CN1763477A - Mixed calibration method for Inertial measurement unit capable of eliminating gyro constant drift - Google Patents

Abstract

The invention discloses a method for marking IMU each item error coefficient precisely, which comprises the following steps: marking the gyroscopic scale factor and gyroscopic installment error in the IMU error model through dynamic calibration experiment; substituting the error value in the symmetrical 24 position static calibration experiment of adjacent position; adapting the symmetrical position error cancellation law to mark IMU residual each item error coefficient within gyroscopic constant drift, error item of gyroscope and acceleration, accelerometer constant bias, accelerometer marking factor and accelerometer fixation error.

Description

A kind of Inertial Measurement Unit mixed calibration method of eliminating the gyroscope constant value drift influence

Technical field

The present invention relates to the error calibrating method of a kind of Inertial Measurement Unit (IMU), can be used for demarcating flexible gyroscope IMU, liquid floated gyroscope IMU or MEMS gyro IMU.

Background technology

Inertial Measurement Unit (IMU) is the core component of inertial navigation system, its error comprises ascertainment error and stochastic error two parts, wherein ascertainment error be systematic error account for total error about 90%, therefore must set up the mathematical model of IMU ascertainment error before use, and determine every error coefficient in the model by the method for test, this process is called the demarcation of IMU.Traditional scaling method has speed rating test method and the test of multiposition static demarcating, and the precision of speed rating test is very high, but can only calibrate the fractional error coefficient; The Least Square in Processing test figure is adopted in the test of multiposition static demarcating usually, can calibrate whole error coefficients, but precision is lower, and least square method makes unsettled gyroscope constant value drift pollute other every error coefficients, the calibration result that causes different multiposition testing programs to obtain is inconsistent, and difference is very big, is referred to as " the inconsistent problem of error coefficient ".Therefore, above-mentioned two kinds of traditional scaling methods all can not be finished the accurate demarcation of IMU.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of IMU mixing method for precisely marking of being association of activity and inertia of eliminating gyroscope constant value drift influence in the test of multiposition static demarcating is provided.

Technical solution of the present invention is: a kind of Inertial Measurement Unit (IMU) mixed calibration method of eliminating the gyroscope constant value drift influence, it is characterized in that at first calibrating the gyro constant multiplier in the imu error model and the alignment error of gyro by the dynamic calibration test, then in the 24 position static demarcating tests of substitution adjacent position symmetry, and adopt symmetric position error phase elimination to calibrate all the other every error coefficients of IMU, comprise gyroscope constant value drift, the relevant error term of gyro with acceleration, accelerometer often is worth biasing, the constant multiplier of accelerometer and the alignment error of accelerometer, concrete steps are as follows:

(1) set up the global error model of Inertial Measurement Unit (IMU), the global error model comprises angular velocity channel error model and acceleration channel error model.Comprise the spiral shell constant multiplier in the angular velocity channel error model once and the relevant error term of alignment error, gyro of quadratic term, gyroscope constant value drift, gyro with acceleration; Acceleration channel error model comprises accelerometer constant multiplier, accelerometer and often is worth biasing and alignment error etc., totally 36 error coefficients;

(2) according to gyrostatic angular velocity measurement scope among the IMU, utilize rate table to carry out the test of IMU dynamic calibration, IMU is fixed on the rate table, make turntable with different angular velocity rotations, and the data of record IMU output;

(3) adopt least square method to calculate the gyro constant multiplier once and quadratic term, that utilizes gyroscope constant value sum of errors and the relevant error of acceleration when turning clockwise IMU in the dynamic test and being rotated counterclockwise IMU offsets the alignment error of calculating gyro;

(4) utilize position turntable to carry out 24 position static demarcating tests of adjacent position symmetry, IMU is fixed on the turntable, revolving-turret makes three coordinate axis of xyz of IMU overlap with local geographic coordinate system, the sensing of three coordinate axis of change, in the time of will obtaining three coordinate axis 24 positions, the output data of each of each position spool;

(5) according to IMU on each position each output data and rotational-angular velocity of the earth and acceleration of gravity in the relation between the projection components on each, on the basis of IMU global error mathematical model, adopt symmetric position error phase elimination, once item, gyro constant multiplier quadratic term and gyro misalignment substitution of gyro constant multiplier with the dynamic calibration test is determined calculates all every error coefficients of IMU.

Principle of the present invention is: the angular velocity of input is much larger than every sum of errors rotational-angular velocity of the earth of gyro in the dynamic calibration test, and therefore the gyro constant multiplier that calibrates once, the alignment error precision of gyro constant multiplier quadratic term and gyro is very high.The gyro constant multiplier that precision is very high once, in the alignment error substitution multiposition static demarcating test of gyro constant multiplier quadratic term and gyro, adopt symmetric position error phase elimination to determine remaining every error coefficient, symmetric position error phase elimination utilizes the error part of IMU on two symmetric positions identical, the principle that part is opposite, can realize the separation of error by simply adding deduct, this method is simple, explicit physical meaning; Because adopted the testing program of adjacent position symmetry, can think in the short time that gyroscope constant value drift is constant again, therefore, avoid gyroscope constant value drift to influence the problem of other error terms, improve the stated accuracy of IMU.

The present invention's advantage compared with prior art is: the present invention combines the advantage of dynamic calibration and two kinds of methods of static demarcating, promptly can calibrate whole 36 error coefficients of IMU, improved the precision of demarcating again, and 24 position static demarcating testing programs of adjacent position symmetry have been designed, adopt symmetric position error phase elimination, eliminate the influence of gyroscopic drift, solve the inconsistent problem of calibration result in the IMU static demarcating, realized the accurate demarcation of IMU the IMU stated accuracy.

Description of drawings

Fig. 1 is a sound mixed calibration process flow diagram of the present invention;

Fig. 2 is 24 position static demarcating test method synoptic diagram of adjacent position of the present invention symmetry.

Embodiment

As shown in Figure 1, 2, concrete grammar of the present invention is as follows:

1, sets up the global error model of IMU, comprise angular velocity channel error model and the acceleration channel error model of IMU, respectively suc as formula shown in (1)～(3) and formula (4)～(6).

Angular velocity channel error model:

${\stackrel{\‾}{\mathrm{\ω}}}_x=K_{x1}{\mathrm{\ω}}_x+K_{x2}{\mathrm{\ω}}_x^2+M_{\mathrm{xy}}{\mathrm{\ω}}_y+M_{\mathrm{xz}}{\mathrm{\ω}}_z+D_x+D_{\mathrm{xx}}{f}_x+D_{\mathrm{xy}}{f}_y+D_{\mathrm{xz}}{f}_z---\left(1\right)$

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

${\stackrel{\‾}{\mathrm{\ω}}}_z=K_{z1}{\mathrm{\ω}}_z+K_{z2}{\mathrm{\ω}}_z^2+M_{\mathrm{zx}}{\mathrm{\ω}}_x+M_{\mathrm{zy}}{\mathrm{\ω}}_y+D_z+D_{\mathrm{zx}}{f}_x+D_{\mathrm{zy}}{f}_y+D_{\mathrm{zz}}{f}_z---\left(3\right)$

ω wherein _x, ω _yAnd ω _zBe respectively the x that takes in the experiment, y, the angle increment (umber of pulse) of z axle output, ω _x, ω _yAnd ω _z, be respectively x, y, the angular velocity of z axle input is exactly angle increment here, and unit is a rad.S _x, S _y, S _zBe scale-up factor, M _Yx, M _Xz, M _ZxBe alignment error, D _x, D _y, D _zBe constant value drift, D _Xx, D _Yy, D _Zz, D _Xy, D _Yz, D _ZxBe relevant with g.

Acceleration channel error model:

f _x＝k _x(f _x+B _x+I _xyf _y+I _xzf _z) (4)

f _y＝k _y(f _y+B _y+I _yxf _x+I _yzf _z) (5)

f _z＝k _z(f _z+B _z+I _zyf _y+I _zxf _x) (6)

F wherein _x, f _yAnd f _zBe respectively the x that takes in the experiment, y, the specific force (umber of pulse) of z axle output, f _x, f _yAnd f _z, be respectively x, y, the acceleration of z axle input is exactly specific force here, and unit is m/s ²k _x, k _y, k _zFor than force coefficient, I _Yz, I _Yz, I _Xz, I _XyBe alignment error, B _x, B _y, B _zBe constant value drift.

2, carry out the dynamic calibration test, IMU is installed on three rate tables, adjust turntable then, the inner frame of turntable and middle frame are in the surface level, the z axle of IMU overlaps with the Z axle of turntable, and turntable is under the closed-loop working state.Give the 5 °/s of Z axle input of three rate tables, 10 °/s, 20 °/s, 30 °/s, 40 °/s, 50 °/s,, n °/s, wherein n represents the angular velocity measurement scope of IMU, m angular velocity all writes down the data of 5 minutes IMU output to each angular velocity altogether, and revolving-turret makes the z axle of IMU overlap with the reverse of Z axle of turntable, turntable is under the closed-loop working state, give the 5 °/s of Z axle input of three rate tables again, 10 °/s, 20 °/s, 30 °/s, 40 °/s, 50 °/s ... n °/s, n represents the angular velocity measurement scope of IMU, and m angular velocity all writes down the data of 5 minutes IMU output to each angular velocity altogether.

In like manner, revolving-turret makes the Z axle of turntable overlap with x axle, the y axle of IMU, repeats above work.

3, utilize the dynamic calibration test for data to calculate gyro constant multiplier once item, gyro constant multiplier quadratic term and gyro misalignment.

(1) calculating of constant multiplier

When the Z of IMU axle rotates with angular velocity omega, the angular velocity of three axle inputs of IMU is as follows:

ω _z＝ω+ω _iesin (7)

ω _x＝ω _iecoscosθ(t) (8)

ω _y＝ω _iecossinθ(t) (9)

ω wherein _x, ω _yAnd ω _zBe respectively X, the Y of IMU and the angular velocity of Z axle input and add the projection of rotational-angular velocity of the earth on three axles, ω _IeBe rotational-angular velocity of the earth, is a local latitude, θ (t) for t constantly the outside framework of turntable revolve angle with north orientation.

When turntable rotated a circle, θ (t) changed to 2 π from 0, and all every integrations that contain sin θ (t) and cos θ (t) are zero.IMU speed trial time error model conversion is like this:

${\stackrel{\‾}{\mathrm{\ω}}}_x=K_{x1}{\mathrm{\ω}}_x+K_{x2}{\mathrm{\ω}}_x^2+D_x+D_{\mathrm{xx}}{f}_x+D_{\mathrm{xy}}{f}_y+D_{\mathrm{xz}}{f}_z---\left(10\right)$

${\stackrel{\‾}{\mathrm{\ω}}}_y=K_{y1}{\mathrm{\ω}}_y+K_{y2}{\mathrm{\ω}}_y^2+D_y+D_{\mathrm{yx}}{f}_x+D_{\mathrm{yy}}{f}_y+D_{\mathrm{yz}}{f}_z---\left(11\right)$

${\stackrel{\‾}{\mathrm{\ω}}}_z=K_{z1}{\mathrm{\ω}}_z+K_{z2}{\mathrm{\ω}}_z^2+D_z+D_{\mathrm{zx}}{f}_x+D_{\mathrm{zy}}{f}_y+D_{\mathrm{zz}}{f}_z---\left(12\right)$

When the Z of IMU axle rotates with angular velocity omega, when turntable rotated to a week just, three angular velocity passages can be set up following equation:

ω _x＝M _xz(ω+ω _iesin)+D _x+D _xzg (13)

ω _y＝M _yz(ω+ωsin)+D _y+D _yzg (14)

${\stackrel{\‾}{\mathrm{\ω}}}_z=K_{z1}{\mathrm{\ω}}_z+K_{z2}{\mathrm{\ω}}_z^2+D_z+D_{\mathrm{zz}}g---\left(15\right)$

Can get according to formula (13)～(15):

$\left[\begin{array}{c}{\stackrel{\‾}{\mathrm{\ω}}}_{z1}\\ {\stackrel{\‾}{\mathrm{\ω}}}_{-z1}\\ M\\ {\stackrel{\‾}{\mathrm{\ω}}}_{-z6}\end{array}\right]=\left[\begin{array}{cccc}1& g& {\mathrm{\ω}}_1& {\mathrm{\ω}}_1^2\\ 1& -g& {-\mathrm{\ω}}_1& {\mathrm{\ω}}_1^2\\ M& M& M& M\\ 1& -g& -{\mathrm{\ω}}_6& {\mathrm{\ω}}_6^2\end{array}\right]\left[\begin{array}{c}{D}_z\\ D_{\mathrm{zz}}\\ K_{z1}\\ K_{z2}\end{array}\right]---\left(16\right)$

Following formula can be expressed as:

ω＝C·K (17)

Wherein C is 12 * 12 matrix, and ω and K are 12 * 1 column vector, ω _Z1The expression IMU the Z axle overlap with turntable Z axle, turntable around the Z axle with angular velocity omega _Z1The output of the Z axle of IMU during rotation.ω _-z1The expression IMU the Z axle oppositely overlap with turntable Z axle, turntable around the Z axle with angular velocity omega _Z1The output of the Z axle of IMU during rotation.

The computing formula that can be got constant multiplier in the IMU speed rating test by formula (17) is as follows:

K＝(C ^T·C)·C ^-1ω (18)

Can solve z axle gyro constant multiplier once and quadratic term by formula (18), the gyro constant multiplier that in like manner can solve x axle and y axle once and quadratic term.

(2) calculating of alignment error

Alignment error is that the error angle between gyroscope and each system of IMU housing causes, alignment error makes gyrostatic sensitive axes not overlap with the coordinate axis of IMU, thereby make that the sensitive axes of gyro is non-orthogonal, in to the big angular velocity of IMU input, the angular velocity error that alignment error produces is very important.

According to formula (17) and formula (18) as can be known, the x axle of correspondence and y axle are output as when IMU reverses:

ω _x-＝-M _xz(ω+ω _iesin)+D _x+D _xzg (19)

ω _y-＝-M _yz(ω+ωsin)+D _y+D _yzg (20)

According to formula (17), the alignment error computing formula that formula (18), formula (19) and formula (20) can get IMU in the dynamic calibration test is as follows:

M _xz＝( ω _x- ω _x-)/2(ω _z+ω _iesin) (21)

M _yz＝( ω _y- ω _y-)/2(ω _z+ω _iesin) (22)

Wherein, ω _X-And ω _Y-The z axle of expression expression IMU overlaps with turntable Z axle, turntable around the Z axle with angular velocity-ω _Z1The output of the x axle of IMU and y axle during rotation.

The computing formula that in like manner can get other alignment errors is as follows:

M _yz＝( ω _y- ω _y-)/2(ω _x+ω _iesin) (23)

M _zx＝( ω _z- ω _z-)/2(ω _x+ω _iesin) (24)

M _xy＝( ω _x- ω _x-)/2(ω _y+ω _iesin) (25)

M _zy＝( ω _z- ω _z-)/2(ω _y+ω _iesin) (26)

The dress error is irrelevant with the angular velocity of peace input, but because influence factors such as gyroscope stochastic error, it is slightly different that different input angular velocities resolve the alignment error that obtains, average resolving the alignment error that obtains under the different input angular velocity situations, finally obtain determining in the speed rating test alignment error of IMU:

$M=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{M}_i}{n}---\left(27\right)$

4,24 position static demarcating testing programs of design adjacent position symmetry, and utilize rate table to carry out 24 position static demarcating tests, as shown in Figure 2, concrete steps are as follows:

(1) IMU is installed on the three-axle table, the middle frame of adjustment turntable and inner frame are in surface level, and outside framework refers to north, three of IMU coordinate axis just overlap fully with sky, northeast coordinate system like this, after treating that then the turntable complete stability gets off, in this position, i.e. the 1st location records 5-minute data;

(2) outside framework of revolving-turret, each half-twist be to another position, treat that the turntable complete stability gets off after, the record 5-minute data, totally 4 positions that rotate a circle comprise the 1st position, each position is write down 5-minute data respectively, has write down the 1-4 position data altogether;

(3) finish after the experiment of preceding 4 positions, inner frame turning axle 90 degree of rotating table make the y axle of IMU overlap with turntable Z axle, after treating that the turntable complete stability gets off, in this position, i.e. the 5th location records 5-minute data, the outside framework of revolving-turret then, each half-twist is to another position, treat that the turntable complete stability gets off after, the record 5-minute data, totally 4 positions rotate a circle, comprise the 5th position, each position is write down 5-minute data respectively, has write down the 5-9 position data altogether;

(4) the inside casing turning axle 90 of rotating table degree makes the y axle of IMU overlap with turntable Y-axis negative sense, treat that the turntable complete stability gets off after, in this position, i.e. the 9th location records 5-minute data.The housing of rotating table, per 90 degree are as a position, and a circle is totally 4 positions, comprises the 9th position, and 5-minute data is all write down in each position, has write down the 9-13 position data altogether;

(5) inside casing turning axle 90 degree of rotating table, the y axle of IMU is overlapped with turntable Z axle negative sense, as the 13rd the experiment position, treat that the turntable complete stability gets off after, in this position, i.e. the 13rd location records 5-minute data, the housing of rotating table, per 90 degree are as a position, one circle is totally 4 positions, comprise the 13rd position, 5-minute data is all write down in each position, has write down the 13-16 position data altogether;

(6) the inside casing turning axle-270 of rotating table degree makes the y axle of IMU overlap with the turntable Y-axis, rotating table center turning axle 90 degree, the x axle of Inertial Measurement Unit is overlapped with turntable Z axle, as the 17th the experiment position, treat that the turntable complete stability gets off after, in this position, i.e. the 17th location records 5-minute data, the housing of rotating table, per 90 degree are as a position, and a circle is totally 4 positions, comprise that each position, the 17th position all writes down 5-minute data, write down the 17-20 position data altogether;

(7) the center turning axle-180 of rotating table degree, the x axle of IMU is overlapped with turntable Z axle negative sense, as the 21st the experiment position, treat that the turntable complete stability gets off after, in this position, i.e. the 21st location records 5-minute data, the housing of rotating table, per 90 degree are as a position, and a circle comprises the 21st position in totally 4 positions, 5-minute data is all write down in each position, has write down the 21-24 position data altogether.

5, utilize 24 position static demarcating test for data, adopt symmetric position error phase elimination to calculate every error coefficient.

With the x of IMU, y, z respectively with the x of the geographical coordinate system in sky, northeast, y, the z axle overlaps, IMU output this moment with the pass of input is:

ω _x1＝D _x+M _xyω _iecos+M _xzω _iesin+D _xzg (28)

ω _y1＝K _y1ω _iecos+K _y2(ω _iecos) ²+D _y+M _yzω _iesin+D _yzg (29)

ω _z1＝K _z1ω _iesin+K _z2(ω _iecos) ²+D _z+M _zyω _iecos+D _zzg (30)

Rotate 180 degree around the z of IMU axle then, IMU angular velocity passage output this moment with the pass of input is:

ω _x2＝D _x-M _xyω _iecos+M _xzω _iesin+D _xzg (31)

ω _y2＝-K _y1ω _iecos+K _y2(ω _iecos) ²+D _y+M _yzω _iesin+D _yzg (32)

ω _z2＝K _z1ω _iesin+K _z2(ω _iecos) ²+D _z-M _zyω _iecos+D _zzg (33)

By formula (28)-(31), (29)-(32) and (30)-(33):

In like manner, with the gyro constant multiplier determined in the dynamic calibration test once and quadratic term, the gyro misalignment substitution by other symmetrical positions, can solve whole error coefficient in the IMU global error model.

Claims (2)

1, a kind of Inertial Measurement Unit mixed calibration method of eliminating the gyroscope constant value drift influence is characterized in that may further comprise the steps:

(1) set up the global error model of Inertial Measurement Unit (IMU), the global error model comprises angular velocity channel error model and acceleration channel error model.Comprise the spiral shell constant multiplier in the angular velocity channel error model once and the relevant error term of alignment error, gyro of quadratic term, gyroscope constant value drift, gyro with acceleration; Acceleration channel error model comprises accelerometer constant multiplier, accelerometer and often is worth biasing and alignment error etc., totally 36 error coefficients;

(2) according to gyrostatic angular velocity measurement scope among the IMU, utilize rate table to carry out the test of IMU dynamic calibration, IMU is fixed on the rate table, make turntable with different angular velocity rotations, and the data of record IMU output;

(3) adopt least square method to calculate the gyro constant multiplier once and quadratic term, that utilizes gyroscope constant value sum of errors and the relevant error of acceleration when turning clockwise IMU in the dynamic test and being rotated counterclockwise IMU offsets the alignment error of calculating gyro;

(4) utilize position turntable to carry out 24 position static demarcating tests of adjacent position symmetry, IMU is fixed on the turntable, revolving-turret makes three coordinate axis of xyz of IMU overlap with local geographic coordinate system, the sensing of three coordinate axis of change, in the time of will obtaining three coordinate axis 24 positions, the output data of each of each position spool;

(5) according to IMU on each position each output data and rotational-angular velocity of the earth and acceleration of gravity in the relation between the projection components on each, on the basis of IMU global error mathematical model, adopt symmetric position error phase elimination, once item, gyro constant multiplier quadratic term and gyro misalignment substitution of gyro constant multiplier with the dynamic calibration test is determined calculates all every error coefficients of IMU.

2, a kind of Inertial Measurement Unit mixed calibration method of eliminating the gyroscope constant value drift influence according to claim 1, it is characterized in that: 24 position static demarcating test method steps of adjacent position symmetry are as follows:

(1) IMU is installed on the three-axle table, the middle frame of adjustment turntable and inner frame are in surface level, and outside framework refers to north, three of IMU coordinate axis just overlap fully with sky, northeast coordinate system like this, after treating that then the turntable complete stability gets off, in this position, i.e. the 1st location records 5-minute data;

(2) outside framework of revolving-turret, each half-twist be to another position, treat that the turntable complete stability gets off after, the record 5-minute data, totally 4 positions that rotate a circle comprise the 1st position, each position is write down 5-minute data respectively, has write down the 1-4 position data altogether;

(3) finish after the experiment of preceding 4 positions, inner frame turning axle 90 degree of rotating table make the y axle of IMU overlap with turntable Z axle, after treating that the turntable complete stability gets off, in this position, i.e. the 5th location records 5-minute data, the outside framework of revolving-turret then, each half-twist is to another position, treat that the turntable complete stability gets off after, the record 5-minute data, totally 4 positions rotate a circle, comprise the 5th position, each position is write down 5-minute data respectively, has write down the 5-9 position data altogether;

(4) the inside casing turning axle 90 of rotating table degree makes the y axle of IMU overlap with turntable Y-axis negative sense, treat that the turntable complete stability gets off after, in this position, i.e. the 9th location records 5-minute data.The housing of rotating table, per 90 degree are as a position, and a circle is totally 4 positions, comprises the 9th position, and 5-minute data is all write down in each position, has write down the 9-13 position data altogether;

(5) inside casing turning axle 90 degree of rotating table, the y axle of IMU is overlapped with turntable Z axle negative sense, as the 13rd the experiment position, treat that the turntable complete stability gets off after, in this position, i.e. the 13rd location records 5-minute data, the housing of rotating table, per 90 degree are as a position, one circle is totally 4 positions, comprise the 13rd position, 5-minute data is all write down in each position, has write down the 13-16 position data altogether;

(6) the inside casing turning axle-270 of rotating table degree makes the y axle of IMU overlap with the turntable Y-axis, rotating table center turning axle 90 degree, the X-axis of Inertial Measurement Unit is overlapped with turntable Z axle, as the 17th the experiment position, treat that the turntable complete stability gets off after, in this position, i.e. the 17th location records 5-minute data, the housing of rotating table, per 90 degree are as a position, and a circle is totally 4 positions, comprise that each position, the 17th position all writes down 5-minute data, write down the 17-20 position data altogether;

(7) the center turning axle-180 of rotating table degree, the X-axis of IMU is overlapped with turntable Z axle negative sense, as the 21st the experiment position, treat that the turntable complete stability gets off after, in this position, i.e. the 21st location records 5-minute data, the housing of rotating table, per 90 degree are as a position, and a circle comprises the 21st position in totally 4 positions, 5-minute data is all write down in each position, has write down the 21-24 position data altogether.

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