CN110488222B - UWB positioning method combining SVM (support vector machine) and barycentric coordinate under NLOS (non line of sight) condition - Google Patents
UWB positioning method combining SVM (support vector machine) and barycentric coordinate under NLOS (non line of sight) condition Download PDFInfo
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Abstract
The invention discloses a UWB positioning method combining SVM and barycentric coordinates under NLOS conditions, and belongs to the technical field of wireless sensor networks. The method comprises the following steps: identifying whether the collected measured value is NLOS or LOS propagation condition by using SVM algorithm, and relieving the measurement error caused by NLOS; step two: constructing a distance square matrix by using the measurement value under the LOS condition and the measurement value after the NLOS is relieved, and obtaining the relative position of each UWB node by using an MDS algorithm; step three: calculating a generalized barycentric coordinate about an unknown node according to the relative position obtained by the MDS algorithm; step four: and calculating the actual coordinates of the unknown nodes by combining the generalized barycentric coordinates and the known coordinates of each anchor node. The method provided by the invention can effectively identify NLOS in a complex environment and effectively improve the positioning accuracy of UWB.
Description
Technical Field
The invention relates to the technical field Of wireless sensor networks, in particular to a UWB (Ultra Wide Band, UWB) positioning method combining SVM (support Vector machine) and barycentric coordinates under the condition Of NLOS (Non-Line-Of-Sight).
Background
With the rapid development of wireless sensor network technology, wireless sensor positioning technology has become a research hotspot at present, and has important significance and very wide application prospect in various fields such as commerce, industry, military and the like. In recent years, UWB has been developed rapidly, and has the advantages of high transmission rate, low power consumption, strong interference immunity, strong multipath resolution, strong penetration capability, etc., which make it have excellent performance in wireless sensor positioning. However, in some complex environments (such as indoor, underground tunnel, etc.), due to the dense obstacles, the wireless sensor can randomly switch between LOS (Line-Of-Sight) propagation and NLOS propagation. In the NLOS environment, due to the absence of a direct signal path, propagation time delay is caused, and a positive deviation is generated, so that a ranging error of UWB increases, which greatly affects positioning accuracy.
It is a current research hotspot to correctly identify and mitigate NLOS in a mixed LOS and NLOS environment. The algorithms researched at present are mostly divided into two types, one is an identification algorithm, the measurement values under LOS and NLOS conditions are distinguished through the identification algorithm, and then the measurement values under LOS conditions are only used for positioning, so that the method can often cause positioning failure when the NLOS conditions are serious, and the positioning performance is greatly influenced; the other is a mitigation algorithm, all data is input into the mitigation algorithm for processing, the algorithm is usually high in computational complexity, and the positioning performance is deteriorated with the increase of NLOS measurement data.
The invention aims to solve the UWB positioning problem under the NLOS propagation condition, and provides a UWB positioning method combining an SVM and barycentric coordinates under the NLOS condition. The method identifies the measured value under the NLOS propagation condition by using the SVM algorithm, can effectively relieve the error caused by the NLOS, and simultaneously carries out positioning by using the measured value under the LOS condition and the relieved NLOS measured value. The method creatively combines the two algorithms of identification and mitigation, and greatly improves the positioning precision.
Disclosure of Invention
The invention aims to provide a UWB positioning method combining an SVM (support vector machine) and a barycentric coordinate under an NLOS (non-line-of-sight) condition aiming at the defects of the prior art, so as to solve the problem of inaccurate positioning caused by the influence of the NLOS on UWB positioning in a complex environment.
The purpose of the invention is realized by the following technical scheme: a UWB positioning method combining SVM and barycentric coordinates under NLOS condition comprises the following steps:
step 1: the method comprises the steps of using UWB radio to carry out multiple measurements in an indoor LOS environment and an NLOS environment respectively, collecting Channel Impulse Response (CPR) in the LOS environment and the NLOS environment respectively, and extracting characteristic samples representing propagation conditions according to the CPR.
Step 2: an SVC (Support Vector Classifier, SVC) is constructed, feature samples extracted under NLOS and LOS conditions and corresponding labels respectively form feature matrixes, and the feature matrixes are input into the SVC for training to obtain the trained SVC.
And step 3: an SVM (Support Vector regression, SVR) is constructed, and the feature samples extracted under the NLOS and LOS conditions and the corresponding output values (distance between UWB nodes) are input into an SVM for training to obtain the trained SVR.
And 4, step 4: collecting new channel impulse response (CPR), extracting a characteristic sample representing a propagation condition, inputting the characteristic sample into a trained SVC, classifying whether a measured value belongs to a LOS propagation condition or an NLOS propagation condition by using the trained SVC, and judging whether the number of the measured values under the LOS propagation condition meets a positioning requirement (for example, if the positioning space is a two-dimensional space, the number of the measured values is not less than 3, if the positioning space is a three-dimensional space, the number of the measured values is not less than 4), if the requirement is met, constructing a distance square matrix by using the measured values under the LOS propagation condition, and inputting the distance square matrix into an MDS (Multi-Dimension Scaling, MDS) algorithm to obtain a relative position; if the number of the measured values under the LOS propagation condition can not meet the positioning requirement, the trained SVR is used for relieving the measured values under the NLOS condition, namely the feature samples under the NLOS condition are input into the trained SVR to obtain new corresponding output values, the relieved measured values and the measured values under the LOS condition are selected to construct a distance square matrix, and the relative position is obtained through an MDS algorithm.
And 5: and calculating barycentric coordinates of the unknown node (the node with unknown coordinates and to be positioned) by using the relative position acquired by the MDS algorithm, and calculating the actual position coordinates of the unknown node by using the barycentric coordinates and the coordinates of the known anchor node (the node with known coordinates).
Further, in step 1, the features extracted according to CPR include:
received signal strength epsilonrThe calculation formula is as follows:
where r (t) is the received signal amplitude at time t;
the distance d between nodes is calculated according to the following formula:
d=c(ti-t0)
where c is the speed of light, tiTo receive time, t0Is a response request time;
maximum amplitude r of received signalmaxThe calculation formula is as follows:
the peak value κ is calculated as follows:
wherein mu|r|As an average of the amplitudes of the received signals,t is the variance of the amplitude of the received signal, and T is the sampling time;
average excess delay time TMEDThe calculation formula is as follows:
wherein ψ (t) ═ r (t) ceiling2/εr
Root mean square delay spread time TRMSThe calculation formula is as follows:
further, the step 2 specifically includes the following steps:
constructing a nonlinear classifier using a Radial Basis (RBF) kernel, performing a feature transformation using the Radial Basis (RBF) kernel, the Radial Basis (RBF) kernel K (x ', Y') being as follows:
K(x′,Y′)=exp(-γ||x′-Y′||2)
wherein, gamma is a nuclear parameter, x 'is an input characteristic sample, and Y' is a corresponding label value.
The objective function of the SVM classifier SVC is as follows:
s.t.Yk(wTxk+b)-1≥0,k=1,2,…,n
wherein w and b are classifier parameters and are obtained through training; x is the number ofkFor the kth feature sample, YkIs the label of the kth characteristic sample, and n is the total number of the characteristic samples.
And optimizing the objective function by adopting a Lagrange dual function and a Radial Basis Function (RBF) kernel function, wherein the optimization result is as follows:
wherein alpha iskIs a lagrange multiplier.
Further, the step 3 specifically includes the following steps:
constructing a regressor SVR structure and parameters of a support vector machine using a Radial Basis (RBF) kernel function, K (x ', y'), as follows:
where γ is a kernel parameter, σ is a width of a kernel function, x 'is an input feature sample, and y' is a corresponding output value, i.e., a distance between UWB nodes.
The objective function of the SVM regressor SVR is as follows:
s.t.|(wTxk+b)-yk|≤ε,k=1,2,…,n
wherein w and b are regressor parameters and are obtained by training; n is the total number of characteristic samples, xkFor the kth feature sample, ykAnd epsilon is the error range for the kth corresponding output value.
And optimizing the objective function by adopting a Lagrange dual function and a Radial Basis Function (RBF) kernel function, wherein the optimization result is as follows:
wherein alpha iskIs a lagrange multiplier.
Further, in step 4, the distance square matrix is input to the MDS algorithm to obtain the relative position, which specifically includes:
obtaining a distance square matrix:
wherein d isijThe distance between the ith UWB node and the jth UWB node is calculated;
calculating a central matrix J:
n is the total number of UWB nodes, I is the identity matrix, 1NA matrix of nx 1 and a value of 1;
normalized distance squared matrix:
carrying out singular value decomposition on the X to obtain a singular value Lambda and a singular value vector V;
X=VAVT
arranging the singular values Lambda in the order from large to small, and extracting the maximum singular value and the corresponding singular value vector V which have the same number with the dimension of the positioning space (for example, the number is 2 if the positioning space is a two-dimensional space, and the number is 3 if the positioning space is a three-dimensional space)1Constructing the extracted singular value into a diagonal matrix Lambda1Diagonal matrix Λ to be constructed1And singular value vector V1Multiplying to obtain a relative coordinate matrix Q of each UWB node:
wherein Q represents a formula of:(x′i,y′i) Is the relative position of the unknown node (x'1,y′1),(x′2,y′2),…,(x′N-1,y′N-1) The relative position of the 1 st, 2 nd, … th, N-1 st anchor nodes.
Further, in step 5, the calculating of barycentric coordinates of unknown nodes using the relative positions obtained by the MDS algorithm specifically includes: regarding the relative position of the unknown node as the generalized barycenter of other nodes, and solving the generalized barycenter coordinates by the following formula:
a1*x′1+a2*x′2+…+aN-1*x′N-1=x′i
a1*y′1+a2*y′2+…+aN-1*y′N-1=y′i
a1+a2+…+aN-1=1
wherein (a)1,a2,...,aN-1) Is a generalized barycentric coordinate.
Further, in step 5, the actual position coordinates are calculated by the following formula:
xi=a1*x1+a2*x2+…+aN-1*xN-1
yi=a1*y1+a2*y2+…+aN-1*yN-1
wherein (x)i,yi) For the actual position coordinates of the unknown node, (x)1,y1),(x2,y2),…,(xN-1,yN-1) Is the real coordinate of the 1 st, 2 nd, … th, N-1 th anchor node.
The invention has the beneficial effects that: the invention combines SVM and gravity center coordinate method, effectively distinguishes the measured value under NLOS propagation condition from the measured value under LOS condition by using SVM classifier, and relieves the measured value under NLOS propagation condition by using SVM regressor, thus greatly reducing the distance measurement error brought by NLOS. Meanwhile, an unknown node is positioned by using a generalized gravity center coordinate method based on MDS, and the problem that the positioning fails due to the fact that no intersection point or a plurality of intersection points exist in the traditional geometric positioning algorithm frequently is solved. The two algorithms are creatively combined, so that the positioning performance is ensured, and the UWB positioning precision under the NLOS propagation condition is greatly improved. Along with the development of portable equipment, UWB's range of application is more and more extensive, like personnel's tracking, unmanned aerial vehicle, unmanned vehicle's location etc.. The invention has wide application range and has great effect on economic development.
Drawings
Fig. 1 is a flowchart of a UWB positioning method combining SVM and barycentric coordinates under NLOS conditions according to an embodiment of the present invention;
FIG. 2 is a diagram of an SVM training process;
FIG. 3 is a signal diagram of a non-direct wave and a direct wave under propagation conditions;
FIG. 4 is a flow chart of an MDS algorithm;
FIG. 5 is a representation of barycentric coordinates of an unknown node with respect to an anchor node.
Detailed Description
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
As shown in fig. 1, the UWB locating method combining SVM and barycentric coordinates under NLOS condition provided by the present invention includes the following steps:
(1) the method comprises the steps of respectively carrying out a plurality of times of extensive measurement in an indoor LOS environment and an NLOS environment by adopting UWB radio conforming to FCC, respectively collecting CPR (signal diagram shown in figure 3 under a group of non-direct wave and direct wave propagation conditions) under the NLOS condition and the LOS condition, and extracting characteristic samples capable of representing the propagation conditions according to the CPR, wherein the main extracted characteristics comprise: the signal receiving intensity, the maximum signal receiving amplitude, the peak value, the average excess delay time, the root mean square delay spread time and the like are as follows:
received signal strength epsilonrThe calculation formula is as follows:
where r (t) is the received signal amplitude at time t;
the distance d between nodes is calculated according to the following formula:
d=c(ti-t0)
where c is the speed of light, tiTo receive time, t0Is a response request time;
maximum amplitude r of received signalmaxThe calculation formula is as follows:
the peak value κ is calculated as follows:
wherein mu|r|For receiving messagesThe average of the magnitude of the signal,t is the variance of the amplitude of the received signal, and T is the sampling time;
average excess delay time TMEDThe calculation formula is as follows:
wherein ψ (t) ═ r (t) ceiling2/εr
Root mean square delay spread time TRMSThe calculation formula is as follows:
(2) constructing an SVM Classifier SVC (Support Vector Classifier, SVC), inputting feature samples extracted under NLOS and LOS conditions and feature matrixes formed by the corresponding labels into an SVM for training, and obtaining the trained SVC, as shown in fig. 2, specifically as follows:
constructing a nonlinear classifier using a Radial Basis (RBF) kernel, performing a feature transformation using the Radial Basis (RBF) kernel, the Radial Basis (RBF) kernel K (x ', Y') being as follows:
K(x′,Y′)=exp(-γ||x′-Y′||2)
wherein, gamma is a nuclear parameter, x 'is an input characteristic sample, and Y' is a corresponding label value.
The objective function of the SVM classifier SVC is as follows:
s.t.Yk(wTxk+b)-1≥0,k=1,2,…,n
wherein w and b are classifier parameters and are obtained through training; x is the number ofkAs the kth feature sample,YkIs the label of the kth characteristic sample, and n is the total number of the characteristic samples.
And optimizing the objective function by adopting a Lagrange dual function and a Radial Basis Function (RBF) kernel function, wherein the optimization result is as follows:
wherein alpha iskIs a lagrange multiplier.
(3) An SVR (Support Vector Regressor, SVR) is constructed, and a feature sample extracted under NLOS and LOS conditions and a corresponding output value (distance between UWB nodes) are input into an SVM for training, so as to obtain a trained SVR, as shown in fig. 2, specifically as follows:
constructing a regressor SVR structure and parameters of a support vector machine using a Radial Basis (RBF) kernel function, K (x ', y'), as follows:
where γ is a kernel parameter, σ is a width of a kernel function, x 'is an input feature sample, and y' is a corresponding output value, i.e., a distance between UWB nodes.
The objective function of the SVM regressor SVR is as follows:
s.t.|(wTxk+b)-yk|≤ε,k=1,2,…,n
wherein w and b are regressor parameters and are obtained by training; n is the total number of characteristic samples, xkFor the kth feature sample, ykAnd epsilon is the error range for the kth corresponding output value.
And optimizing the objective function by adopting a Lagrange dual function and a Radial Basis Function (RBF) kernel function, wherein the optimization result is as follows:
wherein alpha iskIs a lagrange multiplier.
(4) Collecting a new channel impulse response (CPR), extracting a characteristic sample capable of representing a propagation condition, inputting the characteristic sample into a trained classifier SVC, classifying whether the collected measured value belongs to a LOS propagation condition or an NLOS propagation condition, judging whether the number of the measured values under the LOS propagation condition meets a positioning requirement (for example, if the positioning space is a two-dimensional space, the number of the measured values is not less than 3, and if the positioning space is a three-dimensional space, the number of the measured values is not less than 4), if the requirement is met, constructing a distance square matrix by using the measured values under all the LOS propagation conditions, and inputting the distance square matrix into an MDS (Multi-Dimension Scaling, MDS) algorithm to obtain the relative position of a corresponding node; if the number of the measured values under the LOS propagation condition can not meet the positioning requirement, the trained SVR is used for relieving the measured values under the NLOS condition, namely the feature samples under the NLOS condition are input into the trained SVR to obtain new corresponding output values, then the relieved measured values and the measured values under the LOS condition are selected to construct a distance square matrix, and the relative position of the corresponding node is obtained through an MDS algorithm.
As shown in fig. 4, which is a flow of an MDS algorithm, the present invention uses an MDS-based generalized barycentric coordinate method to locate UWB, wherein the MDS algorithm is specifically implemented as follows:
step 1, squaring the measured distance processed by the SVM to obtain a distance square matrix D.
Wherein d isijThe distance between the ith UWB node and the jth UWB node is calculated;
step 2, calculating a central matrix J:
where N is the total number of UWB nodes, I is the identity matrix, 1NA matrix of nx 1 and a value of 1;
step 4, carrying out singular value decomposition on the X to obtain a singular value Lambda and a singular value vector V:
X=VAVT
wherein Q represents a formula of:(x′i,y′i) Is the relative position of the unknown node (x'1,y′1),(x′2,y′2),…,(x′N-1,y′N-1) The relative position of the 1 st, 2 nd, … th, N-1 st anchor nodes.
(5) And (3) taking the unknown node as the generalized gravity center of the anchor node (any 3 anchor nodes need to meet the condition of non-collinearity) by using the relative position of each node obtained by the MDS algorithm, and then calculating the generalized gravity center coordinate of the unknown node relative to the anchor node. And calculating the real coordinates of the unknown nodes by using the generalized barycentric coordinates and the real coordinates of the related anchor nodes.
Fig. 5 is a diagram showing barycentric coordinates of unknown nodes with respect to anchor nodes, where each node is a representation of a relative position obtained through MDS in a coordinate system in a specific example, node i is an unknown node, and nodes i, j, and k are anchor nodes. The MDS algorithm does not change the distance relationship between any two points, so that the generalized barycentric coordinate calculated by using the relative coordinates obtained by the MDS algorithm is consistent with the generalized barycentric coordinate between the actual coordinates. Wherein, the calculation of the generalized barycentric coordinates is as follows:
a1*x′1+a2*x′2+…+aN-1*x′N-1=x′i
a1*y′1+a2*y′2+…+aN-1*y′N-1=y′i
a1+a2+…+aN-1=1
wherein (a)1,a2,...,aN-1) Is a generalized barycentric coordinate.
The actual position coordinates are calculated by:
xi=a1*x1+a2*x2+…+aN-1*xN-1
yi=a1*y1+a2*y2+…+aN-1*yN-1
wherein (x)i,yi) For the actual position coordinates of the unknown node, (x)1,y1),(x2,y2),…,(xN-1,yN-1) Is the real coordinate of the 1 st, 2 nd, … th, N-1 th anchor node.
Finally, the above description is a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily modify the technical solution of the present invention or substitute the same within the technical scope of the present invention, and the technical solution should be covered by the claims of the present invention.
Claims (7)
1. An UWB positioning method combining SVM and barycentric coordinates under NLOS condition is characterized in that the method comprises the following steps:
step 1: using UWB radio to respectively carry out multiple measurements in an indoor LOS environment and an NLOS environment, respectively collecting CPR (channel impulse response) in the LOS environment and the NLOS environment, and extracting characteristic samples representing propagation conditions according to the CPR;
step 2: constructing an SVC classifier SVC, inputting feature matrixes formed by feature samples extracted under NLOS and LOS conditions and corresponding labels into the SVM for training to obtain the trained SVC; the method specifically comprises the following steps:
constructing a nonlinear classifier using a Radial Basis (RBF) kernel, performing a feature transformation using the Radial Basis (RBF) kernel, the Radial Basis (RBF) kernel K (x ', Y') being as follows:
K(x′,Y′)=exp(-γ||x′-Y′||2)
wherein gamma is a nuclear parameter, x 'is an input characteristic sample, and Y' is a corresponding label value;
the objective function of the SVM classifier SVC is as follows:
s.t.Yk(wTxk+b)-1≥0,k=1,2,...,n
wherein w and b are classifier parameters and are obtained through training; x is the number ofkFor the kth feature sample, YkThe label of the kth characteristic sample is obtained, and n is the total number of the characteristic samples;
and optimizing the objective function by adopting a Lagrange dual function and a Radial Basis Function (RBF) kernel function, wherein the optimization result is as follows:
wherein alpha iskIs a lagrange multiplier;
and step 3: constructing an SVM (support vector machine) regressor SVR, inputting feature samples extracted under NLOS (non line of sight) and LOS (line of sight) conditions and corresponding output values into an SVM (support vector machine) for training to obtain a trained SVR, wherein the output values are distances between UWB nodes;
and 4, step 4: collecting new channel impulse response (CPR), extracting a characteristic sample representing a propagation condition, inputting the characteristic sample into a trained SVC, classifying whether a measured value belongs to an LOS (LoS) propagation condition or an NLOS (NLOS) propagation condition by using the trained SVC, judging whether the number of the measured values under the LOS propagation condition meets a positioning requirement, if so, constructing a distance square matrix by using the measured value under the LOS propagation condition, and inputting the distance square matrix into an MDS (minimum signal strength) algorithm to obtain a relative position; if the number of the measured values under the LOS propagation condition can not meet the positioning requirement, the trained SVR is used for relieving the measured values under the NLOS condition, namely the feature samples under the NLOS condition are input into the trained SVR to obtain new corresponding output values, then the relieved measured values and the measured values under the LOS condition are selected to construct a distance square matrix, and the relative position is obtained through an MDS algorithm;
and 5: and calculating barycentric coordinates of the unknown node by using the relative position acquired by the MDS algorithm, and calculating the actual position coordinates of the unknown node by using the barycentric coordinates and the coordinates of the known anchor node.
2. The UWB positioning method of claim 1 wherein the SVM and barycentric coordinates combination under NLOS condition comprises the following steps, wherein the step 1, the feature extracted according to CPR comprises:
received signal strength epsilonrThe calculation formula is as follows:
where r (t) is the received signal amplitude at time t;
the distance d between nodes is calculated according to the following formula:
d=c(ti-t0)
where c is the speed of light, tiTo receive time, t0Is a response request time;
maximum amplitude r of received signalmaxThe calculation formula is as follows:
the peak value κ is calculated as follows:
wherein mu|r|As an average of the amplitudes of the received signals,t is the variance of the amplitude of the received signal, and T is the sampling time;
average excess delay time TMEDThe calculation formula is as follows:
wherein ψ (t) ═ r (t) ceiling2/εr;
Root mean square delay spread time TRMSThe calculation formula is as follows:
3. the UWB positioning method combining SVM and barycentric coordinates under NLOS condition according to claim 1, wherein said step 3 specifically comprises the following contents:
constructing a regressor SVR structure and parameters of a support vector machine using a Radial Basis (RBF) kernel function, K (x ', y'), as follows:
wherein, gamma is a kernel parameter, sigma is the width of a kernel function, x 'is an input characteristic sample, and y' is a corresponding output value;
the objective function of the SVM regressor SVR is as follows:
s.t.|(wTxk+b)-yk|≤ε,k=1,2,...,n
wherein w and b are regressor parameters and are obtained by training; n is the total number of characteristic samples, xkFor the kth feature sample, ykIs the kth corresponding output value, and epsilon is the error range;
and optimizing the objective function by adopting a Lagrange dual function and a Radial Basis Function (RBF) kernel function, wherein the optimization result is as follows:
wherein alpha iskIs a lagrange multiplier.
4. The UWB positioning method combining SVM and barycentric coordinates under NLOS conditions according to claim 1, wherein in said step 4, said positioning requirement is specifically: the positioning space is a two-dimensional space, so that the measured value is required to be not less than 3, and the positioning space is a three-dimensional space, so that the measured value is required to be not less than 4.
5. The UWB positioning method according to claim 1, wherein the SVM and the barycentric coordinate combination under the NLOS condition are used to obtain the UWB positioning method, and the distance square matrix is input into the MDS algorithm to obtain the relative position in the step 4, specifically as follows:
obtaining a distance square matrix:
wherein d isijThe distance between the ith UWB node and the jth UWB node is calculated;
calculating a central matrix J:
n is the total number of UWB nodes, I is the identity matrix, 1NA matrix of nx 1 and a value of 1;
normalized distance squared matrix:
carrying out singular value decomposition on the X to obtain a singular value Lambda and a singular value vector V;
X=VAVT
arranging the singular values Lambda in the order from large to small, and extracting the maximum singular value with the same number as the positioning space dimensionality and the corresponding singular value vector V1Constructing the extracted singular value into a diagonal matrix Lambda1Diagonal matrix Λ to be constructed1And singular value vector V1Multiplying to obtain a relative coordinate matrix Q of each UWB node
6. The UWB positioning method of claim 5 wherein the SVM and the barycentric coordinate combination under the NLOS condition is characterized in that, in the step 5, the calculation of the barycentric coordinate about the unknown node by using the relative position obtained by the MDS algorithm is specifically as follows: regarding the relative position of the unknown node as the generalized barycenter of other nodes, and solving the generalized barycenter coordinates by the following formula:
a1*x′1+a2*x′2+…+aN-1*x′N-1=x′i
a1*y′1+a2*y′2+…+aN-1*y′N-1=y′i
a1+a2+…+aN-1=1
wherein (a)1,a2,...,aN-1) Is a generalized barycentric coordinate.
7. The UWB positioning method of claim 6 wherein the SVM and the barycentric coordinate combination under the NLOS condition is based on the following formula, and the actual position coordinate is calculated in the step 5 by the following formula:
xi=a1*x1+a2*x2+…+aN-1*xN-1
yi=a1*y1+a2*y2+…+aN-1*yN-1
wherein (x)i,yi) For the actual position coordinates of the unknown node, (x)1,y1),(x2,y2),…,(xN-1,yN-1) Is 1, 2, …, N-1The true coordinates of the anchor node.
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CN111432364B (en) * | 2020-03-25 | 2021-05-11 | 哈尔滨工程大学 | Radial basis function neural network-based non-line-of-sight error suppression method |
CN111541988B (en) * | 2020-04-17 | 2021-11-23 | 北京理工大学重庆创新中心 | Three-dimensional indoor positioning method based on barycentric coordinate and Taylor expansion |
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