RIS-assisted wireless fingerprint positioning method based on deep learning

Abstract

The present invention belongs to the field of communication positioning and relates to a RIS-assisted wireless fingerprint positioning method based on deep learning. The method comprises adjusting the load impedance value of the RIS reflector unit to obtain multiple RIS configurations and collect RSSI fingerprint maps; performing feature selection on the collected RSSI fingerprint maps using a feature selection algorithm, and training a deep learning model using a feature subset of estimated points; inputting the feature subset of the points to be estimated into the trained deep learning model to predict the initial positions of the points to be estimated; constructing Thiessen polygons using these as discrete points to determine a positioning area; calculating the average deviation value within the positioning area, and calculating the positioning position of the points to be estimated using an improved weighted K-nearest neighbor method. The present invention can better learn the features between RSSI fingerprint data, more accurately predicting user location coordinates, thereby improving positioning efficiency, positioning performance, and positioning accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of communication positioning, and in particular relates to a RIS-assisted wireless fingerprint positioning method based on deep learning. Background Art

[0002] In recent years, with the gradual development of wireless communications, the demand for location-based services has increased significantly, and related positioning services have demonstrated tremendous commercial value. Wireless fingerprint positioning (WFL) is the most commonly used positioning application. This technology is well-researched, widely deployed, and tested. Traditional WFL methods first establish a fingerprint database of user locations offline. Then, in the online phase, real-time RSSI measurements are compared with the fingerprint database to estimate the user's location. To improve WFL accuracy, multiple access points (APs) must be deployed to increase fingerprint diversity, which in turn increases infrastructure deployment costs and the cost of training data collection and processing. These issues are often addressed by using additional data points obtained from existing Wi-Fi infrastructure or ray tracers. However, high computational costs and unstable positioning accuracy remain pressing challenges in WFL.

[0003] Reconfigurable smart surface (RIS) technology introduces the concept of an "intelligent radio environment." This means that by designing the size, load impedance, and shape of RIS reflective elements, the amplitude and phase of the incident electromagnetic wave can be modified, enabling the reconfiguration of the wireless propagation environment. This is also the cornerstone of the path toward sixth-generation (6G) mobile communications. Therefore, utilizing RIS to improve the performance of wireless communications is an important and promising research direction, and many scholars have conducted extensive research on this topic, such as reducing multipath fading, resolving blocking issues in non-line-of-sight communications, improving multi-user downlink rates, enhancing MIMO diversity and throughput gain, maximizing wireless power transmission, and improving energy efficiency. In wireless localization (WFL), utilizing RIS can avoid the overhead of deploying multiple access points and also provide good positioning performance, but related work is limited. Del Hougne et al. proposed a scheme that leverages the additional configuration freedom provided by RIS to map fingerprints into received signals for indoor positioning and experimentally validated this concept. He et al. used a path loss (LOS) model to study the theoretical performance limitations of a single-anchor multiple-input, multiple-output (MIMO) system. They also investigated the impact of the number of RIS reflective elements on performance and proposed an adaptive phase shifter based on a hierarchical codebook. Wymeersch et al. analyzed the RIS-assisted downlink positioning problem from the perspective of the Fisher Information Matrix (FIM), and based on this, selected the optimal RIS configuration to minimize user location uncertainty. Ly et al. studied using RIS to improve wireless fingerprint positioning accuracy. They also proposed using existing machine learning algorithms to perform feature selection on the raw fingerprint dataset to reduce computational complexity. They then used the K-nearest neighbor (KNN) algorithm, a neural network (NN) algorithm, and a random forest (RF) algorithm to classify the processed dataset and ultimately determine the user location. However, this solution suffers from low positioning accuracy and limited flexibility when operating in demanding environments. Summary of the Invention

[0004] To address these issues, this paper proposes a deep learning-based RIS-assisted wireless fingerprint positioning method. During the positioning phase, this method leverages the nonlinear learning capabilities of deep learning algorithms to train the collected RSSI fingerprint map to achieve an initial prediction of the user's location. The predicted location points are then used as discrete points to construct a Thiessen polygon region. Within the positioning region, the average deviation is further calculated to improve the weighted K-nearest neighbor algorithm, ultimately achieving precise positioning.

[0005] The present invention provides a RIS-assisted wireless fingerprint positioning method based on deep learning, the method comprising:

[0006] By adjusting the load impedance value of the RIS reflection unit, a variety of RIS configurations are obtained, thereby collecting multiple RSSI fingerprint maps corresponding to each user, including the RSSI fingerprint map of the estimated point and the RSSI fingerprint map of the point to be estimated;

[0007] The feature selection algorithm is used to select features from the collected RSSI fingerprint map to obtain feature subsets containing multiple RIS configurations, including feature subsets of estimated points and feature subsets of points to be estimated.

[0008] Using the feature subset of the estimated points to train a deep learning model, and performing prediction and classification on the feature subset of the estimated points;

[0009] Input the feature subset of the point to be estimated into the trained deep learning model to predict the initial positioning position of the point to be estimated;

[0010] Using the initial positioning position of the point to be estimated as a discrete point to construct a Thiessen polygon, and using the Thiessen polygon to determine the positioning area;

[0011] The average deviation value is calculated in the positioning area, and the accurate positioning position of the point to be estimated is calculated using the improved weighted K-nearest neighbor method.

[0012] Beneficial effects of the present invention:

[0013] 1) In the positioning stage, the present invention introduces a deep learning algorithm. Since it can perform nonlinear learning, it can better learn the features between RSSI fingerprint data and predict the user's location coordinates more accurately.

[0014] 2) The present invention introduces Thiessen polygons to dynamically divide the positioning area, thereby improving the positioning efficiency.

[0015] 3) The present invention introduces the average deviation value when adjusting the position coordinates, further improves the WKNN algorithm, improves the positioning performance, and makes the positioning accuracy more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic diagram of a communication system model according to an embodiment of the present invention;

[0017] Figure 2 is a schematic diagram of an end-to-end system model based on impedance change according to an embodiment of the present invention;

[0018] Figure 3 Schematic diagram of different effects of RIS on incident signals according to an embodiment of the present invention;

[0019] Figure 4 This is a flow chart of a RIS-assisted fingerprint positioning method based on deep learning according to an embodiment of the present invention;

[0020] Figure 5 This is a structural diagram of the CNN model used in an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0022] Figure 1 Schematic diagram of a communication system model according to an embodiment of the present invention; Figure 1 As shown, it includes a single-antenna base station (BS), a reconfigurable intelligent surface (RIS), and a single-antenna user equipment (UE), and the base station can control the configuration of the RIS through a controller. The RIS is a two-dimensional plane composed of a large number of super atoms, on which M low-cost, passive reflection units are integrated. Due to hardware limitations, the complex value (including amplitude and phase shift) of each reflection unit is quantized into N discrete phase values ​​ranging from 0 to 2π. Therefore, the RIS may have D=N M Each RIS configuration will produce a slightly different fingerprint map (radio map). However, this is a very large number and there will be a lot of redundancy, so feature selection is required to screen out Q (Q < < D) RIS configurations to reduce computational complexity and improve positioning accuracy.

[0023] In order to accurately simulate the received signal strength value (RSSI) of UE under different RIS configurations, an end-to-end (E2E) model based on impedance change is adopted, such as Figure 2 As shown. The signal transmission between the base station and the user can be expressed as:

[0024] V BS =H E2E V UE (1)

[0025] Among them, V BS Represents the input of the transmitter, V UE Indicates the output of the receiving end. E2E Represents the channel transfer function between the base station and the user. Through order reduction processing, we can get:

[0026] H E2E=y0(H BU -H RU Ψ RIS H BR ) (2)

[0027] Among them, y0 represents the mismatch factor between the transmitter and the receiver, H BR represents the channel gain between the base station and RIS, H RU Represents the channel gain between the user and the RIS. RIS is a matrix of rank M, representing the configuration state of RIS, which can be expressed as:

[0028] Ψ RIS =(A SS +A RIS ) -1 (3)

[0029] Among them, A SS A is a full-rank matrix that represents the self-impedance (elements on the diagonal of the matrix) and mutual impedance (elements on the off-diagonal of the matrix) of the RIS reflector unit when no load is connected to the terminal of the element. RIS is a diagonal matrix containing the load impedance values ​​of M RIS reflection units. It is worth noting that the BS can control the amplitude and phase shift of the RIS elements by setting the appropriate bias voltage and changing the resistance load of the elements through the controller. Therefore, in practice, the reflection coefficient of each unit can be adjusted, and the different effects of RIS on the incident electromagnetic wave are as follows: Figure 3 As shown, including reflection, beamforming, refraction, etc.

[0030] Basic positioning principle: When a user sends a wireless fingerprint positioning request, the base station will periodically send Q wireless signals every t (t = 100ms) milliseconds. At the same time, it will also reset the load impedance of the RIS element to configure the RIS, that is, the qth transmission signal corresponds to the qth RIS configuration (1≤q≤Q). The user's location p Unknown, needs to be estimated. The user receives Q signals and calculates the received signal strength value (RSSI) R(p), then:

[0031] R(p)=[R1(p),R2(p),...,R Q (p)]+[E1,E2,...,E Q ] (4)

[0032] Among them, R k and E k They represent the noise-free part and the noise part of RSSI respectively, k∈{1,2,...,Q}, E represents the mean is 0, and the variance is σ 2Then the real-time measured RSSI fingerprint map value R(p) is compared with the RSSI fingerprint map value in the wireless fingerprint database. For comparison, where:

[0033]

[0034] in, and They represent the noise-free part and the noise part of the kth RSSI in the lth user sample in the wireless fingerprint database, respectively. E represents the mean value of 0 and the variance is σ 2 Gaussian white noise. l∈{1,2,...,L}, L represents the number of RSSI fingerprint map samples of the user, that is, the number of sample locations of the user.

[0035] Finally, by minimizing R(p) and The difference between the two finds the most likely location of the user l * :

[0036]

[0037] Many existing algorithms can be used for comparison and matching, such as KNN (K-Nearest-Neighbors), Bayesian Classification, AdaBoost, and Support Vector Machines (SVM). The KNN algorithm is the most classic, calculating the position of a measurement point by selecting the K nearest neighbors and taking a weighted average. However, this method is inefficient. When the environment is demanding, traditional machine learning algorithms are ineffective in training data, lack flexibility, and are computationally complex, resulting in poor positioning accuracy.

[0038] The positioning error can be expressed as:

[0039]

[0040] Among them, p is the user's real location, is the estimated location of the user obtained using the wireless fingerprint positioning algorithm, l * ∈{1,2,...,L}. Average all possible positions of p∈V to get the absolute expected error:

[0041]

[0042] Converted to root mean square error (RMS):

[0043]

[0044] From equations (7) to (9), it can be seen that the positioning error is related to the user position p, the number of user samples L, and the noise power σ 2 and the RIS configuration number Q. Therefore, the performance and accuracy of RIS-assisted WFL depend on the fingerprint algorithm used. Although WFL algorithms have been extensively studied by many scholars, the reconfigurable nature of RIS introduces many new possibilities for communication systems. Finding a more suitable fingerprint positioning algorithm remains a serious problem.

[0045] Based on the above analysis, Figure 4 This is a flow chart of the RIS-assisted fingerprint positioning method based on deep learning according to an embodiment of the present invention. Figure 4 As shown in the figure, the method mainly includes two stages: data processing and positioning estimation. First, by adjusting the load impedance value of the RIS reflector unit, D configurations are obtained, thereby collecting D RSSI fingerprint maps, which are then saved as an RSSI fingerprint database; second, each RIS configuration is used as a fingerprint feature, and the original data is selected using an existing machine learning algorithm to obtain a feature subset containing Q configurations; finally, a deep learning algorithm is used to predict and classify the feature subset, and the predicted results are combined with the Thiessen polygon method to further improve the positioning accuracy and determine the positioning area; finally, in order to obtain the precise position of the point to be measured, the average deviation value is calculated within the positioning area, thereby improving the weighted K nearest neighbor algorithm and calculating the positioning position of the point to be estimated.

[0046] Specifically, a RIS-assisted wireless fingerprint positioning method based on deep learning includes:

[0047] 101. By adjusting the load impedance value of the RIS reflection unit, a variety of RIS configurations are obtained, thereby collecting multiple RSSI fingerprint maps corresponding to each user, including RSSI fingerprint maps of estimated points and RSSI fingerprint maps of points to be estimated;

[0048] In an embodiment of the present invention, it is necessary to collect the RSSI fingerprint map of each user, wherein the position coordinates of the RSSI fingerprint map of the estimated point in the RSSI fingerprint map can be marked by a person skilled in the art. In some embodiments, the sampling area can also be gridded, and part of the RSSI fingerprint map data can be collected in each grid area, and the grid code is used as a label; for example, if the positioning area is divided into 100 grids, then the real labels used are 1 to 100, and each number represents a fixed grid area. The label number of the grid area can be used as the known positioning position of the estimated point. The position coordinates of the RSSI fingerprint map of the point to be estimated are unknown, and need to be predicted and estimated through subsequent steps to achieve the positioning position prediction of the point to be estimated.

[0049] 102. Perform feature selection on the collected RSSI fingerprint map using a feature selection algorithm to obtain feature subsets containing multiple RIS configurations, including feature subsets of estimated points and feature subsets of points to be estimated;

[0050] In this embodiment of the present invention, to achieve higher positioning accuracy and reduce computational complexity, it is necessary to utilize existing feature selection algorithms to perform feature selection on the original dataset, thereby obtaining Q (Q<<D) RIS configuration subsets. Because the optimal feature subset is dependent on heuristics and specific biases, the present invention employs a wrapper algorithm for feature selection to improve accuracy. Among these wrapper methods, the gene selection algorithm is the most practical and effective. The specific search process is as follows.

[0051] 1) Individual initialization: Generate a number of D-bit binary-coded initial groups randomly, where 1 indicates the selection of the corresponding RIS configuration and 0 indicates no selection.

[0052] 2) Fitness function: In order to minimize the positioning error while ensuring that the number of selected configurations does not exceed Q, the fitness function is defined as:

[0053]

[0054] Among them, Per represents the individual in the population, represents the positioning error. f×max(0,|Per|1-Q) is the penalty value, where f is a positive constant and |Per|1 is the number of selected RIS configurations. The principle of the genetic algorithm is to select the individual with the minimum fitness. If the number of selected RIS configurations is less than or equal to Q, the penalty value is 0.

[0055] 3) Feature selection: Using the elite selection operator, some of the best individuals in the previous generation are brought into the next generation.

[0056] 4) Feature crossover: Generate new individuals through uniform crossover to ensure the stability of the population and evolve towards the optimal solution.

[0057] 5) Feature variation: To prevent individual variation, the variation probability is set low enough so that good enough individuals are inherited from the previous generation.

[0058] 6) Feature termination: When the number of generations reaches the threshold or the fitness value remains unchanged, the feature selection process is terminated.

[0059] In a preferred embodiment of the present invention, to improve the diversity of the feature subset population, the original genetic algorithm's initial population is randomly selected from the original RSSI fingerprint map. In this embodiment of the present invention, all collected RSSI fingerprint maps can be preprocessed using a conventional recursive feature elimination algorithm to screen out some feature subsets. The screened feature subsets are used as part of the genetic algorithm's initial population, while the remaining part is randomly generated. Compared with traditional genetic algorithms, this can increase the diversity of the initial population while reducing the complexity of the genetic algorithm.

[0060] It is understandable that in the embodiment of the present invention, it is necessary to perform feature selection on the RSSI fingerprint map of the estimated point and the RSSI fingerprint map of the point to be estimated respectively. This can reduce the complexity of the model input, eliminate RIS configurations that are not related to the prediction, and thus improve the model prediction accuracy.

[0061] 103. Training a deep learning model using the feature subset of the estimated points, and performing prediction classification on the feature subset of the estimated points;

[0062] In the embodiment of the present invention, a deep learning model based on a convolutional neural network (CNN) model is selected to quickly locate the initial positioning point of the user to be estimated, laying the foundation for further precise positioning. The structure is as follows: Figure 5 Therefore, the input of the neural network is the data of the RSSI fingerprint map, and the output is the initial positioning position of the user's estimated point, that is, the predicted area label.

[0063] In step 102, this embodiment has performed feature selection on the RSSI fingerprint map of the estimated point, and deleted irrelevant features and redundant features in the RSSI fingerprint map of the estimated point as a training set sample, thereby improving the speed of model training and classification effect.

[0064] Specifically, in this embodiment, the training set samples are used to perform multiple rounds of training on the deep learning model to obtain a reliable convolutional neural network model, such as Figure 5As shown, the convolution layer is composed of several convolution units, which use convolution kernels for local perception and extract features from the input data after repeated convolution operations. The ReLU (Rectified Linear Unit) activation function is used between each hidden layer to prevent gradient disappearance and nonlinear problems between data. If the features obtained are learned directly after the convolution layer, overfitting problems will occur. At the same time, in order to reduce the number of parameters required for the model and effectively output features, a pooling layer is needed to further adjust the data. On the other hand, doing so can also increase the computing speed and reduce computing pressure. Finally, the initial positioning position estimation point of each user's area is predicted in the fully connected layer. Here, a regression learning model is used to minimize the loss function, which is defined as follows:

[0065]

[0066] Among them, θ represents all parameters in the neural network, and MSE is the mean square error; is the true label of the training data ( belongs to 1-100), is the predicted label.

[0067] 104. Input the feature subset of the point to be estimated into the trained deep learning model to predict the initial positioning position of the point to be estimated;

[0068] In an embodiment of the present invention, after the deep learning model is trained, it can be used to predict the RSSI fingerprint map of the point to be estimated. The feature subset of the point to be estimated is input into the trained deep learning model, and the initial positioning position of the point to be estimated is obtained using the output of the trained deep learning model; wherein the feature subset of the point to be estimated includes multiple RIS fingerprint maps of the point to be estimated.

[0069] 105. Using the initial positioning position of the point to be estimated as a discrete point to construct a Thiessen polygon, and using the Thiessen polygon to determine the positioning area;

[0070] In this embodiment of the present invention, a Thiessen polygon refers to a method of dividing a given point set into multiple polygonal sets within a specific two-dimensional space. Each polygon contains exactly one point from the set, and any point within the polygon is closest to a point in the corresponding set. The polygon is called the Thiessen polygon region of the point. This embodiment uses the initial location of the point to be estimated obtained in step 104 as the discrete point partition region of the Thiessen polygon.

[0071] 106. Calculate the average deviation value in the positioning area, and use the improved weighted K-nearest neighbor method to calculate the positioning position of the point to be estimated.

[0072] In the embodiment of the present invention, the weighted KNN algorithm is a relatively common positioning algorithm. Its principle is to calculate the Euclidean distance between the RSSI value collected online and the RSSI value in the fingerprint database, select the K neighboring points closest to the measurement point as positioning labels, use the distance weight as the weight of the label, and set the estimated coordinates as the result, as shown in formulas (12), (13), and (14):

[0073]

[0074] Among them, Q is the number of RIS configurations, RSSI i is the received signal strength value of the test point under the i-th configuration, RSSI ij is the received signal strength value of the jth reference point under the i-th configuration, D j It is the Euclidean distance between the signal strength of the measured point and the reference point.

[0075]

[0076]

[0077] Among them, w i is the weight value of the i-th reference point, η is the correction coefficient, (x i ,y i ) is the position coordinate of the i-th reference point, and (x, y) is the position of the point to be measured.

[0078] This paper improves on the traditional weighted K-nearest neighbor algorithm. In each positioning area, N reference points with known positioning positions are selected and weighted K-nearest neighbor calculation is performed on these N reference points to obtain the estimated positioning position. The error between the known positioning position and the estimated positioning position is calculated to obtain the average deviation value in the current area. The initial positioning position predicted by the deep learning model is added to the average deviation value to obtain:

[0079]

[0080] Where (x, y) represents the final location of the point to be estimated, (x', y') represents the initial location coordinates predicted by the deep learning model, and (Δx, Δy) is the average deviation value in the current area.

[0081] In each Thiessen polygon area, the position coordinates obtained by the deep learning algorithm are added to the average deviation value and the average deviation calculated by formula (15). Finally, the user's accurate positioning position coordinates are defined as follows:

[0082] (x,y)=(x',y')+(Δx,Δy) (16)

[0083] Among them, (xi ,y i ) represents the known positioning coordinates of the reference point, (x i ',y i ') represents the estimated positioning coordinates of the reference point calculated by the weighted K nearest neighbor method.

[0084] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing the relevant hardware through a program, and the program can be stored in a computer-readable storage medium, which may include: ROM, RAM, disk or CD, etc.

[0085] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A RIS-assisted wireless fingerprint positioning method based on deep learning, characterized in that: The method comprises: By adjusting the load impedance value of the RIS reflection unit, a variety of RIS configurations are obtained, thereby collecting multiple RSSI fingerprint maps corresponding to each user, including the RSSI fingerprint map of the estimated point and the RSSI fingerprint map of the point to be estimated; Performing feature selection on the collected RSSI fingerprint map using a feature selection algorithm to obtain a feature subset containing multiple RIS configurations, including a feature subset of estimated points and a feature subset of points to be estimated; performing feature selection on the collected RSSI fingerprint map using the feature selection algorithm includes: 1) Individual initialization: A number of D-bit binary-coded initial groups are randomly generated, and each individual in the initial group takes 1 to indicate that the corresponding RIS configuration is selected, and takes 0 to indicate that the corresponding RIS configuration is not selected; 2) Fitness function: In order to minimize the positioning error, the individual with the minimum fitness is selected. If the number of selected RIS configurations is less than or equal to Q, the penalty value is 0. The fitness function is defined as: Among them, Per represents the individual in the population, represents the positioning error; f×max(0,|Per|1-Q) is the penalty value, f is a positive constant, and |Per|1 is the number of selected RIS configurations; 3) Feature selection: Using the elite selection operator, some of the best individuals in the previous generation are brought into the next generation; 4) Feature crossover: Generate new individuals through uniform crossover to ensure the stability of the population and evolve towards the optimal solution; 5) Termination of iteration: When the number of generations reaches the threshold or the fitness value remains unchanged, the feature selection process is terminated; Using the feature subset of the estimated points to train a deep learning model, and performing prediction and classification on the feature subset of the estimated points; Input the feature subset of the point to be estimated into the trained deep learning model to predict the initial positioning position of the point to be estimated; Using the initial positioning position of the point to be estimated as a discrete point to construct a Thiessen polygon, and using the Thiessen polygon to determine the positioning area; The average deviation value is calculated in the positioning area, and the accurate positioning position of the point to be estimated is calculated using the improved weighted K-nearest neighbor method.

2. The RIS-assisted wireless fingerprint positioning method based on deep learning according to claim 1 is characterized in that: The initial positioning position of the point to be estimated is used as a discrete point to construct a Thiessen polygon, and the Thiessen polygon is used to determine that the positioning area is included in a specific two-dimensional space. The initial positioning positions of the point to be estimated are used as a discrete point set, and each discrete point in the discrete point set is used as a center point to divide the space into multiple polygon sets. In each polygon, there is only one discrete point in the discrete point set, and any discrete point in the polygon is the shortest distance to the discrete point in the corresponding discrete point set, which is used as the discrete point division positioning area of ​​the Thiessen polygon.

3. The RIS-assisted wireless fingerprint positioning method based on deep learning according to claim 1 is characterized in that: The method of calculating the accurate positioning position of the point to be estimated by using the improved weighted K-nearest neighbor method includes selecting N reference points with known positioning positions in each positioning area, performing weighted K-nearest neighbor calculation on the N reference points to obtain the estimated positioning position, calculating the error between the known positioning position and the estimated positioning position, and obtaining the average deviation value in the current area; The initial positioning position predicted by the deep learning model is added to the average deviation value to determine the accurate positioning position of the point to be estimated.

4. The RIS-assisted wireless fingerprint positioning method based on deep learning according to claim 3 is characterized in that: The calculation formula of the improved weighted K-nearest neighbor method is expressed as: (x,y)=(x',y')+(Δx,Δy) Where (x, y) represents the final location of the point to be estimated, (x', y') represents the initial location coordinates predicted by the deep learning model, and (Δx, Δy) is the average deviation value in the current area.

5. The RIS-assisted wireless fingerprint positioning method based on deep learning according to claim 4 is characterized in that: The calculation formula of the average deviation in the current area is expressed as: Among them, (x i ,y i ) represents the known positioning coordinates of the reference point, (x' i ,y' i ) represents the estimated positioning coordinates of the reference point calculated by the weighted K nearest neighbor method.

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