CN102221371B - Method for high precision compensation of photoelectric theodolite vertical angle - Google Patents

Abstract

The invention relates to a method for high precision compensation of vertical angles of electronic total stations and electronic theodolites with angle compensation. A mathematical model for high precision compensation of vertical angles is provided; electronic levelers are disposed respectively in directions parallel to a transverse axis and a collimation axis of a theodolite; an inclined angle of a vertical axis of the theodolite is characterized by inclined angles in directions of the transverse axis and the collimation axis of the theodolite; the inclined angles in directions of the transverse axis and the collimation axis are the measured output of the electronic levelers in corresponding directions, and are used as matrix elements to establish an initial matrix when the vertical axis of the theodolite is inclined; the rotation process during the angle measurement of the theodolite is represented by a corresponding matrix; and finally a real measuring model value of the theodolite vertical angle is obtained in the presence of vertical axis inclination errors. Compared with the prior art, the invention has the advantage that a precise mathematical model established by coordinate transformation is provided, and the new model is used in the high precision measurement of theodolite vertical angles; therefore the compensation precision is higher, and the error compensation scope is larger; and the method is easy to carry out.

Description

A kind of method for high precision compensation of photoelectric theodolite vertical angle

Technical field

The invention belongs to the electrical type mapping instrument technology field, relate to the vertical angle high-accuracy compensation method of the instrument of surveying and mappings such as a kind of electronic total station that is applied to angle compensation, electronic theodolite.

Background technology

For instrument of surveying and mappings such as electronic theodolites, carry out accurate measurement of angle, its prerequisite is transverse axis, vertical pivot and the collimation axis three axle pairwise orthogonals of transit, and transverse axis level, vertical pivot vertical.Wherein, the orthogonality of three between centers of transit is the structural requirement of instrument itself, is instrument one of qualified parameter index whether when dispatching from the factory.Transverse axis level and vertical pivot vertical then are to be guaranteed by operating personnel in the use procedure of instrument, by adjusting the level of placing with transverse axis on the transit, make the level bubble all placed in the middle on the both direction of quadrature, guarantee the vertical pivot vertical (transverse axis level) of transit with this.Yet, be subjected to the objective environment condition influence, be difficult to make the level bubble fully placed in the middle simultaneously on the both direction of quadrature, in actual mechanical process, just bubble is adjusted within the error allowed band, but not accurately leveling.At this moment, therefore the actual heeling condition that is in of the vertical pivot of transit, can produce certain error to the angle measurement result, in order to obtain high-precision vertical angle measured value, just need to compensate Vertical Axis Tilt Error.

Current, the Vertical Axis Tilt Error compensation model that domestic and international high-precision electronic transit and total powerstation adopt is derived based on the spherical trigonometry principle mostly, supposed that in derivation the vertical pivot angle of inclination is very little, and having carried out a large amount of mathematical approaches processes, coupled problem when having ignored different errors and existing simultaneously, therefore, existing error compensating method can only be to the approximate compensation of Vertical Axis Tilt Error, can not reflect accurately the impact that vertical pivot tilts actual angle is measured, and be only suitable for the less situation of Vertical Axis Tilt Error, situation when larger for Vertical Axis Tilt Error, and inapplicable.

In addition, only the measurement impact on horizontal angle compensates for Vertical Axis Tilt Error usually for the outer high-precision electronic transit of Present Domestic and total powerstation, and the measurement of vertical angle is seldom compensated.Along with the progress of technology, and people are more and more higher to the requirement of vertical angle measuring accuracy, and the vertical angle measuring error of being brought by Vertical Axis Tilt Error is also needed badly and is compensated.Therefore, need a kind of new Vertical Axis Tilt Error compensation method of research.

Summary of the invention

For above-mentioned prior art situation, the object of the invention is to, a kind of method that can carry out high-accuracy compensation in a big way on Vertical Axis Tilt Error on the impact of vertical direction angle measurement value is proposed.

From existing to carry out the thinking of measurement of azimuth based on coordinate transform different, basic conception of the present invention is to compensate for the measuring error to vertical angle of being brought by Vertical Axis Tilt Error, and a kind of vertical angle high-accuracy compensation mathematical model is provided.Settle respectively two electronic levels being parallel to transit transverse axis and collimation axis direction, the vertical pivot angle of inclination of transit is characterized with transit X direction and the axial pitch angle of collimation, the axial pitch angle of described X direction pitch angle and collimation is the measurement output of electronic level on the respective direction, initial matrix when setting up the inclination of transit vertical pivot with the pitch angle of this both direction as matrix element, with the rotary course of transit angle measurement with corresponding matrix representation, when having obtained at last Vertical Axis Tilt Error and having existed, the true measurement mode offset of transit vertical angle.Its concrete steps are as follows:

Step 1: under transit three axles state perpendicular to each other, with transverse axis, collimation axis and the vertical pivot of transit be respectively X, Y, Z axis is set up the quadrature rectangular coordinate system;

Step 2: in the actual measurement process, when the run-off the straight of transit vertical pivot, the angle of inclination that forms in transit transverse axis and collimation axis direction is respectively v _x, v _y(as shown in Figure 1).Described transverse axis angle of inclination v _xAnd collimation axis angle of inclination v _yRefer to a kind of angle that can measure in real time by the electronic level settled on the respective direction.At this moment, the initial transformation matrix that is produced by the inclination of transit vertical pivot is:

$C_1=\left(\begin{array}{ccc}{\cos v}_x& 0& -{\sin v}_x\\ 0& {\cos v}_y& {\sin v}_y\\ {\sin v}_x{\cos v}_y& {-\cos v}_x\sin v_y& {\cos v}_x{\cos v}_y\end{array}\right)$

Step 3: when transit was observed target, if the measured value of horizontal angle is α, the measured value of vertical angle was β, and then rotation matrix is respectively:

$C_2=\left(\begin{array}{ccc}\cos \mathrm{\α}& \sin \mathrm{\α}& 0\\ -\sin \mathrm{\α}& \cos \mathrm{\α}& 0\\ 0& 0& 1\end{array}\right)$

$C_3=\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\β}& \sin \mathrm{\β}\\ 0& -\sin \mathrm{\β}& \cos \mathrm{\β}\end{array}\right)$

Step 4: total rotation matrix is:

$C=C_2^3{C}_1^2{C}_v$

$=\left(\begin{array}{ccc}\cos \mathrm{\α}\cos v_x& \sin \mathrm{\α}\cos v_y& -\cos \mathrm{\α}{\sin v}_x+\sin \mathrm{\α}{\sin v}_y\\ -\sin \mathrm{\α}\cos \mathrm{\β}{\cos v}_x+\sin \mathrm{\β}\sin v_x\cos v_y& \cos \mathrm{\α}\cos \mathrm{\β}\cos v_y-\sin {\mathrm{\β}\cos v}_x\sin v_y& \sin \mathrm{\α}\cos \mathrm{\β}\sin v_x+\cos \mathrm{\α}\cos \mathrm{\β}\sin v_y+\sin \mathrm{\β}\cos v_x\cos v_y\\ \sin \mathrm{\α}\sin \mathrm{\β}\cos v_x+\cos {\mathrm{\β}\sin v}_x{\cos v}_y& -\cos \mathrm{\α}\sin \mathrm{\β}\cos v_y-\cos \mathrm{\β}\cos v_x\sin v_y& -\sin \mathrm{\α}\sin \mathrm{\β}\sin v_x-\cos \mathrm{\α}\sin \mathrm{\β}\sin v_y+\cos \mathrm{\β}{\cos v}_x\cos v_y\end{array}\right)$

Step 5: when obtaining having Vertical Axis Tilt Error according to step 4, after the vertical angle compensation that transit turns over, just can obtain actual value α _rFor:

${\mathrm{\α}}_r=\arctan \left(\frac{\sin \mathrm{\α}\cos \mathrm{\β}\sin v_x+\cos \mathrm{\α}\cos \mathrm{\β}\sin v_y+\sin \mathrm{\β}\cos v_x{\cos v}_y}{\sqrt{{(-\sin \mathrm{\α}\cos \mathrm{\β}\cos v_x+\sin \mathrm{\β}\sin v_x\cos v_y)}^2+{(\cos \mathrm{\α}\cos \mathrm{\β}\cos v_y-\sin \mathrm{\β}\cos v_x\sin v_y)}^2}}\right)$

(1)

The superiority that the present invention compares with prior art is, because what prior art adopted is a kind of model of approximate processing, and the vertical pivot pitch angle is difficult for measuring, compensation method is difficult for implementing, proposed by the invention is a kind of accurate mathematical model of setting up by coordinate transform, and new model is applied in the high-acruracy survey of transit vertical angle, so compensation precision is higher, the error compensation scope is larger, and easy to implement.

Description of drawings

Fig. 1 is the coordinate system synoptic diagram that makes up with transit three axles

Wherein: X-axis-transit transverse axis; Y-axis-transit collimation axis; Z axis-transit vertical pivot; V-vertical pivot pitch angle;

X ₁Axle-transverse axis points to when existing vertical pivot to tilt; Y ₁Axle-collimation axis points to when existing vertical pivot to tilt;

Z ₁Axle-vertical pivot points to when existing vertical pivot to tilt; v _xTransverse axis departed from the angle of horizontal direction when-vertical pivot tilted;

v _yCollimation axis departed from the angle of horizontal direction when-vertical pivot tilted.

Fig. 2 is Vertical Axis Tilt Error compensation principle block diagram

Embodiment

Now by reference to the accompanying drawings the present invention is further described:

Referring to Fig. 1: be three axles of electronic total station, electronic theodolite shown in the figure, wherein: X-axis-transit transverse axis; Y-axis-transit collimation axis; Z axis-transit vertical pivot; V-vertical pivot pitch angle; X ₁Axle-transverse axis points to when existing vertical pivot to tilt; Y ₁Axle-collimation axis points to when existing vertical pivot to tilt; Z ₁Axle-vertical pivot points to when existing vertical pivot to tilt; v _xTransverse axis departed from the angle of horizontal direction when-vertical pivot tilted; v _yCollimation axis departed from the angle of horizontal direction when-vertical pivot tilted.The inventive method, settle respectively two electronic levels being parallel to transit transverse axis and collimation axis direction, the vertical pivot angle of inclination of transit is characterized with transit X direction and the axial pitch angle of collimation, the axial pitch angle of described X direction pitch angle and collimation is the measurement output of electronic level on the respective direction, the initial matrix C when setting up the inclination of transit vertical pivot with the pitch angle of this both direction as matrix element ₁, take collimation axis as measuring axle, in the measuring process, at first rotate around vertical pivot, obtain a rotation matrix C ₂, again take transverse axis as turning axle, obtain rotation matrix C ₃, like this, namely get rotation matrix C always, the mathematical model of setting up according to the present invention (1), in the time of just can obtaining having Vertical Axis Tilt Error, actual value α after the vertical angle compensation that transit turns over _r

Referring to Fig. 2: show Vertical Axis Tilt Error compensation principle block diagram.In specific implementation process, can be by settling respectively two electronic levels being parallel to transit transverse axis and collimation axis direction, when having obtained vertical pivot and having tilted, transit transverse axis pitch angle v _xWith collimation axis pitch angle v _y, and with v _xAnd v _yBe input in the Vertical Axis Tilt Error compensating module, described Vertical Axis Tilt Error compensating module, a kind of general single chip that after programming, is solidified with Vertical Axis Tilt Error model of the present invention, X direction electronic level output v when the angle information β of the vertical circle output of the angle information α of horizontal dial output, transit and the vertical pivot that measures tilt _xWith collimation axis direction electronic level output v _yBe input to respectively the different input ports of single-chip microcomputer, through the mathematics manipulation of Vertical Axis Tilt Error compensating module, the accurate angle information after being compensated is by the actual value α of the output port of single-chip microcomputer output vertical angle _R.。

Claims (1)

1. method for high precision compensation of photoelectric theodolite vertical angle, it is characterized in that: compensate for the measuring error to vertical angle of being brought by Vertical Axis Tilt Error, settle respectively two electronic levels being parallel to transit transverse axis and collimation axis direction, the vertical pivot angle of inclination of transit is characterized with transit X direction and the axial pitch angle of collimation, initial matrix when setting up the inclination of transit vertical pivot with the pitch angle of this both direction as matrix element, with the rotary course of transit angle measurement with corresponding matrix representation, when having obtained at last Vertical Axis Tilt Error and having existed, the true measurement model of transit vertical angle, concrete steps are as follows:

Step 1: under transit three axles state perpendicular to each other, with transverse axis, collimation axis and the vertical pivot of transit be respectively X, Y, Z axis is set up the quadrature rectangular coordinate system;

Step 2: in the actual measurement process, when the run-off the straight of transit vertical pivot, the angle of inclination that forms in transit transverse axis and collimation axis direction is respectively v _x, v _yDescribed transverse axis angle of inclination v _xAnd collimation axis angle of inclination v _yRefer to a kind of angle that can measure in real time by the electronic level settled on the respective direction; At this moment, the initial transformation matrix that is produced by the inclination of transit vertical pivot is:

$C_1=\left(\begin{array}{ccc}\cos v_x& 0& -\sin v_x\\ 0& \cos v_y& \sin v_y\\ \sin v_x\cos v_y& -\cos v_x\sin v_y& \cos v_x\cos v_y\end{array}\right)$

Step 3: when transit was observed target, if the measured value of horizontal angle is α, the measured value of vertical angle was β, and then rotation matrix is respectively:

$C_2=\left(\begin{array}{ccc}\cos \mathrm{\α}& \sin \mathrm{\α}& 0\\ -\sin \mathrm{\α}& \cos \mathrm{\α}& 0\\ 0& 0& 1\end{array}\right)$

$C_3=\left(\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\β}& \sin \mathrm{\β}\\ 0& -\sin \mathrm{\β}& \cos \mathrm{\β}\end{array}\right)$

Step 4: total rotation matrix is:

$C=C_2^3{C}_1^2{C}_3$

$=\left(\begin{array}{ccc}\cos \mathrm{\α}\cos v_x& \sin \mathrm{\α}\cos v_y& -\cos \mathrm{\α}\sin v_x+\sin \mathrm{\α}\sin v_y\\ -\sin \mathrm{\α}\cos \mathrm{\β}\cos v_x+\sin \mathrm{\β}\sin v_x\cos v_y& \cos \mathrm{\α}\cos \mathrm{\β}\cos v_y-\sin \mathrm{\β}\cos v_x\sin v_y& \sin \mathrm{\α}\cos \mathrm{\β}\sin v_x+\cos \mathrm{\α}\cos \mathrm{\β}\sin v_y+\sin \mathrm{\β}\cos v_x\cos v_y\\ \sin \mathrm{\α}\sin \mathrm{\β}\cos v_x+\cos \mathrm{\β}\sin v_x\cos v_y& -\cos \mathrm{\α}\sin \mathrm{\β}\cos v_y-\cos \mathrm{\β}\cos v_x\sin v_y& -\sin \mathrm{\α}\sin \mathrm{\β}\sin v_x-\cos \mathrm{\α}\sin \mathrm{\β}\sin v_y+\cos \mathrm{\β}\cos v_x\cos v_y\end{array}\right)$

Step 5: obtain according to step 4

$a_r=\arctan \left(\frac{\sin \mathrm{\α}\cos \mathrm{\β}\sin v_x+\cos \mathrm{\α}\cos \mathrm{\β}\sin v_y+\sin \mathrm{\β}\cos v_x\cos v_y}{\sqrt{{(-\sin \mathrm{\α}\cos \mathrm{\β}\cos v_x+\sin \mathrm{\β}\sin v_x\cos v_y)}^2+{(\cos \mathrm{\α}\cos \mathrm{\β}\cos v_y-\sin \mathrm{\β}\cos v_x\sin v_y)}^2}}\right)$

α _rActual value after the vertical angle compensation that transit turns over when having Vertical Axis Tilt Error.

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