CN103616035A - Performance parameter calibration method of laser strapdown inertial navigation system - Google Patents

Abstract

The invention discloses a performance parameter calibration method of a laser strapdown inertial navigation system. According to the performance parameter calibration method, a marble flat plate and an overturning bracket or a low-precision rotary table are/is taken as calibration equipment, and an output speed of laser strapdown inertial navigation under a navigation mode is taken as an observation amount according to the characteristic of laser strapdown inertial navigation. According to the method disclosed by the invention, parameter calibration can be successfully carried out on the laser strapdown inertial navigation and the cost of calibration equipment and the limit on a calibration testing field are reduced; the problems that an existing calibration method needs a high-precision rotary table and the requirements on the field and the equipment are high are solved.

Description

A kind of Ring Laser Gyroscope SINS performance parameter calibration method

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

At present to be used to organize the method that the demarcation of inertia device performance parameter adopts be to carry out speed-location position in high precision turntable to traditional strapdown, this scaling method requires Laser strapdown inertial navigation accurately to aim at local geographic coordinate system, 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, equipment, place are limited larger, and calibration cost is high.

Summary of the invention

Technical matters to be solved by this invention is, not enough for prior art, and a kind of Ring Laser Gyroscope SINS performance parameter calibration method is provided, and 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 Ring Laser Gyroscope SINS performance parameter calibration method, and the method is:

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

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

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 the projection at Ring Laser Gyroscope SINS coordinate system of accelerometer and gyro error; 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 _ijkthe gyroscopic drift causing for acceleration; ω _bi---the projection of absolute angle speed in Ring Laser Gyroscope SINS coordinate system; I=x, y, z; J=x, y, z; I ≠ j;

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

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

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

θ=90°：

$\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_{\mathrm{xy}}g-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}-g{\mathrm{\β}}_{\mathrm{yz}}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}+g{\mathrm{\β}}_{\mathrm{zx}};\\ \mathrm{\δ}{\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_z-{\mathrm{\α}}_{\mathrm{zy}}g+g{\mathrm{\β}}_{x}t+g{\mathrm{\β}}_{x}t+g{\mathrm{\β}}_{\mathrm{xx}}\frac{\mathrm{\π}}{2};\end{array}$

θ=180°：

$\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=\frac{{2\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}g+2g{\mathrm{\β}}_{\mathrm{zx}}-2{\mathrm{\α}}_{\mathrm{xz}}g;\\ \mathrm{\δ}{\stackrel{\·}{V}}_N=-2{\mathrm{\α}}_y+g{\mathrm{\β}}_{x}t+g{\mathrm{\β}}_{\mathrm{xx}}\mathrm{\π};\end{array}$

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

γ=90°：

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

γ=180°：

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

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

ψ=90°：

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

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) demarcate gyro misalignment:

Utilize following formula to estimate β _zxand β _yx:

Wherein,

Utilize following formula to estimate β _zyand β _xy:

Wherein,

Utilize following formula 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:

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

N-passage:

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

Wherein,

for inertial navigation east orientation accelerometer output acceleration, δ V _efor Ring Laser Gyroscope SINS east orientation is measured passage output speed, Φ _nfor Ring Laser Gyroscope SINS north orientation is measured passage output rotational angle,

for Ring Laser Gyroscope SINS north orientation, measure passage output rotational angular velocity, R is the radius of gyration,

for Ring Laser Gyroscope SINS north orientation accelerometer output acceleration, δ V _nfor Ring Laser Gyroscope SINS north orientation is measured passage output speed, Φ _efor Ring Laser Gyroscope SINS east orientation is measured passage output rotational angle,

for Ring Laser Gyroscope SINS east orientation is measured passage output 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:

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

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) determine the direction cosine matrix between Ring Laser Gyroscope SINS coordinate system and local geographic coordinate system

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

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 is respectively the angle of pitch of Ring Laser Gyroscope SINS, roll angle and position angle;

4) rotation mould turnover, guarantees that the time of the navigation mode of Ring Laser Gyroscope SINS work is 2～5 minutes, obtains the absolute angle speed omega 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 the roll angle γ of Ring Laser Gyroscope SINS and position angle ψ 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 the error model of Ring Laser Gyroscope SINS and absolute angle speed omega _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) gyro error is transformed into local geographic coordinate system from Ring Laser Gyroscope SINS coordinate system, obtains:

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

δ ω _upfor the output of rotation axis to responsive gyro; for absolute angle speed omega _bprojection in Ring Laser Gyroscope SINS coordinate system;

8) by the formula of the formula substitution step 7) of step 6), obtain 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) the formula integration to step 8), obtains:

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

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

Compared with prior art, the beneficial effect that the present invention has is: the calibration facility that the present invention adopts is marble flat board and turnover bracket (also available low precision turntable), characteristic according to Laser strapdown inertial navigation, adopt the output speed of Laser strapdown inertial navigation under navigation mode as observed quantity, a large amount of experimental results show that method of the present invention can be successfully to Laser strapdown inertial navigation demarcate, reduced calibration facility cost and to demarcating the restriction of test site.

Embodiment

The error model of being used to 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 that acceleration causes (deflection error); ω _bi: the projection of absolute angle speed in carrier coordinate system.

In demarcating test, generally do not consider gyro deflection error.The object of demarcating is exactly to determine above parameter.

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

E-passage:

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

N-passage:

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

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

Due to what adopt, be the Laser strapdown ins error model of simplifying, the time that therefore Laser strapdown inertial navigation is operated in navigation mode after each rotation is 2～5 minutes.

Ignore in error model

with

, can again obtain error model as follows:

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

Φ wherein _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 (being 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 is 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 need to change to guarantee the navigation time (otherwise error model (2) is by invalid) of navigation mode.

The Laser strapdown inertial navigation of take rotation θ angle is example, and under above-mentioned rotation, navigation error model can be with formal construction below.In rotary course, the absolute angle speed 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 with respect to

the projection of big or small earth autobiography angular velocity be left in the basket, consider that carrier coordinate system is with respect to the initial orientation of 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 demarcating for the first time, each axle of carrier strictly to be aimed at, but require carrier coordinate system with respect 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:

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

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

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

Above formula is carried out to integration, obtains:

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

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

Accelerometer error is adopted to similar method, and in fact, certain force is projected as carrier coordinate system:

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

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

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

Acceleration error is projected as local geographic coordinate system:

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

Bring formula (10) 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:

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

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

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

$\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_{\mathrm{xy}}g-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}-g{\mathrm{\β}}_{\mathrm{yz}}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}+g{\mathrm{\β}}_{\mathrm{zx}};\\ \mathrm{\δ}{\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_z-{\mathrm{\α}}_{\mathrm{zy}}g+g{\mathrm{\β}}_{x}t+g{\mathrm{\β}}_{\mathrm{xx}}\frac{\mathrm{\π}}{2};\end{array}$

When θ=180 °

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

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

Other rotation angle γ, the velocity survey equation under ψ, also can calculate as stated above.

Rotation γ angle obtains velocity error and measures:

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

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

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

When γ=180 °,

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

Rotation ψ angular measurement model is:

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

When ψ=90 °

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

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, except gyro misalignment, all have demarcated out and compensated, program below can be used for estimating β _ij.

The 1st step rotation θ=90 °

Measurement model:

The 2nd step rotation θ=180 °

Measurement model:

The 3rd step is estimated β _zxand β _yx

The 4th step rotation γ=90 °

Measurement model:

The 5th step rotation γ=180 °

Measurement model:

The 6th step is estimated β _zyand β _xy

The 7th step rotation ψ=180 °

Measurement model:

The 8th step is estimated β _zyand β _xy

Here (15) have been utilized, (16), (18), the measurement model equation that (19) are set up.

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

δV ^t=δV ^I+δV ^II (20)

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

δ V ^iI---the cumulative velocity error (2-3min) of measurement after rotary course.

Second portion in equation (20) is left in the basket with respect to first, so calibration algorithm utilization 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 after aligning finishes, system enters navigation mode;

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

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

said procedure rotates different angles repeatedly to be carried out, and obtains enough measurements export to calibrate each parameter with this;

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

utilize the speed output of level and smooth mistake and the parameter that measurement model estimates accelerometer and gyro;

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

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

Two kinds of mode comparing results of table 1

From two groups of calibration results, can find out, two kinds of differences of demarcating mode meet index request, prove that scaling method of the present invention is feasible.

Claims (2)

1. a Ring Laser Gyroscope SINS performance parameter calibration method, is characterized in that, the method is:

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

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

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 the projection at Ring Laser Gyroscope SINS coordinate system of accelerometer and gyro error; 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 _ijkthe gyroscopic drift causing for acceleration; ω _bi---the projection of absolute angle speed in Ring Laser Gyroscope SINS coordinate system; I=x, y, z; J=x, y, z; I ≠ j;

3) utilize following formula 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, the angle of pitch that θ is Ring Laser Gyroscope SINS, t is for demarcating the test duration;

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

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

θ=90°：

$\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=-{\mathrm{\α}}_{\mathrm{xz}}g+{\mathrm{\α}}_{\mathrm{xy}}g-g\frac{{\mathrm{\β}}_y}{\stackrel{\·}{\mathrm{\θ}}}-g{\mathrm{\β}}_{\mathrm{yz}}+g\frac{{\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}+g{\mathrm{\β}}_{\mathrm{zx}};\\ \mathrm{\δ}{\stackrel{\·}{V}}_N=-{\mathrm{\α}}_y-{\mathrm{\α}}_{\mathrm{yz}}g-{\mathrm{\α}}_z-{\mathrm{\α}}_{\mathrm{zy}}g+g{\mathrm{\β}}_{x}t+g{\mathrm{\β}}_{x}t+g{\mathrm{\β}}_{\mathrm{xx}}\frac{\mathrm{\π}}{2};\end{array}$

θ=180°：

$\begin{array}{c}\mathrm{\δ}{\stackrel{\·}{V}}_E=\frac{{2\mathrm{\β}}_z}{\stackrel{\·}{\mathrm{\θ}}}g+2g{\mathrm{\β}}_{\mathrm{zx}}-2{\mathrm{\α}}_{\mathrm{xz}}g;\\ \mathrm{\δ}{\stackrel{\·}{V}}_N=-2{\mathrm{\α}}_y+g{\mathrm{\β}}_{x}t+g{\mathrm{\β}}_{\mathrm{xx}}\mathrm{\π};\end{array}$

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

γ=90°：

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

γ=180°：

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

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

ψ=90°：

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

Utilize following formula to estimate β _zxand β _yx:

Wherein,

Utilize following formula to estimate β _zyand β _xy:

Wherein,

Utilize following formula to estimate β _xzand β _yz:

Wherein,

2. Ring Laser Gyroscope SINS performance parameter calibration method according to claim 1, is characterized in that, in described step 3), and 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:

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

N-passage:

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

Wherein,

for inertial navigation east orientation accelerometer output acceleration, δ V _efor Ring Laser Gyroscope SINS east orientation is measured passage output speed, Φ _nfor Ring Laser Gyroscope SINS north orientation is measured passage output rotational angle,

for Ring Laser Gyroscope SINS north orientation, measure passage output rotational angular velocity, R is the radius of gyration, for Ring Laser Gyroscope SINS north orientation accelerometer output acceleration, δ V _nfor Ring Laser Gyroscope SINS north orientation is measured passage output speed, Φ _efor Ring Laser Gyroscope SINS east orientation is measured passage output rotational angle, for Ring Laser Gyroscope SINS east orientation is measured passage output 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:

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

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) determine the direction cosine matrix between Ring Laser Gyroscope SINS coordinate system and local geographic coordinate system

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

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 is respectively the angle of pitch of Ring Laser Gyroscope SINS, roll angle and position angle;

4) rotation mould turnover, guarantees that the time of the navigation mode of Ring Laser Gyroscope SINS work is 2～5 minutes, obtains the absolute angle speed omega 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 the roll angle γ of Ring Laser Gyroscope SINS and position angle ψ 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 the error model of Ring Laser Gyroscope SINS and absolute angle speed omega _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) gyro error is transformed into local geographic coordinate system from Ring Laser Gyroscope SINS coordinate system, obtains:

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

δ ω _upfor the output of rotation axis to responsive gyro;

for absolute angle speed omega _bprojection in Ring Laser Gyroscope SINS coordinate system;

8) by the formula of the formula substitution step 7) of step 6), obtain 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) the formula integration to step 8), obtains:

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

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