CN104567932A - High-precision fiber-optic gyroscope inertial measurement device calibration method - Google Patents

Abstract

The invention discloses a high-precision fiber-optic gyroscope inertial measurement device calibration method which comprises the following steps: S1, respectively forwards turning a fiber-optic gyroscope inertial measurement device by 90 degrees, 180 degrees and 270 degrees for three times according to three axes of oi shaft (i refers to X, Y and Z), reversely rotating the device by 90 degrees, 180 degrees and 270 degrees for three times, and returning to an initial position; and S2, totally moving by 19 positions comprising the previous 18 turning positions and the initial position, fully exciting the error of the instrument under static and dynamic conditions, and performing optimal estimation by utilizing a parameter estimation method. According to the method disclosed by the invention, repeated electrification and power failure are not needed, the device is only turned according to a certain sequence, the parameters can be identified, and the influence caused by inconsistent reference in the repeated electrification and calibration process is avoided.

Description

A kind of high-precision optical fiber gyro inertial measurement unit scaling method

Technical field

The present invention relates to optical fiber gyro inertial measurement device field, particularly a kind of high-precision optical fiber gyro inertial measurement unit scaling method.

Background technology

The mark that satellite develops as high and new technology, plays very important role in the national defence and economic construction of China.Accuracy of attitude determination is the prerequisite that satellite stablizes obtaining information effectively, satellite attitude control system is one of important system ensureing attitude of satellite precision, and inertia device is the extremely crucial sensor in satellite attitude control system, it directly affects precision and the performance of attitude control system.

Fibre optic gyroscope is a kind of all solid state inertia type instrument, and it has the advantage not available for traditional electro-mechanical instrument.The closed-loop system that it is made up of optical device and electron device, determine own angular velocity by the phase differential detecting two-beam, therefore structurally it is the gyroscope of complete solid state, without any moving component.Fibre optic gyroscope is just with its principle and structural advantage, it is made to have obvious advantage in many applications, especially in product reliability and the very high spacecraft of life requirements, its principal feature shows the following aspects: (1) is all solid state: the parts of fibre optic gyroscope are all solid-state, has the characteristic of anti-vacuum, anti-vibration and impact; (2) long-life: fibre optic gyroscope critical optical device used all can the meeting spatial long life requirement of applying 15 years; (3) high reliability: fibre optic gyroscope structural design is flexible, production technology is relatively simple, can carry out the Redundancy Design of circuit easily to it, or adopts redundancy gyroscope to form inertial measurement system, can improve the reliability of system like this.

The existing calibration technique to optical fiber gyro inertial measurement device is obtained separately by different pilot projects, wherein zero inclined being averaged by multiple position is obtained, constant multiplier rotates multiple angular velocity matching by positive negative direction and obtains, and alignment error obtains by rotating the large angular velocity of the whole circle of positive negative direction.This calibration process inevitably produces and repeatedly adds power operation, and there is the inconsistent problem of benchmark, makes calibration result introduce a large amount of personal error.And above-mentioned calibration process to relate to the time longer, the nominal time reaches several hours.Existing scaling method is all calculate parameter under the operating mode of static (comprising static position and turntable uniform motion), does not consider the error of instrument in dynamic process.

Summary of the invention

The technical problem to be solved in the present invention is: provide one high-precision optical fiber gyro inertial measurement unit scaling method fast, accurately, overcomes scaling method of the prior art and there is manpower error greatly, the problem that process time is long.

Technical scheme of the present invention is:

A kind of high-precision optical fiber gyro inertial measurement unit scaling method, comprise the following steps, S1, by inertial measurement unit of optical fiber gyroscope respectively according to oi axle (i=X, Y, Z) three axle forwards overturn 90 °, 180 °, 270 ° three reverse rotations 90 ° again, 180 °, 270 ° get back to initial position three times, carry out altogether the upset of 18 positions; S2,18 position upsets add that initial position has 19 positions altogether, if inertial measurement unit of optical fiber gyroscope body coordinate system is b, the error model relation setting up gyroscope and accelerometer is as follows: $\left\{\begin{array}{c}\mathrm{\δ}{\mathrm{\ω}}_{\mathrm{ib}}^b=D+M\·{\mathrm{\ω}}_{\mathrm{ib}}^b\\ {\mathrm{\δf}}^b=B+K\·f^b\end{array}\right.,$ Wherein: ${\mathrm{\δ\ω}}_{\mathrm{ib}}^b=\left[\begin{array}{c}{\mathrm{\δ\ω}}_{\mathrm{ibx}}^b\\ {\mathrm{\δ\ω}}_{\mathrm{iby}}^b\\ {\mathrm{\δ\ω}}_{\mathrm{ibz}}^b\end{array}\right]$ Be three gyrostatic measuring error, $D=\left[\begin{array}{c}{D}_x\\ D_y\\ D_z\end{array}\right]$ For gyrostatic zero is inclined, $M=\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{xy}}& M_{\mathrm{xz}}\\ M_{\mathrm{yx}}& M_{\mathrm{yy}}& M_{\mathrm{yz}}\\ M_{\mathrm{zx}}& M_{\mathrm{zy}}& M_{\mathrm{zz}}\end{array}\right]$ For gyrostatic coupling coefficient, ${\mathrm{\ω}}_{\mathrm{ib}}^b=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b\\ {\mathrm{\ω}}_{\mathrm{iby}}^b\\ {\mathrm{\ω}}_{\mathrm{ibz}}^b\end{array}\right]$ For gyrostatic output valve, ${\mathrm{\δf}}^b=\left[\begin{array}{c}{\mathrm{\δf}}_x^b\\ {\mathrm{\δf}}_y^b\\ {\mathrm{\δf}}_z^b\end{array}\right]$ Be the measuring error of three accelerometers, $B=\left[\begin{array}{c}{B}_x\\ B_y\\ B_z\end{array}\right]$ For zero of accelerometer is inclined, $K=\left[\begin{array}{ccc}{K}_{\mathrm{xx}}& 0& 0\\ K_{\mathrm{yx}}& K_{\mathrm{yy}}& 0\\ K_{\mathrm{zx}}& K_{\mathrm{zy}}& K_{\mathrm{zz}}\end{array}\right]$ For the coupling coefficient of accelerometer, $f^b=\left[\begin{array}{c}{f}_x^b\\ f_y^b\\ f_z^b\end{array}\right]$ For accelerometer output valve.

Further, comprise the following steps, S3, if navigation coordinate is n, velocity error equation and the attitude error equations of setting up simplification are as follows:

$\left\{\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}^n=f^n\×\mathrm{\φ\δ}{f}^n\\ \stackrel{\·}{\mathrm{\φ}}=-{\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}-{\mathrm{\δ\ω}}_{\mathrm{ib}}^n\end{array}\right.$

Wherein: $\mathrm{\δ}{\stackrel{\·}{V}}^n=\left[\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_x^n\\ \mathrm{\δ}{\stackrel{\·}{V}}_y^n\\ \mathrm{\δ}{\stackrel{\·}{V}}_z^n\end{array}\right]$ Be the acceleration error of three axles, $\stackrel{\·}{\mathrm{\φ}}=\left[\begin{array}{c}{\stackrel{\·}{\mathrm{\φ}}}_x\\ {\stackrel{\·}{\mathrm{\φ}}}_y\\ {\stackrel{\·}{\mathrm{\φ}}}_z\end{array}\right]$ Be the attitude angle acceleration error of three axles, $\mathrm{\φ}=\left[\begin{array}{c}{\mathrm{\φ}}_x\\ {\mathrm{\φ}}_y\\ {\mathrm{\φ}}_z\end{array}\right]$ Be the attitude error of three axles, $f^n=\left[\begin{array}{c}{f}_x^n\\ f_y^n\\ f_z^n\end{array}\right]$ For accelerometer is in the output of navigational coordinate system n, ${\mathrm{\ω}}_{\mathrm{ie}}^n=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{iex}}^n\\ {\mathrm{\ω}}_{\mathrm{iey}}^n\\ {\mathrm{\ω}}_{\mathrm{iez}}^n\end{array}\right]$ For the projection value of ground velocity component under navigational coordinate system, ${\mathrm{\δf}}^n=\left[\begin{array}{c}{\mathrm{\δf}}_x^n\\ {\mathrm{\δf}}_y^n\\ {\mathrm{\δf}}_z^n\end{array}\right]$ For accelerometer is in the measuring error of navigational coordinate system n, ${\mathrm{\δ\ω}}_{\mathrm{ib}}^n=\left[\begin{array}{c}{\mathrm{\δ\ω}}_{\mathrm{ibx}}^n\\ {\mathrm{\δ\ω}}_{\mathrm{iby}}^n\\ {\mathrm{\δ\ω}}_{\mathrm{ibz}}^n\end{array}\right]$ For gyroscope is in the measuring error of navigational coordinate system n.

Further, initial alignment, position upset and static navigational three process computations are comprised; Wherein,

Initial alignment process: inertial measurement unit of optical fiber gyroscope carries out the 0th position (initial position) the attitude conversion that initial alignment obtains 0 is:

$C_{b_0}^n={\left[\begin{array}{c}{\left(f^b\right)}^T\\ {\left({\mathrm{\ω}}_{\mathrm{ib}}^b\right)}^T\\ {(f^b\×{\mathrm{\ω}}_{\mathrm{ib}}^b)}^T\end{array}\right]}^{-1}\·\left[\begin{array}{c}{\left(f^b\right)}^T\\ {\left({\mathrm{\ω}}_{\mathrm{ie}}^n\right)}^T\\ {(f^n\×{\mathrm{\ω}}_{\mathrm{ie}}^n)}^T\end{array}\right]$

Under m position, the measuring error of accelerometer under navigational coordinate system is:

${\mathrm{\δf}}^n=C_{b_0}^n\·\mathrm{\δ}{f}^{b_0}=C_{b_0}^n\·C_{b_m}^{b_0}\·\mathrm{\δ}{f}^{b_m}=C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·\mathrm{\δ}{f}^{b_m}$

Then computing velocity error is:

$\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}^n=f^n\×\mathrm{\φ}+\mathrm{\δ}{f}^n\\ =f^n\×\mathrm{\φ}+C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·\mathrm{\δ}{f}^{b_m}\\ =f^n\×\mathrm{\φ}+C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·\mathrm{\δ}{f}^{b_m}\\ =f^n\×\mathrm{\φ}+C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·(B+K\·f^{b_m})\\ \≈f^n\×\mathrm{\φ}+C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·K\·f^{b_m}\end{array}$

Initial alignment process, that is:

$f^n\×\mathrm{\φ}=-C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·K\·f^{b_m}$

Then can calculate at m site error angle initial value φ _x0, φ _y0and φ _z0;

Position switching process: inertial measurement unit of optical fiber gyroscope initial alignment under m position completes the moment and is designated as t ₀, under a certain axle oi (i=X, Y, Z) turn to (m+1) position, flip angle speed is the angle of upset is 90 °, and having overturn the moment is t _b, ignore gyrostatic constant value drift and impact, then the attitude error angle produced be approximately:

$\begin{array}{c}\stackrel{\·}{\mathrm{\φ}}=-{\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}-{\mathrm{\δ\ω}}_{\mathrm{ib}}^n\\ =-{\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}-C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·{\mathrm{\δ\ω}}_{i{b}_m}^{b_m}\\ \≈-C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·{\mathrm{\δ\ω}}_{{\mathrm{ib}}_m}^{b_m}\end{array}$

Wherein: result as follows:

${\mathrm{\δ\ω}}_{{\mathrm{ib}}_m}^{b_m}\≈\left[\begin{array}{c}{M}_{\mathrm{xi}}\\ M_{\mathrm{yi}}\\ M_{\mathrm{zi}}\end{array}\right]\·{\stackrel{\·}{\mathrm{\θ}}}_i,(i=X,Y,Z)$

At (t ₀, t _b) in the time, the attitude angular error of generation is:

$\mathrm{\Δ\φ}=-{\∫}_{t_0}^{t_b}(C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·{\mathrm{\δ\ω}}_{{\mathrm{ib}}_m}^{b_m})\mathrm{dt};$

Static navigational process: turn to (m+1) position in the switching process of position after, having overturn the moment is t _b, start static navigational, navigation finish time is t _e, to system calibrating error equation at (t _b, t _e) time period integration, obtain the velocity error δ V in this time period ⁿwith attitude angle φ:

$\left\{\begin{array}{c}{\mathrm{\δV}}^n={\∫}_{t_b}^{t_e}(f^n\×\mathrm{\φ}+{\mathrm{\δf}}^n)\mathrm{dt}\\ \mathrm{\φ}=-{\∫}_{t_b}^{t_e}({\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}+{\mathrm{\δ\ω}}_{\mathrm{ib}}^n)\mathrm{dt}\end{array}\right.$

Write static navigational process medium velocity error equation as following form:

$\left\{\begin{array}{c}{\mathrm{\δV}}_x^n\left(t\right)=\mathrm{\δ}{V}_x^n\left(t_b\right)+a_{1x}^n\·(t-t_b)+a_{2x}^n\·{(t-t_b)}^2+{\mathrm{\δV}}_{\mathrm{Dx}}\\ {\mathrm{\δV}}_y^n\left(t\right)={\mathrm{\δV}}_y^n\left(t_b\right)+a_{1y}^n\·(t-t_b)+a_{2y}^n\·{(t-t_b)}^2+{\mathrm{\δV}}_{\mathrm{Dy}}\\ {\mathrm{\δV}}_z^n\left(t\right)={\mathrm{\δV}}_z^n\left(t_b\right)+a_{1z}^n\·(t-t_b)+a_{2z}^n\·{(t-t_b)}^2+{\mathrm{\δV}}_{\mathrm{Dz}}\end{array}\right.$

Wherein: for t _bmoment speed error value, δ V _dx, δ V _dywith δ V _dzrepresent the margin of error after three axle rate integratings, be respectively three direction velocity error Monomial coefficients and quadratic term coefficient;

Write attitude error equations in static navigational process as following form:

$\left\{\begin{array}{c}{\mathrm{\φ}}_x={\mathrm{\φ}}_{x0}+\mathrm{\Δ}{\mathrm{\φ}}_x+u_x\·(t-t_b)\\ {\mathrm{\φ}}_y={\mathrm{\φ}}_{\mathrm{yz}}+\mathrm{\Δ}{\mathrm{\φ}}_y+u_y\·(t-t_b)\\ {\mathrm{\φ}}_z={\mathrm{\φ}}_{z0}+\mathrm{\Δ}{\mathrm{\φ}}_z+u_z\·(t-t_b)\end{array}\right.$

Wherein:

$u=\left[\begin{array}{c}{u}_x\\ u_y\\ u_z\end{array}\right]{\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}{\mathrm{\δ\ω}}_{\mathrm{ib}}^n.$

Wherein, u represents attitude error equations Monomial coefficient.

Further, least squares identification is adopted to go out M _xx, M _yy, M _zz, M _xy, M _xz, M _yx, M _yz, M _zx, M _zy, D _x, D _y, D _z, K _xx, K _yy, K _zz, K _yx, K _zx, K _zy, B _x, B _y, B _zamount to 21 parameter amounts.

Further, set up measurement equation be:

Z _i＝H _i·X _i+V _i(i＝x,y,z)

Wherein: $Z_i=\left[\begin{array}{c}{\mathrm{\δV}}_i^n\left(t_{b+1}\right)-{\mathrm{\δV}}_i^n\left(t_b\right)\\ {\mathrm{\δV}}_i^n\left(t_{b+2}\right)-{\mathrm{\δV}}_i^n\left(t_b\right)\\ ...\\ {\mathrm{\δV}}_i^n\left(t_e\right)-{\mathrm{\δV}}_i^n\left(t_b\right)\end{array}\right],H_y=H_z=\left[\begin{array}{ccc}1& (t_{b+1}-t_b)& {(t_{b+1}-t_b)}^2\\ 1& (t_{b+2}-t_b)& {(t_{b+2}-t_b)}^2\\ ...& ...& ...\\ 1& (t_e-t_b)& {(t_e-t_b)}^2\end{array}\right],$ $H_x=\left[\begin{array}{cc}1& (t_{b+1}-t_b)\\ 1& (t_{b+2}-t_b)\\ ...& ...\\ 1& (t_e-t_b)\end{array}\right]\text{,}{X}_x=\left[\begin{array}{c}\mathrm{\δ}{V}_{\mathrm{Dx}}\\ a_{1x}^n\\ a_{2x}^n\end{array}\right],X_y=\left[\begin{array}{c}{\mathrm{\δV}}_{\mathrm{Dy}}\\ a_{1y}^n\\ a_{2y}^n\end{array}\right],X_z=\left[\begin{array}{c}{\mathrm{\δV}}_{\mathrm{Dz}}\\ a_{1z}^n\\ a_{2z}^n\end{array}\right]$

Utilize Least Square Method state vector X _i, be calculated as follows:

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

(1) under identical base condition, without the need to repeatedly adding power-off, only optical fiber gyro inertial measurement device being overturn in a certain order, the identification of parameter can be completed, avoid repeating to power on and the inconsistent impact caused of calibration process benchmark.

(2) this method fully motivates the error of instrument under Static and dynamic operating mode, and utilizes method for parameter estimation to carry out optimal estimation, realizes system-level optimum.

(3) compare with other types inertial measurement unit of optical fiber gyroscope method of testing, the method is a kind of quick calibrating method, simple, and whole calibration process is no more than half an hour, improves demarcation efficiency, has saved human and material resources.

(4) compare with other types inertial measurement unit of optical fiber gyroscope method of testing, the method, without the need to distinguishing constant multiplier and alignment error, avoids the error of calculation calculating alignment error and produce in a small amount.

Accompanying drawing explanation

Fig. 1 is the realization flow figure of scaling method of the present invention;

Fig. 2 is the measuring position schematic diagram of scaling method of the present invention.

Embodiment

For the problems of the prior art, the invention provides a kind of high-precision optical fiber gyro inertial measurement unit scaling method, the method need not change frock, and carries out under same operating, and ensure the consistance of reference field, only complete a pilot project, test operation is simple; This scaling method test period is shorter, only needs about half an hour.The method fully motivates the error of instrument under Static and dynamic operating mode, and utilizes method for parameter estimation to carry out optimal estimation; Compare with other types inertial measurement unit of optical fiber gyroscope method of testing, the method is simple, improves demarcation efficiency, has saved human and material resources.

Technical scheme of the present invention is:

High-precision optical fiber gyro inertial measurement unit is loaded in hexahedron frock, wherein X-axis, Y-axis, Z axis respectively according to oi axle (i=X, Y, Z) three axle forwards overturn 90 °, 180 °, 270 ° three reverse rotations 90 ° again, 180 °, 270 ° get back to initial position three times, carry out altogether 18 position upsets, added that initial position comprises 19 positions altogether.Such as: get Bei Tiandong, sky east southeast, Nan Didong, east northeast, Nan Didong, sky east southeast, Bei Tiandong, northwest (NW) sky, southwest, sky, Nan Xidi, northwest, Nan Xidi, southwest, sky, northwest (NW) sky, west, backlands, east northeast ground, west, backlands, northwest (NW) sky, east, northern sky demarcate totally 19 positions.

According to the relation between above-mentioned 19 positions, utilize the navigation error equation under each position can obtain constant multiplier, the parameter such as coupling error and zero-bit of gyroscope and accelerometer.

A specific embodiment is as follows:

As shown in Figure 1, inertial measurement unit of optical fiber gyroscope (inertial measuring unit) scaling method comprises the steps:

(1) X-axis of high-precision optical fiber gyro inertial measurement unit, Y-axis, Z axis respectively according to oi axle (i=X, Y, Z) forward overturn 90 °, 180 °, 270 ° reverse rotations 90 ° again, 180 °, 270 ° get back to initial position, carry out 18 position upsets, comprise 19 positions altogether.Such as get Bei Tiandong, sky east southeast, Nan Didong, east northeast, Nan Didong, sky east southeast, Bei Tiandong, northwest (NW) sky, southwest, sky, Nan Xidi, northwest, Nan Xidi, southwest, sky, northwest (NW) sky, west, backlands, east northeast ground, west, backlands, northwest (NW) sky, east, northern sky demarcate totally 19 positions.

(2) set high-precision optical fiber gyro inertial measurement unit body coordinate system as b, the error model relation setting up gyroscope and accelerometer is as follows:

$\left\{\begin{array}{c}{\mathrm{\δ\ω}}_{\mathrm{ib}}^b=D+M\·{\mathrm{\ω}}_{\mathrm{ib}}^b\\ \mathrm{\δ}{f}^b=V+K\·f^b\end{array}\right.$

Wherein: ${\mathrm{\δ\ω}}_{\mathrm{ib}}^b=\left[\begin{array}{c}{\mathrm{\δ\ω}}_{\mathrm{ibx}}^b\\ {\mathrm{\δ\ω}}_{\mathrm{iby}}^b\\ {\mathrm{\δ\ω}}_{\mathrm{ibz}}^b\end{array}\right]$ Be three gyrostatic measuring error, $D=\left[\begin{array}{c}{D}_x\\ D_y\\ D_z\end{array}\right]$ For gyrostatic zero is inclined, $M=\left[\begin{array}{ccc}{M}_{\mathrm{xx}}& M_{\mathrm{xy}}& M_{\mathrm{xz}}\\ M_{\mathrm{yx}}& M_{\mathrm{yy}}& M_{\mathrm{yz}}\\ M_{\mathrm{zx}}& M_{\mathrm{zy}}& M_{\mathrm{zz}}\end{array}\right]$ For gyrostatic coupling coefficient, ${\mathrm{\ω}}_{\mathrm{ib}}^b=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{ibx}}^b\\ {\mathrm{\ω}}_{\mathrm{iby}}^b\\ {\mathrm{\ω}}_{\mathrm{ibz}}^b\end{array}\right]$ For gyrostatic output valve, ${\mathrm{\δf}}^b=\left[\begin{array}{c}{\mathrm{\δf}}_x^b\\ {\mathrm{\δf}}_y^b\\ {\mathrm{\δf}}_z^b\end{array}\right]$ Be the measuring error of three accelerometers, $B=\left[\begin{array}{c}{B}_x\\ B_y\\ B_z\end{array}\right]$ For zero of accelerometer is inclined, $K=\left[\begin{array}{ccc}{K}_{\mathrm{xx}}& 0& 0\\ K_{\mathrm{yx}}& K_{\mathrm{yy}}& 0\\ K_{\mathrm{zx}}& K_{\mathrm{zy}}& K_{\mathrm{zz}}\end{array}\right]$ For the coupling coefficient of accelerometer, $f^b=\left[\begin{array}{c}{f}_x^b\\ f_y^b\\ f_z^b\end{array}\right]$ For accelerometer output valve.

If navigation coordinate is n, set up velocity error equation and attitude error equations as follows:

$\left\{\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}^n=f^n\×\mathrm{\φ}-(2\·{\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×{\mathrm{\δV}}^n-(2\·{\mathrm{\δ\ω}}_{\mathrm{ie}}^n+{\mathrm{\δ\ω}}_{\mathrm{en}}^n)\×V^n+{\mathrm{\δf}}^n\\ \stackrel{\·}{\mathrm{\φ}}={\mathrm{\δ\ω}}_{\mathrm{ie}}^n+{\mathrm{\δ\ω}}_{\mathrm{en}}^n-({\mathrm{\ω}}_{\mathrm{ie}}^n+{\mathrm{\ω}}_{\mathrm{en}}^n)\×\mathrm{\φ}-\mathrm{\δ}{{\mathrm{\ω}}_{\mathrm{ib}}}^n\end{array}\right.$

Consider V in calibration process ⁿ=0, Yi Zhi ignore convected acceleration impact, above-mentioned equation simplification is:

$\left\{\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}^n=f^n\×\mathrm{\φ\δ}{f}^n\\ \stackrel{\·}{\mathrm{\φ}}=-{\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}-{\mathrm{\δ\ω}}_{\mathrm{ib}}^n\end{array}\right.$

Wherein: $\mathrm{\δ}{\stackrel{\·}{V}}^n=\left[\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_x^n\\ \mathrm{\δ}{\stackrel{\·}{V}}_y^n\\ \mathrm{\δ}{\stackrel{\·}{V}}_z^n\end{array}\right]$ Be the velocity error of three axles, $\mathrm{\φ}=\left[\begin{array}{c}{\mathrm{\φ}}_x\\ {\mathrm{\φ}}_y\\ {\mathrm{\φ}}_z\end{array}\right]$ Be the attitude error of three axles, $f^n=\left[\begin{array}{c}{f}_x^n\\ f_y^n\\ f_z^n\end{array}\right]$ For accelerometer is in the output of navigational coordinate system n, ${\mathrm{\ω}}_{\mathrm{ie}}^n=\left[\begin{array}{c}{\mathrm{\ω}}_{\mathrm{iex}}^n\\ {\mathrm{\ω}}_{\mathrm{iey}}^n\\ {\mathrm{\ω}}_{\mathrm{iez}}^n\end{array}\right]$ For the projection value of ground velocity component under navigational coordinate system, ${\mathrm{\δf}}^n=\left[\begin{array}{c}{\mathrm{\δf}}_x^n\\ {\mathrm{\δf}}_y^n\\ {\mathrm{\δf}}_z^n\end{array}\right]$ For accelerometer is in the measuring error of navigational coordinate system n, ${\mathrm{\δ\ω}}_{\mathrm{ib}}^n=\left[\begin{array}{c}{\mathrm{\δ\ω}}_{\mathrm{ibx}}^n\\ {\mathrm{\δ\ω}}_{\mathrm{iby}}^n\\ {\mathrm{\δ\ω}}_{\mathrm{ibz}}^n\end{array}\right]$ For gyroscope is in the measuring error of navigational coordinate system n.

(3) inertial measurement unit of optical fiber gyroscope carries out the 0th position (initial position) the attitude conversion that initial alignment obtains for:

$C_{b_0}^n={\left[\begin{array}{c}{\left(f^b\right)}^T\\ {\left({\mathrm{\ω}}_{\mathrm{ib}}^b\right)}^T\\ {(f^b\×{\mathrm{\ω}}_{\mathrm{ib}}^b)}^T\end{array}\right]}^{-1}\·\left[\begin{array}{c}{\left(f^n\right)}^T\\ {\left({\mathrm{\ω}}_{\mathrm{ie}}^n\right)}^T\\ {(f^n\×{\mathrm{\ω}}_{\mathrm{ie}}^n)}^T\end{array}\right]$

Under m position, the measuring error of accelerometer under navigational coordinate system is:

${\mathrm{\δf}}^n=C_{b_0}^n\·\mathrm{\δ}{f}^{b_0}=C_{b_0}^n\·C_{b_m}^{b_0}\·\mathrm{\δ}{f}^{b_m}=C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·\mathrm{\δ}{f}^{b_m}$

In above formula represent the pose transformation matrix of m relative initial position, computing velocity error is:

$\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}^n=f^n\×\mathrm{\φ}+\mathrm{\δ}{f}^n\\ =f^n\×\mathrm{\φ}+C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·\mathrm{\δ}{f}^{b_m}\\ =f^n\×\mathrm{\φ}+C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·\mathrm{\δ}{f}^{b_m}\\ =f^n\×\mathrm{\φ}+C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·(B+K\·f^{b_m})\\ \≈f^n\×\mathrm{\φ}+C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·K\·f^{b_m}\end{array}$

Initial alignment process, then can calculate horizontal attitude error angle initial value φ under m position _x0and φ _z0.

(4) high-precision optical fiber gyro inertial measurement unit initial alignment under m (1≤m≤18) position completes the moment and is designated as t ₀, under a certain axle oi (i=X, Y, Z) turn to (m+1) position, flip angle speed is the angle of upset is 90 °, and having overturn the moment is t _b, consider that the switching process time is shorter and constant value drift that is high accuracy gyroscope instrument is less (is generally 10 ^-3°/magnitude of h), ignore gyrostatic constant value drift and impact, then the attitude error angle produced be approximately:

$\begin{array}{c}\stackrel{\·}{\mathrm{\φ}}=-{\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}-{\mathrm{\δ\ω}}_{\mathrm{ib}}^n\\ =-{\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}-C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·{\mathrm{\δ\ω}}_{i{b}_m}^{b_m}\\ \≈-C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·{\mathrm{\δ\ω}}_{{\mathrm{ib}}_m}^{b_m}\end{array}$

In above formula represent the component of rotational-angular velocity of the earth relative to inertial coordinates system; gyroscope body series ties up to the measuring error of navigational coordinate system n relative to inertial coordinate; represent the measuring error of gyroscope under m position.Wherein: result as follows:

${\mathrm{\δ\ω}}_{{\mathrm{ib}}_m}^{b_m}\≈\left[\begin{array}{c}{M}_{\mathrm{xi}}\\ M_{\mathrm{yi}}\\ M_{\mathrm{zi}}\end{array}\right]\·{\stackrel{\·}{\mathrm{\θ}}}_i,(i=X,Y,Z);$

At (t ₀, t _b) in the time, the attitude angular error of generation is:

$\mathrm{\Δ\φ}=-{\∫}_{t_0}^{t_b}(C_{b_0}^n\·{\left(C_{b_0}^{b_m}\right)}^T\·{\mathrm{\δ\ω}}_{{\mathrm{ib}}_m}^{b_m})\mathrm{dt};$

(5) to after turning to (m+1) position in step (4), having overturn the moment is t _b, start static navigational, navigation finish time is t _e, to system calibrating error equation at (t _b, t _e) time period integration, obtain the velocity error δ V in this time period ⁿwith attitude error Δ φ:

$\left\{\begin{array}{c}{\mathrm{\δV}}^n={\∫}_{t_b}^{t_e}(f^n\×\mathrm{\φ}+{\mathrm{\δf}}^n)\mathrm{dt}\\ \mathrm{\φ}=-{\∫}_{t_b}^{t_e}({\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}+{\mathrm{\δ\ω}}_{\mathrm{ib}}^n)\mathrm{dt}\end{array}\right.$

Write static navigational process medium velocity error equation and attitude error as following form:

$\left\{\begin{array}{c}{\mathrm{\δV}}_x^n\left(t\right)=\mathrm{\δ}{V}_x^n\left(t_b\right)+a_{1x}^n\·(t-t_b)+a_{2x}^n\·{(t-t_b)}^2+{\mathrm{\δV}}_{\mathrm{Dx}}\\ {\mathrm{\δV}}_y^n\left(t\right)={\mathrm{\δV}}_y^n\left(t_b\right)+a_{1y}^n\·(t-t_b)+a_{2y}^n\·{(t-t_b)}^2+{\mathrm{\δV}}_{\mathrm{Dy}}\\ {\mathrm{\δV}}_z^n\left(t\right)={\mathrm{\δV}}_z^n\left(t_b\right)+a_{1z}^n\·(t-t_b)+a_{2z}^n\·{(t-t_b)}^2+{\mathrm{\δV}}_{\mathrm{Dz}}\end{array}\right.$

Wherein: for t _bmoment speed error value, δ V _dx, δ V _dywith δ V _dzrepresent the margin of error after three axle rate integratings, be respectively three direction velocity error Monomial coefficients and quadratic term coefficient.

Write attitude error equations in static navigational process as following form:

$\left\{\begin{array}{c}{\mathrm{\φ}}_x={\mathrm{\φ}}_{x0}+\mathrm{\Δ}{\mathrm{\φ}}_x+u_x\·(t-t_b)\\ {\mathrm{\φ}}_y={\mathrm{\φ}}_{\mathrm{yz}}+\mathrm{\Δ}{\mathrm{\φ}}_y+u_y\·(t-t_b)\\ {\mathrm{\φ}}_z={\mathrm{\φ}}_{z0}+\mathrm{\Δ}{\mathrm{\φ}}_z+u_z\·(t-t_b)\end{array}\right.$

Wherein:

$u=\left[\begin{array}{c}{u}_x\\ u_y\\ u_z\end{array}\right]{\mathrm{\ω}}_{\mathrm{ie}}^n\×\mathrm{\φ}+{\mathrm{\δ\ω}}_{\mathrm{ib}}^n$

U only represents above-mentioned equation once item error parameter.Set up measurement equation be:

Z _i＝H _i·X _i+V _i(i＝x,y,z)

Wherein: $Z_i=\left[\begin{array}{c}{\mathrm{\δV}}_i^n\left(t_{b+1}\right)-{\mathrm{\δV}}_i^n\left(t_b\right)\\ {\mathrm{\δV}}_i^n\left(t_{b+2}\right)-{\mathrm{\δV}}_i^n\left(t_b\right)\\ ...\\ {\mathrm{\δV}}_i^n\left(t_e\right)-{\mathrm{\δV}}_i^n\left(t_b\right)\end{array}\right],H_y=H_z=\left[\begin{array}{ccc}1& (t_{b+1}-t_b)& {(t_{b+1}-t_b)}^2\\ 1& (t_{b+2}-t_b)& {(t_{b+2}-t_b)}^2\\ ...& ...& ...\\ 1& (t_e-t_b)& {(t_e-t_b)}^2\end{array}\right],$ $H_x=\left[\begin{array}{cc}1& (t_{b+1}-t_b)\\ 1& (t_{b+2}-t_b)\\ ...& ...\\ 1& (t_e-t_b)\end{array}\right]\text{,}{X}_x=\left[\begin{array}{c}\mathrm{\δ}{V}_{\mathrm{Dx}}\\ a_{1x}^n\\ a_{2x}^n\end{array}\right],X_y=\left[\begin{array}{c}{\mathrm{\δV}}_{\mathrm{Dy}}\\ a_{1y}^n\\ a_{2y}^n\end{array}\right],X_z=\left[\begin{array}{c}{\mathrm{\δV}}_{\mathrm{Dz}}\\ a_{1z}^n\\ a_{2z}^n\end{array}\right]$

Utilize Least Square Method state vector X _i, be calculated as follows:

(6) obtain respectively in step (7) in 18 upturned position processes dependent equation, can obtain altogether 18 system of equations totally 90 equations, set up the measurement equation about all error parameters of instrument:

Z＝H·X+V

$Z={{\left[\begin{array}{ccccccccccc}{a}_{1x}^n\left(1\right)& a_{1y}^n\left(1\right)& a_{2y}^n\left(1\right)& a_{1z}^n\left(1\right)& a_{2z}^n\left(1\right)& ...& a_{1x}^n\left(19\right)& a_{1y}^n\left(19\right)& a_{2y}^n\left(19\right)& a_{1z}^n\left(19\right)& a_{2z}^n\left(19\right)\end{array}\right]}^T}_{90\×1}$

$X={\left[\begin{array}{ccccccccccccccccccccc}{M}_{\mathrm{xx}}& M_{\mathrm{yy}}& M_{\mathrm{zz}}& M_{\mathrm{xy}}& M_{\mathrm{xz}}& M_{\mathrm{yx}}& M_{\mathrm{yz}}& M_{\mathrm{zx}}& M_{\mathrm{zy}}& D_x& D_y& D_z& K_{\mathrm{xx}}& K_{\mathrm{yy}}& K_{\mathrm{zz}}& K_{\mathrm{yx}}& K_{\mathrm{zx}}& K_{\mathrm{zy}}& B_x& B_y& B_z\end{array}\right]}^T$

Utilize Least Square Method state vector X, be calculated as follows:

As follows, table 1 illustrates the detail of the present invention 19 positions.

Table 1

Claims (5)

1. a high-precision optical fiber gyro inertial measurement unit scaling method, is characterized in that, comprises the following steps,

S1, by inertial measurement unit of optical fiber gyroscope respectively according to oi axle (i=X, Y, Z) three axle forwards overturn 90 °, 180 °, 270 ° three reverse rotations 90 ° again, 180 °, 270 ° get back to initial position three times, carry out altogether the upset of 18 positions;

S2,18 position upsets add that initial position has 19 positions altogether, if described inertial measurement unit of optical fiber gyroscope body coordinate system is b, the error model relation setting up gyroscope and accelerometer is as follows:

wherein: be three gyrostatic measuring error, for gyrostatic zero is inclined, for gyrostatic coupling coefficient, for gyrostatic output valve,

be the measuring error of three accelerometers, for zero of accelerometer is inclined, for the coupling coefficient of accelerometer, for accelerometer output valve.

2. high-precision optical fiber gyro inertial measurement unit scaling method according to claim 1, is characterized in that, comprise the following steps,

S3, if navigation coordinate is n, velocity error equation and the attitude error equations of setting up simplification are as follows:

Wherein: be the acceleration error of three axles, be the attitude angle acceleration error of three axles, be the attitude error of three axles, for accelerometer is in the output of navigational coordinate system n, for the projection value of ground velocity component under navigational coordinate system, for accelerometer is in the measuring error of navigational coordinate system n, for gyroscope is in the measuring error of navigational coordinate system n.

3. high-precision optical fiber gyro inertial measurement unit scaling method according to claim 1, is characterized in that, comprises initial alignment, position upset and static navigational three process computations; Wherein,

Initial alignment process: described inertial measurement unit of optical fiber gyroscope carries out the attitude conversion that initial alignment obtains under the 0th position (initial position) for:

Under m position, the measuring error of accelerometer under navigational coordinate system is:

Then computing velocity error is:

Initial alignment process, that is:

Then can calculate φ at m site error angle initial value φ _x0, φ _y0and φ _z0;

Position switching process: described inertial measurement unit of optical fiber gyroscope initial alignment under m position completes the moment and is designated as t ₀, under a certain axle oi (i=X, Y, Z) turn to (m+1) position, flip angle speed is the angle of upset is 90 °, and having overturn the moment is t _b, ignore gyrostatic constant value drift and impact, then the attitude error angle produced be approximately:

Wherein: result as follows:

At (t ₀, t _b) in the time, the attitude angular error of generation is:

Static navigational process: turn to (m+1) position in the switching process of position after, having overturn the moment is t _b, start static navigational, navigation finish time is t _e, to system calibrating error equation at (t _b, t _e) time period integration, obtain the velocity error δ V in this time period ⁿwith attitude angle φ:

Write static navigational process medium velocity error equation as following form:

Wherein: for t _bmoment speed error value, δ V _dx, δ V _dywith δ V _dzrepresent the margin of error after three axle rate integratings, be respectively three direction velocity error Monomial coefficients and quadratic term coefficient;

Write attitude error equations in static navigational process as following form:

Wherein:

U represents attitude error equations Monomial coefficient.

4. high-precision optical fiber gyro inertial measurement unit scaling method according to claim 3, is characterized in that, adopts least squares identification to go out M _xx, M _yy, M _zz, M _xy, M _xz, M _yx, M _yz, M _zx, M _zy, D _x, D _y, D _z, K _xx, K _yy, K _zz, K _yx, K _zx, K _zy, B _x, B _y, B _zamount to 21 parameter amounts.

5. high-precision optical fiber gyro inertial measurement unit scaling method according to claim 4, is characterized in that,

Set up measurement equation be:

Z _i＝H _i·X _i+V _i(i＝x,y,z)

Wherein:

Utilize Least Square Method state vector X _i, be calculated as follows:

。