CN103941042A - Method for calibrating multiposition error coefficients of gyroaccelerometer - Google Patents

Abstract

The invention discloses a method for calibrating multiposition error coefficients of a gyroaccelerometer. The method is used for calibrating the error coefficients of the gyroaccelerometer. The method comprises the steps that an error model of the gyroaccelerometeris selected; a diving head angular position rolling test scheme is determined according to the selected error model of the gyroaccelerometer; a rolling test is carried out, and the output of the gyroaccelerometer is measured; the error coefficients of the gyroaccelerometer are determined. According to the method, a dividing head six-position rolling test is adopted to calibrate the simplified error model of the gyroaccelerometer, a dividing head nine-position rolling test is adopted to calibrate the complete error model of the gyroaccelerometer, different calibrating test schemes can be selected reasonably according to different application occasions, the method can be used for error compensation on an accelerometer in the field of navigation and guidance, and the practical precision of a navigation and guidance system is effectively improved.

Description

A kind of gyroaccelerometer multiposition error coefficient scaling method

Technical field

The present invention relates to a kind of gyroaccelerometer multiposition error coefficient scaling method, belong to demarcation and the detection technique field of Aeronautics and Astronautics, navigation navigation gyroaccelerometer.

Background technology

For the numerical value of the each error coefficient of Accurate Calibration gyroaccelerometer mathematical model, feasible scaling method is in gravity field, to carry out multipoint inclination tumbling test.This test is conventionally used and tests with the precision indexer of test fixture, and tested gyroaccelerometer is arranged on test fixture, and the input shaft that makes gyroaccelerometer is accurately perpendicular to the rotating shaft of dividing head.The rotating shaft of dividing head is placed in accurate level, and along east-west direction.Gyroaccelerometer with input shaft direction along local gravity vertical line direction for just putting starting point (0 °), successively northwards or to the south in vertical plane around the axes of rotation skew upset of dividing head, and the output of measuring gyroaccelerometer in position, pre-determined multiple angle.In earth gravity field, the acceleration input direction of each set angle position, big or small different, by the excitation of the different big or small acceleration of gravity inputs in these positions, angle, can solve the solution of each error coefficient.

For the demarcation of accelerometer, the difference of rating test angle location schemes, determined can calibrated error coefficient number and stated accuracy.The existing scaling method of gyroaccelerometer, only measure the output that gyroaccelerometer is just put (θ=0 °) and is inverted two positions of (θ=180 °), calculate zero degree item error coefficient and error coefficient once, the Coefficient Fitting precision obtaining is lower, the high-precision applications occasion that can not satisfy the demand and pay close attention to the non-linear output of gyroaccelerometer and compensate.

Summary of the invention

The technical problem to be solved in the present invention is, for the deficiencies in the prior art, a kind of gyroaccelerometer multiposition error coefficient scaling method is provided, and this method can reasonably be chosen corresponding optimum testing program according to target error model, thereby obtains the calibration result of degree of precision.

The technical scheme that the present invention solves the problems of the technologies described above employing comprises:

A kind of gyroaccelerometer multiposition error coefficient scaling method, comprises the following steps:

Step 1, determine the error model of gyroaccelerometer

For the gyroaccelerometer application scenario that does not relate to nonlinearity erron, the simplification error model of selecting formula (1) below to represent; For the gyroaccelerometer application scenario that relates to nonlinearity erron, the complete error model of selecting formula (2) below to represent:

y＝k ₀+k _1Xa _X+ε (1)

$y=k_0+k_{1X}{a}_X+k_{1Y}{a}_Y+k_{2X}{a}_X^2+{k_{2X}}^{\′}\left|a_X\right|a_X+k_{2\mathrm{XY}}{a}_X{a}_Y+\mathrm{\ϵ}---\left(2\right)$

In formula above, the output that y is gyroaccelerometer; a _xfor the acceleration input of the sensitive axes along gyroaccelerometer; a _yfor the acceleration input along gyroaccelerometer lateral shaft; k ₀for gyroaccelerometer zero degree item error coefficient; k _1Xfor an once error coefficient of gyroaccelerometer; k _1Yfor an once error coefficient of gyroaccelerometer lateral shaft; k _2Xfor gyroaccelerometer quadratic term error coefficient; k _2X' be the quadratic term coefficient of gyroaccelerometer independent of direction; k _2XYfor gyroaccelerometer transverse coupling quadratic term error coefficient; ε is model residual error;

Step 2, determine calibration brilliance position tumbling test scheme according to the error model of selected gyroaccelerometer

Determine in tumbling test, the precession number of turns that the sensitive axes of angle number of positions N, position, each angle gyroaccelerometer that gyroaccelerometer tilts is bound with respect to the tilt angle theta of gravitational vector and when the output of each angular position measurement gyroaccelerometer, and, θ is in a clockwise direction for just, wherein

For simplification error model, getting N is 1,2,3,4,5,6; θ is correspondingly 0 °, 60 °, 120 °, 180 °, 240 °, 300 °; And the bookbinding number of turns is 3;

For complete error model, getting N is 1,2,3,4,5,6,7,8,9; θ is correspondingly 0 °, 40 °, 80 °, 120 °, 160 °, 200 °, 240 °, 280 °, 320 °; And the bookbinding number of turns is 3;

Step 3, the output of carrying out tumbling test and measuring gyroaccelerometer

Gyroaccelerometer is installed on the dividing head with microtest fixture, makes the input shaft of gyroaccelerometer accurately perpendicular to the rotating shaft of dividing head, the rotating shaft of dividing head is placed in accurate level, and along east-west direction; Gyroaccelerometer with its input shaft direction along local gravity vertical line direction for just putting starting point, be 0 ° of starting point, successively northwards or to the south in vertical plane around the axes of rotation skew upset of dividing head, and for the error model of selected gyroaccelerometer, each position, angle of determining in step 2, the output valve y of measurement gyroaccelerometer;

Step 4, determine every error coefficient of gyroaccelerometer.

Preferably, in described step 3, the output valve y of the gyroaccelerometer measuring is for determining journey clocking value,, the output of gyroaccelerometer, is presented as the size and Orientation of its outer shroud precession acceleration, and bookbinding gyroaccelerometer precession angle is some whole circles, measure gyroaccelerometer this some whole circle time used of precession, calculate thus the size of angular velocity of precession.

Preferably, in described step 3, the output valve y of the gyroaccelerometer measuring is timing ga(u)ge numerical value,, the output of gyroaccelerometer, is presented as the size and Orientation of its outer shroud precession acceleration, the time of bookbinding gyroaccelerometer outer shroud precession, measure the relative angle that in this time period, gyroaccelerometer precession turns over, calculate thus the size of angular velocity of precession.

Preferably, in described step 4, utilize least square method to determine every error coefficient of gyroaccelerometer,, for selected gyroaccelerometer error model, the error model equations simultaneousness of testing under N position is expressed as to matrix form: Y=XK+ η, wherein:

Input vector Y is illustrated in the gyroaccelerometer output valve that position, N angle is tested, Y=(y ₁y ₂y ₃... y _n) ';

Coefficient vector K represents every error coefficient of the corresponding error model of gyroaccelerometer, for simplification error model, and K=(k ₀k _1X), for complete error model K=(k ₀k _1Xk _1Yk _2Xk _2X' k _2XY) ';

X is structure matrix, represents spotting error model and the set of testing angle location schemes information under corresponding tumbling test scheme, wherein,

For simplification error model:

$\left[\begin{array}{cc}1& \cos {\mathrm{\θ}}_1\\ 1& \cos {\mathrm{\θ}}_2\\ 1& \cos {\mathrm{\θ}}_3\\ .& .\\ .& .\\ .& .\\ 1& \cos {\mathrm{\θ}}_N\end{array}\right],$

For complete error model:

$X=\left[\begin{array}{cccccc}1& \cos {\mathrm{\θ}}_1& \sin {\mathrm{\θ}}_1& {\cos }^2{\mathrm{\θ}}_1& \left|\cos {\mathrm{\θ}}_1\right|\cos {\mathrm{\θ}}_1& \cos {\mathrm{\θ}}_1\sin {\mathrm{\θ}}_1\\ 1& \cos {\mathrm{\θ}}_2& \sin {\mathrm{\θ}}_2& {\cos }^2{\mathrm{\θ}}_2& \left|\cos {\mathrm{\θ}}_2\right|\cos {\mathrm{\θ}}_2& \cos {\mathrm{\θ}}_2\sin {\mathrm{\θ}}_2\\ 1& \cos {\mathrm{\θ}}_3& \sin {\mathrm{\θ}}_3& {\cos }^2{\mathrm{\θ}}_3& \left|\cos {\mathrm{\θ}}_3\right|\cos {\mathrm{\θ}}_3& \cos {\mathrm{\θ}}_3\sin {\mathrm{\θ}}_3\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ 1& \cos {\mathrm{\θ}}_N& \sin {\mathrm{\θ}}_N& {\cos }^2{\mathrm{\θ}}_N& \left|\cos {\mathrm{\θ}}_N\right|\cos {\mathrm{\θ}}_N& \cos {\mathrm{\θ}}_N\sin {\mathrm{\θ}}_N\end{array}\right],$

And wherein, θ ₁, θ ₂, θ ₃..., θ _nbe respectively in position, N angle, the sensitive axes of gyroaccelerometer is with respect to the angle of inclination of gravitational vector;

Residual vector η=(ε ₁ε ₂ε ₃... ε _n) ', represent the difference that the output of actual observation equation and error model equation model are exported, ε ₁, ε ₂, ε _nbe respectively gyroaccelerometer and be respectively the model residual error in position, N angle;

Then, computing information matrix A=X'X, correlation matrix C=A', constant term matrix B=X'Y,

Thus, according to the solution of expression formula design factor matrix K below:

For simplification error model,

$K=\left[\begin{array}{c}{k}_0\\ k_{1X}\end{array}\right]=\mathrm{CB}=A^{\′}B={\left(X^{\′}X\right)}^{\′}\left(X^{\′}Y\right)$

For complete error model,

$K=\left[\begin{array}{c}{k}_0\\ k_{1X}\\ k_{1y}\\ k_{2X}\\ {k_{2X}}^{\′}\\ k_{2\mathrm{XY}}\end{array}\right]=\mathrm{CB}=A^{\′}B={\left(X^{\′}X\right)}^{\′}\left(X^{\′}Y\right).$

Compared with prior art, gyroaccelerometer multiposition error coefficient scaling method according to the present invention has useful technique effect: the method can be for different application scenarios, reasonably select different rating test schemes.Not high to accuracy requirement, only need to demarcate linear error term occasion, tests by six location schemes; Higher to accuracy requirement, to pay close attention to gyroaccelerometer nonlinearity erron occasion, test by nine location schemes that increased position, angle, can effectively demarcate the some nonlinearity erron items of gyroaccelerometer, the practical error model of gyroaccelerometer is expanded to six by original two error coefficients, can be used for the error compensation of Navigation And Guidance field to accelerometer, effectively improve the practical precision of navigation and guidance system.

Brief description of the drawings

Fig. 1 is according to the scheme of installation of dividing head and gyroaccelerometer in method of testing of the present invention;

Fig. 2 is the schematic flow sheet according to method of testing of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, gyroaccelerometer multiposition error coefficient scaling method according to the present invention is further described in detail.

Fig. 1 is the scheme of installation of dividing head and gyroaccelerometer in method of testing of the present invention.Tested gyroaccelerometer 3 is installed on high precision precision indexer 1 by gyroaccelerometer dividing head sectional fixture 2.The main shaft of rotation precision indexer 1, just can change the sensitive axes 4 of tested gyroaccelerometer 3 and the direction of lateral shaft 5.In the error model of gyroaccelerometer, sensitive axes 4 and lateral shaft 5 are also done X-axis and Y-axis by note, are embodied in the symbol subscript of each error coefficient and input quantity.

Shown in figure 2, gyroaccelerometer multiposition error coefficient scaling method according to the present invention comprises the following steps:

Step 1, determine the error model of gyroaccelerometer

The error model of gyroaccelerometer comprises following two kinds: formula (1) is simplification error model, not containing nonlinearity erron coefficient; Formula (2) is complete error model, contains second nonlinear error coefficient.For the gyroaccelerometer application scenario that does not relate to nonlinearity erron, the simplification error model of selecting formula (1) below to represent; For the gyroaccelerometer application scenario that relates to nonlinearity erron, the complete error model of selecting formula (2) below to represent:

y＝k ₀+k _1Xa _X+ε(1)

$y=k_0+k_{1X}{a}_X+k_{1Y}{a}_Y+k_{2X}{a}_X^2+{k_{2X}}^{\′}\left|a_X\right|a_X+k_{2\mathrm{XY}}{a}_X{a}_Y+\mathrm{\ϵ}---\left(2\right)$

In above formula, the physical meaning of every symbol is as follows:

Y: the output of gyroaccelerometer;

A _x, a _y: respectively along the sensitive axes of gyroaccelerometer and the input of the acceleration of lateral shaft;

K ₀: gyroaccelerometer zero degree item error coefficient;

K _1X: gyroaccelerometer is an error coefficient once;

K _1Y: gyroaccelerometer lateral shaft is an error coefficient once;

K _2X: gyroaccelerometer quadratic term error coefficient;

K _2X': the quadratic term coefficient of gyroaccelerometer independent of direction;

K _2XY: gyroaccelerometer transverse coupling quadratic term error coefficient;

ε: model residual error;

Step 2: determine calibration brilliance position tumbling test scheme according to the error model of selected gyroaccelerometer

In this step, tumbling test scheme to the effect that determine three variablees, that is: in tumbling test, need the sensitive axes of angle number of positions N that given tested gyroaccelerometer tilts, position, each angle gyroaccelerometer to be bound the precession number of turns with respect to the tilt angle theta of gravitational vector (clockwise direction by just) and when the output of each angular position measurement gyroaccelerometer.Wherein, simplification error model is demarcated to the scheme shown in table 1 below that adopts, complete error model is demarcated to the scheme shown in table 2 below that adopts:

Table 1

Table 2

Angle number of positions N determines, its foundation is to carry out optimizing according to the character of " D-optimum " in optimal design theory to obtain.Given because of subregion on, can know by derivation, the acquisition of D-optimal plan is equivalent to the size of the determinant of its information matrix of research A, the size of determinant just can illustrate the height of plans on estimation accuracy.For different discrete test plan ε (N), in given factor space, make testing program (the wherein information matrix A=X'X of the determinant maximum of its information matrix A, X is structure matrix corresponding to test plan), be exactly the D-optimal case in this factor space, by the value d=|detA (ε (N)) of determinant | as the objective function of testing program optimizing problem.Can calculate, along with the increase of N, the size of information matrix determinant d value is the growth of approximate index, illustrates that the estimation accuracy of test plan will increase gradually along with the increasing of location point.But operate the requirement to test efficiency according to Practical Project, not only wish that the d value of testing program wants large, also the number N of desired location will try one's best less and be economical, increase and under the fringe cost bringing, obtain as far as possible many precision and gather in the crops paying position.Be testing program under the prerequisite that meets separation coefficient, 1 position of the every increase of N, quantity of information d that information matrix A comprises increases should be faster.Therefore, above test design principle can be derived and be obtained, in the time of N=6, testing program meets simultaneously positive and negative maximum input, positive and negative left and right, position, testing site symmetrical, the higher valuation degree of confidence of regression equation degree of freedom advantages of higher between two, is the optimal selection of demarcating low order Modulus Model; Along with the continuation of positional number increases, in the time of N=9, optimizing function is obtained maximal phase to recruitment, and along with the increase relative variation of N reduces rapidly, this shows in the time that test plan is increased to 9 schemes from 6 schemes, the multiple maximum that information matrix quantity of information increases.Therefore consider, positional number is to demarcate the optimal test scheme of simplification error model in N=6 value, and positional number is the most economical testing program of demarcating complete error model in N=9 value.

Determining of the tilt angle theta of each angle position gyro accelerometer sensitive axle relative gravity vector, it,, according to being the homogeneity principle of test design, carries out N decile according to dividing head being returned circle 360 °.

Step 3: the output of carrying out tumbling test and measuring gyroaccelerometer

Gyroaccelerometer to be measured is arranged on the dividing head with microtest fixture, the input shaft of the accuracy guarantee gyroaccelerometer by test fixture is accurately perpendicular to the rotating shaft of dividing head, make it to be placed in accurate horizontal level by closing as the rotating shaft of spirit-leveling instrument adjustment dividing head, and along east-west direction; Gyroaccelerometer with its input shaft direction along local gravity vertical line direction for just putting starting point (, 0 °), successively northwards or to the south in vertical plane around the axes of rotation skew upset of dividing head, and for the error model of selected gyroaccelerometer, the output valve y of gyroaccelerometer is measured in each position, angle of determining in above-mentioned steps two.

The output valve y of gyroaccelerometer determines journey clocking value,, the output of gyroaccelerometer, be presented as the size and Orientation of its outer shroud precession acceleration, bookbinding gyroaccelerometer precession angle is some whole circles, measure gyroaccelerometer this some whole circle time used of precession, calculate thus the size of angular velocity of precession.The output valve y of gyroaccelerometer can be also timing ga(u)ge numerical value,, the output of gyroaccelerometer, be presented as the size and Orientation of its outer shroud precession acceleration, the time of bookbinding gyroaccelerometer outer shroud precession, measure the relative angle that in this time period, gyroaccelerometer precession turns over, calculate thus the size of angular velocity of precession.

Step 4: every error coefficient of determining gyroaccelerometer

Every error coefficient of gyroaccelerometer can return the every error coefficient that obtains gyroaccelerometer by least square method

For selected gyroaccelerometer error model, the error model equations simultaneousness of testing is expressed as to matrix form: Y=XK+ η under N position;

Wherein:

(1) input vector Y=(y ₁y ₂y ₃... y _n) ', the gyroaccelerometer output valve of testing in position, N angle;

(2) coefficient vector K is every error coefficient of the corresponding error model of gyroaccelerometer, for simplification error model, and K=(k ₀k _1X), for complete error model K=(k ₀k _1Xk _1Yk _2Xk _2X' k _2XY) ';

(3) X is structure matrix, represents spotting error model and the set of testing angle location schemes information under corresponding tumbling test scheme, wherein, and for simplification error model,

$\left[\begin{array}{cc}1& \cos {\mathrm{\θ}}_1\\ 1& \cos {\mathrm{\θ}}_2\\ 1& \cos {\mathrm{\θ}}_3\\ .& .\\ .& .\\ .& .\\ 1& \cos {\mathrm{\θ}}_N\end{array}\right],$

And for complete error model,

$X=\left[\begin{array}{cccccc}1& \cos {\mathrm{\θ}}_1& \sin {\mathrm{\θ}}_1& {\cos }^2{\mathrm{\θ}}_1& \left|\cos {\mathrm{\θ}}_1\right|\cos {\mathrm{\θ}}_1& \cos {\mathrm{\θ}}_1\sin {\mathrm{\θ}}_1\\ 1& \cos {\mathrm{\θ}}_2& \sin {\mathrm{\θ}}_2& {\cos }^2{\mathrm{\θ}}_2& \left|\cos {\mathrm{\θ}}_2\right|\cos {\mathrm{\θ}}_2& \cos {\mathrm{\θ}}_2\sin {\mathrm{\θ}}_2\\ 1& \cos {\mathrm{\θ}}_3& \sin {\mathrm{\θ}}_3& {\cos }^2{\mathrm{\θ}}_3& \left|\cos {\mathrm{\θ}}_3\right|\cos {\mathrm{\θ}}_3& \cos {\mathrm{\θ}}_3\sin {\mathrm{\θ}}_3\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ 1& \cos {\mathrm{\θ}}_N& \sin {\mathrm{\θ}}_N& {\cos }^2{\mathrm{\θ}}_N& \left|\cos {\mathrm{\θ}}_N\right|\cos {\mathrm{\θ}}_N& \cos {\mathrm{\θ}}_N\sin {\mathrm{\θ}}_N\end{array}\right],$

Wherein, θ ₁, θ ₂, θ ₃..., θ _nbe respectively in position, N angle, the sensitive axes of gyroaccelerometer is with respect to the angle of inclination of gravitational vector;

(4) residual vector η=(ε ₁ε ₂ε ₃... ε _n) ', represent the difference that the output of actual observation equation and error model equation model are exported, wherein, ε ₁, ε ₂, ε _nbe respectively gyroaccelerometer and be respectively the model residual error in position, N angle

Solving by the method for least-squares estimation of error coefficient is calculated as follows:

First calculate three kinds of intermediate quantities: information matrix, correlation matrix and constant term matrix:

Information matrix A=X'X

Correlation matrix C=A'

Constant term matrix B=X'Y

After intermediate quantity has been calculated, solve the solution of matrix of coefficients K by following formula:

For simplification error model, $K=\left[\begin{array}{c}{k}_0\\ k_{1X}\end{array}\right]=\mathrm{CB}=A^{\′}B={\left(X^{\′}X\right)}^{\′}\left(X^{\′}Y\right)$

For complete error model, $K=\left[\begin{array}{c}{k}_0\\ k_{1X}\\ k_{1y}\\ k_{2X}\\ {k_{2X}}^{\′}\\ k_{2\mathrm{XY}}\end{array}\right]=\mathrm{CB}=A^{\′}B={\left(X^{\′}X\right)}^{\′}\left(X^{\′}Y\right).$

By mode above, can determine every error coefficient of gyroaccelerometer, complete thus the demarcation of gyroaccelerometer multiposition error coefficient.

Illustrate the process of determining every error coefficient of gyroaccelerometer by least square method below.

For nine position measurements for complete error model, be correspondingly 0 °, 40 °, 80 °, 120 °, 160 °, 200 °, 240 °, 280 °, 320 ° according to θ and carry out tumbling test, the test value that obtains gyroaccelerometer in each position is:

$Y=\left(\begin{array}{c}493.997\\ 378.519\\ 85.906\\ -246.919\\ -464.231\\ -464.341\\ -247.199\\ 85.586\\ 378.313\end{array}\right)$

The structure matrix X of nine position tests

$X=\left[\begin{array}{cccccc}1& \cos {\mathrm{\θ}}_1& \sin {\mathrm{\θ}}_1& {\cos }^2{\mathrm{\θ}}_1& \left|\cos {\mathrm{\θ}}_1\right|\cos {\mathrm{\θ}}_1& \cos {\mathrm{\θ}}_1\sin {\mathrm{\θ}}_1\\ 1& \cos {\mathrm{\θ}}_2& \sin {\mathrm{\θ}}_2& {\cos }^2{\mathrm{\θ}}_2& \left|\cos {\mathrm{\θ}}_2\right|\cos {\mathrm{\θ}}_2& \cos {\mathrm{\θ}}_2\sin {\mathrm{\θ}}_2\\ 1& \cos {\mathrm{\θ}}_3& \sin {\mathrm{\θ}}_3& {\cos }^2{\mathrm{\θ}}_3& \left|\cos {\mathrm{\θ}}_3\right|\cos {\mathrm{\θ}}_3& \cos {\mathrm{\θ}}_3\sin {\mathrm{\θ}}_3\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ 1& \cos {\mathrm{\θ}}_N& \sin {\mathrm{\θ}}_N& {\cos }^2{\mathrm{\θ}}_N& \left|\cos {\mathrm{\θ}}_N\right|\cos {\mathrm{\θ}}_N& \cos {\mathrm{\θ}}_N\sin {\mathrm{\θ}}_N\end{array}\right]$

θ in formula ₁=0 °; θ ₂=40 °; θ ₃=80 °; θ ₄=120 °; θ ₅=160 °; θ ₆=200 °; θ ₇=240 °; θ ₈=280 °; θ ₉=320 °;

By the formula that solves of above-mentioned known quantity substitution matrix of coefficients K, obtain:

$K=\left[\begin{array}{c}{k}_0\\ k_{1X}\\ k_{1y}\\ k_{2X}\\ {k_{2X}}^{\′}\\ k_{2\mathrm{XY}}\end{array}\right]=\mathrm{CB}=A^{\′}B={\left(X^{\′}X\right)}^{\′}\left(X^{\′}Y\right)=\left[\begin{array}{c}-0.041212\\ 494.034482\\ 0.161891\\ 0.000335\\ 0.005100\\ -0.000137\end{array}\right],$ Solution obtains the value of 6 error coefficients in error model.

At this, it should be noted that, the content of not describing in detail in this instructions, is that description and the prior art that those skilled in the art pass through in this instructions can realize, and therefore, does not repeat.

The foregoing is only the preferred embodiments of the present invention, be not used for limiting the scope of the invention.For a person skilled in the art, do not paying under the prerequisite of creative work, can make some amendments and replacement to the present invention, within all such modifications and replacement all should be encompassed in protection scope of the present invention.

Claims (4)

1. a gyroaccelerometer multiposition error coefficient scaling method, is characterized in that, comprises the following steps:

Step 1, determine the error model of gyroaccelerometer

For the gyroaccelerometer application scenario that does not relate to nonlinearity erron, the simplification error model of selecting formula (1) below to represent; For the gyroaccelerometer application scenario that relates to nonlinearity erron, the complete error model of selecting formula (2) below to represent:

y＝k ₀+k _1Xa _X+ε (1)

$y=k_0+k_{1X}{a}_X+k_{1Y}{a}_Y+k_{2X}{a}_X^2+{k_{2X}}^{\′}\left|a_X\right|a_X+k_{2\mathrm{XY}}{a}_X{a}_Y+\mathrm{\ϵ}---\left(2\right)$

In formula above, the output that y is gyroaccelerometer; a _xfor the acceleration input of the sensitive axes along gyroaccelerometer; a _yfor the acceleration input along gyroaccelerometer lateral shaft; k ₀for gyroaccelerometer zero degree item error coefficient; k _1Xfor an once error coefficient of gyroaccelerometer; k _1Yfor an once error coefficient of gyroaccelerometer lateral shaft; k _2Xfor gyroaccelerometer quadratic term error coefficient; k _2X' be the quadratic term coefficient of gyroaccelerometer independent of direction; k _2XYfor gyroaccelerometer transverse coupling quadratic term error coefficient; ε is model residual error;

Step 2, determine calibration brilliance position tumbling test scheme according to the error model of selected gyroaccelerometer

Determine in tumbling test, the precession number of turns that the sensitive axes of angle number of positions N, position, each angle gyroaccelerometer that gyroaccelerometer tilts is bound with respect to the tilt angle theta of gravitational vector and when the output of each angular position measurement gyroaccelerometer, and, θ is in a clockwise direction for just, wherein

For simplification error model, getting N is 1,2,3,4,5,6; θ is correspondingly 0 °, 60 °, 120 °, 180 °, 240 °, 300 °; And the bookbinding number of turns is 3;

For complete error model, getting N is 1,2,3,4,5,6,7,8,9; θ is correspondingly 0 °, 40 °, 80 °, 120 °, 160 °, 200 °, 240 °, 280 °, 320 °; And the bookbinding number of turns is 3;

Step 3, the output of carrying out tumbling test and measuring gyroaccelerometer

Gyroaccelerometer is installed on the dividing head with microtest fixture, makes the input shaft of gyroaccelerometer accurately perpendicular to the rotating shaft of dividing head, the rotating shaft of dividing head is placed in accurate level, and along east-west direction; Gyroaccelerometer with its input shaft direction along local gravity vertical line direction for just putting starting point, be 0 ° of starting point, successively northwards or to the south in vertical plane around the axes of rotation skew upset of dividing head, and for the error model of selected gyroaccelerometer, each position, angle of determining in step 2, the output valve y of measurement gyroaccelerometer;

Step 4, determine every error coefficient of gyroaccelerometer.

2. gyroaccelerometer multiposition error coefficient scaling method according to claim 1, it is characterized in that, in described step 3, the output valve y of the gyroaccelerometer measuring is for to determine journey clocking value, that is, and and the output of gyroaccelerometer, be presented as the size and Orientation of its outer shroud precession acceleration, bookbinding gyroaccelerometer precession angle is some whole circles, measures gyroaccelerometer this some whole circle time used of precession, calculates thus the size of angular velocity of precession.

3. gyroaccelerometer multiposition error coefficient scaling method according to claim 1, it is characterized in that, in described step 3, the output valve y of the gyroaccelerometer measuring is timing ga(u)ge numerical value, that is, and and the output of gyroaccelerometer, be presented as the size and Orientation of its outer shroud precession acceleration, the time of bookbinding gyroaccelerometer outer shroud precession, measure the relative angle that in this time period, gyroaccelerometer precession turns over, calculate thus the size of angular velocity of precession.

4. gyroaccelerometer multiposition error coefficient scaling method according to claim 1, it is characterized in that, in described step 4, utilize least square method to determine every error coefficient of gyroaccelerometer,, for selected gyroaccelerometer error model, the error model equations simultaneousness of testing under N position is expressed as to matrix form: Y=XK+ η, wherein:

Input vector Y is illustrated in the gyroaccelerometer output valve that position, N angle is tested, Y=(y ₁y ₂y ₃... y _n) ';

Coefficient vector K represents every error coefficient of the corresponding error model of gyroaccelerometer, for simplification error model, and K=(k ₀k _1X), for complete error model K=(k ₀k _1Xk _1Yk _2Xk _2X' k _2XY) ';

X is structure matrix, represents spotting error model and the set of testing angle location schemes information under corresponding tumbling test scheme, wherein,

For simplification error model:

$\left[\begin{array}{cc}1& \cos {\mathrm{\θ}}_1\\ 1& \cos {\mathrm{\θ}}_2\\ 1& \cos {\mathrm{\θ}}_3\\ .& .\\ .& .\\ .& .\\ 1& \cos {\mathrm{\θ}}_N\end{array}\right],$

For complete error model:

$X=\left[\begin{array}{cccccc}1& \cos {\mathrm{\θ}}_1& \sin {\mathrm{\θ}}_1& {\cos }^2{\mathrm{\θ}}_1& \left|\cos {\mathrm{\θ}}_1\right|\cos {\mathrm{\θ}}_1& \cos {\mathrm{\θ}}_1\sin {\mathrm{\θ}}_1\\ 1& \cos {\mathrm{\θ}}_2& \sin {\mathrm{\θ}}_2& {\cos }^2{\mathrm{\θ}}_2& \left|\cos {\mathrm{\θ}}_2\right|\cos {\mathrm{\θ}}_2& \cos {\mathrm{\θ}}_2\sin {\mathrm{\θ}}_2\\ 1& \cos {\mathrm{\θ}}_3& \sin {\mathrm{\θ}}_3& {\cos }^2{\mathrm{\θ}}_3& \left|\cos {\mathrm{\θ}}_3\right|\cos {\mathrm{\θ}}_3& \cos {\mathrm{\θ}}_3\sin {\mathrm{\θ}}_3\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ 1& \cos {\mathrm{\θ}}_N& \sin {\mathrm{\θ}}_N& {\cos }^2{\mathrm{\θ}}_N& \left|\cos {\mathrm{\θ}}_N\right|\cos {\mathrm{\θ}}_N& \cos {\mathrm{\θ}}_N\sin {\mathrm{\θ}}_N\end{array}\right],$

And wherein, θ ₁, θ ₂, θ ₃..., θ _nbe respectively in position, N angle, the sensitive axes of gyroaccelerometer is with respect to the angle of inclination of gravitational vector;

Residual vector η=(ε ₁ε ₂ε ₃... ε _n) ', represent the difference that the output of actual observation equation and error model equation model are exported, ε ₁, ε ₂, ε _nbe respectively gyroaccelerometer and be respectively the model residual error in position, N angle;

Then, computing information matrix A=X'X, correlation matrix C=A', constant term matrix B=X'Y,

Thus, according to the solution of expression formula design factor matrix K below:

For simplification error model,

$K=\left[\begin{array}{c}{k}_0\\ k_{1X}\end{array}\right]=\mathrm{CB}=A^{\′}B={\left(X^{\′}X\right)}^{\′}\left(X^{\′}Y\right)$

For complete error model,

$K=\left[\begin{array}{c}{k}_0\\ k_{1X}\\ k_{1y}\\ k_{2X}\\ {k_{2X}}^{\′}\\ k_{2\mathrm{XY}}\end{array}\right]=\mathrm{CB}=A^{\′}B={\left(X^{\′}X\right)}^{\′}\left(X^{\′}Y\right).$