CN104165638B - 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 dual-axis rotation inertial navigation system multiposition Auto-calibration method

Technical field

The present invention relates to a kind of device error Auto-calibration method of the prompt even technical field of inertial of rotation modulation.

Background technology

Navigation accuracy when the rotation modulation technology that Rotating Inertial Navigation System is used can improve navigation system length boat, but During real system application, navigation accuracy is still affected by inertia device precision, needs to enter rower to inertia device before use Fixed.Majority of demarcating to Inertial Measurement Unit (IMU) is based on high precision turntable at present, needs inertial navigation system to disassemble Deliver to laboratory to carry out, although the method ensure that certain precision, there is operational poor, high cost and repeatability The problems such as error.In addition, inertial device error is not changeless, As time goes on, the error before demarcated Numerical value can not be further continued for using, and needs to re-start demarcation, and this is unfavorable for the use of navigation system during long boat.

Dual-axis rotation inertial navigation system carries two ring stands due to itself, therefore can carry out from principal mark without the help of turntable Fixed, but it is provided that accurate attitude reference like that because ring stand is not as turntable, and therefore existing system level scaling method is being answered There is obstacle during for dual-axis rotation inertial navigation system, need to design new Auto-calibration method.

Content of the invention

It is an object of the invention to provide one kind is applied to dual-axis rotation inertial navigation system, it is to avoid system component regular dismounting, The online calibration method of navigation independence during long boat can be improved.

In order to solve above-mentioned technical problem, the present invention adopts the following technical scheme that：

A kind of dual-axis rotation inertial navigation system multiposition Auto-calibration method, comprises the following steps：

Step 1：Set up device error model and the navigation error equation of dual-axis rotation 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 approximately overlapping with navigational coordinate system；

Step 4, according to X position transposition method rotate ring stand, the velocity error obtaining in each station acquisition navigation calculation And calculate attitude error variable quantity, obtain observed quantity；

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

Device error model of setting up wherein described in step one comprises the following steps：

1st step：Set up the device error model of dual-axis rotation inertial navigation system；Wherein：

The error model of accelerometer is：

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

WhereinFor accelerometer output error, $\mathrm{\Δ}{C}_s^a=\left[\begin{array}{ccc}{K}_{\mathrm{ax}}& 0& 0\\ -S_{\mathrm{ayz}}& K_{\mathrm{ay}}& 0\\ S_{\mathrm{azy}}& {-S}_{\mathrm{azx}}& K_{\mathrm{az}}\end{array}\right]$ It is to be s system from IMU coordinate system To the transition matrix of accelerometer coordinate system, S_aijFor the fix error angle of accelerometer on i and j direction, S_aijIn i=x, y, Z, j=x, y, z and i ≠ j, K_ax、K_ayAnd K_azIt is respectively the accelerometer scale factor error on x, y and z direction, f^sFor speed The input specific force of meter, $\▿={\left[\begin{array}{ccc}{\▿}_x& {\▿}_y& {\▿}_z\end{array}\right]}^T,$ WithFor the accelerometer bias on x, y and z direction；

The error model of gyroscope is：

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

Wherein ε_nFor gyroscope output error, $\mathrm{\Δ}{C}_s^g=\left[\begin{array}{ccc}{K}_{\mathrm{gx}}& S_{\mathrm{gxz}}& {-S}_{\mathrm{gxy}}\\ {-S}_{\mathrm{gyz}}& K_{\mathrm{gy}}& S_{\mathrm{gyx}}\\ S_{\mathrm{gzy}}& {-S}_{\mathrm{gzx}}& K_{\mathrm{gz}}\end{array}\right]$ It is to be tied to gyroscope from IMU coordinate The transition matrix of coordinate system, S_gijFor the fix error angle of gyroscope on i and j direction, S_gijIn i=x, y, z, j=x, y, Z, and i ≠ j, K_gx、K_gy. and K_gzIt is respectively the gyroscope scale factor error on x, y and z direction, ω^sFor input angular velocity, ε =[ε_xε_yε_z]^TInclined for gyroscope zero；

2nd step：Set up the navigation error equation of dual-axis rotation 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,δV_N,δV_UIt is respectively east orientation, north orientation and sky orientation speed error, Δ φ_E、Δφ_NWith Δ φ_UIt is respectively System east orientation, north orientation and sky to misalignment variable quantity,WithIt is respectivelyEast orientation, north orientation and sky to component, ε_E、ε_NAnd ε_UIt is respectively ε_nEast orientation, north orientation and sky to component, g be acceleration of gravity, L be local latitude, ω_ieFor earth rotation Angular speed, φ_E0、φ_N0、φ_U0For system east orientation, north orientation and sky to initial misalignment；

3rd step：Because self-calibration process needs unit to put fine alignment, after unit puts fine alignment, using gyroscope and acceleration The error model parameters of degree meter represent the initial misalignment φ of system_E0、φ_N0、φ_U0, then 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 ε₀=[ε_E0ε_N0ε_U0]^TIt is respectively equivalent acceleration at initial alignment position Degree meter and gyro error, that is,：

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

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

4th step：Extract observed quantity；

In dual-axis rotation inertial navigation system, it is 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,It is the transition matrix being tied to carrier coordinate system from outer shroud rack coordinate,It is to be tied to inner ring from IMU coordinate The transition matrix of rack coordinate system,The attitude matrix calculating for real-time navigation,Put fine alignment finish time for unit Attitude matrix, Δ φ × it is attitude error variation delta φ=[Δ φ_EΔφ_NΔφ_U]^TThe antisymmetric matrix constituting, therefore Have

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

Attitude error equations in formula (3) are carried out by Laplace transform and transplant, 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 $A=\left[\begin{array}{ccc}0& {\mathrm{\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{\ω}}_{\mathrm{ie}}\cos L\\ {-\mathrm{\ω}}_{\mathrm{ie}}\sin L& 0& 0\\ {\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 0\end{array}\right],$ Carry out inverse Laplace transform to formula (9) can obtain

Δ φ (t)=B (t) * φ₀-B(t)*εⁿ(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 integrated obtaining

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

Compared with prior art, the invention has the advantages that：

1) according to the relation between initial misalignment and device error, represent initial misalignment with device error, thus Eliminate the impact of the initial misalignment in position, solve what dual-axis rotation inertial navigation system was existed when using systematic calibration method The problem of no initial attitude benchmark.

2) by Laplace transform and inverse Laplace transform are carried out to attitude error equations, then to velocity error side Journey is integrated directly taking velocity error and attitude error variable quantity as observed quantity, and without taking its first derivative, reduces The impact of noise.

Brief description

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

Specific embodiment

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

The present invention devises X position transposition method, by representing initial misalignment with device error, solves no accurately The problem of initial attitude benchmark is by carrying out Laplace transform and inverse Laplace transform to attitude error equations, then right The method that velocity error equation is integrated avoids differentiates to observed quantity, thus reducing the impact of noise.

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

Define coordinate system first：

Navigational coordinate system O_nX_nY_nZ_nFor：Center is in Inertial Measurement Unit (IMU) center, three axle X_n、Y_n、Z_nRespectively with East, north, sky direction are consistent；

Carrier coordinate system O_bX_bY_bZ_bFor：Initial point is in IMU center, O_bX_b、O_bY_b、O_bZ_bIt is respectively directed to right, the front of carrier And top；

IMU coordinate system O_sX_sY_sZ_sFor：Initial point in IMU center, three axles respectively with three gyroscopes in same direction On, and constitute right hand rectangular coordinate system；

Outer shroud rack coordinate system O_h1X_h1Y_h1Z_h1For：In IMU center, outer ring stand angle is when zero and carrier coordinate system to initial point Overlap；

Interior ring stand coordinate system O_h2X_h2Y_h2Z_h2For：In IMU center, interior ring stand angle is when zero and IMU coordinate system weight to initial point Close；

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

Step 1：Set up device error model and the navigation error equation of dual-axis rotation inertial navigation system；

1st step：Set up the device error model of dual-axis rotation 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, $\mathrm{\Δ}{C}_s^a=\left[\begin{array}{ccc}{K}_{\mathrm{ax}}& 0& 0\\ -S_{\mathrm{ayz}}& K_{\mathrm{ay}}& 0\\ S_{\mathrm{azy}}& {-S}_{\mathrm{azx}}& K_{\mathrm{az}}\end{array}\right]$ It is from IMU coordinate system (s system) To the transition matrix of accelerometer coordinate system, S_aijFor the fix error angle of accelerometer on i and j direction, S_aijIn i=x, Y, z, j=x, y, z and i ≠ j, K_ax、K_ayAnd K_azIt is respectively the accelerometer scale factor error on x, y and z direction, f^sFor speed The input specific force of degree meter, $\▿={\left[\begin{array}{ccc}{\▿}_x& {\▿}_y& {\▿}_z\end{array}\right]}^T,$ WithFor the accelerometer bias on x, y and z direction.

The error model of gyroscope is：

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

Wherein δ ω^sFor gyroscope output error, $\mathrm{\Δ}{C}_s^g=\left[\begin{array}{ccc}{K}_{\mathrm{gx}}& S_{\mathrm{gxz}}& {-S}_{\mathrm{gxy}}\\ {-S}_{\mathrm{gyz}}& K_{\mathrm{gy}}& S_{\mathrm{gyx}}\\ S_{\mathrm{gzy}}& {-S}_{\mathrm{gzx}}& K_{\mathrm{gz}}\end{array}\right]$ It is to be tied to gyro from IMU coordinate The transition matrix of instrument coordinate system, S_gijFor the fix error angle of gyroscope on i and j direction, S_gijIn i=x, y, z, j=x, Y, z, and i ≠ j, K_gx、K_gy. and K_gz. it is respectively the gyroscope scale factor error on x, y and z direction, ω^sFor input angle speed Degree, ε=[ε_xε_yε_z]^TInclined for gyroscope zero.

2nd step：Set up the navigation error equation of dual-axis rotation inertial navigation system

The dual-axis rotation inertial navigation system navigation error equation being applied 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,δV_N,δV_UIt is respectively east orientation, north orientation and sky orientation speed error, Δ φ_E、Δφ_NWith Δ φ_UIt is respectively System east orientation, north orientation and sky to misalignment variable quantity,WithIt is respectivelyEast orientation, north orientation and sky to component, ε_E、ε_NAnd ε_UIt is respectively ε_nEast orientation, north orientation and sky to component, g be acceleration of gravity, L be local latitude, ω_ieFor earth rotation Angular speed, φ_E0、φ_N0、φ_U0For system east orientation, north orientation and sky to initial misalignment.

3rd step：Because self-calibration process needs unit to put fine alignment, after unit puts fine alignment, using gyroscope and acceleration The error parameter of degree meter represents the initial misalignment φ of system_E0、φ_N0、φ_U0, then 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 ε₀=[ε_E0ε_N0ε_U0]^TIt is respectively equivalent acceleration at initial alignment position Meter and gyro error, that is,：

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

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

4th step：Extract observed quantity

In dual-axis rotation inertial navigation system, it is 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,It is the transition matrix being tied to carrier coordinate system from outer shroud rack coordinate,It is to be tied to inner ring from IMU coordinate The transition matrix of rack coordinate system,The attitude matrix calculating for real-time navigation,Put fine alignment finish time for unit Attitude matrix, Δ φ × it is attitude error variation delta φ=[Δ φ_EΔφ_NΔφ_U]^TThe antisymmetric matrix constituting, therefore Have

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

Attitude error equations in formula (3) are carried out by Laplace transform and transplant, 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 $A=\left[\begin{array}{ccc}0& {\mathrm{\ω}}_{\mathrm{ie}}\sin L& -{\mathrm{\ω}}_{\mathrm{ie}}\cos L\\ {-\mathrm{\ω}}_{\mathrm{ie}}\sin L& 0& 0\\ {\mathrm{\ω}}_{\mathrm{ie}}\cos L& 0& 0\end{array}\right].$ Carry out inverse Laplace transform to formula (9) can obtain

Δ φ (t)=B (t) * φ₀-B(t)*εⁿ(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 integrated obtaining

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

Step 2, preheating gyroscope and accelerometer module, it is right to carry out putting fine alignment essence based on the unit of Kalman filtering Accurate；

The present invention adopts《Inertial navigation》(Qin Yongyuan writes, Beijing：Science Press, page 2006,370-371) in unit Put alignment methods, the method is still in premised on a position by inertial navigation system, and gyroscope and accelerometer error are seen respectively The equivalent east orientation of one-tenth, north orientation, sky, to angular speed error and acceleration error, with velocity error as observed quantity, are filtered using Kalman Wave method estimates misalignment.

Step 3, according to fine alignment result rotation vector, adjust carrier positions to approximately overlapping with navigational coordinate system；

Step 4, rotate ring stand according to designed in Fig. 1 X position indexing scheme, in each station acquisition navigation calculation The velocity error that obtains simultaneously calculates attitude error variable quantity, obtains observed quantity

Z (i)=[δ V_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 is

Z=[Z (2), Z (3) ... Z (10)]^T(13)

Step 5, go out to need the error parameter demarcated be according to the navigation results of each position using least-squares calculation

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

WhereinFor quantity of state

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

Estimate, H be coefficient matrix.

Claims (1)

1. a kind of dual-axis rotation inertial navigation system multiposition Auto-calibration method is it is characterised in that comprise the following steps：

Step 1：Set up device error model and the navigation error equation of dual-axis rotation 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 approximately overlapping with navigational coordinate system；

Step 4, rotate ring stand according to X position transposition method, the velocity error obtaining in each station acquisition navigation calculation is simultaneously counted Calculate attitude error variable quantity, obtain observed quantity；

Step 5, go out to need the error demarcated using least-squares calculation according to the navigation results of each position；

Device error model of setting up described in described step one comprises the following steps：

1st step：Set up the device error model of dual-axis rotation inertial navigation system；Wherein：

The error model of accelerometer is：

WhereinFor accelerometer output error,It is to be that s is tied to acceleration from IMU coordinate system The transition matrix of degree meter coordinate system, S_aijFor the fix error angle of accelerometer on i and j direction, S_aijIn i=x, y, z, j= X, y, z and i ≠ j, K_ax、K_ayAnd K_azIt is respectively the accelerometer scale factor error on x, y and z direction, f^sDefeated for speedometer Enter specific force, WithFor the accelerometer bias on x, y and z direction；

The error model of gyroscope is：

Wherein ε_nFor gyroscope output error,It is to be tied to gyroscope coordinate from IMU coordinate The transition matrix of system, S_gijFor the fix error angle of gyroscope on i and j direction, S_gijIn And i ≠ j, K_gx、K_gy. and K_gzIt is respectively the gyroscope scale factor error on x, y and z direction, ω_sFor input angular velocity, ε= [ε_xε_yε_z]^TInclined for gyroscope zero；

2nd step：Set up the navigation error equation of dual-axis rotation inertial navigation system：

Wherein δ V_E,δV_N,δV_UIt is respectively east orientation, north orientation and sky orientation speed error, Δ φ_E、Δφ_NWith Δ φ_UThe system of being respectively east To, north orientation and sky to misalignment variable quantity,WithIt is respectivelyEast orientation, north orientation and sky to component, ε_E、ε_NWith ε_UIt is respectively ε_nEast orientation, north orientation and sky to component, g be acceleration of gravity, L be local latitude, ω_ieFor earth rotation angle speed Degree, φ_E0、φ_N0、φ_U0For system east orientation, north orientation and sky to initial misalignment；

3rd step：Because self-calibration process needs unit to put fine alignment, after unit puts fine alignment, using gyroscope and accelerometer Error model parameters represent the initial misalignment φ of system_E0、φ_N0、φ_U0, then have：

WhereinAnd ε₀=[ε_E0ε_N0ε_U0]^TIt is respectively equivalent accelerometer at initial alignment position And gyro error, that is,：

4th step：Extract observed quantity；

In dual-axis rotation inertial navigation system, it is tied to form vertical just like ShiShimonoseki：

Wherein,It is the transition matrix being tied to carrier coordinate system from outer shroud rack coordinate,It is to be tied to interior ring stand from IMU coordinate to sit The transition matrix of mark system,The attitude matrix calculating for real-time navigation,Put the attitude of fine alignment finish time for unit Matrix, Δ φ × it is attitude error variation delta φ=[Δ φ_EΔφ_NΔφ_U]^TThe antisymmetric matrix constituting, therefore has

Attitude error equations in formula (3) are carried out by Laplace transform and transplant, can obtain

WhereinCarry out inverse Laplace transform to formula (9) can obtain

Δ φ (t)=B (t) * φ₀-B(t)*εⁿ(t) (10)

Wherein * represents convolution,

Velocity error equation is integrated obtaining