CN114048783A - Cellular signal map construction method based on mobile group perception - Google Patents

Cellular signal map construction method based on mobile group perception Download PDF

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CN114048783A
CN114048783A CN202111365159.XA CN202111365159A CN114048783A CN 114048783 A CN114048783 A CN 114048783A CN 202111365159 A CN202111365159 A CN 202111365159A CN 114048783 A CN114048783 A CN 114048783A
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王帅
王海
梅洛瑜
徐鑫
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Abstract

The invention discloses a construction method of a cellular signal map based on mobile group perception, which stores space-time characteristics of signal data by using a three-dimensional tensor, wherein three dimensions of the tensor respectively represent length, width and time dimensions. When a signal map is constructed, potential factor feature collection of MCS signal data is firstly carried out, and then internal features of the MCS signal data are extracted. And then, estimating the missing signal value, and realizing signal recovery by using Bayesian probability tensor decomposition on the basis of potential factor characteristic acquisition to obtain the internal characteristics of the MCS data. And finally, introducing a new multi-view feature fusion module based on learning, embedding the external features into a vector, combining the external features with the internal features, inputting the combined internal features into a full-connection layer, acquiring the signal features and constructing a fine-grained signal diagram.

Description

Cellular signal map construction method based on mobile group perception
Technical Field
The invention relates to the field of signal map construction, in particular to a cellular signal map construction method based on mobile group perception.
Background
With the rapid development of the internet of things in smart cities and the field of automatic driving services, the demand for wireless spectrum resources is increasing day by day, and the wireless coverage environment is more complex. The complex and crowded wireless environment makes the spectrum resources precious. To meet this trend, signal diagrams are an effective indicator of a constant-volume wireless environment, which can be applied to various real-world applications, including network operations, spectrum monitoring, and location-based services. The signal map is a fingerprint database that is tagged with location information for a particular area. We estimate the location of the online fingerprint measurement by comparing it to the fingerprint on the signal map. Furthermore, constructing and analyzing signal maps is a typical way to assess the availability of mobile broadband technologies (e.g. 4G/LTE, 5G) in different regions and to compare different operators.
Since wireless signals are susceptible to various factors, such as automatic adjustment of transmission power, multipath fading, non-line-of-sight propagation, etc., it is difficult to maintain the latest signal diagram on an urban scale in a timely and efficient manner. Many studies on signal map construction rely on labor intensive and time consuming field surveys, which must be conducted regularly to keep up to date the signal map, given that the reference points are predefined, resulting in extremely high costs. To reduce the costs of intensive field investigations, there have also been some studies attempting to construct signal maps using model-based methods and data-driven methods.
The existing signal diagram construction method has two limitations: model-based approaches typically make strong assumptions about the distribution of the signal map (e.g., the ideal propagation space), which greatly limits their ability to model complex real-world wireless environments. Data-driven methods require large amounts of measurement data, which are typically collected by war-driving and population awareness. But these data do not cover all areas of the network and do not closely reflect the user's actual experience. The crowd sensing method does not process the multi-level simultaneous interdependency relationship and extracts the spatial features in a limited local area. Furthermore, fusion of signal internal features with external environmental features lacks a uniform representation.
Disclosure of Invention
In order to solve the problems, the invention discloses a cellular signal map construction method based on mobile group perception, which comprises the following steps:
step 1, representing the space-time characteristics of signal data as three-dimensional tensor S e RI×J×KWherein I, J represents the length and width grid number of the rectangular area; k represents the signal acquisition time span in the grid; sijkRepresenting a signal value received by the mobile device from the base station;
step 2, extracting potential factor characteristics of MCS signal data, and calibrating signal values at a part of a BS coverage crossing region;
step 3, decomposing and recovering the signal value of the unobserved area by adopting a Bayesian probability tensor, namely predicting a missing signal;
step 4, constructing an internal view and an external view; then, a new multi-view feature fusion module based on learning is introduced, high-dimensional features are extracted and embedded into each view by using two networks, and then different views are spliced and fused by using two full-connection layers to generate a fine and accurate signal diagram.
The invention further improves that:
compared with other data sources (such as urban traffic data and noise data), the signal data is more susceptible to environmental influences and shows volatility characteristics. We generally find the approximation by taking the average of a given area. However, due to the different characteristics of each BS (e.g., coverage area, antenna transmit power, etc.), it is not appropriate to directly average the signals in some overlapping BS coverage areas, resulting in signal drift and errors. More importantly, due to various unknown factors, we cannot effectively utilize the relationship between signals received by multiple BSs in the same grid. Therefore, considering the tensor-based method, it is necessary to extract data satisfying the tensor low rank characteristics, and to construct a tensor decomposition method suitable for signal data completion. That is, we need to scale the signal values at portions of the intersection region before constructing the tensor and decomposition.
In the step (2), the method for extracting the latent factor features comprises the following steps:
step 201, describing spatial correlation by using Euclidean distance, and then associating geographical positions on a map, and expressing the distance correlation between BSs by using formula (1):
Figure BDA0003360402660000031
wherein σ2Represents variance, phi (i, j) represents the relationship of positions i, j, | li-lj||2The representation representing the Euclidean distance, i.e.
Figure BDA0003360402660000032
Step 202, expressing the cosine similarity between two high-dimensional signal vectors by using a formula (2), and extracting another feature:
Figure BDA0003360402660000033
wherein the content of the first and second substances,
Figure BDA0003360402660000034
h represents the dimension of the object to be measured,
Figure BDA0003360402660000035
representing the vector of signals received from the H BSs in grid i.
The invention further improves that: by data analysis, we know that signal data approximately obeys normal distribution;
in the step (3), the Bayesian probability tensor decomposition is adopted to predict the missing signal value, and the specific method is as follows:
step 301, assume that the noise term approximation of each observation term follows an independent Gaussian distribution, i.e.
Figure BDA0003360402660000041
Further to the row vector of all factor matrixA priori distributions are made and they are assumed to be multivariate gaussian functions, i.e.
Figure BDA0003360402660000042
Wherein, muu∈ RR,Λu∈RR×RAnd satisfies formula (3), the probability distribution function of which is formula (4):
u,Λu)~Gaussian-Wishart(μ0,β0,W0,v0) (3)
p(μu,Λu|Θ)=N(μu0,(β0Λu)-1)×Wishart(Λu|W0,v0) (4)
step 302, since the accuracy of the signal data is unknown and it cannot be obtained completely through the reciprocal of all observed value variances, in order to improve the robustness of the model, we introduce a flexible conjugate Gamma prior to the accuracy parameter τ, and express the prior function distribution thereof by using formula (5):
Figure BDA0003360402660000043
wherein the parameters U, V, W, tau and the hyperparameter muu,Λu,μv,Λv,μw,Λw,a0,b0Solving by utilizing Gibbs sampling;
step 303. factor matrix U, V, W can pass Ui,vi,wiAnd solving, wherein the calculation method comprises the following steps:
30301, since the noise term of each observation term approximately follows independent Gaussian distribution, the likelihood function is obtained, and the expression is shown as formula (6):
Figure BDA0003360402660000044
in the formula, the Hadamard product is expressed.
30302, because the row vector of the factor matrix obeys multivariate Gaussian distribution, and combines the likelihood function in the step 30401 to obtain the posterior distribution, the expression of which is shown as the formula (7):
Figure BDA0003360402660000051
step 30303, according to the posterior distribution obtained in step 30402, the method can be obtained according to the formula (8) and the formula (9)
Figure BDA0003360402660000052
Figure BDA0003360402660000053
Figure BDA0003360402660000054
Step 304. similarly, u is determined by the method described abovei,vi,wiAnd finally, after the Gibbs sampling algorithm reaches a steady state, all missing values can be estimated through Monte Carlo approximation, and then the estimation of missing signal data is realized.
The invention further improves that: in the step (4), the internal trial and the external trial are firstly built, and the specific method is as follows:
step 40101, the tensor distribution of the recovered terrestrial signals obtained in the step (3) and the characteristics thereof are used as an internal view;
and 40102, mapping the collected information data including the external characteristic signals of the population, the road network and the POI into tensors as external attempts.
5. The cellular signal mapping method based on mobile community perception according to claim 4, wherein in the step (4), two networks are used to extract and embed high-dimensional features for each view respectively, and the specific method is as follows:
40201, for the internal view, dividing the tensor into matrixes according to the update period of the signals and the time dimension to form a coarse-grained signal diagram
Figure BDA0003360402660000055
Introducing an average pooling layer, and integrating the features extracted from the historical signal diagram to obtain a fine-grained signal diagram
Figure BDA0003360402660000061
Step 40202, for the external view, a new context-aware neural network is provided, and external features are embedded; population, road network and POI distribution characteristics and representing them with embedded vectors; specifically, we first collect the extrinsic features and partition them into the same geographic space as the tensor. Then, in order to integrate the background features of different types and enhance the expression capability of the features, embedding the external feature sets of each small grid region to obtain an embedded vector of the background external features;
step 40203, mapping the fine-grained signal diagram obtained in the step 40201 and the external feature vector obtained in the step 40202, and processing by using a convolution layer to enhance the reconstruction of external information;
the invention further improves that: in the step (4), splicing and fusing different views by utilizing two full-connection layers to generate a fine and accurate signal diagram, and the specific method comprises the following steps:
40301, respectively inputting the internal features and the external features into two multi-sensing layers, and then fusing the internal features and the external features with a connecting layer to obtain fine and accurate signal mapping;
step 40302 use Adam optimizer by providing training pairs
Figure BDA0003360402660000062
To learn the proposed model and to calculate the pixel-direction mean square error loss of the back propagation;
step 40303. introduce mask matrix M ∈ R ^ (NI × NJ) in fine-grained signal mapRegions with available data are shown, defining a loss function
Figure BDA0003360402660000063
Training the fusion network to fuse the signal features with the external features, and constructing a fine-grained signal diagram on the basis of a coarse-grained signal diagram restored by tensor
The invention has the beneficial effects that:
two challenges are addressed, including: (1) missing and unreliable MCS data problems; (2) the spatial-temporal uncertainty of the signal propagation. The cellular signal diagram reconstruction method simultaneously captures space-time characteristics of signals between cellular base stations and in the cellular base stations, and utilizes Bayesian tensor decomposition to recover missing signals so as to construct a large-area fine-grained signal diagram. In addition, the method develops a context-aware multi-view fusion network to fully utilize external information and improve the construction precision of the signal diagram.
Drawings
FIG. 1: a flow chart of a cellular signal map construction method based on mobile group perception;
FIG. 2: constructing a system frame diagram by the cellular signal map;
FIG. 3: the overall graph structure of the Bayesian tensor decomposition generation process is generated;
FIG. 4: a multi-view converged network architecture;
FIG. 5: a cellular signal map construction method based on mobile group perception is disclosed.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention. It should be noted that the terms "front," "back," "left," "right," "upper" and "lower" used in the following description refer to directions in the drawings, and the terms "inner" and "outer" refer to directions toward and away from, respectively, the geometric center of a particular component.
As shown in fig. 1 to 5, the present embodiment provides a cellular signal mapping method based on mobile group perception, including the following steps:
step 1, representing the space-time characteristics of signal data as three-dimensional tensor S e RI×J×KWherein I, J represents the length and width grid number of the rectangular area; k represents the signal acquisition time span in the grid; sijkRepresenting a signal value received by the mobile device from the base station;
step 2, extracting potential factor characteristics of MCS signal data, and calibrating signal values at a part of a BS coverage crossing region; compared with other data sources (such as urban traffic data and noise data), the signal data is more easily influenced by the environment and shows volatility characteristics. We generally find the approximation by taking the average of a given area. However, due to the different characteristics of each BS (e.g., coverage, antenna transmit power, etc.), it is not appropriate to directly average the signals in some overlapping BS coverage areas, which can lead to signal drift and errors. More importantly, due to various unknown factors, we cannot effectively utilize the relationship between signals received by multiple BSs in the same grid. Therefore, when considering the tensor-based method, we need to extract data satisfying the tensor low-rank characteristics to construct a tensor decomposition method suitable for signal data completion. That is, we need to scale the signal values at portions of the intersection region before constructing the tensor and decomposition. Inspired by BS knowledge extraction, a suitable latent factor feature extraction method is designed: in general, the closer the two locations, the higher the correlation of the two samples. We describe spatial correlation using euclidean distance and then relate the geographical locations on the map. The distance correlation between BSs is defined as:
Figure BDA0003360402660000081
in addition, we also use cosine similarity between two high-dimensional signal vectors to perform another feature extraction, which is defined as:
Figure BDA0003360402660000082
step 3, decomposing and recovering the signal value of the unobserved area by adopting a Bayesian probability tensor, namely predicting a missing signal;
from data analysis, we know that signal data approximately follows a normal distribution. Therefore, I assume that the noise term of each observation term approximately follows an independent Gaussian distribution and is defined as
Figure BDA0003360402660000091
We further distribute the row vectors of all the factor matrices a priori and assume that they obey a multivariate Gaussian distribution
Figure BDA0003360402660000092
Hyperparameter muu∈RR,Λu∈RR×R. This will enhance the robustness of the model and accelerate the convergence speed, using a sampling algorithm for model reasoning. Wherein the hyperparameter muu,ΛuIs defined as
u,Λu)~Gaussian-Wishart(μ0,β0,W0,v0)
p(μu,Λu|Θ)=N(μu0,(β0Λu)-1)×Wishart(Λu|W0,v0)
Since the accuracy of the signal data is unknown and it cannot be captured completely by the inverse of all observed variances. To improve the robustness of the model, we introduce a flexible conjugate Gamma prior on the model:
Figure BDA0003360402660000093
fig. 2 is an overall diagram structure describing the above-described bayesian tensor decomposition generation process. Wherein the parameters U, V, W, tau and the hyperparameter muu,Λu,μv,Λv,μw,Λw,a0,b0All can pass through the jeanAnd (5) solving the Gaussian sample. Since each observation follows an independent gaussian distribution, its likelihood can be written:
Figure BDA0003360402660000094
obtaining posterior distribution:
Figure BDA0003360402660000101
then, the following is obtained:
Figure BDA0003360402660000102
Figure BDA0003360402660000103
similarly, vj,wkThe above method can be used. And finally, after the Gibbs sampling calculation method reaches a steady state, all missing values can be estimated through Monte Carlo approximation, and then the estimation of the missing signal data is realized.
Step 4, constructing an internal view and an external view; then, a new multi-view feature fusion module based on learning is introduced, high-dimensional features are extracted and embedded into each view by using two networks, and then different views are spliced and fused by using two full-connection layers to generate a fine and accurate signal diagram.
Inside and outside view configuration
And after the missing signals are restored by the tensor, a coarse-grained signal coverage map of the specified area is obtained. Although tensors have a good spatial structure to mine spatio-temporal information, the signals recovered in the same grid may differ significantly at different times due to the influence of dynamic environment. The signal diagram is considered to be constant over a certain update period. However, the final signal map obtained by averaging only the historical signal maps at different times is coarse-grained and inaccurate. Because the external features (population, POI and road network) in the adjacent grids are similar, the signals received in the grids have certain similarity, which is beneficial to constructing a fine-grained signal diagram. Therefore, in order to improve the accuracy of the signal diagram, the fusion of the internal and external features of the multi-view is further realized, and the restored signal distribution tensor and the feature view thereof are taken as an A view. The collected information, including extrinsic signatures of population, road networks and POIs, is mapped into tensors as B-views.
Multi-viewpoint neural fusion
A network that merges the different views to construct the final signal diagram is shown in fig. 3. Firstly, two networks are used for respectively extracting and embedding high-dimensional features into each view, and then two full-connection layers are used for splicing and fusing different views to generate a fine and accurate signal diagram.
In fig. 4, for view a, a complete signal space-time characteristic is expressed in tensor form. Dividing the tensor into matrices according to the update period of the signal diagram, i.e. coarse-grained signal diagram
Figure BDA0003360402660000111
Introducing an average pooling layer, and integrating the features extracted from the historical signal diagram to obtain a fine-grained signal diagram
Figure BDA0003360402660000112
For the B view, we propose a new context-aware neural network, embedding the distribution features of external features (population, road network and POI) and representing them with embedded vectors. Specifically, we first collect the extrinsic features and partition them into the same geographic space as the tensor. Then, in order to integrate these different types of background features and enhance the expressive power of the features, we embed these external feature sets of each small grid region to obtain an embedded vector of the background external features. Finally, the fine-grained signal is mapped and connected with the fine-grained signal, and then the fine-grained signal is processed by the convolutional layer, so that the reconstruction process of external information is enhanced.
To fuse two-part feature embedding, we first input the internal features and the external features into two multi-sensing layers, respectively, and then fuse them with the connection layer, resulting in a fine and precise signal mapping. We use Adam optimizer by providing training pairs
Figure BDA0003360402660000113
The proposed model is learned and the back-propagated pixel-direction mean square error loss is calculated. We introduce a mask matrix M ∈ RNI×NJAreas with available data are represented in the fine-grained signal diagram. We define the loss function:
Figure BDA0003360402660000121
the fusion network solves the problem of space granularity division, enables signal characteristics and external characteristics to be fused, and constructs a fine-granularity signal diagram on the basis of a coarse-granularity signal diagram restored by tensor.
The technical solution of the present embodiment can be applied to the following embodiments:
example 1:
the method is used for constructing a high-quality and fine-grained signal map.
And recovering the signal data according to the MCS space-time data information and external environment information (such as population, roads, POI and BS positions), thereby constructing a fine-grained signal map.
Example 2:
real-time updating and maintenance of cellular signal networks.
Due to environmental impact and population mobility, signal data has strong space-time dependence, so that a signal diagram needs to be updated in real time. And constructing a signal diagram according to the current data information by using the cellular signal diagram constructing system, and providing updates for the user.
Example 3:
the method is used for space positioning and provides geographic information service.
And acquiring signal data by utilizing a cellular signal diagram construction system, and analyzing the distance correlation between the signal intensity and a base station, thereby realizing the spatial positioning of a signal source and providing corresponding geographic information service for users.
This example to evaluate the performance of CSMC, we conducted extensive experimental and ablative studies on a large-scale dataset of over 200GB MCS signal recordings acquired in the shanghai. As shown in tables 1 and 2, the signal estimation error performance of the method is improved by 29% compared with the conventional method.
TABLE 1 MAPE and RMSE results for different methods at 30%, 60%, 90% sampling rate (City)
Figure BDA0003360402660000131
TABLE 2 MAPE and RMSE results for different methods at 30%, 60%, 90% sampling rate (suburban area)
Figure BDA0003360402660000132
Figure BDA0003360402660000141
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features.

Claims (6)

1. A cellular signal map construction method based on mobile group perception is characterized by comprising the following steps:
step 1, representing the space-time characteristics of signal data as three-dimensional tensor S e RI×J×KWherein I, J represents the length and width grid number of the rectangular area; k represents the signal acquisition time span in the grid; sijkRepresenting a signal value received by the mobile device from the base station;
step 2, extracting potential factor characteristics of MCS signal data, and calibrating signal values at a part of a BS coverage crossing region;
step 3, decomposing and recovering the signal value of the unobserved area by adopting a Bayesian probability tensor, namely predicting a missing signal;
step 4, constructing an internal view and an external view; then, a new multi-view feature fusion module based on learning is introduced, high-dimensional features are extracted and embedded into each view by using two networks, and then different views are spliced and fused by using two full-connection layers to generate a fine and accurate signal diagram.
2. The cellular signal mapping method based on mobile group perception according to claim 1, wherein in the step (2), the potential factor feature extraction method is performed as follows:
step 201, describing spatial correlation by using Euclidean distance, and then associating geographical positions on a map, and expressing the distance correlation between BSs by using formula (1):
Figure FDA0003360402650000012
wherein σ2Represents variance, phi (i, j) represents the relationship of positions i, j, | li-lj||2The representation representing the Euclidean distance, i.e.
Figure FDA0003360402650000011
Step 202, expressing the cosine similarity between two high-dimensional signal vectors by using a formula (2), and extracting another feature:
Figure FDA0003360402650000021
wherein the content of the first and second substances,
Figure FDA0003360402650000022
h represents the dimension of the object to be measured,
Figure FDA0003360402650000023
representing the signal vectors received from the H BSs in grid i.
3. The cellular signal map construction method based on mobile group perception according to claim 1, wherein in the step (3), the missing signal values are estimated by Bayesian probability tensor decomposition, and the specific method is as follows:
step 301, assume that the noise term approximation of each observation term follows an independent Gaussian distribution, i.e.
Figure FDA0003360402650000024
The row vectors of all the factor matrices are further distributed a priori and are assumed to be multivariate gaussian functions, i.e. they are
Figure FDA0003360402650000025
Wherein, muu∈RR,Λu∈RR×RAnd satisfies formula (3), the probability distribution function of which is formula (4):
u,Λu)~Gaussian-Wishart(μ0,β0,W0,v0) (3)
p(μu,Λu|Θ)=N(μu0,(β0Λu)-1)×Wishart(Λu|W0,v0) (4)
step 302, since the accuracy of the signal data is unknown and it cannot be obtained completely through the reciprocal of all observed value variances, in order to improve the robustness of the model, we introduce a flexible conjugate Gamma prior to the accuracy parameter τ, and express its prior function distribution by using formula (5):
Figure FDA0003360402650000026
wherein the parameters U, V, W, tau and the hyperparameter muu,Λu,μv,Λv,μw,Λw,a0,b0Solving by utilizing Gibbs sampling;
step 303. factor matrix U, V, W can pass Ui,vi,wiAnd solving, wherein the calculation method comprises the following steps:
30301, since the noise term of each observation term approximately follows independent Gaussian distribution, the likelihood function is obtained, and the expression is shown as formula (6):
Figure FDA0003360402650000031
in the formula, a Hadamard product is represented;
30302, because the row vector of the factor matrix obeys multivariate Gaussian distribution, and combines the likelihood function in the step 30401 to obtain the posterior distribution, the expression of which is shown as the formula (7):
Figure FDA0003360402650000032
step 30303, according to the posterior distribution obtained in step 30402, the method can be obtained according to the formula (8) and the formula (9)
Figure FDA0003360402650000033
Figure FDA0003360402650000034
Figure FDA0003360402650000035
Step 304. similarly, u is determined by the method described abovei,vi,wiAnd finally, after the Gibbs sampling algorithm reaches a steady state, all missing values can be estimated through Monte Carlo approximation, and then the estimation of the missing signal data is realized.
4. The cellular signal mapping method based on mobile group perception according to claim 1, wherein in step (4), the advanced internal and external attempts are constructed as follows:
step 40101, the tensor distribution of the recovered terrestrial signals obtained in the step (3) and the characteristics thereof are used as an internal view;
and 40102, mapping the collected information data including the external characteristic signals of the population, the road network and the POI into tensors as external attempts.
5. The cellular signal mapping method based on mobile community perception according to claim 4, wherein in the step (4), two networks are used to extract and embed high-dimensional features for each view respectively, and the specific method is as follows:
40201, for the internal view, dividing the tensor into matrixes according to the update period of the signals and the time dimension to form a coarse-grained signal diagram
Figure FDA0003360402650000041
Introducing an average pooling layer, and integrating the features extracted from the historical signal diagram to obtain a fine-grained signal diagram
Figure FDA0003360402650000042
Step 40202, for the external view, a new context-aware neural network is provided, and external features are embedded; distribution characteristics of population, road network and POI, and representing the population, road network and POI by embedded vectors; specifically, we first collect the extrinsic features and partition them into the same geographic space as the tensor. Then, in order to integrate the background features of different types and enhance the expression capability of the features, embedding the external feature sets of each small grid region to obtain an embedded vector of the background external features;
and 40203, mapping the fine-grained signal diagram obtained in the step 40201 and the external feature vector obtained in the step 40202, and processing by using a convolutional layer to enhance the reconstruction of external information.
6. The cellular signal map construction method based on mobile group perception according to claim 5, wherein in the step (4), the two full connection layers are used for splicing and fusing different views to generate a fine and accurate signal map, and the specific method is as follows:
40301, respectively inputting the internal features and the external features into two multi-sensing layers, and then fusing the internal features and the external features with a connecting layer to obtain fine and accurate signal mapping;
step 40302 use Adam optimizer by providing training pairs
Figure FDA0003360402650000043
To learn the proposed model and to calculate the pixel-direction mean square error loss of the back propagation;
step 40303, introduce mask matrix M ∈ R ^ (NI × NJ) in fine granularity signal diagram representation has available data area, defined loss function
Figure FDA0003360402650000051
And training the fusion network to fuse the signal features with the external features, and constructing a fine-grained signal diagram on the basis of the coarse-grained signal diagram recovered by the tensor.
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