CN112533288B - Self-calibration method for mobile base station position applied to UWB positioning - Google Patents
Self-calibration method for mobile base station position applied to UWB positioning Download PDFInfo
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- H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract
The invention relates to a UWB positioning technology, in particular to a self-calibration method for the position of a movable base station applied to UWB positioning. The invention solves the problems of low calibration speed and inconvenient base station layout caused by the traditional mobile base station position calibration method. A mobile base station position self-calibration method applied to UWB positioning is realized by adopting the following steps: the method comprises the following steps: placing two base stations at the same edge of a site, taking the two base stations as a 0 th base station and a 1 st base station respectively, and then placing at least two base stations in the site; step two: measuring the distance from each base station to the ground; step three: measuring the distance between every two base stations by using a TOF ranging method; step four: let X be ═ X1,xi,yi,xj,yj]TCalculating an initial value X of the iteration of X from the measurement results0(ii) a Step five: and (3) performing first-order Taylor expansion on the formula (1), and performing iterative computation on X by using a Newton iteration method. The invention is suitable for the construction of local positioning systems in UWB positioning and other wireless positioning technologies.
Description
Technical Field
The invention relates to a UWB positioning technology, in particular to a self-calibration method for the position of a movable base station applied to UWB positioning.
Background
The UWB (Ultra wide band) positioning technology is widely applied to the field of indoor and outdoor positioning due to the advantages of low power consumption, high transmission speed, high multi-path resolution, high system safety, high positioning accuracy (up to the decimeter level), and the like. In the UWB positioning technology, the calibration of the position of a mobile base station is an essential link in the construction of a local positioning system. The conventional mobile base station position calibration method is limited by the principle of the conventional mobile base station, and the calibration of the position of the base station needs to be performed by means of an external measuring tool (such as a total station, a tape measure and the like), so that the calibration speed is slow, and the base station is inconvenient to arrange. Therefore, a mobile base station position self-calibration method applied to UWB positioning needs to be invented, so that the problems of low calibration speed and inconvenience in base station arrangement caused by the traditional mobile base station position calibration method are solved.
Disclosure of Invention
The invention provides a self-calibration method for the position of a movable base station, which is applied to UWB positioning and aims to solve the problems of low calibration speed and inconvenient base station layout caused by the traditional method for calibrating the position of the movable base station.
The invention is realized by adopting the following technical scheme:
a mobile base station position self-calibration method applied to UWB positioning is realized by adopting the following steps:
the method comprises the following steps: placing two base stations at the same edge of a site, taking the two base stations as a 0 th base station and a 1 st base station respectively, and then placing at least two base stations in the site;
each base station is regarded as a space point; defining the ground as an xoy plane of a three-dimensional coordinate system; defining the projection of a straight line passing through the 0 th base station and the 1 st base station on the ground as an x-axis of a three-dimensional coordinate system; defining the ground normal passing through the 0 th base station as the z-axis of the three-dimensional coordinate system;
step two: measuring the distance from each base station to the ground; the measurement results include:
distance z from 0 th base station to ground0Distance z from the 1 st base station to the ground1Distance z between ith base station in site and groundiDistance z between jth base station in site and groundj；
Then, three-dimensional coordinate values of each base station are defined according to the measurement result, which is as follows:
the three-dimensional coordinate value of the 0 th base station is defined as (0,0, z)0) The three-dimensional coordinate value of the 1 st base station is defined as (x)1,0,z1) The three-dimensional coordinate value of the ith base station in the site is defined as (x)i,yi,zi) And the three-dimensional coordinate value of the jth base station in the site is defined as (x)j,yj,zj) (ii) a Wherein x is1、xi、yi、xj、yjAre all unknown quantities;
step three: measuring the distance between every two base stations by using a TOF ranging method; the measurement results include:
distance d between 0 th base station and 1 st base station01Distance d between 0 th base station and ith base station in site0iDistance d between 0 th base station and jth base station in site0jDistance d between the 1 st base station and the ith base station in the field1iDistance d between the 1 st base station and the jth base station in the field1jDistance d between ith base station in site and jth base station in siteij；
The distance between each base station is expressed as follows:
step four: let X be ═ X1,xi,yi,xj,yj]TCalculating an initial value X of the iteration of X from the measurement results0(ii) a The calculation formula is as follows:
X0＝[x10,xi0,yi0,xj0,yj0]T (2)；
M＝d01 2-z10 2-d1i 2+d0i 2+zi0 2-zi1 2 (4)；
N＝d01 2-z10 2-d1j 2+d0j 2+zj1 2-zj0 2 (5)；
step five: performing first-order Taylor expansion on the formula (1), and performing iterative computation on X by using a Newton iteration method;
the first order Taylor expansion is as follows:
Xu＝[x1u,xiu,yiu,xju,yju]T(8)；
the iterative calculation formula is as follows:
Xu+1＝Xu+ΔXu (10)；
ΔXu＝(Hu THu)-1Hu TΔFu (11)；
ΔFu＝D-Du (13)；
D＝[d01,d0i,d0j,d1i,d1j,dij]T (14)；
in formulae (7) to (15): xu+1Represents the value of X after the u-th iteration; xuRepresents the value of X before the u-th iteration; Δ XuAn iteration term representing the u-th iteration; huA coefficient matrix representing a first order Taylor expansion at the u-th iteration;
when Δ XuWhen the current X is smaller than the specified threshold value, the iteration is ended, and the current X isu+1And the three-dimensional coordinate value of each base station is obtained as the final value of X, so that the self-calibration of the position of each base station is realized.
Compared with the traditional mobile base station position calibration method, the mobile base station position self-calibration method applied to UWB positioning disclosed by the invention does not need an external measuring tool, and is based on a TOF ranging method and a Newton iteration method, so that the self-calibration of each base station position is rapidly and accurately realized, the calibration speed is obviously accelerated, and the base station arrangement is greatly facilitated.
The invention effectively solves the problems of low calibration speed and inconvenient base station arrangement caused by the traditional mobile base station position calibration method, and is suitable for the construction of local positioning systems in UWB positioning and other wireless positioning technologies.
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FIG. 1 is a schematic diagram of step three of the present invention.
Detailed Description
A mobile base station position self-calibration method applied to UWB positioning is realized by adopting the following steps:
the method comprises the following steps: placing two base stations at the same edge of a field, taking the two base stations as a 0 th base station and a 1 st base station respectively, and then placing at least two base stations in the field;
each base station is regarded as a space point; defining the ground as an xoy plane of a three-dimensional coordinate system; defining the projection of a straight line passing through the 0 th base station and the 1 st base station on the ground as an x axis of a three-dimensional coordinate system; defining the ground normal passing through the 0 th base station as the z-axis of the three-dimensional coordinate system;
step two: measuring the distance from each base station to the ground; the measurement results include:
distance z from 0 th base station to ground0Distance z from the 1 st base station to the ground1Distance z between ith base station in site and groundiDistance z between jth base station in site and groundj；
Then, defining three-dimensional coordinate values of each base station according to the measurement result, specifically as follows:
the three-dimensional coordinate value of the 0 th base station is defined as (0,0, z)0) The three-dimensional coordinate value of the 1 st base station is defined as (x)1,0,z1) The three-dimensional coordinate value of the ith base station in the site is defined as (x)i,yi,zi) And the three-dimensional coordinate value of the jth base station in the site is defined as (x)j,yj,zj) (ii) a Wherein x is1、xi、yi、xj、yjAre all unknown quantities;
step three: measuring the distance between every two base stations by using a TOF ranging method; the measurement results include:
distance d between 0 th base station and 1 st base station01Distance d between 0 th base station and ith base station in site0iDistance d between 0 th base station and jth base station in site0jDistance d between the 1 st base station and the ith base station in the field1iDistance d between the 1 st base station and the jth base station in the field1jDistance d between ith base station in site and jth base station in siteij；
The distance between each base station is expressed as follows:
step four: let X be ═ X1,xi,yi,xj,yj]TCalculating an initial value X of the iteration of X from the measurement results0(ii) a The calculation formula is as follows:
X0＝[x10,xi0,yi0,xj0,yj0]T (2)；
M＝d01 2-z10 2-d1i 2+d0i 2+zi0 2-zi1 2 (4)；
N＝d01 2-z10 2-d1j 2+d0j 2+zj1 2-zj0 2 (5)；
step five: performing first-order Taylor expansion on the formula (1), and performing iterative computation on X by using a Newton iteration method;
the first order Taylor expansion is as follows:
Xu＝[x1u,xiu,yiu,xju,yju]T (8)；
the iterative calculation formula is as follows:
Xu+1＝Xu+ΔXu (10)；
ΔXu＝(Hu THu)-1Hu TΔFu (11)；
ΔFu＝D-Du (13)；
D＝[d01,d0i,d0j,d1i,d1j,dij]T (14)；
in formulae (7) to (15): xu+1Represents the value of X after the u-th iteration; xuRepresents the value of X before the u-th iteration; Δ XuAn iteration term representing the u-th iteration; huA coefficient matrix representing a first order Taylor expansion at the u-th iteration;
when Δ XuWhen the X is smaller than the specified threshold value, the iteration is ended, and the current X isu+1As the final value of X, thereby obtainingAnd the three-dimensional coordinate value of each base station is obtained, so that the self-calibration of the position of each base station is realized.
While specific embodiments of the invention have been described above, it will be appreciated by those skilled in the art that these are by way of example only, and that the scope of the invention is defined by the appended claims. Various changes and modifications to these embodiments may be made by those skilled in the art without departing from the spirit and scope of the invention, and these changes and modifications are within the scope of the invention.
Claims (1)
1. A mobile base station position self-calibration method applied to UWB positioning is characterized in that: the method is realized by adopting the following steps:
the method comprises the following steps: placing two base stations at the same edge of a field, taking the two base stations as a 0 th base station and a 1 st base station respectively, and then placing at least two base stations in the field;
each base station is regarded as a space point; defining the ground as an xoy plane of a three-dimensional coordinate system; defining the projection of a straight line passing through the 0 th base station and the 1 st base station on the ground as an x axis of a three-dimensional coordinate system; defining the ground normal passing through the 0 th base station as the z-axis of the three-dimensional coordinate system;
step two: measuring the distance from each base station to the ground; the measurement results include:
distance z from 0 th base station to ground0Distance z from the 1 st base station to the ground1Distance z between ith base station in site and groundiThe distance z between the jth base station in the field and the groundj；
Then, defining three-dimensional coordinate values of each base station according to the measurement result, specifically as follows:
the three-dimensional coordinate value of the 0 th base station is defined as (0,0, z)0) The three-dimensional coordinate value of the 1 st base station is defined as (x)1,0,z1) The three-dimensional coordinate value of the ith base station in the site is defined as (x)i,yi,zi) And the three-dimensional coordinate value of the jth base station in the site is defined as (x)j,yj,zj) (ii) a Wherein，x1、xi、yi、xj、yjAre all unknown quantities;
step three: measuring the distance between every two base stations by using a TOF ranging method; the measurement results include:
distance d between 0 th base station and 1 st base station01Distance d between 0 th base station and ith base station in site0iDistance d between 0 th base station and jth base station in site0jDistance d between the 1 st base station and the ith base station in the field1iDistance d between the 1 st base station and the jth base station in the field1jDistance d between ith base station in site and jth base station in siteij；
The distance between each base station is expressed as follows:
step four: let X be ═ X1,xi,yi,xj,yj]TCalculating an initial value X of the iteration of X from the measurement results0(ii) a The calculation formula is as follows:
X0＝[x10,xi0,yi0,xj0,yj0]T (2)；
M＝d01 2-z10 2-d1i 2+d0i 2+zi0 2-zi1 2 (4)；
N＝d01 2-z10 2-d1j 2+d0j 2+zj1 2-zj0 2 (5)；
step five: performing first-order Taylor expansion on the formula (1), and performing iterative computation on X by using a Newton iteration method;
the first order Taylor expansion is as follows:
Xu＝[x1u,xiu,yiu,xju,yju]T (8)；
the iterative calculation formula is as follows:
Xu+1＝Xu+ΔXu (10)；
ΔXu＝(Hu THu)-1Hu TΔFu (11)；
ΔFu＝D-Du (13)；
D＝[d01,d0i,d0j,d1i,d1j,dij]T (14)；
in formulae (7) to (15): xu+1Represents the value of X after the u-th iteration; xuRepresents the value of X before the u-th iteration; Δ XuAn iteration term representing the u-th iteration; huA coefficient matrix representing the first order Taylor expansion at the u-th iteration;
when Δ XuWhen the X is smaller than the specified threshold value, the iteration is ended, and the current X isu+1And the three-dimensional coordinate value of each base station is obtained as the final value of X, so that the self-calibration of the position of each base station is realized.
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