; by transforming the problem of missing reference point recovery into a low-dimensional latent space, the modeling difficulty of subsequent condition generation and diffusion recovery process is reduced.

6. The 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to claim 5, characterized in that, In step 6, prior latent variables and local statistical conditions of the target missing reference point are constructed based on the neighborhood reference point set and corresponding spatial weights. Set a missing reference point for the target. The corresponding set of neighborhood reference points is The first in the neighborhood The latent space characteristics corresponding to each observed reference point are represented as follows: Its corresponding spatial weight is Then the prior representation of the neighborhood latent variables of the missing reference point in the latent space is: ； in, This represents the neighborhood prior representation of the missing reference point of the target in the latent space. Indicates the first Spatial weights corresponding to each neighboring observed reference point Indicates the first Latent space characteristics of a neighboring observed reference point This represents the set of neighboring reference points corresponding to the missing target reference point; the prior neighborhood latent variables are obtained by weighted aggregation of the latent space features of the observed neighboring reference points, and are used to describe the prior information of the local propagation structure around the missing target reference point. After constructing the prior of the neighborhood latent variables, in order to characterize the degree of dispersion of the neighborhood latent space features relative to the prior center, the local statistical condition corresponding to the missing reference point of the target is defined as follows: ； in, This indicates the local statistical conditions corresponding to the missing reference point for the target. Indicates the first Spatial weights corresponding to each neighboring observed reference point Indicates the first Latent space characteristics of a neighboring observed reference point This represents the latent variables prior in the neighborhood of the target's missing reference point. This represents a minimal constant to prevent numerical instability; the local statistical conditions are used to measure the dispersion of the latent space features in the neighborhood of the missing target reference point, in order to reflect the strength of local CSI structure changes.

7. The 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to claim 6, characterized in that, In step 7, under the joint guidance of location conditions, prior neighborhood latent variables, and local statistical conditions, the latent space representation corresponding to the missing target reference point is recovered based on the conditional residual diffusion mechanism. Let the true latent space corresponding to the missing reference point of the target be represented as: The prior representation of the neighborhood latent variables, constructed from the observed reference points in the neighborhood, is as follows: The true latent space residual of the missing reference point relative to the prior of the neighboring latent variables is defined as: ； in, This represents the true latent space residual of the target missing reference point relative to the prior of the neighboring latent variables. This represents the true latent space representation corresponding to the missing reference point of the target. This represents the prior representation of the latent variables in the neighborhood, constructed from the observed reference points in the neighborhood; the true latent space residual is used to characterize the offset of the missing target reference point relative to the center of the local structure in the neighborhood. During the forward diffusion process, the true latent space residual... By gradually adding Gaussian noise, we obtain the first... Noisy residual state at each time step Its probability expression is: ； in, Indicates the first step in the forward diffusion process. Noisy residual state at each time step Conditional distribution, Indicates a Gaussian distribution. This represents the cumulative retention coefficient obtained by multiplying the noise scheduling parameters. Represents the identity matrix; The cumulative retention coefficient Defined as: ； in, Indicates the first The retention coefficients corresponding to each time step Indicates the first Noise scheduling parameters corresponding to each time step Indicates from step 1 to step 2. The cumulative retention factor of the step, Indicates the first The retention coefficients corresponding to each time step; Therefore, the first The noisy residual state at each time step is represented as follows: ； in, Indicates the first The noisy residual state at each time step Represents standard Gaussian noise and satisfies: ； In the reverse recovery process, a conditional residual denoising network is constructed. Based on the noisy residual state at the current time step Time step Normalized position conditions Neighborhood latent variables prior and local statistical conditions The true latent space residual of the target missing reference point is expressed as: ； in, This represents the true latent space residual of the target predicted by the conditional residual denoising network. The parameter is Conditional residual denoising network, This represents the positional condition obtained after normalizing the coordinates of the missing reference point of the target. This represents the prior of the neighborhood latent variable. Indicates local statistical conditions; Based on the predicted true latent space residual To recover the latent space representation corresponding to the missing reference point of the target: ； in, This represents the latent space representation of the recovered target missing reference point; To optimize the conditional residual diffusion model, both residual prediction error and latent space recovery error are constrained; whereby the residual prediction loss is defined as: ； in, This represents the residual prediction loss. This represents the true latent space residual obtained from network prediction. This represents the true latent space residual corresponding to the missing reference point of the target. Represents the square norm 2; Latent space recovery loss is defined as: ； in, Indicates the loss of potential space recovery. This represents the latent space representation of the target missing reference point obtained from the recovery. This represents the true latent space representation corresponding to the missing reference point of the target. The overall training objective of the conditional residual diffusion model is defined as follows: ； in, This represents the overall training objective of the conditional residual diffusion model. This represents the weighting coefficient used to balance the contributions of residual prediction loss and latent space recovery loss.

8. The 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to claim 7, characterized in that, In step 8, the recovered latent space representation of the target missing reference point is decoded and reconstructed to obtain the CSI fingerprint at the missing location, and a complete low-cost localization reference library is constructed. Let the latent space of the target missing reference point recovered in step 7 be represented as follows: Then through the decoder Mapping it back to the original CSI fingerprint space yields the reconstructed CSI fingerprint corresponding to the target missing reference point: ； in, This represents the real-valued CSI eigenvector of the target missing reference point reconstructed from the latent space recovery results. The parameter is decoder mapping, This represents the latent space representation of the recovered target missing reference point; The real-valued CSI feature vector After inverse normalization, the real and imaginary parts are recombined to restore the complex CSI fingerprint matrix corresponding to the missing reference point, as shown below: ； in, This represents the complex CSI fingerprint matrix of the target missing reference points obtained from the final reconstruction. This represents a nonlinear decoding mapping from the latent space to the original CSI fingerprint space; the decoding process is used to convert the structural features recovered in the latent space back into a CSI representation that includes antenna dimension, subcarrier dimension and complex amplitude and phase information; Under sparse sampling conditions, when the number of effective neighboring reference points near the missing target reference point is insufficient, making it difficult to construct a stable neighborhood latent variable prior, a backtracking reconstruction strategy based on inverse distance weighting is used to obtain the CSI fingerprint of the missing target reference point, represented as: ； in, This indicates the target missing reference point CSI fingerprint obtained by reconstructing using a rollback strategy. This represents the inverse distance weights based on spatial distance normalization. Indicates the first CSI fingerprints of observed reference points in a neighborhood, This represents the set of neighboring reference points corresponding to the missing target reference point; the back-down reconstruction strategy is used to ensure that the CSI fingerprint of the missing reference point can be completed when there are insufficient valid neighboring reference points. After reconstructing the CSI fingerprints for all missing reference points, the recovered set of missing CSI fingerprints is denoted as: ； in, This represents the recovered set of missing reference point CSI fingerprints. Indicates the first The location coordinates of the missing reference point Indicates the first CSI fingerprint recovered from missing reference points; The recovered missing reference point CSI fingerprint set Compared with the original sparse fingerprint database By merging these elements, a complete low-cost positioning reference library is constructed, represented as follows: ； in, This represents the completed low-cost positioning reference library. Represents the original sparse fingerprint database. This represents the set of missing reference point CSI fingerprints obtained through recovery.

9. The 6G low-cost indoor positioning method based on sparse CSI fingerprint database completion according to claim 8, characterized in that, In step 9, indoor positioning is achieved based on the completed low-cost positioning reference library; Let the completed low-cost positioning reference library constructed in step 8 be: ； in, This represents the completed low-cost positioning reference library. Represents the original sparse fingerprint database. This represents the recovered set of missing reference point CSI fingerprints; the completed low-cost positioning reference library is used as an offline reference basis for the indoor positioning phase. Let the CSI sample to be located be represented as: ； in, This indicates the CSI samples to be located acquired online. This indicates that the CSI sample to be located is defined in the complex field. Indicates the number of subcarriers. Indicates the number of antennas; In step 9, the CSI sample to be located is... Input the localization model, and combine it with the completed low-cost localization reference library. After completing the location estimation, the predicted location of the sample to be located is obtained: ； in, This indicates the predicted location of the CSI sample to be located. and These represent the x-coordinate and y-coordinate of the predicted location in the indoor plane coordinate system, respectively; The positioning model employs an indoor positioning network based on complex-valued feature modeling and a spatial-frequency joint attention mechanism. This network is used to extract spatial domain features, frequency domain features, and their cross-domain correlation information from the CSI samples to be positioned, and to complete the location estimation based on the completed low-cost positioning reference library. To characterize the supporting effect of the improved low-cost positioning reference library on positioning performance, let the true position coordinates of the sample to be positioned be: ； The positioning error of the sample to be located is defined as: ； in, This represents the positioning error of the sample to be located. This represents the true location coordinates of the sample to be located. The L2 norm operation is used to represent the positioning error, which is used to measure the performance retention effect of the completed low-cost positioning reference library in location estimation.

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