CN101514900A - Method for initial alignment of a single-axis rotation strap-down inertial navigation system (SINS) - Google Patents

Abstract

The invention provides a method for initial alignment of a single-axis rotation strap-down inertial navigation system (SINS). The method comprises the following steps: building a carrier coordinate system and computing a transfer matrix between geographic coordinate systems on the basis of coarse alignment completed by collecting the information output by gyroscopes and accelerometers in the SINS with the carrier being in a static state; establishing Kalman filtering state equations with speed errors as the state variables and measurement equations with the speed errors as the measurement variables; and estimating the misalignment angles of the carrier by the Kalman filtering technique and feeding back to the SINS to complete the initial alignment of the SINS. The invention can overcome the influence on the estimation precision of the azimuth misalignment angles caused by the equivalent gyroscope drift of the geographic coordinate systems and improve the alignment precision.

Description

A kind of strapdown inertial navitation system (SINS) initial alignment method of single shaft rotation

(1) technical field

What the present invention relates to is a kind of measuring method, and the initial attitude that particularly relates to a kind of strapdown inertial navigation system of single shaft rotation is determined method.

(2) background technology

Rotary strapdown inertial navigation system is a kind of autonomous navigational system fully, utilize the line motion and the angular motion parameter in gyroscope and accelerometer measures Inertial Measurement Unit (IMU) relative inertness space, under given starting condition, the angle value of the relative carrier of IMU that provides in conjunction with rotating mechanism, carry out integral operation by computing machine, position, speed and attitude information are provided continuously, in real time.Because rotary strapdown inertial navigation system 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.The initial alignment error is the principal element that causes the inertial navigation system navigation accuracy to be difficult to improve, and the initial alignment error not only shows in the attitude of carrier measurement output the influence of system, and shows in the measurement output of speed and position.Therefore before the rotation strapdown inertial navitation system (SINS) enters navigational state, must at first finish initial alignment process.

According to the motion state of different pedestals, initial alignment can be divided into static-base alignment and moving alignment again.Moving alignment is meant motor-driven or exist under the condition of external disturbance at carrier, and strapdown inertial navitation system (SINS) is finished initial alignment.Moving alignment usually needs external information, the state variable of system is estimated, and carried out the attitude correction after filtering is stable.Static-base alignment is meant carrier under static condition, and the strap down inertial navigation system carries out initial alignment.

Can know that by the error characteristics of analyzing strapdown inertial navitation system (SINS) the difficult point of system's initial alignment and emphasis are the estimations of orientation misalignment.For estimated accuracy and the speed of convergence that improves the orientation misalignment, important will improve azimuth misalignment exactly, and azimuth misalignment and east orientation gyroscopic drift are closely-related.Because carrying out with speed under the static condition of carrier is that the combination of observed quantity is aimed at, system's observability degree is not high, and particularly east orientation gyroscopic drift is unobservable under the geographic coordinate system, causes azimuth misalignment to be difficult to improve.

(3) summary of the invention

The object of the present invention is to provide a kind of can the solution under the static state of carrier, east orientation gyroscopic drift is unobservable under the geographic coordinate system, causes the strapdown inertial navitation system (SINS) initial alignment method of a kind of single shaft rotation of the problem that azimuth misalignment is difficult to improve.

Technical solution of the present invention is: a kind of strapdown inertial navitation system (SINS) initial alignment method of single shaft rotation, it is characterized in that Inertial Measurement Unit is rotated continuously around the carrier azimuth axis that does not overlap with self, by changing the system matrix in the system alignment model, thereby improve the observability of inertial navigation system, 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 preheating, gathers the data of fibre optic gyroscope and quartz accelerometer output then;

(3) fibre optic gyroscope that collects and the data of quartz accelerometer are handled, adopted analytical method to finish the coarse alignment of system, tentatively determine the attitude information of carrier;

Gravitational vector g and gyroscope output and earth rotation angular speed ω according to the output of accelerometer _IeMeasured value determine that tentatively the attitude information of carrier this moment finishes the coarse alignment of system, set up carrier coordinate system b and calculate transition matrix T between the geographic coordinate system n ' _b ⁿ':

For a certain latitude

Have:

g ^t＝[0?0?-g] ^T

With g and ω _IeCan constitute new vector E, that is: an E=g * ω _Ie, can get according to the direction cosine matrix between navigation system and the carrier system again:

$\left.\begin{array}{c}{\stackrel{\‾}{g}}^b=T_{n^{\′}}^b{\stackrel{\‾}{g}}^{n^{\′}}\\ {\stackrel{\‾}{\mathrm{\ω}}}_{\mathrm{ie}}^b=T_{n^{\′}}^b{\stackrel{\‾}{\mathrm{\ω}}}_{\mathrm{ie}}^{n^{\′}}\\ {\stackrel{\‾}{E}}^b=T_{n^{\′}}^b{\stackrel{\‾}{E}}^{n^{\′}}\end{array}\right\}$

Consider the orthogonality of strapdown matrix, that is:

${\left(T_{n^{\′}}^b\right)}^{-1}={\left(T_{n^{\′}}^b\right)}^T=T_b^{n^{\′}}$

G wherein ^b, ω _Ie ^bReplace with the output of gyro and acceleration is approximate.

(4) 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 °.

(5) 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:

(6) foundation is that the Kalman filtering state equation and the velocity error of state variable are the measurement equation of measurement amount with the velocity error;

1) set up the state equation of Kalman filtering:

The state error of rotation strapdown inertial navitation system (SINS) is described with linear first-order differential equation:

$\stackrel{\·}{X}\left(t\right)=A\left(t\right)X\left(t\right)+B\left(t\right)W\left(t\right)$

The state vector of etching system when wherein X (t) is t; A (t) and B (t) are respectively the state matrix and the noise matrix of system; W (t) is the system noise vector;

The state vector of system is:

The white noise vector of system is:

W＝[a _x?a _y?ω _x?ω _y?ω _z?0?0?0?0?0] ^T

δ V wherein _e, δ V _nThe velocity error of representing east orientation, north orientation respectively;

Be respectively IMU coordinate system ox _s, oy _sAxis accelerometer zero partially; ε _x, ε _y, ε _zBe respectively IMU coordinate system ox _s, oy _s, oz _sThe constant value drift of axle gyro; a _x, a _yBe respectively IMU coordinate system ox _s, oy _sThe white noise error of axis accelerometer; ω _x, ω _y, ω _zBe respectively IMU coordinate system ox _s, oy _s, oz _sThe white noise error of axle gyro;

The state-transition matrix of system is:

$A\left(t\right)=\left[\begin{array}{cc}{F}_{5\×5}& T_{5\×5}\\ 0_{5\×5}& 0_{5\×5}\end{array}\right]$

Wherein:

$F_{5\&times;5}=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;2}& {\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;3}\\ {\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;2}& {\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;3}\end{array}\right]$

${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;2}=\left[\begin{array}{cc}\frac{V_n\tan \mathrm{<figure-callout\; id="2"\; label="L\; R\; n"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">L</figure-callout>}}{R_n}& 2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n}\\ -2({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n})& 0\end{array}\right]$

${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;3}=\left[\begin{array}{ccc}0& -f_u& f_n\\ f_u& 0& -f_e\end{array}\right]$

${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;2}=\left[\begin{array}{cc}0& -\frac{1}{R_m}\\ \frac{1}{{\mathrm{<figure-callout\; id="0"\; label="R\; n"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">R</figure-callout>}}_n}& 0\\ \frac{\tan \mathrm{<figure-callout\; id="0"\; label="L\; R\; n"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">L</figure-callout>}}{R_n}& 0\end{array}\right]$

${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;3}=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n}& -({\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_e}{R_n})\\ -({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n})& 0& -\frac{V_n}{R_m}\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_e}{R_n}& \frac{V_{\mathrm{<figure-callout\; id="0"\; label="n\; R\; m"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">n</figure-callout>}}}{R_m}& 0\end{array}\right]$

V _e, V _nThe speed of representing east orientation, north orientation respectively; ω _IeThe expression rotational-angular velocity of the earth; R _m, R _nRepresent earth meridian, fourth of the twelve Earthly Branches radius-of-curvature at the tenth of the twelve Earthly Branches respectively; L represents local latitude; f _e, f _n, f _uBe expressed as respectively navigation coordinate system down east orientation, north orientation, day to specific force.

Make the strapdown matrix T _s ⁿ' be:

$T_s^{n^{\&prime;}}=T_b^{n^{\&prime;}}{T}_s^b=\left[\begin{array}{ccc}{T}_{11}& T_{12}& T_{13}\\ T_{21}& T_{22}& T_{23}\\ T_{31}& T_{32}& T_{33}\end{array}\right]$

Then

$T_{5\&times;5}=\left[\begin{array}{ccccc}{T}_{11}& T_{12}& 0& 0& 0\\ T_{21}& T_{22}& 0& 0& 0\\ 0& 0& T_{11}& T_{12}& T_{13}\\ 0& 0& T_{21}& T_{22}& T_{23}\\ 0& 0& T_{31}& T_{32}& T_{33}\end{array}\right]$

2) set up the measurement equation of Kalman filtering:

The measurement equation of describing the rotation strapdown inertial navitation system (SINS) with linear first-order differential equation is as follows:

Z(t)＝H(t)X(t)+v(t)

Wherein: the measurement vector of etching system during Z (t) expression t; The measurement matrix of H (t) expression system; The measurement noise of v (t) expression system;

The system measurements matrix is:

$H\left(t\right)=\left[\begin{array}{cccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$

Amount is measured as the horizontal velocity error:

v(t)＝[v _e v _n] ^T

(7) utilize step (6) to estimate the platform misalignment, and when fine alignment finishes, come the strapdown attitude matrix of update the system, finish accurate initial alignment with it.

The present invention as observed quantity, has designed the rotary combination alignment methods of a kind of new IMU with speed.In the fine alignment process, by the continuous rotation of IMU, the strapdown matrix becomes the amount that one-period changes.It is unobservable that this method has solved under the carrier quiescent conditions east orientation gyroscopic drift, and the not high problem of orientation misalignment precision that causes thus.Because gyroscopic drift is the key factor that causes strapdown inertial navigation system output navigation error, so after adopting technical scheme of the present invention to carry out initial alignment, can effectively improve the navigation accuracy of strapdown inertial navigation system.

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

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

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

The initial attitude error angle:

Get 1 °, 1 °, 3 ° respectively;

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 method for the invention to obtain carrier east orientation misalignment graph of errors, north orientation misalignment graph of errors and orientation misalignment graph of errors respectively as Fig. 4, Fig. 5, shown in Figure 6.The result shows at carrier under the static and continuous rotating conditions of IMU, adopts method of the present invention can obtain higher alignment precision.

(4) description of drawings

Fig. 1 is the strapdown inertial navitation system (SINS) initial alignment method flow diagram of a kind of single shaft rotation 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 is that new method east orientation misalignment empirical curve is aimed in the rotation strapdown inertial navitation system (SINS) combination based on Kalman filtering of the present invention.

Fig. 5 is that new method north orientation misalignment empirical curve is aimed in the rotation strapdown inertial navitation system (SINS) combination based on Kalman filtering of the present invention.

Fig. 6 is that new method orientation misalignment empirical curve is aimed in the rotation strapdown inertial navitation system (SINS) combination based on Kalman filtering 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, they are bound to navigational computer;

(2) fiber optic gyro strapdown inertial navigation system carries out preheating, gathers the data of fibre optic gyroscope and quartz accelerometer output then;

(3) fibre optic gyroscope that collects and the data of quartz accelerometer are handled, adopted analytical method to finish the coarse alignment of system, tentatively determine the attitude information of carrier;

Gravitational vector g and gyroscope output and earth rotation angular speed ω according to the output of accelerometer _IeMeasured value determine that tentatively the attitude information of carrier this moment finishes the coarse alignment of system, set up carrier coordinate system b and calculate transition matrix T between the geographic coordinate system n ' _b ⁿ':

For a certain latitude

Have:

g ^t＝[0?0?-g] ^T (1)

With g and ω _IeCan constitute new vector E, that is: an E=g * ω _Ie, can get according to the direction cosine matrix between navigation system and the carrier system again:

$\left.\begin{array}{c}{\stackrel{\&OverBar;}{g}}^b=T_{n^{\&prime;}}^b{\stackrel{\&OverBar;}{g}}^{n^{\&prime;}}\\ {\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_{\mathrm{ie}}^b=T_{n^{\&prime;}}^b{\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_{\mathrm{ie}}^{n^{\&prime;}}\\ {\stackrel{\&OverBar;}{E}}^b=T_{n^{\&prime;}}^b{\stackrel{\&OverBar;}{E}}^{n^{\&prime;}}\end{array}\right\}---\left(3\right)$

Consider the orthogonality of strapdown matrix, that is:

${\left(T_{n^{\&prime;}}^b\right)}^{-1}={\left(T_{n^{\&prime;}}^b\right)}^T=T_b^{n^{\&prime;}}---\left(4\right)$

G wherein ^b, ω _Ie ^bReplace with the output of gyro and acceleration is approximate.

(4) 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 °.

(5) 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:

(6) foundation is that the Kalman filtering state equation and the velocity error of state variable are the measurement equation of measurement amount with the velocity error;

1) set up the state equation of Kalman filtering:

The state error of rotation strapdown inertial navitation system (SINS) is described with linear first-order differential equation:

$\stackrel{\&CenterDot;}{X}\left(t\right)=A\left(t\right)X\left(t\right)+B\left(t\right)W\left(t\right)---\left(7\right)$

The state vector of etching system when wherein X (t) is t; A (t) and B (t) are respectively the state matrix and the noise matrix of system; W (t) is the system noise vector;

The state vector of system is:

The white noise vector of system is:

W＝[a _x?a _y?ω _x?ω _y?ω _z?0?0?0?0?0] ^T (9)

δ V wherein _e, δ V _nThe velocity error of representing east orientation, north orientation respectively;

Be respectively IMU coordinate system ox _s, oy _sAxis accelerometer zero partially; ε _x, ε _y, ε _zBe respectively IMU coordinate system ox _s, oy _s, oz _sThe constant value drift of axle gyro; a _x, a _yBe respectively IMU coordinate system ox _s, oy _sThe white noise error of axis accelerometer; ω _x, ω _y, ω _zBe respectively IMU coordinate system ox _s, oy _s, oz _sThe white noise error of axle gyro;

The state-transition matrix of system is:

$A\left(t\right)=\left[\begin{array}{cc}{F}_{5\&times;5}& T_{5\&times;5}\\ 0_{5\&times;5}& 0_{5\&times;5}\end{array}\right]---\left(10\right)$

Wherein:

$F_{5\&times;5}=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;2}& {\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;3}\\ {\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;2}& {\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;3}\end{array}\right]---\left(11\right)$

${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;2}=\left[\begin{array}{cc}\frac{V_n\tan \mathrm{<figure-callout\; id="2"\; label="L\; R\; n"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">L</figure-callout>}}{R_n}& 2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n}\\ -2({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n})& 0\end{array}\right]---\left(12\right)$

${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;3}=\left[\begin{array}{ccc}0& -f_u& f_n\\ f_u& 0& -f_e\end{array}\right]---\left(13\right)$

${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;2}=\left[\begin{array}{cc}0& -\frac{1}{R_m}\\ \frac{1}{{\mathrm{<figure-callout\; id="0"\; label="R\; n"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">R</figure-callout>}}_n}& 0\\ \frac{\tan L}{R_n}& 0\end{array}\right]---\left(14\right)$

${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="A20091007173400182.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;3}=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n}& -({\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_e}{R_n})\\ -({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n})& 0& -\frac{V_n}{R_m}\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_e}{R_n}& \frac{V_n}{R_m}& 0\end{array}\right]---\left(15\right)$

V _e, V _nThe speed of representing east orientation, north orientation respectively; ω _IeThe expression rotational-angular velocity of the earth; R _m, R _nRepresent earth meridian, fourth of the twelve Earthly Branches radius-of-curvature at the tenth of the twelve Earthly Branches respectively; L represents local latitude; f _e, f _n, f _uBe expressed as respectively navigation coordinate system down east orientation, north orientation, day to specific force.

Make the strapdown matrix T _s ⁿ' be:

$T_s^{n^{\&prime;}}=T_b^{n^{\&prime;}}{T}_s^b=\left[\begin{array}{ccc}{T}_{11}& T_{12}& T_{13}\\ T_{21}& T_{22}& T_{23}\\ T_{31}& T_{32}& T_{33}\end{array}\right]---\left(16\right)$

Then

$T_{5\&times;5}=\left[\begin{array}{ccccc}{T}_{11}& T_{12}& 0& 0& 0\\ T_{21}& T_{22}& 0& 0& 0\\ 0& 0& T_{11}& T_{12}& T_{13}\\ 0& 0& T_{21}& T_{22}& T_{23}\\ 0& 0& T_{31}& T_{32}& T_{33}\end{array}\right]---\left(17\right)$

2) set up the measurement equation of Kalman filtering:

The measurement equation of describing the rotation strapdown inertial navitation system (SINS) with linear first-order differential equation is as follows:

Z(t)＝H(t)X(t)+v(t) (18)

Wherein: the measurement vector of etching system during Z (t) expression t; The measurement matrix of H (t) expression system; The measurement noise of v (t) expression system;

The system measurements matrix is:

$H\left(t\right)=\left[\begin{array}{cccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]---\left(19\right)$

Amount is measured as the horizontal velocity error:

v(t)＝[v _e v _n] ^T (20)

(7) utilize step (6) to estimate the platform misalignment, and when fine alignment finishes, come the strapdown attitude matrix of update the system, finish accurate initial alignment with it.

Claims (4)

1, a kind of strapdown inertial navitation system (SINS) initial alignment method of single shaft rotation is characterized in that may further comprise the steps:

(1) utilizes global position system GPS to determine the initial position parameters of carrier, and bind to navigational computer;

(2) gather the fibre optic gyroscope of fiber optic gyro strapdown inertial navigation system and the data of quartz accelerometer output;

(3) fibre optic gyroscope that collects and the data of quartz accelerometer are handled, adopted analytical method to finish the coarse alignment of system, tentatively determine the attitude information of carrier;

(4) 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;

(5) 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;

(6) foundation is that the Kalman filtering state equation and the velocity error of state variable are the measurement equation of measurement amount with the velocity error;

1) set up the state equation of Kalman filtering:

The state error of rotation strapdown inertial navitation system (SINS) is described with linear first-order differential equation:

$\stackrel{\&CenterDot;}{X}\left(t\right)=A\left(t\right)X\left(t\right)+B\left(t\right)W\left(t\right)$

The state vector of etching system when wherein X (t) is t; A (t) and B (t) are respectively the state matrix and the noise matrix of system; W (t) is the system noise vector;

The state vector of system is:

The white noise vector of system is:

W＝[a _x?a _y?ω _z?ω _y?ω _z?0?0?0?0?0] ^T

δ V wherein _e, δ V _nThe velocity error of representing east orientation, north orientation respectively;

Be respectively IMU coordinate system ox _s, oy _sAxis accelerometer zero partially; ε _x, ε _y, ε _zBe respectively IMU coordinate system ox _s, oy _s, oz _sThe constant value drift of axle gyro; a _x, a _yBe respectively IMU coordinate system ox _s, oy _sThe white noise error of axis accelerometer; ω _x, ω _y, ω _zBe respectively IMU coordinate system ox _s, oy _s, oz _sThe white noise error of axle gyro;

The state-transition matrix of system is:

$A\left(t\right)=\left[\begin{array}{cc}{F}_{5\&times;5}& T_{5\&times;5}\\ 0_{5\&times;5}& 0_{5\&times;5}\end{array}\right]$

Wherein:

$F_{5\&times;5}=\left[\begin{array}{cc}{F}_{2\&times;2}& F_{2\&times;3}\\ F_{3\&times;2}& F_{3\&times;3}\end{array}\right]$

$F_{2\&times;2}=\left[\begin{array}{cc}\frac{V_n\tan L}{R_n}& 2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n}\\ -2({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n})& 0\end{array}\right]$

$F_{2\&times;3}=\left[\begin{array}{ccc}0& -f_u& f_n\\ f_u& 0& -f_e\end{array}\right]$

$F_{3\&times;2}=\left[\begin{array}{cc}0& -\frac{1}{R_m}\\ \frac{1}{R_n}& 0\\ \frac{\tan L}{R_n}& 0\end{array}\right]$

$F_{3\&times;3}=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n}& -({\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_e}{R_n})\\ -({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_e\tan L}{R_n})& 0& -\frac{V_n}{R_m}\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_e}{R_n}& \frac{V_n}{R_m}& 0\end{array}\right]$

V _e, V _nThe speed of representing east orientation, north orientation respectively; ω _IeThe expression rotational-angular velocity of the earth; R _m, R _nRepresent earth meridian, fourth of the twelve Earthly Branches radius-of-curvature at the tenth of the twelve Earthly Branches respectively; L represents local latitude; f _e, f _n, f _uBe expressed as respectively navigation coordinate system down east orientation, north orientation, day to specific force;

Make the strapdown matrix T _s ⁿ' be:

$T_s^{n^{\&prime;}}=T_b^{n^{\&prime;}}{T}_s^b=\left[\begin{array}{ccc}{T}_{11}& T_{12}& T_{13}\\ T_{21}& T_{22}& T_{23}\\ T_{31}& T_{32}& T_{33}\end{array}\right]$

Then

$T_{5\&times;5}=\left[\begin{array}{ccccc}{T}_{11}& T_{12}& 0& 0& 0\\ T_{21}& T_{22}& 0& 0& 0\\ 0& 0& T_{11}& T_{12}& T_{13}\\ 0& 0& T_{21}& T_{22}& T_{23}\\ 0& 0& T_{31}& T_{32}& T_{33}\end{array}\right];$

2) set up the measurement equation of Kalman filtering:

The measurement equation of describing the rotation strapdown inertial navitation system (SINS) with linear first-order differential equation is as follows:

Z(t)＝H(t)X(t)+v(t)

Wherein: the measurement vector of etching system during Z (t) expression t; The measurement matrix of H (t) expression system; The measurement noise of v (t) expression system;

The system measurements matrix is:

$H\left(t\right)=\left[\begin{array}{cccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$

Amount is measured as the horizontal velocity error:

v(t)＝[v _e?v _n] ^T；

(7) utilize step (6) to estimate the platform misalignment, and when fine alignment finishes, come the strapdown attitude matrix of update the system, finish accurate initial alignment with it.

2, the strapdown inertial navitation system (SINS) initial alignment method of a kind of single shaft rotation according to claim 1 is characterized in that the method for the attitude information of described preliminary definite carrier is: according to gravitational vector g and the gyroscope output and earth rotation angular speed ω of accelerometer output _IeMeasured value determine that tentatively the attitude information of carrier this moment finishes the coarse alignment of system, set up carrier coordinate system b and calculate transition matrix T between the geographic coordinate system n ' _b ⁿ':

For a certain be 90 ° angle less than latitude

Have:

${\stackrel{\&OverBar;}{g}}^t={\left[\begin{array}{ccc}0& 0& -g\end{array}\right]}^T$

With g and ω _IeConstitute new vector E, that is: an E=g * ω _Ie, get according to the direction cosine matrix between navigation system and the carrier system again:

$\left.\begin{array}{c}{\stackrel{\&OverBar;}{g}}^b=T_{n^{\&prime;}}^b{\stackrel{\&OverBar;}{g}}^{n^{\&prime;}}\\ {\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_{\mathrm{ie}}^b=T_{n^{\&prime;}}^b{\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_{\mathrm{ie}}^{n^{\&prime;}}\\ {\stackrel{\&OverBar;}{E}}^b=T_{n^{\&prime;}}^b{\stackrel{\&OverBar;}{E}}^{n^{\&prime;}}\end{array}\right\}$

Consider the orthogonality of strapdown matrix, that is:

${\left(T_{n^{\&prime;}}^b\right)}^{-1}={\left(T_{n^{\&prime;}}^b\right)}^T=T_b^{n^{\&prime;}}$

G wherein ^b, ω _Ie ^bReplace with the output of gyro and acceleration is approximate.

3, the strapdown inertial navitation system (SINS) initial alignment method of a kind of single shaft rotation according to claim 2 is characterized in that described Inertial Measurement Unit is around carrier coordinate system oy _bAxle is rotated in the forward 45 degree: 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, the strapdown inertial navitation system (SINS) initial alignment method of a kind of single shaft rotation according to claim 3, 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 _bIn the IMU rotation process that forward rotates continuously with angular velocity omega=6 °/s, the transition matrix that the IMU coordinate is tied to carrier coordinate system is:

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