CN101975872A - Method for calibrating zero offset of quartz flexible accelerometer component - Google Patents

Abstract

The invention relates to a method for calibrating zero offset of a quartz flexible accelerometer component, which is a system grade calibrating method using a velocity error as observed quantity. In the method, the conventional calibration equipment is still used, the six-position calibration scheme has simple operation and high calibration accuracy; and compared with conventional multi-position division calibration test, the calibrating time of the method of the invention is greatly shortened, calibration errors caused by rotary table errors when multiple positions are calibrated are reduced, and the navigation performance of a strapdown inertial navigation system can be improved. The invention provides a practical system grade calibration method for the accelerometer component.

Description

The scaling method of quartz flexible accelerometer assembly zero-bit biasing

Technical field

What the present invention relates to is a kind of components and parts scaling method, particularly relates to a kind of calibration technique of quartz flexible accelerometer assembly zero-bit biasing.

Background technology

In strapdown inertial navigation system, accelerometer module is as the sensor of sensitive carrier specific force acceleration, and its precision directly influences the navigation accuracy of strapdown inertial navitation system (SINS).Quartz flexible accelerometer has that structural manufacturing process is simple, cost is low, the reliability advantages of higher.Therefore, the quartz flexible accelerometer assembly that is made of quartz flexible accelerometer is widely used in the strap-down inertial navigation system.

Calibration technique is a kind of method that improves the quartz flexible accelerometer measuring accuracy from the software aspect.The biasing of accelerometer zero-bit is meant when acceleration is zero that the specific force measurement departs from apart from zero point, is very important parameter in the accelerometer calibration experiment.Therefore, in real system,, utilize three-axle table to carry out calibration experiment, demarcate the biasing of accelerometer zero-bit,, reduce the adverse effect that the biasing of accelerometer zero-bit brings system so that carry out correction-compensation in order to improve accuracy of navigation systems.

For the demarcation of quartz flexible accelerometer assembly, can be divided into separate calibration method and system-level standardization according to the difference of observed quantity.Separate calibration directly is output as observed quantity with accelerometer, demarcates its coefficient with least square method.System-level demarcation then is to utilize navigation error (attitude error, velocity error and site error) as observed quantity, with Filtering Estimation accelerometer calibration coefficient.

The quartz flexible accelerometer assembly adopts the separate calibration method usually.When using this method, provide a plurality of revolving table positions by the inertia test table, different acceleration of gravity inputs is provided for like this each quartz flexible accelerometer,, this time can calibrates the parameter of quartz flexible accelerometer in the output of each station acquisition quartz flexible accelerometer.8 positions method, 12 position methods and 24 position methods are arranged usually.Need the parameter of demarcation many more, the measuring position that then needs is many more.The separate calibration method has following shortcoming: handle, real-time is not strong 1), afterwards; 2) data volume is big, needs the data of record many, and along with the increase of calibrating parameters, data volume increases severely, and length expends time in; 3), stated accuracy directly depends on the precision of test table.

Therefore, exploration is suitable for the novel scaling method of rock quartz flexibility accelerometer measuring component, overcome that quartz flexible accelerometer assembly separate calibration method precision was low in the past, the shortcoming of data processing complex, the calibration coefficient that calibrates the quartz flexible accelerometer assembly rapidly and efficiently has positive effect.

Summary of the invention

The object of the present invention is to provide a kind of required turntable number of revolutions few, the nominal time is short, and data processing is simple, and can effectively overcome the scaling method of neighbourhood noise to the quartz flexible accelerometer assembly zero-bit biasing of the influence of rating test.

The object of the present invention is achieved like this:

Step 1, the strapdown inertial navigation system that will be equipped with the quartz flexible accelerometer assembly are positioned on the three shaft position turntables, the main shaft of the X of quartz flexible accelerometer assembly, Y, Z axle gyro respectively with turntable interior, in, the axis of rotation of housing is parallel, strapdown inertial navigation system carries out preheating;

Step 2, to get the strapdown inertial navigation system initial position be reference position; Operate three shaft position turntables to make strapdown inertial navigation system be the quartz flexible accelerometer assembly and rotate 90 degree, 90 degree, 90 degree successively around the housing axle, comprise that reference position is designated as position 1-4 respectively, carry out coarse alignment and Kalman fine alignment respectively in above-mentioned four place values, write down the attitude matrix after each coarse alignment finishes

, and each fine alignment finishes the estimated value of back north orientation misalignment

Step 3, on the basis of position 4, operate three shaft position turntables and make strapdown inertial navigation system rotate 90 degree, and then rotate 90 degree around the center axle around the housing axle, be designated as position 5; On the basis of position 5, operate three shaft position turntables and make strapdown inertial navigation system rotate 180 degree around the center axle, be designated as position 6; In the position 5 and position 6 carry out coarse alignment and Kalman fine alignment respectively, write down the attitude matrix after this twice coarse alignment finishes

, and this twice fine alignment finishes the estimated value of back north orientation misalignment

Step 4, the north orientation misalignment that utilizes above-mentioned six position kalman Filtering Estimation to go out

With

, the zero-bit that solves quartz flexible acceleration assembly by following formula is setovered

With

$\left\{\begin{array}{c}{\▿}_x=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_3\right)-{\widehat{\mathrm{\φ}}}_n\left(t_1\right))}{2}\\ {\▿}_y=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_4\right)-{\widehat{\mathrm{\φ}}}_n\left(t_2\right))}{2}\\ {\▿}_z=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_6\right)-{\widehat{\mathrm{\φ}}}_n\left(t_5\right))}{2}\end{array}\right.---\left(1\right)$

Step 5, estimate quartz flexible accelerometer zero-bit biasing after, utilize following formula to accelerometer module output carry out error compensation

$\left\{\begin{array}{c}{f}_x^b={\hat{f}}_x^b-{\▿}_x\\ f_y^b={\hat{f}}_y^b-{\▿}_y\\ f_z^b={\hat{f}}_z^b-{\▿}_z\end{array}\right.---\left(2\right)$

In the formula, Be the actual output of quartz flexible accelerometer assembly,

For compensating the output of back quartz flexible accelerometer assembly.

The present invention also has following feature:

Utilize the north orientation misalignment that the Kalman Filtering Estimation goes out under six positions to find the solution the biasing of quartz flexible accelerometer assembly zero-bit in the step 4

With

Concrete steps as follows:

Reason coordinate system n is a navigation coordinate system with the world, northeast, the biasing of quartz flexible accelerometer zero-bit

Projection under navigation coordinate system

For

${\▿}^n=C_b^n{\▿}^b---\left(3\right)$

In the formula

$C_b^n=C_p^n{C}_b^p---\left(4\right)$

Wherein

For accelerometer coordinate system b is tied to the transition matrix that navigation coordinate is a n system;

For calculating navigation coordinate is that p is tied to the transition matrix that navigation coordinate is a n system;

Be the rough attitude matrix that obtains behind the coarse alignment, and satisfy:

$C_b^p=\left[\begin{array}{ccc}{C}_{11}& C_{12}& C_{13}\\ C_{21}& C_{22}& C_{23}\\ C_{31}& C_{32}& C_{33}\end{array}\right]$

$=\left[\begin{array}{ccc}\cos \mathrm{\ψ}\cos \mathrm{\γ}+\sin \mathrm{\ψ}\sin \mathrm{\θ}\sin \mathrm{\γ}& \sin \mathrm{\ψ}\cos \mathrm{\θ}& \cos \mathrm{\ψ}\sin \mathrm{\γ}-\sin \mathrm{\ψ}\sin \mathrm{\θ}\cos \mathrm{\γ}\\ \cos \mathrm{\ψ}\sin \mathrm{\θ}\sin \mathrm{\γ}-\sin \mathrm{\ψ}\cos \mathrm{\γ}& \cos \mathrm{\ψ}\cos \mathrm{\θ}& -\sin \mathrm{\ψ}\sin \mathrm{\γ}-\cos \mathrm{\ψ}\sin \mathrm{\θ}\cos \mathrm{\γ}\\ -\cos \mathrm{\θ}\sin \mathrm{\γ}& \sin \mathrm{\θ}& \cos \mathrm{\θ}\cos \mathrm{\γ}\end{array}\right]$

Wherein, θ is the angle of pitch, and γ is the pitch angle,

Be course angle;

Because

The I unit matrix, (4) formula and (3) formula are reduced to

$C_b^p=C_b^n---\left(5\right)$

${\▿}^n=C_b^p{\▿}^b---\left(6\right)$

(6) formula is launched

$\left[\begin{array}{c}{\▿}_e\\ {\▿}_n\\ {\▿}_u\end{array}\right]=\left[\begin{array}{ccc}{C}_{11}& C_{12}& C_{13}\\ C_{21}& C_{22}& C_{23}\\ C_{31}& C_{32}& C_{33}\end{array}\right]\left[\begin{array}{c}{\▿}_x\\ {\▿}_y\\ {\▿}_z\end{array}\right]---\left(7\right)$

In the formula,

With

For the quartz flexible accelerometer zero-bit is biased in projection under the navigation coordinate system, For the quartz flexible accelerometer zero-bit is biased in projection on the accelerometer coordinate system;

(7) get the accelerometer zero-bit in the formula and be biased in the east orientation projection

, and expand into

${\▿}_e=C_{11}{\▿}_x+C_{12}{\▿}_y+C_{13}{\▿}_z---\left(8\right)$

Actual north orientation misalignment error

With theoretical north orientation misalignment error

Between following relation is arranged

${\widehat{\mathrm{\φ}}}_n-{\mathrm{\φ}}_n={\stackrel{\·}{\mathrm{\φ}}}_n+{\mathrm{\Δ\φ}}_n---\left(9\right)$

In the formula,

Be Kalman filtering north orientation misalignment actual estimated value, φ _nBe the theoretical estimated value of north orientation misalignment, Δ φ _nBy the evaluated error that factors such as the error of calculation and model error cause, for same computing machine and same model, it is a constant; Wherein, theoretical north orientation misalignment error

For

${\stackrel{\·}{\mathrm{\φ}}}_n=-\frac{{\▿}_e}{g}=-\frac{C_{11}{\▿}_x+C_{12}{\▿}_y+C_{13}{\▿}_z}{g}---\left(10\right)$

The biasing of acceleration assembly zero-bit

With

Solution procedure be the same; Only derive in detail

The process of resolving, omit With

Concrete derivation not;

Coarse alignment is carried out in position 1, obtains rough attitude matrix

, as shown in Table 1, matrix First row element be

$\left\{\begin{array}{c}{C}_{11}=1\\ C_{12}=0\\ C_{13}=0\end{array}\right.---\left(11\right)$

Then (10) formula is equivalent to

${\stackrel{\·}{\mathrm{\φ}}}_n\left(t_1\right)=-\frac{{\▿}_x}{g}---\left(12\right)$

Coarse alignment is carried out in position 3, obtains rough attitude matrix

, as shown in Table 1, matrix

First row element be

$\left\{\begin{array}{c}{C}_{11}=-1\\ C_{12}=0\\ C_{13}=0\end{array}\right.---\left(13\right)$

Then (10) formula is equivalent to

${\stackrel{\·}{\mathrm{\φ}}}_n\left(t_3\right)=\frac{{\▿}_x}{g}---\left(14\right)$

Simultaneous (12) formula and (14) formula,

Can be expressed as

${\▿}_x=\frac{g({\stackrel{\·}{\mathrm{\φ}}}_n\left(t_3\right)-{\stackrel{\·}{\mathrm{\φ}}}_n\left(t_1\right))}{2}---\left(15\right)$

On the basis of position 1 and position 3 coarse alignments, carry out the Kalman fine alignment respectively, obtain north orientation misalignment estimated value and be

With

, with they difference substitution (9) formulas, subtract each other in twos,

${\widehat{\mathrm{\φ}}}_n\left(t_3\right)-{\widehat{\mathrm{\φ}}}_n\left(t_1\right)={\stackrel{\·}{\mathrm{\φ}}}_n\left(t_3\right)-{\stackrel{\·}{\mathrm{\φ}}}_n\left(t_1\right)---\left(16\right)$

In conjunction with (16) formula and (15) formula, can get

The actual expression formula of finding the solution

${\▿}_x=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_3\right)-{\widehat{\mathrm{\φ}}}_n\left(t_1\right))}{2}---\left(17\right)$

In like manner, on the basis of position 2 and position 4, carry out coarse alignment and Kalman fine alignment respectively, obtain north orientation misalignment estimated value and be

With , can get

The actual expression formula of finding the solution

${\▿}_y=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_4\right)-{\widehat{\mathrm{\φ}}}_n\left(t_2\right))}{2}---\left(18\right)$

On the basis of position 5 and position 6, carry out coarse alignment and Kalman fine alignment respectively, obtain north orientation misalignment estimated value and be

With

, can get The actual expression formula of finding the solution

${\▿}_z=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_6\right)-{\widehat{\mathrm{\φ}}}_n\left(t_5\right))}{2}---\left(19\right)$

The present invention has following advantage: continue to use original calibration facility, six set location position schemes are simple to operate, the stated accuracy height; The test of multipoint relatively in the past separate calibration is shortened the nominal time greatly, reduces the calibrated error that multiposition timing signal turntable error more causes, improves the strapdown inertial navitation system (SINS) navigation performance.

Beneficial effect of the present invention is described as follows:

Matlab simulated conditions: three misalignment φ _e, φ _n, φ _uBe made as 0.1 , 0.1 , 0.5 The inclined to one side value of accelerometer zero-bit is respectively on x, y, the z direction

G=9.78m/s ²Gyroscope constant value drift is respectively ε on x, y, three directions of z _x=0.03/h, ε _y=-0.02/h, ε _z=0.01/h; Corresponding gyro and accelerometer measurement white noise are half of its normal value deviation; Be in north latitude 45.7796 , east longitude 126.6705 , simulation time is 90 seconds.

Attitude matrix after coarse alignment finishes under six positions

As shown in Table 1.

The estimation average of the north orientation misalignment after fine alignment finishes under six positions

As shown in Table 2.

The simulation result of accelerometer zero-bit biasing as shown in Table 3.

As can be seen from Table III, above-mentioned six place value demarcation schemes have realized the accurate demarcation of accelerometer zero-bit biasing, have promoted the navigation accuracy and the efficient of system.

Table one

Table two

Table three

Accelerometer bias	Setting value/(ms -1)	Simulation result/(ms -1)	Measuring accuracy
				The biasing of X-axis accelerometer zero-bit	0.00196	0.00200	98.0％
The biasing of Y-axis accelerometer zero-bit	-0.00293	-0.00290	99.0％
				The biasing of Z axis accelerometer zero-bit	0.00098	0.00098	100.0％

Description of drawings

Fig. 1 is 1 three shaft position turntable orientation, position;

Fig. 2 is 2 three shaft position turntable orientation, position;

Fig. 3 is 3 three shaft position turntable orientation, position;

Fig. 4 is 4 three shaft position turntable orientation, position;

Fig. 5 is 5 three shaft position turntable orientation, position;

Fig. 6 is 6 three shaft position turntable orientation, position;

Fig. 7 is the estimation curve of the 3 times north orientation misalignments in position 1 and position;

Fig. 8 is the estimation curve of the 4 times north orientation misalignments in position 2 and position;

Fig. 9 is the estimation curve of the 6 times north orientation misalignments in position 5 and position;

Figure 10 is that process flow diagram is demarcated in the biasing of quartz flexible accelerometer assembly zero-bit.

Embodiment

For example the present invention is done more detailed description below in conjunction with accompanying drawing:

The measuring method of the described quartz flexible accelerometer assembly of present embodiment zero-bit biasing, its concrete implementation step is as follows:

Step 1, the strapdown inertial navigation system that will be equipped with the quartz flexible accelerometer assembly are positioned on the three shaft position turntables, the main shaft of the X of quartz flexible accelerometer assembly, Y, Z axle gyro respectively with turntable interior, in, the axis of rotation of housing is parallel.Strapdown inertial navigation system carries out preheating, and preheating time is according to concrete default.

Step 2, operation three shaft position turntables make strapdown inertial navigation system (being the quartz flexible accelerometer assembly) adjust to position shown in Figure 1.Gather the output of quartz flexible accelerometer and optic fiber gyroscope component, with acceleration of gravity

And rotational-angular velocity of the earth

Carry out coarse alignment as reference information, obtain rough attitude matrix Coarse alignment switches to kalman filtering fine alignment after finishing.Observe the convergence effect that the north orientation misalignment is estimated, treat that filtering is stable after, get estimation average in the stable back north orientation misalignment one minute as the valuation of the 1 time north orientation misalignment in position

Step 3, on the basis of position 1, operate three shaft position turntables and rotate 90 degree around the housing axle, make strapdown inertial navigation system (being the quartz flexible accelerometer assembly) adjust to position shown in Figure 2.Gather the output of quartz flexible accelerometer and optic fiber gyroscope component, carry out coarse alignment, obtain attitude matrix rough under this position

Be transferred to kalman filtering fine alignment then, get estimation average in the stable back north orientation misalignment one minute as the valuation of the 2 times north orientation misalignments in position

Step 4, on the basis of position 2, operate three shaft position turntables and rotate 90 degree around the housing axle, make strapdown inertial navigation system (being the quartz flexible accelerometer assembly) adjust to position shown in Figure 3.Gather the output of quartz flexible accelerometer and optic fiber gyroscope component, carry out coarse alignment, obtain attitude matrix rough under this position

Be transferred to kalman filtering fine alignment then, get estimation average in the stable back north orientation misalignment one minute as the valuation of the 3 times north orientation misalignments in position

Step 5, on the basis of position 3, operate three shaft position turntables and rotate 90 degree around the housing axle, make strapdown inertial navigation system (being the quartz flexible accelerometer assembly) adjust to position shown in Figure 4.Gather the output of quartz flexible accelerometer and optic fiber gyroscope component, carry out coarse alignment, obtain attitude matrix rough under this position

Be transferred to kalman filtering fine alignment then, get estimation average in the stable back north orientation misalignment one minute as the valuation of the 4 times north orientation misalignments in position

Step 6, on the basis of position 4, operate three shaft position turntables and rotate 90 degree around the housing axle, rotate 90 degree around the center axle then, make strapdown inertial navigation system (being the quartz flexible accelerometer assembly) adjust to position shown in Figure 5.Gather the output of quartz flexible accelerometer and optic fiber gyroscope component, carry out coarse alignment, obtain attitude matrix rough under this position

Be transferred to kalman filtering fine alignment then, get estimation average in the stable back north orientation misalignment one minute as the valuation of the 5 times north orientation misalignments in position

Step 7, on the basis of position 5, operate three shaft position turntables and rotate 180 degree around the center axle, make strapdown inertial navigation system (being the quartz flexible accelerometer assembly) adjust to position shown in Figure 6.Gather the output of quartz flexible accelerometer and optic fiber gyroscope component, carry out coarse alignment, obtain attitude matrix rough under this position

Be transferred to kalman filtering fine alignment then, get estimation average in the stable back north orientation misalignment one minute as the valuation of the 6 times north orientation misalignments in position

Step 8, the north orientation misalignment that utilizes above-mentioned six position kalman Filtering Estimation to go out

With

, the zero-bit that just can solve quartz flexible acceleration assembly X, Y, Z direction is setovered

With

$\left\{\begin{array}{c}{\▿}_x=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_3\right)-{\widehat{\mathrm{\φ}}}_n\left(t_1\right))}{2}\\ {\▿}_y=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_4\right)-{\widehat{\mathrm{\φ}}}_n\left(t_2\right))}{2}\\ {\▿}_z=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_6\right)-{\widehat{\mathrm{\φ}}}_n\left(t_5\right))}{2}\end{array}\right.$

Step 9, estimate quartz flexible accelerometer zero-bit biasing after, just can carry out error compensation to accelerometer module output

$\left\{\begin{array}{c}{f}_x^b={\hat{f}}_x^b-{\▿}_x\\ f_y^b={\hat{f}}_y^b-{\▿}_y\\ f_z^b={\hat{f}}_z^b-{\▿}_z\end{array}\right..$

Claims (1)

1. the scaling method of quartz flexible accelerometer assembly zero-bit biasing is characterized in that:

Step 1, the strapdown inertial navigation system that will be equipped with the quartz flexible accelerometer assembly are positioned on the three shaft position turntables, the main shaft of the X of quartz flexible accelerometer assembly, Y, Z axle gyro respectively with turntable interior, in, the axis of rotation of housing is parallel, strapdown inertial navigation system carries out preheating;

Step 2, to get the strapdown inertial navigation system initial position be reference position; Operate three shaft position turntables to make strapdown inertial navigation system be the quartz flexible accelerometer assembly and rotate 90 degree, 90 degree, 90 degree successively around the housing axle, comprise that reference position is designated as position 1-4 respectively, carry out coarse alignment and Kalman fine alignment respectively in above-mentioned four place values, write down the attitude matrix after each coarse alignment finishes

, and each fine alignment finishes the estimated value of back north orientation misalignment

Step 3, on the basis of position 4, operate three shaft position turntables and make strapdown inertial navigation system rotate 90 degree, and then rotate 90 degree around the center axle around the housing axle, be designated as position 5; On the basis of position 5, operate three shaft position turntables and make strapdown inertial navigation system rotate 180 degree around the center axle, be designated as position 6; In the position 5 and position 6 carry out coarse alignment and Kalman fine alignment respectively, write down the attitude matrix after this twice coarse alignment finishes

, and this twice fine alignment finishes the estimated value of back north orientation misalignment

Step 4, the north orientation misalignment that utilizes above-mentioned six position kalman Filtering Estimation to go out

With

, the zero-bit that solves quartz flexible acceleration assembly by following formula is setovered

With

$\left\{\begin{array}{c}{\▿}_x=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_3\right)-{\widehat{\mathrm{\φ}}}_n\left(t_1\right))}{2}\\ {\▿}_y=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_4\right)-{\widehat{\mathrm{\φ}}}_n\left(t_2\right))}{2}\\ {\▿}_z=\frac{g({\widehat{\mathrm{\φ}}}_n\left(t_6\right)-{\widehat{\mathrm{\φ}}}_n\left(t_5\right))}{2}\end{array}\right.$

Step 5, estimate quartz flexible accelerometer zero-bit biasing after, utilize following formula to accelerometer module output carry out error compensation

$\left\{\begin{array}{c}{f}_x^b={\hat{f}}_x^b-{\▿}_x\\ f_y^b={\hat{f}}_y^b-{\▿}_y\\ f_z^b={\hat{f}}_z^b-{\▿}_z\end{array}\right.$

In the formula, Be the actual output of quartz flexible accelerometer assembly,

For compensating the output of back quartz flexible accelerometer assembly.

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