CN112967353A - Sparse radio frequency tomography method based on Gaussian mixture model - Google Patents

Sparse radio frequency tomography method based on Gaussian mixture model Download PDF

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CN112967353A
CN112967353A CN202110360892.6A CN202110360892A CN112967353A CN 112967353 A CN112967353 A CN 112967353A CN 202110360892 A CN202110360892 A CN 202110360892A CN 112967353 A CN112967353 A CN 112967353A
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钱慧
陈海涛
林荔琳
林楠
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Abstract

The invention relates to a sparse radio frequency tomography method based on a Gaussian mixture model, which comprises the following steps of: step S1, acquiring a wireless link RSS value under the condition of no target, and establishing an environment background link model based on GMM; step S2, matching the collected real-time RSS data with the established environment background link model, reserving an effective link, and filtering a redundant link; the method comprises the steps of S3, learning and training a reconstructed image through a GMM-based prior model according to the random characteristics of an observation background region, obtaining structural feature parameters of the image, reconstructing the image through a GMM-based prior Bayes compressed sensing algorithm, and obtaining a reconstructed image, and S4, restoring the reconstructed image through a compressed space image by using an MRF-based prior image restoration method. The method can effectively reduce the interference caused by the change of the background, reduce the noise of the reconstructed image and improve the imaging quality of the system.

Description

Sparse radio frequency tomography method based on Gaussian mixture model
Technical Field
The invention belongs to the field of equipment-free positioning, and particularly relates to a sparse radio frequency tomography method based on a Gaussian mixture model.
Background
A Device-free Localization (DFL) technology is one of the main research hotspots of the internet of things. The DFL technology can realize positioning of the observation target without carrying any equipment, and has wide application prospect in the fields of traffic, medical treatment, rescue, military and the like. Radio-frequency tomography (RTI) is a classical DFL technique. Because the radio frequency signal can penetrate through non-metallic substances (such as walls, smoke, trees and the like) and is not limited by the intensity of light, the RTI technology is expected to be applied to a plurality of fields such as military affairs, anti-terrorism, fire rescue, medical nursing, night field animal monitoring and the like, intelligent perception is realized in the future Internet of things, and the RTI technology has great development potential. The classical RTI technique adopts a regularization method to solve the problem of uncertainty in image reconstruction. However, the reconstruction performance of regularization methods tends to depend on the number of observation samples. To solve the problem of too long observation time required in the regularization technique, a solution algorithm based on Compressed Sensing (CS) theory is introduced into RTI. The RTI combined with CS can reconstruct image signals from a small number of observation samples, but has a problem that the sampling model does not match the radio frequency observation sample variation. Since in practical communications, radio frequency signals typically exhibit time-variability and instability. Interference exists in the signal transmission environment of the observation area, such as breeze, swinging of tree branches, insects and wireless communication of other frequency bands; meanwhile, a wireless transmission channel of the radio frequency signal has a multipath effect, a target object and other obstacles can reflect, diffract and scatter the signal, and finally a receiving end receives superposition of multiple signals. Therefore, how to deal with the multipath effect of the channel and reduce the interference of noise by constructing an effective model has been a hot issue of CS-RTI research.
Disclosure of Invention
In view of the above, the present invention provides a sparse radio frequency tomography method based on a gaussian mixture model, which effectively solves the problems of multipath effect of a channel and noise reduction.
In order to achieve the purpose, the invention adopts the following technical scheme:
a sparse radio frequency tomography method based on a Gaussian mixture model comprises the following steps:
step S1, acquiring a wireless link RSS value under the condition of no target, and establishing an environment background link model based on GMM;
step S2, matching the collected real-time RSS data with the established environment background link model, reserving an effective link, and filtering a redundant link;
step S3, learning and training a reconstructed image through a GMM-based prior model according to the random characteristics of an observation background region to obtain structural characteristic parameters of the image, and reconstructing the image based on a GMM-based prior Bayesian compressed sensing algorithm to obtain a reconstructed image;
and step S4, restoring the reconstructed image by using the compressed spatial image by adopting an MRF prior-based image restoration method.
Further, the step S1 is specifically:
s11, constructing a wireless sensor node to realize a non-carrying equipment positioning system;
step S12, measuring to obtain RSS value under the condition that no person exists in the observation area;
and step S13, establishing an environment background link model based on the GMM for the wireless link RSS value measured under the condition of no object.
Further, the wireless sensor node realizes that the positioning system of the device without carrying is specifically that a plurality of sensor nodes are deployed around an observation area, two-way wireless links are formed between every two nodes, communication is carried out by sending and receiving radio frequency signals, the observation area is scanned by a communication network formed by the nodes and the wireless links, and a system model is expressed as follows:
y＝W·x+n (1)
in the above formula, y represents the vector of RSS measurements, W is the weight matrix associated with voxel attenuation, x is the reconstructed image, and n represents the system noise.
Further, the model adopted by the weight W is an ellipse model:
Figure BDA0003005491110000031
wherein d is the distance between nodes at two ends of the link, di,j(1) And di,j(2) Respectively the distance from the center of the pixel to the two nodes, and λ is an adjustable parameter describing the width of the ellipse.
Further, the GMM-based environment background link model is as follows:
Figure BDA0003005491110000032
wherein, ynIs a data measurement, C represents the number of Gaussian distributions, λcA corresponding weight for each gaussian distribution. N (y)n|uc,Σc) A probability density function representing a gaussian distribution;
N(yn|uc,Σc) A probability density function representing a gaussian distribution.
Further, the step S3 is specifically:
step S31, learning and training the reconstructed image through a GMM-based prior model according to the random characteristics of the observation background area to obtain the structural characteristic parameter lambda 'of the image'p,k，μ'p,k，∑'p,k；
Step S32, the valid link ybAs input, reconstructing the image according to a Bayes compressed sensing algorithm based on GMM prior to obtain a reconstructed image fp。
Further, the step S32 is specifically:
let fpCompliant with GMM:
Figure BDA0003005491110000041
wherein p represents the number of pixels, λp,k，up,kSum-sigmap,kRespectively representing the weight, mean and variance of the kth Gaussian distribution of the corresponding voxel p; establishing a GMM model for the reconstructed image signal as a posterior probability of Bayesian estimation:
Figure BDA0003005491110000042
estimation of a reconstructed image f using conditional expectationspWherein the expression of the corresponding weight, mean and variance is as follows:
Figure BDA0003005491110000043
further, the step S4 is specifically:
step S41, using MRF to carry out prior learning on the sparse coefficient of the reconstructed image, using the correlation of pixel points to construct a prior model based on MRF, and using Metropolis algorithm to carry out optimal problem estimation on the prior model based on MRF;
and step S42, estimating the unknown number through a CS inversion framework based on the reconstructed image, and restoring the image.
Further, the ADMM algorithm is adopted to carry out image vector
Figure BDA0003005491110000051
And carrying out iterative solution after splitting the solution process.
Compared with the prior art, the invention has the following beneficial effects:
aiming at the problem of performance degradation caused by factors such as multipath interference and environmental noise in the existing CS-RTI system, the invention provides a method for constructing a link background Model based on a Gaussian Mixture Model (GMM). By continuously updating the model parameters, the method adapts to the change of the environment. And then, carrying out prior learning on the image by using the GMM, and reconstructing the image by using a Bayesian compressed sensing algorithm. On the basis, structured learning is proposed to be carried out on the reconstructed image by using a Markov Random Field (MRF), the image is recovered from the Compressed image sample under a Compressed Sensing (CS) framework, the image recovery quality is high, and the system positioning error is small.
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Fig. 1 is a diagram illustrating an implementation of a wireless sensor node as a location system for a portable device in an embodiment of the present invention;
FIG. 2 is a diagram of an elliptical weight model in accordance with an embodiment of the present invention;
FIG. 3 is a flow chart of the system of the present invention;
FIG. 4 is a diagram of a wireless network deployment in an embodiment of the present invention;
fig. 5 is a diagram of a reconstruction result based on a GMM model according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 3, the present invention provides a sparse rf tomography method based on a gaussian mixture model, comprising the following steps:
step S1, acquiring a wireless link RSS value under the condition of no target, and establishing an environment background link model based on GMM;
step S11, referring to fig. 1, in this embodiment, a portable device-free positioning system is implemented by using wireless sensor nodes, a plurality of sensor nodes are deployed around an observation area, two nodes form a bidirectional wireless link therebetween, communication is performed by transmitting and receiving radio frequency signals, and a communication network formed by the nodes and the wireless link scans the observation area. The RTI system uses Received Signal Strength (RSS) to characterize the attenuation levels of different links. And obtaining the attenuation of the image voxel through a mapping relation according to the change value of the RSS and the coordinate of the corresponding sensor node, thereby estimating the target position.
In this embodiment, the system model may be described as a linear model:
y＝W·x+n (1)
in the above formula, y represents the vector of RSS measurements, W is the weight matrix associated with voxel attenuation, x is the reconstructed image, and n represents the system noise.
Preferably, in this embodiment, Wi,jThe matrix is a weighting matrix with dimension of M multiplied by N, and represents the mapping relation between the attenuation value of the jth voxel and the RSS measurement value of the ith link, wherein M is the number of wireless links, and N is the number of the equal-size division voxels.
As shown in fig. 2, the weight model adopted in this embodiment is an ellipse model:
Figure BDA0003005491110000061
wherein d is the distance between nodes at two ends of the link, di,j(1) And di,j(2) Respectively the distance from the center of the pixel to the two nodes, and λ is an adjustable parameter describing the width of the ellipse.
Step S12, the wireless link RSS value measured under the condition of no object is established with an environment background link model based on GMM, the wireless link not affected by the object is called as a redundant link, and y is set asa(ii) a The links affected by the target are called active links, and are set to yb. By means of matching judgment and parameter updating of a link RSS value and a model, an effective link can be judged and selected under the condition of adapting to environment change, and errors caused by redundant links are reduced, wherein a background GMM model is as follows:
Figure BDA0003005491110000071
wherein, ynIs a data measurement, C represents the number of Gaussian distributions, λcA corresponding weight for each gaussian distribution. N (y)n|uc,Σc) A probability density function representing a gaussian distribution.
Step S2, after the background model is built, when the observation target enters the monitoring area, the collected real-time RSS data is matched with the built model, namely parameter training is carried out through the RSS pre-decision model of GMM, and then matching is carried out with the RSS pre-decision model, and effective reservation is keptLink ybFiltering out redundant links ya；
Step S3, learning and training the reconstructed image through a GMM-based prior model according to the random characteristics of the observation background area to obtain the structural characteristic parameter lambda 'of the image'p,k，μ'p,k，∑'p,k. Will be active link ybAs input, image reconstruction is carried out by utilizing the proposed Bayes compressed sensing algorithm based on GMM prior to obtain a reconstructed image fpLet f bepCompliant with GMM:
Figure BDA0003005491110000072
wherein p represents the number of pixels, λp,k，up,kSum-sigmap,kRespectively representing the weight, mean and variance of the kth gaussian distribution of the corresponding voxel p. Similar to the RSS value modeling of the wireless link, a GMM model is established for the reconstructed image signal at this time as a posterior probability of bayesian estimation:
Figure BDA0003005491110000081
estimation of a reconstructed image f using conditional expectationspWherein the expression of the corresponding weight, mean and variance is as follows:
Figure BDA0003005491110000082
Figure BDA0003005491110000083
Figure BDA0003005491110000084
and step S4, restoring the reconstructed image by using the compressed spatial image by adopting an MRF prior-based image restoration method. Firstly, MRF is utilized to carry out prior learning on sparse coefficients of a reconstructed image, and relevance of pixel points is utilized to construct a prior model based on MRF. Wherein, the Metropolis algorithm is adopted to estimate the optimal problem of the MRF model. Secondly, the unknown numbers are estimated by a CS inversion frame for the utilized image samples, and the image is restored. And dividing the variable into two by adopting an ADMM algorithm for iterative solution. The MRF prior based image recovery method captures the structure of a sparse coefficient through MRF, utilizes the local correlation among pixel points, and meanwhile, the CS sparse recovery method can enhance imaging through an MRF model under the condition of a small amount of samples.
Example 1:
in the wireless network testing system composed of 20 wireless sensor nodes, the experiment scene picture and the node layout are shown in fig. 4, 20 sensor nodes are respectively fixed on each support, the distance between each support and the ground is 0.9 m, the interval between adjacent nodes is 1m, a square area of 5 x 5m is defined by the adjacent nodes, and all the sensor nodes work in the 2.4GHz frequency band.
In this embodiment, the received signal strength of each link is measured, a hybrid gaussian model is established for the RSS of the link under observation by using a self-adaptive background hybrid model, and the parameters of the model are updated by using an EM algorithm. The model can adapt to the background changing in real time by a parameter updating method to obtain an RSS attenuation value. The background separation modeling of the Gaussian mixture model is as follows:
Figure BDA0003005491110000091
and K + N is the total number of communication links in the wireless network. Will be active link ybAs reconstruction data, posterior distribution corresponds to, according to bayesian theorem:
Figure BDA0003005491110000092
thereby effectively reconstructing an image, wherein:
Figure BDA0003005491110000093
the posterior probability of x over y is here a gaussian mixture model, which is based on the reconstruction of the GMM. At this time, only the x probability model is reconstructed by the GMM, so we adopt the conditional expectation again to perform single estimation. Obtaining reconstructed image attenuation pixel values
Figure BDA0003005491110000095
Figure BDA0003005491110000094
And finally, effectively restoring the reconstructed image by using the compressed spatial image by adopting an MRF (Markov random field) prior-based image restoration method. The reconstruction of the object through the GMM model at positions 4-2 and 2-3 in the perception region is shown in fig. 5.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (9)

1. A sparse radio frequency tomography method based on a Gaussian mixture model is characterized by comprising the following steps:
step S1, acquiring a wireless link RSS value under the condition of no target, and establishing an environment background link model based on GMM;
step S2, matching the collected real-time RSS data with the established environment background link model, reserving an effective link, and filtering a redundant link;
step S3, learning and training a reconstructed image through a GMM-based prior model according to the random characteristics of an observation background region to obtain structural characteristic parameters of the image, and reconstructing the image based on a GMM-based prior Bayesian compressed sensing algorithm to obtain a reconstructed image;
and step S4, restoring the reconstructed image by using the compressed spatial image by adopting an MRF prior-based image restoration method.
2. The sparse radio frequency tomography method based on the gaussian mixture model as claimed in claim 1, wherein the step S1 specifically comprises:
s11, constructing a wireless sensor node to realize a non-carrying equipment positioning system;
step S12, measuring to obtain RSS value under the condition that no person exists in the observation area;
and step S13, establishing an environment background link model based on the GMM for the wireless link RSS value measured under the condition of no object.
3. The sparse radio frequency tomography method based on the gaussian mixture model as claimed in claim 2, wherein the wireless sensor node implementation of the device-free positioning system is specifically that a plurality of sensor nodes are deployed around an observation area, two-way wireless links are formed between every two nodes, communication is performed by sending and receiving radio frequency signals, the observation area is scanned by a communication network formed by the nodes and the wireless links, and the system model is represented as:
y＝W·x+n
(1)
in the above formula, y represents the vector of RSS measurements, W is the weight matrix associated with voxel attenuation, x is the reconstructed image, and n represents the system noise.
4. The sparse radio frequency tomography method based on Gaussian mixture model as claimed in claim 3, wherein the model adopted by the weight W is an ellipse model:
Figure FDA0003005491100000021
wherein d is the distance between nodes at two ends of the link, di,j(1) And di,j(2) Respectively the distance from the center of the pixel to the two nodes, and λ is an adjustable parameter describing the width of the ellipse.
5. The sparse radio frequency tomography method based on Gaussian mixture model of claim 2, wherein the GMM based environment background link model is as follows:
Figure FDA0003005491100000022
wherein, ynIs a data measurement, C represents the number of Gaussian distributions, λcA corresponding weight for each gaussian distribution. N (y)n|uc,Σc) A probability density function representing a gaussian distribution; n (y)n|uc,Σc) A probability density function representing a gaussian distribution.
6. The sparse radio frequency tomography method based on the gaussian mixture model as claimed in claim 1, wherein the step S3 specifically comprises:
step S31, learning and training the reconstructed image through a GMM-based prior model according to the random characteristics of the observation background area to obtain the structural characteristic parameter lambda 'of the image'p,k，μ'p,k，∑'p,k；
Step S32, the valid link ybAs input, reconstructing the image according to a Bayes compressed sensing algorithm based on GMM prior to obtain a reconstructed image fp。
7. The sparse radio frequency tomography method based on the Gaussian mixture model as claimed in claim 6, wherein the step S32 specifically comprises:
let fpCompliant with GMM:
Figure FDA0003005491100000031
wherein p represents the number of pixels, λp,k，up,kSum-sigmap,kRespectively representing corresponding voxelsThe weight, mean and variance of the kth Gaussian distribution of p; establishing a GMM model for the reconstructed image signal as a posterior probability of Bayesian estimation:
Figure FDA0003005491100000032
estimation of a reconstructed image f using conditional expectationspWherein the expression of the corresponding weight, mean and variance is as follows:
Figure FDA0003005491100000033
Figure FDA0003005491100000034
Figure FDA0003005491100000035
8. the sparse radio frequency tomography method based on the gaussian mixture model as claimed in claim 1, wherein the step S4 specifically comprises:
step S41, using MRF to carry out prior learning on the sparse coefficient of the reconstructed image, using the correlation of pixel points to construct a prior model based on MRF, and using Metropolis algorithm to carry out optimal problem estimation on the prior model based on MRF;
and step S42, estimating the unknown number through a CS inversion framework based on the reconstructed image, and restoring the image.
9. The sparse radio frequency tomography method based on Gaussian mixture model as claimed in claim 1, wherein ADMM algorithm is adopted to vector image
Figure FDA0003005491100000041
And carrying out iterative solution after splitting the solution process.
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