CN103278178A - Flexural deformation measurement method capable of considering transmission delay in transfer alignment - Google Patents

Abstract

The invention provides a flexural deformation measurement method capable of considering transmission delay in transfer alignment. The method comprises the steps: firstly, installing a main inertial navigation system and a sub inertial navigation system on a ship; then building a model of a state updating transmitted to the sub inertial navigation system by the main inertial navigation system; next by using a direction cosine method, calculating out an error caused by the transmission delay and compensating the error; and finally, estimating an installation error angle and a flexural deformation angle between the main and the sub inertial navigation system by a Kalman filter. The flexural deformation measurement method can effectively suppress effects caused by the transmission delay, and thereby improving the measurement precision.

Description

In Transfer Alignment, consider the deflection deformation measuring method of transmission delay

(1) technical field

What the present invention relates to is a kind of measuring method of deflection deformation, specifically a kind of deflection deformation measuring method of considering transmission delay in Transfer Alignment.

(2) background technology

Transfer Alignment is a kind of moving alignment, it refers to utilize the information of the main inertial navigation of having aimed to aim to need a kind of method of the sub-inertial navigation system of aiming at, its basic thought is exactly to be benchmark with the high main inertial navigation information of precision, by the output information of boss's inertial navigation relatively, adopt suitable filtering algorithm to come to such an extent that the error parameter of antithetical phrase inertial navigation system compensates.Since Transfer Alignment have the aligning time short, alignment precision is high, looser to the requirement of inertia device, overcome in the past the drawback of the alignment so that the adopts requirement that can not arrive simultaneously because of time and precision, become the focus of research at present.The precision of Transfer Alignment is subjected to the influence of many-sided factor, as lever arm effect, deflection deformation, transmission delay etc., therefore these disturbing factors is compensated, and will improve the precision of aligning, has certain practical significance.

When carrying out the measurement at deflection deformation angle, owing to main inertial navigation system is installed on the different positions with sub-inertial navigation system, so main inertial navigation will relate to the problem of transmission delay when relevant navigation information is transmitted in sub-inertial navigation.Discover that transmission delay is bigger to the influence of attitude, thus need upgrade attitude matrix, make main, when information matches is carried out in sub-inertial navigation on synchronization.To be considered as the random value of certain limit time delay in the document " in the Transfer Alignment measure postpone compensation method ", set up the Transfer Alignment model that comprises state time delay, and with the Transfer Alignment wave filter to estimating time delay and compensating.It is considered herein that be normal value time delay, by the renewal to attitude matrix, obtained the error term that caused by transmission delay, adopt direction cosine method that error term is compensated, and then with Kalman filtering alignment error angle and deflection deformation angle are estimated.

(3) summary of the invention

The object of the present invention is to provide a kind of deflection deformation measuring method of in Transfer Alignment, considering transmission delay.

The object of the present invention is achieved like this:

(1) two cover strapdown inertial navitation system (SINS) are installed aboard ship, what wherein precision was higher is main inertial navigation system, and what precision was lower is sub-inertial navigation system;

(2) start main inertial navigation system, make it be operated in navigational state;

(3) promoter inertial navigation system, the output data of gathering its gyro and accelerometer;

(4) information (mainly being speed and attitude information) with main inertial navigation system passes to sub-inertial navigation system, finishes initial alignment;

(5) set up the model of main inertial navigation system posture renewal;

(6) according to the information of main inertial navigation system, adopt direction cosine method to calculate the error in the posture renewal model and it is compensated;

(7) set up state equation and the observation equation of system;

(8) go out alignment error angle and deflection deformation angle between main, the sub-inertial navigation system with Kalman Filter Estimation.

The described model of setting up main inertial navigation system posture renewal is:

${\mathrm{\φ}}_m\×=I-C_n^{s^{\′}}\left(t\right)\·C_m^n\left(t\right)-C_n^{s^{\′}}\left(t\right)\·{\stackrel{\·}{C}}_m^n\left(t\right)\·\mathrm{\Δt}$

φ wherein _m* be the antisymmetric matrix of the misalignment between master, the sub-inertial navigation system, I is the unit matrixs of 3 * 3 dimensions, Be t the going to of attitude matrix of sub-inertial navigation system constantly, Be the attitude matrix of t main inertial navigation system of the moment,

Be the t first order derivative of the attitude matrix of main inertial navigation system constantly, the time of Δ t for postponing, its value is a constant.

Described employing direction cosine method calculate in the posture renewal model error and to its compensate into:

The differential equation according to direction cosine matrix can get:

${\stackrel{\·}{C}}_m^n\left(t\right)=C_m^n\left(t\right)\·{\mathrm{\Ω}}_{\mathrm{nm}}^m\left(t\right)$

Wherein: ${\mathrm{\Ω}}_{\mathrm{nm}}^m\left(t\right)=\left[\begin{array}{ccc}0& -{\mathrm{\ω}}_{\mathrm{nmz}}^m\left(t\right)& {\mathrm{\ω}}_{\mathrm{nmy}}^m\left(t\right)\\ {\mathrm{\ω}}_{\mathrm{nmz}}^m\left(t\right)& 0& -{\mathrm{\ω}}_{\mathrm{nmx}}^m\left(t\right)\\ -{\mathrm{\ω}}_{\mathrm{nmy}}^m\left(t\right)& {\mathrm{\ω}}_{\mathrm{nmx}}^m\left(t\right)& 0\end{array}\right],$

It is angular velocity projection on the carrier coordinate system of main inertial navigation of the relative navigation coordinate of the carrier coordinate system system of main inertial navigation.

Because

With Initial value all be as can be known, so can obtain by the differential equation of direction cosine matrix

So just can be to the error term that is caused by transmission delay

Compensate.

Describedly set up the state equation of system and the step of observation equation is:

State equation and the observation equation of system are respectively:

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

Z(t)＝H(t)X(t)+V(t)

In the formula:

State vector X (t) is chosen for:

δ v _E, δ v _NBe respectively east orientation velocity error and north orientation velocity error, φ _Mx, φ _My, φ _MzBe respectively the component of misalignment on three axles between master, the sub-inertial navigation system, φ _Ax, φ _Ay, φ _AzBe respectively the component of alignment error angle on three axles between master, the sub-inertial navigation system, θ _x, θ _y, θ _zBe respectively the component of distortion angle on three axles.

The system noise acoustic matrix is:

a _x, a _yBe respectively east orientation accelerometer error and north orientation accelerometer error, ε _x, ε _y, ε _zBe respectively the component of gyroscopic drift on three.

In the formula:

$A\left(t\right)=\left[\begin{array}{ccccc}{A}_1& A_2& -A_2& 0_{2\×3}& 0_{2\×3}\\ 0_{3\×2}& A_3& -A_3& I_{3\×3}& 0_{3\×3}\\ 0_{3\×2}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}\\ 0_{3\×2}& 0_{3\×3}& 0_{3\×3}& 0_{3\×3}& I_{3\×3}\\ 0_{3\×2}& 0_{3\×3}& 0_{3\×3}& A_4& A_5\end{array}\right]$

Wherein:

$C_{s^{\&prime;}}^n=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right],$ $A_2=\left[\begin{array}{ccc}{c}_{13}{f}_y-c_{12}{f}_z& -c_{13}{f}_x+c_{11}{f}_z& c_{12}{f}_x-c_{11}{f}_z\\ c_{23}{f}_y-c_{22}{f}_z& -c_{23}{f}_x+c_{21}{f}_z& c_{22}{f}_x-c_{21}{f}_z\end{array}\right],$ $f_s^s={\left[\begin{array}{ccc}{f}_x& f_y& f_z\end{array}\right]}^T,$ $A_3=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{nsz}}^s& -{\mathrm{\&omega;}}_{\mathrm{nsy}}^s\\ -{\mathrm{\&omega;}}_{\mathrm{nsz}}^s& 0& {\mathrm{\&omega;}}_{\mathrm{nsx}}^s\\ {\mathrm{\&omega;}}_{\mathrm{nsy}}^s& -{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="nsx\; s"\; filenames="HSA00000889892900021.png,HSA00000889892900031.png"\; state="\{\{state\}\}">nsx</figure-callout>}}^s& 0\end{array}\right],$ $A_4=\left[\begin{array}{ccc}-b_x^2& 0& 0\\ 0& -b_y^2& 0\\ 0& 0& -b_z^2\end{array}\right],$ $A_5=\left[\begin{array}{ccc}-2{\mathrm{\&mu;}}_x& 0& 0\\ 0& -2{\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HSA00000889892900021.png,HSA00000889892900031.png"\; state="\{\{state\}\}">y</figure-callout>}}& 0\\ 0& 0& -2{\mathrm{\&mu;}}_z\end{array}\right].$

v _EBe east orientation speed, ω _IeBe the spin velocity of the earth,

Be the attitude matrix of sub-inertial navigation system,

Be the gyro output of three of sub-inertial navigations, R _eBe earth fourth of the twelve Earthly Branches radius-of-curvature at the tenth of the twelve Earthly Branches,

Be the latitude of locality, A ₄And A ₅In coefficient all are the correlations at deflection deformation angle,

Be angular velocity the projection on sub-inertial navigation system carrier coordinate system of sub-inertial navigation system carrier coordinate system with respect to navigation coordinate system.

In the formula:

The systematic perspective measurement is elected as:

Wherein: observing matrix is H=[I _{5 * 5}0 _{5 * 9}] ^T, V (t) is the measurement noise battle array of system.

Beneficial effect of the present invention is verified by the following method:

(1) Matlab l-G simulation test

The l-G simulation test condition:

The motion model of carrier is: the pitch angle of establishing carrier is ψ, and roll angle is θ, and course angle is γ, then:

$\left\{\begin{array}{c}\mathrm{\&psi;}={\mathrm{\&psi;}}_m\sin ({\mathrm{\&omega;}}_{\mathrm{\&psi;}}t+{\mathrm{\&psi;}}_0)\\ \mathrm{\&theta;}={\mathrm{\&theta;}}_m\sin ({\mathrm{\&omega;}}_{\mathrm{\&theta;}}t+{\mathrm{\&theta;}}_0)\\ \mathrm{\&gamma;}={\mathrm{\&gamma;}}_m\sin ({\mathrm{\&omega;}}_{\mathrm{\&gamma;}}t+{\mathrm{\&gamma;}}_0)\end{array}\right.$

ψ wherein _m=5 °, θ _m=5 °, λ _m=5 °, ω _ψ=2 π/6 (rad/s), ω _θ=2 π/8 (rad/s), ω _γ=2 π/10 (tad/s), initial phase angle: ψ ₀=0 °, θ ₀=0 °, γ ₀=0 °.Initial latitude

Initial longitude λ=126.6705 °; Alignment error angle φ _Ax=1 °, φ _Ay=1 °, φ _Az=1 °; Gyroscope constant value drift is 0.01 °/h; Accelerometer bias is 10 ^-4g ₀, the propagation delay time is 10 seconds.

The evaluated error curve at alignment error angle before and after Simulation results: Fig. 2, Fig. 3 are respectively and compensate, Fig. 4, Fig. 5 are respectively the curve at the distortion angle of the estimation of compensation front and back and reality.

(4) description of drawings

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the evaluated error curve map that does not compensate the alignment error angle of transmission delay;

Fig. 3 is the evaluated error curve map at the alignment error angle of compensation transmission delay;

Estimation and the actual distortion angular curve figure of Fig. 4 for not compensating transmission delay;

Fig. 5 is estimation and the actual distortion angular curve figure of compensation transmission delay.

(5) embodiment

Below the present invention is done concrete description:

(1) two cover strapdown inertial navitation system (SINS) are installed aboard ship, what wherein precision was higher is main inertial navigation system, and what precision was lower is sub-inertial navigation system;

(2) start main inertial navigation system, make it be operated in navigational state;

(3) promoter inertial navigation system, the output data of gathering its gyro and accelerometer;

(4) information (mainly being speed and attitude information) with main inertial navigation system passes to sub-inertial navigation system, finishes initial alignment;

(5) set up the model of main inertial navigation system posture renewal;

The model of main inertial navigation system posture renewal is:

${\mathrm{\&phi;}}_m\&times;=I-C_n^{s^{\&prime;}}\left(t\right)\&CenterDot;C_m^n\left(t\right)-C_n^{s^{\&prime;}}\left(t\right)\&CenterDot;{\stackrel{\&CenterDot;}{C}}_m^n\left(t\right)\&CenterDot;\mathrm{\&Delta;t}$

φ wherein _m* be the antisymmetric matrix of the misalignment between master, the sub-inertial navigation system, I is the unit matrixs of 3 * 3 dimensions,

Be t the going to of attitude matrix of sub-inertial navigation system constantly,

Be the attitude matrix of t main inertial navigation system of the moment,

Be the t first order derivative of the attitude matrix of main inertial navigation system constantly, the time of Δ t for postponing, its value is a constant.

(6) according to the information of main inertial navigation system, adopt direction cosine method to calculate the error in the posture renewal model and it is compensated;

The differential equation according to direction cosine matrix can get:

${\stackrel{\&CenterDot;}{C}}_m^n\left(t\right)=C_m^n\left(t\right)\&CenterDot;{\mathrm{\&Omega;}}_{\mathrm{nm}}^m\left(t\right)$

Wherein: ${\mathrm{\&Omega;}}_{\mathrm{nm}}^m\left(t\right)=\left[\begin{array}{ccc}0& -{\mathrm{\&omega;}}_{\mathrm{nmz}}^m\left(t\right)& {\mathrm{\&omega;}}_{\mathrm{nmy}}^m\left(t\right)\\ {\mathrm{\&omega;}}_{\mathrm{nmz}}^m\left(t\right)& 0& -{\mathrm{\&omega;}}_{\mathrm{nmx}}^m\left(t\right)\\ -{\mathrm{\&omega;}}_{\mathrm{nmy}}^m\left(t\right)& {\mathrm{\&omega;}}_{\mathrm{nmx}}^m\left(t\right)& 0\end{array}\right],$

It is angular velocity projection on the carrier coordinate system of main inertial navigation of the relative navigation coordinate of the carrier coordinate system system of main inertial navigation.

Because

With

Initial value all be as can be known, so can obtain by the differential equation of direction cosine matrix

So just can be to the error term that is caused by transmission delay

Compensate

(7) set up state equation and the observation equation of system;

State equation and the observation equation of system are respectively:

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

Z(t)＝H(t)X(t)+V(t)

In the formula:

State vector X (t) is chosen for:

δ v _E, δ v _NBe respectively east orientation velocity error and north orientation velocity error, φ _Mx, φ _My, φ _MzBe respectively the component of misalignment on three axles between master, the sub-inertial navigation system, φ _Ax, φ _Ay, φ _AzBe respectively the component of alignment error angle on three axles between master, the sub-inertial navigation system, θ _x, θ _y, θ _zBe respectively the component of distortion angle on three axles.

The system noise acoustic matrix is:

a _x, a _yBe respectively east orientation accelerometer error and north orientation accelerometer error, ε _x, ε _y, ε _zBe respectively the component of gyroscopic drift on three.

In the formula:

$A\left(t\right)=\left[\begin{array}{ccccc}{A}_1& A_2& -A_2& 0_{2\&times;3}& 0_{2\&times;3}\\ 0_{3\&times;2}& A_3& -A_3& I_{3\&times;3}& 0_{3\&times;3}\\ 0_{3\&times;2}& 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}\\ 0_{3\&times;2}& 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}& I_{3\&times;3}\\ 0_{3\&times;2}& 0_{3\&times;3}& 0_{3\&times;3}& A_4& A_5\end{array}\right]$

Wherein:

$C_{s^{\&prime;}}^n=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right],$ $A_2=\left[\begin{array}{ccc}{c}_{13}{f}_y-c_{12}{f}_z& -c_{13}{f}_x+c_{11}{f}_z& c_{12}{f}_x-c_{11}{f}_z\\ c_{23}{f}_y-c_{22}{f}_z& -c_{23}{f}_x+c_{21}{f}_z& c_{22}{f}_x-c_{21}{f}_z\end{array}\right],$ $f_s^s={\left[\begin{array}{ccc}{f}_x& f_y& f_z\end{array}\right]}^T,$ $A_3=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{nsz}}^s& -{\mathrm{\&omega;}}_{\mathrm{nsy}}^s\\ -{\mathrm{\&omega;}}_{\mathrm{nsz}}^s& 0& {\mathrm{\&omega;}}_{\mathrm{nsx}}^s\\ {\mathrm{\&omega;}}_{\mathrm{nsy}}^s& -{\mathrm{\&omega;}}_{\mathrm{nsx}}^s& 0\end{array}\right],$ $A_4=\left[\begin{array}{ccc}-b_x^2& 0& 0\\ 0& -b_y^2& 0\\ 0& 0& -b_z^2\end{array}\right],$ $A_5=\left[\begin{array}{ccc}-2{\mathrm{\&mu;}}_x& 0& 0\\ 0& -2{\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HSA00000889892900021.png,HSA00000889892900031.png"\; state="\{\{state\}\}">y</figure-callout>}}& 0\\ 0& 0& -2{\mathrm{\&mu;}}_z\end{array}\right].$

v _EBe east orientation speed, ω _IeBe the spin velocity of the earth,

Be the attitude matrix of sub-inertial navigation system,

Be the gyro output of three of sub-inertial navigations, R _eBe earth fourth of the twelve Earthly Branches radius-of-curvature at the tenth of the twelve Earthly Branches, Be the latitude of locality, A ₄And A ₅In coefficient all are the correlations at deflection deformation angle,

Be angular velocity the projection on sub-inertial navigation system carrier coordinate system of sub-inertial navigation system carrier coordinate system with respect to navigation coordinate system.

In the formula:

The systematic perspective measurement is elected as:

Wherein: observing matrix is H=[I _{5 * 5}0 _{5 * 9}] ^T, V (t) is the measurement noise battle array of system.

(8) go out alignment error angle and deflection deformation angle between main, the sub-inertial navigation system with Kalman Filter Estimation.

Claims (1)

1. in Transfer Alignment, consider the deflection deformation measuring method of transmission delay, it is characterized in that:

(1) two cover strapdown inertial navitation system (SINS) are installed aboard ship, what wherein precision was higher is main inertial navigation system, and what precision was lower is sub-inertial navigation system;

(2) start main inertial navigation system, make it be operated in navigational state;

(3) promoter inertial navigation system, the output data of gathering its gyro and accelerometer;

(4) information (mainly being speed and attitude information) with main inertial navigation system passes to sub-inertial navigation system, finishes initial alignment;

(5) set up the model of main inertial navigation system posture renewal;

The model of main inertial navigation system posture renewal is:

${\mathrm{\&phi;}}_m\&times;=I-C_n^{s^{\&prime;}}\left(t\right)\&CenterDot;C_m^n\left(t\right)-C_n^{s^{\&prime;}}\left(t\right)\&CenterDot;{\stackrel{\&CenterDot;}{C}}_m^n\left(t\right)\&CenterDot;\mathrm{\&Delta;t}$

φ wherein _m* be the antisymmetric matrix of the misalignment between master, the sub-inertial navigation system, I is the unit matrixs of 3 * 3 dimensions, Be t the going to of attitude matrix of sub-inertial navigation system constantly,

Be the attitude matrix of t main inertial navigation system of the moment, Be the t first order derivative of the attitude matrix of main inertial navigation system constantly, the time of Δ t for postponing, its value is a constant.

(6) according to the information of main inertial navigation system, adopt direction cosine method to calculate the error in the posture renewal model and it is compensated;

The differential equation according to direction cosine matrix can get:

${\stackrel{\&CenterDot;}{C}}_m^n\left(t\right)=C_m^n\left(t\right)\&CenterDot;{\mathrm{\&Omega;}}_{\mathrm{nm}}^m\left(t\right)$

Wherein: ${\mathrm{\&Omega;}}_{\mathrm{nm}}^m\left(t\right)=\left[\begin{array}{ccc}0& -{\mathrm{\&omega;}}_{\mathrm{nmz}}^m\left(t\right)& {\mathrm{\&omega;}}_{\mathrm{nmy}}^m\left(t\right)\\ {\mathrm{\&omega;}}_{\mathrm{nmz}}^m\left(t\right)& 0& -{\mathrm{\&omega;}}_{\mathrm{nmx}}^m\left(t\right)\\ -{\mathrm{\&omega;}}_{\mathrm{nmy}}^m\left(t\right)& {\mathrm{\&omega;}}_{\mathrm{nmx}}^m\left(t\right)& 0\end{array}\right],$

It is angular velocity projection on the carrier coordinate system of main inertial navigation of the relative navigation coordinate of the carrier coordinate system system of main inertial navigation.

Because

With

Initial value all be as can be known, so can obtain by the differential equation of direction cosine matrix So just can be to the error term that is caused by transmission delay

Compensate

(7) set up state equation and the observation equation of system;

State equation and the observation equation of system are respectively:

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

Z(t)＝H(t)X(t)+V(t)

In the formula:

State vector X (t) is chosen for:

δ v _E, δ v _NBe respectively east orientation velocity error and north orientation velocity error, φ _Mx, φ _My, φ _MzBe respectively the component of misalignment on three axles between master, the sub-inertial navigation system, φ _Ax, φ _Ay, φ _AzBe respectively the component of alignment error angle on three axles between master, the sub-inertial navigation system, θ _x, θ _y, θ _zBe respectively the component of distortion angle on three axles.

The system noise acoustic matrix is:

a _x, a _yBe respectively east orientation accelerometer error and north orientation accelerometer error, ε _x, ε _y, ε _zBe respectively the component of gyroscopic drift on three, T represents vector or transpose of a matrix.In the formula:

$A\left(t\right)=\left[\begin{array}{ccccc}{A}_1& A_2& -A_2& 0_{2\&times;3}& 0_{2\&times;3}\\ 0_{3\&times;2}& A_3& -A_3& I_{3\&times;3}& 0_{3\&times;3}\\ 0_{3\&times;2}& 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}\\ 0_{3\&times;2}& 0_{3\&times;3}& 0_{3\&times;3}& 0_{3\&times;3}& I_{3\&times;3}\\ 0_{3\&times;2}& 0_{3\&times;3}& 0_{3\&times;3}& A_4& A_5\end{array}\right]$

Wherein:

$C_{s^{\&prime;}}^n=\left[\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right],$ $A_2=\left[\begin{array}{ccc}{c}_{13}{f}_y-c_{12}{f}_z& -c_{13}{f}_x+c_{11}{f}_z& c_{12}{f}_x-c_{11}{f}_z\\ c_{23}{f}_y-c_{22}{f}_z& -c_{23}{f}_x+c_{21}{f}_z& c_{22}{f}_x-c_{21}{f}_z\end{array}\right],$ $f_s^s={\left[\begin{array}{ccc}{f}_x& f_y& f_z\end{array}\right]}^T,$ $A_3=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{nsz}}^s& -{\mathrm{\&omega;}}_{\mathrm{nsy}}^s\\ -{\mathrm{\&omega;}}_{\mathrm{nsz}}^s& 0& {\mathrm{\&omega;}}_{\mathrm{nsx}}^s\\ {\mathrm{\&omega;}}_{\mathrm{nsy}}^s& -{\mathrm{\&omega;}}_{\mathrm{nsx}}^s& 0\end{array}\right],$ $A_4=\left[\begin{array}{ccc}-b_x^2& 0& 0\\ 0& -b_y^2& 0\\ 0& 0& -b_z^2\end{array}\right],$ $A_5=\left[\begin{array}{ccc}-2{\mathrm{\&mu;}}_x& 0& 0\\ 0& -2{\mathrm{\&mu;}}_y& 0\\ 0& 0& -2{\mathrm{\&mu;}}_z\end{array}\right].$

v _EBe east orientation speed, ω _IeBe the spin velocity of the earth,

Be the attitude matrix of sub-inertial navigation system,

Be the gyro output of three of sub-inertial navigations, R _eBe earth fourth of the twelve Earthly Branches radius-of-curvature at the tenth of the twelve Earthly Branches,

Be the latitude of locality, A ₄And A ₅In coefficient all are the correlations at deflection deformation angle,

For sub-inertial navigation system carrier coordinate system with respect to the f among the projection A2 of angular velocity on sub-inertial navigation system carrier coordinate system of navigation coordinate system _x, f _y, f _zAccelerometer output for three of sub-inertial navigations; A3 is

Antisymmetric matrix; Parameter among A4 and the A5 is the constant coefficient in the second order Markovian process.

In the formula:

The systematic perspective measurement is elected as:

Wherein: observing matrix is H=[I _{5 * 5}0 _{5 * 9}] ^T, V (t) is the measurement noise battle array of system.

(8) go out alignment error angle and deflection deformation angle between main, the sub-inertial navigation system with Kalman Filter Estimation.

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