CN105371836A - Mixed type fiber-optic gyroscope signal filtering method based on EEMD and FIR - Google Patents

Abstract

The invention discloses a mixed type fiber-optic gyroscope signal filtering method based on EEMD and FIR. The method specifically comprises the following steps that 1, a fiber-optic gyroscope signal is decomposed through an EEMD algorithm to obtain IMF components and residual errors of all layers; 2, Hilbert transform is performed on the IMF components of all the layers to obtain amplitude values and instantaneous frequencies of all the layers, threshold values are reckoned according to the instantaneous frequencies, and weight values are calculated through the threshold values; 3, FIR filtering processing is performed on the IMF components and the residual errors of all the layers by adopting an FIR filter, and then new IMF components and new residual errors of all the layers are obtained; 4, weighting reconstruction is performed on the new IMF processed by the FIR filter, and finally a denoised result is formed. According to the mixed type fiber-optic gyroscope signal filtering method based on the EEMD and the FIR, the advantages of the two methods are integrated, the data decomposition precision is improved through the EEMD method, low-pass filtering is further performed through the FIR filter method, therefore, the frequency precision during EEMD signal processing is improved, and the filtering effect is significantly enhanced; meanwhile, it is guaranteed that the method is still based on data, modeling does not need to be performed on the data, and the application range is wide.

Description

Based on the mixed type signal of fiber optical gyroscope filtering method of EEMD and FIR

Technical field

The invention belongs to signal of fiber optical gyroscope process field, relate to a kind of signal of fiber optical gyroscope filtering method based on empirical modal process and limited long impulse response wave filter of hybrid processing.

Background technology

Gyro is a kind of instrument based on Sagnac (Sagnac) effect, and its topmost characteristic is stability and precession.Good performance makes it be widely used in Aeronautics and Astronautics and navigational field.Gyro is generally divided into piezolectric gyroscope, electro-mechanical gyro, laser gyro, optical fibre gyro etc.

Optical fibre gyro has compared with the gyro of other types that volume is little, quality is light, low cost and other advantages, makes it be well received, applies more and more extensive.But optical fibre gyro is because inner containing light activated element, easily be subject to the various factors impact that inner structure and temperature drift, outside noise etc. derive from the inner structure of optical fibre gyro own and external interference, very important error term is there is in signal, such as be rich in a large amount of white noises and random walk, overall signal presents a kind of weak relevant and state of non-stationary.So following naive model can be set up for the signal of optical fibre gyro:

On static coordinate system platform, the sensitive axis of gyro is perpendicular to surface level, and the output valve ω (t) of a certain optical fibre gyro of actual measurement is:

ω(t)＝ω _IE+ε(t)。

In formula, ω _iEfor gyro test actual value; ε (t) is gyroscopic drift value.

Gyroscopic drift value is made up of constant value component, periodic component and white noise, that is:

ε(t)＝ε _d+Ω _dsin(2πf _d+θ ₀)+W(t)。

In formula, ε _dbe zero partially, and in the short time, be approximately a constant; Ω _dfor the amplitude of periodic component; f _dfor the frequency of periodic component; θ ₀for initial phase; W (t) is zero mean Gaussian white noise.

Model for signal of fiber optical gyroscope can find that signal of fiber optical gyroscope is a weak relevant and signal for non-stationary.The random noise comprised in signal has fractal property, adopts traditional filtering method effectively cannot remove random noise, so except the filtering process on hardware, software algorithm process is particularly important.In order to reduce the processing pressure of master control borad to data, usually select just to carry out filtering process to signal of fiber optical gyroscope before Signal transmissions is to main control computer.To this, utilize the design proposal of the various wave filters in digital signal processing method, according to the constituent analysis of signal, relatively reasonable wave filter can be designed to realize effect.

Find that signal of fiber optical gyroscope often comprises the non-stationary composition of a lot of spike or sudden change shape in practice, and noise also not necessarily stable white noise.So the Integral Thought of filtering is: first carry out pre-service to signal, the noise section of signal is removed, and then extracts useful signal.

American National academician of the Chinese Academy of Engineering in 1998, NASA chief scientist NortonE.Huang are according to the mathematical theory basis of Modern Mathematics man Hilbert, a kind of analytical approach towards non-stationary nonlinear data is proposed, Hilbert-Huang transform (Hilbert-HuangTransform, HHT) is called by academia.HHT is made up of empirical mode decomposition (EmpiricalModeDecomposition, EMD) and Hilbert analysis of spectrum (HilbertSpectralAnalysis, HSA) two parts.

EMD algorithm is that a kind of one in wavelet analysis method thinking is newly improved one's methods, and its feature does not need to carry out modeling to analytic target, and application surface is more extensive.Input signal is resolved into a series of intrinsic mode function (IntrinsicModeFunction, IMF) adaptively by EMD.The object of EMD algorithm is a limited performance good IMF and residual error sum by signal decomposition bad for performance, and IMF must meet following two character: one, and in whole function, the number of extreme point is equal with the number passing through zero point or differ 1; Its two, at any time, the envelope local mean value defined by local extremum envelope is 0.

Polymerization empirical mode decomposition (EnsembleEmpiricalModeDecomposition, EEMD) algorithm mainly for the mixing phenomenon of EMD algorithm, propose a kind of improvement to add the data analysing method that noise is supplementary means.EEMD algorithm principle is: when additional white noise is evenly distributed on whole time frequency space, the different scale that this time frequency space is just divided into by bank of filters becomes to be grouped into, when signal adds equally distributed white noise background, get on being automatically mapped to the suitable yardstick relevant to background white noise in the signal area of different scale.EEMD is applicable to analyze non-linear, non-stationary signal sequence, more more directly perceived and have adaptive ability than the method such as Short Time Fourier Transform, wavelet decomposition.

Hilbert transform (HilbertTransform, HT) names with famous mathematician David Hilbert (DavidHilbert).By Hilbert transform, can obtain the definition to the instantaneous parameters of short signal and sophisticated signal and calculating, realize the extraction to momentary signal, thus Hilbert transform has very consequence on signal transacting.Use HT to analyze to the IMF being decomposed out by EEMD, just by tectonic knot function and then the information such as its instantaneous frequency can be calculated.

On the other hand, digital filter is also highly used for reference in noise reduction as one of the main method of Digital Signal Algorithm.The concept of wave filter is first proposed by the K.Wagner of the G.Campell of the U.S. and Germany for 1915, and thenceforth so far, filter theory and technology, in constantly develop rapidly, make it be widely used in various electronic equipment.Digital filter includes limit for length's impulse response filter (FIRfilter) and endless impulse response filter (IIRfilter) etc.In digital filter, FIR filter is simple, the stable wave filter of a class formation.Due to the remarkable advantage that can realize any amplitude versus frequency characte under the condition ensureing strict linear phase characteristic of FIR filter, make Finite Impulse Response filter method very effective for the system that some performance requirements such as Speech processing, image procossing, data transmission, radar reception are higher, be also highly suitable for signal of fiber optical gyroscope involved in the present invention simultaneously.

Conventional Finite Impulse Response filter method for designing mainly contains window function metht, Frequency Sampling Method, equiripple approximation method and responds design method etc. arbitrarily.Digital signal processing is exactly use the burst observed to carry out various process in finite interval.Intercept the work of part signal in persistent signal, can be regarded as and carry out by a window burst that Bian collection sees, this window used for intercept signal is called window function.Window function metht is directly perceived, the effective ways of design FIR filter, also claims Fourier series method or window technique.Its key is from time domain, intercepts ideal filter impulse response sequence with window function, to seek the impulse response that suitable impulse response sequence approaches ideal filter, thus reaches the frequency response H (e of designed wave filter ^jw) on frequency domain, approach the frequency response H (e of ideal filter ^jw) object.

Allan variance is proposed by the DavidAllan of NBS at first, is the main method of testing in current optical field and gyro performance test field.The outstanding feature of this method and contribution are that it can characterize and identification to various error source and to whole noise statistics easily meticulously.Owing to there is quantitative relation between the Allan variance of noise and power spectrum density, utilize this relation in time domain, just directly can obtain type and the amplitude of various error source optical fibre gyro from the output data of optical fibre gyro.

The theoretical information of Allan variance is as hereafter:

(1) Allan variance computing method

Allan Variance Method is a kind of time-domain analysis technology, and it can be used for extracting the feature of noise in stochastic process of data.This technology puts forward on the basis of group analysis method, array has been assigned in the group of unit length, the mean value of each group can be calculated, and the conversion of any two data points can be obtained by the mean value of continuous print group, by choosing different group's time or correlation time just can calculate Allan variance.

The calculation procedure of Allan variance is as follows:

A) be t in the sampling period ₀in, get v gyro sample data, so just can have representing of B sample with in K=v/B group, wherein each group.So the mean value of each group just can calculate with following formula:

B) formula solving the average difference of adjacent two groups is as follows:

Here, <> represents whole mean value, and τ is the length of this group.

Can be expressed as by the Allan variance of abbreviation two groups:

C) by a lot of samples in each group are divided into two parts, then reuse Allan formula of variance (until group's length is less than n/2), just can calculate the variance of distinct group length.By being drawn in log-log coordinate by the group length τ of variance yields and expectation, the relation of Allan variance and group's time just can show, and Here it is σ (τ)-τ is two, curve, also becomes Allan variance curve.

D) power spectrum density (PSD) of the main advantage of this method to be Allan variance the be stochastic process with noise own is related.Can prove, Allan variances sigma ²(τ) with the power spectrum S of stochastic process affecting fiber optic gyroscope performance _ωf () has unique determination relation:

${\mathrm{\&sigma;}}^2\left(\mathrm{\&tau;}\right)=4{\&Integral;}_0^{\mathrm{\&infin;}}{S}_{\mathrm{\&omega;}}\left(f\right)\frac{{\sin }^4(\&Pi;f\mathrm{\&tau;})}{{(\&Pi;f\mathrm{\&tau;})}^2}df.$

In formula, S _ωf power spectrum density (PSD) that () is this signal.

Just because of PSD and the Allan variance of noise is relevant, Allan variance is utilized to be a kind of important method to calculate the power spectrum density of different noise.Use power spectrum S _ωf the formula of () replaces the PSD of noise, so just can obtain the relation of noise figure and Allan variance.Therefore, matching and identification can be carried out according to the result of Allan variance analysis to the noise item in gyro.

Allan variance analysis is usually relevant with the multiple noise of optical fibre gyro, mainly contains these several noises such as random walk coefficient, zero inclined instability, rate ramp, quantizing noise, speed random walk and correlation of indices noise.

(2) quantizing noise

The quantizing noise of optical fibre gyro results from simulating signal when being converted to digital signal, and the quantization step size in analog to digital converter determines its size.Quantizing noise represents the level of the lowest resolution of optical fibre gyro usually, and its power spectrum density can be expressed as:

In formula, Q is quantizing noise coefficient.

Can obtain through Integral Processing:

Taken the logarithm in above formula both sides simultaneously:

As can be seen from above formula, the slope in σ (τ) and the log-log coordinate system of group's time is this error that-1 curve has showed in test data.Quantizing noise coefficient can from curve place obtains.

(3) angle random walk

Angle random walk in optical fibre gyro is originated the spontaneous radiation of photon that mainly light source exports.In addition, a kind of correlation time high frequency noise shorter than the sampling time of showing as also can produce this noise.Can be expressed as through revising its power spectrum density:

In formula, N is angle random walk coefficient.

Take the logarithm in formula two ends:

So the slope in the log-log coordinate system of Allan skew and group time σ (τ) has showed this error for-1/2 curve, the coefficient of this noise directly can read from τ=1 of this curve.

(4) zero inclined instability

The electron device of fibre optic gyroscope inside is highstrung to rocking at random, is also because just create unstable skew like this.Due to its low frequency characteristic, show as the fluctuation of zero inclined value in the data.The power spectrum density of this low-frequency noise can be expressed as:

In formula, B _sfor noise amplitude, the unit of angular speed is identical; f ₀for cutoff frequency.Above formula is substituted in group's formula of variance, can be obtained by integration:

In formula, C _ifor Cosin intergal function.

Can prove, τ < < 1/f ₀time, have and as τ > > 1/f ₀time, formula is taken the logarithm, therefore, can find that this error slope that correspond in Allan conversion and group's time log-log coordinate system is one section of level curve of 0, its ordinate indication be the zero inclined instability coefficient of optical fibre gyro

(5) speed random walk

Speed random walk is a stochastic process of not knowing source of error, may be producing for the correlation of indices noise being limited in very long correlation time.Its power spectrum density can be expressed as:

In formula, K is speed random walk coefficient.

Above formula is substituted in group's formula of variance, can be obtained by integration:

Taken the logarithm in formula both sides simultaneously:

So can obtain according to above formula, this error slope that correspond in Allan conversion and the log-log coordinate system of group's time is one section of curve of+1/2, and this noise figure can be obtained by the numerical value on curve during τ=3.

(6) rate ramp

Rate ramp has showed the slow monotonicity conversion a long-time inner fiber gyro intensity of light source.This error is mainly determined by external environment, instead of migration noise.

Rate drift slope can be expressed as:

In formula, R is rate ramp coefficient.

Corresponding Allan variance is:

Taken the logarithm in above formula both sides simultaneously:

Can find out, this error can be from the slope Allan conversion and the log-log coordinate of group's time+1 curve show, this noise figure can from curve read.

(7) the noise figure matching of Allan variance

In general, the data in optical fibre gyro test result can comprise above-mentioned all or part of noise type, and different noises appears in different τ territories.So total Allan variance just can be considered as be every noise Allan variance and, that is:

By minimum variance matching, every noise figure can be obtained:

By 5 rank batten minimum variance matchings, can obtain every noise figure, formula used is as follows:

According to this formula, corresponding noise figure just can be calculated.

As introducing before, signal of fiber optical gyroscope is exactly typical non-linear, non-stationary signal, polymerization empirical mode decomposition method and FIR filter method are applicable to very much processing the noise in signal of fiber optical gyroscope, thus can realize the object of increase and outstanding gyro signal.

Summary of the invention

The object of the invention is to propose a kind of for the many noises of data of optical fiber gyroscope and the denoising method of weak output signal feature, adopt the hybrid filters solutions in conjunction with EEMD and FIR, contrast the precision that traditional filtering algorithm significantly improves optical fibre gyro test on filter effect.

The object of the invention is to be achieved through the following technical solutions:

Based on a mixed type signal of fiber optical gyroscope filtering method of EEMD and FIR, be divided into four steps, concrete steps are as follows:

Step one: utilize EEMD algorithm to decompose signal of fiber optical gyroscope, obtains each layer IMF component and residual error;

Step 2: Hilbert transform is carried out to every layer of IMF component, obtains its amplitude and instantaneous frequency, and extrapolate threshold value according to instantaneous frequency, by threshold calculations weights;

Step 3: adopt FIR filter to carry out FIR filtering process to every layer of IMF component and residual error, obtain new each layer IMF component and residual error;

Step 4: be weighted reconstruct by by the new IMF after FIR filter process, the result after final formation denoising.

In order to increase the effect of polymerization empirical mode decomposition method, two kinds of good digital filtering methods are combined by the present invention's design, and convert the accurate instantaneous frequency obtained in conjunction with HT, design a kind of mixed filtering method of more applicable signal of fiber optical gyroscope.Compared with prior art, tool of the present invention has the following advantages:

1, the present invention proposes the filtering method of mixed polymerization empirical mode decomposition method and FIR filter.This method is the advantage combining two kinds of methods, improves data decomposition precision, then carries out low-pass filtering further by FIR filter method, improve frequency accuracy during EEMD signal transacting, filter effect is obviously strengthened by EEMD method.Ensure that method still based on the method for data simultaneously, modeling need not be carried out to data, widely applicable.

2, the present invention enters Hilbert-Huang transform, utilizes HT to convert the instantaneous frequency calculated and carries out frequency categorization further, in proper order for reconstructing according to the weighting carrying out data, improves filter effect.

Accompanying drawing explanation

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

Fig. 2 is the filter effect comparison diagram of the inventive method;

Fig. 3 is the signal to noise ratio (S/N ratio) Comparative result figure adopting EMD, EEMD and FIR and the inventive method effect;

Fig. 4 is the related coefficient Comparative result figure adopting EMD, EEMD and FIR and the inventive method effect;

Fig. 5 is the process flow diagram implementing Allan variance method of testing;

Fig. 6 is the effect contrast figure after the Allan variance of original signal and employing the inventive method;

Fig. 7 is the effect contrast figure after the Allan variance of employing EMD method and employing the inventive method;

Fig. 8 is the effect contrast figure after the Allan variance of employing EEMD method and employing the inventive method;

Fig. 9 is the effect contrast figure after the Allan variance of employing FIR method and employing the inventive method.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is further described; but be not limited thereto; everyly technical solution of the present invention modified or equivalent to replace, and not departing from the spirit and scope of technical solution of the present invention, all should be encompassed in protection scope of the present invention.

Embodiment one: a kind of mixed type signal of fiber optical gyroscope filtering method based on EEMD and FIR, as shown in Figure 1, be divided into four steps, concrete steps are as follows:

Step one: utilize EEMD algorithm to decompose signal of fiber optical gyroscope.

EEMD decomposition is carried out to signal of fiber optical gyroscope x (t), obtains k IMF component.

1. add to input signal x (t) the white noise n that amplitude is A _q(t), thus the signal x that formation one is new _q(t):

x _q(t)＝x(t)+An _q(t)。

The upper limit of the selection of this amplitude A is generally 0.2 times of input signal peak swing, and range of choice is 0.1 times of signal standards difference to 0.5 times.

2. carry out EMD decomposition to the new signal produced, the intrinsic mode function IMF obtaining this time experiment gathers.

The screening decomposable process of EMD is summarized as follows:

(1) signal x is obtained _qt Local modulus maxima that () is all and minimum point;

(2) generation x is constructed by extreme point respectively _qt the coenvelope function of () and lower envelope function, be designated as respectively with

(3) mean value function of envelope is generated:

$m_{1_q}\left(t\right)=\frac{e_{{\max }_q}\left(t\right)+e_{{\min }_q}\left(t\right)}{2}.$

(4) signal x is tried to achieve _q(t) function difference functions:

$h_{1_q}\left(t\right)=x_q\left(t\right)-m_{1_q}\left(t\right).$

Judge that above formula is two conditions of all reversion IMF definition.Ideally, if meet the condition of IMF hypothesis, then for x _qfirst IMF component of (t); Otherwise will regard original signal as and carry out first two steps operation, try to achieve this process may repeat k step until meet IMF condition, now try to achieve first

(5) residue functions is calculated will be assigned to original signal, constantly right said process is carried out in circulation, and then tries to achieve second IMF component so carry out N time, k IMF component can be obtained, and a residual error function component so far, x _qt () consists of:

$x_q\left(t\right)=\underset{i=1}{\overset{N}{\&Sigma;}}{c}_{i_q}\left(t\right)+r_{k_q}\left(t\right).$

Wherein: for the IMF component of i-th in EMD pilot process, its subscript q shows that this signal derives to add white noise n _qthe new signal x of (t) _qthe decomposition result of (t).

3. for i-th IMF function c _i(t), i=1 ... k, all need repetition step 1. with step 2. Q time, and computation of mean values obtains end value:

$c_i\left(t\right)=\underset{Q\&RightArrow;\mathrm{\&infin;}}{\lim }\frac{1}{Q}\underset{q=1}{\overset{Q}{\&Sigma;}}{c}_{i_q}\left(t\right).$

Wherein: Q is referred to as to gather yardstick, be a positive integer selected in advance, during actual enforcement, select data to be similar to infinity.

Note: set yardstick Q is directly proportional to the Decomposition Accuracy of EEMD algorithm, and set yardstick is larger, and so Decomposition Accuracy is higher.But consider that computing is consuming time, the scope that the present invention is set to gather yardstick Q is 5 ~ 50.

Step 2: carry out Hilbert transform (HilbertTransform, HT) to every layer of IMF, obtains its amplitude and instantaneous frequency, and extrapolates threshold value according to instantaneous frequency.

First, for k the IMF function c obtained in step one _i(t), i=1 ... k, calculates its Hilbert transform y by following formula _i(t):

Secondly, c is calculated by following formula _ithe analytic signal c of (t) _i(t)+jy _ithe envelope amplitude a of (t) _i(t):

$a_i\left(t\right)=\sqrt{{c_i}^2\left(t\right)+{y_i}^2\left(t\right)}.$

Finally, the phase angle theta of analytic signal is calculated by following formula _i(t) and instantaneous frequency f _i(t):

${\mathrm{\&theta;}}_i\left(t\right)=arctan\left(\frac{y_i\left(t\right)}{c_i\left(t\right)}\right),$

$f_i\left(t\right)=\frac{1}{2\mathrm{\&pi;}}\frac{d}{dt}{\mathrm{\&theta;}}_i\left(t\right).$

Due to for signal of fiber optical gyroscope, noise is that frequency is higher relative to the data of gyro itself, so carry out to signal the denoising effect that low-pass filtering can realize signal of fiber optical gyroscope.And because EEMD decomposition method is that signal is divided into multilayer IMF by frequency, so carry out HT conversion for each layer IMF, the frequency f of each layer can be analyzed by the instantaneous frequency obtained _it (), by arranging cutoff frequency f _ct (), just can arrange the weight of weight value reconstruction, thus realize the effect of low-pass filtering.

$\left\{\begin{array}{cc}{f}_i\left(t\right)\&GreaterEqual;f_c\left(t\right),& {\mathrm{\&alpha;}}_i=0\\ f_i\left(t\right)<f_c\left(t\right),& {\mathrm{\&alpha;}}_i=1\end{array}\right..$

Step 3: adopt FIR filter to carry out filtering to IMF.

According to the spectrum analysis of signal of fiber optical gyroscope, the cutoff frequency needed for selection, selects the frequency range after normalization to be 0.1 ~ 0.25 in the present invention.

FIR Filter Parameter Design is carried out to the IMF component of every layer.

FIR filter is a kind of digital filtering method adding finite data window length, and it has good filter effect.The difference equation of the FIR filter on M-1 rank is as follows:

f(n)＝b ₀x(n)+b ₁x(n-1)+…+b _M-1x(n-M-1)

The FIR filter of windowed function is adopted to design, according to the normalized frequency of cutoff frequency and sample frequency, design FIR filter parameter

Adopt iterative formula, the basic step by window function metht design FIR filter:

(1) H _d(e ^jw) be launched into Fourier series, obtain coefficient h _d(n);

(2) by h _dn () is truncated to required length naturally, i.e. 2M+1;

(3) by the h after brachymemma _dn () to move to right M sampling interval, obtains h (n);

(4) h (n) is multiplied by suitable window function w (n), namely obtains the shock response of designed wave filter;

(5) test filter performance.

So adopt the iterative manner of such windowed function can carry out FIR filtering process to every layer of IMF and residual error, obtain new each layer IMF component c' _i(t) and residual error r' _n(t).

Step 4: be weighted reconstruct by by the new IMF after FIR filter process, the result after final formation denoising.

The present invention adopts data weighting mode by signal data new for the heavy formation after denoising, and this signal is the signal after denoising, that is:

$x^{\&prime;}\left(t\right)=\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&alpha;}}_i\&CenterDot;{c^{\&prime;}}_i\left(t\right)+{r^{\&prime;}}_N\left(t\right).$

In formula: x'(t) be the signal after denoising; α _ifor the weights of each component are obtained by step 2; C' _i(t) (i=1,2 ..., N) and r' _nt () is each IMF component after denoising and residual error.

Embodiment two: present embodiment is chosen one group and verified the present invention with the signal data that true fiber gyro exports, thus realize utilizing the inventive method to carry out filtering process to data of optical fiber gyroscope.

First gyro data is chosen.Testing apparatus of the present invention is high-precise uniaxial rate table and dsPIC singlechip Acquisition Processor mainly.And testing sensor is selected is XW-GS1810-100 fibre optic gyroscope.XW-GS1810-100 fibre optic gyroscope is by a kind of all solid state middle accuracy inertial senser element collecting light, mechanical, electrical one of Beijing StarNeto Technology Development Co., Ltd.'s independent research.It has the features such as reliability is high, response band is wide, power supply is simple, power is low, and being mainly applicable to stable platform, dynamically steady picture etc. and controlling application, is the desirable inertia device replacing traditional mechanical gyro.In general, the performance of this fibre optic gyroscope can represent the effect of the optical fibre gyro on current market, can be used for verification algorithm, meets requirement of the present invention.

Obtain the data that optical fibre gyro exports, placed by optical fibre gyro on high-precise uniaxial velocity of variation turntable, allow turntable with constant speed low speed rotation, the data of optical fibre gyro test are transferred at host computer via after single-chip microcomputer process.

This experimental selection gathers the data of optical fiber gyroscope of a hour, nearly 59000 altogether, consider that boundary effect may be decomposed filtering algorithm low frequency to have problems and unnecessary dispersing, so selecting when selecting data border to be stably, to clip beginning and ending two sections when data intercept, selecting 10000 data at equal intervals and testing.

Perform step one: adopt polymerization empirical mode decomposition EEMD method to decompose signal of fiber optical gyroscope data.

Before utilizing EEMD method, need to arrange the parameter of EEMD algorithm, the amplitude A of the white noise namely added also has set yardstick Q parameter.

According to 0.2 times that the upper limit of amplitude A is input signal maximum amplitude, be generally 0.1 times of signal standards difference to 0.5 times.So be 0.0251 according to the standard of this signal of fiber optical gyroscope, amplitude A is selected to be 0.001; Consider that set yardstick Q is larger, Decomposition Accuracy is higher, and method operand is more, so under synthesis precision and operation time, selects set yardstick Q to be 20.

Decompose through EEMD, according to data volume, gyro data is divided into 14 IMF layers.

Perform step 2: utilize each layer IMF of Hilbert transform pairs to carry out HT and analyze by threshold calculations weights.

HT conversion is carried out to each layer IMF, obtains y (t).Because HT conversion is signal is carried out the upset of 90 °, so analytic signal c (t)+jy (t) can be passed through, calculate envelope range value a (t).

And then arc tangent formula can be utilized to calculate the phase angle theta (t) of analytic signal, then by can instantaneous frequency f (t) be obtained to phase angle differential.

Comparing according to carrying out judgement with the cutoff frequency 20Hz of optical fibre gyro, the weights of weighting reconstruct can be calculated.

Perform step 3: adopt FIR filter to carry out low-pass filtering treatment to IMF.

Calculate the FIR filter parameter of the low-pass filtering for IMF according to cutoff frequency 20Hz, realize FIR filter effect by window mode, filtering process is carried out to each layer IMF of the signal of fiber optical gyroscope that EEMD decomposites.

Perform step 4: carry out data fusion to by the data after the process of FIR filter method, according to the weight arranged before, weighting reconstructs the data made new advances, and these data are exactly the filtered result of optical fibre gyro.According to weights, the present invention selects the composition reducing front 4 IMF, and with the value of residual error after increase, thus form low-pass filter, reach filter effect, the result obtained as shown in Figure 2.

In order to prove the validity of the inventive method, experimental selection adopts FIR filter, EMD method, EEMD method to contrast.

Because Optical Fiber Gyroscope itself has been rich in a large amount of noises, thus the object that the present invention is main carries out signal transacting, by choosing suitable denoising method, denoising is carried out to signal, so the data after process and real signal can be analyzed, can denoising effect be compared by the relation between analytic signal with its noise, choose suitable method with this.Conventional analytical parameters is signal to noise ratio (S/N ratio) and related coefficient.

Signal to noise ratio (S/N ratio) refers to the ratio of signal power and noise power, and it is defined as:

$SNR=10\&times;\lg \left(\frac{{\mathrm{power}}_{signal}}{{\mathrm{power}}_{noise}}\right);$

${\mathrm{power}}_{signal}=\frac{1}{N}\underset{k=1}{\overset{N}{\&Sigma;}}{f}^2\left(k\right);$

${\mathrm{power}}_{noise}=\frac{1}{N}\underset{k=1}{\overset{N}{\&Sigma;}}{\left(f\right(k)-\hat{f}(k\left)\right)}^2.$

In formula, power _signalfor the power of actual signal, power _noisefor the power of noise, f (k) is actual signal, for the reconstruction signal after denoising, N is signal length.Computing formula according to SNR can draw, denoising effect is more obvious, and signal to noise ratio (S/N ratio) is larger.

If x (n), y (n) are the deterministic signals of finite energy, its related coefficient is defined as:

${\mathrm{\&rho;}}_{xy}=\frac{\underset{n=0}{\overset{\mathrm{\&infin;}}{\&Sigma;}}x\left(n\right)y\left(n\right)}{{\&lsqb;\underset{n=0}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{x}^2\left(n\right)\underset{n=0}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{y}^2\left(n\right)\&rsqb;}^{1/2}}.$

Obtained according to permitting watt hereby (Schwartz) inequality:

|ρ _xy|≤1。

Work as ρ _xywhen=1, show two signals x (n) and y (n) completely relevant (or equal); Work as ρ _xywhen=0, show that two signals x (n) are completely uncorrelated with y (n); Work as ρ _xybetween during value, show the size of certain degree of correlation between signal x (n) and y (n).

The method of signal to noise ratio (S/N ratio) and related coefficient is enough to the filter strength after showing denoising and distortion phenomenon, so the present invention selects these two kinds of methods verify and choose applicable wavelet analysis method of the present invention.

Experimental data is carried out the calculating of signal ratio and related coefficient, experimental result as shown in Figure 3 and Figure 4.

As can be seen from data result, mixed type polymerization empirical mode decomposition method of the present invention has higher signal to noise ratio (S/N ratio) and related coefficient, that is with the noise contribution in the data of optical fiber gyroscope of the inventive method denoising less and more press close to True Data, comparing additive method has obvious filtering advantage.

On the other hand, in order to verify the effect of data of optical fiber gyroscope signal, for the scaling method of optical fibre gyro, Allan variance is adopted to compare the School Affairs that data are carried out again.

Allan variance a kind ofly has well to the demarcation rule of the optical gyroscope of the Detection results of optical equipment, so the present invention selects Allan variance as the verification method to method of testing.

Known according to introducing above, each overriding noise of optical fibre gyro all can utilize Allan variance analysis method to calculate.Concrete Allan variance analysis flow process as shown in Figure 5.

Gather static normal temperature data of optical fiber gyroscope to carry out classified calculating and record group variance, realize Allan variance analysis process, then by data analysis, the data of matching out each coefficient, both can obtain the situation of corresponding various errors.

Experimental data is divided into groups, is divided into 7 groups, the mean value of adjacent array is subtracted each other, and process is carried out to data obtain group variance, draw log-log coordinate by group's variance and time relationship;

Then, 5 rank batten minimum variance the Fitting Calculation are carried out to group's variance data, be defined according to Allan variance the size that correspondence position obtains every noise.

Because Allan variance has the effect well analyzing optical instrument, so select Allan variance to raw data, traditional E EMD, FIR filter, also have the inventive method to carry out analysis and analyze, verify filtering algorithm with this.Experimental result is as shown in table 1 and Fig. 6-9.

Table 1 is to the Allan variance result of calculation of data of optical fiber gyroscope after multiple filtering method process

	Quantizing noise	Random walk coefficient	Zero inclined instability	Speed random walk	Rate ramp
						Original	0.016403	0.000183	0.011675	0.170891	1.021896
EMD	0.011914	0.000253	0.011013	0.170480	1.019614
						EEMD	0.011673	0.000257	0.010944	0.169751	1.015392
FIR	0.010542	0.000244	0.010266	0.151644	0.926155
						EEMD+FIR	0.004437	0.000296	0.009761	0.154581	0.938575

As can be seen from the results, inventive result has good filter effect, and each noise component has certain advantage.The noise effect of optical fibre gyro number is mainly subject to drift, and this part must be removed during optical fibre gyro is anticipated, so drift instability just seems especially important.As can be seen from list data, algorithm of the present invention has good effect at the inclined instability of process zero, can say that method can have good effect to restraint speckle.

By analyzing result, can find, the noise medium-rate slope noise of optical fibre gyro occupies main status, and rate ramp is a kind of noise error by ectocine, so represent the interference mainly coming from the external world in the random noise for this optical fibre gyro.Also saying as analysis, the test that this raw data is carried out just under a comparatively noisy working environment, so the environment only need improveing the external world, data just can be improved.

And typically, because quantizing noise caused analog-to-digital time, change system enlargement factor can be passed through, change.From numerical value, current test data conversion scheme does not cause very large quantizing noise to optical fibre gyro, concept feasible, shows that data acquisition system (DAS) precision is higher.

And angle random walk is caused by optical fibre gyro internal performance, and speed random walk is also a kind of random quantity, so substantially have no idea to be changed by the external world.Zero inclined instability, mainly caused by alignment error and internal electronic device, so in order to improve this noise, should be noted that fixing means during installation, can be passed through to increase counterweight, pressing plate etc.This experiment adopts bolt fastening mount scheme, is also feasible data.

Analyze from data, the partially unstable numerical value of the angle random walk of this signal of fiber optical gyroscope and zero is minimum, show drive and sensed-mode stability better.

Claims (7)

1., based on a mixed type signal of fiber optical gyroscope filtering method of EEMD and FIR, it is characterized in that described method is divided into four steps, concrete steps are as follows:

Step one: utilize EEMD algorithm to decompose signal of fiber optical gyroscope, obtains each layer IMF component and residual error;

Step 2: Hilbert transform is carried out to every layer of IMF component, obtains its amplitude and instantaneous frequency, and extrapolate threshold value according to instantaneous frequency, by threshold calculations weights;

Step 3: adopt FIR filter to carry out FIR filtering process to every layer of IMF component and residual error, obtain new each layer IMF component and residual error;

Step 4: be weighted reconstruct by by the new IMF after FIR filter process, the result after final formation denoising.

2. the mixed type signal of fiber optical gyroscope filtering method based on EEMD and FIR according to claim 1, is characterized in that the concrete steps of described step one are as follows:

1. add to optical fibre gyro input signal x (t) the white noise n that amplitude is A _q(t), thus the signal x that formation one is new _q(t):

x _q(t)＝x(t)+An _q(t)；

2. carry out EMD decomposition to the new signal produced, the intrinsic mode function IMF obtaining this time experiment gathers x _q(t):

$x_q\left(t\right)=\underset{i=1}{\overset{N}{\&Sigma;}}{c}_{i_q}\left(t\right)+r_{k_q}\left(t\right).$

Wherein: for the IMF component of i-th in EMD pilot process, its subscript q shows that this signal derives to add white noise n _qthe new signal x of (t) _qthe decomposition result of (t), for residual error function component, N is for decomposing number of times;

3. repeat step 1. with step 2. Q time, and computation of mean values, obtains final IMF function, that is:

$c_i\left(t\right)=\underset{Q\&RightArrow;\mathrm{\&infin;}}{\lim }\frac{1}{Q}\underset{q=1}{\overset{Q}{\&Sigma;}}{c}_{i_q}\left(t\right).$

Wherein: Q is referred to as to gather yardstick.

3. the mixed type signal of fiber optical gyroscope filtering method based on EEMD and FIR according to claim 2, it is characterized in that the upper limit of the selection of described amplitude A is 0.2 times of input signal peak swing, range of choice is 0.1 times of signal standards difference to 0.5 times.

4. the mixed type signal of fiber optical gyroscope filtering method based on EEMD and FIR according to claim 1, is characterized in that the scope of described set yardstick Q is 5 ~ 50.

5. the mixed type signal of fiber optical gyroscope filtering method based on EEMD and FIR according to claim 1, is characterized in that the concrete steps of described step 2 are as follows:

(1) by following formula to the k obtained in step one IMF function IMF:c _i(t), t=1,2 ..., k carries out discrete convolution and obtains its Hilbert transform y _i(t):

$y_i\left(t\right)=c_i\left(t\right)*\frac{1}{\mathrm{\&pi;}t};$

(2) c is calculated by following formula _ithe analytic signal c of (t) _i(t)+jy _ithe envelope amplitude a of (t) _i(t):

$a_i\left(t\right)=\sqrt{{c_i}^2\left(t\right)+{y_i}^2\left(t\right)};$

(3) phase angle theta of analytic signal is calculated by following formula _i(t) and instantaneous frequency f _i(t):

${\mathrm{\&theta;}}_i\left(t\right)=arctan\left(\frac{y_i\left(t\right)}{c_i\left(t\right)}\right),$

$f_i\left(t\right)=\frac{1}{2\mathrm{\&pi;}}\frac{d}{dt}{\mathrm{\&theta;}}_i\left(t\right);$

(4) by instantaneous frequency f _i(t) and cutoff frequency f _ct () is carried out judgement and is compared, can calculate the weights α of each component of weighting reconstruct _i:

$\left\{\begin{array}{cc}{f}_i\left(t\right)\&GreaterEqual;f_c\left(t\right),& {\mathrm{\&alpha;}}_i=0\\ f_i\left(t\right)<f_c\left(t\right),& {\mathrm{\&alpha;}}_i=1\end{array}\right..$

6. the mixed type signal of fiber optical gyroscope filtering method based on EEMD and FIR according to claim 5, is characterized in that described cutoff frequency f _ct () scope is 0.1 ~ 0.25.

7. the mixed type signal of fiber optical gyroscope filtering method based on EEMD and FIR according to claim 1, it is characterized in that in described step 4, adopt data weighting mode by signal data new for the heavy formation after denoising, this signal is the signal after denoising, that is:

$x^{\&prime;}\left(t\right)=\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&alpha;}}_i\&CenterDot;{c^{\&prime;}}_i\left(t\right)+{r^{\&prime;}}_N\left(t\right);$

In formula: x'(t) be the signal after denoising; α _ifor the weights of each component are obtained by step 2; C' _i(t) and r' _nt () is each IMF component after denoising and residual error.