CN103292808A - Strapdown inertial navigation system gyro drift and course error correction method by using only position information under one position inertial system - Google Patents

Abstract

The invention relates to a strapdown inertial navigation system gyro drift and course correction technology only by using usage position information without restriction to carrier motion state. Compared with the prior art, the horizontal misalignment angle is needed to be maintained small only in the correction time, and the horizontal misalignment is not needed to be maintained small all the time.

Description

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

One, technical field

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

Two, background technology

For inertial navigation system peculiar to vessel, its difficulty just is that the cycle of operation is long, and the accuracy requirement height 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 total 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 the external reference positional information gyroscopic drift and the course of system are 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 bigger to the restriction of the maneuver mode of carrier, therefore research can effectively reduce the requirement of carrier maneuver mode and be applicable to that the integrated calibration technology of Methods of Strapdown Inertial Navigation System is 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 only use external position information to proofread and correct out the gyroscopic drift of strapdown inertial navitation system (SINS) and the bearing calibration of course error accurately.

The object of the present invention is achieved like this:

The present invention includes the following step:

(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 between ψ angle and the strapdown inertial navitation system (SINS) gyroscopic drift is carried out integration and is found the solution under the inertial system that step (1) is set up, and 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 site error and course error and the inertial system, can get arbitrarily ψ angle increment and the site error in these two moment and the relational expression between the course error between two moment;

(4) at t _nConstantly utilize the external position observed quantity that the alliance error is resetted, the back site error of resetting is zero, and recycling step (2) and step (3) can obtain t _N+1Moment position and course error and t _nCourse error constantly and the relational expression between the gyroscopic drift;

(5) at t _N+1Constantly utilize the external position observed quantity that the alliance error is resetted, the back site error of resetting is zero, and recycling step (2) and step (3) can obtain t _N+2Moment position and course error and t _N+1Course error constantly and the relational expression between the gyroscopic drift;

(6) utilize step (4) and step (5) can obtain t _N+1The moment and t _N+2Site error and t constantly _nThereby course error constantly and the relational expression between the gyroscopic drift are calculated gyroscopic drift and the t of strapdown inertial navitation system (SINS) _nCourse error constantly, and then gyroscopic drift compensated;

(7) utilize step (4) and step (5) to obtain calculating gyroscopic drift and the t of strapdown inertial navitation system (SINS) _nCourse error and t constantly _N+2Relational expression between the course error constantly can calculate t _N+2Course error constantly, thus system's course error is compensated.

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 is not for carrying out the velocity error curve of gyroscopic drift and the correction of course in the embodiments of the invention;

Fig. 3 is not for carrying out the attitude error curve of gyroscopic drift and the correction of course in the embodiments of the invention;

Fig. 4 is not for carrying out the site error curve of gyroscopic drift and the correction of course in the embodiments of the invention;

Fig. 5 is for carrying out the velocity error curve of gyroscopic drift and the correction of course in the embodiments of the invention;

Fig. 6 is for carrying out the attitude error curve of gyroscopic drift and the correction of course in the embodiments of the invention;

Fig. 7 is for carrying out the site error curve of gyroscopic drift and the correction of course in the embodiments of the invention.

Embodiment

The only strapdown inertial navitation system (SINS) gyroscopic drift of use location information and course error bearing calibration under a kind of 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 between ψ angle and the strapdown inertial navitation system (SINS) gyroscopic drift is carried out integration and is found the solution under the inertial system that step (1) is set up, and 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 site error and course error and the inertial system, can get arbitrarily ψ angle increment and the site error in these two moment and the relational expression between the course error between two moment;

(4) at t _nConstantly utilize the external position observed quantity that the alliance error is resetted, the back site error of resetting is zero, and recycling step (2) and step (3) can obtain t _N+1Moment position and course error and t _nCourse error constantly and the relational expression between the gyroscopic drift;

(5) at t _N+1Constantly utilize the external position observed quantity that the alliance error is resetted, the back site error of resetting is zero, and recycling step (2) and step (3) can obtain t _N+2Moment position and course error and t _N+1Course error constantly and the relational expression between the gyroscopic drift;

(6) utilize step (4) and step (5) can obtain t _N+1The moment and t _N+2Site error and t constantly _nThereby course error constantly and the relational expression between the gyroscopic drift are calculated gyroscopic drift and the t of strapdown inertial navitation system (SINS) _nCourse error constantly, and then gyroscopic drift compensated;

(7) utilize step (4) and step (5) to obtain calculating gyroscopic drift and the t of strapdown inertial navitation system (SINS) _nCourse error and t constantly _N+2Relational expression between the course error constantly can calculate t _N+2Course error constantly, thus system's course error is compensated.

Only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under described a kind of inertial system, 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

${\stackrel{\·}{\mathrm{\ψ}}}^i={\mathrm{\ϵ}}^i=C_b^i{\mathrm{\ϵ}}^b---\left(1\right)$

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:

$\stackrel{\·}{C_b^i}=C_b^i({\mathrm{\ω}}_{\mathrm{ib}}^b\×)---\left(2\right)$

In the following formula (2):

Be gyro output;

* be to be exported by gyro

The antisymmetric matrix that constitutes;

Initial value

Determined by following formula (3):

$C_b^i\left(t_0\right)={\left[C_i^n\left(t_0\right)\right]}^{-1}{C}_b^n\left(t_0\right)---\left(3\right)$

In the following formula (3):

Be t ₀Constantly calculated by strapdown inertial navitation system (SINS)

$C_i^n\left(t_0\right)=\left[\begin{array}{ccc}-\sin \left({\mathrm{\&lambda;}}_0\right)& \cos \left({\mathrm{\&lambda;}}_0\right)& 0\\ -\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\&CenterDot;\cos \left({\mathrm{\&lambda;}}_0\right)& -\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\&CenterDot;\sin \left({\mathrm{\&lambda;}}_0\right)& \cos {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\\ \mathrm{<figure-callout\; id="0"\; label="cos\; L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">cos</figure-callout>}{L}_{}{}_0\&CenterDot;\cos \left({\mathrm{\&lambda;}}_0\right)& \mathrm{<figure-callout\; id="0"\; label="cos\; L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">cos</figure-callout>}{L}_{}{}_0\&CenterDot;\sin \left({\mathrm{\&lambda;}}_0\right)& \sin L_0\end{array}\right]---\left(4\right)$

$C_i^n\left(t\right)=\left[\begin{array}{ccc}-\sin ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& \cos ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& 0\\ -\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\&CenterDot;\cos ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& -\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\&CenterDot;\sin ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& \cos {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\\ \mathrm{<figure-callout\; id="0"\; label="cos\; L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">cos</figure-callout>}{L}_{}{}_0\&CenterDot;\cos ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& \mathrm{<figure-callout\; id="0"\; label="cos\; L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">cos</figure-callout>}{L}_{}{}_0\&CenterDot;\sin ({\mathrm{\&lambda;}}_0+{\mathrm{\&omega;}}_{\mathrm{ie}}t)& \sin L_0\end{array}\right]---\left(5\right)$

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.

Only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under described a kind of inertial system 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:

${\mathrm{\&psi;}}^i\left(t\right)={\mathrm{\&psi;}}^i\left(0\right)+\left({\&Integral;}_0^t{C}_b^i\left(t\right)\mathrm{dt}\right){\mathrm{\&epsiv;}}^b---\left(6\right)$

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:

${\mathrm{\&psi;}}^i\left(t_n\right)={\mathrm{\&psi;}}^i\left(0\right)+\left({\&Integral;}_0^{t_n}{C}_b^i\left(t\right)\mathrm{dt}\right){\mathrm{\&epsiv;}}^b---\left(7\right)$

${\mathrm{\&psi;}}^i\left(t_{n+1}\right)={\mathrm{\&psi;}}^i\left(0\right)+\left({\&Integral;}_0^{t_{n+1}}{C}_b^i\left(t\right)\mathrm{dt}\right){\mathrm{\&epsiv;}}^b---\left(8\right)$

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

ψ ⁱ(t _n+1)＝ψ ⁱ( _tn)+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)

Be the transition matrix between carrier coordinate system b and the inertial coordinates system i, ε ^bBe gyroscopic drift.

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

Only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under described a kind of inertial system, 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 $M\left(t\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& -\mathrm{<figure-callout\; id="0"\; label="sec\; L"\; filenames="HSA00000889859600021.png,HSA00000889859600022.png"\; state="\{\{state\}\}">sec</figure-callout>}L& 0\\ 0& -\mathrm{<figure-callout\; id="1"\; label="tan\; L"\; filenames="HSA00000889859600021.png,HSA00000889859600032.png"\; state="\{\{state\}\}">tan</figure-callout>}L& 1\end{array}\right].$

Have according to the transformational relation between the coordinate system:

${\mathrm{\&psi;}}^n\left(t\right)=C_i^n\left(t\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t\right)---\left(12\right)$

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

$P\left(t\right)=M\left(t\right)\&CenterDot;C_i^n\left(t\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t\right)---\left(13\right)$

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:

$P\left(t_n\right)=M\left(t_n\right)\&CenterDot;C_i^n\left(t_n\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_n\right)---\left(14\right)$

$P\left(t_{n+1}\right)=M\left(t_{n+1}\right)\&CenterDot;C_i^n\left(t_{n+1}\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_{n+1}\right)---\left(15\right)$

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:

${\mathrm{\&psi;}}^i\left(t_{n+1}\right|t_n)={\left[M\left(t_{n+1}\right)C_i^n\left(t_{n+1}\right)\right]}^{-1}P\left(t_{n+1}\right)-{\left[M\left(t_n\right)C_i^n\left(t_n\right)\right]}^{-1}P\left(t_n\right)---\left(16\right)$

Only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under described a kind of inertial system is characterized in that: in the described step (4), at t _nConstantly utilize extraneous positional information that system is carried out the position and reset, after the readjustment

$\mathrm{\&delta;K}\left(t_n^{+}\right)=\mathrm{\&delta;K}\left(t_n\right),$ That is:

$P\left(t_n^{+}\right)={\left[\begin{array}{ccc}0& 0& \mathrm{\&delta;K}\left(t_n\right)\end{array}\right]}^T---\left(17\right)$

Therefore exist

Constantly, have according to formula (14):

$P\left(t_n^{+}\right)=M\left(t_n\right)\&CenterDot;C_i^n\left(t_n\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_n^{+}\right)---\left(18\right)$

That is:

$\left[\begin{array}{c}0\\ 0\\ \mathrm{\&delta;K}\left(t_n\right)\end{array}\right]=T\left(t_n\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_n^{+}\right)---\left(19\right)$

Wherein, $T\left(t_n\right)=M\left(t_n\right)C_i^n\left(t_n\right).$

At t _N+1Constantly carry out the observation second time, obtain observed quantity and be this moment: P (t _N+1)=[δ L (t _N+1) δ λ (t _N+1) δ λ (t _N+1)] ^T, the substitution formula has in (15):

P(t _n+1)＝T(t _n+1)·ψ ⁱ(t _n+1) (20)

That is:

$\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+1}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+1}\right)\\ \mathrm{\&delta;K}\left(t_{n+1}\right)\end{array}\right]=T\left(t_{n+1}\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_{n+1}\right)---\left(21\right)$

Can get according to formula (10) and formula (16):

P(t _n+1)＝T(t _n+1)[ψ ⁱ(t _n)+A(t _n+1|t _n)ε ^b] (22)

That is:

$\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+1}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+1}\right)\\ \mathrm{\&delta;K}\left(t_{n+1}\right)\end{array}\right]=T\left(t_{n+1}\right)\&CenterDot;{\left[T\left(t_n\right)\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ \mathrm{\&delta;K}\left(t_n^{+}\right)\end{array}\right]+T\left(t_{n+1}\right)\&CenterDot;A\left(t_{n+1}\right|t_n)\left[\begin{array}{c}{\mathrm{\&epsiv;}}_x\\ {\mathrm{\&epsiv;}}_y\\ {\mathrm{\&epsiv;}}_z\end{array}\right]---\left(23\right)$

The definition matrix:

T _M1＝T(t _n+1)·[T(t _n)] ^-1 (24)

T _A1＝T(t _n+1)·A(t _n+1|t _n) (25)

Then have:

$\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+1}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+1}\right)\\ \mathrm{\&delta;K}\left(t_{n+1}\right)\end{array}\right]=\left[\begin{array}{cccc}{T}_{M1}\left(\mathrm{1,3}\right)& T_{A1}\left(\mathrm{1,1}\right)& T_{A1}\left(\mathrm{1,2}\right)& T_{A1}\left(\mathrm{1,3}\right)\\ T_{M1}\left(\mathrm{2,3}\right)& T_{A1}\left(\mathrm{2,1}\right)& T_{A1}\left(\mathrm{2,2}\right)& T_{A1}\left(\mathrm{2,3}\right)\\ T_{M1}\left(\mathrm{3,3}\right)& T_{A1}\left(\mathrm{3,1}\right)& T_{A1}\left(\mathrm{3,2}\right)& T_{A1}\left(\mathrm{3,3}\right)\end{array}\right]\left[\begin{array}{c}\mathrm{\&delta;K}\left(t_n\right)\\ {\mathrm{\&epsiv;}}_x^b\\ {\mathrm{\&epsiv;}}_y^b\\ {\mathrm{\&epsiv;}}_z^b\end{array}\right]---\left(26\right)$

Order:

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000889859600021.png,HSA00000889859600032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1=\left[\begin{array}{cccc}{T}_{M1}\left(\mathrm{1,3}\right)& T_{A1}\left(\mathrm{1,1}\right)& T_{A1}\left(\mathrm{1,2}\right)& T_{A1}\left(\mathrm{1,3}\right)\\ T_{M1}\left(\mathrm{2,3}\right)& T_{A1}\left(\mathrm{2,1}\right)& T_{A1}\left(\mathrm{2,2}\right)& T_{A1}\left(\mathrm{2,3}\right)\\ T_{M1}\left(\mathrm{3,3}\right)& T_{A1}\left(\mathrm{3,1}\right)& T_{A1}\left(\mathrm{3,2}\right)& T_{A1}\left(\mathrm{3,3}\right)\end{array}\right]---\left(27\right)$

Then:

$\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+1}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+1}\right)\\ \mathrm{\&delta;K}\left(t_{n+1}\right)\end{array}\right]={\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000889859600021.png,HSA00000889859600032.png"\; state="\{\{state\}\}">R</figure-callout>}}_1\left[\begin{array}{c}\mathrm{\&delta;K}\left(t_n\right)\\ {\mathrm{\&epsiv;}}_x^b\\ {\mathrm{\&epsiv;}}_y^b\\ {\mathrm{\&epsiv;}}_z^b\end{array}\right]---\left(28\right)$

Only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under described a kind of inertial system is characterized in that: in the described step (5), at t _N+1Constantly utilize extraneous positional information that system is carried out the position and reset, after the readjustment

$\mathrm{\&delta;K}\left(t_{n+1}^{+}\right)=\mathrm{\&delta;K}\left(t_{n+1}\right),$ That is:

$P\left(t_{n+1}^{+}\right)={\left[\begin{array}{ccc}0& 0& \mathrm{\&delta;K}\left(t_{n+1}\right)\end{array}\right]}^T---\left(29\right)$

Therefore exist

Constantly, have according to formula (13):

$P\left(t_{n+1}^{+}\right)=M\left(t_{n+1}\right)\&CenterDot;C_i^n\left(t_{n+1}\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_{n+1}^{+}\right)---\left(30\right)$

That is:

$\left[\begin{array}{c}0\\ 0\\ \mathrm{\&delta;K}\left(t_{n+1}\right)\end{array}\right]=T\left(t_{n+1}\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_{n+1}^{+}\right)---\left(31\right)$

Wherein, $T\left(t_{n+1}\right)=M\left(t_{n+1}\right)C_i^n\left(t_{n+1}\right).$

At t _N+2Constantly carry out the observation second time, obtain observed quantity and be this moment: P (t _N+2)=[δ L (t _N+2) δ λ (t _N+2) δ K (t _N+2)] ^TSo, have:

P(t _n+2)＝T(t _n+2)·ψ ⁱ(t _n+2) (32)

That is:

$\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+2}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+2}\right)\\ \mathrm{\&delta;K}\left(t_{n+2}\right)\end{array}\right]=T\left(t_{n+2}\right)\&CenterDot;{\mathrm{\&psi;}}^i\left(t_{n+2}\right)---\left(33\right)$

Can get according to formula (10) and formula (16):

P(t _n+2)＝T(t _n+2)[ψ ⁱ(t _n+1)+A(t _n+2|t _n+1)ε ^b] (34)

That is:

$\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+2}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+2}\right)\\ \mathrm{\&delta;K}\left(t_{n+2}\right)\end{array}\right]=T\left(t_{n+2}\right)\&CenterDot;{\left[T\left(t_{n+1}\right)\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ \mathrm{\&delta;K}\left(t_{n+1}^{+}\right)\end{array}\right]+T\left(t_{n+2}\right)\&CenterDot;A\left(t_{n+2}\right|t_{n+1})\left[\begin{array}{c}{\mathrm{\&epsiv;}}_x\\ {\mathrm{\&epsiv;}}_y\\ {\mathrm{\&epsiv;}}_z\end{array}\right]---\left(35\right)$

The definition matrix:

T _M2＝[T(t _n+2)] ^-1T(t _n+1) (36)

T _A2＝T(t _n+2)A(t _n+2|t _n+1) (37)

Wherein, $A\left(t_{n+2}\right|t_{n+1})={\&Integral;}_{t_{n+1}}^{t_{n+2}}{C}_b^i\mathrm{dt}.$

Order:

$R_2=\left[\begin{array}{cccc}{T}_{M2}\left(\mathrm{1,3}\right)& T_{A2}\left(\mathrm{1,1}\right)& T_{A2}\left(\mathrm{1,2}\right)& T_{A2}\left(\mathrm{1,3}\right)\\ T_{M2}\left(\mathrm{2,3}\right)& T_{A2}\left(\mathrm{2,1}\right)& T_{A2}\left(\mathrm{2,2}\right)& T_{A2}\left(\mathrm{2,3}\right)\\ T_{M2}\left(\mathrm{3,3}\right)& T_{A2}\left(\mathrm{3,1}\right)& T_{A2}\left(\mathrm{3,2}\right)& T_{A2}\left(\mathrm{3,3}\right)\end{array}\right]---\left(38\right)$

Then

$\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+2}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+2}\right)\\ \mathrm{\&delta;K}\left(t_{n+2}\right)\end{array}\right]=R_2\left[\begin{array}{c}\mathrm{\&delta;K}\left(t_{n+1}\right)\\ {\mathrm{\&epsiv;}}_x^b\\ {\mathrm{\&epsiv;}}_y^b\\ {\mathrm{\&epsiv;}}_z^b\end{array}\right]---\left(39\right)$

Only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under described a kind of inertial system is characterized in that: in the described step (6), have according to formula (28):

$\mathrm{\&delta;K}\left(t_{n+1}\right)=R_1\left(\mathrm{3,1}\right)\mathrm{\&delta;K}\left(t_n\right)+R_1\left(\mathrm{3,2}\right){\mathrm{\&epsiv;}}_x^b+R_1\left(\mathrm{3,3}\right){\mathrm{\&epsiv;}}_y^b+R_1\left(\mathrm{3,4}\right){\mathrm{\&epsiv;}}_z^b---\left(40\right)$

Then:

$\left[\begin{array}{c}\mathrm{\&delta;K}\left(t_{n+1}\right)\\ {\mathrm{\&epsiv;}}_x^b\\ {\mathrm{\&epsiv;}}_y^b\\ {\mathrm{\&epsiv;}}_z^b\end{array}\right]=\left[\begin{array}{cccc}{R}_1\left(\mathrm{3,1}\right)& R_1\left(\mathrm{3,2}\right)& R_1\left(\mathrm{3,3}\right)& R_1\left(\mathrm{3,4}\right)\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}\mathrm{\&delta;K}\left(t_n\right)\\ {\mathrm{\&epsiv;}}_x^b\\ {\mathrm{\&epsiv;}}_y^b\\ {\mathrm{\&epsiv;}}_z^b\end{array}\right]---\left(41\right)$

Order:

$N=\left[\begin{array}{cccc}{R}_1\left(\mathrm{3,1}\right)& R_1\left(\mathrm{3,2}\right)& R_1\left(\mathrm{3,3}\right)& R_1\left(\mathrm{3,4}\right)\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]---\left(42\right)$

Get according to formula (39) and formula (41):

$\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+2}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+2}\right)\\ \mathrm{\&delta;K}\left(t_{n+2}\right)\end{array}\right]=Q\left[\begin{array}{c}\mathrm{\&delta;K}\left(t_n\right)\\ {\mathrm{\&epsiv;}}_x^b\\ {\mathrm{\&epsiv;}}_y^b\\ {\mathrm{\&epsiv;}}_z^b\end{array}\right]---\left(43\right)$

Wherein, Q=R ₂N.

Get according to formula (28) and formula (43):

$\left[\begin{array}{c}\mathrm{\&delta;K}\left(t_n\right)\\ {\mathrm{\&epsiv;}}_x^b\\ {\mathrm{\&epsiv;}}_y^b\\ {\mathrm{\&epsiv;}}_z^b\end{array}\right]={\left[\begin{array}{cccc}{R}_1\left(\mathrm{1,1}\right)& R_1\left(\mathrm{1,2}\right)& R_1\left(\mathrm{1,3}\right)& R_1\left(\mathrm{1,4}\right)\\ R_1\left(\mathrm{2,1}\right)& R_1\left(\mathrm{2,2}\right)& R_1\left(\mathrm{2,3}\right)& R_1\left(\mathrm{2,4}\right)\\ Q\left(\mathrm{1,1}\right)& Q\left(\mathrm{1,2}\right)& Q\left(\mathrm{1,3}\right)& Q\left(\mathrm{1,4}\right)\\ Q\left(\mathrm{2,1}\right)& Q\left(\mathrm{2,2}\right)& Q\left(\mathrm{2,3}\right)& Q\left(\mathrm{2,4}\right)\end{array}\right]}^{-1}\left[\begin{array}{c}\mathrm{\&delta;L}\left(t_{n+1}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+1}\right)\\ \mathrm{\&delta;L}\left(t_{n+2}\right)\\ \mathrm{\&delta;\&lambda;}\left(t_{n+2}\right)\end{array}\right]---\left(44\right)$

Can calculate gyroscopic drift and the t of strapdown inertial navitation system (SINS) according to formula (44) _nSo course error constantly, but owing to intercouple between equivalent east orientation gyroscopic drift and the course error is the δ K (t that calculates according to formula (44) _n),

Can't separate, have only

Be accurately.

Under described a kind of inertial system only the strapdown inertial navitation system (SINS) gyro of use location information float and course shift correction method, it is characterized in that: in the described step (7), the correction of azimuthal error can utilize (43) formula to resolve:

δK(t _n+2)＝Q(3，1)·δK(t _n)+Q(3，2)·ε _x+Q(3，3)·ε _y+Q(3，4)·ε _z (45) 。

Claims (8)

1. only strapdown inertial navitation system (SINS) gyroscopic drift and the course error bearing calibration of use location 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 between ψ angle and the strapdown inertial navitation system (SINS) gyroscopic drift is carried out integration and is found the solution under the inertial system that step (1) is set up, and 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 site error and course error and the inertial system, can get arbitrarily ψ angle increment and the site error in these two moment and the relational expression between the course error between two moment;

(4) at t _nConstantly utilize the external position observed quantity that the alliance error is resetted, the back site error of resetting is zero, and recycling step (2) and step (3) can obtain t _N+1Moment position and course error and t _nCourse error constantly and the relational expression between the gyroscopic drift;

(5) at t _N+1Constantly utilize the external position observed quantity that the alliance error is resetted, the back site error of resetting is zero, and recycling step (2) and step (3) can obtain t _N+2Moment position and course error and t _N+1Course error constantly and the relational expression between the gyroscopic drift;

(6) utilize step (4) and step (5) can obtain t _N+1The moment and t _N+2Site error and t constantly _nThereby course error constantly and the relational expression between the gyroscopic drift are calculated gyroscopic drift and the t of strapdown inertial navitation system (SINS) _nCourse error constantly, and then gyroscopic drift compensated;

(7) utilize step (4) and step (5) to obtain calculating gyroscopic drift and the t of strapdown inertial navitation system (SINS) _nCourse error and t constantly _N+2Relational expression between the course error constantly can calculate t _N+2Course error constantly, thus system's course error is compensated.

2. according to only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under a kind of inertial system described in the 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 constitutes;

Initial value

Determined by following formula (3):

In the following formula (3):

Be 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. according to only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under a kind of inertial system described in the claim 1, it 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)

Be the transition matrix between carrier coordinate system b and the inertial coordinates system i, ε ^bBe gyroscopic drift.

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. according to only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under a kind of inertial system described in the 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. according to only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under a kind of inertial system described in the claim 1, it is characterized in that: in the described step (4), at t _nConstantly utilize extraneous positional information that system is carried out the position and reset, after the readjustment

That is:

Therefore exist

Constantly, have according to formula (14):

That is:

Wherein,

At t _N+1Constantly carry out the observation second time, obtain observed quantity and be this moment: P (t _N+1)=[δ L (t _N+1) δ λ (t _N+1) δ K (t _N+1)] ^T, the substitution formula has in (15):

P(t _n+1)＝T(t _n+1)·ψ ⁱ(t _n+1) (20)

That is:

Can get according to formula (10) and formula (16):

P(t _n+1)＝T(t _n+1)[ψ ⁱ(t _n)+A(t _n+1|t _n)ε ^b] (22)

That is:

The definition matrix:

T _M1＝T(t _n+1)·[T(t _n)] ^-1 (24)

T _A1＝T(t _n+1)·A(t _n+1|t _n) (25)

Then have:

Order:

Then:

。

6. according to only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under a kind of inertial system described in the claim 1, it is characterized in that: in the described step (5), at t _N+1Constantly utilize extraneous positional information that system is carried out the position and reset, after the readjustment

That is:

Therefore exist

Constantly, have according to formula (13):

That is:

Wherein,

At t _N+2Constantly carry out the observation second time, obtain observed quantity and be this moment: P (t _N+2)=[δ L (t _N+2) δ λ (t _N+2) δ K (t _N+2)] ^TSo, have:

P(t _n+2)＝T(t _n+2)·ψ ⁱ(t _n+2) (32)

That is:

Can get according to formula (10) and formula (16):

P(t _n+2)＝T(t _n+2)[ψ ⁱ(t _n+1)+A(t _n+2|t _n+1)ε ^b] (34)

That is:

The definition matrix:

T _M2＝[T(t _n+2)] ^-1T(t _n+1) (36)

T _A2＝T(t _n+2)A(t _n+2|t _n+1) (37)

Wherein,

Order:

Then

。

7. according to only the strapdown inertial navitation system (SINS) gyroscopic drift of use location information and correction of course method under a kind of inertial system described in the claim 1, it is characterized in that: in the described step (6), have according to formula (28):

Then:

Order:

Get according to formula (39) and formula (41):

Wherein, Q=R ₂N.

Get according to formula (28) and formula (43):

Can calculate gyroscopic drift and the t of strapdown inertial navitation system (SINS) according to formula (44) _nSo course error constantly, but owing to intercouple between equivalent east orientation gyroscopic drift and the course error is the δ K (t that calculates according to formula (44) _n), Can't separate, have only

Be accurately.

According under a kind of inertial system described in the claim 1 only the strapdown inertial navitation system (SINS) gyro of use location information float and course shift correction method, it is characterized in that: in the described step (7), the correction of azimuthal error can utilize (43) formula to resolve:

δK(t _n+2)＝Q(3，1)·δK(t _n)+Q(3，2)·ε _x+Q(3，3)·ε _y+Q(3，4)·ε _z (45) 。

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