CN102168978A - Marine inertial navigation system swing pedestal open loop aligning method - Google Patents

Abstract

The invention relates to a marine inertial navigation system swing pedestal open loop aligning method, referring to that when a ship is in mooring state, a mathematics platform is built inside the inertial navigation system for isolating carrier angular motion, and with the mathematics platform drift angle amount of the inertial navigation system being employed for measuring, the recursion least squares is utilized for aligning and drift calculation. The invention directly utilizes the mathematics platform drift angle amount of the inertial navigation system for measuring and employs recursion least squares for drift angle and drift estimation, which substantially simplifies the calculation of initial aligning process, so the method of the invention is precise, high efficient, easy to achieve, and highly universal.

Description

A kind of marine aided inertial navigation system swaying base open loop alignment methods

Technical field

The present invention relates to a kind of accurate, quick, reliable and stable, marine aided inertial navigation system swaying base open loop alignment methods of being easy to realize, this method equally also can be used for the quiet pedestal and the swaying base initial alignment of other application scenario inertia inertial navigation system, belongs to the inertial navigation field.

Technical background

Characteristics such as inertial navigation system has entirely independently, highly concealed type, high bandwidth, continuous output have strategic importance on national defence, be one of most important equipment in the fields such as Aeronautics and Astronautics, navigation.

Initial alignment is to determine the process of its original state before inertial navigation enters navigational state, and original state comprises initial velocity, position, attitude and gyroscopic drift.The error of initial alignment can influence the navigation performance of system in whole navigation procedure, its level is to influence one of main factor of inertial navigation precision.Applied environments such as naval vessel generally need inertial navigation system can realize high precision alignment under the condition that pedestal waves, and therefore necessarily require to set up in inertial navigation system inside the mathematics/physical platform of isolation carrier movement.Traditional aligning way needs inertial navigation to be in navigational state, pushes away platform drift angle and gyroscopic drift according to site error and velocity error are counter.Utilize this method to need the long aligning time, and error model itself is responsive to linear-apporximation.

Summary of the invention

The technical matters that the present invention solves is: overcome the deficiencies in the prior art, a kind of marine aided inertial navigation system swaying base open loop alignment methods be provided, have accurate, quick, reliable and stable, be easy to characteristics such as realization.

Technical solution of the present invention is: a kind of marine aided inertial navigation system swaying base open loop alignment methods, and performing step is as follows:

(1) imports initial latitude, calculate local rotational-angular velocity of the earth according to initial latitude;

(2) attitude matrix that utilizes coarse alignment to obtain calculates the projection of rotational-angular velocity of the earth on carrier coordinate system, and the projection of rotational-angular velocity of the earth on the carrier coordinate system is deducted from gyroscope output, obtains the relative motion angular velocity of carrier;

(3) upgrade hypercomplex number and attitude of carrier matrix and attitude according to the carrier relative motion angular velocity that obtains in the step (2);

(4) be transformed under the mathematical platform coordinate system according to obtaining of the output of attitude of carrier matrix in the step (3), obtain the east orientation and the north orientation acceleration of carrier under the mathematical platform coordinate system the body axis system accelerometer;

(5) east orientation and the north orientation acceleration of carrier under the mathematical platform coordinate system that obtains according to step (4) calculate east orientation, north orientation mathematical platform drift angle;

(6) east orientation that obtains according to step (5), north orientation mathematical platform drift angle are carried out least square fitting to north east to mathematical platform declination error equation as the measurement amount, obtain the equivalent gyroscopic drift under the platform coordinate system;

(7) the equivalent gyroscopic drift under the platform coordinate system that obtains according to step (6) calculate the transduction boat constantly the mathematical platform drift angle and compensate, utilize the attitude of carrier matrix that calculates in (3), the equivalent gyroscopic drift under the platform coordinate system that step (6) match is obtained is transformed under the carrier coordinate system and compensates.

Principle of the present invention is: by setting up the motion isolation platform, motion angular velocity deduction from gyro output with carrier, the acceleration of gravity projection that the attitude of carrier angle is caused is deduction from accelerometer output, thereby obtains isolating platform coordinate system acceleration and the drift angle measurement down behind the carrier movement; This kind of deriving resolves inertial navigation system error model under the condition, the drift angle measured carry out match, thereby estimate the mean value and the initial platform drift angle of gyroscopic drift.

The present invention's advantage compared with prior art is:

(1) need inertial navigation to be in navigational state during initial alignment under the traditional inertial navigation system swaying base condition peculiar to vessel, utilize that navigation position and velocity error are counter to push away platform drift angle and gyroscopic drift, therefore the propagation of error process time is longer, and model is responsive to nonlinearity erron.The present invention utilizes the position of initial time input as the carrier positions in the whole alignment procedures, and under the ship sway situation, looking its speed is zero, carries out posture renewal with this understanding, and makes up isolation platform, the acceleration under the computing platform coordinate system and platform drift angle.Derivation is at the above error equation that resolves inertial navigation under the condition, and is the measurement amount with the platform drift angle, utilizes least square method to estimate average drift and platform drift angle in the alignment procedures constantly to be revised in the transduction boat.Compare with classic method, this method has reduced Velocity Updating and two links of position renewal, can greatly shorten the aligning time and improve alignment precision.That the inertial navigation system swaying base open loop alignment methods of indication of the present invention has is accurate, quick, reliable and stable, be easy to advantages such as realization.

(2) alignment methods of the present invention is not upgraded inertial navigation position and speed, reduced to aim to measure computation process, and insensitive to nonlinearity erron; Also be applicable to quiet pedestal and the vehicle-mounted initial Alignment of Inertial Navigation System that waits other applied environment simultaneously, have certain versatility.

Description of drawings

Fig. 1 is the new alignment methods schematic flow sheet of indication of the present invention;

Fig. 2 is a moving alignment equivalence north gyro drift estimation curve in the embodiment of the invention;

Fig. 3 be in the embodiment of the invention moving alignment equivalence day to the gyroscopic drift estimation curve;

Fig. 4 is a moving alignment initial orientation platform drift angle estimation curve in the embodiment of the invention;

Fig. 5 aims in the embodiment of the invention to finish back 202 hours navigation east orientation site error curves;

Fig. 6 aims in the embodiment of the invention to finish back 202 hours navigation north orientation site error curves.

Embodiment

Be that example is set forth specific implementation process of the present invention with initial alignment process under certain type Laser-gym Inertial Navigation System sea trial moored condition below.

The new alignment methods process flow diagram that Fig. 1 carries for invention, detailed process is as follows:

1, imports initial latitude, calculate local rotational-angular velocity of the earth according to initial latitude;

2, the attitude matrix that utilizes coarse alignment to obtain calculates the projection of rotational-angular velocity of the earth on carrier coordinate system, and the projection of rotational-angular velocity of the earth on the carrier coordinate system is deducted from gyroscope output, obtains the relative motion angular velocity of carrier, is shown below:

${\mathrm{\&omega;}}_{\mathrm{nb}}^b=\left[\begin{array}{c}{\mathrm{\&omega;}}_X^b\\ {\mathrm{\&omega;}}_Y^b\\ {\mathrm{\&omega;}}_Z^b\end{array}\right]-{\mathrm{<figure-callout\; id="0"\; label="C\; n\; b"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">C</figure-callout>}}_{nb}^{}\left[\begin{array}{c}0\\ {\mathrm{\&omega;}}_N\\ {\mathrm{\&omega;}}_U\end{array}\right]---\left(9\right)$

3, according to the carrier relative motion angular velocity that obtains in the step (2)

Upgrade hypercomplex number and attitude of carrier matrix and attitude, the expression formula of hypercomplex number renewal process is:

$q\left(t_k\right)=(\cos \frac{{\mathrm{\&Delta;\&theta;}}_0}{2}I+\frac{\sin \frac{{\mathrm{\&Delta;\&theta;}}_0}{2}}{{\mathrm{\&Delta;\&theta;}}_0}[\mathrm{\&Delta;\&theta;}\left]\right)q\left(t_{k-1}\right)---\left(10\right)$

Wherein, q (t _K-1) and q (t _k) be respectively t _K-1And t _kHypercomplex number constantly, I is a unit matrix, Δ θ is an equivalent rotating vector, wherein:

$\left[\mathrm{\&Delta;\&theta;}\right]=\left[\begin{array}{cccc}0& -{\mathrm{\&Delta;\&theta;}}_X& -{\mathrm{\&Delta;\&theta;}}_Y& -{\mathrm{\&Delta;\&theta;}}_Z\\ {\mathrm{\&Delta;\&theta;}}_{\mathrm{<figure-callout\; id="0"\; label="X"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">X</figure-callout>}}& 0& {\mathrm{\&Delta;\&theta;}}_Z& -{\mathrm{\&Delta;\&theta;}}_Y\\ {\mathrm{\&Delta;\&theta;}}_Y& -{\mathrm{\&Delta;\&theta;}}_Z& 0& {\mathrm{\&Delta;\&theta;}}_X\\ {\mathrm{\&Delta;\&theta;}}_Z& {\mathrm{\&Delta;\&theta;}}_Y& -{\mathrm{\&Delta;\&theta;}}_{\mathrm{<figure-callout\; id="0"\; label="X"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">X</figure-callout>}}& 0\end{array}\right]$

${\mathrm{\&Delta;\&theta;}}_0=\sqrt{{\mathrm{\&Delta;\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">X</figure-callout>}}^2+{\mathrm{\&Delta;\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">Y</figure-callout>}}^2+{\mathrm{\&Delta;\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">Z</figure-callout>}}^2}$

${\mathrm{\&Delta;\&theta;}}_X=\underset{t_k}{\overset{t_{k+1}}{\&Integral;}}{\mathrm{\&omega;}}_{\mathrm{nbx}}^b\mathrm{dt}$

${\mathrm{\&Delta;\&theta;}}_Y=\underset{t_k}{\overset{t_{k+1}}{\&Integral;}}{\mathrm{\&omega;}}_{\mathrm{nby}}^b\mathrm{dt}$

${\mathrm{\&Delta;\&theta;}}_Z=\underset{t_k}{\overset{t_{k+1}}{\&Integral;}}{\mathrm{\&omega;}}_{\mathrm{nbz}}^b\mathrm{dt}$

Wherein, For

In three components.

Attitude matrix is provided by the hypercomplex number after upgrading:

$C_n^b=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2& 2(q_1{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2+q_0{q}_3)& 2(q_1{q}_3-q_0{q}_2)\\ 2(q_1{q}_2-q_0{q}_3)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2& 2(q_0{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1+q_2{q}_3)\\ 2(q_1{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3+q_0{q}_2)& 2(q_2{q}_3-q_0{q}_1)& {\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">q</figure-callout>}}_0^2-{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2+{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3^2\end{array}\right]$

Wherein, q ₀, q ₁, q ₂And q ₃Be respectively the hypercomplex number q (t after the renewal _k) four components, i.e. q (t _k)=[q ₀q ₁q ₂q ₃].

4, the acceleration of gravity of degree of will speed up instrumentation amount projects on the mathematical platform coordinate system, obtains the error acceleration and the platform drift angle of inertial navigation:

$\left[\begin{array}{c}{\mathrm{\&Delta;A}}_E\left(t_k\right)\\ \mathrm{\&Delta;}{A}_N\left(t_k\right)\\ {\mathrm{\&Delta;A}}_U\left(t_k\right)\end{array}\right]=C_b^n\left(t_k\right)\left[\begin{array}{c}{A}_X^b\left(t_k\right)\\ A_Y^b\left(t_k\right)\\ A_Z^b\left(t_k\right)\end{array}\right]-\left[\begin{array}{c}0\\ 0\\ g\end{array}\right]---\left(11\right)$

$\left[\begin{array}{c}{\mathrm{\&Delta;\&phi;}}_E\left(t_k\right)\\ {\mathrm{\&Delta;\&phi;}}_N\left(t_k\right)\end{array}\right]=\left[\begin{array}{c}{\mathrm{\&Delta;A}}_N\left(t_k\right)/g\\ -{\mathrm{\&Delta;A}}_E\left(t_k\right)/g\end{array}\right]---\left(12\right)$

5, in step (1), (2), (3), (4) are described resolves under the condition, the ins error equation can be expressed as:

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_E={\mathrm{\&omega;}}_u{\mathrm{\&Delta;\&phi;}}_N-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_U+{\mathrm{\&Delta;\&epsiv;}}_E---\left(13\right)$

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_N=-{\mathrm{\&omega;}}_U{\mathrm{\&Delta;\&phi;}}_E+{\mathrm{\&Delta;\&epsiv;}}_N---\left(14\right)$

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_U={\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_E+{\mathrm{\&Delta;\&epsiv;}}_U---\left(15\right)$

Separate (13)～differential equation group shown in (15) formula, the expression formula that obtains platform error angle in the alignment procedures is:

${\mathrm{\&Delta;\&phi;}}_E={\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">E</figure-callout>}0}\cos {\mathrm{\&omega;}}_{e}t+\frac{{\mathrm{\&Delta;\&epsiv;}}_E-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_{U0}+{\mathrm{\&omega;}}_U{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">N</figure-callout>}0}}{{\mathrm{\&omega;}}_e}\sin {\mathrm{\&omega;}}_{e}t---\left(16\right)$

$+\frac{{\mathrm{\&omega;}}_U{\mathrm{\&Delta;\&epsiv;}}_N-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&epsiv;}}_U}{{{\mathrm{\&omega;}}_e}^2}(1-\cos {\mathrm{\&omega;}}_{e}t)$

${\mathrm{\&Delta;\&phi;}}_N={\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">N</figure-callout>}0}+{\mathrm{\&Delta;\&epsiv;}}_{N}t-\frac{{\mathrm{\&Delta;\&epsiv;}}_E-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">U</figure-callout>}0}+{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">N</figure-callout>}0}}{{{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">e</figure-callout>}}}^2}{\mathrm{\&omega;}}_U(1-\cos {\mathrm{\&omega;}}_{e}t)---\left(17\right)$

$-\frac{{\mathrm{\&omega;}}_U{\mathrm{\&Delta;\&epsiv;}}_N-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&epsiv;}}_U}{{{\mathrm{\&omega;}}_e}^2}{\mathrm{\&omega;}}_U(t-\frac{1}{{\mathrm{\&omega;}}_e}\sin {\mathrm{\&omega;}}_{e}t)$

The t that utilizes formula (12) to obtain _kNorth east as measurement, is carried out least square fitting to formula (16) and formula (17) to the mathematical platform drift angle constantly, can obtain average drift and initial platform drift angle in the whole alignment procedures.

6, aim at the finish time, the platform drift angle and the gyroscopic drift that estimate are revised.Suppose that the gyroscopic drift and the initial platform drift angle that estimate in (3) are respectively With

Then transduction boat platform error angle computing formula constantly is as follows:

${{\mathrm{\&Delta;\&phi;}}_E}^{\&prime;}=\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">E</figure-callout>}0}}\cos {\mathrm{\&omega;}}_{e}t+\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_E}-{\mathrm{\&omega;}}_N\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{U0}}+{\mathrm{\&omega;}}_U\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">N</figure-callout>}0}}}{{\mathrm{\&omega;}}_e}\sin {\mathrm{\&omega;}}_{e}t$

(18)

$+\frac{{\mathrm{\&omega;}}_U\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_N}-{\mathrm{\&omega;}}_N\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_U}}{{{\mathrm{\&omega;}}_e}^2}(1-\cos {\mathrm{\&omega;}}_{e}t)$

${{\mathrm{\&Delta;\&phi;}}_N}^{\&prime;}=\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">N</figure-callout>}0}}+\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_{N}t}-\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_E}-{\mathrm{\&omega;}}_N\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{U0}}+{\mathrm{\&omega;}}_U\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">N</figure-callout>}0}}}{{{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">e</figure-callout>}}}^2}{\mathrm{\&omega;}}_U(1-\cos {\mathrm{\&omega;}}_{e}t)$

(19)

$-\frac{{\mathrm{\&omega;}}_U\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_N}-{\mathrm{\&omega;}}_N\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_U}}{{{\mathrm{\&omega;}}_e}^2}{\mathrm{\&omega;}}_U(t-\frac{1}{{\mathrm{\&omega;}}_e}\sin {\mathrm{\&omega;}}_{e}t)$

${{\mathrm{\&Delta;\&phi;}}_U}^{\&prime;}=\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">U</figure-callout>}0}}+\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_U}t+\frac{\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_E}-{\mathrm{\&omega;}}_N\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">U</figure-callout>}0}}+{\mathrm{\&omega;}}_N\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">N</figure-callout>}0}}}{{{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">e</figure-callout>}}}^2}{\mathrm{\&omega;}}_N(1-\cos {\mathrm{\&omega;}}_{e}t)+\frac{{\mathrm{\&omega;}}_N}{{\mathrm{\&omega;}}_e}\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&phi;}}_{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">E</figure-callout>}0}}\sin {\mathrm{\&omega;}}_{e}t---\left(20\right)$

$+\frac{{\mathrm{\&omega;}}_U\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_N}-{\mathrm{\&omega;}}_N\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&epsiv;}}_U}}{{{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">e</figure-callout>}}}^2}{\mathrm{\&omega;}}_N(t-\frac{1}{{\mathrm{\&omega;}}_e}\sin {\mathrm{\&omega;}}_{e}t)$

The transduction boat is revised attitude matrix according to formula (21) constantly:

$C_b^n=\left[\begin{array}{ccc}1& -{{\mathrm{\&Delta;\&phi;}}_U}^{\&prime;}& {{\mathrm{\&Delta;\&phi;}}_N}^{\&prime;}\\ {{\mathrm{\&Delta;\&phi;}}_U}^{\&prime;}& 1& -{{\mathrm{\&Delta;\&phi;}}_E}^{\&prime;}\\ -{{\mathrm{\&Delta;\&phi;}}_N}^{\&prime;}& {{\mathrm{\&Delta;\&phi;}}_E}^{\&prime;}& 1\end{array}\right]C_b^{n^{\&prime;}}---\left(21\right)$

Wherein,

Be the attitude matrix before revising,

For revising later attitude matrix.

Hypercomplex number is calculated with revised attitude matrix element:

${\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HSA00000401183900022.png,HSA00000401183900031.png"\; state="\{\{state\}\}">q</figure-callout>}}_0=0.5\sqrt{1+C_b^n\left(\mathrm{1,1}\right)+C_b^n\left(\mathrm{2,2}\right)+C_b^n\left(\mathrm{3,3}\right)}---\left(22\right)$

${\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_1=(C_b^n\left(\mathrm{2,3}\right)-C_b^n\left(\mathrm{3,2}\right))/\left(4q_0\right)---\left(23\right)$

${\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_2=(C_b^n\left(\mathrm{3,1}\right)-C_b^n\left(\mathrm{1,3}\right))/\left(4q_0\right)---\left(24\right)$

${\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="HSA00000401183900021.png,HSA00000401183900022.png"\; state="\{\{state\}\}">q</figure-callout>}}_3=(C_b^n\left(\mathrm{1,2}\right)-C_b^n\left(\mathrm{2,1}\right))/\left(4q_0\right)---\left(25\right)$

Wherein,

The expression attitude matrix

The capable n of m row, the drift correction formula is:

$\left[\begin{array}{c}{\mathrm{\&Delta;\&epsiv;}}_X\\ {\mathrm{\&Delta;\&epsiv;}}_Y\\ {\mathrm{\&Delta;\&epsiv;}}_Z\end{array}\right]=C_n^b\left[\begin{array}{c}{\mathrm{\&Delta;\&epsiv;}}_E\\ {\mathrm{\&Delta;\&epsiv;}}_N\\ {\mathrm{\&Delta;\&epsiv;}}_U\end{array}\right]---\left(18\right)$

Wherein, Δ ε _X, Δ ε _Y, Δ ε _ZBe respectively equivalent gyroscopic drift under the body axis system to be compensated.

Shown in Fig. 2～4, inertial navigation system utilizes the method for the invention to carry out 8 hours initial alignments under ship sway pedestal condition, equivalence north gyro drifting convergence arrived-0.0005 degree/hour, the back be stabilized in 2 hours 0.0001 degree/hour, the equivalence day to gyroscopic drift converged to+0.0018 the degree/hour, the back be stabilized in two hours 0.0003 degree/hour, initial orientation platform drift angle has converged to 38 rads, is stabilized in 10 rads in back two hours;

Shown in Fig. 5～6, utilize north east that method of the present invention navigated 202 hours after having aimed to site error, right figure as seen, east orientation site error maximum was 4200 meters in 202 hours, 4150 meters of north orientation error maximums; By the trend of entire curve, the gyroscopic drift precision that estimates in the alignment procedures less than 0.0002 the degree/hour;

The content that is not described in detail in the instructions of the present invention belongs to this area professional and technical personnel's known prior art.

It should be noted last that: above embodiment is the unrestricted technical scheme of the present invention in order to explanation only, and all modifications that does not break away from the spirit and scope of the present invention or local the replacement all should be encompassed in the middle of the claim scope of the present invention.

Claims (4)

1. marine aided inertial navigation system swaying base open loop alignment methods is characterized in that performing step is as follows:

(1) imports initial latitude, calculate local rotational-angular velocity of the earth according to initial latitude;

(2) attitude matrix that utilizes coarse alignment to obtain calculates the projection of rotational-angular velocity of the earth on carrier coordinate system, and the projection of rotational-angular velocity of the earth on the carrier coordinate system is deducted from gyroscope output, obtains carrier relative motion angular velocity;

(3) upgrade hypercomplex number and attitude of carrier matrix and attitude according to the carrier relative motion angular velocity that obtains in the step (2);

(4) according to obtaining the attitude of carrier matrix in the step (3), the output of body axis system accelerometer is transformed under the mathematical platform coordinate system, obtain the east orientation and the north orientation acceleration of carrier under the mathematical platform coordinate system;

(5) east orientation and the north orientation acceleration of carrier under the mathematical platform coordinate system that obtains according to step (4) calculate east orientation, north orientation mathematical platform drift angle;

(6) east orientation that obtains according to step (5), north orientation mathematical platform drift angle measurement amount are carried out least square fitting to the error equation of north east to the mathematical platform drift angle, obtain the equivalent gyroscopic drift under the platform coordinate system;

(7) the equivalent gyroscopic drift under the platform coordinate system that obtains according to step (6) calculate the transduction boat constantly the mathematical platform drift angle and compensate, utilize the attitude of carrier matrix that calculates in the step (3), the equivalent gyroscopic drift under the platform coordinate system that step (6) match is obtained is transformed under the carrier coordinate system and compensates.

2. marine aided inertial navigation system swaying base open loop alignment methods according to claim 1 is characterized in that: the carrier relative motion angular speed calculation formula of described step (2) is as follows:

${\mathrm{\&omega;}}_{\mathrm{nb}}^b=\left[\begin{array}{c}{\mathrm{\&omega;}}_X^b\\ {\mathrm{\&omega;}}_Y^b\\ {\mathrm{\&omega;}}_Z^b\end{array}\right]-C_n^b\left[\begin{array}{c}0\\ {\mathrm{\&omega;}}_N\\ {\mathrm{\&omega;}}_U\end{array}\right]---\left(1\right)$

In the following formula (1)

Be carrier relative motion angular velocity,

Be the output angle speed of three gyroscopic compasss,

Be the attitude matrix of carrier, ω _NAnd ω _UBe respectively the north orientation of local rotational-angular velocity of the earth and day to component.

3. marine aided inertial navigation system swaying base open loop alignment methods according to claim 1 is characterized in that: east orientation, north orientation mathematical platform drift angle are calculated as follows in the described step (5):

$\left[\begin{array}{c}{\mathrm{\&Delta;A}}_E\left(t_k\right)\\ \mathrm{\&Delta;}{A}_N\left(t_k\right)\\ {\mathrm{\&Delta;A}}_U\left(t_k\right)\end{array}\right]=C_b^n\left(t_k\right)\left[\begin{array}{c}{A}_X^b\left(t_k\right)\\ A_Y^b\left(t_k\right)\\ A_Z^b\left(t_k\right)\end{array}\right]-\left[\begin{array}{c}0\\ 0\\ g\end{array}\right]---\left(2\right)$

$\left[\begin{array}{c}{\mathrm{\&Delta;\&phi;}}_E\left(t_k\right)\\ {\mathrm{\&Delta;\&phi;}}_N\left(t_k\right)\end{array}\right]=\left[\begin{array}{c}{\mathrm{\&Delta;A}}_N\left(t_k\right)/g\\ -{\mathrm{\&Delta;A}}_E\left(t_k\right)/g\end{array}\right]---\left(3\right)$

Wherein,

With

Being respectively body is the output of accelerometer, Δ A _E(tk), Δ A _N(t _k) and Δ A _U(t _k) be respectively t _kThe sky, northeast of geographic coordinate system is to acceleration error constantly, and g is a local gravitational acceleration, Δ φ _E(t _k) and Δ φ _N(t _k) be respectively t _kMoment east orientation, north orientation mathematical platform drift angle.

4. marine aided inertial navigation system swaying base open loop alignment methods according to claim 1 is characterized in that: step (6) is described utilizes the process of least square fitting gyroscopic drift as follows by the mathematical platform drift angle:

During a. by step (1) to (5) computational mathematics platform drift angle, the state equation of mathematical platform drift angle is as follows:

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_E={\mathrm{\&omega;}}_u{\mathrm{\&Delta;\&phi;}}_N-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_U+{\mathrm{\&Delta;\&epsiv;}}_E---\left(4\right)$

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_N=-{\mathrm{\&omega;}}_U{\mathrm{\&Delta;\&phi;}}_E+{\mathrm{\&Delta;\&epsiv;}}_N---\left(5\right)$

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_U={\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_E+{\mathrm{\&Delta;\&epsiv;}}_U---\left(6\right)$

Wherein, Δ φ _E, Δ φ _NWith Δ φ _UFor east orientation, north orientation with day to the mathematical platform drift angle, Δ ε _E, Δ ε _NWith Δ ε _UBe respectively equivalent east orientation, north orientation and sky to gyroscopic drift, in alignment procedures, be considered as normal value;

B. separate (4)～differential equation group shown in (6) formula, the mathematic(al) representation that obtains platform error angle in the alignment procedures is:

${\mathrm{\&Delta;\&phi;}}_E={\mathrm{\&Delta;\&phi;}}_{E0}\cos {\mathrm{\&omega;}}_{e}t+\frac{{\mathrm{\&Delta;\&epsiv;}}_E-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_{U0}+{\mathrm{\&omega;}}_U{\mathrm{\&Delta;\&phi;}}_{N0}}{{\mathrm{\&omega;}}_e}\sin {\mathrm{\&omega;}}_{e}t---\left(7\right)$

$+\frac{{\mathrm{\&omega;}}_U{\mathrm{\&Delta;\&epsiv;}}_N-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&epsiv;}}_U}{{{\mathrm{\&omega;}}_e}^2}(1-\cos {\mathrm{\&omega;}}_{e}t)$

${\mathrm{\&Delta;\&phi;}}_N={\mathrm{\&Delta;\&phi;}}_{N0}+{\mathrm{\&Delta;\&epsiv;}}_{N}t-\frac{{\mathrm{\&Delta;\&epsiv;}}_E-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_{U0}+{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&phi;}}_{N0}}{{{\mathrm{\&omega;}}_e}^2}{\mathrm{\&omega;}}_U(1-\cos {\mathrm{\&omega;}}_{e}t)---\left(8\right)$

$-\frac{{\mathrm{\&omega;}}_U{\mathrm{\&Delta;\&epsiv;}}_N-{\mathrm{\&omega;}}_N{\mathrm{\&Delta;\&epsiv;}}_U}{{{\mathrm{\&omega;}}_e}^2}{\mathrm{\&omega;}}_U(t-\frac{1}{{\mathrm{\&omega;}}_e}\sin {\mathrm{\&omega;}}_{e}t)$

Wherein, Δ φ _E0, Δ φ _N0With Δ φ _U0Be respectively initial east orientation, north orientation and sky to the mathematical platform drift angle, t is the navigation time, ω _eBe rotational-angular velocity of the earth.

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