TOF (Time of Flight) estimation method of matrix bundle based on partitioning and random SVD (Singular Value Decomposition)

Abstract

The invention provides a TOF (Time of Flight) estimation method of a matrix bundle based on partitioning and random SVD (Singular Value Decomposition). The method comprises the following steps: firstly, acquiring channel state information (CSI) by using a commercial WiFi device, and constructing a CSI matrix; and secondly, performing block overlapping processing on the CSI matrix, constructing an augmented matrix for each CSI data block, and performing SVD decomposition on the augmented matrix, thereby reducing the calculation complexity of SVD decomposition. And then, the time of flight (TOF) of each CSI data block is estimated by using a matrix pencil algorithm, and the minimum TOF is direct path estimation. According to the method designed by the invention, the robustness of the system and the estimation precision of the TOF are improved under the condition that the algorithm complexity is greatly reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of realizing perception by using commercial WiFi equipment, and particularly relates to a Time of Flight (TOF) estimation method based on block and random SVD decomposition, which realizes the estimation of TOF by processing channel state information (CSI). BACKGROUND

[0002] Under the background of rapid iteration of technology, indoor positioning technology has become the core demand in the fields of intelligent security, precise guide, and material tracking. Although the traditional positioning scheme such as GPS performs excellently in outdoor, it faces the bottleneck of serious signal attenuation and insufficient positioning accuracy in indoor scenes. The positioning system based on infrared sensors and vision is limited by the narrowness of the monitoring angle, and it is difficult to realize full coverage monitoring in complex spaces such as airports, hospitals, and large shopping malls. Compared with traditional technologies, the wireless perception positioning based on WiFi shows significant advantages: first, relying on MIMO (Multiple Input Multiple Output) and OFDM (Orthogonal Frequency Division Multiplexing) technologies, this scheme can maintain high-resolution positioning ability in line-of-sight occlusion and non-line-of-sight environments, and effectively suppress multipath interference; second, it naturally avoids the privacy controversy that may be caused by visual positioning; third, the large-scale deployment of commercial WiFi equipment provides a zero-cost hardware basis for this technology - from office buildings to home scenarios, WiFi networks have achieved wide coverage, making it possible to have a low-cost, high-adaptability indoor positioning scheme. Based on the above characteristics, the WiFi wireless perception positioning technology is breaking through the limitations of traditional schemes and becoming the research focus and industrialization direction in the field of indoor positioning.

[0003] In the evolution of wireless positioning technology, fingerprint positioning schemes based on deep learning face two major challenges: first, during the system deployment phase, the target environment needs to be fully signal collected and feature labeled, which requires a large amount of manpower and time cost; second, the positioning accuracy is highly dependent on the stability of the environment, when the spatial layout or electromagnetic environment changes, the system performance may fluctuate significantly. In contrast, positioning methods based on multi-dimensional parameter estimation show stronger environmental adaptability. This technology fuses CSI, Angle of Arrival (AoA), ToF and other multi-dimensional physical layer parameters to build a positioning framework without pre-collecting fingerprint library. This design not only meets the real-time positioning needs, but also effectively reduces the impact of environmental dynamics on positioning results through multi-parameter cross-validation mechanism, significantly improving the robustness of the system. It is worth noting that early positioning systems rely heavily on the Received Signal Strength Indication (RSSI) of WiFi as the core ranging indicator. However, RSSI is easily affected by multipath effects and non-line-of-sight propagation, and its measurement stability and spatial resolution are limited, which has promoted the research and development of multi-dimensional parameter estimation methods. However, RSSI is greatly affected by obstacles, multipath effects and interference in the environment, and the positioning accuracy is relatively low. Subsequently, the IEEE 802.11mc protocol was proposed by the IEEE 802.11 protocol working group TaskGroup mc, which is a Wi-Fi communication protocol for measuring the distance from the terminal to the surrounding base station. The protocol is built around a new data packet type called Fine Time Measurement (FTM) frame. This technology obtains the Round Trip Time (RTT) through Fine Time Measurement-Acknowledgement (FTM-ACK) interaction between the AP and STA at both ends of the FTM measurement link to achieve distance measurement between each other. However, due to the difference in local clock frequency between AP and STA, there is a clock drift between AP and STA, which causes synchronization accuracy problems between AP and STA, making the time recorded by AP and STA when receiving the signal often deviates, which needs to be compensated by using the first path delay or phase offset at the AP and STA receiving the signal to improve the accuracy of distance calculation. Since CSI can more finely perceive channel changes in time, frequency and space domains, and it contains channel amplitude and phase information of multiple subcarriers on multiple links, it has the ability to distinguish different paths, so the first path delay is estimated by CSI.

[0004] However, the multipath effect in indoor Wi-Fi sensing technology is serious, the noise interference is significant, the traditional multi-dimensional parameter estimation algorithm has high complexity and insufficient real-time, and the like, and a high-precision positioning algorithm based on block weighted fusion and random SVD decomposition matrix beam TOF estimation is proposed for the above problems. By introducing the block overlap technology to reduce the dimension of the Hankel matrix, combining the random SVD decomposition to speed up the singular value calculation, and combining the two-dimensional beam space matrix beam algorithm multi-dimensional parameter estimation, the structured CSI matrix is efficiently recovered from the noise, and the low complexity and high resolution TOF estimation is realized. SUMMARY

[0005] The purpose of the present application is to provide a TOF estimation method based on block and random SVD decomposition matrix beam under the WiFi sensing system, which can greatly reduce the complexity of the algorithm and improve the robustness and estimation accuracy of the TOF.

[0006] The TOF estimation method based on block and random SVD decomposition matrix beam according to the present application specifically comprises the following steps:

[0007] Step one: the signal is transmitted by the OFDM system, and the OFDM has 256 subcarriers; the signal has a multipath effect in the wireless channel, and the lth path reaches the uniform linear array, wherein 1≤l≤L; the time of flight of the signal is τ l , the center frequency is f c , and the subcarrier spacing is △f; the receiving end is a single antenna, and the kth subcarrier is on, wherein 1≤k≤K; the CSI of a single subcarrier is represented as:

[0008]

[0009] Wherein, α l represents the complex attenuation of the lth path, σ k represents the channel noise, and j represents the imaginary symbol;

[0010] The CSI information of the WiFi signal is obtained by the receiving end, and since there are 256 subcarriers, the matrix representation of the CSI of a single data packet received is:

[0011] H=[H(1),H(2),H(3),…,H(254),H(255),H(256)]

[0012] Wherein, H(k) represents the CSI data of the kth subcarrier;

[0013] Step two: block overlap processing of CSI, first divide the CSI data into multiple adjacent short CSI data blocks with overlapping parts by block overlap technology, set the block number of CSI data block as β, and set the overlap rate between blocks as ο;

[0014] Due to the existence of overlap, the actual block number will be more than the set CSI data block number β, so first calculate the actual effective block number B as:

[0015]

[0016] The length n of each block of CSI data after block is:

[0017]

[0018] Where N is the length of the unblocked CSI data;

[0019] After calculating the size of each block, calculate the size of the overlapping part:

[0020] O = n x ο

[0021] After calculating the actual effective block number and the size of each block, the CSI data is divided into blocks with overlap according to the size of each block, and the obtained CSI data block is:

[0022] H1 = [H(1), H(2), H(3), …, H(n)]

[0023] H2 = [H(n-O+1), H(n-O+2), …, H(n-O+n)]

[0024]

[0025] H B = [H((B-1) x (n-O)+1), H((B-1) x (n-O)+2), …, H((B-1) x (n-O)+n)] Where H B represents the Bth block of CSI data;

[0026] Step three: construct the Hankle matrix with the length n of the CSI data block obtained after block overlap in step two Expressed as a complex field:

[0027]

[0028] Where, M = n-L+1;

[0029] Construct the augmented matrix Expressed as: Where, Y is the complex conjugate matrix of Y, and P is the permutation matrix, Y is the real field, and Y is the complex field:

[0030]

[0031] Step four: construct a random projection matrix: where r = S n +s, which is used to determine the dimension of the random projection matrix. If r is too small, important information will be lost, and the approximation error will be large. If r is close to the true rank of the matrix or even larger, it is almost as accurate as the complete SVD, but the speed advantage will be reduced. S n is the number of sources, and s is the redundant dimension, which is generally 5-10. The random projection matrix is a random Gaussian matrix, where each element follows a standard normal distribution. The purpose is to map the column space of the original matrix to a low-dimensional space.

[0032] Then, the augmented matrix Y ex Calculate the random projection:

[0033] Y1 = Y ex Ω

[0034] Perform QR decomposition on Y1:

[0035] Y1 = QR

[0036] Get Q is a unit vector whose column vectors are orthogonal to each other. In order to extract the principal subspace direction of the original matrix, while ensuring numerical stability and removing linear correlation, it lays the foundation for subsequent dimension reduction and approximation.

[0037] After obtaining the matrix Q, construct a small matrix:

[0038] Y2 = Q T Y ex

[0039] where Perform SVD decomposition on Y2 to get the left singular matrix of Y2 Map back to the original space to restore the left singular matrix U:

[0040]

[0041] The restored left singular matrix U; keep the first S n left singular vectors to construct the signal subspace U s , and use its shift invariance to establish the relationship between the time delay and the eigenvalue, and construct the matrix pair: (U s2 , Us1 ); wherein, U s1 is removed U s The last row of the obtained matrix, U s2 is removed U s The first row of the obtained matrix;

[0042] Constructing a matrix pencil equation Moore-Penrose pseudo-inverse represented as U s1 , the eigenvalues of the eigenvalue decomposition of Φ are {λ1,..., λ l}, wherein the eigenvalues are τ l is the propagation delay TOF of the path to be solved; the time delay of each block CSI data block is calculated, wherein the minimum time delay is the time delay of the direct diameter required;

[0043] Advantages

[0044] The application provides a TOF estimation method of a matrix pencil based on block and random SVD decomposition.

[0045] The method designed in the application greatly reduces the algorithm complexity, improves the robustness of the system and the estimation accuracy of the TOF. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 The application is a block diagram of a TOF estimation method of a matrix pencil based on block and random SVD decomposition. DETAILED DESCRIPTION

[0047] The application aims to provide a TOF estimation method of a matrix pencil based on block and random SVD decomposition under a WiFi sensing system, which greatly reduces the algorithm complexity, improves the robustness of the system and the estimation accuracy of the TOF.

[0048] The application provides a TOF estimation method of a matrix pencil based on block and random SVD decomposition, which specifically comprises the following steps:

[0049] Step one: the signal is transmitted by an OFDM system, the OFDM has 256 subcarriers; the signal has a multipath effect when propagating in a wireless channel, the lth path reaches a uniform linear array, wherein 1≤l≤L; the time of flight of the signal is τ l , and the center frequency is fc , subcarrier spacing is △f; the receiving end is a single antenna, the kth subcarrier, where 1≤k≤K; the CSI of a single subcarrier is represented as:

[0050]

[0051] where, α l represents the complex attenuation of the lth path, σ k represents channel noise, and j represents the imaginary symbol;

[0052] The CSI information of the WiFi signal obtained by the receiving end is represented as a matrix:

[0053] H=[H(1),H(2),H(3),…,H(254),H(255),H(256)]

[0054] where H(k) represents the CSI data of the kth subcarrier;

[0055] Step two: block overlap processing of CSI, first, the CSI data is divided into multiple short CSI data blocks with overlapping parts between adjacent blocks by block overlap technology, the number of CSI data blocks is set to β, and the overlap rate between blocks is set to ο;

[0056] Because of the overlap, the actual number of blocks will be more than the set CSI data block number β, so the actual effective block number B is calculated as:

[0057]

[0058] The length n of each block of CSI data after block division is:

[0059]

[0060] where N is the length of the unblocked CSI data;

[0061] After calculating the size of each block, the size of the overlapping part is calculated:

[0062] O=n×ο

[0063] After calculating the actual effective block number and the size of each block, the CSI data is divided into blocks according to the size of each block, and the obtained CSI data block is:

[0064] H1=[H(1),H(2),H(3),…,H(n)]

[0065] H2=[H(n-O+1),H(n-O+2),…,H(n-O+n)]

[0066]

[0067] H B = [H((B-1) x (n-0) +1), H((B-1) x (n-0) +2),..., H((B-1) x (n-0) +n)] where H((B-1) x (n-0) +i) = H((B-1) x (n-0) +i-1) + H((B-1) x (n-0) +i-2) +... + H((B-1) x (n-0) +i-n) i = 1, 2,..., n B denotes the B-th block of CSI data;

[0068] Step three: Construct Hankle matrix with the CSI data block of length n obtained by step two denotes the complex field:

[0069]

[0070] where, M = n - L + 1;

[0071] Construct the augmented matrix Y denotes: where, is the complex conjugate matrix of Y, and is the permutation matrix, denotes the real field, and denotes:

[0072]

[0073] Step four: Construct the random projection matrix: where r = S n + s, which is used to determine the dimension of the random projection matrix. If r is too small, important information will be lost, and the approximation error will be large. If r is close to the true rank of the matrix or even larger, it is almost as accurate as complete SVD, but the speed advantage will be reduced. S n is the number of sources, and s is the redundant dimension, which is generally 5-10. The random projection matrix is a random Gaussian matrix, where each element follows a standard normal distribution. The purpose is to map the column space of the original matrix to a low-dimensional space;

[0074] Then calculate the random projection of the augmented matrix Y ex obtained in step three:

[0075] Y1 = Y ex Ω

[0076] Perform QR decomposition on Y1:

[0077] Y1 = QR

[0078] Obtain Q is a unit vector whose column vectors are mutually orthogonal. In order to extract the principal subspace direction of the original matrix, while ensuring numerical stability and removing linear dependence, it lays the foundation for subsequent dimensionality reduction and approximation.

[0079] After obtaining matrix Q, construct a smaller matrix:

[0080] Y2 = Q T Y ex

[0081] in, Performing SVD decomposition on Y2 yields the left singular matrix of Y2. Will Mapping back to the original space, we recover the left singular matrix U:

[0082]

[0083] The recovered left singular matrix U; retaining the first S n The left singular vectors construct the signal subspace U. s By utilizing its translation invariance, the relationship between time delay and eigenvalues ​​is established, and a matrix pair is constructed: (U s2 U s1 ); where U s1 To remove U s The matrix obtained in the last row, U s2 To remove U s The matrix obtained in the first row;

[0084] Constructing matrix bundle equations Represented as U s1 The Moore-Penrose pseudoinverse, obtained by eigenvalue decomposition, yields eigenvalues ​​of Φ as {λ1,…,λ...} l}, where the eigenvalues ​​are τ l The propagation delay (TOF) of the desired path is calculated; the delay of each CSI data block is calculated, where the minimum delay is the propagation delay of the direct path.

Claims

1. A TOF estimation method based on block and random SVD decomposition of matrix pencil Step one: the signal is transmitted by OFDM system, OFDM has 256 subcarriers, and the CSI information of WiFi signal is obtained by the receiver of the receiving end; the signal has multipath effect in the wireless channel, and the 1th path reaches the uniform linear array, wherein 1≤l≤L; the time of flight of the signal is τ l , the center frequency is f c , and the subcarrier spacing is △f; the receiving end is a single antenna, and the 1th subcarrier is on the kth subcarrier, wherein 1≤k≤256; the CSI data of a single data packet received is represented as: H = [H(1), H(2), H(3), …, H(254), H(255), H(256)] wherein H(k) represents the CSI data of the kth subcarrier; Step two: divide the CSI data into multiple short CSI data blocks with overlapping parts between adjacent blocks through block overlap technology, The length n of each block of CSI data after the block is: Wherein, N is the length of the CSI data, B is the number of blocks of the CSI data; After calculating the size of each block, the size of the overlapping part is calculated: O = n x o, wherein o is the overlapping rate between adjacent blocks; After calculating the actual effective block number and the size of each block, the CSI data is divided and overlapped according to the size of each block, and the obtained CSI data block is obtained. Step three: the length of n CSI data block obtained by overlapping the step two is smoothed to remove the interference between coherent signals, and the Hankle matrix is constructed wherein, is represented in the complex field, M = n - L + 1, L is the sliding window size for smoothing between CSI data in the CSI data block; in order to increase the inherent snapshot number, an augmented matrix is defined in the forward and backward ways is represented in the real field, wherein, is the complex conjugate matrix of Y, and is a permutation matrix; Step four: In order to map the column space of the augmented matrix obtained in step three into a low-dimensional space, a random projection matrix is constructed: where r = S n + s, S n is the number of sources, and s is the redundancy dimension; a random projection is performed on Y ex : Y1 = Y ex Ω; in order to extract the principal subspace direction of the original matrix while ensuring numerical stability and removing linear correlation, QR decomposition is performed on Y1: Y1 = QR, and Q is obtained, where Q is a unit vector with orthogonal column vectors; after obtaining the matrix Q, the augmented matrix is mapped into a low-dimensional space: Y2 = Q T Y ex where SVD decomposition is performed on Y2 to obtain the left singular matrix of Y2 and singular values: Step five: the mapping back to the original space, restore the left singular matrix: Mapping back to the original space, restore the left singular matrix: Using its shift invariance to establish the relationship between the delay and eigenvalue, the matrix pair is constructed: (U s2 ,U s1 );Wherein, U s1 is the matrix obtained by removing the last row of U s , U s2 is the matrix obtained by removing the first row of U s ; Construct the matrix pencil equation The Moore-Penrose pseudo-inverse of U s1 is represented as Φ, and the eigenvalues of Φ obtained by eigenvalue decomposition are {λ1,…,λ l}, wherein the eigenvalue is τ l The propagation delay TOF of the path to be solved; The delay of each block CSI data is calculated, and the minimum delay is the propagation delay of the direct diameter.

2. The TOF estimation method based on block weighting and random SVD decomposition of matrix pencil according to claim 1, wherein the step two of block overlap processing of the CSI data comprises the following steps: The block overlap processing of the CSI is performed as follows: first, the CSI data is divided into multiple short CSI data blocks with overlapping parts between adjacent blocks through block overlap technology; the number of blocks of the CSI data is set as β; and the overlap rate between the blocks is set as ο. Since there is overlap, the actual number of blocks is more than the set number of blocks β of the CSI data, so the actual effective block number B is calculated first: The length n of each block of the CSI data after the block is: Wherein, N is the length of the unblocked CSI data; After calculating the size of each block, the size of the overlapping part is calculated: O = n x ο After calculating the actual effective block number and the size of each block, the CSI data is block overlapped according to the size of each block, and the obtained CSI data block is: H1 = [H(1), H(2), H(3), …, H(n)] H2 = [H(n-O+1), H(n-O+2), …, H(n-O+n)] H B = [H((B-1)x(n-0)+1), H((B-1)x(n-0)+2),..., H((B-1)x(n-0)+n)] where H B represents the Bth block of CSI data; the CSI data in the matrix: where α l represents the complex attenuation of the lth path, σ k represents the channel noise, and j represents the imaginary symbol.

3. The TOF estimation method based on block weighting and random SVD decomposition of matrix pencil according to claim 1, wherein the step four of performing random SVD decomposition on the augmented matrix comprises the following steps: Constructing a random projection matrix: wherein, r = S n + s, S n is the number of sources, s is the redundancy dimension, generally taking the value of 5-10; the augmented matrix Y obtained in step three is calculated ex Random projection: Y1 = Y ex Ω QR decomposition is performed on Y1: Y1 = QR Obtained Q is a column vector of mutually orthogonal unit vectors, in order to extract the main subspace direction of the original matrix, while ensuring numerical stability, removing linear correlation, and laying a foundation for subsequent dimension reduction and approximation; After obtaining the matrix Q, the augmented matrix is mapped to a low-dimensional space Y2: Y2 = Q T Y ex wherein, SVD decomposition of Y2 gives the left singular matrix of Y2 mapping back to the original space, restoring the left singular matrix ​

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