CN103941042B - A kind of gyroaccelerometer multiposition error coefficient scaling method - Google Patents

Abstract

The invention discloses a kind of gyroaccelerometer multiposition error coefficient scaling method, for the demarcation of gyroaccelerometer error coefficient, comprising: the error model selecting gyroaccelerometer; According to the error model determination dividing head Angle Position tumbling test scheme of selected gyroaccelerometer; Carry out tumbling test and measure the output of gyroaccelerometer; Determine every error coefficient of gyroaccelerometer.In method of the present invention, adopt dividing head six position tumbling test to demarcate gyroaccelerometer simplification error model, adopt dividing head nine position tumbling test to demarcate gyroaccelerometer complete error model, can for different application scenarios, reasonably select different rating test schemes, can be used for the error compensation of Navigation And Guidance field to accelerometer, effectively improve the practical precision of navigation and guidance system.

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 Aeronautics and Astronautics, the navigation navigation demarcation of gyroaccelerometer and detection technique field.

Background technology

In order to the numerical value of each error coefficient of Accurate Calibration gyroaccelerometer mathematical model, feasible scaling method is in gravity field, carry out multipoint inclination tumbling test.This test uses the precision indexer with test fixture to test usually, is arranged on test fixture by tested gyroaccelerometer, 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 degree, and along east-west direction.Gyroaccelerometer with input shaft direction along local gravity vertical line direction for just to put starting point (0 °), northwards or southwards overturn around the axes of rotation skew of dividing head in vertical plane successively, and measure the output of gyroaccelerometer in pre-determined multiple Angle Position place.In earth gravity field, acceleration input direction, the size of each set angle position are different, by the excitation of the different size acceleration of gravity input in these Angle Position places, can solve the solution of each error coefficient.

For the demarcation of accelerometer, the difference of rating test Angle Position scheme, determining can the number of calibrated error coefficient and stated accuracy.The existing scaling method of gyroaccelerometer, only measure the output that gyroaccelerometer just puts two positions of (θ=0 °) and inversion (θ=180 °), calculate zero degree item error coefficient and once item error coefficient, the Coefficient Fitting precision obtained is lower, can not satisfy the demand and pay close attention to gyroaccelerometer nonlinear object and the high-precision applications occasion compensated.

Summary of the invention

The technical problem to be solved in the present invention is, for the deficiencies in the prior art, there is provided a kind of gyroaccelerometer multiposition error coefficient scaling method, this method can reasonably choose corresponding optimum testing program according to target error model, thus 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 one, determine the error model of gyroaccelerometer

For the gyroaccelerometer application scenario not relating to nonlinearity erron, select the simplification error model that formula (1) below represents; For the gyroaccelerometer application scenario relating to nonlinearity erron, select the complete error model that formula (2) below represents:

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

Step 2, error model determination dividing head Angle Position tumbling test scheme according to selected gyroaccelerometer

Determine in tumbling test, the Angle Position quantity N that gyroaccelerometer tilts, the sensitive axes of each Angle Position place gyroaccelerometer are relative to the tilt angle theta of gravitational vector and the precession number of turns of binding when the output of each angular position measurement gyroaccelerometer, and, θ is just in a clockwise direction, wherein

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

Step 3, carry out tumbling test and measure the output of gyroaccelerometer

Be installed to by gyroaccelerometer on the dividing head with microtest fixture, make the input shaft of gyroaccelerometer accurately perpendicular to the rotating shaft of dividing head, the rotating shaft of dividing head is placed in accurate degree, and along east-west direction; Gyroaccelerometer with its input shaft direction along local gravity vertical line direction for just to put starting point, be 0 ° of starting point, northwards or southwards overturn around the axes of rotation skew of dividing head in vertical plane successively, and for the error model of selected gyroaccelerometer, each Angle Position place determined in step 2, measures the output valve y of gyroaccelerometer;

Step 4, determine every error coefficient of gyroaccelerometer.

Preferably, in described step 3, measure the output valve y of the gyroaccelerometer obtained for determine journey clocking value, namely, 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 the time that this some whole circle of gyroaccelerometer precession is used, calculate the size of angular velocity of precession thus.

Preferably, in described step 3, the output valve y measuring the gyroaccelerometer obtained is time counter value, namely, 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 the size of angular velocity of precession thus.

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

Input vector Y represents the gyroaccelerometer output valve of testing at N number of Angle Position place, 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 the set of spotting error model and test Angle Position scheme 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 at N number of Angle Position place, the sensitive axes of gyroaccelerometer is relative to the angle of inclination of gravitational vector;

Residual vector η=(ε ₁ε ₂ε ₃... ε _n) ', represent the difference that actual observation equation exports and error model equation model exports, ε ₁, ε ₂, ε _nbe respectively gyroaccelerometer and be respectively model residual error at N number of Angle Position place;

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 for different application scenarios, can reasonably select different rating test schemes.Not high to accuracy requirement, only need the occasion of demarcating linear error term, test by six location schemes; Higher to accuracy requirement, to pay close attention to gyroaccelerometer nonlinearity erron occasion, test by nine location schemes adding Angle Position, effectively can 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.

Accompanying drawing explanation

Fig. 1 is the scheme of installation according to 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.Rotate the main shaft of 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 denoted as X-axis and Y-axis, 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 one, 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, containing second nonlinear error coefficient.For the gyroaccelerometer application scenario not relating to nonlinearity erron, select the simplification error model that formula (1) below represents; For the gyroaccelerometer application scenario relating to nonlinearity erron, select the complete error model that formula (2) below represents:

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 acceleration input of lateral shaft;

K ₀: gyroaccelerometer zero degree item error coefficient;

K _1X: gyroaccelerometer is item error coefficient once;

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

K _2X: gyroaccelerometer method for quadratic term error coefficient;

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

K _2XY: gyroaccelerometer transverse coupling method for quadratic term error coefficient;

ε: model residual error;

Step 2: according to the error model determination dividing head Angle Position tumbling test scheme of selected gyroaccelerometer

In this step, tumbling test scheme to the effect that determine three variablees, that is: the Angle Position quantity N needing given tested gyroaccelerometer to tilt in tumbling test, the sensitive axes of each Angle Position place gyroaccelerometer relative to gravitational vector tilt angle theta (clockwise direction by just) and bound the precession number of turns when the output of each angular position measurement gyroaccelerometer.Wherein, carry out simplification error model demarcating the scheme shown in table 1 adopted below, carry out complete error model demarcating the scheme shown in table 2 adopted below:

Table 1

Table 2

The determination of Angle Position quantity N, its foundation carrys out optimizing according to the character of " D-is optimum " in optimal design theory to obtain.On given region, can be known by derivation, the acquisition of D-optimal plan is equivalent to the size of the determinant of its information matrix of research A, and the size of determinant just can illustrate the height of plans on estimation accuracy.Namely for different discrete test plan ε (N), in given factor space, testing program (the wherein information matrix A=X'X making the determinant of its information matrix A maximum, 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 optimization problem.Can calculate, along with the increase of N, the growth of size in approximate index of information matrix determinant d value, namely increasing along with location point be described, the estimation accuracy of test plan will increase gradually.But according to the requirement of Practical Project operation to test efficiency, 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 economical, to obtain how precision as far as possible under the fringe cost brought is increased in position and gather in the crops paying.Namely testing program is under the prerequisite meeting separation coefficient, and N often increases by 1 position, and the quantity of information d that information matrix A comprises increases should be faster.Therefore, above test design principle can be derived and be obtained, as N=6, testing program meets simultaneously positive and negative maximum input, positive and negative left and right, position, testing site symmetrical, regression equation degree of freedom higher valuation degree of confidence advantages of higher between two, is the optimal selection of demarcating lower-degree coefficient model; Along with the continuation of positional number increases, as N=9, optimizing function obtains maximum relative increase, and reduces rapidly along with the increase relative variation of N, this shows when test plan is increased to 9 schemes from 6 schemes, and the multiple that information matrix quantity of information increases is maximum.Therefore consider, positional number is 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.

The determination of the tilt angle theta of each Angle Position gyroaccelerometer sensitive axes relative gravity vector, it, according to the homogeneity principle being test design, carries out N decile according to being returned by dividing head to circle 360 °.

Step 3: carry out tumbling test and measure the output of gyroaccelerometer

Gyroaccelerometer to be measured is arranged on the dividing head of band microtest fixture, by the input shaft of the accuracy guarantee gyroaccelerometer of test fixture accurately perpendicular to the rotating shaft of dividing head, make it to be placed in accurate degree position by the rotating shaft of closing as 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 to put starting point (namely, 0 °), northwards or southwards overturn around the axes of rotation skew of dividing head in vertical plane successively, and for the error model of selected gyroaccelerometer, the output valve y of gyroaccelerometer is measured at each Angle Position place determined in above-mentioned steps two.

The output valve y of gyroaccelerometer determines journey clocking value, namely, 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 the time that this some whole circle of gyroaccelerometer precession is used, calculate the size of angular velocity of precession thus.The output valve y of gyroaccelerometer also can be time counter value, namely, 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 the size of angular velocity of precession thus.

Step 4: the every error coefficient determining gyroaccelerometer

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

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

Wherein:

(1) input vector Y=(y ₁y ₂y ₃... y _n) ', namely in the gyroaccelerometer output valve that N number of Angle Position place tests;

(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 the set of spotting error model and test Angle Position scheme information under corresponding tumbling test scheme, wherein, for simplification error model,

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

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 at N number of Angle Position place, the sensitive axes of gyroaccelerometer is relative to the angle of inclination of gravitational vector;

(4) residual vector η=(ε ₁ε ₂ε ₃... ε _n) ', represent the difference that actual observation equation exports and error model equation model exports, wherein, ε ₁, ε ₂, ε _nbe respectively gyroaccelerometer and be respectively model residual error at N number of Angle Position place

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

First three kinds of intermediate quantities are calculated: 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 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, every error coefficient of gyroaccelerometer can be determined, complete the demarcation of gyroaccelerometer multiposition error coefficient thus.

Illustrate the process of the every error coefficient with least square method determination gyroaccelerometer 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 obtaining 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 °;

What above-mentioned known quantity is substituted into matrix of coefficients K solves formula, obtains:

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

At this, it should be noted that, the content do not described in detail in this instructions, be that those skilled in the art can be realized by the description in this instructions and prior art, therefore, do 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, under the prerequisite not paying creative work, can make some amendments and replacement to the present invention, all such modifications and replacement all should be encompassed within protection scope of the present invention.

Claims (4)

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

Step one, determine the error model of gyroaccelerometer

For the gyroaccelerometer application scenario not relating to nonlinearity erron, select the simplification error model that formula (1) below represents; For the gyroaccelerometer application scenario relating to nonlinearity erron, select the complete error model that formula (2) below represents:

y＝k ₀+k _1Xa _X+ε(1)

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

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

Step 2, error model determination dividing head Angle Position tumbling test scheme according to selected gyroaccelerometer

Determine in tumbling test, the Angle Position quantity N that gyroaccelerometer tilts, the sensitive axes of each Angle Position place gyroaccelerometer are relative to the tilt angle theta of gravitational vector and the precession number of turns of binding when the output of each angular position measurement gyroaccelerometer, and, θ is just in a clockwise direction, wherein

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

Step 3, carry out tumbling test and measure the output of gyroaccelerometer

Be installed to by gyroaccelerometer on the dividing head with microtest fixture, make the input shaft of gyroaccelerometer accurately perpendicular to the rotating shaft of dividing head, the rotating shaft of dividing head is placed in accurate degree, and along east-west direction; Gyroaccelerometer with its input shaft direction along local gravity vertical line direction for just to put starting point, be 0 ° of starting point, northwards or southwards overturn around the axes of rotation skew of dividing head in vertical plane successively, and for the error model of selected gyroaccelerometer, each Angle Position place determined in step 2, measures the output valve y of gyroaccelerometer;

Step 4, determine every error coefficient of gyroaccelerometer to comprise k ₀, k _1X, k _1Y, k _2X, k _2X' and k _2XY.

2. gyroaccelerometer multiposition error coefficient scaling method according to claim 1, it is characterized in that, in described step 3, measure the output valve y of the gyroaccelerometer obtained for determine journey clocking value, that is, 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 the time that this some whole circle of gyroaccelerometer precession is used, calculates the size of angular velocity of precession thus.

3. gyroaccelerometer multiposition error coefficient scaling method according to claim 1, it is characterized in that, in described step 3, the output valve y measuring the gyroaccelerometer obtained is time counter value, that is, 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 the size of angular velocity of precession thus.

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

Input vector Y represents the gyroaccelerometer output valve of testing at N number of Angle Position place, 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 the set of spotting error model and test Angle Position scheme information under corresponding tumbling test scheme, wherein,

For simplification error model:

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

For complete error model:

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

And wherein, θ ₁, θ ₂, θ ₃..., θ _nbe respectively at N number of Angle Position place, the sensitive axes of gyroaccelerometer is relative to the angle of inclination of gravitational vector;

Residual vector η=(ε ₁ε ₂ε ₃... ε _n) ', represent the difference that actual observation equation exports and error model equation model exports, ε ₁, ε ₂, ε _nbe respectively gyroaccelerometer and be respectively model residual error at N number of Angle Position place;

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,

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

For complete error model,

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