CN102278108A - Calibration method for continuous measurement mode of small-bore directional gyro inclinometer - Google Patents

Abstract

The invention provides a calibration method for a continuous measurement mode of a small-bore directional gyro inclinometer. The method provided by the invention comprises the following steps: 1) establishing tabled input and output relation mathematical model; 2) establishing a gyro input and output relation mathematical model; 3) calibrating the inclinometer by adopting a three-axle table through a velocity test and a six-position test; and 4) processing 36 groups of velocity data and 6 groups of position data measured in the step 3) through a computer assisted program by utilizing the mathematical models in the steps 1) and 2), and computing and outputting the gyro scale factors, installation errors and static drifting coefficients of the inclinometer. In the calibration method provided by the invention, the gyro inclinometer can be rapidly and effectively calibrated; the evaluation of the models is accurate and effective; the operation is simple; the calibration of all parameters can be completed in a short time; and the reliability is high.

Description

Small-bore directional gyro inclinometer continuous measurement pattern scaling method

Technical field

The present invention relates to the scaling method of drilling well, belong to the Electromechanical Control technical field with the continuous measurement gyrolevel.

Background technology

Directed drilling is one of great technology of oil and gas development, and some developed countries are applied abroad.The deviational survey direction finder that directed drilling is used has various magnetic instrument and frame gyroscope instrument.These two kinds of general measure technology have obtained certain effect through many decades with improvement, but small-bore drilling measuring is not met the demands.Especially still the magnetic instrument (as fluxgate) of use is owing to originally experience geology and the influence of ferromagnetic material environment on every side in a large number in China, and certainty of measurement is very low, even can not use, not only precision is low for general frame gyroscope instrument, and diameter is big, and the aligning before and after using is calibrated also quite loaded down with trivial details.And drilling well to demarcate with the continuous measurement gyrolevel be to guarantee its key of project.In the prior art, drilling well is not temporarily had the scaling method of moulding with the demarcation of inclinometer, demarcate by rule of thumb usually and exist time-consuming and the degree of accuracy such as is difficult to determine at problem.

Summary of the invention

At the prior art above shortcomings, the purpose of this invention is to provide a kind of energy method efficient, quick and that accurately probing is demarcated with small-bore directional gyro inclinometer.

Realize above-mentioned purpose, the technological means that the present invention adopts is: a kind of small-bore directional gyro inclinometer continuous measurement pattern scaling method, and adopt three-axle table to carry out static demarcating by six position tests, comprise the steps:

1) foundation adds the static input/output relation Mathematical Modeling of table:

With three quartz accelerometers of small-bore directional gyro inclinometer, establish ox at probing _by _bz _bFor inertia combination matrix coordinate system, parallel with carrier coordinate system; It is as follows to set up quartz accelerometer input/output relation Mathematical Modeling:

$\left\{\begin{array}{c}{F}_x=k_x(a_{x0}+a_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{a}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{a}_{\mathrm{zb}}+k_{2x}{a}_{\mathrm{xb}}^2)\\ F_y=k_y(a_{y0}+a_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{a}_{\mathrm{zb}}+k_{2y}{a}_{\mathrm{yb}}^2)\\ F_z=k_z(a_{z0}+a_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{a}_{\mathrm{yb}}+k_{2z}{a}_{\mathrm{zb}}^2)\end{array}\right.---(1-1)$

In the formula, F _x, F _y, F _zBe x _b, y _b, z _bThe table that adds of axle is exported a _Xb, a _Yb, a _ZbFor along three axial acceleration of IMU coordinate system.k _x, k _y, k _zBe x _b, y _b, z _bAxle adds the constant multiplier of table, a _X0, a _Y0, a _Z0Be x _b, y _b, z _bAxle adds the biasing of table, k _2x, k _2y, k _2zBe x _b, y _b, z _bAxle adds the second order nonlinear coefficient (its value is in a small amount) of table, α _Xy, α _Xz, α _Yx, α _Yz, α _Zx, α _ZyFor adding table alignment error (its value is in a small amount);

At the table that adds on the gyrolevel in the present project, ignore a small amount of influence in the following formula, set up following simplified model:

$\left\{\begin{array}{c}\frac{N_x^{+}-N_x^{-}}{\mathrm{\ΔT}}=k_x(a_{x0}+a_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{a}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{a}_{\mathrm{zb}})\\ \frac{N_y^{+}-N_y^{-}}{\mathrm{\ΔT}}=k_y(a_{y0}+a_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{a}_{\mathrm{zb}})\\ \frac{N_z^{+}-N_z^{-}}{\mathrm{\ΔT}}=k_z(a_{z0}+a_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{a}_{\mathrm{yb}})\end{array}\right.---(1-2)$

In the formula,

Be respectively x, y, z axle and add the umber of pulse of table two-way output in sampling period Δ T, all the other symbol implications are the same;

The constant multiplier, biasing, the alignment error that respectively add table are demarcated by the multiposition test;

2) set up the static input/output relation Mathematical Modeling of gyro:

At the three spool flexible gyroscopes of probing, establish ox with small-bore directional gyro inclinometer _by _bz _bBe inertia combination matrix coordinate system, parallel with carrier coordinate system, gyro input/output relation Mathematical Modeling is as follows:

$\left\{\begin{array}{c}{u}_x=k_{\mathrm{gx}}({\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\ϵ}}_x)\\ u_y=k_{\mathrm{gy}}({\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\ϵ}}_y)\\ u_z=k_{\mathrm{gz}}({\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\ϵ}}_z)\end{array}\right.---(2-1)$

In the formula, u _x, u _y, u _zBe IMU coordinate system x _b, y _b, z _bThe voltage output of axle gyro, k _Gx, k _Gy, k _GzBe the constant multiplier of each gyro, α _Xy, α _Xz, α _Yx, α _Yz, α _Zx, α _ZyBe gyro misalignment, its value is in a small amount, but considers that Gyro Precision does not add the height of table, so several coefficients can not be ignored ω _Xb, ω _Yb, ω _ZbFor along IMU coordinate system x _b, y _b, z _bInput angle speed, ε _x, ε _y, ε _zBe each Gyro Static Drift, they are:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_x=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ {\mathrm{\ϵ}}_y=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ {\mathrm{\ϵ}}_z=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.---(2-2)$

In the formula, g _Xb, g _Yb, g _ZbBe the component of gravity acceleration g on three axles of IMU coordinate system;

3) speed trial

Before the test, rate table rotating shaft and one of parallel mounting means of ground vertical line are installed on the speed platform by shown in the table 1 strap down inertial navigation combination, and make by demarcation and spool overlap with speed platform axle; Make speed platform axle with wherein a certain angular speed constant speed rotation by pre-designed rate test point; Turn over opening entry gyroscope output on a certain reference angle position at rate table, and record gyroscope output on some adjacent equal angles symmetric points in a week, a week changeed up to rate table; Then, make backing propeller test, note these data equally with this angular speed;

The mounting means of IMU on the speed platform in the table 1.a speed trial

In the table, OXYZ is a speed platform stage body coordinate system, ox _by _bz _bBe the IMU coordinate system, ω is a turntable speed over the ground, ω _eBe the earth rotation angular speed, φ is local geographic latitude;

Constant multiplier and the alignment error of utilizing the experimental data of gained can demarcate three gyros of IMU;

A) constant multiplier and alignment error are calculated:

Least square fitting is carried out in gyrostatic output when the rejecting turntable is static the gyro output data during from each speed trial then.Directly be given in the speed trial data below, the average equation of each the gyro output valve that is drawn by formula (2-1), (2-2) sees Table 2.Equation is used in the hope of each gyro constant multiplier and alignment error in the table.

Table 2

In the table, ω _Xb=ω (being exactly turntable religion speed angle), ω _Yb=ω+ω _N(component of the religion speed angle speed and the earth), ω _Zb=ω+ω _u(component of the religion speed angle speed and the earth).

Axle is during (j=x, y, z) speed trial, at the trial between in the average of i axle (i=x, y, z) gyro output valve.

Below with x _bThe axle speed trial is an example, introduces the method for being calculated Gyro Calibration factor and alignment error by equation in the table 2.

B) constant multiplier calculates

To x _bX axle gyro is considered in the test of axle n subrate, can get following measured equation by table 2:

$\left[\begin{array}{c}\stackrel{\‾}{u_{\mathrm{xx}}}\left(1\right)\\ .\\ .\\ .\\ \stackrel{\‾}{u_{\mathrm{xx}}}\left(n\right)\end{array}\right]=\left[\begin{array}{cc}1& {\mathrm{\ω}}_{\mathrm{xb}}\left(1\right)\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\ω}}_{\mathrm{xb}}\left(n\right)\end{array}\right]+\left[\begin{array}{c}+a_0{k}_{\mathrm{gx}}\\ k_{\mathrm{gx}}\end{array}\right]+\left[\begin{array}{c}v\left(1\right)\\ .\\ .\\ .\\ v\left(n\right)\end{array}\right]$

Following formula can be expressed as follows:

y＝Xb+v

In the formula, v is test random error vector,

$y=\left[\begin{array}{c}\stackrel{\‾}{u_{\mathrm{xx}}}\left(1\right)\\ .\\ .\\ .\\ \stackrel{\‾}{u_{\mathrm{xx}}}\left(n\right)\end{array}\right],$ $X=\left[\begin{array}{cc}1& {\mathrm{\ω}}_{\mathrm{xb}}\left(1\right)\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\ω}}_{\mathrm{xb}}\left(n\right)\end{array}\right],$ $b=\left[\begin{array}{c}+a_0{k}_{\mathrm{gx}}\\ k_{\mathrm{gx}}\end{array}\right],$ $v=\left[\begin{array}{c}v\left(1\right)\\ .\\ .\\ .\\ v\left(n\right)\end{array}\right]$

By least square method can in the hope of

$\hat{b}={\left(X^{T}X\right)}^{-1}{X}^{T}y$

So just tried to achieve demarcation factor k _Gx

C) alignment error is calculated

To x _bAxle speed size is the forward and backward test of ω, considers y, z axle gyro, can get following measured equation by table 2:

$\left\{\begin{array}{c}\stackrel{\‾}{y_{{\mathrm{yx}}^{+}}}=k_{\mathrm{gy}}({\mathrm{\α}}_{\mathrm{yz}}\mathrm{\ω}+b_0)\\ \stackrel{\‾}{u_{{\mathrm{yx}}^{-}}}=k_{\mathrm{gy}}(-{\mathrm{\α}}_{\mathrm{yz}}\mathrm{\ω}+b_0)\end{array}\right.,$ $\left\{\begin{array}{c}\stackrel{\‾}{u_{{\mathrm{zx}}^{+}}}=k_{\mathrm{gz}}({\mathrm{\α}}_{\mathrm{zy}}\mathrm{\ω}+c_0)\\ \stackrel{\‾}{u_{{\mathrm{zx}}^{-}}}=k_{\mathrm{gz}}(-{\mathrm{\α}}_{\mathrm{zy}}\mathrm{\ω}+c_0)\end{array}\right.$

In the formula,

When being respectively j axle (j=x, y, z) forward and backward speed trial, the average of i axle (i=x, y, z) gyro output valve.

Two set of equations can be in the hope of two alignment error angles from the top

${\mathrm{\α}}_{\mathrm{yz}}=\frac{\stackrel{\‾}{u_{{\mathrm{yx}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{yx}}^{-}}}}{2k_{\mathrm{gy}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{zy}}=\frac{\stackrel{\‾}{u_{{\mathrm{zx}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{zx}}^{-}}}}{2k_{\mathrm{gz}}\mathrm{\ω}}$

With similar method to y _b, z _bEach gyro output average equation during the axle speed trial carries out computing, can be in the hope of other 2 constant multipliers and four alignment error angle, and wherein alignment error is as follows,

${\mathrm{\α}}_{\mathrm{xz}}=\frac{\stackrel{\‾}{u_{{\mathrm{xy}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{xy}}^{-}}}}{2k_{\mathrm{gx}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{zx}}=\frac{\stackrel{\‾}{u_{{\mathrm{zy}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{zy}}^{-}}}}{2k_{\mathrm{gz}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{xy}}=\frac{\stackrel{\‾}{u_{{\mathrm{xz}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{xz}}^{-}}}}{2k_{\mathrm{gx}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{yx}}=\frac{\stackrel{\‾}{u_{{\mathrm{yz}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{yz}}^{-}}}}{2k_{\mathrm{gy}}\mathrm{\ω}}$

D) position test

To the static drift coefficient in the formula (2-2), demarcate by the multiposition test.

Can derive by formula (2-1), (2-2)

$\left\{\begin{array}{c}{u}_x\·(1/k_{\mathrm{gx}})-({\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{zb}})={\mathrm{\ϵ}}_x=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ u_y\·(1/k_{\mathrm{gy}})-({\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{zb}})={\mathrm{\ϵ}}_y=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ u_z\·(1/k_{\mathrm{gz}})-({\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{yb}})={\mathrm{\ϵ}}_z=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.$

When carrying out the static drift test with the moment feedback transmitter on earth, following formula becomes

$\left\{\begin{array}{c}{u}_x\·(1/k_{\mathrm{gx}})-({\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{ey}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{ez}})=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ u_y\·(1/k_{\mathrm{gy}})-({\mathrm{\ω}}_{\mathrm{ey}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{ez}})=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ u_z\·(1/k_{\mathrm{gz}})-({\mathrm{\ω}}_{\mathrm{ez}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{ey}})=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.$

In the formula, ω _Ex, ω _Ey, ω _EzOne ground velocity is at IMU coordinate system x _b, y _b, z _bComponent on the axle.

Consider x axle gyro, n position test can obtain following equation:

$\frac{1}{k_{\mathrm{gx}}}\left[\begin{array}{c}{u}_x\left(1\right)\\ ...\\ u_x\left(n\right)\end{array}\right]-\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ex}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(1\right)\\ ...& ...& ...\\ {\mathrm{\ω}}_{\mathrm{ex}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(n\right)\end{array}\right]\left[\begin{array}{c}1\\ {\mathrm{\α}}_{\mathrm{xz}}\\ {\mathrm{\α}}_{\mathrm{xy}}\end{array}\right]=\left[\begin{array}{cccc}1& g_{\mathrm{xb}}\left(1\right)& g_{\mathrm{yb}}\left(1\right)& g_{\mathrm{zb}}\left(1\right)\\ ...& ...& ...& ...\\ 1& g_{\mathrm{xb}}\left(n\right)& g_{\mathrm{yb}}\left(n\right)& g_{\mathrm{zb}}\left(n\right)\end{array}\right]\left[\begin{array}{c}{a}_0\\ a_x\\ a_y\\ a_z\end{array}\right]$

Also can obtain similar equation to y, z axle gyro, consider the test random error, they can unify to be write as following form:

y＝Xb+v

Wherein, y is observation (a n dimension), and X is observing matrix (n * 4 dimensions), and b is coefficient vector (a n dimension), and v is test random error vector.

$y=\frac{1}{k_{\mathrm{gx}}}\left[\begin{array}{c}{u}_x\left(1\right)\\ ...\\ u_x\left(n\right)\end{array}\right]-\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ex}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(1\right)\\ ...& ...& ...\\ {\mathrm{\ω}}_{\mathrm{ex}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(n\right)\end{array}\right]\left[\begin{array}{c}1\\ {\mathrm{\α}}_{\mathrm{xz}}\\ {\mathrm{\α}}_{\mathrm{xy}}\end{array}\right]$

$X=\left[\begin{array}{cccc}1& g_{\mathrm{xb}}\left(1\right)& g_{\mathrm{yb}}\left(1\right)& g_{\mathrm{zb}}\left(1\right)\\ ...& ...& ...& ...\\ 1& g_{\mathrm{xb}}\left(n\right)& g_{\mathrm{yb}}\left(n\right)& g_{\mathrm{zb}}\left(n\right)\end{array}\right],$ b＝[a ₀?a _x?a _y?a _z] ^T

By least square method,

$\hat{b}={\left(X^{T}X\right)}^{-1}{X}^{T}y$

If b is the m n dimensional vector n, then X must comprise m dimensional linear independent vector, otherwise this method can not be used.

Can all can list a set of equations this moment to each position test, then each static drift coefficient of the direct simultaneous solution of equation that all position tests are listed;

3) adopt three-axle table inclinometer to be demarcated by six position tests:

The first step. will drill with the high accuracy gyroscope inclinometer is fixing and it will be installed on the turntable by frock clamp, with bubble or horizon instrument inclinometer is carried out leveling on three rate tables, allow wherein as far as possible diaxon (as X, Y) maintenance level, the 3rd (as Z) is perpendicular to ground surface;

Second step. the Z axle is placed X, Y-axis level towards the sky.Turntable is rotated counterclockwise around the Z axle, and speed is respectively: 1 °/s, and 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s, note the voltage data that gyro is exported under each speed, add table output umber of pulse, save as document; Sampling time is 5 minutes;

The 3rd step. turntable turns clockwise around the Z axle.Speed is respectively: 1 °/s, and 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s, note gyro output data under each speed, save as document; Sampling time is 5 minutes;

The 4th step. X, Y-axis respectively towards the sky, were repeated for second step, the action of the 3rd step, also respectively with 1 °/s of speed, 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s rotating, and write down gyro output data under the various states, preserve document; Sampling time is 5 minutes;

The 5th step. gyrolevel X, Y, Z axle are placed by following six positions respectively: east, north, sky; East,, north; Ground, west, north; West, sky, north; My god, east, north; North, east; The preservation gyro data is a text document, and the sampling time is 5 minutes;

During six position measurements,, need transposition to finish after 15 seconds and preserve data again to another position from a position, to guarantee that gyro data has been stabilized to current state, test data is just authentic and valid, can not influence calibration result;

4) utilize step 1) and 2) Mathematical Modeling adopt computer aided program, the measured 36 groups of speed datas of step 3) and 6 groups of position datas are handled, calculate output inclinometer gyro constant multiplier, alignment error and static drift coefficient.

Compared to existing technology, the present invention has following beneficial effect: (please replenish as far as possible, be related to the problem of whether authorizing! )

The present invention has designed the small-bore directional gyro inclinometer continuous measurement pattern scaling method of a sleeve forming, can be efficiently quick, and accurately, overall process is demarcated in very easy realization; Has reliability, practical, the characteristics that accuracy and efficient are high.

Description of drawings

Fig. 1 is three-axle table and inclinometer scheme of installation.

Fig. 2 is the six position measurement figures of probing with high accuracy gyroscope inclinometer timing signal.

Fig. 3 is test flow chart (speed and position test do not have sequencing).

Fig. 4 is the gyroscope inertia pipe nipple structural representation of probing with the high accuracy gyroscope inclinometer.

The specific embodiment

The invention provides a kind of small-bore directional gyro inclinometer continuous measurement pattern scaling method, comprise as step: step 1) is set up and is added table input/output relation Mathematical Modeling; Step 2) sets up gyro input/output relation Mathematical Modeling; Step 3) adopts test of three-axle table through-rate and six position tests that inclinometer is demarcated; Step 4) is utilized step 1) and 2) Mathematical Modeling adopt computer aided program, the measured 36 groups of speed datas of step 3) and 6 groups of position datas are handled, calculate output inclinometer gyro constant multiplier, alignment error and static drift coefficient.Adopt scaling method of the present invention to demarcate gyrolevel fast and effectively, model is estimated accurate and effective, and is simple to operate, can finish all parameter calibrations, reliability height within a short period of time.

Below in conjunction with embodiment the present invention is described in further detail.

A kind of probing mainly is made of aboveground control device and underground survey equipment two parts with small-bore directional gyro inclinometer.Aboveground control device is made up of a computer and control module, but connects the feedback information that real-time tracking shows underground survey equipment by cable; Underground survey equipment by head harness, centralizer, collection remote measurement pipe nipple, gyroscope inertia pipe nipple, pressure-proof outer cover, resistance to compression vacuum flask, increase the weight of short circuit, guide shoe directional bond and orientation joint etc. and form.Main sensor device has small-sized flexible gyroscope and three quartz accelerometers of two double freedoms.This probing can realize the continuous measurement of inclinometer with the high accuracy gyroscope inclinometer, has simplified test process greatly, and data read automatically and preserve, and do not need too many artificial manual operations, and computational process is finished by computer fully.

Referring to Fig. 4, gyroscope inertia pipe nipple (inertia measurement group) is made up of elements such as gyrorotor, flexible coupling, torquer, sensor, hysteresis machine and seal casinghousings as the core component of inclinometer.A pair of ball bearing is housed on the gyro base, and with the high speed rotation of support drive motor shaft, driving shaft one end is being adorned the rotor of motor, and the other end is being adorned gyrorotor by flexible coupling, and the torquer coil rack links to each other with base with screw with sensor cluster.The upper and lower end cap electricity consumption bundle welding at gyro base two ends also makes the gyro sealing.The bore of described flexible gyroscope is less than 50mm.

Wherein, gyroscope inertia pipe nipple comprises rotary electric machine 47, and reducer, turning cylinder and sensor (omitting reducer, turning cylinder and sensor among the figure), sensor by 41,42 and three of the small-sized flexible gyroscopes of two double freedoms each other the quartz accelerometer 43,44,45 of quadrature form, the first small-sized flexible gyroscope 41 of two double freedoms is just being transferred to the rotation skeleton each other with the second small-sized flexible gyroscope 42 and is being connected, and three quartz accelerometers 43,44,45 are just being transferred to the rotation skeleton each other and connected.The small-bore directional gyro inclinometer of the present invention continuous measurement pattern scaling method is applicable to this probing with small-bore directional gyro inclinometer, and concrete steps comprise:

One. add table and demarcate

1, adds table input/output relation Mathematical Modeling

With three quartz accelerometers in the small-bore directional gyro inclinometer, establish ox at probing _by _bz _bFor inertia combination matrix coordinate system, parallel with carrier coordinate system.It is as follows to set up quartz accelerometer input/output relation Mathematical Modeling:

$\left\{\begin{array}{c}{F}_x=k_x(a_{x0}+a_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{a}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{a}_{\mathrm{zb}}+k_{2x}{a}_{\mathrm{xb}}^2)\\ F_y=k_y(a_{y0}+a_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{a}_{\mathrm{zb}}+k_{2y}{a}_{\mathrm{yb}}^2)\\ F_z=k_z(a_{z0}+a_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{a}_{\mathrm{yb}}+k_{2z}{a}_{\mathrm{zb}}^2)\end{array}\right.---(1-1)$

In the formula, F _x, F _y, F _zBe x _b, y _b, z _bThe table that adds of axle is exported a _Xb, a _Yb, a _ZbFor along three axial acceleration of IMU coordinate system.k _x, k _y, k _zBe x _b, y _b, z _bAxle adds the constant multiplier of table, a _X0, a _Y0, a _Z0Be x _b, y _b, z _bAxle adds the biasing of table, k _2x, k _2y, k _2zBe x _b, y _b, z _bAxle adds the second order nonlinear coefficient (its value is in a small amount) of table, α _Xy, α _Xz, α _Yx, α _Yz, α _Zx, α _ZyFor adding table alignment error (its value is in a small amount).

At the table that adds on the IMU in the present project, set up following simplified model.

$\left\{\begin{array}{c}\frac{N_x^{+}-N_x^{-}}{\mathrm{\ΔT}}=k_x(a_{x0}+a_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{a}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{a}_{\mathrm{zb}})\\ \frac{N_y^{+}-N_y^{-}}{\mathrm{\ΔT}}=k_y(a_{y0}+a_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{a}_{\mathrm{zb}})\\ \frac{N_z^{+}-N_z^{-}}{\mathrm{\ΔT}}=k_z(a_{z0}+a_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{a}_{\mathrm{yb}})\end{array}\right.---(1-2)$

In the formula,

Be respectively x, y, z axle and add the umber of pulse of table two-way output in sampling period Δ T, all the other symbol implications are the same.

The constant multiplier, biasing, the alignment error that respectively add table can be demarcated by the multiposition test.

The test of 2 multiposition

Adopt three-axle table to demarcate by six position tests.

The 2-1 test method

Three-axle table as shown in Figure 1.OX, OY, OZ are respectively middle annulate shaft, inner axle, the outer annulate shaft of turntable.Oxyz is the inside casing coordinate system, ox, oy axle horizontal when initial, and the oz axle is vertically towards the sky.The IMU assembly with its coordinate system ox _by _bz _bThe mode that overlaps with the inside casing coordinate system is installed on the turntable inside casing respectively.

Choosing six positions as shown in table 1 tests.In each position, hits minute is noted the umber of pulse of sampling time and three axis accelerometer output.After the number end was adopted in some positions, a certain annulate shaft that rotates testing counter arrived the another location and continues above-mentioned test, carries out the test of six positions altogether.Utilize these data just can demarcate biasing, constant multiplier and the alignment error of three axis accelerometer.

Each position of table 1 six position tests and the component of acceleration of gravity on each

In the table, the H-level, U-vertically upward, D-is vertically downward.

2-2 calculates

To position 1 and position 2 tests, with a _Xb=g, a _Yb=a _Zb=0 and a _Xb=-g, a _Yb=a _Zb=0 substitution (1-2) respectively can get following two set of equations:

$\left\{\begin{array}{c}{P}_{{\mathrm{xx}}^{+}}\stackrel{\mathrm{\Δ}}{=}\frac{N_x^{+}-N_x^{-}}{T_{x^{+}}}=k_x(a_{x0}+g)\\ P_{{\mathrm{yx}}^{+}}\stackrel{\mathrm{\Δ}}{=}\frac{N_y^{+}-N_y^{-}}{T_{x^{+}}}=k_y(a_{y0}+{\mathrm{\α}}_{\mathrm{yz}}g)\\ P_{{\mathrm{zx}}^{+}}\stackrel{\mathrm{\Δ}}{=}\frac{N_z^{+}-N_z^{-}}{T_{x^{+}}}=k_z(a_{z0}+{\mathrm{\α}}_{\mathrm{zy}}g)\end{array}\right.---(1-3.a)$

$\left\{\begin{array}{c}{P}_{{\mathrm{xx}}^{-}}\stackrel{\mathrm{\Δ}}{=}\frac{N_x^{+}-N_x^{-}}{T_{x^{-}}}=k_x(a_{x0}-g)\\ P_{{\mathrm{yx}}^{-}}\stackrel{\mathrm{\Δ}}{=}\frac{N_y^{+}-N_y^{-}}{T_{x^{-}}}=k_y(a_{y0}-{\mathrm{\α}}_{\mathrm{yz}}g)\\ P_{{\mathrm{zx}}^{-}}\stackrel{\mathrm{\Δ}}{=}\frac{N_z^{+}-N_z^{-}}{T_{x^{-}}}=k(a_{z0}-{\mathrm{\α}}_{\mathrm{zy}}g)\end{array}\right.---(1-3.b)$

In the formula,

For j axle (j=x, y, z) acceleration be respectively+g ,-during the position test of g, the umber of pulse of output in i axle (i=x, y, z) the two-way accelerometer unit interval,

For j axle (j=x, y, z) acceleration be+g ,-sampling total time of the position test of g.

By formula (1-3.a), (1-3.b) can in the hope of

$\left\{\begin{array}{cc}{k}_x=\frac{P_{{\mathrm{xx}}^{+}}-P_{{\mathrm{xx}}^{-}}}{2g},& {\mathrm{\α}}_{\mathrm{yz}}=\frac{P_{{\mathrm{yx}}^{+}}-P_{{\mathrm{yx}}^{-}}}{{2\mathrm{gk}}_y}\\ a_{x0}=\frac{P_{{\mathrm{xx}}^{+}}+P_{{\mathrm{xx}}^{-}}}{{2k}_x},& {\mathrm{\α}}_{\mathrm{zy}}=\frac{P_{{\mathrm{zx}}^{+}}-P_{{\mathrm{zx}}^{-}}}{{2\mathrm{gk}}_z}\end{array}\right.---(1-4)$

To position 3 and 4,5 and 6 tests, do similarly to handle, can try to achieve other 8 parameters.Provide the result who obtains by computing below.

$\left\{\begin{array}{cccc}{k}_y=\frac{P_{{\mathrm{yy}}^{+}}-P_{{\mathrm{yy}}^{-}}}{2g}& k_z=\frac{P_{{\mathrm{zz}}^{+}}-P_{{\mathrm{zz}}^{-}}}{2g}& {\mathrm{\α}}_{\mathrm{xy}}=\frac{P_{{\mathrm{xz}}^{+}}-P_{{\mathrm{xz}}^{-}}}{{2\mathrm{gk}}_x}& {\mathrm{\α}}_{\mathrm{xz}}=\frac{P_{{\mathrm{xy}}^{+}}-P_{{\mathrm{xy}}^{-}}}{{2\mathrm{gk}}_x}\\ a_{y0}=\frac{P_{{\mathrm{yy}}^{+}}+P_{{\mathrm{yy}}^{-}}}{{2k}_y}& a_{z0}=\frac{P_{{\mathrm{zz}}^{+}}+P_{{\mathrm{zz}}^{-}}}{{2k}_z}& {\mathrm{\α}}_{\mathrm{yx}}=\frac{P_{{\mathrm{yz}}^{+}}-P_{{\mathrm{yz}}^{-}}}{{2\mathrm{gk}}_y}& {\mathrm{\α}}_{\mathrm{zx}}=\frac{P_{{\mathrm{zy}}^{+}}-P_{{\mathrm{zy}}^{-}}}{{2\mathrm{gk}}_2}\end{array}\right.---(1-5)$

It more than is the demarcation that adds table.

Two. Gyro Calibration

1, gyro input/output relation Mathematical Modeling

With three flexible gyroscopes in the small-bore directional gyro inclinometer, establish ox at probing _by _bz _bFor inertia combination matrix coordinate system, parallel with carrier coordinate system.It is as follows to set up gyro input/output relation Mathematical Modeling:

$\left\{\begin{array}{c}{u}_x=k_{\mathrm{gx}}({\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\ϵ}}_x)\\ u_y=k_{\mathrm{gy}}({\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\ϵ}}_y)\\ u_z=k_{\mathrm{gz}}({\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\ϵ}}_z)\end{array}\right.---(2-1)$

In the formula, u _x, u _y, u _zBe IMU coordinate system x _b, y _b, z _bThe output of axle gyro, k _Gx, k _Gy, k _GzBe the constant multiplier of each gyro, α _Xy, α _Xz, α _Yx, α _Yz, α _Zx, α _ZyBe gyro misalignment (its value is in a small amount), ω _Xb, ω _Yb, ω _ZbFor along IMU coordinate system x _b, y _b, z _bInput angle speed, ε _x, ε _y, ε _zBe each Gyro Static Drift, they are:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_x=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ {\mathrm{\ϵ}}_y=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ {\mathrm{\ϵ}}_z=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.---(2-2)$

In the formula, g _Xb, g _Yb, g _ZbBe the component of gravity acceleration g on three axles of IMU coordinate system.

Constant multiplier and alignment error can be demarcated in the through-rate test, and the static drift model coefficient can be demarcated by the multiposition test.

2, speed trial

The 2-1 test method

In order to demarcate the constant multiplier and the alignment error of gyro in the strap down inertial navigation combination, need carry out speed trial.

Before the test, strap down inertial navigation combination is installed on the speed platform (that is, make rate table rotating shaft parallel with ground vertical line) by one of mounting means shown in the table 1, and makes by demarcation and spool overlap with speed platform axle.Make speed platform axle with wherein a certain angular speed constant speed rotation by pre-designed rate test point (generally being no less than 11 points).Turn over opening entry gyroscope output on a certain reference angle position at rate table, and record gyroscope output on some adjacent equal angles symmetric points in a week, changeed a week (can change some weeks during high speed) up to rate table.Make backing propeller test with this angular speed then, note these data equally.

The mounting means of IMU on the speed platform in the table 1.a speed trial

In the table, OXYZ is a speed platform stage body coordinate system, ox _by _bz _bBe the IMU coordinate system, ω is a turntable speed over the ground, ω _eBe the earth rotation angular speed, φ is local geographic latitude.

All speed points are repeated said process.Constant multiplier and the alignment error of utilizing the experimental data of gained can demarcate three gyros of IMU.

2-2 constant multiplier and alignment error are calculated

Reject turntable gyrostatic output when static in the time of will be from each speed trial the gyro output data, carry out least square fitting then.Directly be given in the speed trial data below, the average equation of each the gyro output valve that is drawn by formula (2-1), (2-2) sees Table 2.Equation is used in the hope of each gyro constant multiplier and alignment error in the table.

Table 2

In the table, ω _Xb=ω (being exactly turntable religion speed angle), ω _Yb=ω+ω _N(component of the religion speed angle speed and the earth), ω _Ab=ω+ω _u(component of the religion speed angle speed and the earth).

Axle is during (j=x, y, z) speed trial, at the trial between in the average of i axle (i=x, y, z) gyro output valve.

Below with x _bThe axle speed trial is an example, introduces the method for being calculated Gyro Calibration factor and alignment error by equation in the table 2.

The 2-2-1 constant multiplier calculates

To x _bX axle gyro is considered in the test of axle n subrate, can get following measured equation by table 2:

$\left[\begin{array}{c}\stackrel{\‾}{u_{\mathrm{xx}}}\left(1\right)\\ .\\ .\\ .\\ \stackrel{\‾}{u_{\mathrm{xx}}}\left(n\right)\end{array}\right]=\left[\begin{array}{cc}1& {\mathrm{\ω}}_{\mathrm{xb}}\left(1\right)\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\ω}}_{\mathrm{xb}}\left(n\right)\end{array}\right]+\left[\begin{array}{c}+a_0{k}_{\mathrm{gx}}\\ k_{\mathrm{gx}}\end{array}\right]+\left[\begin{array}{c}v\left(1\right)\\ .\\ .\\ .\\ v\left(n\right)\end{array}\right]$

Following formula can be expressed as follows:

y＝Xb+v

In the formula, v is test random error vector,

$y=\left[\begin{array}{c}\stackrel{\‾}{u_{\mathrm{xx}}}\left(1\right)\\ .\\ .\\ .\\ \stackrel{\‾}{u_{\mathrm{xx}}}\left(n\right)\end{array}\right],$ $X=\left[\begin{array}{cc}1& {\mathrm{\ω}}_{\mathrm{xb}}\left(1\right)\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\ω}}_{\mathrm{xb}}\left(n\right)\end{array}\right],$ $b=\left[\begin{array}{c}+a_0{k}_{\mathrm{gx}}\\ k_{\mathrm{gx}}\end{array}\right],$ $v=\left[\begin{array}{c}v\left(1\right)\\ .\\ .\\ .\\ v\left(n\right)\end{array}\right]$

By least square method can in the hope of

$\hat{b}={\left(X^{T}X\right)}^{-1}{X}^{T}y$

So just tried to achieve demarcation factor k _Gx

The 2-2-2 alignment error is calculated

To x _bAxle speed size is the forward and backward test of ω, considers y, z axle gyro, can get following measured equation by table 2:

$\left\{\begin{array}{c}\stackrel{\‾}{y_{{\mathrm{yx}}^{+}}}=k_{\mathrm{gy}}({\mathrm{\α}}_{\mathrm{yz}}\mathrm{\ω}+b_0)\\ \stackrel{\‾}{u_{{\mathrm{yx}}^{-}}}=k_{\mathrm{gy}}(-{\mathrm{\α}}_{\mathrm{yz}}\mathrm{\ω}+b_0)\end{array}\right.,$ $\left\{\begin{array}{c}\stackrel{\‾}{u_{{\mathrm{zx}}^{+}}}=k_{\mathrm{gz}}({\mathrm{\α}}_{\mathrm{zy}}\mathrm{\ω}+c_0)\\ \stackrel{\‾}{u_{{\mathrm{zx}}^{-}}}=k_{\mathrm{gz}}(-{\mathrm{\α}}_{\mathrm{zy}}\mathrm{\ω}+c_0)\end{array}\right.$

In the formula,

When being respectively j axle (j=x, y, z) forward and backward speed trial, the average of i axle (i=x, y, z) gyro output valve.

Two set of equations can be in the hope of two alignment error angles from the top

${\mathrm{\α}}_{\mathrm{yz}}=\frac{\stackrel{\‾}{u_{{\mathrm{yx}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{yx}}^{-}}}}{2k_{\mathrm{gy}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{zy}}=\frac{\stackrel{\‾}{u_{{\mathrm{zx}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{zx}}^{-}}}}{2k_{\mathrm{gz}}\mathrm{\ω}}$

With similar method to y _b, z _bEach gyro output average equation during the axle speed trial carries out computing, can be in the hope of other 2 constant multipliers and four alignment error angle, and wherein alignment error is as follows,

${\mathrm{\α}}_{\mathrm{xz}}=\frac{\stackrel{\‾}{u_{{\mathrm{xy}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{xy}}^{-}}}}{2k_{\mathrm{gx}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{zx}}=\frac{\stackrel{\‾}{u_{{\mathrm{zy}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{zy}}^{-}}}}{2k_{\mathrm{gz}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{xy}}=\frac{\stackrel{\‾}{u_{{\mathrm{xz}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{xz}}^{-}}}}{2k_{\mathrm{gx}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{yx}}=\frac{\stackrel{\‾}{u_{{\mathrm{yz}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{yz}}^{-}}}}{2k_{\mathrm{gy}}\mathrm{\ω}}$

3 position tests

To the static drift coefficient in the formula (2-2), demarcate by the multiposition test.

Can derive by formula (2-1), (2-2)

$\left\{\begin{array}{c}{u}_x\·(1/k_{\mathrm{gx}})-({\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{zb}})={\mathrm{\ϵ}}_x=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ u_y\·(1/k_{\mathrm{gy}})-({\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{zb}})={\mathrm{\ϵ}}_y=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ u_z\·(1/k_{\mathrm{gz}})-({\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{yb}})={\mathrm{\ϵ}}_z=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.$

When carrying out the static drift test with the moment feedback transmitter on earth, following formula becomes

$\left\{\begin{array}{c}{u}_x\·(1/k_{\mathrm{gx}})-({\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{ey}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{ez}})=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ u_y\·(1/k_{\mathrm{gy}})-({\mathrm{\ω}}_{\mathrm{ey}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{ez}})=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ u_z\·(1/k_{\mathrm{gz}})-({\mathrm{\ω}}_{\mathrm{ez}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{ey}})=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.$

In the formula, ω _Ex, ω _Ey, ω _EzOne ground velocity is at IMU coordinate system x _b, y _b, z _bComponent on the axle.

Consider x axle gyro, n position test can obtain following equation:

$\frac{1}{k_{\mathrm{gx}}}\left[\begin{array}{c}{u}_x\left(1\right)\\ ...\\ u_x\left(n\right)\end{array}\right]-\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ex}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(1\right)\\ ...& ...& ...\\ {\mathrm{\ω}}_{\mathrm{ex}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(n\right)\end{array}\right]\left[\begin{array}{c}1\\ {\mathrm{\α}}_{\mathrm{xz}}\\ {\mathrm{\α}}_{\mathrm{xy}}\end{array}\right]=\left[\begin{array}{cccc}1& g_{\mathrm{xb}}\left(1\right)& g_{\mathrm{yb}}\left(1\right)& g_{\mathrm{zb}}\left(1\right)\\ ...& ...& ...& ...\\ 1& g_{\mathrm{xb}}\left(n\right)& g_{\mathrm{yb}}\left(n\right)& g_{\mathrm{zb}}\left(n\right)\end{array}\right]\left[\begin{array}{c}{a}_0\\ a_x\\ a_y\\ a_z\end{array}\right]$

Also can obtain similar equation to y, z axle gyro, consider the test random error, they can unify to be write as following form:

y＝Xb+v

Wherein, y is observation (a n dimension), and X is observing matrix (n * 4 dimensions), and b is coefficient vector (a n dimension), and v is test random error vector.

$y=\frac{1}{k_{\mathrm{gx}}}\left[\begin{array}{c}{u}_x\left(1\right)\\ ...\\ u_x\left(n\right)\end{array}\right]-\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ex}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(1\right)\\ ...& ...& ...\\ {\mathrm{\ω}}_{\mathrm{ex}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(n\right)\end{array}\right]\left[\begin{array}{c}1\\ {\mathrm{\α}}_{\mathrm{xz}}\\ {\mathrm{\α}}_{\mathrm{xy}}\end{array}\right]$

$X=\left[\begin{array}{cccc}1& g_{\mathrm{xb}}\left(1\right)& g_{\mathrm{yb}}\left(1\right)& g_{\mathrm{zb}}\left(1\right)\\ ...& ...& ...& ...\\ 1& g_{\mathrm{xb}}\left(n\right)& g_{\mathrm{yb}}\left(n\right)& g_{\mathrm{zb}}\left(n\right)\end{array}\right],$ b＝[a ₀?a _x?a _y?a _z] ^T

By least square method,

$\hat{b}={\left(X^{T}X\right)}^{-1}{X}^{T}y$

If b is the m n dimensional vector n, then X must comprise m dimensional linear independent vector, otherwise this method can not be used.

Can all can list a set of equations this moment to each position test, then each static drift coefficient of the direct simultaneous solution of equation that all position tests are listed.

Adopt the inventive method that described probing is demarcated with small-bore directional gyro inclinometer, concrete steps comprise:

The first step. will drill with small-bore directional gyro inclinometer and be fixed on three rate tables, allow wherein as far as possible diaxon (as X, Y) maintenance level, the 3rd (as Z) is perpendicular to ground surface.As shown in Figure 1.

Second step. the Z axle is placed X, Y-axis level towards the sky.Turntable is rotated counterclockwise around the Z axle, and speed is respectively: 1 °/s, and 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s, note the voltage data that gyro is exported under each speed, add table output umber of pulse, save as document.Sampling time is 5 minutes.

The 3rd step. turntable turns clockwise around the Z axle.Speed is respectively: 1 °/s, and 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s, note gyro output data under each speed, save as document.Sampling time is 5 minutes.

The 4th step. X, Y-axis respectively towards the sky, were repeated for second step, the action of the 3rd step, also respectively with 1 °/s of speed, 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s rotating, and write down gyro output data under the various states, preserve document.Sampling time is 5 minutes.

The 5th step. gyrolevel X, Y, Z axle are placed by following six positions respectively: east, north, sky; East,, north; Ground, west, north; West, sky, north; My god, east, north; North, east; The preservation gyro data is a text document, and the sampling time is 5 minutes.

During six position measurements,, need transposition to finish after 15 seconds and preserve data again to another position from a position, to guarantee that gyro data has been stabilized to current state, test data is just authentic and valid, can not influence calibration result.

The 6th step. call the computer aided program that writes, utilize measured 36 groups of speed datas and 6 groups of position datas.Calculate output inclinometer gyro constant multiplier, alignment error and static drift coefficient.

Adopt scaling method of the present invention to demarcate gyrolevel fast and effectively, model is estimated accurate and effective, and is simple to operate, can finish all parameter calibrations, reliability height within a short period of time.

Claims (1)

1. small-bore directional gyro inclinometer continuous measurement pattern scaling method adopts three-axle table to carry out static demarcating by six position tests, comprises the steps:

1) foundation adds the static input/output relation Mathematical Modeling of table:

With three quartz accelerometers of small-bore directional gyro inclinometer, establish ox at probing _by _bz _bFor inertia combination matrix coordinate system, parallel with carrier coordinate system; It is as follows to set up quartz accelerometer input/output relation Mathematical Modeling:

$\left\{\begin{array}{c}{F}_x=k_x(a_{x0}+a_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{a}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{a}_{\mathrm{zb}}+k_{2x}{a}_{\mathrm{xb}}^2)\\ F_y=k_y(a_{y0}+a_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{a}_{\mathrm{zb}}+k_{2y}{a}_{\mathrm{yb}}^2)\\ F_z=k_z(a_{z0}+a_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{a}_{\mathrm{yb}}+k_{2z}{a}_{\mathrm{zb}}^2)\end{array}\right.---(1-1)$

In the formula, F _x, F _y, F _zBe x _b, y _b, z _bThe table that adds of axle is exported a _Xb, a _Yb, a _ZbFor along three axial acceleration of IMU coordinate system.k _x, k _y, k _zBe x _b, y _b, z _bAxle adds the constant multiplier of table, a _X0, a _Y0, a _Z0Be x _b, y _b, z _bAxle adds the biasing of table, k _2x, k _2y, k _2zBe x _b, y _b, z _bAxle adds the second order nonlinear coefficient (its value is in a small amount) of table, α _Xy, α _Xz, α _Yx, α _Yz, α _Zx, α _ZyFor adding table alignment error (its value is in a small amount);

At the table that adds on the gyrolevel in the present project, ignore a small amount of influence in the following formula, set up following simplified model:

$\left\{\begin{array}{c}\frac{N_x^{+}-N_x^{-}}{\mathrm{\ΔT}}=k_x(a_{x0}+a_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{a}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{a}_{\mathrm{zb}})\\ \frac{N_y^{+}-N_y^{-}}{\mathrm{\ΔT}}=k_y(a_{y0}+a_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{a}_{\mathrm{zb}})\\ \frac{N_z^{+}-N_z^{-}}{\mathrm{\ΔT}}=k_z(a_{z0}+a_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{a}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{a}_{\mathrm{yb}})\end{array}\right.---(1-2)$

In the formula,

Be respectively x, y, z axle and add the umber of pulse of table two-way output in sampling period Δ T, all the other symbol implications are the same;

The constant multiplier, biasing, the alignment error that respectively add table are demarcated by the multiposition test;

2) set up the static input/output relation Mathematical Modeling of gyro:

At the three spool flexible gyroscopes of probing, establish ox with small-bore directional gyro inclinometer _by _bz _bBe inertia combination matrix coordinate system, parallel with carrier coordinate system, gyro input/output relation Mathematical Modeling is as follows:

$\left\{\begin{array}{c}{u}_x=k_{\mathrm{gx}}({\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\ϵ}}_x)\\ u_y=k_{\mathrm{gy}}({\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\ϵ}}_y)\\ u_z=k_{\mathrm{gz}}({\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\ϵ}}_z)\end{array}\right.---(2-1)$

In the formula, u _x, u _y, u _zBe IMU coordinate system x _b, y _b, z _bThe voltage output of axle gyro, k _Gx, k _Gy, k _GzBe the constant multiplier of each gyro, α _Xy, α _Xz, α _Yx, α _Yz, α _Zx, α _ZyBe gyro misalignment, its value is in a small amount, but considers that Gyro Precision does not add the height of table, so several coefficients can not be ignored ω _Xb, ω _Yb, ω _ZbFor along IMU coordinate system x _b, y _b, z _bInput angle speed, ε _x, ε _y, ε _zBe each Gyro Static Drift, they are:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_x=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ {\mathrm{\ϵ}}_y=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ {\mathrm{\ϵ}}_z=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.---(2-2)$

In the formula, g _Xb, g _Yb, g _ZbBe the component of gravity acceleration g on three axles of IMU coordinate system;

3) speed trial

Before the test, rate table rotating shaft and one of parallel mounting means of ground vertical line are installed on the speed platform by shown in the table 1 strap down inertial navigation combination, and make by demarcation and spool overlap with speed platform axle; Make speed platform axle with wherein a certain angular speed constant speed rotation by pre-designed rate test point; Turn over opening entry gyroscope output on a certain reference angle position at rate table, and record gyroscope output on some adjacent equal angles symmetric points in a week, a week changeed up to rate table; Then, make backing propeller test, note these data equally with this angular speed;

The mounting means of IMU on the speed platform in the table 1.a speed trial

In the table, OXYZ is a speed platform stage body coordinate system, ox _by _bz _bBe the IMU coordinate system, ω is a turntable speed over the ground, ω _eBe the earth rotation angular speed, φ is local geographic latitude;

Constant multiplier and the alignment error of utilizing the experimental data of gained can demarcate three gyros of IMU;

A) constant multiplier and alignment error are calculated:

Least square fitting is carried out in gyrostatic output when the rejecting turntable is static the gyro output data during from each speed trial then.Directly be given in the speed trial data below, the average equation of each the gyro output valve that is drawn by formula (2-1), (2-2) sees Table 2.Equation is used in the hope of each gyro constant multiplier and alignment error in the table.

Table 2

In the table, ω _Xb=ω (being exactly turntable religion speed angle), ω _Yb=ω+ω _N(component of the religion speed angle speed and the earth), ω _Zb=ω+ω _u(component of the religion speed angle speed and the earth).

Axle is during (j=x, y, z) speed trial, at the trial between in the average of i axle (i=x, y, z) gyro output valve.

Below with x _bThe axle speed trial is an example, introduces the method for being calculated Gyro Calibration factor and alignment error by equation in the table 2.

B) constant multiplier calculates

To x _bX axle gyro is considered in the test of axle n subrate, can get following measured equation by table 2:

$\left[\begin{array}{c}\stackrel{\‾}{u_{\mathrm{xx}}}\left(1\right)\\ .\\ .\\ .\\ \stackrel{\‾}{u_{\mathrm{xx}}}\left(n\right)\end{array}\right]=\left[\begin{array}{cc}1& {\mathrm{\ω}}_{\mathrm{xb}}\left(1\right)\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\ω}}_{\mathrm{xb}}\left(n\right)\end{array}\right]+\left[\begin{array}{c}+a_0{k}_{\mathrm{gx}}\\ k_{\mathrm{gx}}\end{array}\right]+\left[\begin{array}{c}v\left(1\right)\\ .\\ .\\ .\\ v\left(n\right)\end{array}\right]$

Following formula can be expressed as follows:

y＝Xb+v

In the formula, v is test random error vector,

$y=\left[\begin{array}{c}\stackrel{\‾}{u_{\mathrm{xx}}}\left(1\right)\\ .\\ .\\ .\\ \stackrel{\‾}{u_{\mathrm{xx}}}\left(n\right)\end{array}\right],$ $X=\left[\begin{array}{cc}1& {\mathrm{\ω}}_{\mathrm{xb}}\left(1\right)\\ .& .\\ .& .\\ .& .\\ 1& {\mathrm{\ω}}_{\mathrm{xb}}\left(n\right)\end{array}\right],$ $b=\left[\begin{array}{c}+a_0{k}_{\mathrm{gx}}\\ k_{\mathrm{gx}}\end{array}\right],$ $v=\left[\begin{array}{c}v\left(1\right)\\ .\\ .\\ .\\ v\left(n\right)\end{array}\right]$

By least square method can in the hope of

$\hat{b}={\left(X^{T}X\right)}^{-1}{X}^{T}y$

So just tried to achieve demarcation factor k _Gx

C) alignment error is calculated

To x _bAxle speed size is the forward and backward test of ω, considers y, z axle gyro, can get following measured equation by table 2:

$\left\{\begin{array}{c}\stackrel{\‾}{y_{{\mathrm{yx}}^{+}}}=k_{\mathrm{gy}}({\mathrm{\α}}_{\mathrm{yz}}\mathrm{\ω}+b_0)\\ \stackrel{\‾}{u_{{\mathrm{yx}}^{-}}}=k_{\mathrm{gy}}(-{\mathrm{\α}}_{\mathrm{yz}}\mathrm{\ω}+b_0)\end{array}\right.,$ $\left\{\begin{array}{c}\stackrel{\‾}{u_{{\mathrm{zx}}^{+}}}=k_{\mathrm{gz}}({\mathrm{\α}}_{\mathrm{zy}}\mathrm{\ω}+c_0)\\ \stackrel{\‾}{u_{{\mathrm{zx}}^{-}}}=k_{\mathrm{gz}}(-{\mathrm{\α}}_{\mathrm{zy}}\mathrm{\ω}+c_0)\end{array}\right.$

In the formula,

When being respectively j axle (j=x, y, z) forward and backward speed trial, the average of i axle (i=x, y, z) gyro output valve.

Two set of equations can be in the hope of two alignment error angles from the top

${\mathrm{\α}}_{\mathrm{yz}}=\frac{\stackrel{\‾}{u_{{\mathrm{yx}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{yx}}^{-}}}}{2k_{\mathrm{gy}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{zy}}=\frac{\stackrel{\‾}{u_{{\mathrm{zx}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{zx}}^{-}}}}{2k_{\mathrm{gz}}\mathrm{\ω}}$

With similar method to y _b, z _bEach gyro output average equation during the axle speed trial carries out computing, can be in the hope of other 2 constant multipliers and four alignment error angle, and wherein alignment error is as follows,

${\mathrm{\α}}_{\mathrm{xz}}=\frac{\stackrel{\‾}{u_{{\mathrm{xy}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{xy}}^{-}}}}{2k_{\mathrm{gx}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{zx}}=\frac{\stackrel{\‾}{u_{{\mathrm{zy}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{zy}}^{-}}}}{2k_{\mathrm{gz}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{xy}}=\frac{\stackrel{\‾}{u_{{\mathrm{xz}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{xz}}^{-}}}}{2k_{\mathrm{gx}}\mathrm{\ω}},$ ${\mathrm{\α}}_{\mathrm{yx}}=\frac{\stackrel{\‾}{u_{{\mathrm{yz}}^{+}}}-\stackrel{\‾}{u_{{\mathrm{yz}}^{-}}}}{2k_{\mathrm{gy}}\mathrm{\ω}}$

D) position test

To the static drift coefficient in the formula (2-2), demarcate by the multiposition test.

Can derive by formula (2-1), (2-2)

$\left\{\begin{array}{c}{u}_x\·(1/k_{\mathrm{gx}})-({\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{zb}})={\mathrm{\ϵ}}_x=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ u_y\·(1/k_{\mathrm{gy}})-({\mathrm{\ω}}_{\mathrm{yb}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{zb}})={\mathrm{\ϵ}}_y=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ u_z\·(1/k_{\mathrm{gz}})-({\mathrm{\ω}}_{\mathrm{zb}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{xb}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{yb}})={\mathrm{\ϵ}}_z=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.$

When carrying out the static drift test with the moment feedback transmitter on earth, following formula becomes

$\left\{\begin{array}{c}{u}_x\·(1/k_{\mathrm{gx}})-({\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{xz}}{\mathrm{\ω}}_{\mathrm{ey}}+{\mathrm{\α}}_{\mathrm{xy}}{\mathrm{\ω}}_{\mathrm{ez}})=a_0+a_x{g}_{\mathrm{xb}}+a_y{g}_{\mathrm{yb}}+a_z{g}_{\mathrm{zb}}\\ u_y\·(1/k_{\mathrm{gy}})-({\mathrm{\ω}}_{\mathrm{ey}}+{\mathrm{\α}}_{\mathrm{yz}}{\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{yx}}{\mathrm{\ω}}_{\mathrm{ez}})=b_0+b_x{g}_{\mathrm{xb}}+b_y{g}_{\mathrm{yb}}+b_z{g}_{\mathrm{zb}}\\ u_z\·(1/k_{\mathrm{gz}})-({\mathrm{\ω}}_{\mathrm{ez}}+{\mathrm{\α}}_{\mathrm{zy}}{\mathrm{\ω}}_{\mathrm{ex}}+{\mathrm{\α}}_{\mathrm{zx}}{\mathrm{\ω}}_{\mathrm{ey}})=c_0+c_x{g}_{\mathrm{xb}}+c_y{g}_{\mathrm{yb}}+c_z{g}_{\mathrm{zb}}\end{array}\right.$

In the formula, ω _Ex, ω _Ey, ω _EzOne ground velocity is at IMU coordinate system x _b, y _b, z _bComponent on the axle.

Consider x axle gyro, n position test can obtain following equation:

$\frac{1}{k_{\mathrm{gx}}}\left[\begin{array}{c}{u}_x\left(1\right)\\ ...\\ u_x\left(n\right)\end{array}\right]-\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ex}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(1\right)\\ ...& ...& ...\\ {\mathrm{\ω}}_{\mathrm{ex}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(n\right)\end{array}\right]\left[\begin{array}{c}1\\ {\mathrm{\α}}_{\mathrm{xz}}\\ {\mathrm{\α}}_{\mathrm{xy}}\end{array}\right]=\left[\begin{array}{cccc}1& g_{\mathrm{xb}}\left(1\right)& g_{\mathrm{yb}}\left(1\right)& g_{\mathrm{zb}}\left(1\right)\\ ...& ...& ...& ...\\ 1& g_{\mathrm{xb}}\left(n\right)& g_{\mathrm{yb}}\left(n\right)& g_{\mathrm{zb}}\left(n\right)\end{array}\right]\left[\begin{array}{c}{a}_0\\ a_x\\ a_y\\ a_z\end{array}\right]$

Also can obtain similar equation to y, z axle gyro, consider the test random error, they can unify to be write as following form:

y＝Xb+v

Wherein, y is observation (a n dimension), and X is observing matrix (n * 4 dimensions), and b is coefficient vector (a n dimension), and v is test random error vector.

$y=\frac{1}{k_{\mathrm{gx}}}\left[\begin{array}{c}{u}_x\left(1\right)\\ ...\\ u_x\left(n\right)\end{array}\right]-\left[\begin{array}{ccc}{\mathrm{\ω}}_{\mathrm{ex}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(1\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(1\right)\\ ...& ...& ...\\ {\mathrm{\ω}}_{\mathrm{ex}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ey}}\left(n\right)& {\mathrm{\ω}}_{\mathrm{ez}}\left(n\right)\end{array}\right]\left[\begin{array}{c}1\\ {\mathrm{\α}}_{\mathrm{xz}}\\ {\mathrm{\α}}_{\mathrm{xy}}\end{array}\right]$

$X=\left[\begin{array}{cccc}1& g_{\mathrm{xb}}\left(1\right)& g_{\mathrm{yb}}\left(1\right)& g_{\mathrm{zb}}\left(1\right)\\ ...& ...& ...& ...\\ 1& g_{\mathrm{xb}}\left(n\right)& g_{\mathrm{yb}}\left(n\right)& g_{\mathrm{zb}}\left(n\right)\end{array}\right],$ b＝[a ₀?a _x?a _y?a _z] ^T

By least square method,

$\hat{b}={\left(X^{T}X\right)}^{-1}{X}^{T}y$

If b is the m n dimensional vector n, then X must comprise m dimensional linear independent vector, otherwise this method can not be used.

Can all can list a set of equations this moment to each position test, then each static drift coefficient of the direct simultaneous solution of equation that all position tests are listed;

3) adopt three-axle table inclinometer to be demarcated by six position tests:

The first step. will drill with the high accuracy gyroscope inclinometer is fixing and it will be installed on the turntable by frock clamp, with bubble or horizon instrument inclinometer is carried out leveling on three rate tables, allow wherein as far as possible diaxon (as X, Y) maintenance level, the 3rd (as Z) is perpendicular to ground surface;

Second step. the Z axle is placed X, Y-axis level towards the sky.Turntable is rotated counterclockwise around the Z axle, and speed is respectively: 1 °/s, and 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s, note the voltage data that gyro is exported under each speed, add table output umber of pulse, save as document; Sampling time is 5 minutes;

The 3rd step. turntable turns clockwise around the Z axle.Speed is respectively: 1 °/s, and 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s, note gyro output data under each speed, save as document; Sampling time is 5 minutes;

The 4th step. X, Y-axis respectively towards the sky, were repeated for second step, the action of the 3rd step, also respectively with 1 °/s of speed, 5 °/s, 10 °/s, 15 °/s, 20 °/s, 25 °/s rotating, and write down gyro output data under the various states, preserve document; Sampling time is 5 minutes;

The 5th step. gyrolevel X, Y, Z axle are placed by following six positions respectively: east, north, sky; East,, north; Ground, west, north; West, sky, north; My god, east, north; North, east; The preservation gyro data is a text document, and the sampling time is 5 minutes;

During six position measurements,, need transposition to finish after 15 seconds and preserve data again to another position from a position, to guarantee that gyro data has been stabilized to current state, test data is just authentic and valid, can not influence calibration result;

4) utilize step 1) and 2) Mathematical Modeling adopt computer aided program, the measured 36 groups of speed datas of step 3) and 6 groups of position datas are handled, calculate output inclinometer gyro constant multiplier, alignment error and static drift coefficient.

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