CN101514899B - Optical fibre gyro strapdown inertial navigation system error inhibiting method based on single-shaft rotation - Google Patents

Abstract

The invention provides an optical fibre gyro strapdown inertial navigation system error inhibiting method based on single-shaft rotation. The initial position parameters of a carrier are confirmed; the data outputted by an optical fibre gyroscope and a quartz accelerometer are collected; the pose information of the carrier is confirmed by the relation between the output of the accelerometer and an acceleration of gravity as well as the relation between the output of the gyroscope and the earth rotation rate; and the initial aligning of the system is finished; an inertial measuring unit coordinate system rotates by 45 degrees along the front direction of the shaft oyb of a carrier coordinate system and the initial opposite position between the two coordinate systems is confirmed; IMU continuously rotates along the front direction of the orientation shaft ozb of the carrier coordinate system by an angular velocity that Omega is equal to 6 degrees/s. The data generated by the optical fibre gyroscope and the quartz accelerometer after the rotation of the IMU is converted under the carrier coordinate system to obtain the modulating form of the constant deviation of an inertial apparatus. The output vale Omega ib<b> of the optical fibre gyroscope is used to update a strapdown matrix Tb<n>; the speed and the position of the carrier after the IMU is rotated and modulated are calculated. The invention modulates the constant deviation of the inertial device on the directions of three shafts to improve the navigation and location precisions.

Description

Optical fibre gyro strapdown inertial navigation system error inhibiting method based on the single shaft rotation

(1) technical field

What the present invention relates to is a kind of error inhibition method, particularly relates to a kind of error inhibition method of the fiber optic gyro strapdown inertial navigation system based on single shaft rotation.

(2) background technology

Strapdown inertial navigation system SINS is a kind of autonomous navigational system fully, utilize the line motion and the angular motion parameter in gyroscope and accelerometer measures carrier relative inertness space, under given starting condition, carry out integral operation by computing machine, position, speed and attitude information are provided continuously, in real time.Because SINS relies on its own inertial element fully, do not rely on any external information to measure navigational parameter, therefore, it has good concealment,

Be not subjected to the weather condition restriction, advantage such as interference-free is a kind of complete autonomous type, round-the-clock navigational system, has been widely used in fields such as Aeronautics and Astronautics, navigation.According to the ultimate principle of SINS, the existence that SINS inertia device in navigation procedure often is worth deviation is the principal element that causes the inertial navigation system navigation accuracy to be difficult to improve.How effectively limiting the inertial navigation error, to disperse, improve the inertial navigation system precision be the very important problem in inertial navigation field.

In order to improve the precision of strapdown system self, can improve the precision of inertance element on the one hand, but owing to be subjected to the restriction of process technology level, the precision of unconfined raising element is to be difficult to realize; Be exactly the error inhibition technology of taking strapdown inertial navigation system on the other hand, offset of the influence of the error of inertia device automatically system accuracy.The inertance element that so just can use existing precision constitutes the strapdown inertial navigation system of degree of precision.

The error of inertial navigation system suppresses, is not to depend on outside assisting error state is estimated, but the propagation law of research inertial navigation error under the special exercise condition, and limit error according to this rule and disperse, improve the method for navigation accuracy.Rotating inhibition is most typical error inhibition method: by around an axle or a plurality of rotator inertia measuring units (IMU), navigation error is modulated, reach the purpose that navigation accuracy is dispersed, improved to the control navigation error.

The single shaft rotation only can compensate the normal value deviation of inertia device on two sensitive axes directions; Though the twin shaft rotation can compensate the normal value deviation of inertia device on three sensitive axes directions, the complicated reduction that has caused the reliability and the navigation calculation efficient of system of rotating mechanism.Therefore, how the single shaft rotation compensation mode reasonable in design navigation accuracy that improves the optical fiber inertial navigation system has important meaning.

(3) summary of the invention

The object of the present invention is to provide and a kind of Inertial Measurement Unit is rotated continuously around the carrier azimuth axis, the normal value deviation that had both guaranteed inertia device on three sensitive axes directions is modulated, and has avoided the rotating mechanism of the required complexity of twin shaft rotation and the optical fibre gyro strapdown inertial navigation system error inhibiting method based on the single shaft rotation of navigation calculation algorithm again.

Technical solution of the present invention is: a kind of single shaft rotation modulation method of strapdown inertial navitation system (SINS), it is characterized in that Inertial Measurement Unit is rotated continuously around the carrier azimuth axis that does not overlap with self, utilize the relative position relation of IMU coordinate system and carrier coordinate system in the continuous rotation process of Inertial Measurement Unit, can determine that inertia device often is worth the inhibition form of deviation, its concrete steps are as follows:

(1) utilizes global position system GPS to determine the initial position parameters of carrier, they are bound to navigational computer;

(2) fiber optic gyro strapdown inertial navigation system carries out gathering after the preheating data of fibre optic gyroscope and quartz accelerometer output.Wherein, the constant value drift of three gyros is equal, three accelerometer zero drifts are equal.According to output and the relation of acceleration of gravity and the initial alignment that gyroscope is exported the system that finishes with the tentatively definite attitude information (pitch angle θ, roll angle γ and course angle ψ) of carrier at this moment of the relation of earth rotation angular speed of accelerometer, set up the initial strapdown matrix T of inertial navigation system _b ⁿ:

$T_b^n=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}-\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\cos \mathrm{\&theta;}\sin \mathrm{\&psi;}& \sin \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}\\ \cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&psi;}& \sin \mathrm{\&gamma;}\sin \mathrm{\&psi;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}\\ -\sin \mathrm{\&gamma;}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}& \cos \mathrm{\&gamma;}\cos \mathrm{\&theta;}\end{array}\right]$

(3) Inertial Measurement Unit is around carrier coordinate system oy _bAxle is rotated in the forward 45 degree (as accompanying drawing 2), determines the initial relative position between IMU coordinate system and the carrier coordinate system:

Carrier coordinate system and IMU coordinate system have same true origin o, oy _sAxle and oy _bAxle coincides ox _sAxle, oz _sAxle, ox _bAxle and oz _bAxle is positioned at same plane, but oz _sAxle and oz _bThe angle of axle is 45 °, oz _sAxle and ox _bThe angle of axle is 90 °-45 °=45 °.

(4) determine the relative initial position of two coordinate systems relation after, Inertial Measurement Unit is around carrier coordinate system azimuth axis oz _bForward rotates (as accompanying drawing 3) continuously with angular velocity omega=6 °/s:

In the IMU rotation process, the transition matrix that the IMU coordinate is tied to carrier coordinate system is:

(5) data-switching that fibre optic gyroscope and quartz accelerometer after the Inertial Measurement Unit rotation are generated obtains the modulation format that inertia device often is worth deviation under carrier coordinate system:

The output valve of fibre optic gyroscope and accelerometer is respectively ω _Is ^sAnd f _Is ^s:

${\mathrm{\&omega;}}_{\mathrm{is}}^s={\left(T_s^b\right)}^T{\mathrm{\&omega;}}_{\mathrm{ibd}}^b+{\left[\begin{array}{ccc}{\mathrm{\&epsiv;}}_x& {\mathrm{\&epsiv;}}_y& {\mathrm{\&epsiv;}}_z\end{array}\right]}^T+{\mathrm{\&omega;}}_{\mathrm{bs}}^s$

$f_{\mathrm{is}}^s={\left(T_s^b\right)}^T{f}_{\mathrm{ibd}}^b+{\left[\begin{array}{ccc}{\&dtri;}_x& {\&dtri;}_y& {\&dtri;}_z\end{array}\right]}^T+f_{\mathrm{bs}}^s$

Wherein, ${\mathrm{\&omega;}}_{\mathrm{bs}}^s=-{\left(T_s^b\right)}^T{\mathrm{\&omega;}}_{\mathrm{sb}}^b={\left[\begin{array}{ccc}0& 0& \mathrm{\&omega;}\end{array}\right]}^T,$ () ^TThe commentaries on classics order of representing matrix, ω _Ibd ^b, f _Ibd ^bTrue output for carrier movement.ε _x, ε _y, ε _zBe gyrostatic drift error,

Be the accelerometer error of zero.Because s is relative b is only to rotatablely move, and does not have linear relative movement, so $f_{\mathrm{bs}}^s=0,$ So accelerometer output can be expressed as: $f_{\mathrm{is}}^s=T_b^s{f}_{\mathrm{ibd}}^b+{\left[\begin{array}{ccc}{\&dtri;}_x& {\&dtri;}_y& {\&dtri;}_z\end{array}\right]}^T.$

The output of fibre optic gyroscope and accelerometer can be expressed as from the conversion that the IMU coordinate is tied to carrier coordinate system:

${\mathrm{\&omega;}}_{\mathrm{ib}}^b=T_s^b{\mathrm{\&omega;}}_{\mathrm{is}}^s+{\mathrm{\&omega;}}_{\mathrm{sb}}^b,f_{\mathrm{ib}}^b=T_s^b{f}_{\mathrm{is}}^s$

Inertial Measurement Unit is around carrier coordinate system oy _bAxle is rotated in the forward 45 degree, and can obtain ε this moment _zCos45 °=ε _xCos (90 °-45 °),

Carrier coordinate system oz _bBe not subjected to the influence of gyroscope constant value drift and accelerometer zero drift on the direction of principal axis, the line acceleration of motion in the motion angular velocity in carrier relative inertness space and carrier relative inertness space is as follows respectively in the projection of carrier coordinate system at this moment:

$\left\{\begin{array}{c}{\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{bx}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{bx}}+\sqrt{2}/2\cos \mathrm{\&omega;t}({\mathrm{\&epsiv;}}_x+{\mathrm{\&epsiv;}}_z)-\sin \mathrm{\&omega;t}{\mathrm{\&epsiv;}}_y\\ {\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{by}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{by}}+\sqrt{2}/2\sin \mathrm{\&omega;t}({\mathrm{\&epsiv;}}_x+{\mathrm{\&epsiv;}}_Z)+\cos \mathrm{\&omega;t}{\mathrm{\&epsiv;}}_y\\ {\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{bz}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{bz}}\end{array}\right.$

$\left\{\begin{array}{c}{f}_{\mathrm{ib}}^{\mathrm{bx}}=f_{\mathrm{ibd}}^{\mathrm{bx}}+\sqrt{2}/2\cos \mathrm{\&omega;t}({\&dtri;}_x+{\&dtri;}_z)-\sin \mathrm{\&omega;t}{\&dtri;}_y\\ f_{\mathrm{ib}}^{\mathrm{by}}=f_{\mathrm{ibd}}^{\mathrm{by}}+\sqrt{2}/2\sin \mathrm{\&omega;t}({\&dtri;}_x+{\&dtri;}_z)+\cos \mathrm{\&omega;t}{\&dtri;}_y\\ f_{\mathrm{ib}}^{\mathrm{bz}}=f_{\mathrm{ibd}}^{\mathrm{bz}}\end{array}\right.$

Wherein, ω _Ib ^Bx, ω _Ib ^By, ω _Ib ^BzBe respectively the ox of the motion angular velocity in carrier relative inertness space in carrier coordinate system _bAxle, oy _bAxle, oz _bComponent on the axle; f _Ib ^Bx, f _Ib ^By, f _Ib ^BzBe respectively the ox of the linear acceleration in carrier relative inertness space in carrier coordinate system _bAxle, oy _bAxle, oz _bComponent on the axle.

So far, in the carrier coordinate system on the azimuth axis the normal value deviation of inertia device obtain offsetting; The normal value deviation of inertia device is modulated into the amount that the cycle changes on the horizontal direction, and through integral element in the inertial navigation system, it is zero to acting as of system that this often is worth deviation.

(6) the carrier system that step (5) is obtained is the output valve ω of optical fibre gyro down _Ib ^bBring into and adopt the hypercomplex number method in the inertial navigation system the strapdown matrix T _b ⁿUpgrade:

${\mathrm{\&omega;}}_{\mathrm{nb}}^b={\mathrm{\&omega;}}_{\mathrm{ib}}^b-{\left(T_b^n\right)}^T({\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)$

Wherein: ω _Ie ⁿBe the component of rotational-angular velocity of the earth under navigation system; ω _En ⁿFor navigation coordinate is the component of motion angular velocity under navigation system of spherical coordinate system relatively; ω _Nb ^bThe component of motion angular velocity on carrier coordinate system for the relative navigation coordinate of carrier system.

Upgrade hypercomplex number and attitude matrix:

If carrier coordinate system relative to the hypercomplex number of rotating of navigation coordinate system is:

Q＝q ₀+q ₁i _b+q ₂j _b+q ₃k _b

Wherein: i _b, j _b, k _bRepresent carrier coordinate system ox respectively _bAxle, oy _bAxle, oz _bUnit direction vector on the axle.

The instant correction of hypercomplex number can be by separating the hypercomplex number differential equation $\stackrel{\&CenterDot;}{Q}=\frac{1}{2}Q{\mathrm{\&omega;}}_{\mathrm{nb}}^b$ Realize:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_0\\ {\stackrel{\&CenterDot;}{q}}_1\\ {\stackrel{\&CenterDot;}{q}}_2\\ {\stackrel{\&CenterDot;}{q}}_3\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}0& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}\\ {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="nb\; bx"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">nb</figure-callout>}}^{\mathrm{bx}}& 0& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}\\ {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="nb\; bz"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">nb</figure-callout>}}^{\mathrm{bz}}& 0& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}\\ {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}& 0\end{array}\right]\left[\begin{array}{c}{q}_0\\ q_1\\ q_2\\ q_3\end{array}\right]$

Wherein: ω _Nb ^Bx, ω _Nb ^By, ω _Nb ^BzRepresent respectively carrier navigate relatively be motion angular velocity at carrier coordinate system ox _bAxle, oy _bAxle, oz _bComponent on the axle.

Attitude matrix T _b ⁿRenewal process be:

$T_b^n=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2+q_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="H2009100717333E00032.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="H2009100717333E00032.png"\; state="\{\{state\}\}">q</figure-callout>}}_2+q_0{q}_3)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-q_1^2+{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="H2009100717333E00032.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-q_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="H2009100717333E00032.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2+q_3^2\end{array}\right]$

(7) utilize the output valve f of quartz accelerometer _Ib ^bAnd the attitude matrix T of step (6) calculating _b ⁿ, calculate speed and position through IMU rotation modulation back carrier.

1) calculate navigation system acceleration down:

$\left[\begin{array}{c}{f}^{\mathrm{nx}}\\ f^{\mathrm{ny}}\\ f^{\mathrm{nz}}\end{array}\right]=T_b^n\left[\begin{array}{c}{f}_{\mathrm{ib}}^{\mathrm{bx}}\\ f_{\mathrm{ib}}^{\mathrm{by}}\\ f_{\mathrm{ib}}^{\mathrm{bz}}\end{array}\right]$

2) horizontal velocity and the position of calculating carrier:

According to t ₁Carrier east orientation horizontal velocity V constantly _x(t ₁) and north orientation horizontal velocity V _y(t ₁), ask for t ₁The rate of change of carrier horizontal velocity is constantly:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_x\left(t_1\right)=f^{\mathrm{nx}}+(2{\mathrm{\&omega;}}_{\mathrm{ie}}^{\mathrm{nz}}+{\mathrm{\&omega;}}_{\mathrm{en}}^{\mathrm{nz}})V_y\left(t_1\right)\\ {\stackrel{\&CenterDot;}{V}}_y\left(t_1\right)=f^{\mathrm{ny}}-(2{\mathrm{\&omega;}}_{\mathrm{ie}}^{\mathrm{nz}}+{\mathrm{\&omega;}}_{\mathrm{en}}^{\mathrm{nz}})V_x\left(t_1\right)\end{array}\right.$

At t ₂Horizontal velocity and carrier positions are respectively constantly:

$\left\{\begin{array}{c}{V}_x\left(t_2\right)=V_x\left(t_1\right)+{\stackrel{\&CenterDot;}{V}}_x\left(t_1\right)(t_2-t_1)\\ V_y\left(t_2\right)=V_y\left(t_1\right)+{\stackrel{\&CenterDot;}{V}}_y\left(t_1\right)(t_2-t_1)\end{array}\right.$

3) calculate bearer rate sum of errors site error:

$\left\{\begin{array}{c}\mathrm{\&Delta;}{V}_x=V_x\left(t_2\right)-V_{x0}\\ \mathrm{\&Delta;}{V}_y=V_y\left(t_2\right)-V_{y0}\end{array}\right.$

Wherein: V _X0, V _Y0East orientation and the north orientation speed of representing the initial time carrier respectively; Δ V _x, Δ V _yThe variable quantity of representing carrier east orientation, north orientation speed respectively;

λ ₀Longitude and the latitude of representing initial time carrier present position respectively;

Δ λ represents the latitude of carrier, the variable quantity of longitude respectively; R _Xp, R _YpThe radius-of-curvature of representing earth meridian circle, prime vertical respectively; t ₁, t ₂Two the adjacent time points in the process that resolve for inertial navigation system.

The present invention's advantage compared with prior art is: the present invention has broken the rotation of traditional single shaft and can not compensate inertia device on three directions and often be worth the required complex rotation mechanism of deviation and twin shaft rotation and the constraint of navigation calculation algorithm, the angled strapdown inertial navitation system (SINS) error rotation modulation scheme of a kind of turning axle and gyro sensitive axes is proposed, this method can often be worth deviation with the inertia device on three direction of principal axis modulates, and improves navigation and positioning accuracy effectively.

The effect useful to the present invention is described as follows:

Under the Matlab simulated conditions, this method is carried out emulation experiment:

Carrier is done the three-axis swinging motion.Carrier waves around pitch axis, axis of roll and course axle with sinusoidal rule, and its mathematical model is:

$\left\{\begin{array}{c}\mathrm{\&theta;}={\mathrm{\&theta;}}_m\sin ({\mathrm{\&omega;}}_{\mathrm{\&theta;}}+{\mathrm{\&phi;}}_{\mathrm{\&theta;}})\\ \mathrm{\&gamma;}={\mathrm{\&gamma;}}_m\sin ({\mathrm{\&omega;}}_{\mathrm{\&gamma;}}+{\mathrm{\&phi;}}_{\mathrm{\&gamma;}})\\ \mathrm{\&psi;}={\mathrm{\&psi;}}_m\sin ({\mathrm{\&omega;}}_{\mathrm{\&psi;}}+{\mathrm{\&phi;}}_{\mathrm{\&psi;}})+k\end{array}\right.$

Wherein: θ, γ, ψ represent the angle variables of waving of pitch angle, roll angle and course angle respectively; θ _m, γ _m, ψ _mThe angle amplitude is waved in expression accordingly respectively; ω _θ, ω _γ, ω _ψRepresent corresponding angle of oscillation frequency respectively; φ _θ, φ _γ, φ _ψRepresent corresponding initial phase respectively; ω _i=2 π/T _i, i=θ, γ, ψ, T _iRepresent corresponding rolling period, k is the angle, initial heading.Get during emulation: θ _m=12 °, γ _m=15 °, ψ _m=10 °, T _θ=8s, T _γ=10s, T _ψ=6s, k=0.

Carrier initial position: 45.7796 ° of north latitude, 126.6705 ° of east longitudes;

The initial attitude error angle: three initial attitude error angles are zero;

Equatorial radius: R _e=6378393.0m;

Ellipsoid degree: e=3.367e-3;

The earth surface acceleration of gravity that can get by universal gravitation: g ₀=9.78049;

Rotational-angular velocity of the earth (radian per second): 7.2921158e-5;

The gyroscope constant value drift: 0.01 degree/hour;

Accelerometer bias: 10 ^-4g ₀

Constant: π=3.1415926;

Utilize the described method of invention to obtain attitude of carrier angle error curve, velocity error curve and site error curve respectively as Fig. 4, Fig. 5, shown in Figure 6.The result shows and waves under the disturbed condition, adopts the inventive method can obtain high orientation precision.

(4) description of drawings

Fig. 1 is the strapdown inertial navigation system error inhibiting method process flow diagram based on the rotation of IMU single shaft of the present invention;

Fig. 2 is the initial relative position relation of initial time IMU coordinate system and carrier coordinate system;

Fig. 3 is in the IMU rotation process, the relative position relation of IMU coordinate system and carrier coordinate system;

Fig. 4 waves under the condition for carrier, the attitude of carrier angle error empirical curve based on IMU when static;

Fig. 5 waves under the condition for carrier, the bearer rate error experiments curve based on IMU when static;

Fig. 6 waves under the condition for carrier, the carrier positions error experiments curve based on IMU when static.

Fig. 7 waves under the condition for carrier, the attitude of carrier angle error empirical curve that rotates continuously based on the IMU single shaft of the present invention;

Fig. 8 waves under the condition for carrier, the bearer rate error experiments curve that rotates continuously based on the IMU single shaft of the present invention;

Fig. 9 waves under the condition for carrier, the carrier positions error experiments curve that rotates continuously based on the IMU single shaft of the present invention.

(5) embodiment

Below in conjunction with accompanying drawing the specific embodiment of the present invention is described in detail:

(1) utilizes global position system GPS to determine the initial position parameters of carrier (comprising longitude, latitude), they are bound to navigational computer.

(2) fiber optic gyro strapdown inertial navigation system carries out gathering after the preheating data of fibre optic gyroscope and quartz accelerometer output.Wherein, the constant value drift of three gyros is equal, three accelerometer zero drifts are equal.According to output and the relation of acceleration of gravity and the initial alignment that gyroscope is exported the system that finishes with the tentatively definite attitude information (pitch angle θ, roll angle γ and course angle ψ) of carrier at this moment of the relation of earth rotation angular speed of accelerometer, set up the initial strapdown matrix T of inertial navigation system _b ⁿ:

$T_b^n=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}-\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\cos \mathrm{\&theta;}\sin \mathrm{\&psi;}& \sin \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}\\ \cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&psi;}& \sin \mathrm{\&gamma;}\sin \mathrm{\&psi;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}\\ -\sin \mathrm{\&gamma;}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}& \cos \mathrm{\&gamma;}\cos \mathrm{\&theta;}\end{array}\right]---\left(1\right)$

(3) Inertial Measurement Unit is around carrier coordinate system oy _bAxle is rotated in the forward 45 degree (as accompanying drawing 2), determines the initial relative position between IMU coordinate system and the carrier coordinate system:

Carrier coordinate system and IMU coordinate system have same true origin o, oy _sAxle and oy _bAxle coincides ox _sAxle, oz _sAxle, ox _bAxle and oz _bAxle is positioned at same plane, but oz _sAxle and oz _bThe angle of axle is 45 °, oz _sAxle and ox _bThe angle of axle is 90 °-45 °=45 °.

(4) determine the relative initial position of two coordinate systems relation after, Inertial Measurement Unit is around carrier coordinate system azimuth axis oz _bForward rotates (as accompanying drawing 3) continuously with angular velocity omega=6 °/s:

In the IMU rotation process, the transition matrix that the IMU coordinate is tied to carrier coordinate system is:

(5) data-switching that fibre optic gyroscope and quartz accelerometer after the Inertial Measurement Unit rotation are generated obtains the modulation format that inertia device often is worth deviation under carrier coordinate system:

The output valve of fibre optic gyroscope and accelerometer is respectively ω _Is ^sAnd f _Is ^s:

${\mathrm{\&omega;}}_{\mathrm{is}}^s={\left(T_s^b\right)}^T{\mathrm{\&omega;}}_{\mathrm{ibd}}^b+{\left[\begin{array}{ccc}{\mathrm{\&epsiv;}}_x& {\mathrm{\&epsiv;}}_y& {\mathrm{\&epsiv;}}_z\end{array}\right]}^T+{\mathrm{\&omega;}}_{\mathrm{bs}}^s$

$f_{\mathrm{is}}^s={\left(T_s^b\right)}^T{f}_{\mathrm{ibd}}^b+{\left[\begin{array}{ccc}{\&dtri;}_x& {\&dtri;}_y& {\&dtri;}_z\end{array}\right]}^T+f_{\mathrm{bs}}^s---\left(3\right)$

Wherein, ${\mathrm{\&omega;}}_{\mathrm{bs}}^s=-{\left(T_s^b\right)}^T{\mathrm{\&omega;}}_{\mathrm{sb}}^b={\left[\begin{array}{ccc}0& 0& \mathrm{\&omega;}\end{array}\right]}^T,$ () ^TThe commentaries on classics order of representing matrix, ω _Ibd ^b, f _Ibd ^bTrue output for carrier movement.ε _x, ε _y, ε _zBe gyrostatic drift error,

Be the accelerometer error of zero.Because s is relative b is only to rotatablely move, and does not have linear relative movement, so $f_{\mathrm{bs}}^s=0,$ So accelerometer output can be expressed as: $f_{\mathrm{is}}^s=T_b^s{f}_{\mathrm{ibd}}^b+{\left[\begin{array}{ccc}{\&dtri;}_x& {\&dtri;}_y& {\&dtri;}_z\end{array}\right]}^T.$

The output of fibre optic gyroscope and accelerometer can be expressed as from the conversion that the IMU coordinate is tied to carrier coordinate system:

${\mathrm{\&omega;}}_{\mathrm{ib}}^b=T_s^b{\mathrm{\&omega;}}_{\mathrm{is}}^s+{\mathrm{\&omega;}}_{\mathrm{sb}}^b,f_{\mathrm{ib}}^b=T_s^b{f}_{\mathrm{is}}^s---\left(4\right)$

Inertial Measurement Unit is around carrier coordinate system oy _bAxle is rotated in the forward 45 degree, and the constant value drift of three gyros equates that three accelerometer zero drifts equate that can obtain ε this moment _z45 °=ε of cos _xCos (90 °-45 °),

Carrier coordinate system oz _bBe not subjected to gyroscope constant value drift and acceleration on the direction of principal axis

The influence of degree meter zero drift, the motion angular velocity and the carrier relative inertness space in carrier relative inertness space at this moment

The line acceleration of motion as follows respectively in the projection of carrier coordinate system:

$\left\{\begin{array}{c}{\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{bx}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{bx}}+\sqrt{2}/2\cos \mathrm{\&omega;t}({\mathrm{\&epsiv;}}_x+{\mathrm{\&epsiv;}}_z)-\sin \mathrm{\&omega;t}{\mathrm{\&epsiv;}}_y\\ {\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{by}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{by}}+\sqrt{2}/2\sin \mathrm{\&omega;t}({\mathrm{\&epsiv;}}_x+{\mathrm{\&epsiv;}}_z)+\cos \mathrm{\&omega;t}{\mathrm{\&epsiv;}}_y\\ {\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{bz}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{bz}}\end{array}\right.$

$\left\{\begin{array}{c}{f}_{\mathrm{ib}}^{\mathrm{bx}}=f_{\mathrm{ibd}}^{\mathrm{bx}}+\sqrt{2}/2\cos \mathrm{\&omega;t}({\&dtri;}_x+{\&dtri;}_z)-\sin \mathrm{\&omega;t}{\&dtri;}_y\\ f_{\mathrm{ib}}^{\mathrm{by}}=f_{\mathrm{ibd}}^{\mathrm{by}}+\sqrt{2}/2\sin \mathrm{\&omega;t}({\&dtri;}_x+{\&dtri;}_z)+\cos \mathrm{\&omega;t}{\&dtri;}_y\\ f_{\mathrm{ib}}^{\mathrm{bz}}=f_{\mathrm{ibd}}^{\mathrm{bz}}\end{array}\right.---\left(5\right)$

Wherein, ω _Ib ^Bx, ω _Ib ^By, ω _Ib ^BzBe respectively the ox of the motion angular velocity in carrier relative inertness space in carrier coordinate system _bAxle, oy _bAxle, oz _bComponent on the axle; f _Ib ^Bx, f _Ib ^By, f _Ib ^BzBe respectively the ox of the linear acceleration in carrier relative inertness space in carrier coordinate system _bAxle, oy _bAxle, oz _bComponent on the axle.

So far, in the carrier coordinate system on the azimuth axis the normal value deviation of inertia device obtain offsetting; The normal value deviation of inertia device is modulated into the amount that the cycle changes on the horizontal direction, and through integral element in the inertial navigation system, it is zero to acting as of system that this often is worth deviation.

(6) the carrier system that step (5) is obtained is the output valve ω of optical fibre gyro down _Ib ^bBring into and adopt the hypercomplex number method in the inertial navigation system the strapdown matrix T _b ⁿUpgrade:

${\mathrm{\&omega;}}_{\mathrm{nb}}^b={\mathrm{\&omega;}}_{\mathrm{ib}}^b-{\left(T_b^n\right)}^T({\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)---\left(6\right)$

Wherein: ω _Ie ⁿBe the component of rotational-angular velocity of the earth under navigation system; ω _En ⁿFor navigation coordinate is the component of motion angular velocity under navigation system of spherical coordinate system relatively; ω _Nb ^bThe component of motion angular velocity on carrier coordinate system for the relative navigation coordinate of carrier system.

Upgrade hypercomplex number and attitude matrix:

If carrier coordinate system relative to the hypercomplex number of rotating of navigation coordinate system is:

Q＝q ₀+q ₁i _b+q ₂j _b+q ₃k _b (7)

Wherein: i _b, j _b, k _bRepresent carrier coordinate system ox respectively _bAxle, oy _bAxle, oz _bUnit direction vector on the axle.

The instant correction of hypercomplex number can be by separating the hypercomplex number differential equation $\stackrel{\&CenterDot;}{Q}=\frac{1}{2}Q{\mathrm{\&omega;}}_{\mathrm{nb}}^b$ Realize:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_0\\ {\stackrel{\&CenterDot;}{q}}_1\\ {\stackrel{\&CenterDot;}{q}}_2\\ {\stackrel{\&CenterDot;}{q}}_3\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}0& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}\\ {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}& 0& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}\\ {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="nb\; bz"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">nb</figure-callout>}}^{\mathrm{bz}}& 0& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}\\ {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}& 0\end{array}\right]\left[\begin{array}{c}{q}_0\\ q_1\\ q_2\\ q_3\end{array}\right]---\left(8\right)$

Wherein: ω _Nb ^Bx, ω _Nb ^By, ω _Nb ^BzRepresent respectively carrier navigate relatively be motion angular velocity at carrier coordinate system ox _bAxle, oy _bAxle, oz _bComponent on the axle.

Attitude matrix T _b ⁿRenewal process as follows:

$T_b^n=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2+q_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="H2009100717333E00032.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="H2009100717333E00032.png"\; state="\{\{state\}\}">q</figure-callout>}}_2+q_0{q}_3)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-q_1^2+{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="H2009100717333E00032.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-q_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="H2009100717333E00032.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2+q_3^2\end{array}\right]---\left(9\right)$

(7) utilize the output valve f of quartz accelerometer _Ib ^bAnd the attitude matrix T of step (6) calculating _b ⁿ, calculate speed and position through IMU rotation modulation back carrier.

1) calculate navigation system acceleration down:

$\left[\begin{array}{c}{f}^{\mathrm{nx}}\\ f^{\mathrm{ny}}\\ f^{\mathrm{nz}}\end{array}\right]=T_b^n\left[\begin{array}{c}{f}_{\mathrm{ib}}^{\mathrm{bx}}\\ f_{\mathrm{ib}}^{\mathrm{by}}\\ f_{\mathrm{ib}}^{\mathrm{bz}}\end{array}\right]---\left(10\right)$

2) horizontal velocity and the position of calculating carrier:

According to t ₁Carrier east orientation horizontal velocity V constantly _x(t ₁) and north orientation horizontal velocity V _y(t ₁), ask for t ₁The rate of change of carrier horizontal velocity is constantly:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_x\left(t_1\right)=f^{\mathrm{nx}}+(2{\mathrm{\&omega;}}_{\mathrm{ie}}^{\mathrm{nz}}+{\mathrm{\&omega;}}_{\mathrm{en}}^{\mathrm{nz}})V_y\left(t_1\right)\\ {\stackrel{\&CenterDot;}{V}}_y\left(t_1\right)=f^{\mathrm{ny}}-(2{\mathrm{\&omega;}}_{\mathrm{ie}}^{\mathrm{nz}}+{\mathrm{\&omega;}}_{\mathrm{en}}^{\mathrm{nz}})V_x\left(t_1\right)\end{array}\right.---\left(11\right)$

At t ₂Horizontal velocity and carrier positions are respectively constantly:

$\left\{\begin{array}{c}{V}_x\left(t_2\right)=V_x\left(t_1\right)+{\stackrel{\&CenterDot;}{V}}_x\left(t_1\right)(t_2-t_1)\\ V_y\left(t_2\right)=V_y\left(t_1\right)+{\stackrel{\&CenterDot;}{V}}_y\left(t_1\right)(t_2-t_1)\end{array}\right.---\left(12\right)$

3) calculate bearer rate sum of errors site error:

$\left\{\begin{array}{c}\mathrm{\&Delta;}{V}_x=V_x\left(t_2\right)-{\mathrm{<figure-callout\; id="0"\; label="V\; x"\; filenames="H2009100717333E00012.png,H2009100717333E00022.png"\; state="\{\{state\}\}">V</figure-callout>}}_x\\ \mathrm{\&Delta;}{V}_y=V_y\left(t_2\right)-V_{y0}\end{array}\right.---\left(14\right)$

Wherein: V _X0, V _Y0East orientation and the north orientation speed of representing the initial time carrier respectively; Δ V _x, Δ V _yThe variable quantity of representing carrier east orientation, north orientation speed respectively;

λ ₀Longitude and the latitude of representing initial time carrier present position respectively;

Δ λ represents the latitude of carrier, the variable quantity of longitude respectively; R _Xp, R _YpThe radius-of-curvature of representing earth meridian circle, prime vertical respectively; t ₁, t ₂Two the adjacent time points in the process that resolve for inertial navigation system.

Claims (2)

1. optical fibre gyro strapdown inertial navigation system error inhibiting method based on single shaft rotation is characterized in that may further comprise the steps:

(1) utilizes global position system GPS to determine the initial position parameters that comprises longitude, latitude of carrier, they are bound to navigational computer;

(2) gather the fibre optic gyroscope of fiber optic gyro strapdown inertial navigation system and the data of quartz accelerometer output, wherein, the constant value drift of three gyros equates, three accelerometer zero drifts equate, tentatively determine pitch angle θ, roll angle γ and the course angle ψ attitude information of carrier at this moment according to the output of accelerometer and the relation and the gyroscope output of acceleration of gravity with the relation of earth rotation angular speed, finish the initial alignment of system, set up the initial strapdown matrix T of inertial navigation system _b ⁿ:

$T_b^n=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}-\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\cos \mathrm{\&theta;}\sin \mathrm{\&psi;}& \sin \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}\\ \cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&psi;}& \sin \mathrm{\&gamma;}\sin \mathrm{\&psi;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}\\ -\sin \mathrm{\&gamma;}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}& \cos \mathrm{\&gamma;}\cos \mathrm{\&theta;}\end{array}\right];$

(3) Inertial Measurement Unit is around carrier coordinate system oy _bAxle is rotated in the forward 45 degree, determines the initial relative position between IMU coordinate system and the carrier coordinate system:

Carrier coordinate system and IMU coordinate system have same true origin o, oy _sAxle and oy _bAxle coincides ox _sAxle, oz _sAxle, ox _bAxle and oz _bAxle is positioned at same plane, but oz _sAxle and oz _bThe angle of axle is 45 °, oz _sAxle and ox _bThe angle of axle is 90 °-45 °=45 °;

(4) determine the relative initial position of two coordinate systems relation after, Inertial Measurement Unit is around carrier coordinate system azimuth axis oz _bForward rotates continuously with angular velocity omega=6 °/s;

(5) data-switching that fibre optic gyroscope and quartz accelerometer after the Inertial Measurement Unit rotation are generated obtains the modulation format that inertia device often is worth deviation under carrier coordinate system:

The output valve of fibre optic gyroscope and accelerometer is respectively ω _Is ^sAnd f _Is ^s:

${\mathrm{\&omega;}}_{\mathrm{is}}^s={\left(T_s^b\right)}^T{\mathrm{\&omega;}}_{\mathrm{ibd}}^b+{\left[\begin{array}{ccc}{\mathrm{\&epsiv;}}_x& {\mathrm{\&epsiv;}}_y& {\mathrm{\&epsiv;}}_z\end{array}\right]}^T+{\mathrm{\&omega;}}_{\mathrm{bs}}^s$

$f_{\mathrm{is}}^s={\left(T_s^b\right)}^T{f}_{\mathrm{ibd}}^b+{\left[\begin{array}{ccc}{\&dtri;}_x& {\&dtri;}_y& {\&dtri;}_z\end{array}\right]}^T+f_{\mathrm{bs}}^s$

Wherein,

() ^TThe commentaries on classics order of representing matrix, ω _Ibd ^b, f _Ibd ^bBe the true output of carrier movement, ε _x, ε _y, ε _zBe gyrostatic drift error,

Be the accelerometer error of zero; Because s is relative b is only to rotatablely move, and does not have linear relative movement, so

So accelerometer output can be expressed as:

The output of fibre optic gyroscope and accelerometer can be expressed as from the conversion that the IMU coordinate is tied to carrier coordinate system:

${\mathrm{\&omega;}}_{\mathrm{ib}}^b=T_s^b{\mathrm{\&omega;}}_{\mathrm{is}}^s+{\mathrm{\&omega;}}_{\mathrm{sb}}^b,$ $f_{\mathrm{ib}}^b=T_s^b{f}_{\mathrm{is}}^s$

Inertial Measurement Unit is around carrier coordinate system oy _bAxle is rotated in the forward 45 degree, and the constant value drift of three gyros equates that three accelerometer zero drifts equate that can obtain ε this moment _zCos45 °=ε _xCos (90 °-45 °),

Carrier coordinate system oz _bBe not subjected to the influence of gyroscope constant value drift and accelerometer zero drift on the direction of principal axis, the line acceleration of motion in the motion angular velocity in carrier relative inertness space and carrier relative inertness space is as follows respectively in the projection of carrier coordinate system at this moment:

$\left\{\begin{array}{c}{\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{bx}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{bx}}+\sqrt{2}/2\cos \mathrm{\&omega;t}({\mathrm{\&epsiv;}}_x+{\mathrm{\&epsiv;}}_z)-\sin \mathrm{\&omega;t}{\mathrm{\&epsiv;}}_y\\ {\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{by}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{by}}+\sqrt{2}/2\sin \mathrm{\&omega;t}({\mathrm{\&epsiv;}}_x+{\mathrm{\&epsiv;}}_z)+\cos \mathrm{\&omega;t}{\mathrm{\&epsiv;}}_y\\ {\mathrm{\&omega;}}_{\mathrm{ib}}^{\mathrm{bz}}={\mathrm{\&omega;}}_{\mathrm{ibd}}^{\mathrm{bz}}\end{array}\right.$

$\left\{\begin{array}{c}{f}_{\mathrm{ib}}^{\mathrm{bx}}=f_{\mathrm{ibd}}^{\mathrm{bx}}+\sqrt{2}/2\cos \mathrm{\&omega;t}({\&dtri;}_x+{\&dtri;}_z)-\sin \mathrm{\&omega;t}{\&dtri;}_y\\ f_{\mathrm{ib}}^{\mathrm{by}}=f_{\mathrm{ibd}}^{\mathrm{by}}+\sqrt{2}/2\sin \mathrm{\&omega;t}({\&dtri;}_x+{\&dtri;}_z)+\cos \mathrm{\&omega;t}{\&dtri;}_y\\ f_{\mathrm{ib}}^{\mathrm{bz}}=f_{\mathrm{ibd}}^{\mathrm{bz}}\end{array}\right.$

Wherein, ω _Ib ^Bx, ω _Ib ^By, ω _Ib ^BzBe respectively the ox of the motion angular velocity in carrier relative inertness space in carrier coordinate system _bAxle, oy _bAxle, oz _bComponent on the axle; f _Ib ^Bx, f _Ib ^By, f _Ib ^BzBe respectively the ox of the linear acceleration in carrier relative inertness space in carrier coordinate system _bAxle, oy _bAxle, oz _bComponent on the axle;

(6) the carrier system that step (5) is obtained is the output valve ω of optical fibre gyro down _Ib ^bBring into and adopt the hypercomplex number method in the inertial navigation system the strapdown matrix T _b ⁿUpgrade:

${\mathrm{\&omega;}}_{\mathrm{nb}}^b={\mathrm{\&omega;}}_{\mathrm{ib}}^b-{\left(T_b^n\right)}^T({\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)$

Wherein: ω _Ie ⁿBe the component of rotational-angular velocity of the earth under navigation system; ω _En ⁿFor navigation coordinate is the component of motion angular velocity under navigation system of spherical coordinate system relatively; ω _Nb ^bThe component of motion angular velocity on carrier coordinate system for the relative navigation coordinate of carrier system;

Upgrade hypercomplex number and attitude matrix:

If carrier coordinate system relative to the hypercomplex number of rotating of navigation coordinate system is:

Q＝q ₀+q ₁i _b+q ₂j _b+q ₃k _b

Wherein: i _b, j _b, k _bRepresent carrier coordinate system ox respectively _bAxle, oy _bAxle, oz _bUnit direction vector on the axle;

The instant correction of hypercomplex number can be by separating the hypercomplex number differential equation

Realize:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_0\\ {\stackrel{\&CenterDot;}{q}}_1\\ {\stackrel{\&CenterDot;}{q}}_2\\ {\stackrel{\&CenterDot;}{q}}_3\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}0& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}\\ {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}& 0& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}\\ {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}& 0& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}\\ {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bz}}& {\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{by}}& -{\mathrm{\&omega;}}_{\mathrm{nb}}^{\mathrm{bx}}& 0\end{array}\right]\left[\begin{array}{c}{q}_0\\ q_1\\ q_2\\ q_3\end{array}\right]$

Wherein: ω _Nb ^Bx, ω _Nb ^By, ω _Nb ^BzRepresent respectively carrier navigate relatively be motion angular velocity at carrier coordinate system ox _bAxle, oy _bAxle, oz _bComponent on the axle;

Attitude matrix T _b ⁿRenewal process as follows:

$T_b^n=\left[\begin{array}{ccc}{q}_0^2+q_1^2-q_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{q}_2+q_0{q}_3)& q_0^2-q_1^2+q_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& q_0^2-q_1^2-q_2^2+q_3^2\end{array}\right];$

(7) utilize the output valve f of quartz accelerometer _Ib ^bAnd the attitude matrix T of step (6) calculating _b ⁿ, calculate speed and position through IMU rotation modulation back carrier;

Described calculating through the speed of IMU rotation modulation back carrier and the method for position is:

1) calculate navigation system acceleration down:

$\left[\begin{array}{c}{f}^{\mathrm{nx}}\\ f^{\mathrm{ny}}\\ f^{\mathrm{nz}}\end{array}\right]=T_b^n\left[\begin{array}{c}{f}_{\mathrm{ib}}^{\mathrm{bx}}\\ f_{\mathrm{ib}}^{\mathrm{by}}\\ f_{\mathrm{ib}}^{\mathrm{bz}}\end{array}\right];$

2) horizontal velocity and the position of calculating carrier:

According to t ₁Carrier east orientation horizontal velocity V constantly _x(t ₁) and north orientation horizontal velocity V _y(t ₁), ask for t ₁The rate of change of carrier horizontal velocity is constantly:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_x\left(t_1\right)=f^{\mathrm{nx}}+({2\mathrm{\&omega;}}_{\mathrm{ie}}^{\mathrm{nz}}+{\mathrm{\&omega;}}_{\mathrm{en}}^{\mathrm{nz}})V_y\left(t_1\right)\\ {\stackrel{\&CenterDot;}{V}}_y\left(t_1\right)=f^{\mathrm{ny}}-({2\mathrm{\&omega;}}_{\mathrm{ie}}^{\mathrm{nz}}+{\mathrm{\&omega;}}_{\mathrm{en}}^{\mathrm{nz}})V_x\left(t_1\right)\end{array}\right.$

At t ₂Horizontal velocity and carrier positions are respectively constantly:

$\left\{\begin{array}{c}{V}_x\left(t_2\right)=V_x\left(t_1\right)+{\stackrel{\&CenterDot;}{V}}_x\left(t_1\right)(t_2-t_1)\\ V_y\left(t_2\right)=V_y\left(t_1\right)+{\stackrel{\&CenterDot;}{V}}_y\left(t_1\right)(t_2-t_1)\end{array}\right.$

3) calculate bearer rate sum of errors site error:

$\left\{\begin{array}{c}{\mathrm{\&Delta;V}}_x=V_x\left(t_2\right)-V_{x0}\\ {\mathrm{\&Delta;V}}_y=V_y\left(t_2\right)-V_{y0}\end{array}\right.$

Wherein: V _X0, V _Y0East orientation and the north orientation speed of representing the initial time carrier respectively; Δ V _x, Δ V _yThe variable quantity of representing carrier east orientation, north orientation speed respectively;

λ ₀Longitude and the latitude of representing initial time carrier present position respectively;

Δ λ represents the latitude of carrier, the variable quantity of longitude respectively; R _Xp, R _YpThe radius-of-curvature of representing earth meridian circle, prime vertical respectively; t ₁, t ₂Two the adjacent time points in the process that resolve for inertial navigation system.

2. the optical fibre gyro strapdown inertial navigation system error inhibiting method based on single shaft rotation according to claim 1, it is characterized in that described determine the relative initial position relation of two coordinate systems after, Inertial Measurement Unit is around carrier coordinate system azimuth axis oz _bForward rotates in the step continuously with angular velocity omega=6 °/s, and in the IMU rotation process, the transition matrix that the IMU coordinate is tied to carrier coordinate system is:

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