CN102768043A - Integrated attitude determination method without external observed quantity for modulated strapdown system - Google Patents

Abstract

The invention provides an integrated attitude determination method without external observed quantity for a modulated strapdown system. The method comprises the steps of: determining initial position parameters of a carrier by a global positioning system (GPS) and binding the parameters to a navigation computer; acquiring data output by a fiber optic gyros and a quartz accelerometer, and processing the data; setting an inertial measurement unit (IMU) single shaft four position rotation stopping scheme; converting the accelerometer output to a carrier semi-fixed coordinate system; designing an infinite impulse response (IIR) digital high-pass filter, and carrying out filtering on the carrier velocity resolved under a navigation system; subtracting the filtered velocity from a velocity calculated by the modulated strapdown system, and using the difference as a system observed quantity; and estimating attitude information of the modulated strapdown inertial navigation system by a Kalman filtering technique. The method provided by the invention does not need external auxiliary equipment to provide observation information, and can effectively solve the problem of mismatching between the frequency of information supply by the auxiliary equipment and the frequency of cultivation of the modulated strapdown system, and realize integrated attitude determination of the modulated strapdown inertial navigation system.

Description

A kind of modulation type strapdown system assembled gesture that does not have semblance measure is confirmed method

(1) technical field

What the present invention relates to is a kind of measuring method, and in particular a kind of modulation type strapdown system assembled gesture that does not have semblance measure is confirmed method.

(2) background technology

In strapdown inertial navigation system; All inertial measurement component are directly installed on the carrier; What inertance element was exported is exactly angular velocity and the acceleration of carrier with respect to inertial space; By computing machine the acceleration information that records under the carrier coordinate system is transformed into navigation coordinate system and carries out navigation calculation again, be equivalent to utilize the gyroscope output data in computing machine, to make up of the reference of a mathematical platform as navigation calculating.Because the servo control mechanism that strapdown system has platform framework and links to each other, thereby simplified hardware, compare with the platform inertial navigation have that volume is little, in light weight, cost is low, reliability advantages of higher relatively.Just because of above advantage, it has obtained widespread use at Aeronautics and Astronautics, navigation and a lot of civil area.

The rotation modulation technique is a kind of automatic correcting method of inertial navigation system.The modulation type strapdown inertial navigation system adds rotating mechanism and angle-measuring equipment in the outside of SINS, and navigation calculation still adopts the inertial navigation algorithm.It need not introduce external calibration information, can be automatically the normal value deviation of inertia device in the system be averaged, and reaches and offsets the influence of drift to system accuracy.Thereby can improve the precision that inertial navigation system works long hours, give full play to the advantage of inertial navigation " autonomous type ".Use the rotation modulation technique; Can also use the inertia device of lower accuracy; Constitute the inertial navigation system of degree of precision, help reducing the cost of inertial navigation system, simultaneously owing to introduce the observability degree that extraneous motion can improve the inertial navigation system partial parameters effectively.

The initial attitude error is one of main error source of inertial navigation system, and the error of initial attitude not only shows on the attitude index the influence of systematic error, and shows obtaining of speed and positional information.The precision of the accuracy affects navigation that initial attitude is confirmed.Motion state by pedestal is divided, and the initial attitude of inertial navigation system confirms that method can be divided into two types, and promptly quiet pedestal initial attitude is confirmed and moving pedestal initial attitude is confirmed.So-called quiet pedestal initial attitude confirms to be meant that inertia measurement is combined in the initial attitude information of confirming carrier under the static fully situation of carrier.At present, this technology is comparative maturity, can reach quite high precision through multiposition method and Kalman filtering.But quiet pedestal initial attitude confirms that technology can not adapt to their rapid-action requirements for numerous airborne and shipborne weapons system, confirms method so the emphasis of current research mainly concentrates on moving pedestal initial attitude.So-called moving pedestal initial attitude confirms to be meant that inertia measurement is combined under the situation of carrier movement or external disturbance accomplishes.Its difficult point is to construct wave filter quick, stable, strong robustness, and the observability and the observability degree of filter status are estimated, thus the devise optimum wave filter.According to the situation of using external information, can confirm that method is divided three classes with moving the pedestal initial attitude: outside damp type, delivery type and external auxiliary attitude information formula.

The function of wave filter is exactly to allow the signal of a certain component frequency to pass through smoothly, and the signal of other a part of frequency then receives bigger inhibition, and it comes down to a frequency selection circuit.Infinite impulse response (IIR) wave filter belongs to classical wave filter, supposes that promptly the useful component in the input signal occupies different frequency bands separately with the composition that hope is removed.This supposition has met objective law to a certain extent, and for Hi-pass filter, the HFS of sample sequence comprises useful signal, and low frequency part then mainly is by Schuler period vibration control.Therefore through Hi-pass filter reasonable in design, just can reach the purpose of removing the Schuler period vibration.

(3) summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiency of prior art, provide a kind of modulation type strapdown system assembled gesture that does not have semblance measure to confirm method.

Technical solution of the present invention is: a kind of modulation type strapdown system assembled gesture that does not have semblance measure is confirmed method; It is characterized in that adopting the Inertial Measurement Unit uniaxial four-position rotation and stop; The method for distilling of carrier instantaneous velocity is proposed; According to the error characteristics of instantaneous velocity, adopt the Schuler period in infinite impulse response (IIR) the digital high-pass filter filtering bearer rate, the velocity information that filtered velocity information and inertial reference calculation are gone out is made difference afterwards as the observed quantity of system; Adopt Kalman Filter Technology to realize the assembled gesture of SINS, its concrete steps are following:

(1) confirms the initial position parameters of carrier through GPS, they are bound to navigational computer;

(2) the modulation type SINS carries out preheating and prepares, and gathers data that fibre optic gyroscope and quartz accelerometer export and data are handled;

(3) IMU adopts 4 commentaries on classics to stop the transposition scheme that order is a swing circle (like accompanying drawing 2);

Order 1, IMU is set out by position A, turn clockwise 180 ° to the position B, and in the position B residence time T _sOrder 2, IMU is set out by position B, the 90 ° of in-position C that turn clockwise, and in the position C residence time T _sOrder 3, IMU is set out by position C, be rotated counterclockwise 180 ° to the position D, the D residence time T in the position _sOrder 4, IMU are set out by position D and are rotated counterclockwise 90 ° and get back to position A, and in the position A residence time T _sMove according to the sequential loop of order 1～4 then.

Carry out at 180 ° of the each rotations of IMU or 90 ° of intervals.To symmetric position, on these two symmetrical positions, the constant value drift of inertia sensitive element can be cancelled out each other when carrying out navigation calculating on the horizontal direction from 180 ° of rotated position.Arrive the another one reposition through half-twist.

(4) output of degree of will speed up meter is transformed into carrier semi-fixed axes system, utilizes the integral element in the modulation type SINS to extract carrier instantaneous linear velocity information;

1) introduces carrier semi-fixed axes system

With the naval vessel center of gravity is that the carrier semi-fixed axes is an initial point, longitudinal axis OY _dPoint to the main of naval vessel and go to direction transverse axis OX _dBe parallel to surface level perpendicular to the longitudinal axis, point to the starboard direction when not having pitching on the naval vessel.Z-axis OZ _dVertical with preceding diaxon, upwards be just (like accompanying drawing 3) along the ship vertical pivot.ψ wherein _GBe the base course angle, the γ angle is course angle of oscillation (is yaw angle definition itself and base course angle in the same way for just).The introducing that the carrier semi-fixed axes is makes measurement result and angular motion break away from basically, can describe the instantaneous line motion on naval vessel exactly, therefore adopts carrier semi-fixed axes system as studying the base coordinate system that the instantaneous line in naval vessel moves or is called translation.

2) set up the transition matrix that Inertial Measurement Unit coordinate system and carrier semi-fixed axes are

At first set up between carrier coordinate system and the carrier semi-fixed axes system and differ three rotation angle, can be considered semi-fixed axes system and after three rotations, overlap with carrier coordinate system, three angles are respectively: pitch angle α, roll angle β and yaw angle γ (like accompanying drawing 4).Carrier coordinate system (b system) is transformed into the direction cosine matrix

of carrier semi-fixed axes system (d system)

$C_b^d=\left[\begin{array}{ccc}\cos \mathrm{\γ}\cos \mathrm{\β}& \sin \mathrm{\γ}\cos \mathrm{\α}+\cos \mathrm{\γ}\sin \mathrm{\β}\sin \mathrm{\α}& \sin \mathrm{\γ}\sin \mathrm{\α}-\cos \mathrm{\γ}\sin \mathrm{\β}\cos \mathrm{\α}\\ -\sin \mathrm{\γ}\cos \mathrm{\β}& \cos \mathrm{\γ}\cos \mathrm{\α}+\sin \mathrm{\γ}\sin \mathrm{\β}\sin \mathrm{\α}& \cos \mathrm{\γ}\sin \mathrm{\α}-\sin \mathrm{\γ}\sin \mathrm{\β}\cos \mathrm{\α}\\ \sin \mathrm{\β}& -\cos \mathrm{\β}\sin \mathrm{\α}& \cos \mathrm{\β}\cos \mathrm{\α}\end{array}\right]$

Existing inertial navigation system can provide comparatively accurate attitude angle information; Wherein two attitude angle information of level are pitch angle information and roll angle information; And course information provides course angle information ψ; This is different from yaw angle γ, but the operator on naval vessel can provide base course information ψ accurately _G, can get

γ＝ψ-ψ _G

In the accounting equation with γ substitution

, can obtain the direction cosine matrix that carrier coordinate system is transformed into carrier semi-fixed axes system.

Because there is the transposition campaign around azimuth axis in the relative carrier of Inertial Measurement Unit, so the transition matrix between inertia measurement coordinate system (s coordinate system) and the carrier coordinate system can utilize following formula to calculate:

$C_s^b=\left[\begin{array}{ccc}\cos \mathrm{\&omega;t}& -\sin \mathrm{\&omega;<figure-callout\; id="0"\; label="t"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">t</figure-callout>}& 0\\ \sin \mathrm{\&omega;t}& \cos \mathrm{\&omega;<figure-callout\; id="0"\; label="t"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">t</figure-callout>}& 0\\ 0& 0& 1\end{array}\right]$

In the formula, ω t representes the relative angle relation of the relative carrier coordinate system of Inertial Measurement Unit.Therefore can obtain the direction cosine matrix that the Inertial Measurement Unit coordinate system is transformed into carrier semi-fixed axes system:

$C_s^d=C_b^d{C}_s^b$

(5) infinite impulse response digital high-pass filter (IIR) reasonable in design, the bearer rate that navigation system is calculated is down carried out high-pass filtering and is handled;

1) confirms the technical indicator of institute's design digital Hi-pass filter

High-pass digital filter f _P1, f _S1, δ _p, δ _sTechnical indicator be according to signal characteristic and SF f _sGiven.Wherein, f _P1Be cut-off frequecy of passband, f _S1Be stopband cutoff frequency, δ _pBe passband ripple, promptly depart from the maximal value of unity gain in the filter transmission band, the passband edge gain is 1-δ _p, δ _sBe stop band ripple, promptly depart from the maximal value of unity gain in the filter stop band, the gain of stopband edge place wave filter is δ _sThe attenuation alpha of passband and stopband _p, α _sBe defined as-20log (1-δ respectively _p) ,-20log (1-δ _s).

The Schuler period oscillator signal belongs to low frequency signal comparatively speaking, and be 84.4 minutes oscillation period.And the instantaneous line motion in naval vessel is caused that by the marine environment factor topmost generation reason is the influence of wave, so the instantaneous line motion in naval vessel is frequency and the to-and-fro movement unanimous on the whole of wave frequency.And the motion of the instantaneous line in naval vessel belongs to high frequency motion with respect to the navigation campaign on naval vessel, and the period of motion is shorter, and generally about 1.5 seconds～10 seconds, frequency is 0.67 hertz.Different according on the kinetic characteristic of heave swaying surge motion and naval vessel routine work campaign, the technical requirement of the wave filter that designing institute needs, concrete design objective is adjusted according to filter effect in process of the test, is as the criterion to reach the optimal filtering effect.

2) technical indicator is transformed into analog filter from digital filter

Bilinearity transform method is adopted in the conversion of technical indicator from the analog filter to the digital filter, and the technical indicator of design digital Hi-pass filter is f _P1, f _S1, δ _p, δ _s, t _s=0.0102.At first should obtain digital marginal frequency Ω, because 2 π are corresponding SF f _s, and f _s=1/t _sSo, have:

$\frac{f_{p1}}{f_s}=\frac{{\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">p</figure-callout>}1}}{2\mathrm{\&pi;}}$

$\frac{f_{s1}}{f_s}=\frac{{\mathrm{\&Omega;}}_{s1}}{2\mathrm{\&pi;}}$

The institute in the hope of:

Ω _s1＝2πf _s1/f _s

Ω _p1＝2πf _p1/f _s

Frequency inverted according to bilinearity transform method concerns ω=2f _sTan (Ω/2) continues conversion to be had:

${\mathrm{\&Omega;}}_p=\tan \left(\frac{{\mathrm{\&omega;}}_p}{2}\right)$

${\mathrm{\&Omega;}}_s=\tan \left(\frac{{\mathrm{\&omega;}}_s}{2}\right)$

The technical indicator of digital high-pass filter just is converted into the technical indicator of mimic high pass filter with this.

Assembled gesture error model when (6) setting up the carrier moored condition according to the moving pedestal error equation of modulation type SINS, the speed that directly calculates with speed and the modulation type SINS that obtains after the high-pass filtering is made difference and is then measured as systematic perspective.Utilize Kalman Filter Technology to realize confirming of modulation type SINS assembled gesture;

Foundation is made difference afterwards as the Kalman filter model of observed quantity with the speed that directly calculates through horizontal velocity after the high-pass filtering and modulation type SINS;

The state error of modulation type SINS is described with linear first-order differential equation:

$\stackrel{\&CenterDot;}{X}=\mathrm{AX}+\mathrm{BW}$

Wherein, X is the state vector of system; A and B are respectively the state matrix and the noise matrix of system; W 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:

$A=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;2}^1& {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\&times;3}& {\tilde{T}}_{2\&times;2}& {\mathrm{<figure-callout\; id="2"\; label="O"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{2\&times;3}\\ {\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;2}^2& {\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;3}^3& {\mathrm{<figure-callout\; id="3"\; label="O"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{3\&times;2}& {\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">T</figure-callout>}}_{3\&times;3}\\ {\mathrm{<figure-callout\; id="5"\; label="O"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{5\&times;2}& {\mathrm{<figure-callout\; id="5"\; label="O"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{5\&times;3}& {\mathrm{<figure-callout\; id="5"\; label="O"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{5\&times;2}& {\mathrm{<figure-callout\; id="5"\; label="O"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{5\&times;3}\end{array}\right]$

${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;2}^1=\left[\begin{array}{cc}\frac{V_N}{R_n}\tan L^{\&prime;}& 2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E}{R_n}\tan L\\ -(2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{2V_E}{R_n}\tan L)& 0\end{array}\right]$

${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;2}^2=\begin{array}{}\left[\begin{array}{cc}0& -\frac{1}{R_m}\\ \frac{1}{{\mathrm{<figure-callout\; id="0"\; label="R\; n"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">R</figure-callout>}}_n}& 0\\ \frac{\tan \mathrm{<figure-callout\; id="0"\; label="L\; R\; n"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">L</figure-callout>}}{R_n}& 0\end{array}\right]\end{array}$

${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;3}^3=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E\tan L}{R_n}& -({\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R_n})\\ -({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E\tan L}{R_n})& 0& -\frac{V_N}{R_m}\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R_n}& \frac{V_{\mathrm{<figure-callout\; id="0"\; label="N\; R\; m"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">N</figure-callout>}}}{R_m}& 0\end{array}\right]$

${\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\&times;3}=\left[\begin{array}{ccc}0& -f_U& f_N\\ f_U& 0& f_E\end{array}\right]$

${\tilde{T}}_{2\&times;2}=\left[\begin{array}{cc}{T}_{11}& T_{12}\\ T_{21}& T_{22}\end{array}\right]$

${\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">T</figure-callout>}}_{3\&times;6}=\left[\begin{array}{ccc}-T_{11}& -T_{12}& -T_{13}\\ -T_{21}& -T_{22}& -T_{23}\\ -T_{31}& -T_{32}& -T_{33}\end{array}\right]$

V _E, V _NThe speed of representing east orientation, north orientation respectively; ω _x, ω _y, ω _zThree input angular velocities representing gyro 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 representes local latitude; L ' expression moored condition initial time carrier latitude information; f _E, f _N, f _UBe expressed as respectively navigation coordinate system down east orientation, north orientation, day to specific force.

2) set up the measurement equation of Kalman filtering:

The measurement equation of describing the modulation type SINS with linear first-order differential equation is following:

Z＝HX+V

Wherein: Z representes the measurement vector of system; H representes the measurement matrix of system; V representes the measurement noise of system;

The system measurements matrix is:

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

Amount is measured as the east orientation speed V that the modulation type SINS resolves _E, north orientation speed V _NHandle the east orientation speed obtain respectively with through high-pass filtering

North orientation speed

Poor:

$Z=\left[\begin{array}{c}{V}_E-{\tilde{V}}_E\\ V_N-{\tilde{V}}_N\end{array}\right]$

The present invention's advantage compared with prior art is: the present invention has broken in the modulation type SINS assembled gesture deterministic process external unit provides information frequency and modulation type SINS that information frequency this problem that do not match is provided; In the modulation type SINS under the Inertial Measurement Unit four-position rotation and stop scheme; This characteristic of high frequency components information of waving and swinging motion of utilizing the Schuler period information that has low frequency in the carrier instantaneous velocity information and carrier moored condition to exist; Proposition utilizes the Schuler period item in the IIR digital high-pass filter filtering carrier instantaneous velocity information; Filtered speed and inertial reference calculation speed are done the observed quantity of difference back as system, adopt Kalman Filter Technology to realize the assembled gesture of SINS.Therefore not needing external unit is that it provides reference information.

Effect to the present invention is useful is explained as follows:

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

Carrier is done the three-axis swinging motion.Carrier waves around pitch axis, axis of roll and course axle with sinusoidal rule, and its mathematical model is:

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

Wherein: θ, γ, ψ represent the angle variables of waving of pitch angle, roll angle and course angle respectively; θ _m, γ _m, ψ _mThe angle amplitude is waved in expression accordingly respectively; ω _θ, ω _γ, ω _ψRepresent corresponding angle of oscillation frequency respectively; φ _θ, φ _γ, φ _ψRepresent corresponding initial phase respectively; ω _i=2 π/T _i, i=θ, γ, ψ, T _iRepresent corresponding rolling period, k is the angle, initial heading.Get during emulation: θ _m=6 °, γ _m=12 °, ψ _m=10 °, T _θ=8s, T _γ=10s, T _ψ=6s, k=0 °.

The swaying of carrier, surging and hang down and swing the linear velocity that causes and be:

In the formula, i=x, y, z be geographic coordinate system east orientation, north orientation, day to.

is that [0,2 π] goes up the equally distributed random phase of obedience.

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

The initial attitude error angle: three initial attitude error angles are zero;

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;

Gyroscope random walk:

Accelerometer bias: 10 ^-4g ₀

Accelerometer noise: 10 ^-6g ₀

Constant: π=3.1415926;

The mathematical model parameter of IMU four-position rotation and stop scheme:

The dead time of four positions: T _s=5min;

The time that consumes when rotating 180 ° and 90 °: T _z=12s;

Rotate in the process of 180 ° and 90 °, the acceleration and deceleration time in each transposition respectively is 4s;

Utilize method of the present invention to obtain modulation type strapdown system misalignment curve, as shown in Figure 5.The result shows and waves under the disturbed condition, adopts the inventive method can obtain higher alignment precision.

(4) description of drawings

Fig. 1 confirms method flow diagram for a kind of modulation type strapdown system assembled gesture that does not have semblance measure of the present invention;

Fig. 2 is an IMU uniaxial four-position rotation and stop of the present invention;

Fig. 3 is that definition carrier semi-fixed axes of the present invention is;

Fig. 4 is the transformational relation of carrier coordinate system of the present invention and carrier semi-fixed axes system;

Fig. 5 is the misalignment curve of the modulation type strapdown system Kalman Filter Estimation of no semblance measure of the present invention.

(5) embodiment

Describe in detail below in conjunction with the accompanying drawing specific embodiments of the invention:

(1) confirms the initial position parameters of carrier through GPS, they are bound to navigational computer;

(2) the modulation type SINS carries out preheating and prepares, and gathers data that fibre optic gyroscope and quartz accelerometer export and data are handled;

(3) IMU adopts 4 commentaries on classics to stop the transposition scheme that order is a swing circle (like accompanying drawing 2);

Order 1, IMU is set out by position A, turn clockwise 180 ° to the position B, and in the position B residence time T _sOrder 2, IMU is set out by position B, the 90 ° of in-position C that turn clockwise, and in the position C residence time T _sOrder 3, IMU is set out by position C, be rotated counterclockwise 180 ° to the position D, the D residence time T in the position _sOrder 4, IMU are set out by position D and are rotated counterclockwise 90 ° and get back to position A, and in the position A residence time T _sMove according to the sequential loop of order 1～4 then.

Carry out at 180 ° of the each rotations of IMU or 90 ° of intervals.To symmetric position, on these two symmetrical positions, the constant value drift of inertia sensitive element can be cancelled out each other when carrying out navigation calculating on the horizontal direction from 180 ° of rotated position.Arrive the another one reposition through half-twist.

(4) output of degree of will speed up meter is transformed into carrier semi-fixed axes system, utilizes the integral element in the modulation type SINS to extract carrier instantaneous linear velocity information;

1) introduces carrier semi-fixed axes system

With the naval vessel center of gravity is that the carrier semi-fixed axes is an initial point, longitudinal axis OY _dPoint to the main of naval vessel and go to direction transverse axis OX _dBe parallel to surface level perpendicular to the longitudinal axis, point to the starboard direction when not having pitching on the naval vessel.Z-axis OZ _dVertical with preceding diaxon, upwards be just (like accompanying drawing 3) along the ship vertical pivot.ψ wherein _GBe the base course angle, the γ angle is course angle of oscillation (is yaw angle definition itself and base course angle in the same way for just).The introducing that the carrier semi-fixed axes is makes measurement result and angular motion break away from basically, can describe the instantaneous line motion on naval vessel exactly, therefore adopts carrier semi-fixed axes system as studying the base coordinate system that the instantaneous line in naval vessel moves or is called translation.

2) set up the transition matrix that Inertial Measurement Unit coordinate system and carrier semi-fixed axes are

At first set up between carrier coordinate system and the carrier semi-fixed axes system and differ three rotation angle, can be considered semi-fixed axes system and after three rotations, overlap with carrier coordinate system, three angles are respectively: pitch angle α, roll angle β and yaw angle γ (like accompanying drawing 4).Carrier coordinate system (b system) is transformed into the direction cosine matrix

of carrier semi-fixed axes system (d system)

$C_b^d=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&beta;}& \sin \mathrm{\&gamma;}\cos \mathrm{\&alpha;}+\cos \mathrm{\&gamma;}\sin \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \sin \mathrm{\&gamma;}\sin \mathrm{\&alpha;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}\\ -\sin \mathrm{\&gamma;}\cos \mathrm{\&beta;}& \cos \mathrm{\&gamma;}\cos \mathrm{\&alpha;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \cos \mathrm{\&gamma;}\sin \mathrm{\&alpha;}-\sin \mathrm{\&gamma;}\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}\\ \sin \mathrm{\&beta;}& -\cos \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \cos \mathrm{\&beta;}\cos \mathrm{\&alpha;}\end{array}\right]---\left(1\right)$

Existing inertial navigation system can provide comparatively accurate attitude angle information; Wherein two attitude angle information of level are pitch angle information and roll angle information; And course information provides course angle information ψ; This is different from yaw angle γ, but the operator on naval vessel can provide base course information ψ accurately _G, can get

γ＝ψ-ψ _G (2)

In the accounting equation with γ substitution

, can obtain the direction cosine matrix that carrier coordinate system is transformed into carrier semi-fixed axes system.

Because there is the transposition campaign around azimuth axis in the relative carrier of Inertial Measurement Unit, so the transition matrix between inertia measurement coordinate system (s coordinate system) and the carrier coordinate system can utilize following formula to calculate:

$C_s^b=\left[\begin{array}{ccc}\cos \mathrm{\&omega;t}& -\sin \mathrm{\&omega;<figure-callout\; id="0"\; label="t"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">t</figure-callout>}& 0\\ \sin \mathrm{\&omega;t}& \cos \mathrm{\&omega;<figure-callout\; id="0"\; label="t"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">t</figure-callout>}& 0\\ 0& 0& 1\end{array}\right]---\left(3\right)$

In the formula, ω t representes the relative angle relation of the relative carrier coordinate system of Inertial Measurement Unit.Therefore can obtain the direction cosine matrix that the Inertial Measurement Unit coordinate system is transformed into carrier semi-fixed axes system:

$C_s^d=C_b^d{C}_s^b---\left(4\right)$

(5) infinite impulse response digital high-pass filter (IIR) reasonable in design, the bearer rate that navigation system is calculated is down carried out high-pass filtering and is handled;

1) confirms the technical indicator of institute's design digital Hi-pass filter

High-pass digital filter f _P1, f _S1, δ _p, δ _sTechnical indicator be according to signal characteristic and SF f _sGiven.Wherein, f _P1Be cut-off frequecy of passband, f _S1Be stopband cutoff frequency, δ _pBe passband ripple, promptly depart from the maximal value of unity gain in the filter transmission band, the passband edge gain is 1-δ _p, δ _sBe stop band ripple, promptly depart from the maximal value of unity gain in the filter stop band, the gain of stopband edge place wave filter is δ _sThe attenuation alpha of passband and stopband _p, α _sBe defined as-20log (1-δ respectively _p) ,-20log (1-δ _s).

The Schuler period oscillator signal belongs to low frequency signal comparatively speaking, and be 84.4 minutes oscillation period.And the instantaneous line motion in naval vessel is caused that by the marine environment factor topmost generation reason is the influence of wave, so the instantaneous line motion in naval vessel is frequency and the to-and-fro movement unanimous on the whole of wave frequency.And the motion of the instantaneous line in naval vessel belongs to high frequency motion with respect to the navigation campaign on naval vessel, and the period of motion is shorter, and generally about 1.5 seconds～10 seconds, frequency is 0.67 hertz.Different according on the kinetic characteristic of heave swaying surge motion and naval vessel routine work campaign, the technical requirement of the wave filter that designing institute needs, concrete design objective is adjusted according to filter effect in process of the test, is as the criterion to reach the optimal filtering effect.

2) technical indicator is transformed into analog filter from digital filter

Bilinearity transform method is adopted in the conversion of technical indicator from the analog filter to the digital filter, and the technical indicator of design digital Hi-pass filter is f _P1, f _S1, δ _p, δ _s, t _s=0.0102.At first should obtain digital marginal frequency Ω, because 2 π are corresponding SF f _s, and f _s=1/t _sSo, have:

$\frac{f_{p1}}{f_s}=\frac{{\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">p</figure-callout>}1}}{2\mathrm{\&pi;}}$ (5)

$\frac{f_{s1}}{f_s}=\frac{{\mathrm{\&Omega;}}_{s1}}{2\mathrm{\&pi;}}$

The institute in the hope of:

Ω _s1＝2πf _s1/f _s (6)

Ω _p1＝2πf _p1/f _s

Frequency inverted according to bilinearity transform method concerns ω=2f _sTan (Ω/2) continues to be converted to:

${\mathrm{\&Omega;}}_p=\tan \left(\frac{{\mathrm{\&omega;}}_p}{2}\right)$ (7)

${\mathrm{\&Omega;}}_s=\tan \left(\frac{{\mathrm{\&omega;}}_s}{2}\right)$

The technical indicator of digital high-pass filter just is converted into the technical indicator of mimic high pass filter with this.

Assembled gesture error model when (6) setting up the carrier moored condition according to the moving pedestal error equation of modulation type SINS, the speed that directly calculates with speed and the modulation type SINS that obtains after the high-pass filtering is made difference and is then measured as systematic perspective.Utilize Kalman Filter Technology to realize confirming of modulation type SINS assembled gesture;

Foundation is made difference afterwards as the Kalman filter model of observed quantity with the speed that directly calculates through horizontal velocity after the high-pass filtering and modulation type SINS;

1) set up the state equation of Kalman filtering:

The state error of modulation type SINS is described with linear first-order differential equation:

$\stackrel{\&CenterDot;}{X}=\mathrm{AX}+\mathrm{BW}---\left(8\right)$

Wherein, X is the state vector of system; A and B are respectively the state matrix and the noise matrix of system; W 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 (10)

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:

$A=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;2}^1& {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\&times;3}& {\tilde{T}}_{2\&times;2}& {\mathrm{<figure-callout\; id="2"\; label="O"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{2\&times;3}\\ {\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;2}^2& {\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;3}^3& {\mathrm{<figure-callout\; id="3"\; label="O"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{3\&times;2}& {\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">T</figure-callout>}}_{3\&times;3}\\ {\mathrm{<figure-callout\; id="5"\; label="O"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{5\&times;2}& {\mathrm{<figure-callout\; id="5"\; label="O"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{5\&times;3}& {\mathrm{<figure-callout\; id="5"\; label="O"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{5\&times;2}& {\mathrm{<figure-callout\; id="5"\; label="O"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">O</figure-callout>}}_{5\&times;3}\end{array}\right]---\left(11\right)$

${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\&times;2}^1=\left[\begin{array}{cc}\frac{V_N}{R_n}\tan L^{\&prime;}& 2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E}{R_n}\tan L\\ -(2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{2V_E}{R_n}\tan L)& 0\end{array}\right]---\left(12\right)$

${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;2}^2=\begin{array}{c}\left[\begin{array}{cc}0& -\frac{1}{R_m}\\ \frac{1}{{\mathrm{<figure-callout\; id="0"\; label="R\; n"\; filenames="HSA00000733656800032.png"\; state="\{\{state\}\}">R</figure-callout>}}_n}& 0\\ \frac{\tan L}{R_n}& 0\end{array}\right]---\left(13\right)\end{array}$

${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\&times;3}^3=\left[\begin{array}{ccc}0& {\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E\tan L}{R_n}& -({\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R_n})\\ -({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E\tan L}{R_n})& 0& -\frac{V_N}{R_m}\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R_n}& \frac{V_N}{R_m}& 0\end{array}\right]---\left(14\right)$

${\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\&times;3}=\left[\begin{array}{ccc}0& -f_U& f_N\\ f_U& 0& f_E\end{array}\right]---\left(15\right)$

${\tilde{T}}_{2\&times;2}=\left[\begin{array}{cc}{T}_{11}& T_{12}\\ T_{21}& T_{22}\end{array}\right]---\left(16\right)$

${\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HSA00000733656800021.png,HSA00000733656800032.png"\; state="\{\{state\}\}">T</figure-callout>}}_{3\&times;6}=\left[\begin{array}{ccc}-T_{11}& -T_{12}& -T_{13}\\ -T_{21}& -T_{22}& -T_{23}\\ -T_{31}& -T_{32}& -T_{33}\end{array}\right]---\left(17\right)$

V _E, V _NThe speed of representing east orientation, north orientation respectively; ω _x, ω _y, ω _zThree input angular velocities representing gyro 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 representes local latitude; L ' expression moored condition initial time carrier latitude information; f _E, f _N, f _UBe expressed as respectively navigation coordinate system down east orientation, north orientation, day to specific force.

2) set up the measurement equation of Kalman filtering:

The measurement equation of describing the modulation type SINS with linear first-order differential equation is following:

Z＝HX+V (18)

Wherein: Z representes that the measurement vector H of system representes the measurement matrix of system; V representes the measurement noise of system;

The system measurements matrix is:

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

Amount is measured as the east orientation speed V that the modulation type SINS resolves _E, north orientation speed V _NHandle the east orientation speed obtain respectively with through high-pass filtering

North orientation speed Poor:

$Z=\left[\begin{array}{c}{V}_E-{\tilde{V}}_E\\ V_N-{\tilde{V}}_N\end{array}\right]---\left(20\right)$ 。

Claims (5)

1. a modulation type strapdown system assembled gesture that does not have semblance measure is confirmed method, it is characterized in that may further comprise the steps:

(1) confirms the initial position parameters of carrier through GPS, they are bound to navigational computer;

(2) the modulation type SINS carries out preheating and prepares, and gathers data that fibre optic gyroscope and quartz accelerometer export and data are handled;

(3) IMU adopts 4 commentaries on classics to stop the transposition scheme that order is a swing circle (like accompanying drawing 2);

Order 1, IMU is set out by position A, turn clockwise 180 ° to the position B, and in the position B residence time T _sOrder 2, IMU is set out by position B, the 90 ° of in-position C that turn clockwise, and in the position C residence time T _sOrder 3, IMU is set out by position C, be rotated counterclockwise 180 ° to the position D, the D residence time T in the position _sOrder 4, IMU are set out by position D and are rotated counterclockwise 90 ° and get back to position A, and in the position A residence time T _sMove according to the sequential loop of order 1～4 then.

Carry out at 180 ° of the each rotations of IMU or 90 ° of intervals.To symmetric position, on these two symmetrical positions, the constant value drift of inertia sensitive element can be cancelled out each other when carrying out navigation calculating on the horizontal direction from 180 ° of rotated position.Arrive the another one reposition through half-twist.

(4) output of degree of will speed up meter is transformed into carrier semi-fixed axes system, utilizes the integral element in the modulation type SINS to extract carrier instantaneous linear velocity information;

1) introduces carrier semi-fixed axes system

With the naval vessel center of gravity is that the carrier semi-fixed axes is an initial point, longitudinal axis OY _dPoint to the main of naval vessel and go to direction transverse axis OX _dBe parallel to surface level perpendicular to the longitudinal axis, point to the starboard direction when not having pitching on the naval vessel.Z-axis OZ _dVertical with preceding diaxon, upwards be just (like accompanying drawing 3) along the ship vertical pivot.ψ wherein _GBe the base course angle, the γ angle is course angle of oscillation (is yaw angle definition itself and base course angle in the same way for just).The introducing that the carrier semi-fixed axes is makes measurement result and angular motion break away from basically, can describe the instantaneous line motion on naval vessel exactly, therefore adopts carrier semi-fixed axes system as studying the base coordinate system that the instantaneous line in naval vessel moves or is called translation.

2) set up the transition matrix that Inertial Measurement Unit coordinate system and carrier semi-fixed axes are

At first set up between carrier coordinate system and the carrier semi-fixed axes system and differ three rotation angle, can be considered semi-fixed axes system and after three rotations, overlap with carrier coordinate system, three angles are respectively: pitch angle α, roll angle β and yaw angle γ (like accompanying drawing 4).Carrier coordinate system (b system) is transformed into the direction cosine matrix

of carrier semi-fixed axes system (d system)

$C_b^d=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&beta;}& \sin \mathrm{\&gamma;}\cos \mathrm{\&alpha;}+\cos \mathrm{\&gamma;}\sin \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \sin \mathrm{\&gamma;}\sin \mathrm{\&alpha;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}\\ -\sin \mathrm{\&gamma;}\cos \mathrm{\&beta;}& \cos \mathrm{\&gamma;}\cos \mathrm{\&alpha;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \cos \mathrm{\&gamma;}\sin \mathrm{\&alpha;}-\sin \mathrm{\&gamma;}\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}\\ \sin \mathrm{\&beta;}& -\cos \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \cos \mathrm{\&beta;}\cos \mathrm{\&alpha;}\end{array}\right]$

Existing inertial navigation system can provide comparatively accurate attitude angle information; Wherein two attitude angle information of level are pitch angle information and roll angle information; And course information provides course angle information ψ; This is different from yaw angle γ, but the operator on naval vessel can provide base course information ψ accurately _G, can get

γ＝ψ-ψ _G

In the accounting equation with γ substitution

, can obtain the direction cosine matrix that carrier coordinate system is transformed into carrier semi-fixed axes system.

Because there is the transposition campaign around azimuth axis in the relative carrier of Inertial Measurement Unit, so the transition matrix between inertia measurement coordinate system (s coordinate system) and the carrier coordinate system can utilize following formula to calculate:

$C_s^b=\left[\begin{array}{ccc}\cos \mathrm{\&omega;t}& -\sin \mathrm{\&omega;t}& 0\\ \sin \mathrm{\&omega;t}& \cos \mathrm{\&omega;t}& 0\\ 0& 0& 1\end{array}\right]$

In the formula, ω t representes the relative angle relation of the relative carrier coordinate system of Inertial Measurement Unit.Therefore can obtain the direction cosine matrix that the Inertial Measurement Unit coordinate system is transformed into carrier semi-fixed axes system:

$C_s^d=C_b^d{C}_s^b$

(5) infinite impulse response digital high-pass filter (IIR) reasonable in design, the bearer rate that navigation system is calculated is down carried out high-pass filtering and is handled;

1) confirms the technical indicator of institute's design digital Hi-pass filter

High-pass digital filter f _P1, f _S1, δ _p, δ _sTechnical indicator be according to signal characteristic and SF f _sGiven.Wherein, f _P1Be cut-off frequecy of passband, f _S1Be stopband cutoff frequency, δ _pBe passband ripple, promptly depart from the maximal value of unity gain in the filter transmission band, the passband edge gain is 1-δ _p, δ _sBe stop band ripple, promptly depart from the maximal value of unity gain in the filter stop band, the gain of stopband edge place wave filter is δ _sThe attenuation alpha of passband and stopband _p, α _sBe defined as-20log (1-δ respectively _p) ,-20log (1-δ _s).

The Schuler period oscillator signal belongs to low frequency signal comparatively speaking, and be 84.4 minutes oscillation period.And the instantaneous line motion in naval vessel is caused that by the marine environment factor topmost generation reason is the influence of wave, so the instantaneous line motion in naval vessel is frequency and the to-and-fro movement unanimous on the whole of wave frequency.And the motion of the instantaneous line in naval vessel belongs to high frequency motion with respect to the navigation campaign on naval vessel, and the period of motion is shorter, and generally about 1.5 seconds～10 seconds, frequency is 0.67 hertz.Different according on the kinetic characteristic of heave swaying surge motion and naval vessel routine work campaign, the technical requirement of the wave filter that designing institute needs, concrete design objective is adjusted according to filter effect in process of the test, is as the criterion to reach the optimal filtering effect.

2) technical indicator is transformed into analog filter from digital filter

Bilinearity transform method is adopted in the conversion of technical indicator from the analog filter to the digital filter, and the technical indicator of design digital Hi-pass filter is f _P1, f _S1, δ _p, δ _s, t _s=0.0102.At first should obtain digital marginal frequency Ω, because 2 π are corresponding SF f _s, and f _s=1/t _sSo, have:

$\frac{f_{p1}}{f_s}=\frac{{\mathrm{\&Omega;}}_{p1}}{2\mathrm{\&pi;}}$

$\frac{f_{s1}}{f_s}=\frac{{\mathrm{\&Omega;}}_{s1}}{2\mathrm{\&pi;}}$

The institute in the hope of:

Ω _s1＝2πf _s1/f _s

Ω _p1＝2πf _p1/f _s

Frequency inverted according to bilinearity transform method concerns ω=2f _sTan (Ω/2) continues conversion to be had:

${\mathrm{\&Omega;}}_p=\tan \left(\frac{{\mathrm{\&omega;}}_p}{2}\right)$

${\mathrm{\&Omega;}}_s=\tan \left(\frac{{\mathrm{\&omega;}}_s}{2}\right)$

The technical indicator of digital high-pass filter just is converted into the technical indicator of mimic high pass filter with this.

Assembled gesture error model when (6) setting up the carrier moored condition according to the moving pedestal error equation of modulation type SINS, the speed that directly calculates with speed and the modulation type SINS that obtains after the high-pass filtering is made difference and is then measured as systematic perspective.Utilize Kalman Filter Technology to realize confirming of modulation type SINS assembled gesture;

Foundation is made difference afterwards as the Kalman filter model of observed quantity with the speed that directly calculates through horizontal velocity after the high-pass filtering and modulation type SINS;

The state error of modulation type SINS is described with linear first-order differential equation:

$\stackrel{\&CenterDot;}{X}=\mathrm{AX}+\mathrm{BW}$

Wherein, X is the state vector of system; A and B are respectively the state matrix and the noise matrix of system; W 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:

$A=\left[\begin{array}{cccc}{F}_{2\&times;2}^1& f_{2\&times;3}& {\tilde{T}}_{2\&times;2}& O_{2\&times;3}\\ F_{3\&times;2}^2& F_{3\&times;3}^3& O_{3\&times;2}& T_{3\&times;3}\\ O_{5\&times;2}& O_{5\&times;3}& O_{5\&times;2}& O_{5\&times;3}\end{array}\right]$

$F_{2\&times;2}^1=\left[\begin{array}{cc}\frac{V_N}{R_n}\tan L^{\&prime;}& 2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E}{R_n}\tan L\\ -(2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{2V_E}{R_n}\tan L)& 0\end{array}\right]$

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

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

$f_{2\&times;3}=\left[\begin{array}{ccc}0& -f_U& f_N\\ f_U& 0& f_E\end{array}\right]$

${\tilde{T}}_{2\&times;2}=\left[\begin{array}{cc}{T}_{11}& T_{12}\\ T_{21}& T_{22}\end{array}\right]$

$T_{3\&times;6}=\left[\begin{array}{ccc}-T_{11}& -T_{12}& -T_{13}\\ -T_{21}& -T_{22}& -T_{23}\\ -T_{31}& -T_{32}& -T_{33}\end{array}\right]$

V _E, V _NThe speed of representing east orientation, north orientation respectively; ω _x, ω _y, ω _zThree input angular velocities representing gyro 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 representes local latitude; L ' expression moored condition initial time carrier latitude information; f _E, f _N, f _UBe expressed as respectively navigation coordinate system down east orientation, north orientation, day to specific force.

2) set up the measurement equation of Kalman filtering:

The measurement equation of describing the modulation type SINS with linear first-order differential equation is following:

Z＝HX+V

Wherein: Z representes the measurement vector of system; H representes the measurement matrix of system; V representes the measurement noise of system;

The system measurements matrix is:

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

Amount is measured as the east orientation speed V that the modulation type SINS resolves _E, north orientation speed V _NHandle the east orientation speed obtain respectively with through high-pass filtering North orientation speed

Poor:

$Z=\left[\begin{array}{c}{V}_E-{\tilde{V}}_E\\ V_N-{\tilde{V}}_N\end{array}\right]$

2. a kind of modulation type strapdown system assembled gesture that does not have semblance measure according to claim 1 is confirmed method, it is characterized in that described IMU adopts 4 commentaries on classics to stop the transposition scheme that order is a swing circle, specifically comprises the steps:

Order 1, IMU is set out by position A, turn clockwise 180 ° to the position B, and in the position B residence time T _sOrder 2, IMU is set out by position B, the 90 ° of in-position C that turn clockwise, and in the position C residence time T _sOrder 3, IMU is set out by position C, be rotated counterclockwise 180 ° to the position D, the D residence time T in the position _sOrder 4, IMU are set out by position D and are rotated counterclockwise 90 ° and get back to position A, and in the position A residence time T _sMove according to the sequential loop of order 1～4 then.

Carry out at 180 ° of the each rotations of IMU or 90 ° of intervals.To symmetric position, on these two symmetrical positions, the constant value drift of inertia sensitive element can be cancelled out each other when carrying out navigation calculating on the horizontal direction from 180 ° of rotated position.Arrive the another one reposition through half-twist.

3. a kind of modulation type strapdown system assembled gesture that does not have semblance measure according to claim 1 is confirmed method; The output that it is characterized in that described degree of will speed up meter is transformed into carrier semi-fixed axes system; Utilize the integral element in the modulation type SINS to extract carrier instantaneous linear velocity information, specifically comprise the steps:

1) introduces carrier semi-fixed axes system

With the naval vessel center of gravity is that the carrier semi-fixed axes is an initial point, longitudinal axis OY _dPoint to the main of naval vessel and go to direction transverse axis OX _dBe parallel to surface level perpendicular to the longitudinal axis, point to the starboard direction when not having pitching on the naval vessel.Z-axis OZ _dVertical with preceding diaxon, upwards be just (like accompanying drawing 3) along the ship vertical pivot.ψ wherein _GBe the base course angle, the γ angle is course angle of oscillation (is yaw angle definition itself and base course angle in the same way for just).The introducing that the carrier semi-fixed axes is makes measurement result and angular motion break away from basically, can describe the instantaneous line motion on naval vessel exactly, therefore adopts carrier semi-fixed axes system as studying the base coordinate system that the instantaneous line in naval vessel moves or is called translation.

2) set up the transition matrix that Inertial Measurement Unit coordinate system and carrier semi-fixed axes are

At first set up between carrier coordinate system and the carrier semi-fixed axes system and differ three rotation angle, can be considered semi-fixed axes system and after three rotations, overlap with carrier coordinate system, three angles are respectively: pitch angle α, roll angle β and yaw angle γ (like accompanying drawing 4).Carrier coordinate system is transformed into the direction cosine matrix of carrier semi-fixed axes system

$C_b^d=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&beta;}& \sin \mathrm{\&gamma;}\cos \mathrm{\&alpha;}+\cos \mathrm{\&gamma;}\sin \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \sin \mathrm{\&gamma;}\sin \mathrm{\&alpha;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}\\ -\sin \mathrm{\&gamma;}\cos \mathrm{\&beta;}& \cos \mathrm{\&gamma;}\cos \mathrm{\&alpha;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \cos \mathrm{\&gamma;}\sin \mathrm{\&alpha;}-\sin \mathrm{\&gamma;}\sin \mathrm{\&beta;}\cos \mathrm{\&alpha;}\\ \sin \mathrm{\&beta;}& -\cos \mathrm{\&beta;}\sin \mathrm{\&alpha;}& \cos \mathrm{\&beta;}\cos \mathrm{\&alpha;}\end{array}\right]$

Existing inertial navigation system can provide comparatively accurate attitude angle information; Wherein two attitude angle information of level are pitch angle information and roll angle information; And course information provides course angle information ψ; This is different from yaw angle γ, but the operator on naval vessel can provide base course information ψ accurately _G, can get

γ＝ψ-ψ _G

In the accounting equation with γ substitution

, can obtain the direction cosine matrix that carrier coordinate system is transformed into carrier semi-fixed axes system.

Because there is the transposition campaign around azimuth axis in the relative carrier of Inertial Measurement Unit, so the transition matrix between inertia measurement coordinate system (s coordinate system) and the carrier coordinate system can utilize following formula to calculate:

$C_s^b=\left[\begin{array}{ccc}\cos \mathrm{\&omega;t}& -\sin \mathrm{\&omega;t}& 0\\ \sin \mathrm{\&omega;t}& \cos \mathrm{\&omega;t}& 0\\ 0& 0& 1\end{array}\right]$

In the formula, ω t representes the relative angle relation of the relative carrier coordinate system of Inertial Measurement Unit.Therefore can obtain the direction cosine matrix that the Inertial Measurement Unit coordinate system is transformed into carrier semi-fixed axes system:

$C_s^d=C_b^d{C}_s^b$

4. a kind of modulation type strapdown system assembled gesture that does not have semblance measure according to claim 1 is confirmed method; It is characterized in that described infinite impulse response digital high-pass filter (IIR) reasonable in design; The bearer rate that navigation system calculates is down carried out the high-pass filtering processing, specifically comprise the steps:

1) confirms the technical indicator of institute's design digital Hi-pass filter

High-pass digital filter f _P1, f _S1, δ _p, δ _sTechnical indicator be according to signal characteristic and SF f _sGiven.Wherein, f _P1Be cut-off frequecy of passband, f _S1Be stopband cutoff frequency, δ _pBe passband ripple, promptly depart from the maximal value of unity gain in the filter transmission band, the passband edge gain is 1-δ _p, δ _sBe stop band ripple, promptly depart from the maximal value of unity gain in the filter stop band, the gain of stopband edge place wave filter is δ _sThe attenuation alpha of passband and stopband _p, α _sBe defined as-20log (1-δ respectively _p) ,-20log (1-δ _s).

The Schuler period oscillator signal belongs to low frequency signal comparatively speaking, and be 84.4 minutes oscillation period.And the instantaneous line motion in naval vessel is caused that by the marine environment factor topmost generation reason is the influence of wave, so the instantaneous line motion in naval vessel is frequency and the to-and-fro movement unanimous on the whole of wave frequency.And the motion of the instantaneous line in naval vessel belongs to high frequency motion with respect to the navigation campaign on naval vessel, and the period of motion is shorter, and generally about 1.5 seconds～10 seconds, frequency is 0.67 hertz.Different according on the kinetic characteristic of heave swaying surge motion and naval vessel routine work campaign, the technical requirement of the wave filter that designing institute needs, concrete design objective is adjusted according to filter effect in process of the test, is as the criterion to reach the optimal filtering effect.

2) technical indicator is transformed into analog filter from digital filter

Bilinearity transform method is adopted in the conversion of technical indicator from the analog filter to the digital filter, and the technical indicator of design digital Hi-pass filter is f _P1, f _S1, δ _p, δ _s, t _s=0.0102.At first should obtain digital marginal frequency Ω, because 2 π are corresponding SF f _s, and f _s=1/t _sSo, have:

$\frac{f_{p1}}{f_s}=\frac{{\mathrm{\&Omega;}}_{p1}}{2\mathrm{\&pi;}}$

$\frac{f_{s1}}{f_s}=\frac{{\mathrm{\&Omega;}}_{s1}}{2\mathrm{\&pi;}}$

The institute in the hope of:

Ω _s1＝2πf _s1/f _s

Ω _p1＝2πf _p1/f _s

Frequency inverted according to bilinearity transform method concerns ω=2f _sTan (Ω/2) continues conversion to be had:

${\mathrm{\&Omega;}}_p=\tan \left(\frac{{\mathrm{\&omega;}}_p}{2}\right)$

${\mathrm{\&Omega;}}_s=\tan \left(\frac{{\mathrm{\&omega;}}_s}{2}\right)$

The technical indicator of digital high-pass filter just is converted into the technical indicator of mimic high pass filter with this.

5. a kind of modulation type strapdown system assembled gesture that does not have semblance measure according to claim 1 is confirmed method; It is characterized in that described assembled gesture error model when setting up the carrier moored condition according to the moving pedestal error equation of modulation type inertial navigation system; The speed that directly calculates with the speed that obtains after the high-pass filtering and inertial navigation system is done the difference back and is measured as systematic perspective, specifically comprises the steps:

Foundation is made difference afterwards as the Kalman filter model of observed quantity with the speed that directly calculates through horizontal velocity after the high-pass filtering and modulation type SINS;

The state error of modulation type SINS is described with linear first-order differential equation:

$\stackrel{\&CenterDot;}{X}=\mathrm{AX}+\mathrm{BW}$

Wherein, X is the state vector of system; A and B are respectively the state matrix and the noise matrix of system; W 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:

$A=\left[\begin{array}{cccc}{F}_{2\&times;2}^1& f_{2\&times;3}& {\tilde{T}}_{2\&times;2}& O_{2\&times;3}\\ F_{3\&times;2}^2& F_{3\&times;3}^3& O_{3\&times;2}& T_{3\&times;3}\\ O_{5\&times;2}& O_{5\&times;3}& O_{5\&times;2}& O_{5\&times;3}\end{array}\right]$

$F_{2\&times;2}^1=\left[\begin{array}{cc}\frac{V_N}{R_n}\tan L^{\&prime;}& 2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E}{R_n}\tan L\\ -(2{\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{2V_E}{R_n}\tan L)& 0\end{array}\right]$

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

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

$f_{2\&times;3}=\left[\begin{array}{ccc}0& -f_U& f_N\\ f_U& 0& f_E\end{array}\right]$

${\tilde{T}}_{2\&times;2}=\left[\begin{array}{cc}{T}_{11}& T_{12}\\ T_{21}& T_{22}\end{array}\right]$

$T_{3\&times;6}=\left[\begin{array}{ccc}-T_{11}& -T_{12}& -T_{13}\\ -T_{21}& -T_{22}& -T_{23}\\ -T_{31}& -T_{32}& -T_{33}\end{array}\right]$

V _E, V _NThe speed of representing east orientation, north orientation respectively; ω _x, ω _y, ω _zThree input angular velocities representing gyro 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 representes local latitude; L ' expression moored condition initial time carrier latitude information; f _E, f _N, f _UBe expressed as respectively navigation coordinate system down east orientation, north orientation, day to specific force.

2) set up the measurement equation of Kalman filtering:

The measurement equation of describing the modulation type SINS with linear first-order differential equation is following:

Z＝HX+V

Wherein: Z representes the measurement vector of system; H representes the measurement matrix of system; V representes the measurement noise of system;

The system measurements matrix is:

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

Amount is measured as the east orientation speed V that the modulation type SINS resolves _E, north orientation speed V _NHandle the east orientation speed obtain respectively with through high-pass filtering North orientation speed

Poor:

$Z=\left[\begin{array}{c}{V}_E-{\tilde{V}}_E\\ V_N-{\tilde{V}}_N\end{array}\right]$

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