Fingerprint database reconstruction positioning method based on multiple intelligent reflecting surfaces

Abstract

The invention discloses a fingerprint database reconstruction positioning algorithm based on multiple intelligent reflecting surfaces, and belongs to the technical field of calculation, reckoning or counting. The intelligent reflecting surface (IRS) has flexible deployment and expansibility, is commonly used as a wireless relay, can change the propagation environment of wireless signals, and provides a new opportunity for the situation that the positioning service cannot be carried out in the environment with serious NLOS (Non Line Of Sight). The invention provides a fingerprint database reconstruction positioning algorithm based on an intelligent reflecting surface. The method comprises the following steps: firstly, constructing a 5G positioning system based on an intelligent reflecting surface, and reflecting a signal by using a plurality of IRSs deployed in the air, so that a base station can overcome the influence of NLOS to receive a positioning signal of a to-be-positioned point; an angle domain power expectation matrix of a received signal is extracted as fingerprint data information to form a partial fingerprint database, and a low-rank matrix fitting algorithm is utilized to reconstruct a complete fingerprint database, so that the workload of constructing the fingerprint database is greatly reduced. And finally, increasing the difference between the fingerprint data in combination with a maximum ratio merging thought, then carrying out fingerprint matching of a point to be positioned by using a weighted K-Nearest Neighbor (WKNN) algorithm, and estimating the position of the point to be positioned. Simulation results show that the positioning precision of the fingerprint reconstruction positioning method of the intelligent reflecting surface reaches the sub-meter level in a large NLOS complex environment, the positioning precision is obviously improved compared with a traditional fingerprint positioning algorithm, and it is proved that the algorithm has a good positioning effect.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly to a fingerprint database reconstruction positioning method based on a multi-intelligent reflecting surface, belonging to the technical field of computing, reckoning or counting. Background Art

[0002] Nowadays, society is constantly developing towards informatization and intelligence, and positioning services have gradually become one of the indispensable needs of people. Location-based services have been applied in many aspects, such as location-based shared bicycles, route planning for daily travel, industrial Internet applications, emergency rescue services, road traffic control, autonomous driving technologies, etc. In the face of the increasing demand for positioning services, positioning methods based on mobile communication technologies have gradually attracted people's attention. Especially in recent years, with the continuous development of 5G technology, many studies on positioning methods based on 5G-related technologies have emerged. Therefore, 5G-based wireless positioning technology has become a current research hotspot.

[0003] Location-based services have gradually become an irreplaceable part of people's lives, but traditional positioning methods can no longer meet people's current needs. Although traditional positioning methods combining trilateration or triangulation have achieved good positioning results, the measurement and calculation of this method require the cooperation of multiple base stations, so a large amount of information exchange overhead will be generated. To solve this problem, fingerprint-based positioning methods have gradually attracted people's attention. The fingerprint positioning method first constructs a fingerprint database required for positioning in the offline stage, and then in the online stage, matches the fingerprint data of the user to be located received in real time with the data in the fingerprint database, and finally obtains the coordinates of the user to be located. The fingerprint positioning method reduces the overhead on the base station to a certain extent. However, since a comprehensive fingerprint database needs to be constructed in the early stage of fingerprint positioning, the workload of this positioning method is increased. Moreover, in the case of a non-line-of-sight (NLOS) path where the base station and the user cannot directly communicate, the positioning accuracy of the above several positioning methods will be very poor or even completely unable to perform positioning. Summary of the Invention

[0004] The present invention provides a fingerprint database reconstruction positioning method based on a multi-intelligent reflecting surface for the deficiencies existing in the prior art.

[0005] An intelligent reflective surface (IRS) consists of a large-scale passive reflection array, and obtains a customized reflected wave velocity by regulating electromagnetic characteristics such as the amplitude, phase, and polarization of incident electromagnetic waves. It has flexible deployment and easy expandability and is often used as a wireless relay, which can change the wireless signal propagation environment and also provides a new opportunity for the situation where positioning services cannot be performed in an environment with severe non-line-of-sight (NLOS).

[0006] This paper proposes a fingerprint database reconstruction and positioning method based on multi-intelligent reflecting surfaces. First, a 5G positioning system based on intelligent reflecting surfaces is constructed. Multiple IRSs deployed in the air reflect signals, enabling the base station to receive positioning signals of the point to be located by overcoming the influence of NLOS. The angular-domain power expectation matrix (APEM) of the received signal is extracted as fingerprint data information to form a partial fingerprint database. The low-rank matrix fitting (LMaFit) algorithm is used to reconstruct the complete fingerprint database, greatly reducing the workload of constructing the fingerprint database. Finally, the idea of maximum ratio combining is used to increase the gap between fingerprint data, and then the weighted K-nearest neighbor (WKNN) algorithm is used for fingerprint matching of the point to be located to estimate the position of the point to be located.

[0007] A fingerprint database reconstruction and positioning method based on multi-intelligent reflecting surfaces of the present invention includes the following three steps:

[0008] 1) Construct a positioning system based on intelligent reflecting surfaces, which has a base station with multiple antennas and multiple IRSs capable of signal reflection. There is no direct line-of-sight path between the base station and the user to be located in the system, and the signal transmitted by the user to be located reaches the base station through reflection by the IRS.

[0009] 2) In the fingerprint database construction stage, using APEM as fingerprint data, a local fingerprint database is constructed with partial fingerprint reference points, and then the complete fingerprint database is reconstructed in combination with the LMaFit algorithm.

[0010] 3) In the online matching stage, using the idea of maximum ratio combining, the fingerprint data of each fingerprint reference point is multiplied by its corresponding signal-to-noise ratio as the weight, and then the WKNN algorithm is used for fingerprint matching of the point to be located.

[0011] The specific method of step 1) is as follows:

[0012] Construct a positioning system based on intelligent reflecting surfaces. The system model consists of a base station, intelligent reflecting surfaces, and a user to be located. Assume there is only one base station in the system, denoted as BS, configured with W antennas arranged in a uniform horizontal linear array, denoted as AN = {AN1 … AN w … AN W}, with an antenna spacing of d. The user to be located in the system is denoted as US, configured with a single antenna. Assume there are M intelligent reflecting surfaces configured in the system, denoted as IRS = {IRS1 … IRS m … IRS M}, where IRSm Denote the \(m\) -th intelligent reflecting surface, and each intelligent reflecting surface is composed of \(K\) reflecting elements arranged in a uniform horizontal linear array, denoted as \(RE=\{RE_1,\cdots,RE_K\}\), and the spacing between the reflecting elements is also \(d\). Assume that there is no direct signal path between the user to be located and the base station, and the user to be located can communicate with the base station through the intelligent reflecting surface. In this system, the signal of the user to be located received by the base station is divided into two stages. First, from the user to be located to the intelligent reflecting surface, and then from the intelligent reflecting surface to the base station. Suppose the channels in both stages are Rayleigh fading channels, and the channel fading coefficient \(\alpha\) is a complex Gaussian random variable with zero mean and variance \(\sigma^2\), that is k … \(RE_K\) K \(\sigma^2\). Further, the details of the two - stage signal of the user to be located received by the base station in step 1) are as follows. Denote the stage from the user equipment (UE) transmitting the signal to the intelligent reflecting surface (IRS) as the UE - IRS stage. Denote the channel from the UE to the \(k\) -th reflecting element of the IRS as which is specifically expressed as shown in Equation (1)

[0013] m the UE - IRS stage, and denote the channel from the UE to the \(k\) -th reflecting element of the IRS as m the UE - IRS stage, and denote the channel from the UE to the \(k\) -th reflecting element of the IRS as m the \(k\) -th reflecting element of the IRS as which is specifically expressed as shown in Equation (1)

[0014]

[0015] where is the total number of signal paths of the channel from the UE to the \(k\) -th reflecting element of the IRS, m \(L_{k}\) is the total number of signal paths of the channel from the UE to the \(k\) -th reflecting element of the IRS, \(\beta_{kl}\) represents the \(l\) -th signal path among them, \(\beta_{kl}\) represents the \(l\) -th signal path among them, \(l\) -th is the channel fading coefficient of the \(l\) -th signal path, \(\lambda\) is the signal wavelength, \(\theta_{kl}\) is the angle of arrival of the \(l\) -th signal path, and its range is \([0,\pi]\).

[0016] Denote the total channel of the UE - IRS stage as m \(\mathbf{h}_{u - i}\), where where \(\mathbf{h}_{u - i}\) represents a \(K\times1\) complex matrix, which is specifically expressed as shown in Equation (2):

[0017]

[0018] Denote the stage from the IRS m to the base station (BS) as the IRS - BS stage. Denote the channel from the \(k\) -th reflecting element of the IRS to the \(w\) -th antenna of the BS as m the IRS - BS stage. Denote the channel from the \(k\) -th reflecting element of the IRS to the \(w\) -th antenna of the BS as m which is specifically expressed as shown in Equation (3):

[0019]

[0020] Among them, is the total number of the path from the k-th reflection unit of the IRS to the w-th antenna of the BS, m represents the c-th path among them, is the -th channel fading coefficient of the path. Here, λ is the signal wavelength, is the arrival angle of the path , is the departure angle of the path , and their ranges are both [0, π].

[0021] Therefore, assume that the channel experienced by the signal transmitted by the US after passing through the k-th reflection unit of the IRS m and arriving at the w-th antenna of the BS is expressed as Its specific expression is Equation (4):

[0022]

[0023] where [Ξ m k is the reflection coefficient of the k-th reflection unit of the IRS m , and its specific expression is Equation (5):

[0024]

[0025] In Equation (5), represents the reflection amplitude of the k-th reflection unit of the IRS m , and assume represents the reflection phase of the k-th reflection unit of the IRS m .

[0026] To sum up, assume that the total channel for the IRS m to assist the US and the BS in communication can be expressed as Among them, represents a complex matrix of W rows and 1 column. Its specific expression is shown in Equation (6)

[0027]

[0028] where diag(Ξ m ) represents the reflection coefficient matrix of the IRS m , and its specific expression is shown in Equation (7)

[0029]

[0030] In addition, there is:

[0031] ​​

[0032] Let Equation (6) can be rewritten as Equation (9).

[0033]

[0034] where Specifically, as shown in Equation (10).

[0035]

[0036] And let As the cascaded channel of BS-IRS m -US, its specific expression is shown in Equation (11).

[0037]

[0038] Using the method estimated by the Discrete Fourier Transform (DFT), the cascaded channel Υ m is transformed from the spatial domain to the angular domain. Let the DFT matrix of W points be whose elements satisfy Therefore, the cascaded channel Υ m in the angular domain is shown in Equation (12).

[0039]

[0040] where V is specifically shown in Equation (13).

[0041]

[0042] In summary, after being reflected by the IRS m the signal sent by the US received by the BS is whose specific expression is shown in Equation (14).

[0043]

[0044] where ρ is the transmit power, β mUS is the large-scale fading coefficient from the US through the IRS m to the BS, is the total channel of BS-IRS m -US, s is the signal transmitted by the US, and n is Gaussian white noise with a mean of zero and a variance of σ 2 .

[0045] Furthermore, the specific method of step 2) is as follows:

[0046] There are N fingerprint reference points evenly distributed in the positioning system. Let the coordinates of the nth fingerprint reference point be LOC n =(x n , y n , z n ). Then the signal received by the BS after being reflected by the IRS m is The corresponding fingerprint data f′ n is expressed as shown in Equation (17)

[0047] f′ n =[fp1x,..., fp mn ,..., fp Mn (15)

[0048] where fp mn =[E(|Y mn |)] T , |·| represents taking the modulus operation on each term in the matrix, E(·) represents taking the expectation of the matrix, and [·] T represents transposing the matrix. Therefore, f′ n is a one-dimensional row vector with M×W columns. After being combined with the coordinates of this point, it forms the complete fingerprint f n of this point, and its specific expression is

[0049] f n =[LOC n f′ n (16)

[0050] Suppose LOC = [LOC1,..., LOC n ,..., LOC N T represents the summary of the coordinate values of N fingerprint reference points, and its specific expression is

[0051]

[0052] F′ = [f′1,..., f′ n ,..., f′ N T represents the summary of the fingerprint data of N fingerprint reference points, and its specific expression is

[0053]

[0054] Then the constructed fingerprint database F is specifically shown in Equation (21)

[0055]

[0056] ​​Subsequently, in the case of collecting fingerprint data in part of the fingerprint database, the LMaFit algorithm is used to construct a complete fingerprint database. This algorithm first samples the fingerprint database F′, and the number of sampled elements is much smaller than the total number N×(M×W) of elements in the fingerprint database F′. Let Γ be the subscript set of the sampled elements. Given the fingerprint data corresponding to Γ, after reconstruction by the LMaFit algorithm, the fingerprint database X′ is obtained, which is the reconstructed fingerprint database of the fingerprint database F′.

[0057] Define G Γ as the projection mapping of the fingerprint database F′ on Γ:

[0058]

[0059] According to the relevant theory of matrix reconstruction, the reconstructed fingerprint database X′ satisfies Equation (23):

[0060]

[0061] where min represents minimization, s.t. represents the constraint condition. rank(X′) represents the rank of X′. Equation (23) means that if there exists a unique low-rank matrix X′ that satisfies the above conditions, then this matrix is the complete estimation matrix of matrix F′. Considering that the computational complexity of this problem is extremely large, the Low Rank Matrix Fitting (LMaFit) algorithm is used to transform the rank minimization problem Equation (23) into the following problem:

[0062]

[0063] Let the rank of matrix F′ be r. An intermediate matrix I is introduced for convenient calculation, and two matrices U and R with dimensions N×r and (M×W)×r respectively are introduced as matrices to be estimated, that is, X′ = UR T .

[0064] Equation (24) is non-convex. For the convenience of calculation, it is transformed into the following Lagrangian form:

[0065]

[0066] where <Ω, G Γ > = ∑ a，b Ω a，b (G Γ ) a，b is the inner product of matrices. Matrix Ω is the Lagrange multiplier and satisfies Ω = G Γ (Ω). Because there is Equation (25) can be transformed into:

[0067]

[0068] Differentiate the above equation and set the differential equation equal to 0, thus obtaining the optimization condition for Equation (24) as

[0069]

[0070] Since there is the last equation of Equation (27) can be written as where Γ c is the complement of Γ. Use the fixed-point iteration method to solve Equation (27). First, transform the first equation in Equation (27) into the following form:

[0071] UR T R = IR (26)

[0072] This equation can be solved in the following way:

[0073] U = IR(R T R) + = I(R + ) T (27)

[0074] where R + is the Moore-Penrose pseudoinverse of R. According to Equation (29), the matrix U can be updated in the iteration. Similarly, the matrices I and R can be updated in the iteration from the remaining conditions of Equation (27).

[0075] During the process of computing convergence, adopt the method of dynamically selecting the step size ω in each iteration. The specific method is as follows. Let E i-1 (ω) represent the error matrix of the previous iteration with the step size equal to ω, and E i (ω) be the error matrix of this iteration with the step size equal to ω. Then the calculation formula for the error rate is:

[0076] σ(ω) = ||E i (ω)|| F-norm / ||E i-1 (ω)|| F-norm (28)

[0077] During the iteration process, if σ(ω) > 1, it indicates that the error has not decreased, and the parameter ω will be set to 1 in the next iteration. If σ(ω) ≤ 1, it indicates that the error has decreased during the iteration process. At this time, keep the value of the parameter ω in the previous iteration unchanged. In addition, to obtain a faster iteration speed, a parameter σ1 can be added in the next iteration. When σ(ω) > σ1, the value of ω can be appropriately increased. The stopping criterion for this algorithm is:

[0078]

[0079] Among them, step represents the number of iterations, and error represents the minimum allowable error.

[0080] After obtaining the reconstructed fingerprint database X′, it can be merged with the corresponding coordinates to obtain the complete reconstructed fingerprint library X, as shown in Equation (32):

[0081] X = [LOC X′] (30)

[0082] Furthermore, the specific method of step 3) is as follows:

[0083] Let the coordinates of US be LOC US =(x US , y US , z US ), and the fingerprint data be f′ US =[fp 1US ,..., fp MUS , then its fingerprint is:

[0084] f US =[LOC US , fp 1US ,..., fp MUS (31)

[0085] During the offline database building stage, the reconstructed fingerprint database X′ has been obtained. In the online matching and positioning stage, first, using the maximum ratio combining idea, the fingerprint data of each fingerprint reference point is multiplied by its corresponding signal-to-noise ratio to increase the gap between fingerprint data. The signal-to-noise ratio SNR m represents the signal-to-noise ratio of the channel between the BS and the US after reflection by the IRS m , and its calculation formula is:

[0086]

[0087] Among them, σ 2 represents the average power of noise.

[0088] Then, use the WKNN algorithm to perform similarity matching between the fingerprint data of the US that has been combined by the maximum ratio and the fingerprint data in the fingerprint library. The Euclidean distance is used to measure the similarity of fingerprints. The greater the distance, the lower the similarity, and vice versa. Let X i =[fp 1i ,..., fp Mi be the i-th fingerprint data in the reconstructed fingerprint database X, and the calculation formula for the similarity between the fingerprint data of the US and the i-th fingerprint data is as follows

[0089]

[0090] Among them, SNR im is the one through the IRSm After reflection, the signal-to-noise ratio of the channel between the BS and the i-th fingerprint reference point. After performing similarity measurements with all fingerprint data points in the database, select the coordinates [LOC1,..., LOC S corresponding to the S (S≥3) fingerprint data points with the highest similarity. Then, use the WKNN algorithm to assign different weights weight to the coordinates corresponding to fingerprint data points with different similarities, and its calculation formula is Equation (36):

[0091]

[0092] where ε is a very small positive number used to avoid the denominator being zero. After obtaining the weights corresponding to the coordinates of the S reference points, the estimated coordinates LOC′ of US can be obtained by calculating through Equation (37) US :

[0093]

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

[0095] This paper proposes a fingerprint database reconstruction and positioning method based on multi-intelligent reflecting surfaces. First, a 5G positioning system based on intelligent reflecting surfaces is designed, which has a multi-antenna base station and multiple IRSs that can reflect signals in the system. There is no direct line-of-sight path between the base station and the user to be located in the system, and the signal transmitted by the user to be located reaches the base station through reflection by the IRS. Secondly, this algorithm uses the angular domain power expectation matrix as fingerprint data and utilizes the high spatial resolution of the multi-input multi-output multi-antenna technology. In addition, this algorithm adopts a low-rank matrix fitting reconstruction algorithm to reconstruct the complete fingerprint database to reduce the huge workload brought by the large amount of data required to establish a complete fingerprint database, thereby reducing the workload of fingerprint collection. Finally, the Euclidean distance is used to determine the similarity of fingerprints, and the maximum ratio combination algorithm and the weighted K-nearest neighbor algorithm are combined to estimate the coordinates of the user to be located. Finally, through simulation, it is verified that the proposed method can reduce the workload of fingerprint database construction by 40%, and when the sampling interval is less than 2.5m, the probability of obtaining sub-meter positioning accuracy is 80%. Description of the Drawings

[0096] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings, where:

[0097] Figure 1 is the positioning system model based on intelligent reflecting surfaces;

[0098] Figure 2 is US-IRS m Schematic diagram of signal propagation in the stage;

[0099] Figure 3 For IRS m - Schematic diagram of signal propagation in the BS stage;

[0100] Figure 4 It is a comparison diagram of the proposed algorithm with the traditional fingerprint positioning algorithm and the non - reconstruction fingerprint database positioning algorithm based on intelligent reflecting surface (IRS - URFL). Specific implementation manners

[0101] The following further describes the specific implementation manners of the present invention in conjunction with the accompanying drawings.

[0102] Figure 1 Positioning system model based on intelligent reflecting surface. The model consists of a base station, an intelligent reflecting surface, and a user to be located. Assume that there is only one base station in the system, denoted as BS, which is configured with W antennas arranged in a uniform horizontal linear array, denoted as AN = {AN1 … AN w … AN W}, and the antenna spacing is d. The user to be located in the system is denoted as US, which is configured with a single antenna. Assume that there are M intelligent reflecting surfaces in the system, denoted as IRS = {IRS1 … IRS m … IRS M}, where IRS m represents the m - th intelligent reflecting surface, and each intelligent reflecting surface is composed of K reflecting units arranged in a uniform horizontal linear array, denoted as RE = {RE1 … RE k … RE K}, and the spacing between the reflecting units is also d. Assume that there is no direct signal path between the user to be located and the base station, and the user to be located can communicate with the base station through the intelligent reflecting surface. The signal of the user to be located received by the base station in this system is divided into two stages. First, from the user to be located to the intelligent reflecting surface, and then from the intelligent reflecting surface to the base station. Assume that the channels in both stages are Rayleigh fading channels, and the channel fading coefficient α is a complex Gaussian random variable with a mean of zero and a variance of i.e.,

[0103] Figure 2 US - IRS m Schematic diagram of signal propagation in the stage. Let the channel from US to the k - th reflecting unit of IRS m be denoted as and its specific expression is shown in Equation (1)

[0104]

[0105] where is the total number of signal paths of the channel from US to the k - th reflecting unit of IRS m , Denote the \(l\)-th channel path therein. is the channel fading coefficient of the \(l\)-th channel path, \(\lambda\) is the signal wavelength, is the angle of arrival of the path, and its range is \([0, \pi]\).

[0106] Figure 3 IRS m -BS stage signal propagation schematic diagram. Let the stage from IRS m to BS be denoted as the IRS m -BS stage. Let the channel from the \(k\)-th reflection unit of IRS m to the \(w\)-th antenna of BS be denoted as and its specific expression is shown in Equation (3):

[0107]

[0108] where, is the m total number of channel paths from the \(k\)-th reflection unit of IRS to the \(w\)-th antenna of BS, denotes the \(c\)-th channel path among them, is the channel fading coefficient of the \(c\)-th channel path, where \(\lambda\) is the signal wavelength, is the angle of arrival of the path, is the angle of departure of the path, and their ranges are both \([0, \pi]\).

[0109] Figure 4Comparison graph of the proposed algorithm with traditional fingerprint positioning algorithms and the IRS-URFL (Intelligent Reflecting Surface - Unreconstructed Fingerprint Library Localization) algorithm. The abscissa represents the signal-to-noise ratio SNR (dB), and the ordinate represents the positioning error (m). The blue curve represents the positioning error of the traditional fingerprint matching algorithm, the red curve represents the positioning error of the proposed IRS-RFL algorithm, and the yellow curve represents the positioning error of the IRS-URFL algorithm. The results show that when SNR = 5dB, the error of the Traditional RSS algorithm is 3.35m, the error of the IRS-RFL algorithm is 0.97m, and the error of the IRS-URFL algorithm is 0.92m. When SNR = 25dB, the error of the Traditional RSS algorithm is 1.41m, the error of the IRS-RFL algorithm is 0.60m, the error of the IRS-URFL algorithm is 0.92m, and the error of the IRS-URFL algorithm is 0.57m. As SNR increases, all three positioning algorithms show better positioning effects. Among these three algorithms, the IRS-URFL algorithm has the highest positioning accuracy and the smallest positioning error, and the positioning accuracy of the IRS-RFL algorithm is higher than that of the Traditional RSS algorithm. First, both the IRS-URFL algorithm and the IRS-RFL algorithm use APEM fingerprints. This type of fingerprint contains more information compared to RSS fingerprints, and the correspondence between this information and spatial positions is stronger, which is beneficial for the system to improve positioning accuracy. Therefore, the positioning error of the Traditional RSS algorithm is larger than that of the IRS-URFL algorithm and the IRS-RFL algorithm. Additionally, since the IRS-RFL algorithm uses the LMafit reconstruction algorithm, there is a certain error between the reconstructed fingerprint database and the directly collected fingerprint database without reconstruction. Therefore, the positioning error of the IRS-RFL algorithm is relatively larger than that of the IRS-URFL algorithm.

Claims

1. A fingerprint database reconstruction and positioning method based on a multi-intelligent reflecting surface, characterized in that Including the following steps: 1) Construct a positioning system for an Intelligent Reflective Surface (IRS), which has a multi-antenna base station and multiple IRSs capable of signal reflection. There is no direct line-of-sight path between the base station and the user to be located in the system, and the signal transmitted by the user to be located reaches the base station through reflection by the IRSs. 2) In the fingerprint database construction phase, use the Angular-domain power expectation matrix (APEM) as fingerprint data, construct a local fingerprint database using some fingerprint reference points, and then reconstruct the complete fingerprint database in combination with the Low-Rank Matrix Fitting (LMaFit) algorithm. 3) In the online matching phase, using the maximum ratio combining idea, multiply the fingerprint data of each fingerprint reference point by its corresponding signal-to-noise ratio as weights, and then use the Weighted K-Nearest Neighbor (WKNN) algorithm for fingerprint matching of the point to be located.

2. The fingerprint database reconstruction and positioning method based on multiple intelligent reflecting surfaces according to claim 1, wherein In step 1), a positioning system of an intelligent reflecting surface (IRS) is constructed, which consists of a base station, an intelligent reflecting surface, and a user to be positioned. And there is only one base station in this system, denoted as BS, which is configured with W antennas arranged in a uniform horizontal linear array, denoted as AN = {AN1…AN w …AN W}, the antenna spacing is d, the user to be positioned is denoted as US, which is configured with a single antenna, and is configured with M intelligent reflecting surfaces, denoted as IRS = {IRS1…IRS m …IRS M}, where IRS m represents the m-th intelligent reflecting surface, and each intelligent reflecting surface is composed of K reflection units arranged in a uniform horizontal linear array, denoted as RE = {RE1…RE k …RE K}, and the reflection unit spacing is also d. It is assumed that there is no direct signal path between the user to be located and the base station, and the user to be located can communicate with the base station through the intelligent reflective surface; In this system, the signal of the user to be located received by the base station is divided into two stages. First, it travels from the user to be located to the intelligent reflecting surface, and then from the intelligent reflecting surface to the base station. Assuming that the channels in both stages are Rayleigh fading channels, and the channel fading coefficient α is a complex Gaussian random variable with a mean of zero and a variance of , that is 3. A fingerprint database reconstruction and positioning method based on a multi-intelligent reflecting surface according to claim 1, characterized in that, The two-stage details of the signal of the user to be located received by the base station in step 1) are as follows; assume that the US transmits a signal to the IRS m The stage is denoted as US-IRS m stage. Assume that the channel from the US to the k-th reflection unit of the IRS m is denoted as Its specific expression is shown in Equation (1). wherein, is the total number of the k-th reflection unit channel paths from US to IRS, m represents the l-th channel path among them, is the channel fading coefficient of the l-th channel path, λ is the signal wavelength, is the angle of arrival of the path, and its range is [0, π].​ Set US-IRS m The total channel in the stage is where represents a complex matrix of K rows and 1 column, and the specific representation is as shown in Equation (2): Let the stage from the IRS m to the BS be denoted as the IRS m -BS stage; let the channel from the k-th reflection unit of the IRS m to the w-th antenna of the BS be denoted as and its specific expression is shown in Equation (3): wherein, is the total number of the signal path from the k-th reflection unit of the IRS to the w-th antenna of the BS, m and represents the c-th signal path among them, is the channel fading coefficient of the -th signal path, where λ is the signal wavelength, is the angle of arrival of the path , and is the angle of departure of the path , and their ranges are both [0, π]. ​ Therefore, let the signal transmitted by the US reach the \(w\)-th antenna of the BS through the \(k\)-th reflection unit of the IRS m and the channel experienced is expressed as and its specific expression is Equation (4): where [Ξ m k is the reflection coefficient of the k-th reflection unit of the IRS m , and its specific expression is Equation (5):​ In Equation (5), represents the reflection amplitude of the k-th reflecting element of the IRS m , assuming that represents the reflection phase of the k-th reflecting element of the IRS m . In summary, let the IRS m The total channel assisting the communication between the US and the BS can be expressed as where represents a complex matrix of W rows and 1 column; its specific expression is shown in Equation (6) where diag(Ξ m ) represents the reflection coefficient matrix of the IRS m , and its specific expression is shown in Equation (7). In addition, there is: Let Equation (6) can be rewritten as Equation (9) Among them Specifically, as shown in the expression of formula (10) And let serve as the cascaded channel of BS-IRS m -US, and its specific expression is shown in Equation (11) The method of estimating using the Discrete Fourier Transform (DFT) transforms the cascaded channel Υ m from the spatial domain to the angular domain. Let the DFT matrix of W points be whose elements satisfy Therefore, the cascaded channel Υ m is represented in the angular domain as shown in Equation (12) Where V is specifically expressed as shown in Equation (13) In summary, after reflection by the IRS m the signal sent by the US and received by the BS is and its specific expression is shown in Equation (14). where ρ is the transmit power, β mUS is the large-scale fading coefficient from the US to the BS via the IRS m , and is the total channel from the BS to the IRS to the US, s is the signal transmitted by the US, and n is the Gaussian white noise with zero mean and variance σ m . 2 ​ 4. A 5G positioning system and fingerprint database reconstruction positioning method based on a multi-intelligent reflecting surface according to claim 1, characterized in that, The specific method in step 2) is as follows; there are N fingerprint reference points evenly distributed in the positioning system, and the coordinates of the nth fingerprint reference point are LOC n =(x n , y n , z n ), then the signal received by the BS after being reflected by the IRS m is and its corresponding fingerprint data f′ n is expressed as shown in equation (17) f′ n = [fp 1n ,..., fp mn ,..., fp Mn (15) where, fp mn = [E(|Y mn |)] T , |·| represents taking the modulus operation on each term in the matrix, E(·) represents taking the expectation of the matrix, and [·] T represents transposing the matrix; thus, f′ n is a one-dimensional row vector with M×W columns, which is combined with the coordinates of this point to form the complete fingerprint f n of this point, and its specific representation is f n = [LOC n f' n (16) There is LOC = [LOC1,..., LOC n ,..., LOC N T which represents the summary of the coordinate values of N fingerprint reference points, and is specifically represented as​ F′ = [f1′,..., f′ n ,..., f′ N T represents the summary of fingerprint data of N fingerprint reference points, and is specifically represented as​ Then the constructed fingerprint database F is specifically expressed as shown in Equation (21) Subsequently, in the case of collecting fingerprint data in part of the fingerprint database, the LMaFit algorithm is used to construct the complete fingerprint database; this algorithm first samples the fingerprint database F′, and the number of sampled elements is much smaller than the total number N×(M×W) of elements in the fingerprint database F′; let Γ be the subscript set of the sampled elements, and in the case of knowing the fingerprint data corresponding to Γ, after reconstruction by the LMaFit algorithm, the fingerprint database X′ is obtained, which is the reconstructed fingerprint database of the fingerprint database F′. Define G Γ as the projection mapping of the fingerprint database F′ onto Γ: According to the relevant theory of matrix reconstruction, the reconstructed fingerprint database X′ satisfies Equation (23): Where min represents minimization, s.t. represents the constraint condition; rank(X′) represents the rank of X′; Equation (23) means that if there is a unique low-rank matrix X′ that satisfies the above conditions, then this matrix is the complete estimation matrix of the matrix F′; considering that the computational complexity of this problem is extremely large, the Low Rank Matrix Fitting (LMaFit) algorithm is used to transform the rank minimization problem of Equation (23) into the following problem: Let the rank of matrix F′ be r. Introduce an intermediate matrix I for convenient calculation. Introduce two matrices U and R with dimensions N×r and (M×W)×r respectively as the matrices to be estimated, that is, X′ = UR T . Equation (24) is non-convex. For the convenience of calculation, it is transformed into the following Lagrangian form: where <Ω, G Γ > = ∑ a，b Ω a，b (G Γ ) a，b is the inner product of matrices, the matrix Ω is a Lagrange multiplier and satisfies Ω = G Γ (Ω); because there is Equation (25) can be transformed into: Differentiate the above equation and set the differential equation equal to 0, so as to obtain the optimization condition of Equation (24) as Since there is Then the last equation of Equation (27) can be written as where Γ c is the complement of Γ; Using the fixed-point iteration method to solve Equation (27), first transform the first equation in Equation (27) into the following form: UR T R = IR (26) This equation can be solved in the following way: U = IR (R T R) + = I (R + ) T (27) where R + is the Moore-Penrose pseudoinverse of R; according to Equation (29), the matrix U can be updated in the iteration. Similarly, according to the remaining conditions of Equation (27), the matrices I and R can be updated in the iteration. During the process of computing convergence, a method of dynamically selecting the step size ω in each iteration is adopted; the specific method is as follows. Let E i-1 (ω) represent the error matrix of the iteration when the previous step size is equal to ω, and E i (ω) be the error matrix when the current step size is equal to ω. Then the calculation formula for the error rate is as follows: σ(ω) = ||E i (ω)|| F-norm / ||E i-1 (ω)|| F-norm (28) During the iteration process, if σ(ω) > 1, it indicates that the error has not decreased, and the parameter ω will be set to 1 in the next iteration; if σ(ω) ≤ 1, it indicates that the error has decreased during the iteration process, and the value of the parameter ω in the previous iteration remains unchanged at this time; in addition, to obtain a faster iteration speed, a parameter σ1 can be added in the next iteration. When σ(ω) > σ1, the value of ω can be appropriately increased; the stopping criterion of this algorithm is: Among them, step represents the number of iterations, and error represents the minimum allowable error. After obtaining the reconstructed fingerprint database X′, merging it with the corresponding coordinates can obtain the complete reconstructed fingerprint database X, as shown in Equation (32): X = [LOC X′] (30) 5. A fingerprint database reconstruction and positioning method based on a multi-intelligent reflecting surface according to claim 1, characterized in that, The specific method in step 3) is as follows: Let the coordinates of US be LOC US =(x US , y US , z US ), and the fingerprint data be f' US =[fp 1US ,..., fp MUS , then its fingerprint is: f US = [LOC US , fp 1US ,..., fp MUS (31) During the offline database construction phase, the reconstructed fingerprint database X′ has been obtained. In the online matching and positioning phase, first, using the maximum ratio combining idea, the fingerprint data of each fingerprint reference point is multiplied by its corresponding signal-to-noise ratio to increase the difference between fingerprint data; the signal-to-noise ratio SNR m represents the signal-to-noise ratio of the channel between the BS and the US after reflection through the IRS m and its calculation formula is: Among them, σ 2 represents the average power of the noise. Then, the WKNN algorithm is used to perform similarity matching between the fingerprint data of the US that has undergone maximum ratio combining and the fingerprint data in the fingerprint database; the Euclidean distance is used to measure the similarity of fingerprints. The greater the distance, the lower the similarity, and vice versa. Let X i = [fp 1i ..., fp Mi be the i-th fingerprint data in the reconstructed fingerprint database X. The calculation formula for the similarity between the fingerprint data of the US and the i-th fingerprint data is as follows Among them, SNR im is the signal-to-noise ratio of the channel between the BS and the i-th fingerprint reference point after reflection by the IRS m ​ After performing similarity measurement with all fingerprint data points in the database, select the coordinates [LOC1,..., LOC S corresponding to the S (S≥3) fingerprint data points with the highest similarity from them. Then, using the WKNN algorithm, different weights weight are assigned to the coordinates corresponding to fingerprint data points with different similarities, and its calculation formula is Equation (36): where ε is a very small positive number used to avoid the case of a zero denominator; after obtaining the weights corresponding to the coordinates of S reference points, the estimated coordinates LOC′ of US can be obtained through calculation using Equation (37). US :

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