CN105443112A - Whole-space error compensation method of mining inclinometer - Google Patents

Abstract

The invention discloses a whole-space error compensation method of a mining inclinometer. The method comprises the steps that at least six different measuring points are selected in the whole space, a correction coefficient of an inner pipe error is determined according to collected three-axis acceleration of the measuring points and values of a three-axis magnetic sensor, and a measurement parameter of a drilling hole is calculated again according to the correction coefficient of the inner pipe error finally; a measuring inner pipe is arranged in an installation outer pipe and is rotated by one circle in two mutually perpendicular planes of the installation outer pipe, values of the three-axis magnetic sensor at different angles are collected at the same time, fitting of two planes is conducted on the collected values of the three-axis magnetic sensor at different angles is conducted according to a least square method, two angles of an installation error are determined according to the two planes obtained through fitting, and then calculation is conducted on drilling gestures. By means of the whole-space error compensation method of the mining inclinometer, the problem that due to the fact that for an existing mining inclinometer, a coordinate system formed by the measuring inner pipe and a carrier coordinate system of the installation outer pipe are not orthogonal, the measuring result is poorer is solved, the installation error in the installation process is compensated, and the whole-space drilling inclinometry system error can be compensated rapidly and effectively.

Description

The total space error compensating method of mining inclinometer

Technical field

The invention belongs to inclinometer Error Compensation Technology field, be specifically related to a kind of total space error compensating method of mining inclinometer.

Background technology

Current, China has become coal production and consumption the first big country, and safety of coal mines problem is also more and more subject to country and pays close attention to.The large-area applications of clinograph in coal mine underground construction and gas drainage under suction, greatly improves gas drainage under suction efficiency, reduces mine safety accidents.Mining drilling inclinometer adopts magnetic sensor to measure magnetic field of the earth size to determine bore direction usually, resolves dip angle of hole and tools for angle by built-in 3-axis acceleration sensor simultaneously.But the measurement environment residing for clinograph is severe, comprises the various disturbing magnetic field such as Hard Magnetic and soft magnetism; Sensor all can produce certain error in the process manufactured and install simultaneously, thus affects whole certainty of measurement.Therefore, in order to improve the certainty of measurement of clinograph, error compensation definitely must be carried out to clinograph.

At present, the error compensating method for clinograph is more.2003, Nanjing Aero-Space University Yang Xin was brave, and the people such as Huang Shengguo propose a kind of compensation method based on ellipse hypothesis error model, and method is simple, feasible but only can revise environmental error.2003, Li Xisheng, Wang Jiaxin were at the scaling method of paper " development of high-precision electronic compass " middle least square linear fit, and this method affects very large by data volume, data volume all may cause compensation effect poor too greatly or very little.2003, the people such as naval engineering university Hu Haibin, Lin Chunsheng were to Optimal Parameters in model, and construct the method that object function utilizes the conjugate gradient in mathematical optimization, obtain higher precision, but method is comparatively complicated, data volume is larger.

In sum, although said method obtains compensation effect definitely, due to the particularity that application colliery domain object exists, above-mentioned error compensating method can not be applicable to field, colliery completely.Mining drilling inclinometer is normally made up of pipe in measurement and installation outer tube two parts; Owing to installing, outer tube quality is heavy, volume is large, and timing signal cannot be demarcated together with pipe in measurement.Existing error compensating method adopts pipe in first calibration measurements, be assembled to again in the outer tube be connected with drilling rod and go to measure drilling track, in measuring, the concrete installation situation of pipe and installation outer tube affects by artificial and machining, thus introduces new alignment error, reduces certainty of measurement.

Summary of the invention

In view of this, main purpose of the present invention is the total space error compensating method providing a kind of mining inclinometer.

For achieving the above object, technical scheme of the present invention is achieved in that

The embodiment of the present invention provides a kind of total space error compensating method of mining inclinometer, the method is: in the total space, select the survey mark that at least six different, determine the correction factor of interior pipe error according to the 3-axis acceleration of described survey mark collected and the numerical value of magnetic sensor, finally again resolve the measurement parameter of boring according to the correction factor of interior pipe error; Being assembled to by pipe in measurement installs among outer tube, rotate a circle respectively in two orthogonal planes of installing outer tube, gather the numerical value of the magnetic sensor of different angles simultaneously, according to least square method to the numerical value of the magnetic sensor of collection different angles matching two planes respectively, according to two angles of two plane determination alignment errors that matching obtains, and then boring attitude is resolved.

In such scheme, described pipe in measuring to be circled installing two orthogonal plane internal rotations of outer tube, gather the numerical value of the magnetic sensor of different angles simultaneously, be specially: in described measurement, pipe is positioned at and demarcates on turntable;

Turntable will be demarcated when rotating to tools for angle α=0 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=-15 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=15 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=55 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=-55 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor.

In such scheme, described interior pipe error coefficient comprises zero point error and the sensitivity error of sensor.

In such scheme, described according to least square method numerical value difference matching two planes to the magnetic sensor of collection different angles, be specially: carry out fit Plane respectively according to the numerical value of least square method to the magnetic sensor gathering different angles, the general expression of space plane equation is:

Ax+By+Cz+D＝0；

$z=-\frac{A}{C}x-\frac{B}{C}y-\frac{D}{C};$

Note $a_0=-\frac{A}{C},a_1=-\frac{B}{C},a_2=-\frac{D}{C};$

Then have:

z＝a ₀x+a ₁y+a ₂；

For n the numerical value put of the different angles that magnetic sensor collects, wherein, n>=3, (x _i, y _i, z _i) i=1,2 ... n, according to least square method this n the above-mentioned plane equation of some matching, then will make formula

$S_p=\underset{i=1}{\overset{n}{\Σ}}{(a_0{x}_i+a_1{y}_i+a_2-z_i)}^2$ Value minimum, S be made _pminimum, should meet:

$\frac{\∂S_p}{\∂a_k}=0,k=0,1,2,$

Then have:

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)x _i＝0

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)y _i＝0；

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)＝0

a ₀Σx _i ²+a ₁Σx _iy _i+a ₂Σy _i＝Σy _iz _i

a ₀Σx _iy _i+a ₁Σy _i ²+a ₂Σx _i＝Σz _i

a ₀Σx _i+a ₁Σy _i+a ₂n＝Σz _i

:

$\left(\begin{array}{c}{a}_0\\ a_1\\ a_2\end{array}\right)={\left(\begin{array}{ccc}\Σ{x_i}^2& \Σx_i{y}_i& \Σx_i\\ \Σx_{i}y& \Σ{y_i}^2& \Σy_i\\ \Σx_i& \Σy_i& n\end{array}\right)}^{-1}\left(\begin{array}{c}\Σx_i{z}_i\\ \Σy_i{z}_i\\ \Σz_i\end{array}\right)$

A is solved by above formula ₀, a ₁, a ₂, fit Plane equation can be obtained.

In such scheme, two angles of described two plane determination alignment errors according to matching acquisition, and then boring attitude is resolved, be specially:

When there is not alignment error in pipe in measuring and installation outer tube, due to the angle that magnetic sensor Z axis is in 90 ° with plane all the time, therefore the magnetic-field component of Z-direction remains unchanged, so calculate by the method for averaging the theoretical planes equation that magnetic sensor exports numerical value, that is:

$q=\frac{\underset{i=1}{\overset{n}{\Σ}}{z}_i}{n},(i=1,2...n)$

So calculate fix error angle by fit Plane and theoretical planes, if the normal vector of fit Plane is (b ₁, b ₂, b ₃), the normal vector of theoretical planes is (c ₁, c ₂, c ₃), the angle of two planes can be obtained:

$cos\mathrm{\α}=\frac{\stackrel{\→}{b}\·\stackrel{\→}{c}}{\left|\stackrel{\→}{b}\right|\left|\stackrel{\→}{c}\right|}=\frac{b_1{c}_1+b_2{c}_2+b_3{c}_3}{\sqrt{{b_1}^2+{b_2}^2+{b_3}^2}\·\sqrt{{c_1}^2+{c_2}^2+{c_3}^2}}$

In like manner calculate the angle β of an other plane, therefore, the model of alignment error angle can be write as follows:

$\left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)=\left(\begin{array}{ccc}cos\mathrm{\α}& 0& -sin\mathrm{\α}\\ 0& 1& 0\\ sin\mathrm{\α}& 0& \cos \mathrm{\α}\end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& cos\mathrm{\β}& sin\mathrm{\β}\\ 0& -sin\mathrm{\β}& \cos \mathrm{\β}\end{array}\right)\left(\begin{array}{c}{X}_0\\ Y_0\\ Z_0\end{array}\right)$

In formula, X, Y, Z are respectively magnetic sensor output component, X ₀, Y ₀, Z ₀for magnetic sensor exports original value, according to the angle of the alignment error that two planes of matching acquisition are determined, in conjunction with 3-axis acceleration sensor G _x, G _y, G _zb is exported with magnetic sensor _x, B _y, B _z, and then boring attitude is resolved.

In such scheme, described inclination angle is: $\mathrm{\θ}=-arctan\frac{G_Y}{{({G_X}^2+{G_Z}^2)}^{1/2}}$

Tools for angle:

Azimuth:

Compared with prior art, beneficial effect of the present invention:

The present invention only processes two mutually orthogonal planes on existing clinograph outer tube, efficiently solve existing mining inclinometer and measure the coordinate system of interior pipe formation and the non-orthogonal problem making measurement result poor of installation outer tube carrier coordinate system, namely the interior pipe of quality and small volume has been demarcated, alignment error again in effective compensation installation process, can quick, effective compensation total space drillhole inclination survey systematic error.

Accompanying drawing explanation

Fig. 1 provides a kind of flow chart of total space error compensating method of mining inclinometer for the embodiment of the present invention;

Fig. 2 provides a kind of structural representation of installation outer tube of total space error compensating method of mining inclinometer for the embodiment of the present invention.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

The embodiment of the present invention provides a kind of total space error compensating method of mining inclinometer, as shown in Figure 1, the method is: in the total space, select the survey mark that at least six different, determine the correction factor of interior pipe error according to the 3-axis acceleration of described survey mark collected and the numerical value of magnetic sensor, finally again resolve the measurement parameter of boring according to the correction factor of interior pipe error; Being assembled to by pipe in measurement installs among outer tube, rotate a circle respectively in two orthogonal planes of installing outer tube, as shown in Figure 2, gather the numerical value of the magnetic sensor of different angles simultaneously, carry out fit Plane respectively according to the numerical value of least square method to the magnetic sensor gathering different angles, the general expression of space plane equation is:

Ax+By+Cz+D＝0；

$z=-\frac{A}{C}x-\frac{B}{C}y-\frac{D}{C};$

Note $a_0=-\frac{A}{C},a_1=-\frac{B}{C},a_2=-\frac{D}{C};$

Then have:

z＝a ₀x+a ₁y+a ₂；

The numerical value of n point (n>=3) of the different angles that magnetic sensor is collected, (x _i, y _i, z _i) i=1,2 ... n, according to least square method this n the above-mentioned plane equation of some matching, then will make formula $S_p=\underset{i=1}{\overset{n}{\Σ}}{(a_0{x}_i+a_1{y}_i+a_2-z_i)}^2$ Value minimum, S be made _pminimum, should meet:

$\frac{\∂S_p}{\∂a_k}=0,k=0,1,2,$

Then have:

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)x _i＝0

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)y _i＝0；

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)＝0

a ₀Σx _i ²+a ₁Σx _iy _i+a ₂Σy _i＝Σy _iz _i

a ₀Σx _iy _i+a ₁Σy _i ²+a ₂Σx _i＝Σz _i

a ₀Σx _i+a ₁Σy _i+a ₂n＝Σz _i

:

$\left(\begin{array}{c}{a}_0\\ a_1\\ a_2\end{array}\right)={\left(\begin{array}{ccc}\Σ{x_i}^2& \Σx_i{y}_i& \Σx_i\\ \Σx_{i}y& \Σ{y_i}^2& \Σy_i\\ \Σx_i& \Σy_i& n\end{array}\right)}^{-1}\left(\begin{array}{c}\Σx_i{z}_i\\ \Σy_i{z}_i\\ \Σz_i\end{array}\right)$

A is solved by above formula ₀, a ₁, a ₂, fit Plane equation can be obtained.

When there is not alignment error in pipe in measuring and installation outer tube, due to the angle that magnetic sensor Z axis is in 90 ° with plane all the time, therefore the magnetic-field component of Z-direction remains unchanged, so we can calculate the theoretical planes equation that magnetic sensor exports numerical value by the method for averaging, that is:

$q=\frac{\underset{i=1}{\overset{n}{\Σ}}{z}_i}{n},(i=1,2...n)$

So can fix error angle be calculated by fit Plane and theoretical planes.If the normal vector of fit Plane is (b ₁, b ₂, b ₃), the normal vector of theoretical planes is (c ₁, c ₂, c ₃), the angle of two planes can be obtained:

$cos\mathrm{\α}=\frac{\stackrel{\→}{b}\·\stackrel{\→}{c}}{\left|\stackrel{\→}{b}\right|\left|\stackrel{\→}{c}\right|}=\frac{b_1{c}_1+b_2{c}_2+b_3{c}_3}{\sqrt{{b_1}^2+{b_2}^2+{b_3}^2}\·\sqrt{{c_1}^2+{c_2}^2+{c_3}^2}}$

In like manner can calculate the angle β of an other plane, therefore, the model of alignment error angle can be write as follows:

$\left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)=\left(\begin{array}{ccc}cos\mathrm{\α}& 0& -sin\mathrm{\α}\\ 0& 1& 0\\ sin\mathrm{\α}& 0& \cos \mathrm{\α}\end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& cos\mathrm{\β}& sin\mathrm{\β}\\ 0& -sin\mathrm{\β}& \cos \mathrm{\β}\end{array}\right)\left(\begin{array}{c}{X}_0\\ Y_0\\ Z_0\end{array}\right)$

In formula, X, Y, Z are respectively magnetic sensor output component, X ₀, Y ₀, Z ₀for magnetic sensor exports original value.According to the angle of the alignment error that two planes of matching acquisition are determined, in conjunction with 3-axis acceleration sensor G _x, G _y, G _zb is exported with magnetic sensor _x, B _y, B _z, and then boring attitude is resolved.

The inclination angle that can obtain calculating is:

$\mathrm{\θ}=-arctan\frac{G_Y}{{({G_X}^2+{G_Z}^2)}^{1/2}}$

Tools for angle:

Azimuth:

Described by measure in pipe install outer tube two orthogonal planes in rotate a circle respectively, gather the numerical value of the magnetic sensor of different angles simultaneously, be specially: in described measurement, pipe is positioned at and demarcates on turntable, with spirit bubble, on turntable, leveling is carried out to inclinometer, allow magnetic sensor X, Y-axis maintenance level, Z axis, perpendicular to ground, connects RS485 communication interface, opening power;

Turntable will be demarcated when rotating to tools for angle α=0 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=-15 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=15 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=55 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=-55 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor.

Described interior pipe error coefficient comprises zero point error and the sensitivity error of sensor.

The above, be only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.

Claims (6)

1. the total space error compensating method of a mining inclinometer, it is characterized in that, the method is: in the total space, select the survey mark that at least six different, determine the correction factor of interior pipe error according to the 3-axis acceleration of described survey mark collected and the numerical value of magnetic sensor, finally again resolve the measurement parameter of boring according to the correction factor of interior pipe error; Being assembled to by pipe in measurement installs among outer tube, rotate a circle respectively in two orthogonal planes of installing outer tube, gather the numerical value of the magnetic sensor of different angles simultaneously, according to least square method to the numerical value of the magnetic sensor of collection different angles matching two planes respectively, according to two angles of two plane determination alignment errors that matching obtains, and then boring attitude is resolved.

2. the total space error compensating method of mining inclinometer according to claim 1, it is characterized in that: described pipe in measuring to be circled installing two orthogonal plane internal rotations of outer tube, gather the numerical value of the magnetic sensor of different angles simultaneously, be specially: in described measurement, pipe is positioned at and demarcates on turntable;

Turntable will be demarcated when rotating to tools for angle α=0 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=-15 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=15 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=55 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor;

Turntable will be demarcated when rotating to tools for angle α=-55 °, rotate successively angle of inclination beta=15 °, 55 ° ,-15 ° ,-55 °, azimuth rotate successively γ=0 °, 90 °, 180 °, 270 °, measure the numerical value of magnetic sensor.

3. the total space error compensating method of mining inclinometer according to claim 1 and 2, is characterized in that: described interior pipe error coefficient comprises zero point error and the sensitivity error of sensor.

4. the total space error compensating method of mining inclinometer according to claim 3, it is characterized in that, described according to least square method numerical value difference matching two planes to the magnetic sensor of collection different angles, be specially: carry out fit Plane respectively according to the numerical value of least square method to the magnetic sensor gathering different angles, the general expression of space plane equation is:

Ax+By+Cz+D＝0；

$z=-\frac{A}{C}x-\frac{B}{C}y-\frac{D}{C};$

Note $a_0=-\frac{A}{C},a_1=-\frac{B}{C},a_2=-\frac{D}{C};$

Then have:

z＝a ₀x+a ₁y+a ₂；

For n the numerical value put of the different angles that magnetic sensor collects, wherein, n>=3, (x _i, y _i, z _i) i=1,2 ... n, according to least square method this n the above-mentioned plane equation of some matching, then will make formula value minimum, S be made _pminimum, should meet:

$\frac{\∂S_p}{\∂a_k}=0,k=0,1,2,$

Then have:

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)x _i＝0

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)y _i＝0；

Σ2(a ₀x _i+a ₁y _i+a ₂-z _i)＝0

a ₀Σx _i ²+a ₁Σx _iy _i+a ₂Σy _i＝Σy _iz _i

a ₀Σx _iy _i+a ₁Σy _i ²+a ₂Σx _i＝Σz _i

a ₀Σx _i+a ₁Σy _i+a ₂n＝Σz _i

:

$\left(\begin{array}{c}{a}_0\\ a_1\\ a_2\end{array}\right)={\left(\begin{array}{ccc}{{\mathrm{\Σx}}_i}^2& {\mathrm{\Σx}}_i{y}_i& {\mathrm{\Σx}}_i\\ {\mathrm{\Σx}}_{i}y& {{\mathrm{\Σy}}_i}^2& {\mathrm{\Σy}}_i\\ {\mathrm{\Σx}}_i& {\mathrm{\Σy}}_i& n\end{array}\right)}^{-1}\left(\begin{array}{c}{\mathrm{\Σx}}_i{z}_i\\ {\mathrm{\Σy}}_i{z}_i\\ {\mathrm{\Σz}}_i\end{array}\right)$

A is solved by above formula ₀, a ₁, a ₂, fit Plane equation can be obtained.

5. the total space error compensating method of mining inclinometer according to claim 4, is characterized in that, two angles of described two plane determination alignment errors according to matching acquisition, and then resolves boring attitude, is specially:

When there is not alignment error in pipe in measuring and installation outer tube, due to the angle that magnetic sensor Z axis is in 90 ° with plane all the time, therefore the magnetic-field component of Z-direction remains unchanged, so calculate by the method for averaging the theoretical planes equation that magnetic sensor exports numerical value, that is:

$q=\frac{\underset{i=1}{\overset{n}{\Σ}}{z}_i}{n},(i=1,2...n)$

So calculate fix error angle by fit Plane and theoretical planes, if the normal vector of fit Plane is (b ₁, b ₂, b ₃), the normal vector of theoretical planes is (c ₁, c ₂, c ₃), the angle of two planes can be obtained:

$cos\mathrm{\α}=\frac{\stackrel{\→}{b}\·\stackrel{\→}{c}}{\left|\stackrel{\→}{b}\right|\left|\stackrel{\→}{c}\right|}=\frac{b_1{c}_1+b_2{c}_2+b_3{c}_3}{\sqrt{{b_1}^2+{b_2}^2+{b_3}^2}\·\sqrt{{c_1}^2+{c_2}^2+{c_3}^2}}$

In like manner calculate the angle β of an other plane, therefore, the model of alignment error angle can be write as follows:

$\left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)=\left(\begin{array}{ccc}cos\mathrm{\α}& 0& -sin\mathrm{\α}\\ 0& 1& 0\\ sin\mathrm{\α}& 0& \cos \mathrm{\α}\end{array}\right)\left(\begin{array}{ccc}1& 0& 0\\ 0& cos\mathrm{\β}& sin\mathrm{\β}\\ 0& -sin\mathrm{\β}& \cos \mathrm{\β}\end{array}\right)\left(\begin{array}{c}{X}_0\\ Y_0\\ Z_0\end{array}\right)$

In formula, X, Y, Z are respectively magnetic sensor output component, X ₀, Y ₀, Z ₀for magnetic sensor exports original value, according to the angle of the alignment error that two planes of matching acquisition are determined, in conjunction with 3-axis acceleration sensor G _x, G _y, G _zb is exported with magnetic sensor _x, B _y, B _z, and then boring attitude is resolved.

6. the total space error compensating method of mining inclinometer according to claim 5, is characterized in that,

Described inclination angle is: $\mathrm{\θ}=-arctan\frac{G_Y}{{({G_X}^2+{G_Z}^2)}^{1/2}}$

Tools for angle:

Azimuth: