CN1818555A - Microinertia measuring unit precisive calibration for installation fault angle and rating factor decoupling - Google Patents

Abstract

An accurate calibration method of micro inertia measuring unit by decoupling erection error angle (EEA)with scale factor includes setting up MIMU integral error model and separating couple between EEA of accelerometer and gyroscope and scale factor ,using position error canceling method to calculate out and to separate out scale factor and EEA of accelerometer as well as using least square method and iteration method to calculate out EEA of gyroscope and its relative error items in 10 position static calibration test and in 3 direction positive and negative rate test ,then using interpolation method to calculate out scale factor of gyroscope .

Description

The micro inertial measurement unit method for precisely marking of alignment error angle and constant multiplier decoupling zero

Technical field

The present invention relates to the MIMU method for precisely marking of a kind of alignment error angle and constant multiplier decoupling zero, be used for calculating the every error coefficient of MIMU global error model, be specially adapted to have the MIMU demarcation at big alignment error angle, this method is equally applicable to flexure gyroscope Inertial Measurement Unit (IMU) and liquid floated gyroscope IMU.

Background technology

The MIMU that is made up of the micro-electro-mechanical gyroscope and the accelerometer of three quadrature settings is the core component of micro-inertial navigation system, its precision has determined the navigation accuracy of micro-inertial navigation system, therefore deterministic systematic error accounts for about 90% of total error in the MIMU error source, deterministic systematic error is separated, demarcates, is compensated raising MIMU precision is had decisive role.

Traditional scaling method is adopted in the demarcation of MIMU at present substantially, mainly comprises several methods such as multiposition static demarcating, dynamic rate demarcation and sound mixed calibration.Wherein static demarcating is to utilize terrestrial gravitation acceleration and earth rotation angular speed to find the solution the MIMU error coefficient at each component, this method comprises multiple scaling methods such as 12 positions, 24 positions, can accurately demarcate accelerometer error coefficient among the MIMU, but gyrostatic stated accuracy is very low; The dynamic rate scaling method has improved gyrostatic error calibration precision among the MIMU, but can only calibrate the fractional error coefficient; That the sound mixed calibration method has overcome is quiet, the deficiency of moving two kinds of scaling methods, can not only calibrate all error coefficients, has improved stated accuracy simultaneously, becomes present MIMU and demarcates main flow direction.

Existing sound mixed calibration method has been widely used in the demarcation of MIMU, all is based on the existing error modelling, and angular velocity channel error model is in the existing MIMU error model:

${\stackrel{\‾}{\mathrm{\ω}}}_x=K_{x1}{\mathrm{\ω}}_x+K_{x2}{\mathrm{\ω}}_x^2+M_{\mathrm{xy}}{\mathrm{\ω}}_y+M_{\mathrm{xz}}{\mathrm{\ω}}_z+D_x+D_{\mathrm{xx}}{f}_x+D_{\mathrm{xy}}{f}_y+D_{\mathrm{xz}}{f}_z$

${\stackrel{\‾}{\mathrm{\ω}}}_y=K_{y1}{\mathrm{\ω}}_y+K_{y2}{\mathrm{\ω}}_y^2+M_{\mathrm{yx}}{\mathrm{\ω}}_x+M_{\mathrm{yz}}{\mathrm{\ω}}_z+D_y+D_{\mathrm{yx}}{f}_x+D_{\mathrm{yy}}{f}_y+D_{\mathrm{yz}}{f}_z$

${\stackrel{\‾}{\mathrm{\ω}}}_z=K_{z1}{\mathrm{\ω}}_z+K_{z2}{\mathrm{\ω}}_z^2+M_{\mathrm{zx}}{\mathrm{\ω}}_x+M_{\mathrm{zy}}{\mathrm{\ω}}_y+D_z+D_{\mathrm{zx}}{f}_x+D_{\mathrm{zy}}{f}_y+D_{\mathrm{zz}}{f}_z)$

ω wherein _x, ω _yAnd ω _zRepresent the analog voltage of x among the MIMU, y, the output of z axle gyroscope respectively; ω _x, ω _yAnd ω _zRepresent the actual angular speed of x, y, the input of z axle respectively; K _T1, K _T2Be respectively gyroscope constant multiplier once item and quadratic term; M _Yx, M _Xz, M _ZxBe the alignment error item; D _x, D _y, D _zRepresent x, y, z axle gyroscope often to be worth biasing; D _IjRepresent output of i axle gyroscope and the relevant error term of j axial ratio power; f _x, f _yAnd f _zRepresent the actual specific force of x, y, the input of z axle respectively.Acceleration channel error model is in the existing MIMU error model:

f _x＝k _ax(f _x+B _x+I _xyf _y+I _xyf _z)

f _y＝k _ay(f _y+B _y+I _yxf _x+I _yzf _z)

f _z＝k _az(f _z+B _z+I _zyf _y+I _zxf _x)

F wherein _x, f _yAnd f _zRepresent the analog voltage of x among the MIMU, y, the output of z axis accelerometer respectively; k _Ax, k _Ay, k _AzRepresent x, y, z axis accelerometer constant multiplier; I _IjRepresent the alignment error item of i axis accelerometer and j axle; B _x, B _y, B _zRepresent x, y, z axis accelerometer often to be worth biasing.Gyroscope in above-mentioned angular velocity and the acceleration channel error model and accelerometer alignment error item are actually constant multiplier and alignment error angle coupling coefficient, so existing sound mixed calibration method can not accurate Calculation alignment error angle, thereby can't provide tutorial message for further revising the alignment error angle, this method does not have to calculate the gyroscope constant multiplier under the negative rotating speed simultaneously, thereby has caused gyroscope constant multiplier degree of asymmetry error; In addition, the rating test equipment requirements that this method adopts is sought north, thereby has increased test difficulty and workload.

Summary of the invention

Technology of the present invention is dealt with problems and is: the deficiency that overcomes existing MIMU scaling method, the micro inertial measurement unit method for precisely marking of a kind of alignment error angle and constant multiplier decoupling zero is proposed, this method is simple, quick, precision is high, experimental facilities need not refer to north, has realized the decoupling zero at gyroscope, accelerometer constant multiplier and alignment error angle among the MIMU.

Technical solution of the present invention is: the micro inertial measurement unit method for precisely marking of alignment error angle and constant multiplier decoupling zero, and its characteristics are to realize through the following steps:

(1) based on the MIMU error characteristics, considered constant multiplier and alignment error angle coupled problem, set up MIMU global error model;

(2) utilize two-axis position platform or turntable (need not to refer to north) to carry out 10 position static demarcating tests;

(3) according to the static demarcating test figure, adopt symmetric position error phase elimination calculating accelerometer, gyroscope often to be worth biasing, utilize acceleration passage decoupling method to calculate accelerometer constant multiplier and alignment error angle;

(4) utilize single shaft rate table (need not to refer to north) and three frocks to carry out the positive and negative speed trial in 3 orientation;

(5) according to the positive and negative speed experimental data in 3 orientation, adopt least square method and cyclic iterative to separate gyroscope constant multiplier and the coupling of alignment error angle among the MIMU one by one, constant multiplier, gyroscope alignment error angle under the low current intelligence of computing gyroscope, find the solution the relevant error term of gyroscope output in conjunction with the static demarcating test figure, and adopt constant multiplier under the high current intelligence of method of interpolation segmentation accurate Calculation gyroscope with specific force.

10 position static demarcating test methods in the described step (2) are: x, y, the z axle that MIMU is set respectively with the geographic coordinate system sky to overlapping and rotating 180 ° of 6 positions to axle horizontal around the sky; Be provided with x, y, the z of MIMU any one with geographic coordinate system ground to overlaps and around ground to 180 ° of 2 position of axle horizontal rotation; The z axle that MIMU is set in geographical surface level, x, y axle respectively with the geographic coordinate system sky to the y of angle at 45 and MIMU axle in geographical surface level, x, z axle respectively with the geographic coordinate system sky to angle at 45 2 positions, realize totally 10 static position.

Acceleration passage decoupling method in the described step (3) is to utilize the z axle of MIMU in geographical surface level, x, the y axle respectively with the geographic coordinate system sky to the y of angle at 45 and MIMU axle in geographical surface level, x, the z axle respectively with the geographic coordinate system sky to angle at 45 2 positions, list each axis accelerometer input/output state equation according to acceleration channel error model, in conjunction with each axis accelerometer input/output state equation under other 8 position, calculate accelerometer alignment error angle earlier by phase division and inverse trigonometric function method, calculate the accelerometer constant multiplier then, finally realize the decoupling zero of acceleration passage.

Constant multiplier method under the high current intelligence of method of interpolation segmentation computing gyroscope of described step (5): utilize the alignment error angle of trying to achieve, calculate the constant multiplier of each interpolation rotating speed point under the high current intelligence, adopt constant multiplier under the high current intelligence of linear interpolation method segmentation computing gyroscope.

Principle of the present invention is: influence the error mechanism that accelerometer is exported according to accelerometer constant multiplier, alignment error angle, set up MIMU acceleration channel error model.Influence the error mechanism that gyroscope is exported according to gyroscope constant multiplier, alignment error angle and the relevant error term of gyroscope output, set up angular velocity channel error model with specific force.Utilize the error part of MIMU on the symmetric position identical, the principle that part is opposite realizes the separation of error by simply adding deduct, and calculates accelerometer and gyroscope and often is worth biasing.Utilize to change an alignment error angle, other error term invariance principle by the phase division, is eliminated other error term and is disturbed, separate acceleration meter constant multiplier and the coupling of alignment error angle.Utilize dynamic calibration test in rotating the complete cycle process in the MIMU surface level gyroscope sensitively revolutions angular speed integration be zero principle, eliminate the calibrated error that the earth rotation angular speed causes.Utilize the angular speed of importing in the dynamic calibration test much larger than the every error by principle of gyroscope, gyroscope constant multiplier that accurately calibrates and alignment error angle coupling coefficient.Utilize the approximation theory one by one of cyclic iterative, separate the coupling at gyroscope constant multiplier and alignment error angle.

The present invention's advantage compared with prior art is:

(1) the present invention is based on the complete error model design of MIMU, solved alignment error angle and constant multiplier coupled problem, calibrate accelerometer and gyroscope alignment error angle among the MIMU, can provide guidance for further revising the alignment error angle.The error model that overcomes existing scaling method employing can't be isolated the shortcoming of constant multiplier and the coupling of alignment error angle.

(2) all rating test equipment of the present invention's employing do not need to seek north, have reduced testing requirements and difficulty, improve and demarcate efficient.

(3) more existing scaling method, the scaling method that the present invention relates to is simple, explicit physical meaning, workload is little, the time is short, and gyroscopic drift is little to the calibration result pollution level.

(4) adopt constant multiplier under least square method, the low current intelligence of cyclic iterative computing gyroscope respectively, calculated amount when having reduced to work under the low current intelligence, adopt constant multiplier under the high current intelligence of method of interpolation segmentation computing gyroscope, reduced constant multiplier nonlinearity erron under the high current intelligence.And this method is utilized positive and negative speed experimental data, and more existing sound mixed calibration method has reduced constant multiplier degree of asymmetry error.

Description of drawings

Fig. 1 is the MIMU method for precisely marking process flow diagram of alignment error of the present invention angle and constant multiplier decoupling zero;

Fig. 2 is the synoptic diagram that concerns between the two-axis position platform coordinate system that the present invention relates to and this coordinate system and the sky, geographic coordinate system northeast;

Fig. 3 is the synoptic diagram that concerns between the rate table coordinate system that the present invention relates to and this coordinate system and the sky, geographic coordinate system northeast;

Fig. 4 is the MIMU coordinate system synoptic diagram that the present invention relates to;

Fig. 5 is 10 position static demarcating test procedure synoptic diagram among the present invention.

Embodiment

The concrete implementation step of the technology of the present invention solution at first defines each coordinate system that uses in the specific implementation process as shown in Figure 1, and Fig. 2 is the relation between two-axis position platform coordinate system OXYZ and this coordinate system and the sky, geographic coordinate system northeast; Fig. 3 is rate table coordinate system O _TX _TY _TZ _TAnd the relation between this coordinate system and the sky, geographic coordinate system northeast; Fig. 4 is MIMU coordinate system oxyz, and concrete implementation step is as follows:

1, big based on MIMU alignment error angle, differentiate rate variance, characteristic such as drift is big, constant multiplier is non-linear and the degree of asymmetry error is big, set up the complete error model of MIMU, adopt the alignment error angle to replace the alignment error coefficient that has now in the error model, separated the coupling of constant multiplier and alignment error angle.The angular velocity channel error model of MIMU is:

ω in formula (1)～(3) _x, ω _yAnd ω _zRepresent the analog voltage of x among the MIMU, y, the output of z axle gyroscope respectively; ω _x, ω _yAnd ω _zRepresent the actual angular speed of x, y, the input of z axle respectively; K _x, K _y, K _zRepresent x, y, z axle gyroscope constant multiplier respectively; _IjRepresent the alignment error angle of i axle gyroscope deflection j axle; D _x, D _y, D _zRepresent x, y, z axle gyroscope often to be worth biasing respectively; D _IjRepresent output of i axle gyroscope and the relevant error term of j axial ratio power; f _x, f _yAnd f _zRepresent the actual specific force of x, y, the input of z axle respectively.MIMU acceleration channel error model is:

f _x＝k _ax[cos(θ _xy)cos(θ _xz)f _x+sin(θ _xz)f _y+sin(θ _xz)f _z]+B _x (4)

f _y＝k _ay[cos(θ _yx)cos(θ _yz)f _y+sin(θ _yx)f _x+sin(θ _yz)f _z]+B _y (5)

f _z＝k _az[cos(θ _zy)cos(θ _zx)f _z+sin(θ _zy)f _y+sin(θ _zx)f _x]+B _z (6)

F in formula (4)～(6) _x, f _yAnd f _zRepresent the analog voltage of x among the MIMU, y, the output of z axis accelerometer respectively; k _Ax, k _Ay, k _AzRepresent x, y, z axis accelerometer constant multiplier; θ _IjRepresent the alignment error angle of i axis accelerometer deflection j axle; B _x, B _y, B _zRepresent x, y, z axis accelerometer often to be worth biasing.

2, utilize two-axis position platform (need not to seek north) to carry out 10 position static demarcating tests, as shown in Figure 6, concrete steps are as follows:

(1) the MIMU level is installed on the two-axis position platform, position of rotation platform housing makes position table coordinate system Z axle and geographic coordinate system sky to overlapping, the rotation inside casing guarantees that MIMU coordinate system oxyz overlaps with position table coordinate system OXYZ, this position is the 1st position, treat that the position table complete stability gets off back startup MIMU to its preheating 20～30 minutes, then in 1～5 minute MIMU output data of this location records;

(2) 180 ° of the position table inside casings (head-down position platform) that turn clockwise, x, y, the z axle that makes MIMU respectively with position table coordinate system-X ,-Y, Z axle overlap, this position is the 2nd position, treat that the position table complete stability gets off after, in 1～5 minute MIMU output data of this location records;

(3) be rotated counterclockwise 90 ° of position table housings (from-X axis apparent place platform), x, y, the z axle of MIMU are overlapped with position table coordinate system-X, Z, Y-axis respectively, this position is the 3rd position, treat that the position table complete stability gets off after, in 1～5 minute MIMU output data of this location records;

(4) be rotated counterclockwise 180 ° of position table inside casings, x, y, the z axle that makes MIMU respectively with position table coordinate system X, Z ,-Y-axis overlaps, this position is the 4th position, treat that the position table complete stability gets off after, in 1～5 minute MIMU output data of this location records;

(5) be rotated counterclockwise 90 ° of position table inside casings, 90 ° of the position table that turns clockwise then housings, x, y, the z axle that makes MIMU respectively with position table coordinate system Z ,-Y, X-axis overlap, this position is the 5th position, after treating that the position table complete stability gets off, in 1～5 minute MIMU output data of this location records;

(6) turn clockwise 180 ° of position table inner frames, x, y, the z axle that makes MIMU respectively with position table coordinate system Z, Y ,-X-axis overlaps, this position is the 6th position, treat that the position table complete stability gets off after, in 1～5 minute MIMU output data of this location records;

(7) turn clockwise 180 ° of position table housings, x, y, the z axle that makes MIMU respectively with position table coordinate system-Z ,-Y ,-X-axis overlaps, this position is the 7th position, treat that the position table complete stability gets off after, in 1～5 minute MIMU output data of this location records;

(8) be rotated counterclockwise 180 ° of inside casings, x, the y of MIMU, z axle are overlapped with position table coordinate system-Z, Y, X-axis respectively, this position is the 8th position, treat that the position table complete stability gets off after, in 1～5 minute MIMU output data of this location records;

(9) turn clockwise 180 ° of inside casings, be rotated counterclockwise 135 ° of position table housings then, the z axle that makes MIMU and position table coordinate system-X overlaps, the y axle is in 45 ° of the inclined to one side Y-axis of position table coordinate system Z, the x axle be in position table coordinate system Z partially-45 ° of Y-axis, this position is the 9th position, treat that the position table complete stability gets off after, at this location records 1～5-minute data;

(10) be rotated counterclockwise 45 ° of position table housings, be rotated counterclockwise 90 ° of position table inside casings then, be rotated counterclockwise 45 ° of housings once more, the y axle of MIMU is overlapped with position table coordinate system-X, the x axle is positioned at 45 ° of the inclined to one side Y-axis of position table coordinate system Z, the z axle be positioned at position table coordinate system Z partially-45 ° of Y-axis, this position is the 10th position, treat that the position table complete stability gets off after, at this location records 1～5-minute data, so far, 10 position envelope tests are all finished.

3, utilize 10 position static demarcating test figures, computing gyroscope often is worth biasing and all error coefficients of accelerometer.

(1) according to the 1st～8 position in the static 10 location positions test, accelerometer and gyroscope often are worth biasing among employing symmetric position error phase elimination, the calculating MIMU.

The 5th position, promptly in the MIMU coordinate system x, y, z axle respectively with position table coordinate system Z ,-Y, X-axis overlap, the angle that assumed position platform coordinate system Y-axis departs from the geographic coordinate system north orientation is ψ, MIMU acceleration passage is output as under this position:

f _x5＝k _axcos(θ _xy)cos(θ _xz)·g+B _x (7)

f _y5＝k _aysin(θ _yx)g+B _y (8)

f _y5＝k _azsin(θ _zx)g+B _z (9)

F in the formula _IjRepresent MIMU i axis accelerometer aanalogvoltage output when the j position, g represents acceleration of gravity.MIMU angular velocity passage is output as:

(10)

(11)

(12)

ω in the formula _IjRepresent MIMU i axle gyroscope aanalogvoltage output when the j position, φ represents the latitude of local position.

The 6th position, promptly in the MIMU coordinate system x, y, z axle respectively with MIMU coordinate system Z, Y ,-X-axis overlaps, this position MIMU accelerometer passage is output as:

f _x6＝k _axcos(θ _xy)cos(θ _xz)·g+B _x (13)

f _y6＝k _aysin(θ _yx)g+B _y (14)

f _z6＝k _azsin(θ _zx)g+B _z (15)

Behind the 5th change in location to the 6 positions, the initial fleet angle of horizontal direction becomes Ψ+180 ° by Ψ because sin (ψ+180 °)=-sin (ψ), cos (ψ+180 °)=-cos (ψ), the 6th position angle speed passage is output as:

(16)

(17)

(18)

Simultaneous equations (7)～(18), list acceleration passage among the MIMU and be at the mean value of 5,6 positions output:

f _x6/5＝( f _x6+ f _x5)/2＝k _axcos(θ _xy)cos(θ _xz)·g+B _x (19)

f _y6/5＝( f _y6+ f _y5)/2＝k _aysin(θ _yx)g+B _y (20)

f _z6/5＝( f _z6+ f _z5)/2＝k _azsin(θ _zx)g+B _z (21)

F in the formula _Ij/kRepresent MIMU at j, k two positions i axis accelerometer aanalogvoltage output mean value, utilize symmetric position phase elimination to eliminate earth rotation angular speed ω _IeTo the axial gyrostatic influence of surface level, list angular velocity passage among the MIMU and be at the mean value of 5,6 positions output:

ω _x6/5＝( ω _x6+ ω _x5)/2＝K _xcos( _xy)cos( _xz)sin(φ)ω _ie+D _x+D _xxg (22)

ω _y6/5＝( ω _y6+ ω _y5)/2＝K _ysin( _yx)sin(φ)ω _ie+D _y+D _yxg (23)

ω _z6/5＝( ω _z6+ ω _z5)/2＝K _zsin( _zx)sin(φ)ω _ie+D _z+D _zxg (24)

ω in the formula _Ij/kRepresent MIMU at j, k two positions i axle gyroscope aanalogvoltage output mean value, in like manner, can try to achieve under 1～4,7～8 positions that the mean value of acceleration passage output is among the MIMU:

f _x2/1＝( f _x2+ f ₁)/2＝k _axsin(θ _xz)·g+B _x (25)

f _y2/1＝( f _y2+ f _y1)/2＝k _aysin(θ _yz)g+B _y (26)

f _z2/1＝( f _z2+ f _z1)/2＝k _azcos(θ _zy)cos(θ _zx)g+B _z (27)

f _x4/3＝( f _x4+ f ₃)/2＝k _axsin(θ _xy)·g+B _x (28)

f _y4/3＝( f _y4+ f _y3)/2＝k _aycos(θ _yz)cos(θ _yx)g+B _y (29)

f _z4/3＝( f _z4+ f _z3)/2＝k _azsin(θ _zy)g+B _z (30)

f _x8/7＝( f _x8+ f _x7)/2＝k _axcos(θ _xy)cos(θ _xz)·(-g)+B _x (31)

f _y8/7＝( f _y8+ f _y7)/2＝k _aysin(θ _yx)(-g)+B _y (32)

f _z8/7＝( f _z8+ f _z7)/2＝k _azsin(θ _zx)(-g)+B _z (33)

The mean value that the angular velocity passage is exported among the MIMU under 1～4,7～8 positions is:

ω _x2/1＝( ω _x2+ ω _x1)/2＝K _xsin( _xz)sin(φ)ω _ie+D _x+D _xzg (34)

ω _y2/1＝( ω _y2+ ω _y1)/2＝K _ysin( _yz)sin(φ)ω _ie+D _y+D _yzg (35)

ω _z2/1＝( ω _z2+ ω _z1)/2＝K _zcos( _zy)cos( _zx)sin(φ)ω _ie+D _z+D _zzg (36)

ω _x4/3＝( ω _x4+ ω _x3)/2＝K _xsin( _xy)sin(φ)ω _ie+D _x+D _xyg (37)

ω _y4/3＝( ω _y4+ ω _y3)/2＝K _ycos( _yx)cos( _yz)sin(φ)ω _ie+D _y+D _yyg (38)

ω _z4/3＝( ω _z4+ ω _z3)/2＝K _zsin( _zy)sin(φ)ω _ie+D _z+D _zyg (39)

ω _x8/7＝( ω _x8+ ω _x7)/2＝K _xcos( _xy)cos( _xz)sin(φ)(-ω _ie)+D _x+D _xx(-g) (40)

ω _y8/7＝( ω _y8+ ω _y7)/2＝K _ysin( _yx)sin(φ)(-ω _ie)+D _y+D _yx(-g) (41)

ω _z8/7＝( ω _z8+ ω _z7)/2＝K _zsin( _zx)sin(φ)(-ω _ie)+D _z+D _zx(-g) (42)

Simultaneous equations (19) and (31), (20) and (32), (21) and (33), try to achieve x among the MIMU, y respectively, z directional acceleration meter often is worth biasing and is respectively:

B _x＝( f _x6/5+ f _x8/7)/2 (43)

B _y＝( f _y6/5+ f _y8/7)/2 (44)

B _z＝( f _z6/5+ f _z8/7)/2 (45)

Simultaneous equations (22) and (40), (23) and (41), (24) and (42), try to achieve x among the MIMU, y respectively, z axle gyroscope often is worth biasing and is respectively:

D _x＝( ω _x6/5+ ω _x8/7)/2 (46)

D _y＝( ω _y6/5+ ω _y8/7)/2 (47)

D _z＝( ω _z6/5+ ω _z8/7)/2 (48)

(2) according to the acceleration channel data of record in the 10 position static demarcating tests, utilize acceleration passage decoupling method to calculate accelerometer alignment error angle, constant multiplier among the MIMU.

In the 9th position, promptly the z axle overlaps with position table coordinate system-X-axis respectively in the MIMU coordinate system, the x axle be positioned at the Z axle partially-45 ° of Y-axis, the y axle is positioned at 45 ° of the inclined to one side Y-axis of Z axle, the x of MIMU, y two axial accelerometers are output as under this position:

f _x9＝k _axcos(45°-θ _xz)cos(θ _xz)+B _x (49)

f _y9＝k _aycos(45°-θ _yx)cos(θ _yz)g+B _y (50)

In the 10th position, promptly the y axle overlaps with position table coordinate system-X-axis respectively in the MIMU coordinate system, the z axle be positioned at the Z axle partially-45 ° of Y-axis, the x axle is positioned at 45 ° of the inclined to one side Y-axis of Z axle, the z axial acceleration meter of MIMU is output as under this position:

f _z10＝k _azcos(θ _zy)cos(45°-θ _zx)g+B _z (51)

Simultaneous formula (25), (19) and (49), resolve that system of equations is tried to achieve x axis accelerometer alignment error angle and constant multiplier is:

k _ax＝( f _x6/5-B _x)/cos(θ _xy)cos(θ _xz) (54)

Simultaneous formula (26), (29) and (50), resolve that system of equations is tried to achieve y axis accelerometer alignment error angle and constant multiplier is:

k _ay＝( f _y4/3-B _y)/cos(θ _yx)cos(θ _yz) (57)

Simultaneous formula (27), (30) and (51), resolve that system of equations is tried to achieve z axis accelerometer alignment error angle and constant multiplier is:

k _az＝( f _z2/1-B _z)/cos(θ _zx)cos(θ _zy) (60)

4, utilize single shaft rate table (need not to refer to north) and three frocks to carry out the positive and negative speed trial in 3 orientation

Carry out the dynamic rate rating test, overlook turntable, for just changeing, rotate to be counter-rotating in a clockwise direction when the setting turntable rotates in a counter-clockwise direction.MIMU is horizontally fixed on single shaft rate table center by three quadrature frock clamps, makes z axle and the turntable Z of MIMU _TAxle overlaps.Gather 1～5 minute MIMU output data after 20～30 minutes to MIMU power supply preheating, the speed of rotation turntable is gathered 1～5 minute MIMU output data for 180 ° afterwards.Setting turntable then just changes, the output of record gyroscope, stall; The turntable counter-rotating, the output of record gyroscope, stall.Turntable input angle speed changes by order from small to large, respectively to n °/10/s of rate table input ,-n °/10/s, 2n °/10/s ,-2n °/10/s, 3n °/10/s ,-3n °/10/s ..., n °/s ,-n °/s totally 20 angular speeds, n °/s represents the maximum positive corner speed of MIMU measurement range, guaranteeing to gather under the prerequisite of rotating the complete cycle data, each angular speed is all being write down the data of the MIMU output about 1～5 minute.Under static state gather 1～5 minute MIMU output data at last, the speed of rotation turntable is gathered 1～5 minute MIMU output data for 180 ° again.

In like manner, three the quadrature frock clamps that overturn, the x axle, y axle that makes MIMU respectively with the Z of turntable _TAxle overlaps, and repeats above work, finishes the positive and negative speed trial in 3 orientation.

5, utilize the dynamic calibration test figure, adopt constant multiplier under least square method and successive iteration method computing gyroscope alignment error angle and low, the high current intelligence of gyroscope.

(1) gyrostatic alignment error angle reaches constant multiplier under the low current intelligence among the calculating MIMU.

As the z of MIMU axle and turntable Z _TAxle overlaps, and turntable is with angular velocity Ω _jDuring rotation, the angular velocity of three axle inputs of MIMU is:

ω _zz＝Ω _j+ω _iesin(φ) (61)

ω _zy＝ω _iecos(φ)cos(Ω _jt+ψ _T) (62)

ω _zx＝ω _iecos(φ)sin(Ω _jt+ψ _T) (63)

ω wherein _Zx, ω _ZyAnd ω _ZzBe respectively z axle and the turntable Z of MIMU _TWhen axle overlaps, the angular velocity of its x, y and the input of z axle; Ω _jRepresent the turntable input angular velocity; T represents rotation time; ω _IeBe rotational-angular velocity of the earth; φ is a local latitude; ψ _TBe the y axle of rotation initial time MIMU and the angle of north orientation.After turntable rotated several weeks, all comprised cos (Ω _jT+ ψ) and cos (Ω _jT+ ψ) every integration is zero.If ω _Zxj, ω _Zyj, ω _ZzjFor being z axle and the turntable Z of MIMU _TWhen axle overlaps, j angular speed Ω of turntable input _jThe time x, y, z axial gyroscope output mean value be:

If each gyroscope output mean value is ω during beginning test position 1 _Axs1, ω _Zys1, ω _Zzs1Each gyroscope output mean value is ω during position 2 _Zxs2, ω _Zys2, ω _Zzs2, during end during test position 1 each gyroscope output mean value be ω _Zxe1, ω _Zye1, ω _Zze1, each gyroscope output mean value is ω during position 2 _Zxe2, ω _Zye2, ω _Zze2, in the time of can testing beginning, x, y, z axle gyroscope output mean value ω among the MIMU _Zxs, ω _Zys, ω _ZzsEach gyroscope output mean value ω during with end _Zxe, ω _Zye, ω _ZzeFor:

ω _zxs＝( ω _zxs1+ ω _zxs2)/2＝K _xsin( _xz)ω _iesin(φ)+D _x+D _xzg (67)

ω _zys＝( ω _zys1+ ω _zys2)/2＝K _ysin( _yz)ω _iesin(φ)+D _y+D _yzg (68)

ω _zzs＝( ω _zzs1+ ω _zzs2)/2＝K _zcos( _zx)cos( _zy)ω _iesin(φ)+D _z+D _zzg (69)

ω _zxe＝( ω _zxe1+ ω _zxe2)/2＝K _xsin( _xz)ω _iesin(φ)+D _x+D _xzg (70)

ω _zye＝( ω _zye1+ ω _zye2)/2＝K _ysin( _yz)ω _iesin(φ)+D _y+D _yzg (71)

ω _zze＝( ω _zze1+ ω _zze2)/2＝K _zcos( _zx)cos( _zy)ω _iesin(φ)+D _z+D _zzg (72)

Eliminate the earth rotation angular speed to gyrostatic influence, the mean value ω of output when each gyroscope of MIMU is static _Zxr, ω _Zyr, ω _ZzrFor:

ω _zxr＝( ω _zxs+ ω _zxe)/2 (73)

ω _zyr＝( ω _zys+ ω _zye)/2 (74)

ω _zzr＝( ω _zzs+ ω _zze)/2 (75)

At j input angle speed Ω _jThe time, eliminated earth rotation angular speed, gyroscope and often be worth the relevant error term interference of biasing, gyroscope output with specific force, try to achieve x among the MIMU, y, z gyroscope output valve is:

ω _zzj＝ ω _zzj- ω _zzr＝K _zcos( _zx)cos( _zy)Ω _j (76)

ω _zxj＝ ω _zxj- ω _zxr＝K _xsin( _xz)Ω _j (77)

ω _zyj＝ ω _zyj- ω _zyr＝K _ysin( _yz)Ω _j (78)

In like manner, can try to achieve x, when the y axle overlaps with turntable z axle respectively, after having eliminated earth rotation angular speed, gyroscope and often being worth biasing, the relevant error term interference of gyroscope output, try to achieve z axle gyroscope output valve and be with specific force as MIMU:

ω _xzj＝ ω _xzj- ω _xzr＝K _zsin( _zx)Ω _j (79)

ω _yzj＝ ω _yzj- ω _yzr＝K _zsin( _zy)Ω _j (80)

According to formula (76), (79) and (80), ask with least square method that z axle gyroscope constant multiplier and alignment error angle coupling coefficient are among the MIMU:

Adopt process of iteration to separate gyroscope alignment error angle and constant multiplier coupling, concrete steps are as follows:

A. at first get K _zCos ( _Zx) cos ( _Zy) as the initial value K of constant multiplier under the low current intelligence of gyroscope _z ⁰, constant multiplier iteration precision thresholding ε is set;

B. with constant multiplier K _z ⁱAlignment error angle is tried to achieve in substitution equation (82), (83) respectively _Zx ⁱAnd _Zy ⁱ

C. with alignment error angle _Zx ⁱ, _Zy ⁱSubstitution equation (81) is tried to achieve constant multiplier K _z ⁱ

D. the constant multiplier value of checking twice iterative computation in front and back to go out, when $\left|\right|K_z^i-K_z^{i-1}\left|\right|\≤\mathrm{\ϵ}$ The time, finishing iteration is K _z ⁱ, _Zx ⁱ, _Zy ⁱAs constant multiplier, alignment error value under the low current intelligence of the gyroscope of finally finding the solution, be back to step (b) continuation iteration respectively otherwise calculate;

E. with the K that tries to achieve _z ⁱ, _Zx ⁱ, _Zy ⁱ, D _zIn substitution equation (34), (39), (24), can try to achieve output of z axle gyroscope and the relevant error term D of z axial ratio power respectively _Zz, with the relevant error term D of y axial ratio power _Zy, with the relevant error term D of x axial ratio power _Zx

According to above method, in like manner can be in the hope of constant multiplier K under x, the low current intelligence of y axle gyroscope among the MIMU _x, K _y, alignment error angle _Xy, _Xz, _Yx, _YzAnd relevant D of angular velocity output and axial specific force _Xx, D _Xy, D _Xz, D _Yy, D _Yx, D _YzSo far, calculate all calibration coefficients of MIMU.

(2) calculate among the MIMU constant multiplier under the gyrostatic high current intelligence.

Because under high current intelligence, the nonlinearity erron of MIMU constant multiplier is bigger, adopt constant multiplier under the high current intelligence of method of interpolation segmentation computing gyroscope, improve the MIMU precision.

At first, according to MIMU angular velocity passage dynamic range, constant multiplier nonlinear characteristic, actual working environment and accuracy requirement etc. dynamically critical rotary speed point of height is set, generally with ‖ Ω _j‖=3n °/10/s is as the dynamic critical rotary speed point of height, will be greater than the interpolation rotating speed point of each speed of 3n °/10/s as high dynamic segmentation interpolation, in the alignment error substitution equation (76) of having tried to achieve, calculate the constant multiplier of each interpolation rotating speed point respectively, adopt constant multiplier K under the high current intelligence of linear interpolation method segmentation computing gyroscope then _ZtFor:

K _z，t＝K _z，i+(K _z，i+1-K _z，i)(Ω _t-Ω _i)/(Ω _i+1-Ω _i) (84)

K in the formula (84) _{Z, t}Represent constant multiplier under the high current intelligence of z axle gyroscope, K _{Z, i}Represent z axle i rotating speed interpolation point gyroscope constant multiplier, Ω _iRepresent i rotating speed interpolation point rotating speed, Ω _tInitial speed (the Ω that representative is calculated _i≤ Ω _t≤ Ω _I+1).

In like manner can try to achieve constant multiplier under x, the high current intelligence of y axle gyroscope, this method has not only reduced under the high current intelligence gyroscope constant multiplier nonlinearity erron among the MIMU, and has reduced calculated amount under the low current intelligence.

The scaling method that designs though the present invention is based on the MIMU error characteristics is not only applicable to MIMU, is equally applicable to flexure gyroscope IMU and liquid floated gyroscope IMU.

It is known that the content that is not described in detail in the instructions of the present invention belongs to this area professional and technical personnel

Prior art.

Claims (4)

1, the micro inertial measurement unit method for precisely marking of alignment error angle and constant multiplier decoupling zero, its characteristics are to realize through the following steps:

(1) sets up MIMU global error model;

(2) utilize two-axis position platform or turntable to carry out 10 position static demarcating tests;

(3) according to the static demarcating test figure, adopt symmetric position error phase elimination calculating accelerometer, gyroscope often to be worth biasing, utilize acceleration passage decoupling method to calculate accelerometer constant multiplier and alignment error angle;

(4) utilize single shaft rate table and three frocks to carry out the positive and negative speed trial in 3 orientation;

(5) according to the positive and negative speed experimental data in 3 orientation, adopt least square method and cyclic iterative to separate gyroscope constant multiplier and the coupling of alignment error angle among the MIMU one by one, constant multiplier, gyroscope alignment error angle under the low current intelligence of computing gyroscope, find the solution the relevant error term of gyroscope output in conjunction with the static demarcating test figure, and adopt constant multiplier under the high current intelligence of method of interpolation segmentation accurate Calculation gyroscope with specific force.

2, the micro inertial measurement unit method for precisely marking of alignment error angle according to claim 1 and constant multiplier decoupling zero is characterized in that: 10 position static demarcating test methods in the described step (2) are: x, y, the z axle that MIMU is set respectively with the geographic coordinate system sky to overlapping and rotating 180 ° of 6 positions to axle horizontal around the sky; Be provided with x, y, the z of MIMU any one with geographic coordinate system ground to overlaps and around ground to 180 ° of 2 position of axle horizontal rotation; The z axle that MIMU is set in geographical surface level, x, y axle respectively with the geographic coordinate system sky to the y of angle at 45 and MIMU axle in geographical surface level, x, z axle respectively with the geographic coordinate system sky to angle at 45 2 positions, realize totally 10 static position.

3, the micro inertial measurement unit method for precisely marking of alignment error according to claim 1 angle and constant multiplier decoupling zero, it is characterized in that: acceleration passage decoupling method is to utilize the z axle of MIMU in geographical surface level in the described step (3), x, the y axle respectively with the geographic coordinate system sky to the y of angle at 45 and MIMU axle in geographical surface level, x, the z axle respectively with the geographic coordinate system sky to angle at 45 2 positions, list each axis accelerometer input/output state equation according to acceleration channel error model, in conjunction with each axis accelerometer input/output state equation under above-mentioned other 8 position, calculate accelerometer alignment error angle earlier by phase division and inverse trigonometric function method, calculate the accelerometer constant multiplier then, finally realize the decoupling zero of acceleration passage.

4, the micro inertial measurement unit method for precisely marking of alignment error angle according to claim 1 and constant multiplier decoupling zero, it is characterized in that: constant multiplier method under the high current intelligence of method of interpolation segmentation computing gyroscope of described step (5): utilize the alignment error angle of trying to achieve, calculate the constant multiplier of each interpolation rotating speed point under the high current intelligence, adopt constant multiplier under the high current intelligence of linear interpolation method segmentation computing gyroscope.

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