CN103471578A - Orthogonal detection-based measuring method using multi-dimensional signal of optical fiber gyroscope - Google Patents

Abstract

The invention provides a method for measuring the angular speed by using an optical fiber gyroscope. The method comprises the steps of carrying out square wave modulation on laser; inputting the laser subjected to the square wave modulation into the optical fiber gyroscope; extracting an output laser signal Iout of the optical fiber gyroscope; generating a series of local orthogonal signals with frequencies being odd number times the frequency of the square wave; correlating the series of generated local orthogonal signals with the laser signal Iout to obtain correlated signals; reducing coefficients of the correlated signals to obtain a series of angular speeds; and carrying out maximum likelihood estimation on the series of angular speeds to obtain a final angular speed, wherein the generated series of local orthogonal signals with frequencies being odd number times the frequency of the square wave is described in the specification, wherein n is equal to 1, 3, 5..., omega is the frequency of the square wave, and theta is a constant number.

Description

A kind of measuring method of the use optical fibre gyro multi-dimensional signal based on quadrature detection

Technical field

The invention belongs to the optical fibre gyro field, more particularly, the novel signal demodulation method that relates to a kind of fibre optic gyroscope of square-wave frequency modulation reaches the measuring method based under principal component analysis (PCA).

Background technology

Gyroscope is a kind of inertia measurement sensor, for measuring the rotational angular velocity of the relatively a certain inertial reference system of its place carrier.Gyroscope is widely used in military affairs and the industrial circle that the guidance of various aircraft and attitude are controlled, and to the precision measurement of the time and space as scientific domains such as gravitational wave detections.The gyroscope of application mainly contains Four types at present: mechanical gyroscope, lasergyro, fibre optic gyroscope (Fiber-optic gyroscope, FOG), and Quantum gyroscope.Wherein lasergyro and fibre optic gyroscope are all the optical gyroscope based on relativistic effect.Beam propagation in optical gyroscope and Photoelectric Detection introduced relatively traditional gyro larger reach in short-term noise when long, so migration coefficient and zero partially degree of stability not as good as some mechanical gyros and quantum gyroscope.It is simple that but optical gyroscope has manufacture craft, compact conformation, small volume, be easy to design and strapdown combination, the low remarkable advantage that waits of maintenance cost, so the demand to fibre optic gyroscope exists to the inertia measurement field always, while improving constantly along with the optical device manufacturing technology level, the various performance parameters of optical gyroscope is constantly improving, and market share improves constantly.

The optical texture basis of optical gyroscope is Sagnac type interferometer, and this structure need to meet the reciprocity conditions such as beam splitter reciprocity, single mode reciprocity, polarization reciprocity.Reciprocity can at utmost guarantee that the spread state of CW light and CCW light is consistent with transmission path, plays the effect of " common mode inhibition ", eliminates the noise of nonreciprocal introducing.Fig. 1 shows the minimum reciprocal structure of fibre optic gyroscope.The use of two coupling mechanisms is in order to guarantee that two-beam is identical through the cumulative phase shift of coupling mechanism, guarantees the coupling mechanism heterogeneite.And the polarizer has guaranteed that two-beam propagates at same polarization mode, i.e. polarization reciprocity.

Adopting polarization maintaining optical fibre is the effective means of heterogeneite that guarantees the optical fibre gyro structure, only by a kind of light of polarization mode for detection of slewing rate, and the polarized light that suppresses another direction is to realize reciprocity.But, in the engineering application, the polarization maintaining optical fibre gyro still exists cost high, to crooked responsive, to problems such as magnetic-field-sensitives.Thereby people have proposed again depolarized scheme, the optical fibre gyro structure that adopts depolarizer and single-mode fiber to build lower cost.But relatively protect inclined to one side structure, depolarized structure detection performance still remains further to be improved.

The detection principle of optical gyroscope is Sagnac effect (Sagnac effect).In the closed light path of optical gyroscope, two-beam generation beat frequency or the interference of (CW) along clockwise direction sent by same light source and counterclockwise (CCW) transmission, utilize the phase place that detects frequency difference or interference fringe to change, just can measure the angular velocity of rotation of light path relative inertness spatial frame of reference.A kind of common expression way of Sagnac effect is that the two-beam of clockwise direction (CW) and counterclockwise (CCW) transmission has produced the poor of optical propagation phase place, i.e. Sagnac phase shift, and expression formula is as follows:

${\mathrm{\&phi;}}_s=\frac{4\mathrm{\&omega;<figure-callout\; id="2"\; label="A\; c"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">A</figure-callout>}}{c^{}}\mathrm{\&Omega;}$ Equation (1)

Wherein ω is light frequency, and c is the light velocity in vacuum, and A is the area that light path is enclosed, and Ω is rotational angular velocity.Sagnac phase place positive and negative light wave start-phase when initially entering the optics loop realizes judgement.In interferometric fiber optic gyroscope (IFOG), the optical fiber (hundreds of rice does not wait to several kilometers) that needs will be longer turns to multiturn gyro coil.In this case, Sagnac effect can be expressed as:

${\mathrm{\&phi;}}_s=2\mathrm{\&pi;}\frac{\mathrm{LD}}{\mathrm{\&lambda;c}}\mathrm{\&Omega;}$ Equation (2)

The length that wherein L is optical fiber, D is the fiber optic coils diameter, the wavelength that λ is light wave.

During fibre optic gyroscope work, need two beam reversal's wave travels to be interfered, according to interference theory, the response function of interference is cosine function I ₀(1+cos ф _s), while being operated in like this minute angular velocities measuring state, can't experience direction, sensitivity simultaneously is sine function, sensitivity is extremely low, for head it off, introduces phase-modulation mechanism in interference type optical fiber gyroscope, in order to improve working point.By a section of light coil, adding phase-modulator, such as LiNO ₃the type Y waveguide, as shown in Figure 2, the function that wherein the Y waveguide device has comprised the polarizer.Add that by the end at fiber optic coils (being fiber optic loop) phase-modulator forms the nonreciprocal modulation that realizes two ways of optical signals.The Y waveguide phase-modulator makes the two-beam ripple be subject to different phase-modulation φ at different time _m(t), just produce a phase differential, as follows

Δ φ (t)=φ _cCW(t)-φ _cW(t)=φ _m(t)-φ _m(t-τ) equation (3)

τ n wherein _effl/c means that light is by the transmission time of whole fiber optic coils length, n _effbe the effective refractive index of optical fiber, m is the meaning of modulation, and φ m is modulation signal.Like this, after applying modulation, longitudinal cosine type interference light intensity signal becomes

$I_{\mathrm{out}}=I_0\{1+\cos [{\mathrm{\&phi;}}_s+\mathrm{\&Delta;\&phi;}\left(t\right)\left]\right\}$ Equation (4)

At present, interferometric fiber optic gyroscope mainly contains sinusoidal phase modulation and two kinds of signal modulation systems of square wave phase modulation.The optical fibre gyro of square-wave frequency modulation adopts the complete-digital closed-loop scheme usually, the optical fibre gyro that is pi/2 for the square-wave frequency modulation amplitude, and the signal subtraction that demodulation method is the front and back semiperiod, extract the phase place of being introduced by rotational angular velocity accordingly.

$I_{\mathrm{out}}=\left\{\begin{array}{c}{I}_0[1+\cos ({\mathrm{\&phi;}}_S+\frac{\mathrm{\&pi;}}{2})],0~\mathrm{\&tau;}\\ I_0[1+\cos ({\mathrm{\&phi;}}_S-\frac{\mathrm{\&pi;}}{2})],\mathrm{\&tau;}~2\mathrm{\&tau;}\end{array}\right.$ Equation (5)

Δ I=I _d(0～τ)-I _d(τ～2 τ)=2I ₀sin φ ₀sin φ _sequation (6)

Wherein, constant Φ ₀it is depth of modulation.Yet, the signal demodulating method of optical fibre gyro under this square-wave frequency modulation has been introduced asynchronous Differential Detection, the signal of difference is the non-synchronous signal of front and back sequential, and this mistiming has brought the asynchronous of noise, and the noise that can't eliminate has been introduced in this traditional difference measurement.Before, our laboratory had once proposed the synchronous test problems in fibre optic gyroscope that numeric field balance detection method solved sine wave modulation.Yet by the generally employing square-wave frequency modulation in the high accuracy gyroscope instrument and closed loop configuration, so this patent, on the basis of the numeric field balance detection patent in laboratory, has further solved the synchronous test problems of the closed loop gyro of square-wave frequency modulation.

Interference type optical fiber gyroscope has been set different precision grades accordingly to the requirement of its different application, the technical requirement that following table is each precision grade.Wherein zero bias stability is the accuracy of detection under measuring while weighing interference type optical fiber gyroscope length, and improving this index is to realize the necessary condition of accurate inertial guidance.And random walk coefficient is the assessment of performance coefficient under gyro is measured in short-term.

The precision grade of table 1 interference type optical fiber gyroscope and technical requirement

Yet, in existing method for measuring angular velocity, the drift that existing faraday's magnetic field effect, temperature fluctuation cause or other low-frequency noises, and the polarization in optical fibre gyro develops and the flicker noise of detector, will cause the i.e. zero bias stability reduction of fluctuation of data zero offset.Need new gyroscope structure and method, suppress zero partially unsettled inducement, or noise is carried out to the elimination in later stage.

And the squelch problem while working for gyroscope, current solution mainly contains two kinds.A kind of is redundant configuration, adopts a plurality of optical fibre gyros to measure mutually and calibrate in the same time and place, can suppress like this measurement instability to a certain degree, yet this scheme has increased system complexity, and debugging difficulty has increased hardware cost simultaneously greatly.Another kind of scheme is for adopting Kalman filtering algorithm to be optimized.But Kalman filter demands is carried out accurate modeling to system, model is subject to the change of environment and lost efficacy simultaneously, and Kalman filtering at larger optical fibre gyro field face affected by environment the problem that result does not restrain like this.

Summary of the invention

For overcome signal in existing square-wave frequency modulation optical fibre gyro process in the problems such as the time delay of the noise that brings of asynchronous demodulation and wave filter and setting parameter complexity, the invention provides a kind of novel quadrature synchronization differential ference spiral disposal route.This disposal route makes us obtain the lower bound of the statistical least estimated variance of optical fibre gyro instrument system.

The technical solution adopted for the present invention to solve the technical problems is: adopt square-wave frequency modulation and the demodulation of quadrature local signal by adopting the fibre optic gyroscope to having the Y waveguide phase-modulator, and the linear combination of carrying out based on principal component analysis (PCA) that the two paths of signals obtained is scheduled to obtains the optical fiber loop rotational angular velocity.

In the present invention in above-mentioned scheme, Optical Fiber Gyroscope by local orthogonal sinusoidal cosine signal and square-wave frequency modulation is carried out relevant treatment, harmonic components in square-wave signal is carried out to separation and Extraction, extract respectively 1 subharmonic in output from Gyroscope, 3 subharmonic, and the phase and magnitude information of 5 subharmonic.Note, can select only to extract 1 subharmonic here, also can select from extracting 7 subharmonic 1 time until the harmonic component of the higher compositions such as 2n-1 subharmonic, we selected 1,3,5 as narration, are not limited thereto in this patent.

Further, wherein demodulation adopts orthogonal demodulation method to obtain I, Q two-way detection signal, and, by the adjusting to the local signal initial phase, make I, the Q two paths of signals is the other side's reference signal each other, makes it balance.The linear scale factor of the each harmonic amplitude that extracts is carried out to reduction, obtain the corresponding wherein contained Sagnac phase information caused by the optical fiber loop angular velocity of rotation.

Further, for each harmonic components, input in matched filter and processed.This wave filter estimates to obtain optimum angular velocity signal by maximum a posteriori probability.The design concept of the matched filter of multiple harmonic amplitude used is that maximum a posteriori probability is estimated, the noise type of the signal based on optical fibre gyro is that white noise is as analysis foundation.

Further, we are to I, and Q signal has carried out the principal component analysis (PCA) processing, and the result of principal component analysis (PCA) is that Q signal carries out linear transformation and obtains independently I ', Q ' by the two-way I of gyroscope demodulation output.The two-way independent signal here can be regarded as two synchronous gyroscopes that work alone.

Further, the Related Component that it is carried out to predetermined linear combination cancellation two-way signal obtains the rotational angular velocity of the fine loop of polishing simultaneously.Realized gyroscope is detected the optimal estimation lower bound of angular velocity signal variance, i.e. Ka Meila-Lao lower bound (CRB).

In one or more examples aspect above-mentioned, described fibre optic gyroscope utilizes wide spectrum light source to be connected realization by polarization maintaining optical fibre successively with fiber coupler, the polarizer, y-shaped waveguide phase-modulator, polarization-maintaining fiber coil.

In one or more examples aspect above-mentioned, the assertive evidence frequency that described modulating frequency is described fibre optic gyroscope.

In one or more examples aspect above-mentioned, the square-wave signal amplitude applied on described phase-modulator be pi/2 or-pi/2, described predetermined linear formula is (Q-I)/2 or (Q+I)/2.

Compared with prior art, the invention has the beneficial effects as follows:

By synchronized orthogonal demodulation and matched filter and principal component analysis (PCA), realize the synchronous demodulation to the interference type optical fiber gyroscope of square-wave frequency modulation, solved the noise that the asynchronous difference in the traditional demodulation method is introduced, compared traditional Sine Modulated demodulation, calculated amount is little, and efficiency is high.At first, can realize by this method the phase place direct-detection under the open loop of the fibre optic gyroscope of square-wave frequency modulation, contrast the open loop gyroscope of traditional Sine Modulated, the method calculated amount is little, efficiency is high, the more important thing is, because the optical fibre gyro of square-wave frequency modulation has higher useful information contrast sine wave modulation, so data overall permanence of this disposal route, all be better than the open loop gyro of traditional sine wave modulation from random walk to zero bias stability, oneself shows concrete Data Comparison in the accompanying drawings.Simultaneously, for the optimization method based on principal component analysis (PCA) subsequently, be the further optimization to the balance detection of square-wave frequency modulation closed-loop fiber optic gyroscope instrument.The advantage of the balance detection of open loop gyro has been described in original patent in laboratory, but the analysis by statistical property and Fisher information to signal of fiber optical gyroscope, the variance inferior boundary that has obtained system is relevant with related coefficient, and the space with further optimization is described.We have adopted principal component analytical method, this method does not cause the delay effect that conventional filter is brought, unlike Kalman filter, the prior model to system has high requirement simultaneously, only need the priori covariance matrix of system to get final product, and can utilize register to realize real-time update, the error that the variation of elimination environment may bring.The present invention has realized the statistics minimum variance demodulation of system, simultaneously on hardware, do not introduce new hardware, and can not bring time delay on algorithm and disperse, comprehensively more than, the present invention has clear superiority and application prospect widely.

The accompanying drawing explanation

Below in conjunction with drawings and Examples, the present invention is further described.

Fig. 1 is the minimum reciprocal structure diagram of optical fibre gyro;

Fig. 2 is the phase-modulation diagram of optical fibre gyro;

Fig. 3 shows the process flow diagram of the detection method of fibre optic gyroscope according to an embodiment of the invention;

Fig. 4 is the structural representation under the novel demodulation method of fibre optic gyroscope according to an embodiment of the invention;

Fig. 5 implements under the laboratory environment of structure the earth is turned to the angular velocity time-domain diagram contrast that under Output speed data in the register of square-wave frequency modulation quadrature detection and isostructure, Sine Modulated 124 subharmonic demodulation obtain in vain according to Fig. 4;

Fig. 6 is the Allan analysis of variance diagram of output data under two kinds of modulation-demo-demodulation methods in Fig. 5;

Fig. 7 is the I obtained of Fig. 4 structure, and the Q data are carried out 2 dimension scatter diagrams before principal component analysis (PCA);

Fig. 8 is 2 dimension scatter diagrams after Fig. 7 data are carried out principal component analysis (PCA);

Fig. 9 is that this is by carrying out the gyroscope output data time-domain diagram after same linear combination is processed to Fig. 7 and Fig. 8 data respectively.

Figure 10 is the Allan analysis of variance diagram of Fig. 9 data

Embodiment

By reference to the accompanying drawings, below the present invention is further elaborated and illustrates.

Fig. 3 is principle diagram of the present invention, and Fig. 4 is the one-piece construction schematic diagram of institute of the present invention foundation.Following narrative structure is based on Fig. 4, and process is based on Fig. 3.For the fibre optic gyroscope output signal of square-wave frequency modulation, the trigonometric function signal by quadrature, as local signal, utilizes the method for correlation demodulation, extracts the harmonic signal of corresponding frequencies, is used for obtaining needed angular velocity and rotates caused phase information.Wherein the Fourier expansion of square-wave signal is:

$\mathrm{Square}\left(t\right)=\underset{n=\mathrm{1,3,5},...}{\mathrm{\&Sigma;}}\frac{4}{\mathrm{n\&pi;}}\sin \mathrm{n\&omega;t}$ Equation (7)

The local oscillator signal LO of the quadrature of selecting is:

${\mathrm{LO}}_I^n=\sin (\mathrm{n\&omega;t}+\mathrm{\&theta;})$ Equation (8)

${\mathrm{LO}}_Q^n=\cos (\mathrm{n\&omega;t}+\mathrm{\&theta;})$

Wherein, ω is modulating frequency, and θ is initial phase, and local signal contains the constant phase difference of 90 °.

After the two-way local signal of quadrature is sent into to multiplier with the signal of gyroscope output respectively, try to achieve respectively the mean value of total hits, can obtain synchronous orthogonal signal, the phase and magnitude information that the integral body of this two paths of signals has comprised the fibre optic gyroscope output signal.Getting the local signal initial phase is 45 °, the signal in orthogonal signal I after being correlated with, and Q:

$I_I^n=\stackrel{\&OverBar;}{I_{\mathrm{out}}\&CenterDot;{\mathrm{LO}}_I^n}=\frac{\sqrt{2}}{\mathrm{n\&pi;}}{I}_0\sin ({\mathrm{\&phi;}}_s+{\mathrm{\&phi;}}_f),n=\mathrm{1,3,5},\&CenterDot;\&CenterDot;\&CenterDot;$ Equation (9)

$I_Q^n=\stackrel{\&OverBar;}{I_{\mathrm{out}}\&CenterDot;{\mathrm{LO}}_Q^n}=\frac{\sqrt{2}}{\mathrm{n\&pi;}}{\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="HDA0000376036400000031.png,HDA0000376036400000032.png"\; state="\{\{state\}\}">I</figure-callout>}}_0\sin ({\mathrm{\&phi;}}_s+{\mathrm{\&phi;}}_f),n=\mathrm{1,3,5},\&CenterDot;\&CenterDot;\&CenterDot;$ Equation (10)

I wherein ₀for the intensity of light source, can be by selecting DC coupling, the mean value entered like this in the output from Gyroscope of collection is intensity of light source I ₀.ф _sfor Sagnac phase place, ф _ffor the step signal that compensation Sagnac phase place is used, make gyroscope realize that 0 speed closed loop detects.For the normalization amplitude, the constant term coefficient of introducing in the time of need to approximately falling the square wave series expansion, ask its inverse trigonometric function can obtain optical fibre gyro the responsive Ω arrived:

${\mathrm{\&Omega;}}_I^n=\frac{\mathrm{\&lambda;<figure-callout\; id="2"\; label="c"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathrm{\&pi;LD}}\arcsin \left(\frac{I_I^n\mathrm{\&pi;}}{\stackrel{\&OverBar;}{I_{\mathrm{out}}}\sqrt{2}}\right),$ Equation (11)

${\mathrm{\&Omega;}}_Q^n=\frac{\mathrm{\&lambda;<figure-callout\; id="2"\; label="c"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathrm{\&pi;LD}}\arcsin \left(\frac{I_Q^n\mathrm{\&pi;}}{\stackrel{\&OverBar;}{I_{\mathrm{out}}}\sqrt{2}}\right),$ Equation (12)

What when the present invention's method used has been saved traditional Sine Modulated, open loop detected is loaded down with trivial details, has reduced calculated amount, has improved the gyroscope work efficiency.Finally utilize signal to pass to the trigger pip of data acquisition system (DAS), can judge sense of rotation and angular velocity size.Like this, we have just extracted the first harmonic in the Optical Fiber Gyroscope.Below the statistical property of the tach signal Ω that arrives of our further analyzing and testing, and take that this analyzes the expression formula that obtains matched filter as basis.

The tach signal Ω demodulated for different local concussion frequency n ω _n, i.e. rotary speed information in different harmonic componentss, its approximate relation of obeying is as follows:

Ω _n～N (Ω, σ _n) equation (13)

Wherein N is gaussian shaped profile, and Ω is the average distributed, σ _nit is the variance yields distributed., by Gaussian distribution, due to the orthogonality between its different frequencys multiplication, obtain probability density function again:

$f\left(\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}\right|\mathrm{\&Omega;})=\underset{n}{\mathrm{\&Pi;}}\frac{1}{{\left({2\mathrm{\&pi;\&sigma;}}_n^2\right)}^{1/2}}\exp [-\frac{({\mathrm{\&Omega;}}_n-{\mathrm{\&Omega;})}^2}{{2\mathrm{\&sigma;}}_n^2}]$ Equation (14)

Wherein

by Ω _nthe vector array formed, according to Bayesian formula, the likelihood function that can obtain Ω is:

$f_{\mathrm{\&Omega;}|\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}}\left(\mathrm{\&Omega;}\right|\stackrel{\&RightArrow;}{\mathrm{\&Omega;}})=\frac{1}{f\left(\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}\right)}{f}_{\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}|\mathrm{\&Omega;}}\left(\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}\right|\mathrm{\&Omega;})f_{\mathrm{\&Omega;}}\left(\mathrm{\&Omega;}\right)$ Equation (15)

Wherein usually be taken as 1.Bring equation (15) into, estimate (MAP) algorithm according to maximum a posteriori, by solving

derivative, when derivative is 0, Ω is maximal possibility estimation

be needed optimum detection amount, corresponding expression formula is:

${\widehat{\mathrm{\&Omega;}}}_{\mathrm{MAP}}\left(\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}\right)=\underset{n}{\mathrm{\&Sigma;}}\frac{A_n^2}{{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="HDA0000376036400000032.png,HDA0000376036400000041.png"\; state="\{\{state\}\}">A</figure-callout>}}_1^2+A_3^2+\&CenterDot;\&CenterDot;\&CenterDot;+A_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">n</figure-callout>}}^2},n=\mathrm{1,3,5},\&CenterDot;\&CenterDot;\&CenterDot;$ Equation (16)

A wherein _n=1/n, i.e. the coefficient of each harmonic wave in the gyro output signal corresponding with signal to noise ratio (S/N ratio), wherein 1 subharmonic is 1, all the other are followed successively by each odd number, and square while of this coefficient becomes positive correlation with variance, so use A _nsubstituted variances sigma _n.

As shown in Figure 4, the tachometer value obtained for demodulation, can generate step signal by register and be input in Y waveguide and carry out closed loop compensation, and in display, 0 detected value after register value and compensation all is shown simultaneously.So the detection limit of Fig. 5 is shown as the 9.66 °/h of earth rotation speed of laboratory latitude of living in (39.9 ° of N).And the gyro time domain numerical value that carries out contrasting before and after principal component analysis (PCA) in Fig. 9 is 0 average detection limit after compensation.

After matched filter, the two-way Ω of the quadrature after optimization _iand Ω _qsignal is obtained.But orthogonal signal are also not exclusively independent, have Related Component therein, and according to the Fisher information analysis to system, can the degenerate effect of difference of related coefficient, in order to realize optimum Differential demodulation algorithm, need to remove the related coefficient of two-way orthogonal signal.Utilize the prior imformation of signal, it is the covariance matrix of two-way orthogonal signal, by principal component analysis (PCA), extract two independent signal directions of two-way orthogonal signal, the two paths of signals that eigenvalue is 1+ ρ and 1-ρ will be redistributed from former orthogonal signal combination and be separated.This two paths of signals falls relevant portion wherein by difference by fully differential, obtains desired independent signal.This wherein, the covariance matrix of the needed priori of principal component analysis (PCA) both can utilize the statistics of gyrostatic when test record, can carry out real-time update by real-time register, guarantees the processing on the environment conversion impact that brings.The Practical Condition of principal component analysis (PCA) is the data zero-means, and for closed-loop fiber optic gyroscope, its angular velocity signal detected can be fallen by the staircase waveform feedback compensation, this has just met the zero-mean requirement of principal component analysis (PCA) just, can use principal component analysis (PCA) to realize the decorrelation of square-wave frequency modulation closed-loop fiber optic gyroscope is processed fully.

Concrete formula is as follows:

$f\left[\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}\left(t\right)\right]=\frac{1}{{2\mathrm{\&pi;\&sigma;}}^2\sqrt{1-\mathrm{\&rho;}}}\exp \{-\frac{1}{2}{[\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}\left(t\right)-\mathrm{\&Omega;}]}^T{\mathrm{\&Sigma;}}^{-1}[\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}\left(t\right)-\mathrm{\&Omega;}\left]\right\}$ Equation (17)

Wherein, $\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}\left(t\right)=\left[\begin{array}{c}{\mathrm{\&Omega;}}_I\left(t\right)\\ {\mathrm{\&Omega;}}_Q\left(t\right)\end{array}\right],\mathrm{\&Sigma;}=\left(\begin{array}{cc}{\mathrm{\&sigma;}}_I^2& {\mathrm{\&rho;\&sigma;}}_I{\mathrm{\&sigma;}}_Q\\ {\mathrm{\&rho;\&sigma;}}_I{\mathrm{\&sigma;}}_Q& {\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">Q</figure-callout>}}^2\end{array}\right)$

Equation (15) is signal Ω _iand Ω _qthe probability distribution of the vector formed, meet Gaussian characteristics, the related coefficient that ρ is the two.When ρ >=0, the linear combination of agreement is (1+Q)/2; When ρ<0, the linear combination of agreement is (I-Q)/2, and this is requirement physically, otherwise useful information can be divided out, if need to extract useful information, must carry out corresponding calculating according to ρ positive and negative, ρ's is positive and negative relevant with our initial phase of local signal.Below, suppose ρ >=0, according to equation (15), by phenanthrene, give up information, the CRB lower bound of trying to achieve is:

$\mathrm{Var}\left[\widehat{\mathrm{\&Omega;}}({\mathrm{\&Omega;}}_I,{\mathrm{\&Omega;}}_Q)\right]\&GreaterEqual;\frac{1+\mathrm{\&rho;}}{4}({\mathrm{\&sigma;}}_I^2+{\mathrm{\&sigma;}}_Q^2)$ Equation (18)

Wherein be the estimator of angular velocity Ω due to concerning system, Ω _i, Ω _qcomprise same rotary speed information Ω ₀, and different noise items, that is,

Ω _i(t)=Ω ₀+ N _q(t) equation (19)

Ω _q(t)=Ω ₀+ N _i(t) equation (20)

By difference processing, can suppress some noise wherein, differentiated noise is expressed as:

${\mathrm{\&Omega;}}_{\mathrm{div}}\left(t\right)=\frac{{\mathrm{\&Omega;}}_Q\left(t\right)+{\mathrm{\&Omega;}}_I\left(t\right)}{2}={\mathrm{\&Omega;}}_0+\frac{N_Q\left(t\right)+N_I\left(t\right)}{2}$ Equation (21)

We can retain needed rotary speed information like this, and in noise, incoherent composition is suppressed.For the closed loop gyro, we adopt Differential Detection to obtain equally, after quadrature demodulation under Differential Detection the detection variance of system be:

$\mathrm{Var}\left[{\mathrm{\&Omega;}}_{\mathrm{div}}\left(t\right)\right]=\frac{1}{4}({\mathrm{\&sigma;}}_I^2+{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">Q</figure-callout>}}^2+2\mathrm{\&rho;}{\mathrm{\&sigma;}}_I{\mathrm{\&sigma;}}_Q)$ Equation (22)

Visible correlation coefficient ρ has increased the detection variance.This wherein, it can not be 1 algebraic value that correlation coefficient ρ is one in the actual physical system because be so two congruent systems, and actual be impossible.Equally, for this expression formula, be because, in agreement linear combination method, ρ >=0 o'clock, need I, the Q addition; And when ρ<0, I, Q is subtracted each other, so the positive and negative of ρ can not affect last expression formula in formula (18) in (22), i.e. ρ positive and negative no matter, only have as ρ and approach to 0, just can reduce system and must detect variance, be i.e. gyrostatic random walk coefficient.By principal component analysis (PCA), the eigenwert by covariance matrix is respectively

with

the matrix that forms of proper vector it is carried out to linear transformation, by the time:

${\stackrel{\&RightArrow;}{\mathrm{\&Omega;}}}^{\&prime;}\left(t\right)=\left[\begin{array}{c}{{\mathrm{\&Omega;}}_I}^{\&prime;}\left(t\right)\\ {{\mathrm{\&Omega;}}_Q}^{\&prime;}\left(t\right)\end{array}\right]=\left(\begin{array}{cc}{c}_{11}& c_{21}\\ c_{12}& c_{22}\end{array}\right)\left[\begin{array}{c}{\mathrm{\&Omega;}}_I\left(t\right)\\ {\mathrm{\&Omega;}}_Q\left(t\right)\end{array}\right]$ Equation (23)

$\left(\begin{array}{cc}{c}_{11}& c_{12}\\ c_{21}& c_{22}\end{array}\right)=\left(\begin{array}{cc}\frac{{\mathrm{\&sigma;}}_I^2-{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">Q</figure-callout>}}^2+\sqrt{{({\mathrm{\&sigma;}}_I^2-{\mathrm{\&sigma;}}_Q^2)}^2+{4\mathrm{\&rho;}}^2{\mathrm{\&sigma;}}_I^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">Q</figure-callout>}}^2}}{{2\mathrm{\&rho;\&sigma;}}_I{\mathrm{\&sigma;}}_Q}a& \frac{{\mathrm{\&sigma;}}_I^2-{\mathrm{\&sigma;}}_Q^2-\sqrt{{({\mathrm{\&sigma;}}_I^2-{\mathrm{\&sigma;}}_Q^2)}^2+{4\mathrm{\&rho;}}^2{\mathrm{\&sigma;}}_I^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="HDA0000376036400000032.png,HDA0000376036400000052.png"\; state="\{\{state\}\}">Q</figure-callout>}}^2}}{{2\mathrm{\&rho;\&sigma;}}_I{\mathrm{\&sigma;}}_Q}b\\ a& b\end{array}\right)$ Equation (24)

A wherein, b is the coefficient for the normalizing proper vector, c _ijit is the matrix interior element that the latent vector after normalization forms.Ideally, i.e. σ _i=σ _qthe time, meet ρ>=0, simultaneously

in S reality, due to σ _iwith σ _qstrictly do not equate, after calculating corresponding eigenvalue corresponding latent vector value with ideally have little deviation.Like this, the new Vector Variance after linear transformation is:

$\mathrm{Var}\left[{\mathrm{\&Omega;}}_{\mathrm{pca}}\left(t\right)\right]=\mathrm{Var}\left[\frac{{\mathrm{\&Omega;}}_I^{\&prime;}\left(t\right)+{\mathrm{\&Omega;}}_Q^{\&prime;}\left(t\right)}{2}\right]=\frac{1+\mathrm{\&rho;}+1-\mathrm{\&rho;}}{4}({\mathrm{\&sigma;}}_I^2+{\mathrm{\&sigma;}}_Q^2)=\frac{1}{2}({\mathrm{\&sigma;}}_I^2+{\mathrm{\&sigma;}}_Q^2)=\mathrm{CRB}$ Equation (24)

So far, the present invention has realized the signal of square-wave frequency modulation gyro is processed and obtained its CRB lower bound.

Fig. 4 shows the structural representation that the novel signal of fibre optic gyroscope is processed according to an embodiment of the invention.Comprising wide spectrum light source, polarization-maintaining coupler, LiNo ₃the waveguide of Y type, 2 kilometers long optical fibers rings, but the signal generator that serial ports is controlled, wherein the sampling rate of capture card is made as the 2M per second, and hits is 200000, and be 0.1s averaging time, bandwidth 10Hz.

Fig. 5 is that 2 use same gyroscope, shown in Fig. 4 to the time domain data figure after the demodulation of square wave modulation orthogonal and the 124 subharmonic demodulation of traditional Sine Modulated.Sampling rate is all 2M, hits 200000.2 groups of data, equally through the diel test, intercept wherein respectively 50000 points the most stably.

Fig. 6 carries out the comparison diagram after the Allan variance analysis to Fig. 5 data.After can seeing the employing new processing method, the Allan variance curve integral body that is the rotating speed of square-wave frequency modulation gyro after synchronous multiple harmonic detection and matched filtering descends in traditional treatment method, and this useful information that also meets the square-wave frequency modulation introducing is more than these characteristics of Sine Modulated.The parameter that its corresponding Allan variance is fitted to is as following table:

Table two: the index contrast of square-wave frequency modulation demodulation and traditional Sine Modulated demodulation result

Fig. 7 and Fig. 8 are the planisphere demonstrations to the two-way orthogonal signal after the demodulation processed of square wave modulation orthogonal, and transverse axis is I, and the longitudinal axis is Q.The correlativity that wherein visible principal component analysis (PCA) has been processed rear cancellation between IQ.Here the phenomenon as a result due to principal component analysis (PCA) depends on I, the size of the related coefficient between the Q two paths of signals, so we have intercepted larger one section of the noise of diel test data middle and later periods, when when long round the clock, after test, issue can be due to each device of system environment such as thermonoise that work is introduced when long long, change and the migration change greatly, two-way quadrature I like this, correlativity between Q signal can increase equally, so we have chosen 50000 same data in test later stage, carries out the effect displaying.

Experiment measuring to as if rotational-angular velocity of the earth, on the surface level of laboratory dimension (north latitude 40.0 degree), theoretical value to be measured be 9.67 degree/hour, but through the staircase waveform compensation, actual gyro output quantity is 0 average.The data output gap is about 0.1 second, and test duration length is about 90 minutes.The local oscillated signal initial phase is chosen for 45 °, so the two paths of signals I after demodulation, the related coefficient of Q is that the linear combination on the occasion of, substitution agreement is calculated, and obtains the result as Fig. 9.Wherein 1 for before processing, and 2 for after processing.Before processing, correlation coefficient ρ is that 0.4416, I road variance is that 0.2057, Q road variance is 0.2194, through the variance of principal component analysis (PCA) direct differential detection, is not 0.1532 (°/h) ², it is 9.4*10 that rear related coefficient is processed in principal component analysis (PCA) ^-15, the variance of Differential Detection is 0.1063 (°/h) ², meet the algebraic relation in equation (24) and equation (22).Illustrate that having of this method improve the characteristics of systematic variance, and then improved the random walk parameter, the above-mentioned rationality that gyroscope signal is analyzed also is described.

Figure 10 is the Allan variance analysis curve of Fig. 9 result, visible, the principal component analysis (PCA) disposal route can be improved the parameter in short-term of system as migration and quantification etc., does not affect the zero bias stability of system, and the analysis of this noisiness to signal of fiber optical gyroscope before perhaps is consistent.The gyro parameter that its corresponding Allan variance is fitted to is as following table:

Table three: the Allan coefficient of variation contrast table before and after principal component analysis (PCA)

Although the disclosed content in front shows exemplary embodiment of the present invention, it should be noted that under the prerequisite of the scope of the present invention that does not deviate from the claim restriction, can carry out multiple change and modification.According to function, step and/or the action of the claim to a method of inventive embodiments described herein, need not carry out with any particular order.In addition, although element of the present invention can be with individual formal description or requirement, also it is contemplated that a plurality of, unless clearly be restricted to odd number.

Although in conjunction with the preferred embodiment that is shown specifically and describes, disclose the present invention, but those skilled in the art are to be understood that, for the invention described above, propose for optical fibre gyro being carried out to method and the device of numeric field balance detection, can also on the basis that does not break away from content of the present invention, make various improvement.Therefore, protection scope of the present invention should be determined by the content of appending claims.

Claims (4)

1. a method of utilizing optical fibre gyro measured angular speed comprises step:

Laser is carried out to square-wave frequency modulation;

To carry out the laser input optical fibre gyro of square-wave frequency modulation;

Extract the Output of laser signal I of optical fibre gyro _out;

Generating a series of frequencies is local orthogonal signal of the odd-multiple of described square wave frequency;

By generated a series of described local orthogonal signal and laser signal I _outsignal after being correlated with;

The coefficient of the signal after described being correlated with is carried out to reduction to obtain a series of angular velocity;

Described a series of angular velocity is carried out to maximal possibility estimation and obtain final angular velocity.

2. the method for measured angular speed according to claim 1, wherein,

Generating a series of frequencies in step is that the local orthogonal signal that generate in the local orthogonal signal of odd-multiple of described square wave frequency are,

${\mathrm{LO}}_I^n=\sin (\mathrm{n\&omega;t}+\mathrm{\&theta;})$

${\mathrm{LO}}_Q^n=\cos (\mathrm{n\&omega;t}+\mathrm{\&theta;})$

Wherein, n=1,3,5......, the frequency that ω is described square wave, θ is constant.

3. the method for measured angular speed according to claim 2, wherein,

By generated a series of described local orthogonal signal and laser signal I _outsignal after being correlated with comprises as follows and calculating:

$I_I^n=\stackrel{\&OverBar;}{I_{\mathrm{out}}\&CenterDot;{\mathrm{LO}}_I^n}=\frac{\sqrt{2}}{\mathrm{n\&pi;}}{I}_0\sin ({\mathrm{\&phi;}}_s+{\mathrm{\&phi;}}_f),n=\mathrm{1,3,5},\&CenterDot;\&CenterDot;\&CenterDot;$ Equation (9)

$I_Q^n=\stackrel{\&OverBar;}{I_{\mathrm{out}}\&CenterDot;{\mathrm{LO}}_Q^n}=\frac{\sqrt{2}}{\mathrm{n\&pi;}}{I}_0\sin ({\mathrm{\&phi;}}_s+{\mathrm{\&phi;}}_f),n=\mathrm{1,3,5},\&CenterDot;\&CenterDot;\&CenterDot;$ Equation (10)

Wherein, ф _sfor Sagnac phase place, ф _fthe step signal of using for compensating the Sagnac phase place.

4. the method for measured angular speed according to claim 1, wherein, described laser is polarization laser.

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