CN109561384B - Wireless sensor network node positioning method under composite noise condition - Google Patents
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Abstract
The invention relates to a wireless sensor network node positioning method under a composite noise condition, belongs to the technical field of wireless networks, and solves the problems that the existing wireless sensor network node positioning excessively depends on distance information between nodes and accurate positioning cannot be realized under the composite noise condition. The method comprises the following steps: selecting a part of anchor nodes and a part of unknown nodes, acquiring relative distance information between any selected anchor node and any selected unknown node and between the selected anchor nodes, constructing a squared Euclidean distance matrix under a composite noise condition, taking the squared Euclidean distance matrix as an observation matrix, taking composite noise as a noise matrix, taking an accurate squared Euclidean distance matrix between the nodes as a target matrix, and solving the target matrix according to the relation that the target matrix superposed noise matrix is equal to the observation matrix; and obtaining the actual position information of each unknown node according to the target matrix. The accurate positioning of the network node under the condition of compound noise by using less node information is realized.
Description
Technical Field
The invention relates to the technical field of wireless networks, in particular to a method for positioning a wireless sensor network node under a composite noise condition.
Background
In a wireless sensor network, the acquisition of the position information of a node is important for various applications. Positioning is one of the most basic wireless sensor network technologies for obtaining accurate node location information, which is a prerequisite for most wireless sensor network applications. The method is limited by node energy, deployment conditions, economic factors and the like, only a few anchor nodes of a general wireless sensor network acquire the position of the anchor nodes by loading a GPS and the like, and the position information of other unknown nodes is calculated by a positioning algorithm.
Existing wireless sensor network positioning algorithms can be divided into two categories: distance-based positioning algorithms and range-less positioning algorithms. The range-based location algorithm obtains euclidean distance or angle information based on different ranging schemes, such as a Radio Signal Strength Indicator (RSSI) and a time difference of arrival (TDOA). In contrast, the range-less location algorithm uses only connectivity information between unknown nodes and beacons. The former can realize more accurate positioning, but has larger calculation and communication overhead; the latter has lower positioning precision but smaller calculation overhead, and is suitable for the application field with low power consumption and low cost. The main idea of the distance-based positioning algorithm is that the distance information between an unknown node and an anchor node and the prior physical coordinates of the anchor node are utilized to perform wireless sensor network node positioning of the unknown coordinate, and positioning methods based on fingerprints, MDS (minimum signal generation), Maximum Likelihood (ML) and the like are provided.
The method can effectively position the wireless sensor network node under the conditions of no noise interference and no data loss, but excessively depends on accurate distance information between nodes, and cannot realize accurate wireless sensor network node positioning under the condition of compound noise.
Disclosure of Invention
In view of the above analysis, the present invention aims to provide a method for positioning a wireless sensor network node under a complex noise condition, so as to solve the problem that the existing method for positioning a wireless sensor network node excessively depends on distance information between nodes, and cannot realize accurate positioning of a wireless sensor network node under a complex noise condition.
The purpose of the invention is mainly realized by the following technical scheme:
a wireless sensor network node positioning method under the condition of compound noise comprises the following steps:
selecting a part of anchor nodes and a part of unknown nodes, acquiring relative distance information between any selected anchor node and any selected unknown node and between the selected anchor nodes, and constructing a squared Euclidean distance matrix under a composite noise condition according to the relative distance information;
taking the squared Euclidean distance matrix under the composite noise condition as an observation matrix, taking the composite noise as a noise matrix, taking the accurate squared Euclidean distance matrix between each node as a target matrix, and solving the target matrix according to the relation that the target matrix superposed noise matrix is equal to the observation matrix;
and obtaining the actual position information of each unknown node in the wireless sensor network according to the target matrix formed by the accurate squared Euclidean distance matrix among the nodes.
The invention has the following beneficial effects: the invention provides a wireless sensor network node positioning method under a composite noise condition, which comprises the steps of constructing a square Euclidean distance matrix under the composite noise condition by utilizing relative distance information of partial nodes, taking the square Euclidean distance matrix as an observation matrix, taking composite noise as a noise matrix, taking an accurate square Euclidean distance matrix between all nodes as a target matrix, and solving the target matrix according to the relation that the target matrix superposed noise matrix is equal to the observation matrix; and obtaining the actual position information of each unknown node in the wireless sensor network according to the target matrix. The method can obtain the position information of all nodes only by using the relative distance information of part of nodes, has small dependence on the distance information among the nodes, can realize the accurate positioning of the wireless sensor network nodes under the condition of compound noise, and improves the positioning accuracy and the positioning efficiency of the positioning of the wireless sensor network nodes.
On the basis of the scheme, the invention is further improved as follows:
further, the squared euclidean distance matrix under the composite noise condition is a matrix of n × n, where n is the number of wireless sensors in the wireless sensor network; each wireless sensor has a unique ID identity, denoted by the number 1, 2.., n;
and writing the obtained corresponding relative distance information into corresponding positions of the square Euclidean distance matrix according to the numbers of the selected part of anchor nodes and the selected part of unknown nodes, wherein the rest positions are 0, thereby forming the square Euclidean distance matrix under the condition of composite noise.
The beneficial effect of adopting the further scheme is that: the wireless sensors are numbered, so that the wireless sensors are in one-to-one correspondence with the square Euclidean distance matrix under the constructed composite noise condition.
Further, the complex noise condition refers to a noise condition including gaussian noise, outlier noise, and impulse noise.
Further, the step of obtaining the target matrix is as follows:
smoothing Gaussian noise, outlier noise and impulse noise respectively based on a norm regularization method, modeling matrix completion under a composite noise condition as a convex optimization problem, and constructing a matrix completion model under the composite noise condition;
and solving the matrix completion model by using an operator splitting technology and an alternating direction multiplier method to obtain the target matrix.
Further, the matrix completion model under the composite noise condition is as follows:
wherein M is an observation matrix, R represents a target matrix, and omega belongs to [ n ]]×[n]For an index set of observation elements, G, O and C respectively represent a Gaussian noise matrix, a outlier noise matrix and an impulse noise matrix, wherein impulse noise comprises row impulse noise and column impulse noise;
mu and lambda are adjustable parameters for balancing three kinds of noise.
The beneficial effect of adopting the further scheme is that: firstly, the nuclear norm of the matrix is approximate to the rank function of the matrix, and then the norm regularization technology is adopted to carry out smoothing processing on the composite noise, so that the structural model is convex, and then the convex optimization technology is conveniently applied to solve.
Further, after a matrix completion model under a composite noise condition is constructed, converting a constrained optimization problem into an unconstrained optimization problem by adopting an alternating direction multiplier method;
the constructed matrix completion model becomes the following form:
and solving the unconstrained optimization problem by combining an operator splitting technology to obtain an accurate squared Euclidean distance matrix between the nodes.
The beneficial effect of adopting the further scheme is that: and the constrained optimization problem is converted into an unconstrained optimization problem, so that the iterative solution of the alternative direction multiplier method is facilitated.
Further, obtaining the actual position information of each unknown node in the wireless sensor network according to the target matrix formed by the accurate squared Euclidean distance matrix among the nodes, and the method comprises the following steps:
calculating a corresponding double-centralization similar matrix according to the target matrix, and performing singular value decomposition on the centralization similar matrix;
calculating a relative coordinate matrix between each node based on a singular value decomposition result of the double-centralization similar matrix:
calculating a coordinate transformation matrix based on the prior physical position of the anchor node and the relative coordinate matrix among the nodes;
converting a relative coordinate matrix between each node into an absolute coordinate matrix between each node through a coordinate conversion matrix;
the elements in the absolute coordinate matrix correspond to actual position information of the node.
The beneficial effect of adopting the further scheme is that: and solving to obtain the actual position information of the unknown node based on the prior physical position of the anchor node according to the internal relation between the accurate squared Euclidean distance between the nodes and the positions of the unknown nodes.
Further, the step of obtaining the relative distance information between any selected anchor node and any selected unknown node comprises:
measuring the signal receiving strength between any selected anchor node and any selected unknown node;
and obtaining the relative distance information between any selected anchor node and any selected unknown node according to a logarithmic attenuation model obeyed by signal receiving strength ranging.
Further, the step of obtaining the relative distance information between the selected anchor nodes comprises:
and obtaining the relative distance information between the selected anchor nodes according to the position information of the selected anchor nodes.
Further, the total number of the selected part of anchor nodes and the selected part of unknown nodes is not less than:
wherein r is the rank of the target matrix;
is to round up upwards;
meanwhile, the number of the anchor nodes is not less than 3.
The beneficial effect of adopting the further scheme is that: the number of the selected anchor nodes and the number of the unknown nodes are limited, so that the observation matrix can be ensured to have enough data volume, and a target matrix can be obtained by utilizing the observation matrix, thereby ensuring the positioning accuracy of the sensor network nodes.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
Fig. 1 is a flowchart of a wireless sensor network node positioning method under a complex noise condition according to an embodiment of the present invention;
fig. 2 is a diagram illustrating the results of node location of a wireless sensor network under complex noise conditions.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
The composite noise condition in the invention refers to a noise condition including Gaussian noise, outlier noise, impulse noise and other noises, and the existence of the composite noise greatly reduces the positioning precision. The invention provides a wireless sensor network node positioning method under a composite noise condition, which is used for solving the problem that the existing wireless sensor network node positioning method excessively depends on distance information between nodes and cannot realize accurate wireless sensor network node positioning under the composite noise condition.
The specific embodiment of the invention discloses a wireless sensor network node positioning method under a composite noise condition, which specifically comprises the following steps as shown in fig. 1:
step S1: selecting a part of anchor nodes and a part of unknown nodes, acquiring relative distance information between any selected anchor node and any selected unknown node and between the selected anchor nodes, and constructing a squared Euclidean distance matrix under a composite noise condition according to the relative distance information;
the wireless sensor network is divided into anchor nodes and unknown nodes according to whether the position of the wireless sensor network is known or not; the number of the anchor nodes and the number of the unknown nodes are both multiple.
In order to better realize the positioning of the wireless sensor network nodes, in this embodiment, the number requirements of the selected part of anchor nodes and part of unknown nodes in the method are determined by the following method:
if the target matrix can be recovered accurately, at least one of the two matrices is required
Distance information, where r is the rank of the target matrix (rank of 4 for the target matrix of the present invention);
is rounded up.
Converting into the number of unknown nodes, the number of nodes at least needing to be known is:
wherein the number of anchor nodes is not less than 3.
The squared Euclidean distance matrix is a matrix of n x n, wherein n is the number of wireless sensors in the wireless sensor network; each wireless sensor has a unique ID, which is denoted by the number 1, 2.
And writing the obtained corresponding relative distance information into corresponding positions of the square Euclidean distance matrix according to the numbers of the selected part of anchor nodes and the selected part of unknown nodes, wherein the rest positions are 0, thereby forming the square Euclidean distance matrix under the condition of composite noise.
Illustratively, if a selected anchor node is numbered i and an unknown node is numbered j, the relative distance between the two nodes is written into the positions of the ith row and the jth column in the squared Euclidean distance matrix, and simultaneously written into the positions of the jth row and the ith column in the squared Euclidean distance matrix.
Step S2: taking the squared Euclidean distance matrix under the composite noise condition as an observation matrix, taking the composite noise as a noise matrix, taking the accurate squared Euclidean distance matrix between each node as a target matrix, and solving the target matrix according to the relation that the target matrix superposed noise matrix is equal to the observation matrix;
step S3: and obtaining the actual position information of each unknown node in the wireless sensor network according to the target matrix formed by the accurate squared Euclidean distance matrix among the nodes.
And solving to obtain the actual position information of the unknown node based on the prior physical position of the anchor node according to the internal relation between the accurate squared Euclidean distance between the nodes and the positions of the unknown nodes.
Compared with the prior art, the method for positioning the wireless sensor network node under the composite noise condition provided by the embodiment utilizes the relative distance information of part of nodes to construct a squared euclidean distance matrix under the composite noise condition, takes the squared euclidean distance matrix as an observation matrix, takes composite noise as a noise matrix, takes an accurate squared euclidean distance matrix between all nodes as a target matrix, and solves the target matrix according to the relation that the target matrix superposed noise matrix is equal to the observation matrix; and obtaining the actual position information of each unknown node in the wireless sensor network according to the target matrix. The method can obtain the position information of all nodes only by using the relative distance information of part of nodes, has small dependence on the distance information among the nodes, can realize the accurate positioning of the wireless sensor network nodes under the condition of compound noise, and improves the positioning accuracy and the positioning efficiency of the positioning of the wireless sensor network nodes.
Specifically, step S1 includes the steps of:
step S11: selecting a part of anchor nodes and a part of unknown nodes, and measuring the Received Signal Strength (RSSI) between any selected anchor node and any selected unknown node;
step S12: obtaining relative distance information between any selected anchor node and any selected unknown node according to a logarithmic attenuation model obeyed by signal receiving strength ranging;
step S13: obtaining the relative distance information between the selected anchor nodes according to the position information of the selected anchor nodes;
step S14: and constructing a Squared Euclidean Distance Matrix (SEDM) under the composite noise condition according to the relative distance information in the steps S12 and S13.
Due to limited communication range, energy limitation and environmental influence, distance information between the anchor node and part of unknown nodes can be obtained only according to the RSSI ranging method. Therefore, the squared euclidean distance matrix constructed as described above contains only partial entries, and most of the distance information is missing.
In the case of fewer measured values, the conventional technique is no longer applicable; if the measured value is more, the denoising effect of the conventional technology is poorer. The method can solve the problems and achieve higher positioning precision, and comprises the following specific steps:
based on the low rank of the SEDM, the problem of solving the distance between nodes according to the distance information between partial nodes is modeled as a matrix completion problem under the condition of compound noise, and the method is realized by the following specific steps:
step S21: based on a norm regularization method, Gaussian noise, outlier noise and impulse noise are smoothed respectively, and matrix completion under a composite noise condition is modeled into a convex optimization problem.
Specifically, the modeling is a matrix completion model as follows:
wherein M is an observation matrix, R represents a target matrix, and omega belongs to [ n ]]×[n]Is an indexed set of observation elements. G, O and C respectively represent a Gaussian noise matrix, a outlier noise matrix and an impulse noise matrix, wherein impulse noise comprises row impulse noise and column impulse noise;
mu and lambda are adjustable parameters for balancing three kinds of noise;
the function involved in the model, e.g. R*、
||O||1、||C||1,2Are convex functions and the functions that consist of these functions are also convex functions. The problem of solving the maximum of the convex function is the convex optimization problem
Step S22: and solving the matrix completion model by using an operator splitting technology and an alternating direction multiplier method to obtain an accurate squared Euclidean distance matrix (namely a target matrix) between the nodes.
Specifically, the method comprises the following steps:
after a matrix completion model under a composite noise condition is constructed, converting a constrained optimization problem into an unconstrained optimization problem by adopting an alternating direction multiplier method;
the constructed matrix completion model becomes the following form:
and solving the unconstrained optimization problem by combining an operator splitting technology to obtain an accurate squared Euclidean distance matrix between the nodes.
And the constrained optimization problem is converted into an unconstrained optimization problem, so that the iterative solution of the alternative direction multiplier method is facilitated.
After an accurate squared Euclidean distance matrix between all nodes is obtained, absolute coordinate information of all unknown nodes of the wireless sensor network is obtained based on a multi-dimensional scale analysis method. Mapping the distance relationship between the wireless sensor nodes to a low-dimensional space; solving the approximate distance between the nodes based on the shortest path, and generating a relative coordinate map which best accords with the distance relation between the nodes; the relative position is converted to a global position using position information of a small number of anchor nodes. Specifically, the method comprises the following steps:
step S31: calculating a corresponding double-centralization similar matrix according to the target matrix, and performing singular value decomposition on the centralization similar matrix;
calculating a double-centered similarity matrix G according to the following relation, and performing singular value decomposition on the double-centered similarity matrix G:
wherein
And I represents an identity matrix, and R is a target matrix.
Step S32: calculating a relative coordinate matrix between each node based on a singular value decomposition result of the double-centralization similar matrix:
d is the sensor position dimension;
step S33: calculating a coordinate transformation matrix based on the prior physical position of the anchor node;
calculating a coordinate transformation matrix based on the prior physical position of the anchor node:
wherein T is the anchor node coordinate.
Step S34: and converting the relative coordinate matrix among the nodes into an absolute coordinate matrix among the nodes through the coordinate conversion matrix.
Converting the relative coordinate matrix into an absolute coordinate matrix through a coordinate conversion matrix:
{T|Ti-T1＝Q×(Wi-W1),i＝k+1,k+2,…,n} (6)
the elements in the absolute coordinate matrix correspond to the actual position information of the node, specifically:
the obtained absolute coordinate matrix is a matrix of d x n, and the a-th column information of the absolute coordinate matrix is the coordinate of the wireless sensor network node with the number of a. When d is 2, the first row of the a-th column and the second row of the a-th column of the absolute coordinate matrix are respectively coordinate information of two dimensions of the wireless sensor network node in the x direction and the y direction; when d is 3, the first row in the a-th column, the second row in the a-th column, and the third row in the a-th column of the absolute coordinate matrix are coordinate information of three dimensions x, y, and z of the wireless sensor network node, respectively.
In another embodiment of the invention, the practicability and effectiveness of the wireless sensor network node positioning method under the composite noise condition are verified by a method for establishing a simulation environment by using Matlab software, and the specific implementation process is as follows:
step S1: scene modeling: 100 nodes are randomly distributed in a square area of 100m multiplied by 100m by using Matlab software, wherein part of the nodes are anchor nodes and contain position information; the other nodes are unknown nodes and do not contain position information;
step S2: generating experimental data: the SEDM is obtained by collecting distance information between part of anchor nodes and unknown nodes and between part of anchor nodes and anchor nodes. And then adding noise into the SEDM, randomly sampling the noise-containing SEDM at the sampling rate of s to obtain an observation matrix M, repeatedly performing 10 times of experiments by taking the observation matrix M as training data of the method, and taking an average value as an experimental result to avoid the contingency.
Step S3: setting a noise environment: according to the difference of the noise environment, the following 4 cases are set:
NONP: it is assumed that the SEDM is not contaminated by any noise, i.e. the values in the observation matrix M are accurate values.
WONP: it is assumed that SEDM is contaminated by gaussian noise and outlier noise. Wherein the Gaussian noise follows a Gaussian distribution with a mean of 0 and a variance of 100; outlier noise follows a laplacian distribution with a mean of 0 and a variance of 10000.
NOWP: it is assumed that the SEDM is contaminated by impulse noise. Where the impulse noise width is 30, obeys a laplacian distribution with a mean of 0 and a variance of 10000.
WOWP: it is assumed that SEDM is contaminated by gaussian noise, outlier noise, and impulse noise. Wherein the Gaussian noise follows a Gaussian distribution with a mean of 0 and a variance of 100; the outlier noise obeys Laplace distribution with the mean value of 0 and the variance of 10000; the impulse noise width is 30, obeying a laplacian distribution with a mean of 0 and a variance of 10000.
Step S4: selecting evaluation indexes: order to
(n ═ 100 denotes the number of nodes) denotes the node coordinate matrix and SEDM, respectively. The performance of the proposed method was evaluated by selecting 3 indices as shown in table 1.
TABLE 1 evaluation index of node positioning accuracy
Step S5: the experimental results are shown in fig. 2, and the experimental data are analyzed: calculating each evaluation index value of the method, and analyzing the node positioning error of the method, can obtain that the node positioning error of the method can reach 0.05m under the condition of compound noise when only 30% distance information can be obtained.
In summary, the embodiments of the present invention provide a method for positioning a wireless sensor network node under a complex noise condition, so that the positioning accuracy of an unknown node is high, a large number of anchor nodes are not required, and the positioning accuracy of the wireless sensor network node under the complex noise condition is improved.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which is stored in a computer readable storage medium, to instruct related hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Claims (5)
1. A wireless sensor network node positioning method under the condition of compound noise is characterized by comprising the following steps:
selecting a part of anchor nodes and a part of unknown nodes, acquiring relative distance information between any selected anchor node and any selected unknown node according to a logarithmic attenuation model obeyed by signal receiving strength ranging, acquiring relative distance information between the selected anchor nodes according to the position information of the selected anchor nodes, and constructing a squared Euclidean distance matrix under a composite noise condition according to the relative distance information;
taking the squared Euclidean distance matrix under the composite noise condition as an observation matrix, taking the composite noise as a noise matrix, taking the accurate squared Euclidean distance matrix between each node as a target matrix, and solving the target matrix according to the relation that the target matrix superposed noise matrix is equal to the observation matrix;
obtaining actual position information of each unknown node in the wireless sensor network according to the target matrix formed by the accurate squared Euclidean distance matrix among the nodes;
the total number of the selected part of anchor nodes and the part of unknown nodes is not less than:
wherein r is the rank of the target matrix;
is to round up upwards;
meanwhile, the number of the anchor nodes is not less than 3;
the squared Euclidean distance matrix under the composite noise condition is a matrix of n x n, and n is the number of the wireless sensors in the wireless sensor network; each wireless sensor has a unique ID identity, denoted by the number 1, 2.., n;
writing the obtained corresponding relative distance information into corresponding positions of a square Euclidean distance matrix according to the numbers of the selected part of anchor nodes and the selected part of unknown nodes, wherein the rest positions are 0, thereby forming the square Euclidean distance matrix under the condition of composite noise;
obtaining the actual position information of each unknown node in the wireless sensor network according to the target matrix formed by the accurate squared Euclidean distance matrix among the nodes, and the method comprises the following steps:
calculating a corresponding double-centralization similar matrix according to the target matrix, and performing singular value decomposition on the centralization similar matrix;
calculating a relative coordinate matrix between each node based on a singular value decomposition result of the double-centralization similar matrix:
calculating a coordinate transformation matrix based on the prior physical position of the anchor node and the relative coordinate matrix among the nodes;
the elements in the absolute coordinate matrix correspond to actual position information of the node.
2. The method of claim 1, wherein the complex noise condition is a noise condition comprising gaussian noise, outlier noise, and impulse noise.
3. The method of claim 2, wherein the step of finding the target matrix is as follows:
smoothing Gaussian noise, outlier noise and impulse noise respectively based on a norm regularization method, modeling matrix completion under a composite noise condition as a convex optimization problem, and constructing a matrix completion model under the composite noise condition;
and solving the matrix completion model by using an operator splitting technology and an alternating direction multiplier method to obtain the target matrix.
4. The method of claim 3, wherein the matrix completion model under the complex noise condition is:
wherein M is an observation matrix, R represents a target matrix, and omega belongs to [ n ]]×[n]For an index set of observation elements, G, O and C respectively represent a Gaussian noise matrix, a outlier noise matrix and an impulse noise matrix, wherein impulse noise comprises row impulse noise and column impulse noise;
mu and lambda are adjustable parameters for balancing three kinds of noise.
5. The method of claim 4, wherein after constructing the matrix completion model under the complex noise condition, the constrained optimization problem is converted to an unconstrained optimization problem using an alternating direction multiplier method;
the constructed matrix completion model becomes the following form:
and solving the unconstrained optimization problem by combining an operator splitting technology to obtain an accurate squared Euclidean distance matrix between the nodes.
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