CN108225329B - Accurate indoor positioning method - Google Patents

Accurate indoor positioning method Download PDF

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CN108225329B
CN108225329B CN201711500556.7A CN201711500556A CN108225329B CN 108225329 B CN108225329 B CN 108225329B CN 201711500556 A CN201711500556 A CN 201711500556A CN 108225329 B CN108225329 B CN 108225329B
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indoor positioning
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correlation
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coordinates
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CN108225329A (en
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杨艳华
杨海锋
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Yang Yanhua
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
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Abstract

The invention relates to an accurate indoor positioning method, which is designed for solving the technical problems that the existing similar methods are easily interfered by other signals, and the positioning accuracy is poor due to errors in node distance measurement. The indoor positioning method is characterized in that the indoor positioning method utilizes the correlation among objects to construct the coordinate distribution of corresponding points in space, and the actual distance of each object is taken as the correlation to form a correlation matrix; then centralizing and decomposing the correlation matrix to obtain the relative position distribution of each point in the space; and finally, converting the relative coordinates of the nodes into absolute coordinates by using mirror image transformation, thereby realizing indoor positioning. The indoor positioning method can accurately realize indoor positioning without interference only by knowing the absolute coordinate positions of a small number of reference nodes in the space; meanwhile, the indoor positioning method provides a technology for converting the space relative coordinates of the reference nodes into space absolute coordinates so as to realize accurate indoor positioning.

Description

Accurate indoor positioning method
Technical Field
The invention relates to an internal positioning method of a wireless technology, in particular to an accurate indoor positioning method.
Background
Indoor positioning technology has not been regarded as important for a long time before because of the application scenario and the precision requirement. However, in recent years, the development of consumer-grade market positioning technology and the marketing of Ultra-precise positioning of UWB (Ultra wide band) technology are becoming more and more important. The existing indoor positioning method is disclosed in chinese patent application No. 201610029239.0, application publication No. 2016.06.15, entitled "indoor positioning system and indoor positioning method"; the indoor positioning method calculates the position coordinates by using electromagnetic field intensity and converting the electromagnetic field intensity into WLAN (Wireless Local Area Networks) signal intensity. However, the above method cannot ensure its accuracy because the electromagnetic field signal is easily interfered by other signals. For example, the invention is named as "indoor positioning method" in application number 201510799403.1, application publication date 2016.02.17 disclosed in chinese patent literature; the indoor positioning method calculates the distance between the terminal and an AP (Wireless Access Point) by using the received signal intensity of the terminal, thereby obtaining the position coordinate. However, because of the error of node ranging according to the signal strength, the distribution of nodes with known positions in the network will have a certain influence on the positioning accuracy.
Disclosure of Invention
In order to overcome the defects, the invention aims to provide an accurate indoor positioning method for the field, so that the technical problems that the existing similar methods are easily interfered by other signals, and the positioning accuracy is poor due to errors in node distance measurement are solved. The purpose is realized by the following technical scheme.
An accurate indoor positioning method is characterized in that the indoor positioning method utilizes the correlation among objects to construct the coordinate distribution of corresponding points in space, and takes the actual distance of each object as the correlation to form a correlation matrix; then centralizing and decomposing the correlation matrix to obtain the relative position distribution of each point in the space; and finally, converting the relative coordinates of the nodes into absolute coordinates by using mirror image transformation, thereby realizing indoor positioning. The indoor positioning method provides an algorithm with high robustness, low energy consumption and high calculation time efficiency, and indoor positioning can be accurately realized without interference only by knowing the absolute coordinate positions of a small number of reference nodes in a space. Meanwhile, the indoor positioning method provides a technology for converting the space relative coordinates of the reference nodes into space absolute coordinates so as to realize accurate indoor positioning.
The specific flow of the indoor positioning method is as follows:
s100: in the conversion process of the relative coordinates, the wider the distribution of the reference nodes, the more stable the positioning performance, and in a two-dimensional space, the spatial relative coordinates of d +1 reference nodes forming the largest d +1 polygon area need to be determined; initializing k to 1, e to 0, determining the center coordinates p of the m reference nodes:
Figure GSB0000194207110000021
selecting a reference node a farthest from the centeri；
S200: d reference nodes are arbitrarily selected from the rest m-1 reference nodes, and all combinations are stored in C(d-1)×rIn, C(d-1)×rIn order to be a combination of the mathematics,
Figure GSB0000194207110000022
where r ═ (m-1) (m-2)/2, d is the spatial dimension in which localization is achieved;
s300: calculating ai，c1k，c2k，...，c(d-1)kArea s of d +1 polygon formed by reference nodeskIf s iskGreater than e, then e ═ skJ is k; if k equals r, continue the next step, otherwise k equals k +1 and repeat the step;
s400: let p beijRepresenting the correlation between objects i and j, Xn×mA coordinate matrix representing corresponding points of each object in the space, wherein n represents the number of the points, and m represents the dimension of the space; dij(X) represents the actual distance between the corresponding points of the objects i and j in the space, and then the actual distance is calculated by the formula
Figure GSB0000194207110000023
Calculating the actual distance and constructing a correlation matrix [ d ]ij]；
S500: for correlation matrix [ d ]ij]Centralizing and decomposing to obtain the distribution of the relative positions of each point in the space;
s600: order (y)1，y2，...，yn) Representing the actual coordinates of the node, (x)1，x2，...，xn) Representing the relative coordinates of the nodes obtained by the method, wherein n is the total number of the nodes, and y is*(xvr + L) wherein ═ represents
Figure GSB0000194207110000024
R denotes a d x d orthogonal rotation matrix, d denotes a spatial dimension,
Figure GSB0000194207110000025
represents an offset; to determine the absolute position of the node for R and L, y*Equivalent of xR + L is a system of equations
Figure GSB0000194207110000026
Solving the solution;
s700: and realizing indoor positioning according to the obtained absolute coordinates.
The distribution comprises the following specific steps:
s510: through a formula d'ij＝dijU performs a correlation matrix [ d ]ij]The data centering, i.e., the data translation process, of (1), wherein u represents the mean of the data samples;
s520: by the formula [ dij]＝u∑V*Proceed correlation matrix [ d ]ij]The singular value decomposition of (a) in the formula represents a conjugate transpose, where the columns of u form a set of pairs [ d ]ij]Is the basis vector of the orthogonal "inputs" or "analyses", these vectors being [ dij][dij]*The feature vector of (2); v's column constitutes a set of pairs [ dij]The basis vectors of the orthogonal "outputs" of (1), these vectors being [ d ]ij]*[dij]The feature vector of (2); according to the processed correlation matrix [ d ]ij]And dijAnd (X) calculating a formula to obtain the distribution of the relative positions of the points in the space.
The concrete steps of the solution are as follows:
s610: three reference nodes (p) with the largest area in two-dimensional space1，p2，p3) Conversion to (q)1，q2，q3) First, p is1p2Is translated so that p1And q is1Coincidence, p2Move to p'2＝p2+q1-p1(ii) a Then q is put1p′2Is rotated so that p'2And q is2Overlapping; let g be p1-q1Then there is
Figure GSB0000194207110000031
Wherein H is v ═ p1p2+q1q2)/||p1p2+q1A mirror matrix of q | |, v being the unit column vector of the H matrix;
s620: by
Figure GSB0000194207110000032
And
Figure GSB0000194207110000033
and deriving R-H-I-vv from the uniqueness of the solutionT，
Figure GSB0000194207110000034
Is the solution of the system of equations, where the I identity matrix.
The indoor positioning method is feasible, the indoor positioning result is accurate, the positioning is convenient and fast, and the application range is wide; the method is suitable for being applied as an indoor positioning method of similar products and improvement of the similar positioning method.
Drawings
FIG. 1 is a block diagram of the process of the present invention.
Detailed Description
The construction and use of the invention will now be further described with reference to the accompanying drawings. The indoor positioning method utilizes the correlation (actual distance in positioning, namely the real distance between two points in space) between objects to construct the coordinate distribution of corresponding points in space, takes the actual distance of each object as the correlation to form a correlation matrix, and then centers and decomposes the correlation matrix to obtain the relative position distribution of each point in space; and finally, converting the relative coordinates of the nodes into absolute coordinates by using mirror image transformation, thereby realizing indoor positioning.
As shown in fig. 1, the specific flow of the indoor positioning method is as follows:
s100: in the conversion process of the relative coordinates, the wider the distribution of the reference nodes, the more stable the positioning performance, and in a two-dimensional space, the spatial relative coordinates of d +1 reference nodes forming the largest d +1 polygon area need to be determined; initializing k to 1, e to 0, determining the center coordinates p of the m reference nodes:
Figure GSB0000194207110000035
selecting a reference node a farthest from the centeri；
S200: d reference nodes are arbitrarily selected from the rest m-1 reference nodes, and all combinations are stored in C(d-1)×rIn, C(d-1)×rIn order to be a combination of the mathematics,
Figure GSB0000194207110000036
wherein r ═ 2 (m-1) and d is achievedThe spatial dimension of the location;
s300: calculating ai，c1k，c2k，...，c(d-1)kArea s of d +1 polygon formed by reference nodeskIf s iskGreater than e, then e ═ skJ is k; if k equals r, continue the next step, otherwise k equals k +1 and repeat the step;
s400: let p beijRepresenting the correlation between objects i and j, Xn×mA coordinate matrix representing corresponding points of each object in the space, wherein n represents the number of the points, and m represents the dimension of the space; dij(X) represents the actual distance between the corresponding points of the objects i and j in the space, and then the actual distance is calculated by the formula
Figure GSB0000194207110000041
Calculating the actual distance and constructing a correlation matrix [ d ]ij]；
S500: for correlation matrix [ d ]ij]Centralizing and decomposing to obtain the distribution of the relative positions of the points in the space.
The distribution comprises the following specific steps:
s510: through a formula d'ij＝dijU performs a correlation matrix [ d ]ij]The data centering, i.e., the data translation process, of (1), wherein u represents the mean of the data samples;
s520: by the formula [ dij]＝u∑V*Proceed correlation matrix [ d ]ij]The singular value decomposition of (a) in the formula represents a conjugate transpose, where the columns of u form a set of pairs [ d ]ij]Is the basis vector of the orthogonal "inputs" or "analyses", these vectors being [ dij][dij]*The feature vector of (2); v's column constitutes a set of pairs [ dij]The basis vectors of the orthogonal "outputs" of (1), these vectors being [ d ]ij]*[dij]The feature vector of (2); according to the processed correlation matrix [ d ]ij]And dij(X) obtaining the distribution of the relative positions of each point in the space by using a calculation formula;
s600: order (y)1，y2，...，yn) Representing the actual coordinates of the node, (x)1，x2，...，xn) Representing the relative coordinates of the nodes obtained by the method, wherein n is the total number of the nodes, and y is*(xvr + L) wherein ═ represents
Figure GSB0000194207110000042
R denotes a d x d orthogonal rotation matrix, d denotes a spatial dimension,
Figure GSB0000194207110000043
represents an offset; to determine the absolute position of the node for R and L, y*Equivalent of xR + L is a system of equations
Figure GSB0000194207110000044
And solving the solution.
The concrete steps of the solution are as follows:
s610: three reference nodes (p) with the largest area in two-dimensional space1，p2，p3) Conversion to (q)1，q2，q3) First, p is1p2Is translated so that p1And q is1Coincidence, p2Move to p'2＝p2+q1-p1(ii) a Then q is put1p′2Is rotated so that p'2And q is2Overlapping; let g be p1-q1Then there is
Figure GSB0000194207110000045
Wherein H is v ═ p1p2+q1q2)/||p1p2+q1A mirror matrix of q | |, v being the unit column vector of the H matrix;
s620: by
Figure GSB0000194207110000046
And
Figure GSB0000194207110000051
and deriving R-H-I-vv from the uniqueness of the solutionT，
Figure GSB0000194207110000052
Is a solution of the system of equations, wherein the I identity matrix;
s700: and realizing indoor positioning according to the obtained absolute coordinates.
In summary, the indoor positioning technology is applied on a larger scale nowadays, and the algorithm provided by the invention can reduce the influence of reference node distribution on positioning accuracy, so that more stable performance is obtained, and the purpose of accurate indoor positioning is achieved. And aiming at large-scale indoor positioning, the algorithm provided by the invention has high-efficiency calculation, removes unnecessary reference nodes, ensures the accuracy and can save the expense of calculation time.

Claims (1)

1. An accurate indoor positioning method is characterized in that the indoor positioning method utilizes the correlation among objects to construct the coordinate distribution of corresponding points in space, and takes the actual distance of each object as the correlation to form a correlation matrix; then centralizing and decomposing the correlation matrix to obtain the relative position distribution of each point in the space; finally, the relative coordinates of the nodes are converted into absolute coordinates by using mirror image transformation, so that indoor positioning is realized;
the specific flow of the indoor positioning method is as follows:
s100: in the conversion process of the relative coordinates, the wider the distribution of the reference nodes, the more stable the positioning performance, and in a two-dimensional space, the spatial relative coordinates of d +1 reference nodes forming the largest d +1 polygon area need to be determined; initializing k to 1, e to 0, determining the center coordinates p of the m reference nodes:
Figure FSB0000194207100000011
selecting a reference node a farthest from the centeri；
S200: d reference nodes are arbitrarily selected from the rest m-1 reference nodes, and all combinations are stored in C(d-1)×rIn, C(d-1)×rIn order to be a combination of the mathematics,
Figure FSB0000194207100000012
where r ═ (m-1) (m-2)/2, d is the spatial dimension in which localization is achieved;
s300: calculating ai，c1k，c2k，...，c(d-1)kArea s of d +1 polygon formed by reference nodeskIf s iskGreater than e, then e ═ skJ is k; if k equals r, continue the next step, otherwise k equals k +1 and repeat the step;
s400: let p beijRepresenting the correlation between objects i and j, Xn×mA coordinate matrix representing corresponding points of each object in the space, wherein n represents the number of the points, and m represents the dimension of the space; dij(X) represents the actual distance between the corresponding points of the objects i and j in the space, and then the actual distance is calculated by the formula
Figure FSB0000194207100000013
Calculating the actual distance and constructing a correlation matrix [ d ]ij]；
S500: for correlation matrix [ d ]ij]Centralizing and decomposing to obtain the distribution of the relative positions of each point in the space;
s510: through a formula d'ij＝dijU performs a correlation matrix [ d ]ij]The data centering, i.e., the data translation process, of (1), wherein u represents the mean of the data samples;
s520: by the formula [ dij]＝u∑V*Proceed correlation matrix [ d ]ij]The singular value decomposition of (a) in the formula represents a conjugate transpose, where the columns of u form a set of pairs [ d ]ij]Is the basis vector of the orthogonal "inputs" or "analyses", these vectors being [ dij][dij]*The feature vector of (2); v's column constitutes a set of pairs [ dij]The basis vectors of the orthogonal "outputs" of (1), these vectors being [ d ]ij]*[dij]The feature vector of (2); according to the processed correlation matrix [ d ]ij]And dij(X) obtaining the distribution of the relative positions of each point in the space by using a calculation formula;
s600: order (y)1，y2，...，yn) Representing the actual coordinates of the node, (x)1，x2，...，xn) Representing the relative coordinates of the nodes obtained by the method, wherein n is the total number of the nodes, and y is*(xvr + L) wherein ═ represents
Figure FSB0000194207100000021
R denotes a d x d orthogonal rotation matrix, d denotes a spatial dimension,
Figure FSB0000194207100000022
represents an offset; to determine the absolute position of the node for R and L, y*Equivalent of xR + L is a system of equations
Figure FSB0000194207100000023
Solving the solution;
s610: three reference nodes (p) with the largest area in two-dimensional space1，p2，p3) Conversion to (q)1，q2，q3) First, p is1p2Is translated so that p1And q is1Coincidence, p2Move to p'2＝p2+q1-p1(ii) a Then q is put1p′2Is rotated so that p'2And q is2Overlapping; let g be p1-q1Then there is
Figure FSB0000194207100000024
Wherein H is v ═ p1p2+q1q2)/||p1p2+q1A mirror matrix of q | |, v being the unit column vector of the H matrix;
s620: by
Figure FSB0000194207100000025
And
Figure FSB0000194207100000026
and deriving R-H-I-vv from the uniqueness of the solutionT，
Figure FSB0000194207100000027
Is a solution of the system of equations, wherein the I identity matrix;
s700: and realizing indoor positioning according to the obtained absolute coordinates.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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CN104302000A (en) * 2014-10-15 2015-01-21 上海交通大学 Indoor positioning method based on signal receiving strength indicator correlation
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CN106228107A (en) * 2016-06-30 2016-12-14 杭州浙达精益机电技术股份有限公司 A kind of supersonic guide-wave rail break monitoring algorithm based on independent component analysis

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101155198A (en) * 2006-09-29 2008-04-02 湖南大学 Wireless sensor network node locating method based on ultra-broadband
CN102231912A (en) * 2011-07-29 2011-11-02 杭州电子科技大学 RSSI ranging-based positioning method for indoor wireless sensor network
CN104302000A (en) * 2014-10-15 2015-01-21 上海交通大学 Indoor positioning method based on signal receiving strength indicator correlation
CN104375133A (en) * 2014-11-11 2015-02-25 西北大学 Estimation method for space two-dimensional DOA
CN106228107A (en) * 2016-06-30 2016-12-14 杭州浙达精益机电技术股份有限公司 A kind of supersonic guide-wave rail break monitoring algorithm based on independent component analysis

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