CN104165638A - Multi-position self-calibration method for biaxial rotating inertial navigation system - Google Patents

Abstract

The invention provides an on-line multi-position self-calibration method for a biaxial rotating inertial navigation system, which avoids regular demounting of system components, and can improve independence of navigation during long endurance. The method comprises the following steps: step 1, establishing a device error model and a navigation error equation of the biaxial rotating inertial navigation system; step 2, preheating a gyroscope and an accelerometer component, and carrying out fine alignment on each single position based on Kalman filtering; step 3, rotating a carrier according to a fine alignment result, and adjusting the position of the carrier to enable the carrier to coincide with a navigation coordinate system almost; step 4, rotating a ring stand according to a ten-position transposition method, collecting speed error obtained by navigation calculation in each position and calculating attitude error variation to obtain observed quantity; and step 5, according to the navigation result of each position, calculating with least square to obtain error needing to be calibrated.

Description

A kind of twin shaft Rotating Inertial Navigation System multiposition Auto-calibration method

Technical field

What the present invention relates to is a kind of prompt device error Auto-calibration method that connects inertial navigation technology field of rotation modulation.

Background technology

Navigation accuracy when the rotation modulation technology that Rotating Inertial Navigation System uses can improve the long boat of navigational system, but in the time that real system is applied, navigation accuracy is still subject to the impact of inertia device precision, need to demarcate inertia device before use.At present to the demarcation majority of Inertial Measurement Unit (IMU) based on high precision turntable, inertial navigation system need to be disassembled and delivers to laboratory and carry out, although the method can ensure certain precision, have that operability is poor, cost is high and the problem such as reproducibility error.In addition, inertial device error is not changeless, and As time goes on, the error numerical value before demarcated can not continue to use again, need to re-start demarcation, the use of navigational system when this is unfavorable for long boat.

Twin shaft Rotating Inertial Navigation System is because self is with two ring stands, therefore can not carry out Auto-calibration by means of turntable, but can provide accurate attitude reference due to ring stand and unlike turntable, therefore there is obstacle in existing system level scaling method in the time being applied to twin shaft Rotating Inertial Navigation System, need to design new Auto-calibration method.

Summary of the invention

The object of the present invention is to provide one to be applicable to twin shaft Rotating Inertial Navigation System, avoid system component regular dismounting, the online calibration method of the independence of navigating can improve long boat time.

In order to solve the problems of the technologies described above, the present invention adopts following technical scheme:

A kind of twin shaft Rotating Inertial Navigation System multiposition Auto-calibration method, comprises the following steps:

Step 1: device error model and the navigation error equation of setting up twin shaft Rotating Inertial Navigation System;

Step 2, preheating gyroscope and accelerometer module, carry out putting fine alignment based on the unit of Kalman filtering;

Step 3, according to fine alignment result rotation vector, adjust carrier positions to approximate be to overlap with navigation coordinate;

Step 4, according to X position transposition method rotate ring stand, the velocity error obtaining at each station acquisition navigation calculation is also calculated attitude error variable quantity, obtains observed quantity;

Step 5, according to the navigation results of each position utilize least-squares calculation go out need demarcate error.

Wherein the device error model of setting up described in step 1 comprises the following steps:

The 1st step: the device error model of setting up twin shaft Rotating Inertial Navigation System; Wherein:

The error model of accelerometer is:

${\▿}_n=\mathrm{\Δ}{C}_s^a{f}^s+\▿---\left(1\right)$

Wherein for accelerometer output error, $\mathrm{\Δ}{C}_s^a=\left[\begin{array}{ccc}{K}_{\mathrm{ax}}& 0& 0\\ -S_{\mathrm{ayz}}& K_{\mathrm{ay}}& 0\\ S_{\mathrm{azy}}& {-S}_{\mathrm{azx}}& K_{\mathrm{az}}\end{array}\right]$ For being the transition matrix that s is tied to accelerometer coordinate system from IMU coordinate system, S _aijfor the alignment error angle of accelerometer in i and j direction, S _aijin i=x, y, z, j=x, y, z and i ≠ j, K _ax, K _ayand K _azbe respectively the accelerometer scale factor error in x, y and z direction, f ^sfor the input specific force of velograph, $\▿={\left[\begin{array}{ccc}{\▿}_x& {\▿}_y& {\▿}_z\end{array}\right]}^T,$ with for the accelerometer bias in x, y and z direction;

Gyrostatic error model is:

${\mathrm{\ϵ}}_n=\mathrm{\Δ}{C}_s^g{\mathrm{\ω}}^s+\mathrm{\ϵ}---\left(2\right)$

Wherein ε _nfor gyroscope output error, $\mathrm{\Δ}{C}_s^g=\left[\begin{array}{ccc}{K}_{\mathrm{gx}}& S_{\mathrm{gxz}}& {-S}_{\mathrm{gxy}}\\ {-S}_{\mathrm{gyz}}& K_{\mathrm{gy}}& S_{\mathrm{gyx}}\\ S_{\mathrm{gzy}}& {-S}_{\mathrm{gzx}}& K_{\mathrm{gz}}\end{array}\right]$ For be tied to the transition matrix of gyroscope coordinate system, S from IMU coordinate _gijfor being gyrostatic alignment error angle in i and j direction, S _gijin i=x, y, z, j=x, y, z, and i ≠ j, K _gx, K _gy. and K _gzbe respectively the gyroscope scale factor error in x, y and z direction, ω ^sfor input angular velocity, ε=[ε _xε _yε _z] ^tfor gyroscope zero inclined to one side;

The 2nd step: the navigation error equation of setting up twin shaft Rotating Inertial Navigation System:

$\left\{\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=-g\·(\mathrm{\Δ}{\mathrm{\φ}}_N+{\mathrm{\φ}}_{N0})+{\▿}_E\\ \mathrm{\δ}{\stackrel{\·}{V}}_N=g\·({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})+{\▿}_N\\ \mathrm{\δ}{\stackrel{\·}{V}}_U={\▿}_U\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_E={\mathrm{\ω}}_{\mathrm{ie}}\sin L\·({\mathrm{\Δ\φ}}_N+{\mathrm{\φ}}_{N0})-{\mathrm{\ω}}_{\mathrm{ie}}\cos L\·({\mathrm{\Δ\φ}}_U+{\mathrm{\φU}}_0)-{\mathrm{\ϵ}}_E\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_N=-{\mathrm{\ω}}_{\mathrm{ie}}\sin L\·({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})-{\mathrm{\ϵ}}_N\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_U={\mathrm{\ω}}_{\mathrm{ie}}\cos L\·{({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})}_E-{\mathrm{\ϵ}}_U\end{array}\right.---\left(3\right)$

Wherein δ V _e, δ V _n, δ V _ube respectively east orientation, north orientation and sky to velocity error, Δ φ _e, Δ φ _nwith Δ φ _ube respectively system east orientation, north orientation and day to misalignment variable quantity, with be respectively east orientation, north orientation and day to component, ε _e, ε _nand ε _ube respectively ε _neast orientation, north orientation and day to component, g is acceleration of gravity, L is local latitude, ω _iefor rotational-angular velocity of the earth, φ _e0, φ _n0, φ _u0for system east orientation, north orientation and day to initial misalignment;

The 3rd step: fine alignment is put by process need unit due to self-calibration, unit is put after fine alignment, adopts the error model parameters of gyroscope and accelerometer to represent the initial misalignment φ of system _e0, φ _n0, φ _u0, have:

$\left\{\begin{array}{c}{\mathrm{\φ}}_{E0}=\frac{{\▿}_{N0}}{g}\\ {\mathrm{\φ}}_{N0}=-\frac{{\▿}_{E0}}{g}\\ {\mathrm{\φ}}_{U0}=\frac{{\mathrm{\ϵ}}_{N0}}{{\mathrm{\ω}}_{\mathrm{ie}}\cos L}\end{array}\right.---\left(4\right)$

Wherein ${{\▿}_0=\left[\begin{array}{ccc}{\▿}_{E0}& {\▿}_{N0}& {\▿}_{U0}\end{array}\right]}^T$ And ε ₀=[ε _e0ε _n0ε _u0] ^tbe respectively accelerometer and the gyro error of the equivalence of initial alignment position, that is:

$\left[\begin{array}{c}{\▿}_{E0}\\ {\▿}_{N0}\\ {\▿}_{U0}\end{array}\right]=C_s^n\left[\begin{array}{c}{\▿}_x\\ {\▿}_y\\ {\▿}_z\end{array}\right]---\left(5\right)$

$\left[\begin{array}{c}{\mathrm{\ϵ}}_{E0}\\ {\mathrm{\ϵ}}_{N0}\\ {\mathrm{\ϵ}}_{U0}\end{array}\right]=C_s^n\left[\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\end{array}\right]---\left(6\right)$

The 4th step: extract observed quantity;

In twin shaft Rotating Inertial Navigation System, be tied to form vertical just like ShiShimonoseki:

$\mathrm{\Δ\φ}\×=I-C_s^n{\left[C_s^{h2}\right]}^T{\left[C_{h1}^b\right]}^T{\left({\tilde{C}}_s^n\right)}^T---\left(7\right)$

Wherein, for be tied to the transition matrix of carrier coordinate system from outer shroud rack coordinate, for be tied to the transition matrix of interior ring stand coordinate system from IMU coordinate, the attitude matrix calculating for real-time navigation, for the fine alignment attitude matrix of the finish time is put by unit, Δ φ × be attitude error variation delta φ=[Δ φ _eΔ φ _nΔ φ _u] ^tthe antisymmetric matrix forming, therefore has

$\left\{\begin{array}{c}{\mathrm{\Δ\φ}}_E=\frac{{(\mathrm{\Δ\φ}\×)}_{32}-{(\mathrm{\Δ\φ}\×)}_{23}}{2}\\ {\mathrm{\Δ\φ}}_N=\frac{{(\mathrm{\Δ\φ}\×)}_{13}-{(\mathrm{\Δ\φ}\×)}_{31}}{2}\\ {\mathrm{\Δ\φ}}_U=\frac{{(\mathrm{\Δ\φ}\×)}_{21}-{(\mathrm{\Δ\φ}\×)}_{12}}{2}\end{array}\right.---\left(8\right)$

Attitude error equations in formula (3) is carried out to Laplace transform transposition, can obtain

$\mathrm{\Δ\φ}\left(s\right)={(\mathrm{sI}-A)}^{-1}[\frac{{\mathrm{\φ}}_0}{s}-{\mathrm{\ϵ}}^n\left(s\right)]---\left(9\right)$

Wherein $A=\left[\begin{array}{ccc}0& {\mathrm{\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{\ω}}_{\mathrm{ie}}\cos L\\ {-\mathrm{\ω}}_{\mathrm{ie}}\sin L& 0& 0\\ {\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 0\end{array}\right],$ Formula (9) is carried out to inverse Laplace transform can be obtained

Δφ(t)＝B(t)*φ ₀-B(t)*ε ⁿ(t) (10)

Wherein * represents convolution, $B\left(t\right)=\left[\begin{array}{ccc}1& {\mathrm{t\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{t\ω}}_{\mathrm{ie}}\cos L\\ {-\mathrm{t\ω}}_{\mathrm{ie}}\sin L& 1& 0\\ t{\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 1\end{array}\right]$

Velocity error equation is carried out to integration can be obtained

$\left\{\begin{array}{c}{\mathrm{\δV}}_E\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}[-g\·({\mathrm{\Δ\φ}}_N\left(\mathrm{\τ}\right)+{\mathrm{\φ}}_{N0})+{\▿}_E\left(\mathrm{\τ}\right)]\mathrm{d\τ}\\ {\mathrm{\δV}}_N\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}[g\·({\mathrm{\Δ\φ}}_E\left(\mathrm{\τ}\right)+{\mathrm{\φ}}_{E0})+{\▿}_N\left(\mathrm{\τ}\right)]\mathrm{d\τ}\\ {\mathrm{\δV}}_U\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}{\▿}_U\left(\mathrm{\τ}\right)\mathrm{d\τ}\end{array}\right.---\left(11\right).$

Compared with prior art, the present invention has following beneficial effect:

1) according to the relation between initial misalignment and device error, represent initial misalignment by device error, thereby eliminate the impact of the initial misalignment in position, solved the problem without initial attitude benchmark that twin shaft Rotating Inertial Navigation System exists in the time using system-level scaling method.

2) by attitude error equations is carried out to Laplace transform and inverse Laplace transform, then velocity error equation is carried out to integration and directly get velocity error and attitude error variable quantity as observed quantity, and need not get its first order derivative, reduce the impact of noise.

Brief description of the drawings

Fig. 1 is X position transposition scheme schematic diagram in the present invention.

Embodiment

Below in conjunction with the drawings and the specific embodiments, the present invention will be further described.

The present invention has designed X position transposition method, by representing initial misalignment by device error, solve the problem without accurate initial attitude benchmark, by attitude error equations is carried out to Laplace transform and inverse Laplace transform, the method of then velocity error equation being carried out to integration has avoided observed quantity to differentiate, thereby has reduced the impact of noise.

Below self-calibrating method of the present invention is described in detail.

First define coordinate system:

Navigation coordinate is O _nx _ny _nz _nfor: center is at Inertial Measurement Unit (IMU) center, three axle X _n, Y _n, Z _nconsistent with east, north, day direction respectively;

Carrier coordinate system O _bx _by _bz _bfor: initial point IMU center, O _bx _b, O _by _b, O _bz _bpoint to respectively right-hand, front and the top of carrier;

IMU coordinate system O _sx _sy _sz _sfor: initial point is in IMU center, three axles respectively with three gyroscopes in same direction, and form right hand rectangular coordinate system;

Outer shroud rack coordinate is O _h1x _h1y _h1z _h1for: initial point is in IMU center, and outer ring stand angle is to overlap with carrier coordinate system for 1 o'clock;

Interior ring stand coordinate system O _h2x _h2y _h2z _h2for: initial point is in IMU center, and interior ring stand angle is to overlap with IMU coordinate system for 1 o'clock;

Tri-direction of principal axis of the x, y, z direction of initialization system and IMU are consistent.Three accelerometers are arranged in three directions of x, y, z, and three gyroscopes are also arranged in three directions of x, y, z.

Step 1: device error model and the navigation error equation of setting up twin shaft Rotating Inertial Navigation System;

The 1st step: the device error model of setting up twin shaft Rotating Inertial Navigation System

The error model of accelerometer is:

${\▿}_n=\mathrm{\Δ}{C}_s^a{f}^s+\▿---\left(1\right)$

Wherein δ a ^sfor accelerometer output error, $\mathrm{\Δ}{C}_s^a=\left[\begin{array}{ccc}{K}_{\mathrm{ax}}& 0& 0\\ -S_{\mathrm{ayz}}& K_{\mathrm{ay}}& 0\\ S_{\mathrm{azy}}& {-S}_{\mathrm{azx}}& K_{\mathrm{az}}\end{array}\right]$ For the transition matrix from IMU coordinate system (s system) to accelerometer coordinate system, S _aijfor being the alignment error angle of accelerometer in i and j direction, S _aijin i=x, y, z, j=x, y, z and i ≠ j, K _ax, K _ayand K _azbe respectively the accelerometer scale factor error in x, y and z direction, f ^sfor the input specific force of velograph, $\▿={\left[\begin{array}{ccc}{\▿}_x& {\▿}_y& {\▿}_z\end{array}\right]}^T,$ with for the accelerometer bias in x, y and z direction.

Gyrostatic error model is:

${\mathrm{\ϵ}}_n=\mathrm{\Δ}{C}_s^g{\mathrm{\ω}}^s+\mathrm{\ϵ}---\left(2\right)$

Wherein δ ω ^sfor gyroscope output error, $\mathrm{\Δ}{C}_s^g=\left[\begin{array}{ccc}{K}_{\mathrm{gx}}& S_{\mathrm{gxz}}& {-S}_{\mathrm{gxy}}\\ {-S}_{\mathrm{gyz}}& K_{\mathrm{gy}}& S_{\mathrm{gyx}}\\ S_{\mathrm{gzy}}& {-S}_{\mathrm{gzx}}& K_{\mathrm{gz}}\end{array}\right]$ For be tied to the transition matrix of gyroscope coordinate system, S from IMU coordinate _gijfor being gyrostatic alignment error angle in i and j direction, S _gijin i=x, y, z, j=x, y, z, and i ≠ j, K _gx, K _gy. and K _gz. be respectively the gyroscope scale factor error in x, y and z direction, ω ^sfor input angular velocity, ε=[ε _xε _yε _z] ^tfor gyroscope zero inclined to one side.

The 2nd step: the navigation error equation of setting up twin shaft Rotating Inertial Navigation System

The twin shaft Rotating Inertial Navigation System navigation error equation that is applicable to multiposition scaling scheme is

$\left\{\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=-g\·(\mathrm{\Δ}{\mathrm{\φ}}_N+{\mathrm{\φ}}_{N0})+{\▿}_E\\ \mathrm{\δ}{\stackrel{\·}{V}}_N=g\·({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})+{\▿}_N\\ \mathrm{\δ}{\stackrel{\·}{V}}_U={\▿}_U\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_E={\mathrm{\ω}}_{\mathrm{ie}}\sin L\·({\mathrm{\Δ\φ}}_N+{\mathrm{\φ}}_{N0})-{\mathrm{\ω}}_{\mathrm{ie}}\cos L\·({\mathrm{\Δ\φ}}_U+{\mathrm{\φU}}_0)-{\mathrm{\ϵ}}_E\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_N=-{\mathrm{\ω}}_{\mathrm{ie}}\sin L\·({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})-{\mathrm{\ϵ}}_N\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_U={\mathrm{\ω}}_{\mathrm{ie}}\cos L\·{({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})}_E-{\mathrm{\ϵ}}_U\end{array}\right.---\left(3\right)$

Wherein δ V _e, δ V _n, δ V _ube respectively east orientation, north orientation and sky to velocity error, Δ φ _e, Δ φ _nwith Δ φ _ube respectively system east orientation, north orientation and day to misalignment variable quantity, with be respectively east orientation, north orientation and day to component, ε _e, ε _nand ε _ube respectively ε _neast orientation, north orientation and day to component, g is acceleration of gravity, L is local latitude, ω _iefor rotational-angular velocity of the earth, φ _e0, φ _n0, φ _u0for system east orientation, north orientation and day to initial misalignment.

The 3rd step: fine alignment is put by process need unit due to self-calibration, unit is put after fine alignment, adopts the error parameter of gyroscope and accelerometer to represent the initial misalignment φ of system _e0, φ _n0, φ _u0, have:

$\left\{\begin{array}{c}{\mathrm{\φ}}_{E0}=\frac{{\▿}_{N0}}{g}\\ {\mathrm{\φ}}_{N0}=-\frac{{\▿}_{E0}}{g}\\ {\mathrm{\φ}}_{U0}=\frac{{\mathrm{\ϵ}}_{N0}}{{\mathrm{\ω}}_{\mathrm{ie}}\cos L}\end{array}\right.---\left(4\right)$

Wherein ${{\▿}_0=\left[\begin{array}{ccc}{\▿}_{E0}& {\▿}_{N0}& {\▿}_{U0}\end{array}\right]}^T$ And ε ₀=[ε _e0ε _n0ε _u0] ^tbe respectively accelerometer and the gyro error of the equivalence of initial alignment position, that is:

$\left[\begin{array}{c}{\▿}_{E0}\\ {\▿}_{N0}\\ {\▿}_{U0}\end{array}\right]=C_s^n\left[\begin{array}{c}{\▿}_x\\ {\▿}_y\\ {\▿}_z\end{array}\right]---\left(5\right)$

$\left[\begin{array}{c}{\mathrm{\ϵ}}_{E0}\\ {\mathrm{\ϵ}}_{N0}\\ {\mathrm{\ϵ}}_{U0}\end{array}\right]=C_s^n\left[\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\end{array}\right]---\left(6\right)$

The 4th step: extract observed quantity

In twin shaft Rotating Inertial Navigation System, be tied to form vertical just like ShiShimonoseki:

$\mathrm{\Δ\φ}\×=I-C_s^n{\left[C_s^{h2}\right]}^T{\left[C_{h1}^b\right]}^T{\left({\tilde{C}}_s^n\right)}^T---\left(7\right)$

Wherein, for be tied to the transition matrix of carrier coordinate system from outer shroud rack coordinate, for be tied to the transition matrix of interior ring stand coordinate system from IMU coordinate, the attitude matrix calculating for real-time navigation, for the fine alignment attitude matrix of the finish time is put by unit, Δ φ × be attitude error variation delta φ=[Δ φ _eΔ φ _nΔ φ _u] ^tthe antisymmetric matrix forming, therefore has

$\left\{\begin{array}{c}{\mathrm{\Δ\φ}}_E=\frac{{(\mathrm{\Δ\φ}\×)}_{32}-{(\mathrm{\Δ\φ}\×)}_{23}}{2}\\ {\mathrm{\Δ\φ}}_N=\frac{{(\mathrm{\Δ\φ}\×)}_{13}-{(\mathrm{\Δ\φ}\×)}_{31}}{2}\\ {\mathrm{\Δ\φ}}_U=\frac{{(\mathrm{\Δ\φ}\×)}_{21}-{(\mathrm{\Δ\φ}\×)}_{12}}{2}\end{array}\right.---\left(8\right)$

Attitude error equations in formula (3) is carried out to Laplace transform transposition, can obtain

$\mathrm{\Δ\φ}\left(s\right)={(\mathrm{sI}-A)}^{-1}[\frac{{\mathrm{\φ}}_0}{s}-{\mathrm{\ϵ}}^n\left(s\right)]---\left(9\right)$

Wherein $A=\left[\begin{array}{ccc}0& {\mathrm{\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{\ω}}_{\mathrm{ie}}\cos L\\ {-\mathrm{\ω}}_{\mathrm{ie}}\sin L& 0& 0\\ {\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 0\end{array}\right].$ Formula (9) is carried out to inverse Laplace transform can be obtained

Δφ(t)＝B(t)*φ ₀-B(t)*ε ⁿ(t) (10)

Wherein * represents convolution, $B\left(t\right)=\left[\begin{array}{ccc}1& {\mathrm{t\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{t\ω}}_{\mathrm{ie}}\cos L\\ {-\mathrm{t\ω}}_{\mathrm{ie}}\sin L& 1& 0\\ t{\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 1\end{array}\right].$

Velocity error equation is carried out to integration can be obtained

$\left\{\begin{array}{c}{\mathrm{\δV}}_E\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}[-g\·({\mathrm{\Δ\φ}}_N\left(\mathrm{\τ}\right)+{\mathrm{\φ}}_{N0})+{\▿}_E\left(\mathrm{\τ}\right)]\mathrm{d\τ}\\ {\mathrm{\δV}}_N\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}[g\·({\mathrm{\Δ\φ}}_E\left(\mathrm{\τ}\right)+{\mathrm{\φ}}_{E0})+{\▿}_N\left(\mathrm{\τ}\right)]\mathrm{d\τ}\\ {\mathrm{\δV}}_U\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}{\▿}_U\left(\mathrm{\τ}\right)\mathrm{d\τ}\end{array}\right.---\left(11\right).$

Step 2, preheating gyroscope and accelerometer module, carry out putting fine alignment fine alignment based on the unit of Kalman filtering;

The present invention adopts " inertial navigation " (Qin Yongyuan work, Beijing: Science Press, 2006,370-371 page) in single position aligning method, the method is still in a position as prerequisite taking inertial navigation system, gyroscope and accelerometer error regard respectively equivalent east orientation, north orientation as, day to angular velocity error and acceleration error, taking velocity error as observed quantity, adopt kalman filter method to estimate misalignment.

Step 3, according to fine alignment result rotation vector, adjust carrier positions to approximate be to overlap with navigation coordinate;

Step 4, rotate ring stand according to X position transposition scheme designed in Fig. 1, the velocity error obtaining at each station acquisition navigation calculation is also calculated attitude error variable quantity, obtains observed quantity

Z(i)＝[δV _E(i),δV _N(i),δV _U(i),Δφ _E(i),Δφ _N(i),Δφ _U(i)] ^T (12)

Wherein i represents positional number.According to the observed quantity of each position, can obtain total observation vector and be

Z＝[Z(2),Z(3),...Z(10)] ^T (13)

Step 5, the error parameter that utilizes least-squares calculation to go out needs demarcation according to the navigation results of each position are

$\hat{X}={\left(H^{T}H\right)}^{-1}{H}^{T}Z---\left(14\right)$

Wherein for quantity of state

$\begin{array}{c}X=[S_{\mathrm{ayz}},S_{\mathrm{azy}},S_{\mathrm{azx}},S_{\mathrm{gxz}},S_{\mathrm{gxy}},S_{\mathrm{gyz}},S_{\mathrm{gyx}},S_{\mathrm{gzy}},S_{\mathrm{gzx}},\\ K_{\mathrm{ax}},K_{\mathrm{ay}},K_{\mathrm{az}},K_{\mathrm{gx}},K_{\mathrm{gy}},K_{\mathrm{gz}},{\▿}_x,{\▿}_y,{\▿}_z,{\mathrm{\ϵ}}_x,{\mathrm{\ϵ}}_y,{\mathrm{\ϵ}}_z]\end{array}---\left(15\right)$

Estimated value, H is matrix of coefficients.

Claims (2)

1. a twin shaft Rotating Inertial Navigation System multiposition Auto-calibration method, is characterized in that, comprises the following steps:

Step 1: device error model and the navigation error equation of setting up twin shaft Rotating Inertial Navigation System;

Step 2, preheating gyroscope and accelerometer module, carry out putting fine alignment based on the unit of Kalman filtering;

Step 3, according to fine alignment result rotation vector, adjust carrier positions to approximate be to overlap with navigation coordinate;

Step 4, according to X position transposition method rotate ring stand, the velocity error obtaining at each station acquisition navigation calculation is also calculated attitude error variable quantity, obtains observed quantity;

Step 5, according to the navigation results of each position utilize least-squares calculation go out need demarcate error.

2. a kind of twin shaft Rotating Inertial Navigation System multiposition Auto-calibration method as claimed in claim 1, is characterized in that, wherein the device error model of setting up described in step 1 comprises the following steps:

The 1st step: the device error model of setting up twin shaft Rotating Inertial Navigation System; Wherein:

The error model of accelerometer is:

${\▿}_n=\mathrm{\Δ}{C}_s^a{f}^s+\▿---\left(1\right)$

Wherein for accelerometer output error, $\mathrm{\Δ}{C}_s^a=\left[\begin{array}{ccc}{K}_{\mathrm{ax}}& 0& 0\\ -S_{\mathrm{ayz}}& K_{\mathrm{ay}}& 0\\ S_{\mathrm{azy}}& {-S}_{\mathrm{azx}}& K_{\mathrm{az}}\end{array}\right]$ For being the transition matrix that s is tied to accelerometer coordinate system from IMU coordinate system, S _aijfor the alignment error angle of accelerometer in i and j direction, S _aijin i=x, y, z, j=x, y, z and i ≠ j, K _ax, K _ayand K _azbe respectively the accelerometer scale factor error in x, y and z direction, f ^sfor the input specific force of velograph, $\▿={\left[\begin{array}{ccc}{\▿}_x& {\▿}_y& {\▿}_z\end{array}\right]}^T,$ with for the accelerometer bias in x, y and z direction;

Gyrostatic error model is:

${\mathrm{\ϵ}}_n=\mathrm{\Δ}{C}_s^g{\mathrm{\ω}}^s+\mathrm{\ϵ}---\left(2\right)$

Wherein ε _nfor gyroscope output error, $\mathrm{\Δ}{C}_s^g=\left[\begin{array}{ccc}{K}_{\mathrm{gx}}& S_{\mathrm{gxz}}& {-S}_{\mathrm{gxy}}\\ {-S}_{\mathrm{gyz}}& K_{\mathrm{gy}}& S_{\mathrm{gyx}}\\ S_{\mathrm{gzy}}& {-S}_{\mathrm{gzx}}& K_{\mathrm{gz}}\end{array}\right]$ For be tied to the transition matrix of gyroscope coordinate system, S from IMU coordinate _gijfor being gyrostatic alignment error angle in i and j direction, S _gijin i=x, y, z, j=x, y, z, and i ≠ j, K _gx, K _gy. and K _gzbe respectively the gyroscope scale factor error in x, y and z direction, ω ^sfor input angular velocity, ε=[ε _xε _yε _z] ^tfor gyroscope zero inclined to one side;

The 2nd step: the navigation error equation of setting up twin shaft Rotating Inertial Navigation System:

$\left\{\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=-g\·(\mathrm{\Δ}{\mathrm{\φ}}_N+{\mathrm{\φ}}_{N0})+{\▿}_E\\ \mathrm{\δ}{\stackrel{\·}{V}}_N=g\·({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})+{\▿}_N\\ \mathrm{\δ}{\stackrel{\·}{V}}_U={\▿}_U\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_E={\mathrm{\ω}}_{\mathrm{ie}}\sin L\·({\mathrm{\Δ\φ}}_N+{\mathrm{\φ}}_{N0})-{\mathrm{\ω}}_{\mathrm{ie}}\cos L\·({\mathrm{\Δ\φ}}_U+{\mathrm{\φU}}_0)-{\mathrm{\ϵ}}_E\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_N=-{\mathrm{\ω}}_{\mathrm{ie}}\sin L\·({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})-{\mathrm{\ϵ}}_N\\ \mathrm{\Δ}{\stackrel{\·}{\mathrm{\φ}}}_U={\mathrm{\ω}}_{\mathrm{ie}}\cos L\·{({\mathrm{\Δ\φ}}_E+{\mathrm{\φ}}_{E0})}_E-{\mathrm{\ϵ}}_U\end{array}\right.---\left(3\right)$

Wherein δ V _e, δ V _n, δ V _ube respectively east orientation, north orientation and sky to velocity error, Δ φ _e, Δ φ _nwith Δ φ _ube respectively system east orientation, north orientation and day to misalignment variable quantity, with be respectively east orientation, north orientation and day to component, ε _e, ε _nand ε _ube respectively ε _neast orientation, north orientation and day to component, g is acceleration of gravity, L is local latitude, ω _iefor rotational-angular velocity of the earth, φ _e0, φ _n0, φ _u0for system east orientation, north orientation and day to initial misalignment;

The 3rd step: fine alignment is put by process need unit due to self-calibration, unit is put after fine alignment, adopts the error model parameters of gyroscope and accelerometer to represent the initial misalignment φ of system _e0, φ _n0, φ _u0, have:

$\left\{\begin{array}{c}{\mathrm{\φ}}_{E0}=\frac{{\▿}_{N0}}{g}\\ {\mathrm{\φ}}_{N0}=-\frac{{\▿}_{E0}}{g}\\ {\mathrm{\φ}}_{U0}=\frac{{\mathrm{\ϵ}}_{N0}}{{\mathrm{\ω}}_{\mathrm{ie}}\cos L}\end{array}\right.---\left(4\right)$

Wherein ${{\▿}_0=\left[\begin{array}{ccc}{\▿}_{E0}& {\▿}_{N0}& {\▿}_{U0}\end{array}\right]}^T$ And ε ₀=[ε _e0ε _n0ε _u0] ^tbe respectively accelerometer and the gyro error of the equivalence of initial alignment position, that is:

$\left[\begin{array}{c}{\▿}_{E0}\\ {\▿}_{N0}\\ {\▿}_{U0}\end{array}\right]=C_s^n\left[\begin{array}{c}{\▿}_x\\ {\▿}_y\\ {\▿}_z\end{array}\right]---\left(5\right)$

$\left[\begin{array}{c}{\mathrm{\ϵ}}_{E0}\\ {\mathrm{\ϵ}}_{N0}\\ {\mathrm{\ϵ}}_{U0}\end{array}\right]=C_s^n\left[\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\end{array}\right]---\left(6\right)$

The 4th step: extract observed quantity;

In twin shaft Rotating Inertial Navigation System, be tied to form vertical just like ShiShimonoseki:

$\mathrm{\Δ\φ}\×=I-C_s^n{\left[C_s^{h2}\right]}^T{\left[C_{h1}^b\right]}^T{\left({\tilde{C}}_s^n\right)}^T---\left(7\right)$

Wherein, for be tied to the transition matrix of carrier coordinate system from outer shroud rack coordinate, for be tied to the transition matrix of interior ring stand coordinate system from IMU coordinate, the attitude matrix calculating for real-time navigation, for the fine alignment attitude matrix of the finish time is put by unit, Δ φ × be attitude error variation delta φ=[Δ φ _eΔ φ _nΔ φ _u] ^tthe antisymmetric matrix forming, therefore has

$\left\{\begin{array}{c}{\mathrm{\Δ\φ}}_E=\frac{{(\mathrm{\Δ\φ}\×)}_{32}-{(\mathrm{\Δ\φ}\×)}_{23}}{2}\\ {\mathrm{\Δ\φ}}_N=\frac{{(\mathrm{\Δ\φ}\×)}_{13}-{(\mathrm{\Δ\φ}\×)}_{31}}{2}\\ {\mathrm{\Δ\φ}}_U=\frac{{(\mathrm{\Δ\φ}\×)}_{21}-{(\mathrm{\Δ\φ}\×)}_{12}}{2}\end{array}\right.---\left(8\right)$

Attitude error equations in formula (3) is carried out to Laplace transform transposition, can obtain

$\mathrm{\Δ\φ}\left(s\right)={(\mathrm{sI}-A)}^{-1}[\frac{{\mathrm{\φ}}_0}{s}-{\mathrm{\ϵ}}^n\left(s\right)]---\left(9\right)$

Wherein $A=\left[\begin{array}{ccc}0& {\mathrm{\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{\ω}}_{\mathrm{ie}}\cos L\\ {-\mathrm{\ω}}_{\mathrm{ie}}\sin L& 0& 0\\ {\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 0\end{array}\right],$ Formula (9) is carried out to inverse Laplace transform can be obtained

Δφ(t)＝B(t)*φ ₀-B(t)*ε ⁿ(t) (10)

Wherein * represents convolution, $B\left(t\right)=\left[\begin{array}{ccc}1& {\mathrm{t\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{t\ω}}_{\mathrm{ie}}\cos L\\ {-\mathrm{t\ω}}_{\mathrm{ie}}\sin L& 1& 0\\ t{\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 1\end{array}\right]$

Velocity error equation is carried out to integration can be obtained

$\left\{\begin{array}{c}{\mathrm{\δV}}_E\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}[-g\·({\mathrm{\Δ\φ}}_N\left(\mathrm{\τ}\right)+{\mathrm{\φ}}_{N0})+{\▿}_E\left(\mathrm{\τ}\right)]\mathrm{d\τ}\\ {\mathrm{\δV}}_N\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}[g\·({\mathrm{\Δ\φ}}_E\left(\mathrm{\τ}\right)+{\mathrm{\φ}}_{E0})+{\▿}_N\left(\mathrm{\τ}\right)]\mathrm{d\τ}\\ {\mathrm{\δV}}_U\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{\mathrm{\τ}=t}{\∫}}{\▿}_U\left(\mathrm{\τ}\right)\mathrm{d\τ}\end{array}\right.---\left(11\right).$