CN103616035B - A kind of performance parameter calibration method of laser strapdown inertial navigation system - Google Patents

Abstract

The invention discloses a kind of performance parameter calibration method of laser strapdown inertial navigation system, adopt marble flat board and turnover bracket or low precision turntable as calibration facility, according to the characteristic of Laser strapdown inertial navigation, under employing navigation mode, the output speed of Laser strapdown inertial navigation is as observed quantity.Method of the present invention successfully can carry out parameter calibration to Laser strapdown inertial navigation, reduces calibration facility cost and to demarcating the restriction of test site, solving existing scaling method and must use high precision turntable, to place and the higher problem of equipment requirement.

Description

A kind of performance parameter calibration method of laser strapdown inertial navigation system

Technical field

The present invention relates to strapdown inertial navigation system, particularly a kind of Laser strapdown inertial navigation performance parameter calibration method.

Background technology

The method that the demarcation that strapdown traditional is at present used to organize inertia device performance parameter adopts carries out rate versus position demarcation in high precision turntable, this scaling method requires that local geographic coordinate system is accurately aimed in Laser strapdown inertial navigation, technical requirement is harsh, otherwise will affect stated accuracy towards error.Although the method precision is higher, must be fixed at the enterprising rower of degree of precision turntable, comparatively greatly, calibration cost is high for equipment, place restriction.

Summary of the invention

Technical matters to be solved by this invention is, not enough for prior art, provides a kind of performance parameter calibration method of laser strapdown inertial navigation system, solves existing scaling method and must use high precision turntable, to place and the higher problem of equipment requirement.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of performance parameter calibration method of laser strapdown inertial navigation system, and the method is:

1) Ring Laser Gyroscope SINS is arranged on mould turnover, mould turnover is placed on flat board, and Ring Laser Gyroscope SINS is aimed at local geographic coordinate system;

2) error model of Ring Laser Gyroscope SINS is set up:

δa _bx=α _x+α _xxa _bx+α _xya _by+α _xza _bz

δa _by=α _y+α _yxa _bx+α _yya _by+α _yza _bz

δa _bz=α _z+α _zxa _bx+α _zya _by+α _zza _bz

δω _bx=β _x+β _xxω _bx+β _xyω _by+β _xzω _bz+(β _xyxa _bx+β _xyya _by+β _xyza _bz)ω _by+(β _xzxa _bx+β _xzya _by+β _xzza _bz)ω _bz

δω _by=β _y+β _yxω _bx+β _yyω _by+β _yzω _bz+(β _yxxa _bx+β _yxya _by+β _yxza _bz)ω _bx+(β _yzxa _bx+β _yzya _by+β _yzza _bz)ω _bz

δω _bz=β _z+β _zxω _bx+β _zyω _by+β _zzω _bz+(β _zxxa _bx+β _zxya _by+β _zxza _bz)ω _bx+(β _zyxa _bx+β _zyya _by+β _zyza _bz)ω _by

Wherein, δ a _bi, δ ω _bifor accelerometer and gyro error are in the projection of Ring Laser Gyroscope SINS coordinate system; α _ifor accelerometer bias; α _iifor accelerometer scale factor; α _ijfor accelerometer alignment error; a _bifor: the projection of terrestrial gravitation; β _ifor gyroscopic drift; β _iifor gyro scale factor; β _ijfor gyro misalignment; β _ijkfor the gyroscopic drift that acceleration causes; ω _bi---the projection of absolute angular velocities in Ring Laser Gyroscope SINS coordinate system; I=x, y, z; J=x, y, z; I ≠ j;

3) following formula is utilized to demarcate β _iand β _ii:

${\∫}_0^t{\mathrm{\δ\ω}}_E\mathrm{dt}={\mathrm{\β}}_{x}t+{\mathrm{\β}}_{\mathrm{xx}}\mathrm{\θ};$

${\∫}_0^t{\mathrm{\δ\ω}}_N\mathrm{dt}=\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}\sin \mathrm{\θ}+{\mathrm{\β}}_{\mathrm{yx}}\sin \mathrm{\θ}+\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}(\cos \mathrm{\θ}-1)+{\mathrm{\β}}_{\mathrm{zx}}(\cos \mathrm{\θ}-1);$

Wherein, θ is the angle of pitch of Ring Laser Gyroscope SINS, and t is for demarcating the test duration (setting before demarcating, rest position time 2 ~ 5min, rotation time≤30s);

4) following formula is utilized to demarcate α _i, α _ii, α _ij:

When the pitching angle theta of rotary laser strapdown inertial navitation system (SINS):

θ=90°：

${\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_{\mathrm{xy}}g-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}-{\mathrm{g\β}}_{\mathrm{yz}}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}+{\mathrm{g\β}}_{\mathrm{zx}};$

${\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_z-{\mathrm{\α}}_{\mathrm{zy}}g+{\mathrm{g\β}}_{x}t+{\mathrm{g\β}}_{\mathrm{xx}}\frac{\mathrm{\π}}{2};$

θ=180°：

${\mathrm{\δ}\stackrel{\·}{V}}_E=\frac{{2\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}g+{2\mathrm{g\β}}_{\mathrm{zx}}-{2\mathrm{\α}}_{\mathrm{xz}}g;$

${\mathrm{\δ}\stackrel{\·}{V}}_N=-{2\mathrm{\α}}_y+{\mathrm{g\β}}_{x}t+{\mathrm{g\β}}_{\mathrm{xx}}\mathrm{\π};$

As the roll angle γ of rotary laser strapdown inertial navitation system (SINS):

γ=90°：

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_x-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_z-{\mathrm{\α}}_{\mathrm{zx}}g-{\mathrm{g\β}}_{y}t-{\mathrm{g\β}}_{\mathrm{yy}}\frac{\mathrm{\π}}{2}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_{\mathrm{yx}}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\γ}}}+{\mathrm{g\β}}_{\mathrm{xy}}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\γ}}}+{\mathrm{g\β}}_{\mathrm{zy}}\end{array};$

γ=180°：

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{2\mathrm{\α}}_x-{\mathrm{g\β}}_{y}t-{\mathrm{g\β}}_{\mathrm{yy}}\mathrm{\π}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{2\mathrm{\α}}_{\mathrm{yz}}g+\frac{{2\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\γ}}}g+{2\mathrm{\β}}_{\mathrm{zy}}g\end{array};$

As the position angle ψ of rotary laser strapdown inertial navitation system (SINS):

ψ=90°：

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_x-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_y+{\mathrm{\α}}_{\mathrm{yz}}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{\mathrm{xz}}-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}-{\mathrm{g\β}}_{\mathrm{yz}}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_x-{\mathrm{\α}}_{\mathrm{xz}}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{\mathrm{xz}}+g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{\mathrm{yz}}\end{array};$

ψ=180°：

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{2\mathrm{\α}}_x-{2\mathrm{\α}}_{\mathrm{xz}}g+{2\mathrm{\β}}_{\mathrm{xz}}g+2\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}g\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{2\mathrm{\α}}_y-{2\mathrm{\α}}_{\mathrm{yz}}g+{2\mathrm{\β}}_{\mathrm{yz}}g+2\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}g\end{array};$

5) gyro misalignment is demarcated:

Following formula is utilized to estimate β _zxand β _yx:

Wherein,

Following formula is utilized to estimate β _zyand β _xy:

Wherein,

Following formula is utilized to estimate β _xzand β _yz:

Wherein,

In described step 3), β _iand β _iithe computation process of calibration formula as follows:

1) simplify the error model of Ring Laser Gyroscope SINS, obtain the simplification error model of following Ring Laser Gyroscope SINS:

E-passage:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-g{\mathrm{\Φ}}_N+{\mathrm{\δa}}_E\\ {\stackrel{\·}{\mathrm{\Φ}}}_N=\frac{{\mathrm{\δV}}_E}{R}+{\mathrm{\δ\ω}}_N\end{array};$

N-passage:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_N={\mathrm{g\Φ}}_E+{\mathrm{\δa}}_N\\ {\stackrel{\·}{\mathrm{\Φ}}}_E=-\frac{{\mathrm{\δV}}_N}{R}+{\mathrm{\δ\ω}}_E\end{array};$

Wherein, for inertial navigation east orientation accelerometer exports acceleration, δ V _efor Ring Laser Gyroscope SINS east orientation Measurement channel output speed, Φ _nfor Ring Laser Gyroscope SINS north orientation Measurement channel exports rotational angle, for Ring Laser Gyroscope SINS north orientation Measurement channel exports rotational angular velocity, R is the radius of gyration, for Ring Laser Gyroscope SINS north orientation accelerometer exports acceleration, δ V _nfor Ring Laser Gyroscope SINS north orientation Measurement channel output speed, Φ _efor Ring Laser Gyroscope SINS east orientation Measurement channel exports rotational angle, for Ring Laser Gyroscope SINS east orientation Measurement channel exports rotational angular velocity, δ a _e, δ a _nfor the accelerometer error projection in local geographic coordinate system, δ ω _e, δ ω _nfor the gyro error projection in local geographic coordinate system; G is acceleration of gravity;

2) ignore in above-mentioned simplification error model with , obtain new error model:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{g\Φ}}_N\left(0\right)+{\mathrm{\δa}}_E-g{\∫}_{t_0}^t{\mathrm{\δ\ω}}_N\mathrm{dt}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N={\mathrm{g\Φ}}_E\left(0\right)+{\mathrm{\δa}}_N+g{\∫}_{t_0}^t{\mathrm{\δ\ω}}_E\mathrm{dt}\end{array};$

Wherein, Φ _e(0), Φ _n(0) be horizontal aligument error, and:

$\begin{array}{c}{\mathrm{\Φ}}_N\left(0\right)=\frac{1}{g}({\mathrm{\α}}_x+{\mathrm{\α}}_{\mathrm{xz}}g)\\ {\mathrm{\Φ}}_E\left(0\right)=-\frac{1}{g}({\mathrm{\α}}_y+{\mathrm{\α}}_{\mathrm{yz}}g)\end{array};$

3) direction cosine matrix between Ring Laser Gyroscope SINS coordinate system and local geographic coordinate system is determined

$C_b^{\mathrm{LL}}=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right];$

c ₁₁=cosγcosψ+sinθsinγsinψ

c ₁₂=cosθsinψ

c ₁₃=sinγcosψ-sinθcosγsinψ

c ₂₁=-cosγsinψ+sinθsinγcosψ

Wherein, c ₂₂=cos θ cos ψ;

c ₂₃=-sinγsinψ-sinθcosγcosψ

c ₃₁=-cosθsinγ

c ₃₂=sinθ

c ₃₃=cosθcosγ

θ, γ, ψ are respectively the angle of pitch of Ring Laser Gyroscope SINS, roll angle and position angle;

4) rotate mould turnover, ensure that the time of the navigation mode of Ring Laser Gyroscope SINS work is 2 ~ 5 minutes, obtain the absolute angular velocities ω of Ring Laser Gyroscope SINS in rotary course _b:

${\mathrm{\ω}}_b=\left[\begin{array}{c}\stackrel{\·}{\mathrm{\θ}}\\ 0\\ 0\end{array}\right];$

Wherein, for angular velocity of rotation;

5) suppose that roll angle γ and the position angle ψ of Ring Laser Gyroscope SINS keep motionless, the pitching angle theta of rotary laser strapdown inertial navitation system (SINS), obtains the new direction cosine matrix between Ring Laser Gyroscope SINS coordinate system and local geographic coordinate system

$C_{b^{\′}}^{\mathrm{LL}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ 0& \sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right];$

6) according to error model and the absolute angular velocities ω of Ring Laser Gyroscope SINS _b, obtain:

$\begin{array}{c}{\mathrm{\δ\ω}}_{\mathrm{bx}}={\mathrm{\β}}_x+{\mathrm{\β}}_{\mathrm{xx}}\stackrel{\·}{\mathrm{\θ}}\\ {\mathrm{\δ\ω}}_{\mathrm{by}}={\mathrm{\β}}_y+{\mathrm{\β}}_{\mathrm{yx}}\stackrel{\·}{\mathrm{\θ}}\\ {\mathrm{\δ\ω}}_{\mathrm{bz}}={\mathrm{\β}}_z+{\mathrm{\β}}_{\mathrm{zx}}\stackrel{\·}{\mathrm{\θ}}\end{array};$

7) by gyro error from Ring Laser Gyroscope SINS ordinate transform to local geographic coordinate system, obtain:

$\left[\begin{array}{c}{\mathrm{\δ\ω}}_E\\ {\mathrm{\δ\ω}}_N\\ {\mathrm{\δ\ω}}_{\mathrm{Up}}\end{array}\right]=C_{b^{\′}}^{\mathrm{LL}}\left[\begin{array}{c}{\mathrm{\δ\ω}}_{\mathrm{bx}}\\ {\mathrm{\δ\ω}}_{\mathrm{by}}\\ {\mathrm{\δ\ω}}_{\mathrm{bz}}\end{array}\right]=\left[\begin{array}{c}{\mathrm{\δ\ω}}_x^b\\ {\mathrm{\δ\ω}}_y^b\cos \mathrm{\θ}-{\mathrm{\δ\ω}}_z^b\sin \mathrm{\θ}\\ {\mathrm{\δ\ω}}_y^b\sin \mathrm{\θ}+{\mathrm{\δ\ω}}_z^b\cos \mathrm{\θ}\end{array}\right];$

δ ω _upfor rotation axis is to the output of responsive gyro; for absolute angular velocities ω _bprojection in Ring Laser Gyroscope SINS coordinate system;

8) formula of step 6) is substituted in the formula of step 7), obtains gyro error being projected as in local geographic coordinate system:

$\begin{array}{c}{\mathrm{\δ\ω}}_E={\mathrm{\β}}_x+{\mathrm{\β}}_{\mathrm{xx}}\stackrel{\·}{\mathrm{\θ}}\\ {\mathrm{\δ\ω}}_N={\mathrm{\β}}_y\cos \mathrm{\θ}+{\mathrm{\β}}_{\mathrm{yx}}\stackrel{\·}{\mathrm{\θ}}\cos \mathrm{\θ}-{\mathrm{\β}}_z\sin \mathrm{\θ}-{\mathrm{\β}}_{\mathrm{zx}}\stackrel{\·}{\mathrm{\θ}}\sin \mathrm{\θ}\end{array};$

δ ω _efor rotating output, the δ ω of rear east orientation gyro _nfor rotating the output of rear north gyro;

9) to the formula integration of step 8), obtain:

${\∫}_0^t{\mathrm{\δ\ω}}_E\mathrm{dt}={\mathrm{\β}}_{x}t+{\mathrm{\β}}_{\mathrm{xx}}\mathrm{\θ};$

${\∫}_0^t{\mathrm{\δ\ω}}_N\mathrm{dt}=\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}\sin \mathrm{\θ}+{\mathrm{\β}}_{\mathrm{yx}}\sin \mathrm{\θ}+\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}(\cos \mathrm{\θ}-1)+{\mathrm{\β}}_{\mathrm{zx}}(\cos \mathrm{\θ}-1).$

Compared with prior art, the beneficial effect that the present invention has is: the calibration facility that the present invention adopts is the dull and stereotyped and turnover bracket of marble (also can with low precision turntable), according to the characteristic of Laser strapdown inertial navigation, under employing navigation mode, the output speed of Laser strapdown inertial navigation is as observed quantity, a large amount of experiments proves that method of the present invention can successfully be demarcated Laser strapdown inertial navigation, reduces calibration facility cost and the restriction to demarcation test site.

Embodiment

The error model of used group is as follows:

δa _bx=α _x+α _xxa _bx+α _xya _by+α _xza _bz

δa _by=α _y+α _yxa _bx+α _yya _by+α _yza _bz

δa _bz=α _z+α _zxa _bx+α _zya _by+α _zza _bz

δω _bx=β _x+β _xxω _bx+β _xyω _by+β _xzω _bz+(β _xyxa _bx+β _xyya _by+β _xyza _bz)ω _by+(β _xzxa _bx+β _xzya _by+β _xzza _bz)ω _bz

δω _by=β _y+β _yxω _bx+β _yyω _by+β _yzω _bz+(β _yxxa _bx+β _yxya _by+β _yxza _bz)ω _bx+(1)(β _yzxa _bx+β _yzya _by+β _yzza _bz)ω _bz

δω _bz=β _z+β _zxω _bx+β _zyω _by+β _zzω _bz+(β _zxxa _bx+β _zxya _by+β _zxza _bz)ω _bx+(β _zyxa _bx+β _zyya _by+β _zyza _bz)ω _by

In formula (1): δ a _bi, δ ω _bi, (i=x, y, z)---accelerometer and gyro error are in the projection of carrier system; α _i: accelerometer bias; α _ii: accelerometer scale factor; α _ij: accelerometer alignment error (i ≠ j); a _bi: the projection of certain force; β _i: gyroscopic drift; β _ii: gyro scale factor; β _ij: gyro misalignment (i ≠ j); β _ijk: the gyroscopic drift (flexure error) that acceleration causes; ω _bi: the projection of absolute angular velocities in carrier coordinate system.

Gyro flexure error is not generally considered in demarcation test.The object of demarcating determines above parameter exactly.

In order to study this scaling method, need the error model providing Laser strapdown inertial navigation simplification.Single channel Laser strapdown ins error model has following form:

E-passage:

$\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=-g{\mathrm{\Φ}}_N+\mathrm{\δ}{a}_E\\ {\stackrel{\·}{\mathrm{\Φ}}}_N=\frac{{\mathrm{\δV}}_E}{R}+{\mathrm{\δ\ω}}_N\end{array}$

N-passage:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_N={\mathrm{g\Φ}}_E+{\mathrm{\δa}}_N\\ {\stackrel{\·}{\mathrm{\Φ}}}_E=-\frac{{\mathrm{\δV}}_N}{R}+{\mathrm{\δ\ω}}_E\end{array}$

Wherein δ a _e, δ a _n, δ ω _e, δ ω _nfor the accelerometer in local geographic coordinate system and gyro error projection.

Due to employing is the Laser strapdown ins error model simplified, and the time being therefore operated in navigation mode in the rear Laser strapdown inertial navigation of each rotation is 2 ~ 5 minutes.

Ignore in error model with , can again obtain error model as follows:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{g\Φ}}_N\left(0\right)+{\mathrm{\δa}}_E-g{\∫}_{t_0}^t{\mathrm{\δ\ω}}_N\mathrm{dt}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N={\mathrm{g\Φ}}_E\left(0\right)+{\mathrm{\δa}}_N+g{\∫}_{t_0}^t{\mathrm{\δ\ω}}_E\mathrm{dt}\end{array}---\left(2\right)$

Wherein Φ _e(0), Φ _n(0) be horizontal aligument error, and obtain according to equation (2) and error model (1):

$\begin{array}{c}{\mathrm{\Φ}}_N\left(0\right)=\frac{1}{g}({\mathrm{\α}}_x+{\mathrm{\α}}_{\mathrm{xz}}g)\\ {\mathrm{\Φ}}_E\left(0\right)=-\frac{1}{g}({\mathrm{\α}}_y+{\mathrm{\α}}_{\mathrm{yz}}g)\end{array}---\left(3\right)$

Direction cosine matrix between carrier (i.e. Ring Laser Gyroscope SINS) coordinate system and local geographic coordinate system can be write as following form by pitching, roll and position angle:

$C_b^{\mathrm{LL}}=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right]---\left(4\right)$

Wherein:

c ₁₁=cosγcosψ+sinθsinγsinψ

c ₁₂=cosθsinψ

c ₁₃=sinγcosψ-sinθcosγsinψ

c ₂₁=-cosγsinψ+sinθsinγcosψ

c ₂₂=cosθcosψ

c ₂₃=-sinγsinψ-sinθcosγcosψ

c ₃₁=-cosθsinγ

c ₃₂=sinθ

c ₃₃=cosθcosγ

θ, γ, ψ are respectively the pitching of carrier, roll and position angle.

This scaling method comprises the specific upset order of Laser strapdown inertial navigation different rotation angle under navigation mode.Each is after twice upset, and Laser strapdown inertial navigation needs conversion with the navigation time (otherwise error model (2) is by invalid) ensureing navigation mode.

Rotate θ angle for Laser strapdown inertial navigation, under above-mentioned rotation, navigation error model can with formal construction below.In rotary course, the absolute angular velocities of carrier system has following form:

${\mathrm{\ω}}_b=\left[\begin{array}{c}\stackrel{\·}{\mathrm{\θ}}\\ 0\\ 0\end{array}\right]---\left(5\right)$

for angular velocity of rotation.

In equation above relative to the projection of size earth autobiography angular velocity be left in the basket, consider the initial orientation of carrier coordinate system relative to local geographic coordinate system, direction cosine matrix can obtain at hypothesis ψ, form under γ is enough little, there is no need to require in first time is demarcated, each for carrier axle strictly to be aimed at, but require that carrier coordinate system is relative to local geographic coordinate system initial orientation rough alignment (1-3 °).

Under above-mentioned hypothesis, the transition matrix between carrier and local geographic coordinate system has following form:

$C_b^{\mathrm{LL}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ 0& \sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]$

With gyroscope error model (1) and carrier angular velocity equation (5), can obtain:

$\begin{array}{c}{\mathrm{\δ\ω}}_x^b={\mathrm{\β}}_x+{\mathrm{\β}}_{\mathrm{xx}}\stackrel{\·}{\mathrm{\θ}}\\ {\mathrm{\δ\ω}}_y^b={\mathrm{\β}}_y+{\mathrm{\β}}_{\mathrm{yx}}\stackrel{\·}{\mathrm{\θ}}\\ {\mathrm{\δ\ω}}_z^b={\mathrm{\β}}_z+{\mathrm{\β}}_{\mathrm{zx}}\stackrel{\·}{\mathrm{\θ}}\end{array}---\left(6\right)$

Again gyro error is tied to the conversion of local Department of Geography from carrier as follows:

$\left[\begin{array}{c}{\mathrm{\δ\ω}}_E\\ {\mathrm{\δ\ω}}_N\\ {\mathrm{\δ\ω}}_{\mathrm{Up}}\end{array}\right]=C_b^{\mathrm{LL}}\left[\begin{array}{c}{\mathrm{\δ\ω}}_x^b\\ {\mathrm{\δ\ω}}_y^b\\ {\mathrm{\δ\ω}}_z^b\end{array}\right]=\left[\begin{array}{c}{\mathrm{\δ\ω}}_x^b\\ {\mathrm{\δ\ω}}_y^b\cos \mathrm{\θ}-{\mathrm{\δ\ω}}_z^b\sin \mathrm{\θ}\\ {\mathrm{\δ\ω}}_y^b\sin \mathrm{\θ}+{\mathrm{\δ\ω}}_z^b\cos \mathrm{\θ}\end{array}\right]---\left(7\right)$

Bring equation (6) into equation (7), gyro error is projected as local geographic coordinate system:

$\begin{array}{c}{\mathrm{\δ\ω}}_E={\mathrm{\β}}_x+{\mathrm{\β}}_{\mathrm{xx}}\stackrel{\·}{\mathrm{\θ}}\\ {\mathrm{\δ\ω}}_N={\mathrm{\β}}_y\cos \mathrm{\θ}+{\mathrm{\β}}_{\mathrm{yx}}\stackrel{\·}{\mathrm{\θ}}\cos \mathrm{\θ}-{\mathrm{\β}}_z\sin \mathrm{\θ}-{\mathrm{\β}}_{\mathrm{zx}}\stackrel{\·}{\mathrm{\θ}}\sin \mathrm{\θ}\end{array}$

Integration is carried out to above formula, obtains:

${\∫}_0^t{\mathrm{\δ\ω}}_E\mathrm{dt}={\mathrm{\β}}_{x}t+{\mathrm{\β}}_{\mathrm{xx}}\mathrm{\θ}---\left(8\right)$

${\∫}_0^t{\mathrm{\δ\ω}}_N\mathrm{dt}=\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}\sin \mathrm{\θ}+{\mathrm{\β}}_{\mathrm{yx}}\sin \mathrm{\θ}+\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}(\cos \mathrm{\θ}-1)+{\mathrm{\β}}_{\mathrm{zx}}(\cos \mathrm{\θ}-1)---\left(9\right)$

Similar method is adopted to accelerometer error, in fact, certain force being projected as in carrier coordinate system:

$\left[\begin{array}{c}{\mathrm{\α}}_x^b\\ {\mathrm{\α}}_y^b\\ {\mathrm{\α}}_z^b\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\θ}& \sin \mathrm{\θ}\\ 0& -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]\left[\begin{array}{c}0\\ 0\\ g\end{array}\right]=\left[\begin{array}{c}0\\ g\sin \mathrm{\θ}\\ g\cos \mathrm{\θ}\end{array}\right]$

The projection form of accelerometer error in carrier coordinate system can be described as:

$\begin{array}{c}{\mathrm{\δ\α}}_x^b={\mathrm{\α}}_x+{\mathrm{\α}}_{\mathrm{xy}}g\sin \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{xy}}g\cos \mathrm{\θ}\\ {\mathrm{\δ\α}}_y^b={\mathrm{\α}}_y+{\mathrm{\α}}_{\mathrm{yy}}g\sin \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{yz}}g\cos \mathrm{\θ}\\ {\mathrm{\δ\α}}_z^b={\mathrm{\α}}_z+{\mathrm{\α}}_{\mathrm{zy}}g\sin \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{zz}}g\cos \mathrm{\θ}\end{array}---\left(10\right)$

Acceleration error is projected as local geographic coordinate system:

$\begin{array}{c}{\mathrm{\δ\α}}_E={\mathrm{\δ\α}}_x^b\\ {\mathrm{\δ\α}}_N={\mathrm{\δ\α}}_y^b\cos \mathrm{\θ}-{\mathrm{\δ\α}}_z^b\sin \mathrm{\θ}\end{array}---\left(11\right)$

Formula (10) is brought into (11), can obtain:

$\begin{array}{c}{\mathrm{\δa}}_E={\mathrm{\α}}_x+{\mathrm{\α}}_{\mathrm{xy}}g\sin \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{xz}}g\cos \mathrm{\θ}\\ {\mathrm{\δa}}_N={\mathrm{\α}}_y\cos \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{yy}}g\sin \mathrm{\θ}\cos \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{yz}}g{\cos }^2\mathrm{\θ}-\\ {\mathrm{\α}}_z\sin \mathrm{\θ}-{\mathrm{\α}}_{\mathrm{zy}}g{\sin }^2\mathrm{\θ}-{\mathrm{\α}}_{\mathrm{zz}}g\cos \mathrm{\θ}\sin \mathrm{\θ}\end{array}---\left(12\right)$

Aggregative formula (2), (3), (8), (9), (12), velocity survey model can be described as:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_{\mathrm{xy}}g\sin \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{xz}}g\cos \mathrm{\θ}-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}-\\ {\mathrm{g\β}}_{\mathrm{yz}}\sin \mathrm{\θ}-g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}(\cos \mathrm{\θ}-1)-{\mathrm{g\β}}_{\mathrm{zx}}(\cos \mathrm{\θ}-1)\end{array}---\left(13\right)$

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g+{\mathrm{\α}}_y\cos \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{yy}}g\sin \mathrm{\θ}\cos \mathrm{\θ}+{\mathrm{\α}}_{\mathrm{yz}}g{\cos }^2\mathrm{\θ}-\\ {\mathrm{\α}}_z\sin \mathrm{\θ}-{\mathrm{\α}}_{\mathrm{zy}}g{\sin }^2\mathrm{\θ}-{\mathrm{\α}}_{\mathrm{zz}}g\cos \mathrm{\θ}\sin \mathrm{\θ}+{\mathrm{g\β}}_{x}t+{\mathrm{g\β}}_{\mathrm{xx}}\mathrm{\θ}\end{array}---\left(14\right)$

When θ=90 °, above-mentioned equation can be changed into:

${\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_{\mathrm{xy}}g-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}-{\mathrm{g\β}}_{\mathrm{yz}}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}+{\mathrm{g\β}}_{\mathrm{zx}};$

${\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_z-{\mathrm{\α}}_{\mathrm{zy}}g+{\mathrm{g\β}}_{x}t+{\mathrm{g\β}}_{\mathrm{xx}}\frac{\mathrm{\π}}{2};$

When θ=180 °

${\mathrm{\δ}\stackrel{\·}{V}}_E=\frac{{2\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}g+2g{\mathrm{\β}}_{\mathrm{zx}}-{2\mathrm{\α}}_{\mathrm{xz}}g;$

${\mathrm{\δ}\stackrel{\·}{V}}_N=-{2\mathrm{\α}}_y+g{\mathrm{\β}}_{x}t+g{\mathrm{\β}}_{\mathrm{xx}}\mathrm{\π};$

Velocity survey equation under other rotation angle γ, ψ, also can calculate as stated above.Rotate γ angle and obtain velocity error measurement:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_x-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_x\cos \mathrm{\γ}-{\mathrm{\α}}_{\mathrm{xx}}g\sin \mathrm{\γ}\cos \mathrm{\γ}+{\mathrm{\α}}_{\mathrm{xz}}g{\cos }^2\mathrm{\γ}+{\mathrm{\α}}_z\sin \mathrm{\γ}\\ -{\mathrm{\α}}_{\mathrm{zx}}g{\sin }^2\mathrm{\γ}+{\mathrm{\α}}_{\mathrm{zz}}g\cos \mathrm{\γ}\sin \mathrm{\γ}-g{\mathrm{\β}}_{y}t-{\mathrm{g\β}}_{\mathrm{yy}}\mathrm{\γ}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g+{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yx}}g\sin \mathrm{\γ}+{\mathrm{\α}}_{\mathrm{yz}}g\cos \mathrm{\γ}+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\γ}}}\sin \mathrm{\γ}\\ +{\mathrm{g\β}}_{\mathrm{xy}}\sin \mathrm{\γ}-g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\γ}}}(\cos \mathrm{\γ}-1)-{\mathrm{g\β}}_{\mathrm{zy}}(\cos \mathrm{\γ}-1)\end{array}---\left(15\right)$

When γ=90 °, above-mentioned equation becomes:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_x-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_z-{\mathrm{\α}}_{\mathrm{zx}}g-{\mathrm{g\β}}_{y}t-{\mathrm{g\β}}_{\mathrm{yy}}\frac{\mathrm{\π}}{2}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_{\mathrm{yx}}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\γ}}}+{\mathrm{g\β}}_{\mathrm{xy}}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\γ}}}+{\mathrm{g\β}}_{\mathrm{zy}}\end{array}$

When γ=180 °,

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{2\mathrm{\α}}_x-{\mathrm{g\β}}_{y}t-{\mathrm{g\β}}_{\mathrm{yy}}\mathrm{\π}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{2\mathrm{\α}}_{\mathrm{yz}}g+\frac{{2\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\γ}}}g+{2\mathrm{\β}}_{\mathrm{zy}}g\end{array}---\left(16\right)$

Rotating ψ angular measurement model is:

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_x-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_x\cos \mathrm{\ψ}+{\mathrm{\α}}_{\mathrm{xz}}g\cos \mathrm{\ψ}+{\mathrm{\α}}_y\sin \mathrm{\ψ}+{\mathrm{\α}}_{\mathrm{yz}}g\sin \mathrm{\ψ}\\ -g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}(\cos \mathrm{\ψ}-1)-{\mathrm{g\β}}_{\mathrm{xz}}(\cos \mathrm{\ψ}-1)-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}\sin \mathrm{\ψ}-{\mathrm{\β}}_{\mathrm{yz}}g\sin \mathrm{\ψ}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_x\sin \mathrm{\ψ}-{\mathrm{\α}}_{\mathrm{xz}}g\sin \mathrm{\ψ}+{\mathrm{\α}}_y\cos \mathrm{\ψ}+{\mathrm{\α}}_{\mathrm{yz}}g\cos \mathrm{\ψ}\\ +g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}\sin \mathrm{\ψ}+{\mathrm{g\β}}_{\mathrm{xz}}\sin \mathrm{\ψ}-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}(\cos \mathrm{\ψ}-1)-{\mathrm{g\β}}_{\mathrm{yz}}(\cos \mathrm{\ψ}-1)\end{array}---\left(17\right)$

When ψ=90 °

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{\mathrm{\α}}_x-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_y+{\mathrm{\α}}_{\mathrm{yz}}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{\mathrm{xz}}-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}-{\mathrm{g\β}}_{\mathrm{yz}}\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_x-{\mathrm{\α}}_{\mathrm{xz}}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{\mathrm{xz}}+g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{\mathrm{yz}}\end{array}---\left(18\right)$

When ψ=180 °

$\begin{array}{c}{\mathrm{\δ}\stackrel{\·}{V}}_E=-{2\mathrm{\α}}_x-{2\mathrm{\α}}_{\mathrm{xz}}g+{2\mathrm{\β}}_{\mathrm{xz}}g+2\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}g\\ {\mathrm{\δ}\stackrel{\·}{V}}_N=-{2\mathrm{\α}}_y-{2\mathrm{\α}}_{\mathrm{yz}}g+{2\mathrm{\β}}_{\mathrm{yz}}g+2\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}g\end{array}---\left(19\right)$

Gyro misalignment calibration process is as follows:

Suppose that all calibrating parameters are except gyro misalignment, all demarcate out and compensate, program below can be used for estimating β _ij.

1st step rotates θ=90 °

Measurement model:

2nd step rotates θ=180 °

Measurement model:

3rd step estimates β _zxand β _yx

4th step rotates γ=90 °

Measurement model:

5th step rotates γ=180 °

Measurement model:

6th step estimates β _zyand β _xy

7th step rotates ψ=180 °

Measurement model:

8th step estimates β _zyand β _xy

Here make use of (15), (16), (18), the measurement model equation that (19) are set up.

What it is emphasized that the equation of definition only describes is error in rotary course, and total velocity error model comprises:

δV ^t=δV ^I+δV ^II

δ V ⁱ---the velocity error in rotary course, as (13), (14);

δ V ^iI---the measurement progressive rate error (2-3min) after rotary course.

Part II in equation (20) is left in the basket relative to Part I, and what therefore calibration algorithm used is equation (13) and (14).

Scaling method step of the present invention is summarized as follows:

inertial navigation system is arranged on mould turnover and is placed in dull and stereotyped upper (or on low precision turntable), and the local geographic coordinate system of rough alignment;

laser strapdown inertial navigation enters alignment pattern, and aim at after terminating, system enters navigation mode;

system casing rotates different angles (once or twice) in order, and preserves the output speed (2-5min) of Laser strapdown inertial navigation;

system exits, and (should refer to navigation mode) gets back to initial position;

said procedure repeatedly rotates different angles and performs, and obtains enough measurement output calibrate each parameter with this;

the velocity survey model of each position is set up, and carries out level and smooth (in the short time, speed should be straight line, and its differential should be constant value) in advance the speed stored;

utilize smoothed speed output and measurement model to estimate the parameter of accelerometer and gyro;

estimation routine can adopt traditional least square or Kalman filtering algorithm.

Traditional turntable speed is added the scaling method of position and this scaling method to be used to group to same set of Laser strapdown respectively and to demarcate, calibration result is as table 1:

Table 1 two kinds of mode comparing results

As can be seen from two groups of calibration results, two kinds of differences of demarcating mode meet index request, prove that scaling method of the present invention is feasible.

Claims (1)

1. a performance parameter calibration method of laser strapdown inertial navigation system, is characterized in that, the method is:

1) Ring Laser Gyroscope SINS is arranged on mould turnover, mould turnover is placed on flat board, and Ring Laser Gyroscope SINS is aimed at local geographic coordinate system;

2) error model of Ring Laser Gyroscope SINS is set up:

δa _bx＝α _x+α _xxa _bx+α _xya _by+α _xza _bz

δa _by＝α _y+α _yxa _bx+α _yya _by+α _yza _bz

δa _bz＝α _z+α _zxa _bx+α _zya _by+α _zza _bz

δω _bx＝β _x+β _xxω _bx+β _xyω _by+β _xzω _bz+(β _xyxa _bx+β _xyya _by+β _xyza _bz)ω _by+(β _xzxa _bx+β _xzya _by+β _xzza _bz)ω _bz

δω _by＝β _y+β _yxω _bx+β _yyω _by+β _yzω _bz+(β _yxxa _bx+β _yxya _by+β _yxza _bz)ω _bx+(β _yzxa _bx+β _yzya _by+β _yzza _bz)ω _bz

δω _bz＝β _z+β _zxω _bx+β _zyω _by+β _zzω _bz+(β _zxxa _bx+β _zxya _by+β _zxza _bz)ω _bx+(β _zyxa _bx+β _zyya _by+β _zyza _bz)ω _by

Wherein, δ a _bi, δ ω _bifor accelerometer and gyro error are in the projection of Ring Laser Gyroscope SINS coordinate system; α _ifor accelerometer bias; α _iifor accelerometer scale factor; α _ijfor accelerometer alignment error; a _bifor the projection of terrestrial gravitation; β _ifor gyroscopic drift; β _iifor gyro scale factor; β _ijfor gyro misalignment; β _ijkfor the gyroscopic drift that acceleration causes; ω _bi---the projection of absolute angular velocities in Ring Laser Gyroscope SINS coordinate system; I=x, y, z; J=x, y, z; I ≠ j;

3) following formula is utilized to demarcate β _iand β _ii:

${\∫}_0^t{\mathrm{\δ\ω}}_{E}dt={\mathrm{\β}}_{x}t+{\mathrm{\β}}_{xx}\mathrm{\θ};$

${\∫}_0^t{\mathrm{\δ\ω}}_{N}dt=\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}\sin \mathrm{\θ}+{\mathrm{\β}}_{yx}sin\mathrm{\θ}+\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}(cos\mathrm{\θ}-1)+{\mathrm{\β}}_{zx}(cos\mathrm{\θ}-1);$

Wherein, θ is the angle of pitch of Ring Laser Gyroscope SINS, and t is for demarcating the test duration;

4) following formula is utilized to demarcate α _i, α _ii, α _ij:

When the pitching angle theta of rotary laser strapdown inertial navitation system (SINS):

θ＝90°：

$\mathrm{\δ}{\stackrel{\·}{V}}_E=-{\mathrm{\α}}_{xz}g+{\mathrm{\α}}_{xy}g-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}-{\mathrm{g\β}}_{yz}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}+{\mathrm{g\β}}_{zx};$

$\mathrm{\δ}{\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{yz}g-{\mathrm{\α}}_z-{\mathrm{\α}}_{zy}g+{\mathrm{g\β}}_{x}t+{\mathrm{g\β}}_{xx}\frac{\mathrm{\π}}{2};$

θ＝180°：

$\mathrm{\δ}{\stackrel{\·}{V}}_E=\frac{2{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}g+2{\mathrm{g\β}}_{zx}-2{\mathrm{\α}}_{xz}g;$

$\mathrm{\δ}{\stackrel{\·}{V}}_N=-2{\mathrm{\α}}_y+{\mathrm{g\β}}_{x}t+{\mathrm{g\β}}_{xx}\mathrm{\π};$

As the roll angle γ of rotary laser strapdown inertial navitation system (SINS):

γ＝90°：

$\mathrm{\δ}{\stackrel{\·}{V}}_E=-{\mathrm{\α}}_x-{\mathrm{\α}}_{xz}g+{\mathrm{\α}}_z-{\mathrm{\α}}_{zx}g-{\mathrm{g\β}}_{y}t-{\mathrm{g\β}}_{yy}\frac{\mathrm{\π}}{2}$

$\mathrm{\δ}{\stackrel{\·}{V}}_N=-{\mathrm{\α}}_{yz}g-{\mathrm{\α}}_{yx}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\γ}}}+{\mathrm{g\β}}_{xy}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\γ}}}+{\mathrm{g\β}}_{zy};$

γ＝180°：

$\mathrm{\δ}{\stackrel{\·}{V}}_E=-2{\mathrm{\α}}_x-{\mathrm{g\β}}_{y}t-{\mathrm{g\β}}_{yy}\mathrm{\π}$

$\mathrm{\δ}{\stackrel{\·}{V}}_N=-2{\mathrm{\α}}_{yz}g+\frac{2{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\γ}}}g+2{\mathrm{\β}}_{zy}g;$

As the position angle ψ of rotary laser strapdown inertial navitation system (SINS):

ψ＝90°：

$\mathrm{\δ}{\stackrel{\·}{V}}_E=-{\mathrm{\α}}_x-{\mathrm{\α}}_{xz}g+{\mathrm{\α}}_y+{\mathrm{\α}}_{yz}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{xz}-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}-{\mathrm{g\β}}_{yz}$

$\mathrm{\δ}{\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{yz}g-{\mathrm{\α}}_x-{\mathrm{\α}}_{xz}g+g\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{xz}+g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}+{\mathrm{g\β}}_{yz};$

ψ＝180°：

$\mathrm{\δ}{\stackrel{\·}{V}}_E=-2{\mathrm{\α}}_x-2{\mathrm{\α}}_{xz}g+2{\mathrm{\β}}_{xz}g+2\frac{{\mathrm{\β}}_x}{\stackrel{\·}{\mathrm{\ψ}}}g$

$\mathrm{\δ}{\stackrel{\·}{V}}_N=-2{\mathrm{\α}}_y-2{\mathrm{\α}}_{yz}g+2{\mathrm{\β}}_{yz}g+2\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\ψ}}}g;$

5) gyro misalignment is demarcated:

Following formula is utilized to estimate β _zxand β _yx:

Wherein,

Following formula is utilized to estimate β _zyand β _xy:

Wherein,

Following formula is utilized to estimate β _xzand β _yz:

Wherein,

Described step 3) in, β _iand β _iithe computation process of calibration formula as follows:

1) simplify the error model of Ring Laser Gyroscope SINS, obtain the simplification error model of following Ring Laser Gyroscope SINS:

E-passage:

$\mathrm{\δ}{\stackrel{\·}{V}}_E=-{\mathrm{g\Φ}}_N+{\mathrm{\δa}}_E$

${\stackrel{\·}{\mathrm{\Φ}}}_N=\frac{{\mathrm{\δV}}_E}{R}+{\mathrm{\δ\ω}}_N;$

N-passage:

$\mathrm{\δ}{\stackrel{\·}{V}}_N={\mathrm{g\Φ}}_E+{\mathrm{\δa}}_N$

${\stackrel{\·}{\mathrm{\Φ}}}_E=-\frac{{\mathrm{\δV}}_N}{R}+{\mathrm{\δ\ω}}_E;$

Wherein, for inertial navigation east orientation accelerometer exports acceleration, δ V _efor Ring Laser Gyroscope SINS east orientation Measurement channel output speed, Φ _nfor Ring Laser Gyroscope SINS north orientation Measurement channel exports rotational angle, for Ring Laser Gyroscope SINS north orientation Measurement channel exports rotational angular velocity, R is the radius of gyration, for Ring Laser Gyroscope SINS north orientation accelerometer exports acceleration, δ V _nfor Ring Laser Gyroscope SINS north orientation Measurement channel output speed, Φ _efor Ring Laser Gyroscope SINS east orientation Measurement channel exports rotational angle, for Ring Laser Gyroscope SINS east orientation Measurement channel exports rotational angular velocity, δ a _e, δ a _nfor the accelerometer error projection in local geographic coordinate system, δ ω _e, δ ω _nfor the gyro error projection in local geographic coordinate system; G is acceleration of gravity;

2) ignore in above-mentioned simplification error model with , obtain new error model:

$\mathrm{\δ}{\stackrel{\·}{V}}_E=-{\mathrm{g\Φ}}_N\left(0\right)+{\mathrm{\δa}}_E-g{\∫}_{t_0}^t{\mathrm{\δ\ω}}_{N}dt$

$\mathrm{\δ}{\stackrel{\·}{V}}_N={\mathrm{g\Φ}}_E\left(0\right)+{\mathrm{\δa}}_N+g{\∫}_{t_0}^t{\mathrm{\δ\ω}}_{E}dt;$

Wherein, Φ _e(0), Φ _n(0) be horizontal aligument error, and:

${\mathrm{\Φ}}_N\left(0\right)=\frac{1}{g}({\mathrm{\α}}_x+{\mathrm{\α}}_{xz}g)$

${\mathrm{\Φ}}_E\left(0\right)=-\frac{1}{g}({\mathrm{\α}}_y+{\mathrm{\α}}_{yz}g);$

3) direction cosine matrix between Ring Laser Gyroscope SINS coordinate system and local geographic coordinate system is determined

$C_b^{LL}=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right];$

c ₁₁＝cosγcosψ+sinθsinγsinψ

c ₁₂＝cosθsinψ

c ₁₃＝sinγcosψ-sinθcosγsinψ

c ₂₁＝-cosγsinψ+sinθsinγcosψ

Wherein, c ₂₂=cos θ cos ψ;

c ₂₃＝-sinγsinψ-sinθcosγcosψ

c ₃₁＝-cosθsinγ

c ₃₂＝sinθ

c ₃₃＝cosθcosγ

θ, γ, ψ are respectively the angle of pitch of Ring Laser Gyroscope SINS, roll angle and position angle;

4) rotate mould turnover, ensure that the time of the navigation mode of Ring Laser Gyroscope SINS work is 2 ~ 5 minutes, obtain the absolute angular velocities ω of Ring Laser Gyroscope SINS in rotary course _b:

${\mathrm{\ω}}_b=\left[\begin{array}{c}\stackrel{\·}{\mathrm{\θ}}\\ 0\\ 0\end{array}\right];$

Wherein, for angular velocity of rotation;

5) suppose that roll angle γ and the position angle ψ of Ring Laser Gyroscope SINS keep motionless, the pitching angle theta of rotary laser strapdown inertial navitation system (SINS), obtains the new direction cosine matrix between Ring Laser Gyroscope SINS coordinate system and local geographic coordinate system

$C_{b^{\′}}^{LL}=\left[\begin{array}{ccc}1& 0& 0\\ 0& cos\mathrm{\θ}& -\sin \mathrm{\θ}\\ 0& sin\mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right];$

6) according to error model and the absolute angular velocities ω of Ring Laser Gyroscope SINS _b, obtain:

${\mathrm{\δ\ω}}_{bx}={\mathrm{\β}}_x+{\mathrm{\β}}_{xx}\stackrel{\·}{\mathrm{\θ}}$

${\mathrm{\δ\ω}}_{by}={\mathrm{\β}}_y+{\mathrm{\β}}_{yx}\stackrel{\·}{\mathrm{\θ}};$

${\mathrm{\δ\ω}}_{bz}={\mathrm{\β}}_z+{\mathrm{\β}}_{zx}\stackrel{\·}{\mathrm{\θ}}$

7) by gyro error from Ring Laser Gyroscope SINS ordinate transform to local geographic coordinate system, obtain:

$\left[\begin{array}{c}{\mathrm{\δ\ω}}_E\\ {\mathrm{\δ\ω}}_N\\ {\mathrm{\δ\ω}}_{Up}\end{array}\right]=C_{b^{\′}}^{LL}\left[\begin{array}{c}{\mathrm{\δ\ω}}_{bx}\\ {\mathrm{\δ\ω}}_{by}\\ {\mathrm{\δ\ω}}_{bz}\end{array}\right]=\left[\begin{array}{c}{\mathrm{\δ\ω}}_x^b\\ {\mathrm{\δ\ω}}_y^b\cos \mathrm{\θ}-{\mathrm{\δ\ω}}_z^b\sin \mathrm{\θ}\\ {\mathrm{\δ\ω}}_y^b\sin \mathrm{\θ}+{\mathrm{\δ\ω}}_z^b\cos \mathrm{\θ}\end{array}\right];$

δ ω _upfor rotation axis is to the output of responsive gyro; for absolute angular velocities ω _bprojection in Ring Laser Gyroscope SINS coordinate system;

8) by step 6) formula substitute into step 7) formula in, obtain gyro error being projected as in local geographic coordinate system:

${\mathrm{\δ\ω}}_E={\mathrm{\β}}_x+{\mathrm{\β}}_{xx}\stackrel{\·}{\mathrm{\θ}}$

${\mathrm{\δ\ω}}_N={\mathrm{\β}}_{y}cos\mathrm{\θ}+{\mathrm{\β}}_{yx}\stackrel{\·}{\mathrm{\θ}}cos\mathrm{\θ}-{\mathrm{\β}}_{z}sin\mathrm{\θ}-{\mathrm{\β}}_{zx}\stackrel{\·}{\mathrm{\θ}}sin\mathrm{\θ};$

δ ω _efor rotating output, the δ ω of rear east orientation gyro _nfor rotating the output of rear north gyro;

9) to step 8) formula integration, obtain:

${\∫}_0^t{\mathrm{\δ\ω}}_{E}dt={\mathrm{\β}}_{x}t+{\mathrm{\β}}_{xx}\mathrm{\θ};$

${\∫}_0^t{\mathrm{\δ\ω}}_{N}dt=\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}sin\mathrm{\θ}+{\mathrm{\β}}_{yx}sin\mathrm{\θ}+\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}(cos\mathrm{\θ}-1)+{\mathrm{\β}}_{zx}(cos\mathrm{\θ}-1).$