CN117528413A - UWB base station self-calibration method based on multidimensional scale transformation - Google Patents
UWB base station self-calibration method based on multidimensional scale transformation Download PDFInfo
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- H—ELECTRICITY
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- H—ELECTRICITY
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Abstract
According to the UWB base station self-calibration method provided by the invention, a plurality of base stations are newly increased in the area where the target base station is located; obtaining a distance matrix representing the distance between any two base stations; converting the distance matrix into an inner product matrix; extracting k eigenvalues of the inner product matrix and corresponding eigenvectors as a basis of a k-dimensional space for dimension reduction; projecting the eigenvalue of the inner product matrix and the corresponding eigenvector thereof onto k-dimensional space to obtain a dimension-reduction coordinate matrix; acquiring the real coordinates of an anchor base station, and calculating the transformation relation of the coordinates of the anchor base station; and obtaining the real coordinates of the target base station by using the transformation relation and the dimension-reduction coordinate matrix so as to realize the self-calibration of the target base station. According to the method, the relative matrix is obtained through the distance measurement between the base stations, the real coordinates of the target base stations are automatically calculated, the calibration difficulty of the target base stations is reduced, the deployment efficiency of the base stations is improved, the flexibility of subsequent configuration is improved, and the problems of low efficiency, large limit, low speed and the like in manual measurement in the prior art are solved.
Description
Technical Field
The invention belongs to the technical field of positioning, and particularly relates to a self-calibration method of a UWB base station based on multidimensional scaling.
Background
UWB (Ultra wide band) is a carrier-free communication technology, utilizes non-sinusoidal wave narrow pulse transmission data of nanosecond (ns) to picosecond (ps) level, has the working frequency band of 3.25 GHZ-6.75 GHZ, has advantages of high precision, anti-interference, wide range, low power consumption and the like, and is widely used in the positioning field.
The UWB positioning technology realizes positioning based on time differences of receiving a plurality of wireless signals by a receiving device, for example, TOF (Time of Flight) algorithm calculates a distance between a base station and a tag according to a propagation speed and a time difference of the UWB signals in space, and the distance can be converted into coordinates by a trilateral positioning algorithm to realize high-precision indoor positioning. However, the UWB positioning technology needs to be operated with the position coordinates of the known base station, so before the UWB positioning technology is used, the base station and the actual field arrangement coordinates need to be calibrated in a matching manner.
The traditional base station calibration method is to calibrate by manually measuring the distance (meter ruler, laser ranging, etc.). When a plurality of base stations or mobile base stations exist in the system, the base station calibration method has the problems of low deployment efficiency, low speed, inflexible modification and the like. And manual measurement of the base station position is difficult to achieve in some special positioning scenarios (aerial, marine).
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a self-calibration method of a UWB base station based on multidimensional scaling, which reduces the calibration difficulty of a target base station and solves the problems of low efficiency, large limit, low speed and the like in the manual measurement in the prior art.
A UWB base station self-calibration method based on multidimensional scale transformation comprises the following steps:
newly increasing a plurality of base stations in the area where the target base station is located;
obtaining a distance matrix representing the distance between any two base stations;
converting the distance matrix into an inner product matrix;
extracting k eigenvalues of the inner product matrix and corresponding eigenvectors as a basis of a k-dimensional space for dimension reduction;
projecting the eigenvalue of the inner product matrix and the corresponding eigenvector thereof onto k-dimensional space to obtain a dimension-reduction coordinate matrix;
defining a plurality of newly added base stations in the area as anchor base stations;
acquiring the real coordinates of the anchor base station, and calculating the transformation relation between the real coordinates and the dimension-reduction coordinate matrix in the anchor base station;
and obtaining the real coordinates of the target base station by using the transformation relation and the dimension-reduction coordinate matrix so as to realize the self-calibration of the target base station.
Further, the distance matrix creating method includes:
acquiring coordinates of all base stations under a preset coordinate system, and constructing an original coordinate matrix;
calculating the distance between any two base stations by using the original coordinate matrix, and constructing a distance matrix according to all the distances; the distance between two base stations is weighted according to the distance obtained by multiple times of calculation.
Further, the preset coordinate system is constructed by the following method:
and taking the connecting line of two base stations as an X positive half axis, and constructing a Y positive half axis, so that all base stations fall into quadrants where the X axis and the Y positive half axis are located.
Further, converting the distance matrix into an inner product matrix specifically includes:
acquiring a centralizing matrix;
the distance matrix is converted into an inner product matrix using a centering matrix.
Further, the centering matrix H is:
wherein I is an n-order identity matrix, n is the number of base stations, a is an n-dimensional vector of all 1, a T A transposed matrix of a;
the inner product matrix B is:
wherein D is a distance matrix.
Further, extracting k eigenvalues of the inner product matrix and corresponding eigenvectors thereof as the k-dimensional space of the dimension reduction specifically includes:
solving the function |λi-b|=0 to obtain the eigenvalue λ of the inner product matrix;
the maximum k eigenvalues and their corresponding eigenvectors are defined as k-wiki of k-dimensional space.
Further, the dimension-reduction coordinate matrix X is:
wherein J is k The kth eigenvalue, v, that is the largest of the inner product matrix nk Is the kth element of the eigenvector corresponding to the nth eigenvalue.
Further, calculating the transformation relation between the real coordinates and the dimension-reduction coordinate matrix in the anchor base station specifically includes:
acquiring the coordinate of the ith anchor point base station in the dimension-reduction coordinate matrix, and defining the coordinate as a conversion coordinate Ai mds ；
Solving R.Ai by least square method MDS +T≡ai; wherein Ai is the true coordinate of the ith anchor point base station, R is a rotation matrix, and T is a translation matrix;
the transformation relationship includes a rotation matrix and a translation matrix.
Further, the real coordinates X1 of the target base station are:
X1＝R·X MDS +T；
wherein X is MDS The coordinates of the target base station in the dimension-reduction coordinate matrix.
Further, the optimization method of the distance matrix comprises the following steps:
averaging the weights of the last distance matrix D to obtain a comprehensive weight c;
creating a new distance matrix, defined as a first distance matrix D';
optimized distance matrix D new The method comprises the following steps:
D new ＝(D+D′·c)/2。
according to the technical scheme, the UWB base station self-calibration method based on the multi-dimensional scale transformation, provided by the invention, obtains the relative matrix through the pairwise ranging between the base stations, automatically calculates the real coordinates of the target base station, reduces the calibration difficulty of the target base station, improves the deployment efficiency of the base station, improves the flexibility of subsequent configuration, and solves the problems of low efficiency, large limit, low speed and the like in the manual measurement in the prior art.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. Like elements or portions are generally identified by like reference numerals throughout the several figures. In the drawings, elements or portions thereof are not necessarily drawn to scale.
Fig. 1 is a flowchart of a UWB base station self-calibration method provided in an embodiment.
Fig. 2 is a schematic diagram of an additional base station in an area according to an embodiment.
Detailed Description
Embodiments of the technical scheme of the present invention will be described in detail below with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical aspects of the present invention, and thus are merely examples, and are not intended to limit the scope of the present invention. It is noted that unless otherwise indicated, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.
It should be understood that the terms "comprises" and "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
As used in this specification and the appended claims, the term "if" may be interpreted as "when..once" or "in response to a determination" or "in response to detection" depending on the context. Similarly, the phrase "if a determination" or "if a [ described condition or event ] is detected" may be interpreted in the context of meaning "upon determination" or "in response to determination" or "upon detection of a [ described condition or event ]" or "in response to detection of a [ described condition or event ]".
Examples:
a multi-dimensional scaling based UWB base station self-calibration method, see fig. 1, comprising:
s1: newly increasing a plurality of base stations in the area where the target base station is located;
s2: obtaining a distance matrix representing the distance between any two base stations;
s3: converting the distance matrix into an inner product matrix;
s4: extracting k eigenvalues of the inner product matrix and corresponding eigenvectors as a basis of a k-dimensional space for dimension reduction;
s5: projecting the eigenvalue of the inner product matrix and the corresponding eigenvector thereof onto k-dimensional space to obtain a dimension-reduction coordinate matrix;
s6: defining a plurality of newly added base stations in the area as anchor base stations;
s7: acquiring the real coordinates of the anchor base station, and calculating the transformation relation between the real coordinates and the dimension-reduction coordinate matrix in the anchor base station;
s8: and obtaining the real coordinates of the target base station by using the transformation relation and the dimension-reduction coordinate matrix so as to realize the self-calibration of the target base station.
In this embodiment, the UWB base station self-calibration method first newly increases a plurality of base stations in the area where the target base station is located, and distance between any two base stations is obtained by ranging two by two, so as to construct a distance matrix. The distance matrix is then converted into an inner product matrix for further analysis of the structure of the data. And then, extracting k eigenvalues and corresponding eigenvectors of the inner product matrix to serve as bases of the k-dimensional space with reduced dimensions, and projecting the inner product matrix to the k-dimensional space to obtain coordinates with reduced dimensions. And finally, obtaining a transformation relation according to the coordinates of the anchor base station after the dimension reduction and the real coordinates, and transforming the coordinates of the target base station after the dimension reduction according to the transformation relation to obtain the real coordinates of the target base station.
According to the UWB base station self-calibration method, the relative matrix is obtained through the pairwise ranging between the base stations, the real coordinates of the target base station are automatically calculated, the calibration difficulty of the target base station is reduced, the deployment efficiency of the base station is improved, the flexibility of subsequent configuration is improved, and the problems of low efficiency, large limit, low speed and the like in the manual measurement in the prior art are solved.
Further, in some embodiments, the method for creating the distance matrix includes:
acquiring coordinates of all base stations under a preset coordinate system, and constructing an original coordinate matrix;
calculating the distance between any two base stations by using the original coordinate matrix, and constructing a distance matrix according to all the distances; the distance between two base stations is weighted according to the distance obtained by multiple times of calculation.
In this embodiment, a preset coordinate system is created, and coordinates of all base stations under the preset coordinate system are obtained, so as to obtain an original coordinate matrix. And calculating the distance between any two base stations in the original coordinate matrix by using a TOF algorithm to obtain j distances. For example, if the number of base stations is n, j=n≡2. The distance between two base stations can be calculated m times, and the m times of distance weighting is used for calculating an average value to obtain the final distance between the two base stations, wherein the weighting used by weighting can be obtained comprehensively according to various factors such as signal strength, noise size, first path receiving power, total receiving power and the like.
Further, in some embodiments, the preset coordinate system is constructed by:
and taking the connecting line of two base stations as an X positive half axis, and constructing a Y positive half axis, so that all base stations fall into quadrants where the X axis and the Y positive half axis are located.
In this embodiment, referring to fig. 2, it is assumed that a base station A0 and a base station A1 are newly added in the area where the target base station is located, where the base station A0 is an origin of a preset coordinate system, coordinates are (0, 0), a connection line between the base station A0 and the base station A1 is taken as an X positive half axis, the coordinates of the base station A1 are (0, d 01), d01 is a distance between the base station A0 and the base station A1, and other base stations fall into any point in quadrants where the X axis and the Y positive half axis are located.
Further, in some embodiments, converting the distance matrix into an inner product matrix specifically includes:
acquiring a centralizing matrix;
the distance matrix is converted into an inner product matrix using a centering matrix.
The centering matrix H is:
wherein I is an n-order identity matrix, n is the number of base stations, a is an n-dimensional vector of all 1, a T A transposed matrix of a;
the inner product matrix B is:
wherein D is a distance matrix.
In the present embodiment, the centering matrix is mainly used for centering the distance matrix so that the data is symmetrical with respect to the origin, wherein
The inner product matrix mainly represents the inner product relationship between the data for further analysis of the structure of the data.
Further, in some embodiments, extracting k eigenvalues of the inner product matrix and their corresponding eigenvectors as the reduced-dimension k-dimensional space specifically includes:
solving the function |λi-b|=0 to obtain the eigenvalue λ of the inner product matrix;
the maximum k eigenvalues and their corresponding eigenvectors are defined as k-wiki of k-dimensional space.
In this embodiment, the eigenvalue λ of the inner product matrix can be obtained by solving the function |λi-b|=0.
Wherein a is mn For the value of the inner product matrix B, the maximum 2 eigenvalues lambda are selected 1 ，λ 2 Solving for |lambda I-B|v i Non-zero solution of =0, where v i Lambda is lambda i And taking the characteristic value and the characteristic vector as a 2-dimensional basis of the 2-dimensional space after the dimension reduction.
Further, in some embodiments, the dimension-reduction coordinate matrix X is:
wherein J is k The kth eigenvalue, v, that is the largest of the inner product matrix nk Is the kth element of the eigenvector corresponding to the nth eigenvalue.
In this embodiment, the eigenvalues of the inner product matrix and their corresponding eigenvectors are projected onto a 2-dimensional basis, so as to obtain coordinates after dimension reduction. For example when k=2,
i.e. first construct a eigenvector matrix V and a diagonal matrix Λ consisting of the square root of eigenvalues 1/2 Then, a dimension-reducing coordinate matrix X is calculated, and each behavior in the dimension-reducing coordinate matrix X is that one base station is in 2 dimensionsCoordinates in space.
Further, in some embodiments, calculating the transformation relationship between the real coordinates and the dimension-reduction coordinate matrix in the anchor base station specifically includes:
acquiring coordinates of an anchor point base station in a dimension-reduction coordinate matrix, and defining the coordinates as conversion coordinates Ai mds ；
Solving R.Ai by least square method MDS +T≡ai; wherein Ai is the real coordinates of the anchor base station, R is a rotation matrix, and T is a translation matrix;
the transformation relationship includes a rotation matrix and a translation matrix.
In the embodiment, the method calculates the transformation relation between the real coordinates and the coordinates after dimension reduction through the real coordinates of the anchor base stations, and rotates and translates the coordinates after dimension reduction of the target base station by utilizing the transformation relation to obtain the real coordinates of the target base station. For example, coordinates of 3 anchor base stations after dimension reduction are extracted from a dimension reduction coordinate matrix X and are respectively A0 MDS ，A1 mds ，Ai mds The method comprises the steps of carrying out a first treatment on the surface of the Obtaining the real coordinates of 3 anchor base stations, namely A0, A1 and Ai, and constructing the following functions:
R·A0 MDS +T≈A0；R·A1 MDS +T≈A1；R·Ai MDS +T≈Ai。
solving the rotation matrix R and the translation matrix T by a least square method, namely
Further, in some embodiments, the true coordinates X1 of the target base station are:
X1＝R·X MDS +T；
wherein X is MDS The coordinates of the target base station in the dimension-reduction coordinate matrix.
In this embodiment, the method rotates and translates the coordinate of the target base station after the dimension reduction, so as to obtain the real coordinate of the target base station.
Further, in some embodiments, the optimization method of the distance matrix includes:
averaging the weights of the last distance matrix D to obtain a comprehensive weight c;
creating a new distance matrix, defined as a first distance matrix D';
optimized distance matrix D new The method comprises the following steps:
D new ＝(D+D′·c)/2。
in this embodiment, the method may further optimize the distance matrix, and average the weights of the distance matrix calculated last time to obtain the integrated weight c calculated last time. Newly selecting a new base station to create a distance matrix as D', and carrying out weighted average on the distance matrix D with the last distance matrix D to obtain the latest distance matrix D new Distance matrix D new And converting the calibration data into an inner product matrix to participate in the calibration of a new round.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention, and are intended to be included within the scope of the appended claims and description.
Claims (10)
1. The self-calibration method of the UWB base station based on the multidimensional scale transformation is characterized by comprising the following steps:
newly increasing a plurality of base stations in the area where the target base station is located;
obtaining a distance matrix representing the distance between any two base stations;
converting the distance matrix into an inner product matrix;
extracting k eigenvalues of the inner product matrix and corresponding eigenvectors thereof as a basis of a k-dimensional space for dimension reduction;
projecting the eigenvalue of the inner product matrix and the eigenvector corresponding to the eigenvalue to the k-dimensional space to obtain a dimension-reduction coordinate matrix;
defining a plurality of newly added base stations in the area as anchor base stations;
acquiring the real coordinates of the anchor base station, and calculating the transformation relation between the real coordinates in the anchor base station and the dimension-reduction coordinate matrix;
and obtaining the real coordinates of the target base station by using the transformation relation and the dimension-reduction coordinate matrix so as to realize the self-calibration of the target base station.
2. The multi-dimensional scaling based UWB base station self calibration method of claim 1 wherein the distance matrix creation method comprises:
acquiring coordinates of all base stations under a preset coordinate system, and constructing an original coordinate matrix;
calculating the distance between any two base stations by using the original coordinate matrix, and constructing the distance matrix according to all the distances; the distance between the two base stations is weighted according to the distance obtained by multiple times of calculation.
3. The multi-dimensional scaling based UWB base station self calibration method of claim 2 wherein the preset coordinate system is constructed by:
and taking the connecting line of two base stations as an X positive half axis, and constructing a Y positive half axis, so that all base stations fall into quadrants where the X axis and the Y positive half axis are located.
4. The multi-dimensional scaling based UWB base station self calibration method of claim 1 wherein said converting the distance matrix into an inner product matrix comprises:
acquiring a centralizing matrix;
the distance matrix is converted into the inner product matrix using the centering matrix.
5. The multi-dimensional scaling based UWB base station self calibration method of claim 4 wherein the centering matrix H is:
wherein I is an n-order identity matrix, n is the number of the base stations, a is an n-dimensional vector of all 1, a T A transposed matrix of a;
the inner product matrix B is:
wherein D is the distance matrix.
6. The method for self-calibration of a UWB base station based on multi-dimensional scaling according to claim 5, wherein the extracting k eigenvalues of the inner product matrix and their corresponding eigenvectors as the reduced-dimension k-dimensional space specifically comprises:
solving a function |λi-b|=0 to obtain a eigenvalue λ of the inner product matrix;
defining the maximum k eigenvalues and the corresponding eigenvectors as k-dimensional base of the k-dimensional space.
7. The multi-dimensional scaling based UWB base station self calibration method of claim 6 wherein the dimension reduction coordinate matrix X is:
wherein J is k The kth eigenvalue, v, being the largest of the inner product matrices nk And the k element in the feature vector corresponding to the n feature value.
8. The self-calibration method of a UWB base station based on multi-dimensional scaling according to claim 7, wherein the calculating the transformation relation between the real coordinates in the anchor base station and the dimension-reduced coordinate matrix specifically comprises:
acquiring the coordinate of the ith anchor point base station in the dimension-reduction coordinate matrix, and defining the coordinate as a conversion coordinate Ai mds ；
Solving R.Ai by least square method MDS +T≡ai; wherein Ai is the true coordinate of the ith anchor point base station, R is a rotation matrix, and T is a translation matrix;
the transformation relationship includes a rotation matrix and a translation matrix.
9. The multi-dimensional scaling-based UWB base station self calibration method of claim 8 wherein the true coordinates X1 of the target base station are:
X1＝R·X MDS +T；
wherein X is MDS And the coordinates of the target base station in the dimension-reduction coordinate matrix.
10. The multi-dimensional scaling based UWB base station self calibration method of claim 2 wherein the distance matrix optimization method comprises:
averaging the weight of the last distance matrix D to obtain a comprehensive weight c;
creating a new distance matrix, defined as a first distance matrix D';
optimized distance matrix D new The method comprises the following steps:
D new ＝(D+D′·c)/2。
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