CN112180322B - Method for establishing basic coordinate system of space positioning system - Google Patents
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Abstract
A method for establishing a basic coordinate system of a space positioning system belongs to the technical field of wireless positioning, and the step of establishing the basic coordinate system is as follows: at least four non-coplanar base stations A, B, C and D are randomly installed to form a basic positioning system; establishing a left-handed space positioning system or a right-handed space positioning system; calculating the distance between every two base stations; calculating the coordinates of the base stations A, B, C and D in the virtual coordinate system; verifying the relation between the left chiral coordinate system, the right chiral coordinate system and the virtual coordinate system; determining vertical coordinate Z of D-point base station D Taking the value of (a); fitting an alpha plane under a virtual coordinate system; rotating a beta plane of the virtual coordinate system; the virtual coordinate system is translated. The invention adopts gesture recognition algorithm to realize three-dimensional space positioning, and adopts a beacon space moving method to determine the position of the base station in the reference coordinate system.
Description
Technical Field
The invention relates to the technical field of wireless positioning, in particular to a method for establishing a basic coordinate system of a space positioning system.
Background
In 'a UWB base station coordinate self-calibration method' patent applied by rho and kong lin, 2016 (application publication No. CN 106211080A), a tag is used to calibrate the position of a base station after the base station is changed, but there is no material description in the patent on how to use the tag to automatically calibrate the coordinates of the base station.
In 2017, a patent of "method for establishing coordinate systems among base stations in a positioning system" filed by zhaxing chapter and the like (application publication No. CN 106990389A), the method for establishing a coordinate system by using distances among base stations solves the problem that in the prior art, a coordinate system is established by using a measuring instrument such as a total station or a laser range finder to perform manual measurement, but has the problem that when the positioning system establishes the coordinate system, the approximate directions of the base stations need to be determined first, and positioning data cannot be normally acquired even if the non-line-of-sight distance or the directions are unclear.
In 2018, a patent of UWB system positioning base station calibration method and device applied by tian shi wei et al (application publication No. CN 109218967A) proposes that a manual measurement mode is used to measure the real coordinate value of the base station to be calibrated in the current positioning environment, and then a reference coordinate system is established.
In 2019, patent of UWB base station coordinate automatic calibration method and system based on optimization theory, applied by xu cheng et al (application publication No. CN 110290463A), proposes that a minimum UWB system is first constructed by placing base stations and labels at corresponding positions, and optimization processing is performed on the sum of residual errors of all theoretical distances and actual measured distances by using optimization theory, so as to calibrate the system.
In practical application, base stations distributed randomly need to be calibrated, and a spatial coordinate system is established as a primary condition for calibration, in a conventional calibration algorithm, the directions of the base stations need to be set manually, or coordinates need to be designated, and in this embodiment, the spatial coordinate system is established by identifying the rule of movement of a beacon in a space.
Therefore, the research on the method for establishing the coordinate system and measuring the position of the base station with low labor cost and high accuracy is a problem that needs to be solved by researchers in the field.
Disclosure of Invention
The invention provides a method for establishing a basic coordinate system of a space positioning system by establishing a 3D positioning system reference coordinate system chirality identification and calibration method and adopting a positioning beacon to do special motion in a positioning system signal coverage range so as to determine the chirality of a positioning system and the relative coordinate of each base station, so that a third-party device is not needed to be used for measuring the coordinates of the base stations when the base stations are installed.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for establishing a basic coordinate system of a space positioning system comprises the following steps:
at least four non-coplanar base stations A, B, C and D are randomly installed to form a basic positioning system;
establishing a left-handed space positioning system or a right-handed space positioning system;
calculating the distance between every two base stations;
calculating the coordinates of the base stations A, B, C and D in the virtual coordinate system;
verifying the relation between the left chiral coordinate system, the right chiral coordinate system and the virtual coordinate system;
determining vertical coordinate Z of D-point base station D Taking the value of (A);
fitting an alpha plane under a virtual coordinate system;
rotating a beta plane of the virtual coordinate system;
the virtual coordinate system is translated.
Further, the condition of local area distribution density of the distributed local positioning base stations is met, four non-coplanar base stations are randomly installed, and the signal coverage areas of the four base stations have a public signal area.
Furthermore, a vector formed by the base station A and the base station C by taking the base station A as a coordinate origin
For the X-axis, with reference to the X-axis, the Y-axis is established in a plane ABC, the Z-axis pointing to the location of the base station DAnd (5) establishing a right chiral space coordinate system in the vertical direction.
Furthermore, a vector formed by the base station A and the base station B by taking the base station A as a coordinate origin
And establishing a Y axis in a plane ABC by taking the X axis as a reference, and establishing a left-handed space coordinate system by pointing a Z axis in the vertical direction of the position of the base station D.
Further, the right chiral coordinate system and the virtual coordinate system are established in the same direction.
Further, the distance between every two base stations is obtained by measuring the base stations in the basic positioning system and averaging.
Further, the virtual coordinate system is a mirror image of the left-handed coordinate system, and the virtual coordinate system is consistent with the right-handed coordinate system.
Further, fitting an alpha plane under a virtual coordinate system, wherein a unitized normal vector corresponding to the alpha plane is N.
Further, when the coordinate measured in the virtual coordinate system is β, the coordinate α in the new reference coordinate system is represented as α = R β.
Further, the mathematical expression of translation followed by rotation is α = R (β + e) 1 ) The mathematical expression of rotation before translation is alpha = R beta + e 2 。
The invention has the following beneficial effects for the prior art:
according to the invention, a left-handed space coordinate system and a right-handed space coordinate system are adopted, and the coordinates of four basic base stations can be obtained by simultaneously calculating the distance measurement characteristics of the system, so that three-dimensional space positioning is realized; determining the position of a base station in a reference coordinate system by adopting a method that a beacon moves in a space with UWB positioning technology; the relative position of the beacon moving plane and the plane where the virtual coordinate system is located is adjusted, so that control and measurement are facilitated. The algorithm is insensitive to the installation position of the UWB positioning base station, the installation and debugging efficiency can be improved, the algorithm complexity is low, and the real-time performance can be ensured; the invention has the advantages of high efficiency, random installation and deployment of the positioning base station and easy realization.
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 embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic diagram of a right-handed spatial coordinate system according to the present invention;
FIG. 2 is a schematic diagram of the left-handed spatial coordinate system of the present invention;
FIG. 3 is a schematic diagram of a point in a right-handed chiral coordinate system of the present invention coinciding with a virtual mapping point;
FIG. 4 is a schematic diagram of a point in a left-handed coordinate system and a virtual mapping point in a mirror image according to the present invention;
FIG. 5 is a schematic view of the invention with the alpha plane perpendicular to the vertical;
fig. 6 is a schematic view of the invention with the beta plane perpendicular to the vertical.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it is to be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplification of description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
The present embodiment is explained with reference to fig. 1 to 6: a method for establishing a basic coordinate system of a space positioning system comprises the following steps:
under the condition of meeting the local area distribution density of distributed local positioning base stations, at least four non-coplanar base stations A, B, C and D are randomly installed to form a basic positioning system, and the signal coverage areas of the four base stations have public signal areas;
the steps of establishing the left-handed space positioning system are as follows: vector formed by base station A and base station B by taking base station A as coordinate origin
Establishing a Y axis in a plane ABC by taking the X axis as a reference, and establishing a left-handed spatial coordinate system by taking a Z axis as a vertical direction of the position of the base station D;
the steps of establishing the right chiral space positioning system are as follows: vector formed by base station A as coordinate origin and base stations A and C
Establishing a Y axis in a plane ABC by taking the X axis as a reference, and establishing a right chiral space coordinate system by taking a Z axis as a vertical direction of the position of the base station D;
as a preferred scheme, the right chiral coordinate system and the virtual coordinate system are set in the same direction;
by the arrangement, the base station is randomly installed in the space, and the left-handed coordinate system and the right-handed coordinate system can be obtained due to the fact that the coordinate directions of the base station are different.
Example 2
In the embodiment described in the first embodiment, the distance between two base stations is obtained by measuring the base stations in the basic positioning system, and they are respectively expressed as
By setting each azimuth vector, subsequent calculation is facilitated.
Further optimized, a virtual coordinate system is established by taking the right-handed space positioning system as a standard, wherein
The coordinates of the base stations A, B, C, D are A (0, 0), B (X) B ,Y B ,0)，C(b，0，0)，D(X D ，Y D ，Z D ),
Wherein,
s represents the area of the delta ABC,
then the
V represents the volume of the triangular pyramid D-ABC
G＝(c 2 +d 2 -e 2 ) 2
H＝(b 2 +d 2 -f 2 ) 2
K＝(b 2 +c 2 -a 2 ) 2
Then:
when d is 2 -Z D 2 -X D 2 >At the time of 0, the number of the first electrode,
d 2 -Z D 2 -X D 2 when =0, Y D ＝0。
With the arrangement, the specific coordinate values of the base station in the virtual coordinate system can be obtained through calculation, so as to determine the position of the base station.
Example 3
To describe the present embodiment with reference to the first to second embodiments, the positions of the actual base stations a ', B', C ', and D' in the virtual coordinate system are the length mapping between two base stations, that is, the actual base stations a ', B', C ', and D' are mapped to the lengths of two base stations
The virtual coordinate system and the coordinate system corresponding to the actual base station have mirror images or are consistent according to the mapping relation.
Preferably, when the point in the right-handed coordinate system corresponds to the virtual mapping point one by one and the positions of the points coincide, the beacon Q moves in space according to the y → x → z track, and in the virtual coordinate system, a Q 'point also moves along the y' → x '→ z' track, and the vector coordinate system formed by the movement track is the right-handed spatial coordinate system track;
furthermore, when a point in the left-handed coordinate system is mirrored from the virtual mapping point, the beacon Q moves in space along the y → x → z trajectory, and in the virtual coordinate system, a Q ' point also moves along the y ' → x ' → z ', and the corresponding y ' → x ' → z ' trajectory is the left-handed spatial coordinate system trajectory;
according to the arrangement, the left and right chiral space coordinate systems are distinguished through the difference of the motion tracks, and the difference of the chirality determines the difference of the algorithm;
the beacon Q is located at the point O at the initial moment, and the distance from the beacon Q to four points A, B, C and D is respectively L through the ranging values in the ranging system of the right chiral coordinate system A 、L B 、L C 、L D Calculating the coordinate Q 'of the beacon Q at O by a four-point space positioning method, obtaining corresponding coordinates X', Y 'and Z' of the beacon Q at X, Y and Z, and expressing the motion track obtained by a virtual coordinate system as a vector
According to the right-hand screw rule, vector pair
And
perform outer product operation, i.e.
Thereby to obtain
In that
Projection onto
The inner product of (a) is a positive value, which indicates that the right chiral coordinate system is consistent with the virtual coordinate system;
still further, the beacon Q is located at the point O at the initial time, and the distance from the beacon Q to four points a, B, C and D is L through the ranging values in the left-handed coordinate system ranging system A 、L B 、L C 、L D Calculating the coordinate Q 'of the beacon Q at O by a four-point space positioning method, obtaining the corresponding coordinates X', Y 'and Z' of the beacon Q at X, Y and Z, and expressing the motion track obtained from a virtual coordinate system by using a vector as
According to the right-hand screw rule, for the vector
And
do an outer product operation, i.e.
Thereby, the device
In that
Projection onto
The inner product of (b) is a negative value, which indicates that the left-handed coordinate system and the virtual coordinate system are mirror images;
by means of the arrangement, when the initial calculation is carried out, the right chiral coordinate system is consistent with the virtual coordinate system when the vertical coordinate of the D base station is positive, and the left chiral coordinate system is mirrored with the virtual coordinate system when the vertical coordinate of the D base station is negative, so that the actual coordinates of the base stations A, B, C and D in the virtual coordinate system can be determined.
Example 4
In the embodiment described in conjunction with the first to third embodiments, the 3D space plane expression is
Ax + By + Cz + D =0, wherein
A series of coordinate points (x) in the alpha plane measured by the 3D ranging type space positioning system i ,y i ,z i ),i＝1,…,n,
According to the least square idea, when the square sum of the distances from all sampling points to the plane is minimum, the corresponding plane is the plane to be solved, assuming that the minimum value is f,
namely, it is
Order to
To obtain
Order to
By bringing formula (4.2) into formula (4.1)
The formula (4.3) is a quadratic form with respect to the vectors (A, B, C),
namely, it is
Order to
Get f = N' PN
For | | | N' | =1, P is a quadratic form f of a real symmetric matrix, when f obtains the minimum value, the value of the vector N is the eigenvector corresponding to the minimum eigenvalue of the matrix P, a plane can be fitted according to the acquired data, and the unitized normal vector corresponding to the plane is N; thus, the solution of the alpha plane is completed.
Example 5
To describe the present embodiment with reference to the first to fourth embodiments, the method for rotating the β plane of the virtual coordinate system includes the following specific steps:
in the virtual coordinate system, assume that a normal vector M = (0, 1) of the β plane, a normal vector of the α plane is N in the virtual coordinate system, and a rotation vector of the β plane to the α plane is N
K＝M×N
K is a unit vector, assuming a unit rotation vector K = [ K = x ，k y ，k z ],k x 、k y 、k z Coordinate values of three axes are expressed, so that an antisymmetric array corresponding to a unit rotation vector K is obtained
Cosine value of rotation angle
R＝I+K′sinθ+(1-cosθ)K′ 2
The coordinate measured in the virtual coordinate system is beta, and the coordinate alpha in the new reference coordinate system is represented as
α＝Rβ
Calculating to obtain the rotation angle and the rotation relation between the alpha plane and the beta plane;
preferably, the step of translating the virtual coordinate system comprises: the mathematical expression of translation first and rotation later is
α＝R(β+e 1 )
Further optimization, e 1 Representing a translation vector relative to a virtual coordinate system.
Alternatively, the mathematical expression of rotation followed by translation is
α＝Rβ+e 2 。
Further optimization, e 2 Representing a translation vector relative to the virtual coordinate system after rotation; the adjustment method may be translation first and rotation second or rotation first and translation second, with no sequential provision.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A method for establishing a basic coordinate system of a space positioning system is characterized in that the step of establishing the basic coordinate system is as follows:
at least four non-coplanar base stations A, B, C and D are randomly installed to form a basic positioning system;
establishing a left-handed space positioning system or a right-handed space positioning system,
the establishment of the right-handed spatial localization system comprises the following steps:
taking the base station A as the origin of coordinates, the base stations A and C form a structureA vector of
Establishing a Y axis in a plane ABC by taking the X axis as a reference, and establishing a space coordinate system by taking a Z axis as a vertical direction of the position of the base station D;
the establishment of the left-handed spatial localization system comprises the following steps:
vector formed by base station A and base station B by taking base station A as coordinate origin
Establishing a Y axis in a plane ABC by taking the X axis as a reference, and establishing a space coordinate system by taking a Z axis as a vertical direction of the position of the base station D; calculating the distance between every two base stations;
calculating the coordinates of the base stations A, B, C and D in the virtual coordinate system: establishing a virtual coordinate system by taking a right chiral coordinate system as a standard, wherein the coordinates of the base stations A, B, C and D are A (0, 0) and B (X) B ,Y B ,0)，C(b，0，0)，D(X D ，Y D ，Z D )；
The positions of the actual base stations A ', B', C 'and D' in the virtual coordinate system are the mapping of the lengths between every two base stations, i.e. the mapping is carried out
A ', B', C ', D' are respectively mapped with A, B, C and D, and the virtual coordinate system and the coordinate system corresponding to the actual base station have mirror images or are consistent according to the mapping relation;
verifying the relation between the left-handed coordinate system, the right-handed coordinate system and the virtual coordinate system: when the point in the right-handed coordinate system corresponds to the virtual mapping point one by one and the positions are consistent, the beacon Q is moved in the space according to the y → x → z track, in the virtual coordinate system, a point Q 'also moves along the y' → x '→ z', and the vector coordinate system formed by the moving track is the right-handed space coordinate system track;
the beacon Q is located at the point O at the initial moment, and the distance from the beacon Q to the four points A, B, C and D is respectively L through the ranging values in the ranging system of the right chiral coordinate system A 、L B 、L C 、L D Calculating the coordinate Q 'of the beacon Q at O by a four-point space positioning method, obtaining the corresponding coordinates X', Y 'and Z' of the beacon Q at X, Y and Z, and expressing the motion track obtained from a virtual coordinate system by using a vector as
For vector
And
do an outer product operation, i.e.
Thereby to obtain
In that
Projection onto
The inner product of (b) is a positive value, which indicates that the right chiral coordinate system is consistent with the virtual coordinate system;
when the point in the left-handed coordinate system is mirrored with the virtual mapping point, the beacon Q moves in space and moves according to the y → x → z trajectory, and in the virtual coordinate system, a Q ' point also moves along the y ' → x ' → z ', and the corresponding y ' → x ' → z ' movement trajectory is the left-handed spatial coordinate system trajectory;
the beacon Q at the initial moment is at the point O, and the distance measurement value in the distance measurement system of the left-handed coordinate system is used as the beaconThe distances from the mark Q to the four points A, B, C and D are respectively L A 、L B 、L C 、L D Calculating the coordinate Q 'of the beacon Q at O by a four-point space positioning method, obtaining corresponding coordinates X', Y 'and Z' of the beacon Q at X, Y and Z, and expressing the motion track obtained by a virtual coordinate system as a vector
For vector
And
do an outer product operation, i.e.
Thereby to obtain
In that
Projection onto
The inner product of (a) is a negative value, which indicates that the left-handed coordinate system and the virtual coordinate system are mirror images;
determining vertical coordinate Z of D-point base station D Determining the coordinates of the actual base stations A, B, C and D in the virtual coordinate system;
fitting an alpha plane under a virtual coordinate system, wherein the alpha plane is a measuring plane of a space positioning system;
rotating a beta plane of a virtual coordinate system, wherein the beta plane is a horizontal plane of the virtual coordinate system, namely an OXY plane;
the beta plane of the virtual coordinate system is translated such that the measurement plane and the horizontal plane of the virtual coordinate system are parallel.
2. The method as claimed in claim 1, wherein four non-coplanar base stations are installed randomly to satisfy the local area distribution density of the distributed local positioning base stations, and the signal coverage of the four base stations has a common signal area.
3. The method as claimed in claim 1, wherein the distance between two base stations is obtained by measuring and averaging the base stations in the base positioning system.
4. The method of claim 1, wherein the α plane is fitted to the virtual coordinate system, and the unitary normal vector corresponding to the α plane is N.
5. The method of claim 1, wherein the horizontal plane β plane of the virtual coordinate system is rotated to be parallel to the α plane of the measurement plane of the spatial positioning system, which is represented as α = R β, and R is a rotation matrix of the β plane to the α plane.
6. The method of claim 1, wherein the mathematical expression of translation followed by rotation is α = R (β + e) 1 ) The mathematical expression of rotation followed by translation is α = R β + e 2 ，e 1 Representing translation vectors relative to a virtual coordinate system, e 2 Representing a translation vector relative to the virtual coordinate system after rotation.
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