CN103308046A - Correction method of gyroscope drift of strapdown inertial navigation system by using position and course information under inertial system - Google Patents

Abstract

The invention discloses a correction method of gyroscope drift of a strapdown inertial navigation system by using position and course information under an inertial system. Compared with the traditional method, the correction method only requires keeping a horizontal misalignment angle as a small angle at a correction moment, and does not require keeping the horizontal misalignment angle as the small angle all the time.

Description

The strapdown inertial navitation system (SINS) gyroscopic drift bearing calibration of use location and course information under a kind of inertial system

One, technical field

What the present invention relates to is a kind of integrated calibration technology, particularly relate to the strapdown inertial navitation system (SINS) gyroscopic drift alignment technique of use location and course information under a kind of inertial system, relate in particular to a kind of need not the to limit use location of carrier movement state and the strapdown inertial navitation system (SINS) gyroscopic drift alignment technique of course information.

Two, background technology

For ship's inertial navigation system, its difficulty just is that the cycle of operation is long, and accuracy requirement is high, must regularly carry out biharmonic to system and proofread and correct.With regard to Methods of Strapdown Inertial Navigation System, the precision of gyro has determined the precision of whole system to a great extent, improve the precision of system, and its key is exactly to improve Gyro Precision.Adopt system-level algorithm can effectively reduce cost, by introducing external reference information the gyroscopic drift of system is proofreaied and correct, can limit the error of inertial navigation system, improve the precision of inertial navigation system.The alignment technique comparative maturity of current platform formula inertial navigation system, but be not suitable for Methods of Strapdown Inertial Navigation System, and larger to the restriction of the maneuver mode of carrier, therefore research can effectively reduce the requirement of carrier maneuver mode and the integrated calibration technology that is applicable to Methods of Strapdown Inertial Navigation System are significant and practical value for the precision that improves strapdown inertial navitation system (SINS).

Three, summary of the invention

Goal of the invention: the object of the present invention is to provide does not a kind ofly need to limit the carrier movement state and just can utilize external position and course information to proofread and correct out the bearing calibration of the gyroscopic drift of strapdown inertial navitation system (SINS) accurately.

The object of the present invention is achieved like this:

The present invention includes the following step:

(1) navigation coordinate system is projected under the inertial system with the azimuth of computing machine coordinate system, obtain the differential expressions of the ψ equation under the inertial system, and then obtain the relational expression between the ψ angle and strapdown inertial navitation system (SINS) gyroscopic drift under the inertial system;

(2) relational expression under the inertial system of step (1) being set up between ψ angle and the strapdown inertial navitation system (SINS) gyroscopic drift is carried out integration, can get arbitrarily the relational expression between the ψ angle increment and gyroscopic drift between two moment;

(3) set up the relation between the ψ angle under position and course error and the inertial system, can get arbitrarily the constantly relational expression between upper/lower positions and the course error of ψ angle increment between two moment and two;

(4) utilize step (2) and step (3) can obtain relational expression between twice position and course error and the gyroscopic drift, thereby calculate gyroscopic drift and the compensation of strapdown inertial navitation system (SINS), improve navigation accuracy.

Method of the present invention has the following advantages:

Therefore 1. classic method is to set up the ψ angle equation under the OEPQ coordinate system, needs the motion state of restriction carrier to be: low speed, etc. the latitude motion, and be not suitable for Methods of Strapdown Inertial Navigation System.And the present invention does not need to limit the carrier movement state, especially is fit to Methods of Strapdown Inertial Navigation System.

2. compare with classic method, it is that low-angle gets final product that the present invention only needs at the horizontal misalignment of corrected time maintenance, does not need horizontal misalignment to remain on low-angle always.

Description of drawings

Fig. 1 is the strapdown inertial navitation system (SINS) gyroscopic drift bearing calibration process flow diagram of indication of the present invention;

Fig. 2 does not carry out the site error curve that gyroscopic drift is proofreaied and correct in the embodiments of the invention;

Fig. 3 does not carry out the speed-error curve that gyroscopic drift is proofreaied and correct in the embodiments of the invention;

Fig. 4 does not carry out the attitude error curve that gyroscopic drift is proofreaied and correct in the embodiments of the invention;

Fig. 5 carries out the site error curve that gyroscopic drift is proofreaied and correct in the embodiments of the invention;

Fig. 6 carries out the speed-error curve that gyroscopic drift is proofreaied and correct in the embodiments of the invention;

Fig. 7 carries out the attitude error curve that gyroscopic drift is proofreaied and correct in the embodiments of the invention.

Embodiment:

1. ψ equation being projected as under inertial coordinates system:

${\stackrel{\·}{\mathrm{\ψ}}}^i={\mathrm{\ϵ}}^i=C_b^i{\mathrm{\ϵ}}^b---\left(20\right)$

In the following formula (20): For calculating the projection of differential under inertial coordinates system i of the azimuth between navigation coordinate system and the computing machine coordinate system, ε ⁱBe the projection of gyroscopic drift under inertial coordinates system i.ε ^bBe the gyroscopic drift of the strapdown inertial navitation system (SINS) projection at carrier coordinate system b,

Be the transition matrix between carrier coordinate system b and the inertial coordinates system i, can be obtained in real time by gyro output:

$\stackrel{\·}{C_b^i}=C_b^i({\mathrm{\ω}}_{\mathrm{ib}}^b\×)---\left(21\right)$

In the following formula (21):

Be gyro output;

* be to be exported by gyro

The antisymmetric matrix that consists of:

Initial value

Determined by following formula (22):

$C_b^i\left(t_0\right)={\left[C_i^n\left(t_0\right)\right]}^{-1}{C}_b^n\left(t_0\right)---\left(22\right)$

In the following formula (22):

T ₀Constantly calculated by strapdown inertial navitation system (SINS);

$C_i^n\left(t_0\right)=\left[\begin{array}{ccc}-\sin \left({\mathrm{\&lambda;}}_0\right)& \cos \left({\mathrm{\&lambda;}}_0\right)& 0\\ -\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\&CenterDot;\cos \left({\mathrm{\&lambda;}}_0\right)& -\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\&CenterDot;\sin \left({\mathrm{\&lambda;}}_0\right)& \cos {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\\ \mathrm{<figure-callout\; id="0"\; label="cos\; L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">cos</figure-callout>}{L}_{}{}_0\&CenterDot;\cos \left({\mathrm{\&lambda;}}_0\right)& \mathrm{<figure-callout\; id="0"\; label="cos\; L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">cos</figure-callout>}{L}_{}{}_0\&CenterDot;\sin \left({\mathrm{\&lambda;}}_0\right)& \sin L_0\end{array}\right]---\left(23\right)$

$C_i^n\left(t\right)=\left[\begin{array}{ccc}-\sin ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& \cos ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& 0\\ -\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\&CenterDot;\cos ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& -\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\&CenterDot;\sin ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& \cos {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\\ \mathrm{<figure-callout\; id="0"\; label="cos\; L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">cos</figure-callout>}{L}_{}{}_0\&CenterDot;\cos ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& \mathrm{<figure-callout\; id="0"\; label="cos\; L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">cos</figure-callout>}{L}_{}{}_0\&CenterDot;\sin ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& \sin L_0\end{array}\right]---\left(24\right)$

In the following formula (24): latitude L ₀With longitude λ ₀Can be by t ₀External position information provides ω constantly _IeBeing the earth rotation angular speed, is accurately known.T is from t ₀The time that constantly begins to calculate.

By above step, set up the gyroscopic drift of strapdown inertial navitation system (SINS) and the relation between the ψ angle.

2. can solve (20) formula integration:

${\mathrm{\&psi;}}^i\left(t\right)={\mathrm{\&psi;}}^i\left(0\right)+\left({\&Integral;}_0^t{C}_b^i\left(t\right)\mathrm{dt}\right){\mathrm{\&epsiv;}}^b---\left(25\right)$

In the following formula (25), ψ ⁱ(0) is t ₀ψ constantly ⁱInitial value.

Get any two moment t _nAnd t _N+1, can draw according to (25) formula:

${\mathrm{\&psi;}}^i\left(t_n\right)={\mathrm{\&psi;}}^i\left(0\right)+\left({\&Integral;}_0^{t_n}{C}_b^i\left(t\right)\mathrm{dt}\right){\mathrm{\&epsiv;}}^b---\left(26\right)$

${\mathrm{\&psi;}}^i\left(t_{n+1}\right)={\mathrm{\&psi;}}^i\left(0\right)+\left({\&Integral;}_0^{t_{n+1}}{C}_b^i\left(t\right)\mathrm{dt}\right){\mathrm{\&epsiv;}}^b---\left(27\right)$

Can be obtained by following formula (26) and formula (27):

ψ ⁱ(t _n+1)＝ψ ⁱ(t _n)+ψ ⁱ(t _n+1|t _n) (28)

In the following formula (28), ψ ⁱ(t _N+1| t _n) ψ that produces for gyroscopic drift ⁱIncrement:

ψ ⁱ(t _n+1|t _n)＝A(t _n+1|t _n)ε ^b (29)

In the following formula (29) $A\left(t_{n+1}\right|t_n)={\&Integral;}_{t_n}^{t_{n+1}}{C}_b^i\left(t\right)\mathrm{dt}.$

Set up ψ under the inertial coordinates system by (29) following formula ⁱIncrement and strapdown inertial navitation system (SINS) gyroscopic drift ε ^bBetween relation.

3. at first need to control strapdown inertial navitation system (SINS) and be operated in the horizontal damping state, behind system stability, the lateral error angle φ of strapdown inertial navitation system (SINS) _xAnd φ _yThe accelerometer bias that only depends on east orientation and north orientation.General high-precision inertial navigation system accelerometer bias is better than 1 * 10 ^-4So g is φ _xAnd φ _yBe generally less than 0.5 jiao minute, can ignore, i.e. φ _x=0, φ _y=0.

Therefore, the definition according to coordinate system has following relation:

Φ＝δθ+ψ (30)

In the following formula (30), Φ represents to calculate the projection that the azimuth between navigation coordinate system and the navigation coordinate system is fastened at navigation coordinate:

Φ＝[φ _x φ _y φ _z] ^T (31)

δ θ represents the projection that the azimuth between computing machine coordinate system and the navigation coordinate system is fastened at navigation coordinate.

δθ＝[δθ _x δθ _y δθ _z] ^T＝[-δL δλ·cosL δλ·sinL] ^T (33)

In the following formula (32), δ L is latitude error, and δ λ is trueness error.

Can find out according to above definition:

$\left.\begin{array}{c}\mathrm{\&delta;}{\mathrm{\&theta;}}_x=-{\mathrm{\&psi;}}_x^n\\ {\mathrm{\&delta;\&theta;}}_y=-{\mathrm{\&psi;}}_y^n\\ {\mathrm{\&phi;}}_z={\mathrm{\&delta;\&theta;}}_z+{\mathrm{\&psi;}}_z^n\end{array}\right\}---\left(33\right)$

By external accessory, we can obtain accurately latitude L, longitude λ and course K information, and the calculating latitude of strapdown inertial navitation system (SINS) is L _c, the calculating longitude is λ _c, the calculating course is K _c, so the position of strapdown inertial navitation system (SINS) and course error are:

$\left.\begin{array}{c}\mathrm{\&delta;L}=L_c-L\\ \mathrm{\&delta;\&lambda;}={\mathrm{\&lambda;}}_c-\mathrm{\&lambda;}\\ {\mathrm{\&phi;}}_z=\mathrm{\&delta;K}=K_c-K\end{array}\right\}---\left(34\right)$

Can be derived by formula (30), formula (33)～formula (34):

$\left[\begin{array}{c}\mathrm{\&delta;L}\\ \mathrm{\&delta;\&lambda;}\\ \mathrm{\&delta;K}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& -\mathrm{<figure-callout\; id="0"\; label="sec\; L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">sec</figure-callout>}L& 0\\ 0& -\mathrm{<figure-callout\; id="1"\; label="tan\; L"\; filenames="HSA00000889853000022.png"\; state="\{\{state\}\}">tan</figure-callout>}L& 1\end{array}\right]\&CenterDot;\left[\begin{array}{c}{\mathrm{\&psi;}}_x^n\\ {\mathrm{\&psi;}}_y^n\\ {\mathrm{\&psi;}}_z^n\end{array}\right]---\left(35\right)$

Note P (t)=[δ L δ λ δ K] ^T $M\left(t\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& -\mathrm{<figure-callout\; id="0"\; label="sec\; L"\; filenames="HSA00000889853000021.png,HSA00000889853000022.png"\; state="\{\{state\}\}">sec</figure-callout>}L& 0\\ 0& -\mathrm{<figure-callout\; id="1"\; label="tan\; L"\; filenames="HSA00000889853000022.png"\; state="\{\{state\}\}">tan</figure-callout>}L& 1\end{array}\right].$

Transformational relation according to coordinate system has:

${\mathrm{\&psi;}}^n\left(t\right)=C_i^n\left(t\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t\right)---\left(36\right)$

So have:

$P\left(t\right)=M\left(t\right)\&CenterDot;C_i^n\left(t\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t\right)---\left(37\right)$

Following formula is set up the relation between the ψ angle under position and course error and the inertial system, to moment t _nAnd t _N+1, can draw according to formula (37):

$P\left(t_n\right)=M\left(t_n\right)\&CenterDot;C_i^n\left(t_n\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_n\right)---\left(38\right)$

$P\left(t_{n+1}\right)=M\left(t_{n+1}\right)\&CenterDot;C_i^n\left(t_{n+1}\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_{n+1}\right)---\left(39\right)$

Can obtain according to following formula (38) and formula (39):

${\mathrm{\&psi;}}^i\left(t_{n+1}\right|t_n)={\left[M\left(t_{n+1}\right)C_i^n\left(t_{n+1}\right)\right]}^{-1}P\left(t_{n+1}\right)-{\left[M\left(t_n\right)C_i^n\left(t_n\right)\right]}^{-1}P\left(t_n\right)---\left(40\right)$

4. by (29) formula and (40) formula, can obtain:

$A\left(t_{n+1}\right|t_n){\mathrm{\&epsiv;}}^b={\left[M\left(t_{n+1}\right)C_i^n\left(t_{n+1}\right)\right]}^{-1}P\left(t_{n+1}\right)-{\left[M\left(t_n\right)C_i^n\left(t_n\right)\right]}^{-1}P\left(t_n\right)---\left(41\right)$

Therefore can obtain:

${\mathrm{\&epsiv;}}^b=A{\left(t_{n+1}\right|t_n)}^{-1}{\left[M\left(t_{n+1}\right)C_i^n\left(t_{n+1}\right)\right]}^{-1}P\left(t_{n+1}\right)-A{\left(t_{n+1}\right|t_n)}^{-1}{\left[M\left(t_n\right)C_i^n\left(t_n\right)\right]}^{-1}P\left(t_n\right)---\left(42\right)$ 。

Claims (5)

1. the strapdown inertial navitation system (SINS) gyroscopic drift bearing calibration of use location and course information under the inertial system is characterized in that performing step is as follows:

(1) navigation coordinate system and the azimuth ψ of computing machine coordinate system are projected under the inertial coordinates system, obtain the differential expressions of the ψ equation under the inertial system, and then obtain the relational expression between the ψ angle and strapdown inertial navitation system (SINS) gyroscopic drift under the inertial system;

(2) relational expression under the inertial system of step (1) being set up between ψ angle and the strapdown inertial navitation system (SINS) gyroscopic drift is carried out Integration Solving, can get arbitrarily the relational expression between the ψ angle increment and gyroscopic drift between two moment;

(3) set up the relation between the ψ angle under position and course error and the inertial system, can get arbitrarily ψ angle increment and the position in these two moment and the relational expression between the course error between two moment;

(4) utilize step (2) and step (3) can obtain relational expression between the two constantly gyroscopic drifts of positions and course error and strapdown inertial navitation system (SINS), thereby calculate gyroscopic drift and the compensation of strapdown inertial navitation system (SINS), raising navigation accuracy.

2. the strapdown inertial navitation system (SINS) gyroscopic drift bearing calibration of use location and course information under a kind of inertial system described in according to claim 1, it is characterized in that: the relational expression under the inertial system described in the described step (1) between ψ angle and the strapdown inertial navitation system (SINS) gyroscopic drift is:

In the following formula (1):

For calculating the projection of differential under inertial coordinates system i of the azimuth between navigation coordinate system and the computing machine coordinate system; ε ⁱThe projection of gyroscopic drift under inertial coordinates system i for strapdown inertial navitation system (SINS); ε ^bBe the gyroscopic drift of the strapdown inertial navitation system (SINS) projection at carrier coordinate system b; Be the transition matrix between carrier coordinate system b and the inertial coordinates system i, can be obtained in real time by gyro output:

In the following formula (2): Be gyro output;

* be to be exported by gyro

The antisymmetric matrix that consists of;

Initial value

Determined by following formula (3):

In the following formula (3):

T ₀Constantly calculated by strapdown inertial navitation system (SINS)

In following formula (4) and (5): latitude L ₀With longitude λ ₀Can be by t ₀External position information provides constantly: ω _IeBeing the earth rotation angular speed, is accurately known; T is from t ₀The time that constantly begins to calculate.

3. the strapdown inertial navitation system (SINS) gyroscopic drift bearing calibration of use location and course information under a kind of inertial system described in according to claim 1 is characterized in that: in the described step (2) between any two moment the implementation procedure of the relational expression between ψ angle increment and the gyroscopic drift be:

Can solve (1) formula equal sign two ends while integration:

In the following formula (6), ψ ⁱ(0) is t ₀ψ constantly ⁱInitial value.

Get any two moment t _nAnd t _N+1, can draw according to (6) formula:

Can be obtained by following formula (7) and (8)

ψ ⁱ(t _n+1)＝ψ ⁱ(t _n)+ψ ⁱ(t _n+1|t _n) (9)

In the following formula (9), ψ ⁱ(t _N+1| t _n) ψ that produces for gyroscopic drift ⁱIncrement:

ψ ⁱ(t _n+1|t _n)＝A(t _n+1|t _n)ε ^b (10)

In the following formula (10)

Set up ψ under the inertial coordinates system by following formula (10) ⁱIncrement and strapdown inertial navitation system (SINS) gyroscopic drift ε ^bBetween relation.

4. the strapdown inertial navitation system (SINS) gyroscopic drift bearing calibration of use location and course information under a kind of inertial system described in according to claim 1, it is characterized in that: the implementation procedure of ψ angle increment and the position in these two moment and the relational expression between the course error is as follows between any two moment described in the described step (3):

The ψ angle in the projection of navigation coordinate system and the relational expression between position and the course error is:

P(t)＝M(t).ψ ⁿ(t) (11)

P (t)=[δ L δ λ δ K] in the following formula (11) ^T

Have according to the transformational relation between the coordinate system:

To obtain in (12) formula substitution (11) formula:

Following formula (13) is set up the relation between the ψ angle, then t under position and course error and the inertial system _nThe moment and t _N+1Shi Keyou:

Can obtain according to formula (14) and formula (15) that ψ angle increment and the position in these two moment and the relational expression between the course error are under the inertial system:

。

5. the strapdown inertial navitation system (SINS) gyroscopic drift bearing calibration of use location and course information under a kind of inertial system described in according to claim 1 is characterized in that: two described in the described step (4) constantly the position and the relational expression between the gyroscopic drift of course error and strapdown inertial navitation system (SINS) be:

The calculating formula that can obtain strapdown inertial navitation system (SINS) gyroscopic drift by (17) formula is:

Strapdown inertial navitation system (SINS) gyroscopic drift compensation formula is:

In the following formula (19), Be the output of the gyro after the compensation.

Images