CN112180322A - Method for establishing basic coordinate system of space positioning system - Google Patents
Method for establishing basic coordinate system of space positioning system Download PDFInfo
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- CN112180322A CN112180322A CN202010846313.4A CN202010846313A CN112180322A CN 112180322 A CN112180322 A CN 112180322A CN 202010846313 A CN202010846313 A CN 202010846313A CN 112180322 A CN112180322 A CN 112180322A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
- G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
- G06F16/29—Geographical information databases
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
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: randomly installing at least four non-coplanar base stations A, B, C, D 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 station A, B, C, 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 stationDTaking 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-dimensionThe invention has the advantages of high efficiency, random installation and deployment of the positioning base station and easy realization.
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' applied by yunklin et al (application publication No. CN 106211080a) in 2016, a label 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 automatically calibrate the coordinates of the base station by using the label.
In 2017, a patent of "method for establishing coordinate system between base stations in positioning system" filed by zhao chapter, et al (application publication No. CN 106990389a) proposes that a method for establishing coordinate system by using distance between base stations solves the problem that in the prior art, a coordinate system is established by manually measuring by using measuring instruments such as a total station and a laser range finder, but has the problems that when the coordinate system is established, the positioning system firstly needs to clarify the approximate orientation of each base station, and cannot normally acquire positioning data even when the non-line-of-sight or the orientation is unclear.
In 2018, a patent of UWB system positioning base station calibration method and device applied by tianshiwei et al (application publication No. CN 109218967a) proposes that a real coordinate value of a base station to be calibrated in a current positioning environment is measured by using a manual measurement mode, and a reference coordinate system is further established.
In 2019, patent of UWB base station coordinate automatic calibration method and system based on optimization theory, applied by schl et al (application publication No. CN 110290463a), proposes that a base station and a label are placed at corresponding positions, a minimum UWB system is constructed, optimization processing is performed on residual errors of all theoretical distances and actual measured distances by using optimization theory, and then the system is calibrated.
In practical application, base stations distributed randomly need to be calibrated, and the primary condition of calibration is to establish a spatial coordinate system, in a conventional calibration algorithm, the directions of the base stations need to be set manually, or coordinates need to be designated, in this embodiment, the spatial coordinate system is established by identifying the rule that a beacon moves 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:
randomly installing at least four non-coplanar base stations A, B, C, D 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 station A, B, C, 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 stationDTaking 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 common signal area.
Further, a vector formed by the base station A, C with the base station A as the origin of coordinates
And establishing a Y axis in the plane ABC by taking the X axis as a reference, and establishing a right chiral space coordinate system by pointing the Z axis in the vertical direction of the position of the base station D.
Further, a vector formed by the base station A, B with the base station A as the origin of coordinates
And establishing a Y axis in the plane ABC by taking the X axis as a reference, and establishing a left-handed space coordinate system by pointing the 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 by α ═ R β.
Further, the mathematical expression of translation first and rotation second is α ═ R (β + e)1) The mathematical expression of rotation followed by translation is α ═ R β + e2。
The invention has the following beneficial effects for the prior art:
the invention adopts a left-handed space coordinate system and a right-handed space coordinate system, and simultaneously calculates by the self distance measurement characteristics to obtain the coordinates of four basic base stations, thereby realizing three-dimensional space positioning; 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 complexity of the algorithm is low, and the instantaneity 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 description of the embodiments or the prior art 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 should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within 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 simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular 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, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; 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 the distributed local positioning base stations, at least four non-coplanar base stations A, B, C, D are randomly installed to form a basic positioning system, and the signal coverage areas of the four base stations have a common signal area;
the steps of establishing the left-handed space positioning system are as follows: vector formed by base station A, B with base station A as the origin of coordinates
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, C with base station A as the origin of coordinates
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 station A, B, C, D are A (0,0,0), B (X)B,YB,0)，C(b，0，0)，D(XD，YD，ZD),
Wherein the content of the first and second substances,
s represents the area of the delta ABC,
then
V represents the volume of the triangular pyramid D-ABC
G＝(c2+d2-e2)2
H＝(b2+d2-f2)2
K＝(b2+c2-a2)2
Then:
when d is2-ZD 2-XD 2When the pressure is higher than 0, the pressure is higher,
d2-ZD 2-XD 2when equal to 0, YD＝0。
With the arrangement, the specific coordinate values of the base station in the virtual coordinate system can be obtained through calculation, so that the position of the base station can be determined.
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
Wherein A ', B', C ', D' and A, B, C, D are respectively mapped with each other, and according to the mapping relation, the virtual coordinate system and the corresponding seat of the real base stationThe target system is mirrored or consistent.
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 the point in the left-handed coordinate system is mirrored from the virtual mapping point, the beacon Q moves in space 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 ' 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 at the point O at the initial moment, and the distance from the beacon Q to the A, B, C, D is L respectively through the ranging values in the ranging system of the right chiral coordinate systemA、LB、LC、LDCalculating coordinate Q 'of beacon Q at O by four-point space positioning method, obtaining corresponding coordinates X', Y 'and Z' of beacon Q at X, Y, Z, and expressing the motion locus obtained from virtual coordinate system as vector
According to the right-hand screw rule, vector pair
And
do an 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 distances from the beacon Q to the A, B, C, D four points are respectively L through the ranging values in the left-handed coordinate system ranging systemA、LB、LC、LDCalculating coordinate Q 'of beacon Q at O by four-point space positioning method, obtaining corresponding coordinates X', Y 'and Z' of beacon Q at X, Y, Z, and expressing the motion locus obtained from virtual coordinate system as vector
According to the right-hand screw rule, vector pair
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;
with this arrangement, when the initial calculation indicates that the vertical coordinate of the D base station is a positive value, the right-handed coordinate system is identical to the virtual coordinate system, and when the vertical coordinate of the D base station is a negative value, the left-handed coordinate system is mirrored with the virtual coordinate system, so that the actual coordinate of the base station A, B, C, 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 spatial plane expression is
Ax + By + Cz + D ═ 0, where
A series of coordinate points (x) in the alpha plane measured by the 3D ranging type space positioning systemi,yi,zi),i＝1,Λ,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
The formula (4.2) is brought into the formula (4.1)
Equation (4.3) is a quadratic form about vector (A, B, C), i.e.
Order to
Get f ═ N' PN
For 1, P is a quadratic form f of a real symmetric matrix, when f obtains a minimum value, the value of the vector N is a feature vector corresponding to the minimum feature value 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 this embodiment with reference to the first to the fourth embodiments, the specific steps of rotating the β plane of the virtual coordinate system are as follows:
in the virtual coordinate system, it is assumed that a normal vector M of the β plane is (0,0,1), 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, thereby obtaining an antisymmetric array corresponding to the unit rotation vector K
Rotation angle satisfies
According to the Rodrigues rotation algorithm, the rotation matrix from the beta plane to the alpha plane is
R＝I+K sinθ+(1-cosθ)KK′
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, the rotation relation of 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+e1)
Further optimization, e1Representing a translation vector relative to a virtual coordinate system.
Alternatively, the mathematical expression of rotation followed by translation is
α＝Rβ+e2。
Further optimization, e2A translation vector representing the virtual coordinate system after the rotation; the adjustment method may be translation first and then rotation or rotation first and then translation, 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 (10)
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:
randomly installing at least four non-coplanar base stations A, B, C, D 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 station A, B, C, 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 stationDTaking 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.
2. The method as claimed in claim 1, wherein four non-coplanar base stations are randomly installed to satisfy the distribution density of local areas of the distributed local positioning base stations, and the signal coverage area of the four base stations has a common signal area.
3. The method as claimed in claim 2, wherein the base station A is used as the origin of coordinates and the base station A, C forms a vector
And establishing a Y axis in the plane ABC by taking the X axis as a reference, and establishing a right chiral space coordinate system by pointing the Z axis in the vertical direction of the position of the base station D.
4. The method as claimed in claim 3, wherein the base station A is used as the origin of coordinates and the base station A, B forms a vector
And establishing a Y axis in the plane ABC by taking the X axis as a reference, and establishing a left-handed space coordinate system by pointing the Z axis in the vertical direction of the position of the base station D.
5. The method as claimed in claim 4, wherein the right-handed coordinate system is aligned with the virtual coordinate system.
6. The method as claimed in claim 5, wherein the distance between two base stations is obtained by measuring and averaging the base stations in the base positioning system.
7. The method as claimed in claim 6, wherein the virtual coordinate system is a mirror image of the left-handed coordinate system, and the virtual coordinate system is identical to the right-handed coordinate system.
8. The method of claim 7, wherein the α -plane is fitted to the virtual coordinate system, and the unitary normal vector corresponding to the α -plane is N.
9. The method of claim 8, wherein the coordinate measured in the virtual coordinate system is β, and the coordinate α in the new reference coordinate system is represented as α ═ R β.
10. The method of claim 9, 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 + e2。
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