Channel state information indoor positioning method based on graph isomorphic network

Abstract

The invention discloses a channel state information (CSI) indoor positioning method based on a graph isomorphic network (GIN). The method comprises the following steps: firstly, carrying out local outlier factor (LOF) detection on each subcarrier in CSI amplitude measurement, and removing abnormal points in a CSI amplitude measurement value; and then, a Morlet wavelet function is utilized to obtain a time-frequency graph of a CSI measurement value, and a CSI image is constructed by utilizing color mapping. A corresponding graph topological structure is constructed based on the CSI image, super-pixel segmentation is performed on the CSI image through an SLIC algorithm, then node selection and adjacent side relation construction are realized, and position features and color features of nodes are integrated to form a feature matrix; and finally, carrying out classification learning by utilizing GIN, and training a final position estimation model. The method has the advantages of high efficiency, reliability and realizability.

Description

Technical Field

[0001] The design of the present invention relates to a channel state information (CSI) indoor positioning method based on a graph isomorphic network (GIN), which converts CSI data collected by WIFI indoor positioning into a CSI image, and then converts it into a graph topology structure. Indoor positioning is achieved through training and classification of a graph neural network, and belongs to the field of artificial intelligence application and indoor positioning technology. Background Art

[0002] With the rapid development of wireless communications and the popularity of mobile devices, location-based services such as indoor navigation and indoor tracking have exploded. How to provide reliable and accessible positioning information to users of location-based services is an important issue. Global satellite navigation systems are mature and developed in outdoor positioning, but due to the complex indoor wireless propagation environment, there is no direct path for satellite signals, so satellite positioning systems have poor positioning performance in indoor environments.

[0003] So far, many indoor positioning systems based on wireless networks have been proposed. People can provide different services for different users in different scenarios through mobile cellular communication systems, satellite communication systems, ultra-wideband, WIMAX, Bluetooth, radio frequency identification, wireless local area network and other technologies. At the same time, due to the large-scale deployment of commercial WiFi devices in indoor environments, its low cost and convenient deployment advantages, indoor Wi-Fi positioning has become a research hotspot. Because every household and public place now has large-scale Wi-Fi communication equipment, and many working and living environments cannot do without Wi-Fi signals, the indoor positioning method based on Wi-Fi is the easiest to achieve large-scale application.

[0004] There are two mainstream algorithms in the existing Wi-Fi indoor positioning solutions: geometry-based and fingerprint-based positioning algorithms. The geometry-based positioning method measures the propagation delay and direction of the Wi-Fi signal and calculates the corresponding position using geometric theorems. Typical positioning measurement parameters include the use of arrival time (TOA), arrival time difference (TDOA), and arrival angle (AOA). The fingerprint-based method establishes a fingerprint database in the offline training phase and estimates the target location based on real-time measurements in the online phase. The received signal strength indication (RSSI) and channel state information (CSI) are usually used as fingerprint indicators. RSSI is a single-dimensional measurement that indicates the magnitude of the received signal strength and provides information about the overall strength of the signal during transmission, but it lacks detailed information about the signal, such as propagation path, interference, and frequency characteristics. Therefore, RSSI is often used in wireless networks to measure the connection quality between devices, but its accuracy is relatively low and is easily affected by interference and multipath propagation. CSI is a multi-dimensional measurement that provides more detailed information about the channel state. It includes multiple parameters such as phase and amplitude on the subcarrier. It not only provides information about the signal strength, but also provides detailed data about the time domain and frequency domain characteristics of the channel state, including the signal propagation path, phase information, and spectrum characteristics. In scenarios such as indoor positioning, gesture recognition, and optimization of wireless communication systems, CSI is usually selected as the object of application research because more detailed channel information is needed to achieve high-precision operations.

[0005] The biggest advantage of using Wi-Fi signal feature fingerprints for positioning is that it does not require additional hardware equipment to be deployed, and it is a very cost-saving method. Professor Wang [1] and others proposed a deep learning network based on DeepFi to achieve indoor target positioning. The essence of this method is to use the weights in the deep network as fingerprints, and use the greedy learning algorithm to train the weights of the CNN network. This algorithm greatly reduces the complexity of the network. Finally, in the online stage, a probabilistic data fusion method based on radial basis function is used to estimate the position of the target. Reference [2] studied a positioning algorithm based on CSI amplitude fingerprint. The algorithm uses a multidimensional scaling analysis method to calculate the Euclidean distance and time reversal resonance intensity between the unit to be measured and the reference point, and finally uses the KNN algorithm to estimate the position, but this is not the final position. The conjugate gradient method is also used to improve the triangular centroid algorithm to obtain a position estimate. The final positioning result is obtained by combining the position estimate with the position estimated by KNN. Experimental results show that compared with some existing algorithms, the positioning error has been improved. The PhaseFi[3] positioning system uses calibrated CSI phase information as the positioning fingerprint. The authors first extract the original phase from the original CSI and then use the linear transformation method to calibrate the phase. The positioning process is divided into a training phase and an online phase. In the training phase, CNN is used to train the input phase data. In the online phase, a probabilistic method based on radial basis function is used to estimate the target position. Experimental results verify the effectiveness and stability of the system. Although the fingerprint-based scheme generally provides more accurate positioning results, its bottleneck lies in finding the nonlinear relationship between the target position and the corresponding fingerprint. The graph convolutional network (GCN) proposed in recent years provides another dimension for extracting features from non-Euclidean data structures. Since the non-Euclidean data structure generated by the fingerprint positioning system has different propagation environments, it is a worthy research direction to apply GCN to mine the geometric relationship between different access points and extract their intrinsic features. The model is based on the graph neural network (GNN), which basically extends the concept of CNN. It uses geometric information for learning and reasoning through the graph, can consider the global relationship between nodes, is conducive to the modeling of complex relationships between signal features, can also capture spatial invariance, and has a certain adaptability to the changes of signal features at different locations.

[0006] Several neural network models have been developed for graph learning, which have achieved better performance than traditional techniques. Inspired by the Fourier transform of graphs, Defferrard et al. [4] proposed a graph coconvolution operation as an analog of the standard convolution used in CNNs. Just as the convolution operation in the image spatial domain is equivalent to multiplication in the frequency domain, the coconvolution operator defined by the graph Laplacian polynomials is equivalent to filtering in the graph spectral domain. In particular, applying Chebyshev polynomials to the graph Laplacian results in spatially localized filtering. Reference [5] proposed an image localization system based on graph neural networks (GNNs). The important features of each image are extracted using a pre-trained ResNet50 convolutional neural network (CNN) architecture. Next, the extracted features are fed into the GNN to find the pose regression problem for each image by treating the image features as nodes in the graph and formulating the pose estimation problem as node pose regression or by modeling the image features themselves as a graph. The two proposed methods are extensively compared with the state-of-the-art single image localization methods and show that the use of GNNs can improve the performance in both indoor and outdoor environments. Reference [6] proposed a few-shot transfer learning system that uses only a small amount of labeled data from the current environment and reuses a large amount of existing labeled data previously collected in other environments, thereby greatly reducing the data collection and labeling costs for positioning in each new environment. The core method is few-shot transfer learning based on graph neural network (GNN) and its modification. Experimental results in real-world environments show that the proposed system achieves performance comparable to that of the convolutional neural network (CNN) model, with 40 times less labeled data. Reference [7] uses point cloud and RGB feature information to accurately obtain indoor three-dimensional space. Using a new visual positioning system (VPS) method, the user's location can be determined by matching the target pose information estimated by the improved point graph neural network (GNN) with the pose information labels of voxel database objects addressed in predefined voxel units. Summary of the invention

[0007] The present invention discloses a channel state information (CSI) indoor positioning method based on a graph isomorphic network (GIN). First, a local outlier factor (LOF) is detected for each subcarrier in the CSI amplitude measurement to remove abnormal points in the CSI amplitude measurement value. Then, the Morlet wavelet function is used to obtain the time-frequency diagram of the CSI measurement value, and the CSI image is constructed using color mapping. Then, a corresponding graph topology structure is constructed based on the CSI image, and the CSI image is superpixel segmented by the SLIC algorithm to realize node selection and neighbor edge relationship construction, and the position features and color features of the nodes are integrated to form a feature matrix. Finally, GIN is used for classification learning to train the final position estimation model. The method achieves the advantages of high efficiency, reliability and feasibility.

[0008] The technical solution adopted by the present invention to solve the technical problem is:

[0009] A channel state information indoor positioning method based on graph isomorphic network, the method comprising the following steps:

[0010] (I) Offline stage,

[0011] Step 1: Data Preprocessing

[0012] The received channel state information (CSI) amplitude value is preprocessed for subsequent CSI image fingerprint construction.

[0013] Step 2: CSI Image Build

[0014] The preprocessed CSI amplitude measurement values ​​are transformed into CSI images using the wavelet transform method.

[0015] Step 3: Graph structure construction of CSI image

[0016] Step 3-1: Use the SLIC algorithm to perform superpixel segmentation on the CSI image.

[0017] Step 3-2: Select nodes of the graph structure based on the superpixel segmentation results.

[0018] Step 3-3: Use the distance measurement between nodes to construct the adjacency matrix of the graph structure.

[0019] Step 3-4: Use the position and color information of the nodes to construct the feature matrix of the graph structure.

[0020] Step 4: Classification Learning

[0021] A graph isomorphism network (GIN) is built for classification learning to obtain a location estimation model.

[0022] (ii) Online stage,

[0023] Step 1: Data Preprocessing

[0024] The obtained CSI amplitude measurement value is preprocessed using the method of step 1 in the offline phase.

[0025] Step 2: CSI Image Build

[0026] Using the method of step 2 in the offline phase, the CSI image is constructed using the preprocessed CSI amplitude measurements.

[0027] Step 3: Graph structure construction of CSI image

[0028] Using the method in step 3 of the offline phase, the graph structure of the CSI image is obtained.

[0029] Step 4: Position Estimation

[0030] The location estimation model obtained in step 4 of the offline phase is used to complete the location estimation.

[0031] The data preprocessing in step 1 in the offline stage of the method includes the following steps:

[0032] The basic concepts involved are as follows:

[0033] (1) The distance between two CSI amplitude values

[0034] d(Amp j ,Amp p ): represents the distance from the jth CSI amplitude value to the pth CSI amplitude value.

[0035] (2) kth distance

[0036] dist k (Amp j ): The distance between the k-th closest CSI amplitude value and the j-th CSI amplitude value (from near to far) is called the k-neighborhood distance of the j-th CSI amplitude value.

[0037] (3) kth distance neighborhood

[0038] N k (j): The k-th distance neighborhood of the j-th CSI amplitude value is all CSI amplitude values ​​within the k-th distance, including the k-th distance.

[0039] (4) Reachable distance

[0040] reachdist k (Amp j ,Amp p ): Select the largest of the direct distance between two CSI amplitude values ​​and the k-th distance from the j-th CSI amplitude value as the reachable distance from the j-th CSI amplitude value. If the j-th CSI amplitude value is outside the k-neighboring distance of the p-th CSI amplitude value, then the reachable distance is the direct distance between the two CSI amplitude values. If the j-th CSI amplitude value is within the k-neighboring distance of the p-th CSI amplitude value, then the reachable distance is the k-th distance.

[0041] (5) Local reachable density

[0042] lrd k (j): represents the inverse of the average reachable distance of the j-th CSI amplitude value, which is the sum of the distances in its k-neighborhood divided by the number of CSI amplitude value measurements in the neighborhood.

[0043] (6) Local outlier factor

[0044] LOF k (j): The ratio of the average local reachable density of all CSI amplitude values ​​in the k-th distance neighborhood of the j-th CSI amplitude value to the local reachable density of the j-th CSI amplitude value.

[0045] Step 1-2: Perform a local outlier factor (LOF) test on each subcarrier in the CSI amplitude measurement. For each subcarrier, calculate the distance from the CSI amplitude value to all other CSI amplitude values, find the kth closest CSI amplitude value to it, and calculate the LOF value. If the LOF value is larger, it is more abnormal, and vice versa, if it is smaller, it is more normal. Specifically, first calculate the jth CSI amplitude value Amp under the i-th subcarrier. j The k-neighbor distance to other amplitude values ​​is obtained as follows:

[0046] dist k (Amp j )=d(Amp j ,Amp p )

[0047] Among them, Amp p Indicates the CSI amplitude value closest to the jth CSI amplitude value k, d(Amp j ,Amp p ) represents the Euclidean distance from the jth CSI amplitude value to the pth CSI amplitude value. Then, Amp is calculated according to the following formula: j To Amp p The reachable distance:

[0048] reachdist k (Amp j ,Amp p )=max{dist k (Amp j ),d(Amp j ,Amp p )}

[0049] Then calculate Amp based on the reachable distance j The local reachability density is the inverse of the average reachable distance of all CSI amplitude values ​​in the k-neighborhood of the j-th CSI amplitude value. The specific formula is as follows:

[0050]

[0051] Among them, N k (j) represents Amp jThen calculate Amp j The local outlier factor is the ratio of the average local reachable density of all CSI amplitude values ​​in the k-neighborhood of the j-th CSI amplitude value to the local reachable density of the j-th CSI amplitude value itself. The specific formula is as follows:

[0052]

[0053] If Amp j If the LOF value of the jth amplitude measurement value is much larger than 1, then the local density of the jth amplitude measurement value is much smaller than the average value of the local reachable density of all CSI amplitude values ​​of the subcarrier in the k neighborhood, and it can be determined as an abnormal point, otherwise it is a normal point.

[0054] Step 1-3: Filter out the CSI amplitude values ​​detected as abnormal points in step 1-2

[0055] Step 1-4: Normalize the CSI signal after outliers are filtered out, and scale all values ​​to the interval [0, 1]. The normalization operation formula is as follows:

[0056]

[0057] Amp i Indicates the CSI amplitude value of the i-th subcarrier, Amp min Indicates the minimum value of the CSI amplitude, Amp max Indicates the maximum value of the CSI amplitude.

[0058] Wherein, step 2 of the offline phase CSI image construction includes the following steps:

[0059] Step 2-1: Select the Morlet wavelet function and calculate the expression of the wavelet transform coefficient as follows:

[0060]

[0061] Where Amp represents the CSI amplitude measurement vector, It represents the wavelet function after scaling and translation. It is the daughter wavelet obtained by operating the mother wavelet ψ(t). a* represents the scale parameter, which controls the scaling of the wavelet function. The scale a* is usually inversely proportional to the frequency. b* represents the translation parameter, which controls the position of the wavelet function. By changing the size of b*, the signal can be analyzed at different time points.

[0062] Step 2-2: Construct a two-dimensional image. According to the scaling scale a* and translation parameter b* in step 2-1, the corresponding frequency and time parameters are mapped to the two-dimensional plane to form a time-frequency matrix. Finally, the time-frequency diagram of the signal is obtained, where the horizontal axis of the image represents time and the vertical axis represents frequency.

[0063] Step 2-3: Use the colormap "viridis" in the matplotlib library to map the two-dimensional matrix values ​​to different color spaces. It is a continuous color gradient that starts from blue, gradually transitions to green, and finally to yellow. This color mapping maps the minimum value to blue, the middle value to green, and the maximum value to yellow, and provides a smooth transition between blue, green, and yellow, so that the details and levels of the data can be carefully displayed.

[0064] Wherein, step 3 of the CSI graph structure construction in the offline stage of the method includes the following steps:

[0065] Step 3-1: Use the SLIC algorithm to perform superpixel segmentation on the CSI image.

[0066] (1) Initialize the center point (cluster center): Convert the time-frequency graph obtained in step 2 from RGB space to LAB space, divide the image of size N (the number of pixels is N) into K superpixel blocks, and the range size of each superpixel block includes pixels, let For each pixel block length value, initialize the center point of each pixel block

[0067] (2) Gradient calculation and center point adjustment: Use the differential method to calculate the gradient and readjust the center point. Traverse the 8-region pixel points of the center point of the initial pixel block, calculate the pixel point with the minimum gradient value, and use it as the new center point. The formula for differential calculation of the gradient is as follows:

[0068] Gradient(x,y)=dx(i,j)+dy(i,j);

[0069] dx(i,j)=I(i+1,j)-I(i,j);

[0070] dy(i,j)=I(i,j+1)-I(i,j);

[0071] Among them, (x, y) represents the initial pixel center coordinates, (i, j) is used to represent the position index of the pixel traversed during the gradient calculation process, dx(i, j) represents the gradient value along the x-axis at the pixel point (i, j), dy(i, j) represents the gradient value along the y-axis at the pixel point (i, j), and I(i, j) represents the weighted average grayscale value of the three RGB channels of the image at the pixel point (i, j).

[0072] (3) Pixel clustering and cluster center iteration: Traverse the pixels in the 2S*2S neighborhood of the center of each superpixel block and calculate the distance to the center of each superpixel block. Use the K-means clustering algorithm to classify the pixels and use the transformed Euclidean distance formula to measure the distance. The distance measurement includes color distance and spatial distance. The formula is as follows:

[0073]

[0074] Among them, l i ,a i ,b i ,x i ,y i Represents the LAB color space value and position of the center point of each superpixel block, l j ,a j ,b j ,x j ,y j Represents the LAB color space value and position of the pixel in the 2S*2S neighborhood, d c Represents the color distance, d s Represents the spatial distance, N s is the maximum spatial distance within a cluster, N c is the maximum color distance within the cluster, take N c =m, the fixed constant m (value range [1,40], generally 10) is the maximum possible distance in the LAB space. The final distance metric D' is as follows:

[0075]

[0076] According to the distance from the pixel point in the 2S*2S neighborhood to the center of each pixel block, the pixel is divided into the closest cluster, and all the pixels in the new cluster are averaged to obtain the new cluster center. Finally, iterate again according to the above steps until the error converges.

[0077] (4) Enhanced connectivity: Connectivity control is performed to solve the problems of multiple connectivity, too small superpixel size, and single superpixel being cut into multiple discontinuous superpixels in the iteratively completed clustering. The main idea is to create a new label table with all elements -1, and reallocate discontinuous superpixels and superpixels with too small size to adjacent superpixels in a "Z"-shaped direction (from left to right, from top to bottom), and assign the traversed pixels to the corresponding labels until all points are traversed.

[0078] Step 3-2: Select nodes of the graph structure based on the superpixel segmentation results.

[0079] The center point of each cluster (superpixel block) processed by the SLIC algorithm can be used as a node

[0080] Step 3-3: Use the distance measurement between nodes to construct the adjacency matrix of the graph structure.

[0081] (1) For each center point (node) of each superpixel block in step 3-2, the Euclidean distance between it and other nodes is calculated as follows:

[0082]

[0083] Among them, Eij represents the Euclidean distance between the center points (nodes) of two superpixel blocks, and r', g', and b' represent the color value of each pixel in the three channels of the color space of the node.

[0084] (2) Use the k-NN algorithm based on the calculated Euclidean distance to find the k nearest neighbor nodes for each node and establish an edge between the node and these k nearest neighbor nodes.

[0085] (3) A two-dimensional adjacency matrix is ​​constructed based on the adjacent edge relationship of the graph structure. Its rows and columns correspond to each node in the graph. The elements in the matrix indicate whether there is an edge or connection between the nodes. If there is an edge between the nodes, the corresponding matrix element is set to 1, otherwise it is 0.

[0086] Step 3-4: Use the position and color information of the nodes to construct the feature matrix of the graph structure.

[0087] (1) Node location features: The coordinates of the center position of the superpixel block obtained after processing by the SLIC algorithm are used as the location features of the nodes in the graph structure.

[0088] (2) Node color feature: Calculate the average LAB value of all pixels in each superpixel block as the node color feature.

[0089] (3) Node fusion feature: The position feature and color feature of each node are merged to form a node fusion feature matrix.

[0090] Wherein, the classification learning in step 4 in the offline stage of the method includes the following steps:

[0091] Step 4-1: Use three GIN graph convolutional layers to aggregate neighbor node feature vectors to update node features, and use the ReLU activation function for nonlinear transformation after each GIN layer.

[0092] Step 4-2: Use a Graph Readout layer and select the global sum pooling method to aggregate all node information into a global feature vector representation of the entire graph, and add L2 regularization after graph pooling to prevent overfitting.

[0093] Step 4-3: Use an MLP multi-layer perceptron layer to perform nonlinear mapping on the aggregated feature vector, and add a Softmax layer after the MLP to achieve multi-classification.

[0094] The beneficial effects of the present invention are:

[0095] (1) The present invention adopts the method of removing singular points by using the local outlier factor (LOF), which takes into account the local density of the data and can effectively identify outliers in areas of different densities. It has good robustness to noise and non-uniformly distributed data, has relatively low computational complexity, and can quickly identify outliers.

[0096] (2) The present invention uses a method of converting time series data into a two-dimensional image using wavelet transform, which can provide time and frequency information at the same time, so that the local characteristics of the time series data in the time and frequency domain can be revealed, and the changes of the signal at different times and frequencies can be more intuitively reflected. It not only provides a richer data representation, but also enhances the interpretability and operability of the data.

[0097] (3) The present invention implements a method for constructing an image into a graph structure by superpixel segmentation based on the SLIC algorithm, which retains the color features of the image. The structuring of the image helps to capture the spatial relationship and high-level structure in the image, and the node selection method helps to improve the stability and robustness of the graph structure. At the same time, the SLIC algorithm is relatively simple, easy to implement, and has high computational efficiency.

[0098] (4) The present invention uses the GIN graph isomorphism network for classification learning to achieve indoor location recognition and positioning. It enhances the ability to distinguish graph structures, allowing the model to capture fine-grained differences in the graph, thereby improving the performance of graph-level classification tasks, and adopts a message-based mechanism, making it more efficient when processing large-scale graph data, which helps to achieve more accurate indoor positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments in conjunction with the accompanying drawings.

[0100] Figure 1 : Specific flow chart of the algorithm of the present invention;

[0101] Figure 2 : The collected CSI signal amplitude containing 60 subcarriers;

[0102] Figure 3 : The result of CSI signal amplitude after LOF preprocessing;

[0103] Figure 4 : The CSI signal amplitude at different locations is mapped by wavelet transform;

[0104] Figure 5 : The process of constructing the neighboring edge matrix in the graph structure;

[0105] Figure 6 : The process of constructing node feature matrix in graph structure;

[0106] Figure 7 : The graph neural network model framework used in the present invention. DETAILED DESCRIPTION

[0107] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0108] This experiment collected and measured the indoor environment of the 7th floor of the research building of Nanjing University of Posts and Telecommunications, and selected 35 reference position points (RPs), with each adjacent reference point spaced 0.6 meters apart. In the experiment, the present invention selected two channels, that is, using two transmitting antennas to transmit signals and using a computer terminal with one receiving antenna to receive signals, to form a CSI amplitude fingerprint containing 60 subcarriers, and each position point contains 1000 data packets.

[0109] Figure 2 The display shows multiple CSI signals collected from the same reference point, each of which consists of 60 subcarriers. During the collection process, due to various uncertain factors, very few CSI signals may be subject to large noise interference and be significantly different from other signals. Therefore, in order to improve signal quality, these affected signals need to be denoised or outlier processed.

[0110] The present invention uses the Local Outlier Factor (LOF) algorithm to detect outliers or outliers on the CSI amplitude containing 60 subcarriers and 1000 data packets. The core idea of ​​the LOF algorithm is to compare the local density of a data point with the local density of its neighbors, and identify whether a data point is an outlier by the local density deviation. The specific CSI amplitude outlier detection process is as follows:

[0111] For each subcarrier, calculate the distance from the CSI amplitude value to all other CSI amplitude values, find the CSI amplitude value closest to it, and calculate the LOF value. If the LOF value is larger, it is more abnormal, and vice versa, if it is smaller, it is more normal. Specifically, first calculate the j-th CSI amplitude value Amp under the i-th subcarrier j The k-neighbor distance to other amplitude values ​​is obtained as follows:

[0112] dist k (Amp j )=d(Amp j ,Amp p )

[0113] Among them, Amp p Indicates the CSI amplitude value closest to the jth CSI amplitude value k, d(Amp j ,Amp p ) represents the Euclidean distance from the jth CSI amplitude value to the pth CSI amplitude value. Then, Amp is calculated according to the following formula: j To Amp p The reachable distance:

[0114] reachdist k (Amp j ,Amp p )=max{dist k (Amp j ),d(Amp j ,Amp p )}

[0115] Then calculate Amp based on the reachable distance j The local reachability density is the inverse of the average reachable distance of all CSI amplitude values ​​in the k-neighborhood of the j-th CSI amplitude value. The specific formula is as follows:

[0116]

[0117] Among them, N k (j) represents Amp j Then calculate Amp j The local outlier factor is the ratio of the average local reachable density of all CSI amplitude values ​​in the k-neighborhood of the j-th CSI amplitude value to the local reachable density of the j-th CSI amplitude value itself. The specific formula is as follows:

[0118]

[0119] If Amp jIf the LOF value of the jth amplitude measurement value is much larger than 1, then the local density of the jth amplitude measurement value is much smaller than the average value of the local reachable density of all CSI amplitude values ​​of the subcarrier in the k neighborhood, and it can be determined as an abnormal point, otherwise it is a normal point.

[0120] Figure 3 The results of outlier detection and filtering are achieved by using the LOF algorithm based on the CSI amplitude data containing 1000 data packets and 60 subcarriers at the same reference point. As can be seen from the figure, by identifying and removing outliers through the LOF algorithm, the distribution of CSI amplitude data becomes more compact, and the data points are closer to the central trend of the data set, which improves the stability of data features and makes the changes of features smoother at different time points or under different conditions.

[0121] Next, the CSI signal after outliers are filtered out is normalized, and all values ​​are proportionally scaled to the interval [0, 1]. The normalization operation formula is as follows:

[0122]

[0123] Amp i Indicates the CSI amplitude value of the i-th subcarrier, Amp min Indicates the minimum value of the CSI amplitude, Amp max Indicates the maximum value of the CSI amplitude value. Then the collected CSI amplitude values ​​containing 60 subcarriers are merged to obtain a one-dimensional measurement data vector. The present invention uses the wavelet transform method in the time-frequency analysis method to convert the one-dimensional CSI amplitude sequence data into a two-dimensional time-frequency diagram.

[0124] The Morlet wavelet function is selected according to the fused one-dimensional CSI amplitude measurement value Amp, and the expression for calculating the wavelet transform coefficient is as follows:

[0125]

[0126] Where Amp represents the CSI amplitude measurement vector, It represents the wavelet function after scaling and translation. It is the daughter wavelet obtained by operating the mother wavelet ψ(t). a* represents the scale parameter, which controls the scaling of the wavelet function. The scale a* is usually inversely proportional to the frequency. b* represents the translation parameter, which controls the position of the wavelet function. By changing the size of b*, the signal can be analyzed at different time points.

[0127] According to the definition of wavelet transform, the specific encoding steps of the CSI signal amplitude Amp(t) are as follows:

[0128] Step 1 Determine the following parameters: Signal length Amp len , sampling frequency samplerate , mother wavelet function Morlet, center frequency sliding step cenfre step ;

[0129] Step 2 Calculate the maximum center frequency Set the current center frequency cenfre now , initialize the time-frequency matrix;

[0130] Step 3: According to the center frequency and wavelet function, the mother wavelet is scaled and translated in time and frequency to adapt to different scales of the signal. For each scaled and translated mother wavelet, it is convolved with the time series data to obtain the time distribution vector of the current frequency, and then the time-frequency matrix is ​​updated;

[0131] Step 4 determines whether the current center frequency is greater than the maximum center frequency. If so, output the time-frequency matrix; otherwise, update the current frequency cenfre now =cenfre now +cenfre step , then jump back to step 2.

[0132] Based on the above wavelet coefficients, a two-dimensional image is constructed. According to the above steps, the scaling scale a and translation parameter b are mapped to the two-dimensional plane corresponding to the frequency and time parameters respectively to form a time-frequency matrix, and finally the time-frequency diagram of the signal is obtained, in which the horizontal axis of the image represents time and the vertical axis represents frequency. At the same time, the colormap color mapping "viridis" in the matplotlib library is used to map the two-dimensional matrix values ​​to different color spaces. It is a continuous color gradient that starts from blue, gradually transitions to green, and finally fades to yellow. This color mapping maps the minimum value to blue, the middle value to green, and the maximum value to yellow, and provides a smooth transition between blue, green, and yellow, so that the details and levels of the data can be carefully displayed. Figure 4 The CSI amplitudes at three different reference points are composed using the wavelet transform method in this paper. As can be seen from the figure, the composition results corresponding to the same reference point are quite similar, while the composition results corresponding to different reference points are quite different.

[0133] Next, the present invention uses the SLIC (Simple Linear Iterative Clustering) algorithm to perform superpixel segmentation on the CSI time-frequency diagram obtained by wavelet transform. The specific SLIC algorithm implementation steps are as follows:

[0134] (1) Initialize the center point (cluster center): Convert the time-frequency graph obtained in step 2 from RGB space to LAB space. First, divide each channel value in the RGB space by 255 to convert it to a decimal between 0 and 1, and obtain R*=R / 255, G*=G / 255, B*=B / 255, where R, G, and B are the original color components. Secondly, perform inverse gamma correction on each RGB channel value, and f(x) is the inverse gamma function, and obtain r*=f(R*), g*=f(G*), and b*=f(B*). Then convert the RGB color from the RGB color space to the XYZ color space using the following matrix multiplication: [X,Y,Z]=[M]*[r*,g*,b*], where M is a 3×3 matrix:

[0135]

[0136] Next, convert the XYZ color from the XYZ color space to the LAB color space. Calculate using the following formula:

[0137]

[0138] L'=116*f Y -16,A'=500×(f X -f Y ),B'=200×(f Y -f Z )

[0139] Where X n ,Y n ,Z n is the standard value of the D65 reference white point, f X ,f Y ,f Z is the value of X, Y, Z after inverse gamma correction, L', A', B' are the final LAB color space values. The image of size N (the number of pixels is N) is divided into K super pixel blocks, and the range size of each super pixel block contains pixels, let For each pixel block length value, initialize the center point of each pixel block

[0140] (2) Gradient calculation and center point adjustment: Use the differential method to calculate the gradient and readjust the center point. Traverse the 8-region pixel points of the center point of the initial pixel block, calculate the pixel point with the minimum gradient value, and use it as the new center point. The formula for differential calculation of the gradient is as follows:

[0141] Gradient(x,y)=dx(i,j)+dy(i,j);

[0142] dx(i,j)=I(i+1,j)-I(i,j);

[0143] dy(i,j)=I(i,j+1)-I(i,j);

[0144] Among them, (x, y) represents the initial pixel center coordinates, (i, j) is used to represent the position index of the pixel traversed during the gradient calculation process, dx(i, j) represents the gradient value along the x-axis at the pixel point (i, j), dy(i, j) represents the gradient value along the y-axis at the pixel point (i, j), and I(i, j) represents the weighted average grayscale value of the three RGB channels of the image at the pixel point (i, j).

[0145] (3) Pixel clustering and cluster center iteration: Traverse the pixels in the 2S*2S neighborhood of the center of each superpixel block and calculate the distance to the center of each superpixel block. Use the K-means clustering algorithm to classify the pixels and use the transformed Euclidean distance formula to measure the distance. The distance measurement includes color distance and spatial distance. The formula is as follows:

[0146]

[0147] Among them, l i ,a i ,b i ,x i ,y i Represents the LAB color space value and position of the center point of each superpixel block, l j ,a j ,b j ,x j ,y j Represents the LAB color space value and position of the pixel in the 2S*2S neighborhood, d c Represents the color distance, d s Represents the spatial distance, N s is the maximum spatial distance within a cluster, N c is the maximum color distance within the cluster, take N c =m, the fixed constant m (value range [1,40], generally 10) is the maximum possible distance in the LAB space. The final distance metric D' is as follows:

[0148]

[0149] According to the distance from the pixel point in the 2S*2S neighborhood to the center of each pixel block, the pixel is divided into the closest cluster, and all the pixels in the new cluster are averaged to obtain the new cluster center. Finally, iterate again according to the above steps until the error converges.

[0150] (4) Enhanced connectivity: Connectivity control is performed to solve the problems of multiple connectivity, too small superpixel size, and single superpixel being cut into multiple discontinuous superpixels in the iteratively completed clustering. The main idea is to create a new label table with all elements -1, and reallocate discontinuous superpixels and superpixels with too small size to adjacent superpixels in a "Z"-shaped direction (from left to right, from top to bottom), and assign the traversed pixels to the corresponding labels until all points are traversed.

[0151] In the clustering process of the SLIC algorithm, the present invention uses the center point of each cluster (superpixel block) as a node. These center points are the results after the iterative convergence of the clustering algorithm and also represent the position and characteristics of each superpixel block.

[0152] After the node selection is completed, the distance measurement between nodes is used to construct the adjacency matrix of the graph structure. The Euclidean distance between the center point (node) of each superpixel block and other nodes is calculated as follows:

[0153]

[0154] Among them, Eij represents the Euclidean distance between the center points (nodes) of two superpixel blocks, and r', g', and b' respectively represent the color values ​​of each pixel in the three channels of the node's color space. According to the calculated Euclidean distance, the k-NN algorithm is used to find the k nearest neighbor nodes for each node, and an edge is established between the node and the k nearest neighbor nodes. A two-dimensional adjacency matrix is ​​constructed based on the neighbor-edge relationship of the graph structure, and its rows and columns correspond to each node in the graph, and the elements in the matrix indicate whether there is an edge or connection between the nodes. If there is an edge between the nodes, the corresponding matrix element is set to 1, otherwise it is 0. The position and color information of the node are further used to construct the feature matrix of the graph structure. For each superpixel block, the center position is the node coordinate feature, and the color feature information of the node is obtained by calculating the average value of the LAB values ​​of all pixels in each superpixel block. Specifically, the node feature matrix F in the graph structure can be expressed by the following formula:

[0155] F=(f1,f2,...,f n ) T

[0156]

[0157] Among them, f i represents the node feature vector of the i-th superpixel, N i represents the total number of pixels in superpixel i, (L j ,A j ,B j) represents the LAB color value of the jth pixel, (X j ,Y j ) represents the position coordinates of the jth pixel in the image. Figure 6 The specific construction method of the node feature matrix is ​​to fuse the node position features and color features into a five-dimensional feature vector for subsequent network training.

[0158] Finally, the present invention uses a model based on the GIN graph isomorphism network to perform classification learning of graph structures. This model effectively captures and represents the topological structure of the graph through a unique node feature aggregation mechanism. GIN enhances the expressive power of graph embedding through its unique aggregation mechanism, enabling it to show higher performance and potential in tasks such as graph classification. Figure 7 The proposed GIN network architecture consists of three GIN layers, a Readout layer and an MLP layer. The input of the network architecture is the CSI amplitude information graph structure representation and the corresponding node features constructed using superpixel segmentation technology.

[0159] First, we use the GIN graph convolution layer to aggregate the neighbor node feature vectors to update the node features. The superposition of multiple layers of graph convolution can more effectively capture the local structural information in the graph, and use the ReLU activation function for nonlinear transformation.

[0160] Next, for the graph classification task, we construct the embedding of the entire graph through the embedding of the nodes, that is, adding a Graph Readout operation, which is regarded as a graph pooling or graph coarsening process, mainly through global pooling or aggregation technology to integrate the updated features of all nodes in the graph into a single graph-level feature representation. Specifically, we use the global sum pooling method to summarize the feature vectors of all nodes, and then generate a global feature vector that can represent the entire graph, namely the graph embedding. This graph embedding captures the key information of all nodes in the graph and provides a comprehensive feature representation for the graph classification task. The READOUT function in the graph isomorphic neural network is the SUM function, which obtains the graph features of the iteration by summing the features of all nodes obtained in each iteration, and then concatenates the graph features of each iteration to obtain the final graph features:

[0161]

[0162] Among them, t' represents the number of iterations, v represents the current node, and h G represents the characterization vector of each graph G, h vRepresents the representation vector of each node v. The reason why we concatenate the graph features of each iteration instead of adding them is that the representations of nodes in different layers belong to different feature spaces. Through the readout operation, the number of nodes involved in graph classification can be reduced, thereby reducing the number of parameters and redundant information that the model needs to learn, which helps to reduce the computational burden of the model and enables subsequent multi-layer perceptron MLP layers to be trained and inferred more efficiently, thereby improving classification accuracy. To prevent overfitting, adding L2 regularization after graph pooling helps improve the generalization ability of the model.

[0163] Then, we aggregate the features of each node with the features of the adjacent nodes to obtain the graph-level features, which are input into the multi-layer perceptron MLP layer, and use MLP to perform nonlinear mapping on the aggregated feature vector. The specific process is as follows:

[0164]

[0165] in, represents the feature vector of node v at the t'th iteration, v represents the current node, u represents the adjacent node, MLP is a multi-layer perceptron, (t') is a learnable parameter, and N(v) is the set of neighbor nodes of node v. In addition, a Softmax layer is added after the multi-layer perceptron MLP for multi-classification problems, which normalizes the output of the MLP to obtain the final classification result.

[0166] The GIN network of the present invention demonstrates excellent performance by learning the global feature representation of the graph, highlights its potential and value in analyzing complex graph structures, and improves its accuracy in indoor positioning.

Claims

1. A channel state information indoor positioning method based on graph isomorphic network, characterized in that: The method comprises the following steps:

1. Offline stage Step 1: Data preprocessing, Preprocess the received channel state information (CSI) amplitude value for subsequent CSI image fingerprint construction. Step 2: CSI image construction, The pre-processed CSI amplitude measurement value is transformed into a CSI image using the wavelet transform method. Step 3: Construction of the graph structure of the CSI image. Step 3-1: Use the SLIC algorithm to implement superpixel segmentation of the CSI image. Step 3-2: Select nodes of the graph structure based on the superpixel segmentation results. Step 3-3: Use the distance measurement between nodes to construct the adjacency matrix of the graph structure. Step 3-4: Use the position and color information of the nodes to construct the feature matrix of the graph structure. Step 4: Classification learning; Build a graph isomorphism network (GIN) for classification learning and obtain a location estimation model; (II) Online stage Step 1: Data preprocessing, The obtained CSI amplitude measurement value is preprocessed using the method of step 1 in the offline phase. Step 2: CSI image construction, Using the method of step 2 in the offline phase, the CSI image is constructed using the preprocessed CSI amplitude measurements. Step 3: Construction of the graph structure of the CSI image, Using the method in step 3 of the offline phase, the graph structure of the CSI image is obtained. Step 4: Position estimation, The location estimation model obtained in step 4 of the offline phase is used to complete the location estimation.

2. The channel state information indoor positioning method based on graph isomorphic network according to claim 1, characterized in that: In the offline phase, step 1 data preprocessing includes the following steps: The basic concepts involved are as follows: (1) The distance between two CSI amplitude values d(Amp j ,Amp p ): represents the distance from the jth CSI amplitude value to the pth CSI amplitude value, (2) kth distance, dist k (Amp j ): The distance between the k-th closest CSI amplitude value and the j-th CSI amplitude value (from near to far) is called the k-neighborhood distance of the j-th CSI amplitude value. (3) kth distance neighborhood, N k (j): The k-th distance neighborhood of the j-th CSI amplitude value, that is, all CSI amplitude values ​​within the k-th distance, including the k-th distance, (4) Reachable distance, reachdist k (Amp j ,Amp p ): Select the largest of the direct distance between two CSI amplitude values ​​and the k-th distance from the j-th CSI amplitude value as the reachable distance from the j-th CSI amplitude value. If the j-th CSI amplitude value is outside the k-neighboring distance of the p-th CSI amplitude value, then the reachable distance is the direct distance between the two CSI amplitude values. If the j-th CSI amplitude value is within the k-neighboring distance of the p-th CSI amplitude value, then the reachable distance is the k-th distance. (5) Local reachability density, lrd k (j): represents the inverse of the average reachable distance of the j-th CSI amplitude value. The average reachable distance is the sum of the distances in its k-neighborhood divided by the number of all CSI amplitude value measurements in the neighborhood. (6) Local outlier factor, LOF k (j): the ratio of the average local reachable density of all CSI amplitude values ​​in the k-th distance neighborhood of the j-th CSI amplitude value to the local reachable density of the j-th CSI amplitude value, Step 1-2: Perform a local outlier factor (LOF) test on each subcarrier in the CSI amplitude measurement. For each subcarrier, calculate the distance from the CSI amplitude value to all other CSI amplitude values, find the CSI amplitude value closest to it, and calculate the LOF value. If the LOF value is larger, it means it is more abnormal. On the contrary, if it is smaller, it means it is more normal. First, calculate the j-th CSI amplitude value Amp under the i-th subcarrier. j The k-neighbor distance to other amplitude values ​​is obtained as follows: dist k (Amp j )=d(Amp j ,Amp p ), Among them, Amp p Indicates the CSI amplitude value closest to the jth CSI amplitude value k, d(Amp j ,Amp p ) represents the Euclidean distance from the jth CSI amplitude value to the pth CSI amplitude value. Secondly, Amp is calculated according to the following formula: j To Amp p The reachable distance: reachdist k (Amp j ,Amp p )=max{dist k (Amp j ),d(Amp j ,Amp p )}, Then calculate Amp based on the reachable distance j The local reachability density is the inverse of the average reachable distance of all CSI amplitude values ​​in the k-neighborhood of the j-th CSI amplitude value. The specific formula is as follows: Among them, N k (j) represents Amp j The k-distance neighborhood of Amp is then calculated j The local outlier factor is the average of the local reachable densities of all CSI amplitude values ​​in the k-neighborhood of the j-th CSI amplitude value. The local reachable density lrd of the j-th CSI amplitude value itself k The specific formula is as follows: If Amp j If the LOF value of the jth amplitude measurement value is much greater than 1, then the local density of the jth amplitude measurement value is much smaller than the average local reachable density of all CSI amplitude values ​​of the subcarrier in the k neighborhood, and it can be determined as an abnormal point, otherwise it is a normal point. Step 1-3: Filter out the CSI amplitude values ​​detected as abnormal points in step 1-2. Step 1-4: Normalize the CSI signal after outliers are filtered out, and scale all values ​​to the interval [0, 1]. The normalization operation formula is as follows: Amp i Indicates the CSI amplitude value of the i-th subcarrier, Amp min Indicates the minimum value of the CSI amplitude, Amp max Indicates the maximum value of the CSI amplitude.

3. The channel state information indoor positioning method based on graph isomorphic network according to claim 1, characterized in that: In the offline phase, step 2 CSI image construction includes the following steps: Step 2-1: Select the Morlet wavelet function and calculate the expression of the wavelet transform coefficient as follows: Where Amp represents the CSI amplitude measurement vector, It represents the wavelet function after scaling and translation. It is the daughter wavelet obtained by operating the mother wavelet ψ(t). a* represents the scale parameter, which controls the scaling of the wavelet function. The scale a* is usually inversely proportional to the frequency. b* represents the translation parameter, which controls the position of the wavelet function. By changing the size of b*, the signal can be analyzed at different time points. Step 2-2: Construct a two-dimensional image. According to the scaling scale a* and translation parameter b* in step 2-1, the corresponding frequency and time parameters are mapped to the two-dimensional plane to form a time-frequency matrix. Finally, the time-frequency diagram of the signal is obtained, where the horizontal axis of the image represents time and the vertical axis represents frequency. Step 2-3: Use the colormap "viridis" in the matplotlib library to map the two-dimensional matrix values ​​to different color spaces. It is a continuous color gradient that starts from blue, gradually transitions to green, and finally gradients to yellow. This color mapping maps the minimum value to blue, the middle value to green, and the maximum value to yellow, and provides a smooth transition between blue, green, and yellow, thereby meticulously showing the details and levels of the data.

4. The channel state information indoor positioning method based on graph isomorphic network according to claim 1, characterized in that: In the offline phase, step 3 of CSI graph structure construction includes the following steps: Step 3-1: Use the SLIC algorithm to implement superpixel segmentation of the CSI image. (1) Initialize the center point (cluster center): The time-frequency graph obtained by the offline step 2 is converted from RGB space to LAB space, and the image of size N (the number of pixels is N) is divided into K superpixel blocks. The size of each superpixel block contains pixels, let For each pixel block length value, initialize the center point of each pixel block (2) Gradient calculation and center point adjustment: Gradient calculation is performed using the differential method. The center point is readjusted. The eight pixel areas of the center point of the initial pixel block are traversed to calculate the pixel point with the minimum gradient value and use it as the new center point. The formula for differential gradient calculation is as follows: Gradient(x,y)=dx(i,j)+dy(i,j); dx(i,j)=I(i+1,j)-I(i,j); dy(i,j)=I(i,j+1)-I(i,j); Among them, (x, y) represents the initial pixel center coordinates, (i, j) is used to represent the position index of the pixel traversed during the gradient calculation process, dx(i, j) represents the gradient value along the x-axis at the pixel point (i, j), dy(i, j) represents the gradient value along the y-axis at the pixel point (i, j), and I(i, j) represents the weighted average grayscale value of the three RGB channels of the image at the pixel point (i, j). (3) Pixel clustering and cluster center iteration: Traverse the pixels in the 2S*2S neighborhood of the center of each superpixel block, calculate the distance from the pixel to the center of each superpixel block, classify the pixels with the help of the K-means clustering algorithm, and measure the distance using the transformed Euclidean distance formula. The distance measurement includes color distance and spatial distance. The formula is as follows: Among them, l i ,a i ,b i ,x i ,y i Represents the LAB color space value and position of the center point of each superpixel block, l j ,a j ,b j ,x j ,y j Represents the LAB color space value and position of the pixel in the 2S*2S neighborhood, d c Represents the color distance, d s Represents the spatial distance, N s is the maximum spatial distance within a cluster, N c is the maximum color distance within the cluster, take N c =m, the fixed constant m is the maximum distance of the LAB space, and the final distance metric D' is as follows: According to the distance from the pixel point in the 2S*2S neighborhood to the center of each pixel block, the pixels are divided into the closest clusters, and all the pixels in the new cluster are averaged to obtain the new cluster center. Finally, the above steps are repeated until the error converges. (4) Enhanced connectivity: Connectivity is controlled to solve the problems of multiple connectivity, small superpixel size, and single superpixel being cut into multiple discontinuous superpixels in the iteratively completed clustering. The main idea is to create a new label table with all elements -1. Discontinuous superpixels and superpixels with small size are reallocated to adjacent superpixels in a "Z"-shaped direction, from left to right and from top to bottom. The traversed pixels are assigned to the corresponding labels until all points are traversed. Step 3-2: Select nodes of the graph structure based on the superpixel segmentation results. The center point of each cluster (superpixel block) processed by the SLIC algorithm is used as a node. Step 3-3: Use the distance measurement between nodes to construct the adjacency matrix of the graph structure. (1) For each superpixel block in step 3-2, the Euclidean distance between the center point (node) and other nodes is calculated as follows: Among them, E ij represents the Euclidean distance between the center points (nodes) of two superpixel blocks, r', g', b' respectively represent the color value of each pixel in the three channels of the RGB color space, (2) Use the k-NN algorithm based on the calculated Euclidean distance to find the k nearest neighbor nodes for each node, and establish an edge between the node and these k nearest neighbor nodes. (3) A two-dimensional adjacency matrix is ​​constructed based on the adjacent edge relationship of the graph structure. Its rows and columns correspond to each node in the graph. The elements in the matrix indicate whether there is an edge or connection between the nodes. If there is an edge between the nodes, the corresponding matrix element is set to 1, otherwise it is 0. Step 3-4: Use the position and color information of the nodes to construct the feature matrix of the graph structure. (1) Node location features: The coordinates of the center position of the superpixel block obtained after SLIC algorithm processing are used as the node location features in the graph structure. (2) Node color feature: Calculate the average LAB value of all pixels in each superpixel block as the node color feature. (3) Node fusion feature: The position feature and color feature of each node are merged to form a node fusion feature matrix.

5. The channel state information indoor positioning method based on graph isomorphic network according to claim 1, characterized in that: In the offline phase, step 4 classification learning includes the following steps: Step 4-1: Use three GIN graph convolutional layers to aggregate neighbor node feature vectors to update node features, and use the ReLU activation function for nonlinear transformation after each GIN layer. Step 4-2: Use a Graph Readout layer and select the global sum pooling method to aggregate all node information into a global feature vector representation of the entire graph, and add L2 regularization after graph pooling to prevent overfitting. Step 4-3: Use an MLP multi-layer perceptron layer to perform nonlinear mapping on the aggregated feature vector, and add a Softmax layer after the MLP to achieve multi-classification.

Images