CN103674001A - Fiber gyroscope denoising method based on enhanced adaptive time-frequency peak value filtration - Google Patents

Abstract

The invention discloses a fiber gyroscope denoising method based on enhanced adaptive time-frequency peak value filtration. The fiber gyroscope denoising method comprises the steps of resizing a noise-containing output signal of an original fiber gyroscope, encoding the noise-containing output signal of the original fiber gyroscope into a frequency modulation analysis signal of which the amplitude value is a constant, selecting an optimal window length, optimizing a signal transient frequency estimation range, estimating a transient frequency of the frequency modulation signal according to a pseudo-Wingner-Ville distribution peak value, demodulating a transient frequency estimation peak value of the modulation signal and performing back-resizing to recover the denoised output signal of the fiber gyroscope. The method disclosed by the invention can be used for denoising signals of inertial equipment such as the fiber gyroscope. Compared with the conventional gyroscope denoising method, the method disclosed by the invention is flexible to implement, can effectively track dynamic signals such as an original signal and does not have time delay. By the adoption of the enhanced adaptive time-frequency peak value filtration method, the method can be used for optimize the frequency estimation range to obtain a better frequency estimation value of an encoded signal.

Description

A kind of optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering

Technical field

The present invention relates to a kind of optical fibre gyro denoising method, relate in particular to a kind of optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering, belong to inertial navigation technology field.

Background technology

Fiber strapdown inertial navigation system system bulk is little, precision is high, reliability is strong, independence is high, cost is relatively low, in fields such as Aeronautics and Astronautics, navigations, is widely used.As one of core parts of inertial navigation system, the output accuracy of optical fibre gyro directly affects the performance of inertial navigation system.In real work, be subject to the impact of ambient noise, the useful signal of optical fibre gyro tends to be submerged in a large amount of noises, greatly reduces gyrostatic measuring accuracy.Therefore how noise decrease becomes the problem of needing solution badly on the impact of optical fibre gyro useful signal.

For the signal processing method of optical fibre gyro, scholar both domestic and external has carried out a large amount of research, and main method has Kalman filtering method, small echo (bag) filter method, neural net method etc.Kalman filtering method adopts optimum Kalman filter to carry out Real-Time Filtering to gyro and accelerometer signal.In this algorithm, optimum Kalman filtering parameter need to be calculated in advance, and under current intelligence, the output signal that different rotary angular speed is corresponding is different, therefore need to change the moment in the stage computer card Kalman Filtering parameter value of turning rate.Small echo (bag) filter method adopts one-dimensinal discrete small wave transformation or wavelet packet to signal of fiber optical gyroscope real-time de-noising.But for dynamic gyro signal, the larger signal that particularly suddenlys change, wavelet transformation is the trend of tracking signal in time, and have certain time delay.Neural net method adopts the drifting error model of RBF neural network gyro, and gyroscopic drift error is compensated.But the method need to be accumulated certain data volume and be carried out realizing the modeling of neural network to error.

In Time-Frequency Analysis Method, wavelet filteration method is widely used aspect gyroscope signal process, additive method as the application based on Wigner-Ville distribution, the distribution of Cohen class etc. seldom.Consideration is applied to optical fibre gyro denoising by the time-frequency peak filtering method distributing based on Wigner-Ville, for the noise processed of gyro provides new thinking.Do not find at present relevant patent both at home and abroad.Domestic have paper to propose to adopt time-frequency peak filtering method to carry out the elimination of seismic signal noise, the Master's thesis < < writing as Song Pengtao based on time become the Denoising of Seismic Data research > > (Jilin University of the long time-frequency peak filtering of window, in June, 2012), also there is paper to propose adaptive pseudo-Wigner-Ville location mode abroad, paper < < Nonlinear IF Estimation Based on the Pseudo WVD Adapted Using the Improved Sliding Pairwise ICI Rule > > (the IEEE Signal Processing Letters writing as Jonatan Lerga etc., in November, 2009).

Summary of the invention

Technical matters

The technical problem to be solved in the present invention is to provide a kind of optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering, the method forwards signal of fiber optical gyroscope to frequency domain analysis from time domain, original signal is modulated into the instantaneous frequency of an analytic signal, on this basis, adopt pseudo-Wigner-Ville distribution to extract the instantaneous frequency of this frequency modulated signal of peak estimation of signal time-frequency conversion, recover original signal, be applicable to the denoising process of optical fibre gyro.

Technical scheme

In order to solve above-mentioned technical matters, the optical fibre gyro denoising method (IATFPF, Enhanced adaptive time-frequency peak filtering) based on strengthening self-adaptation time-frequency peak filtering of the present invention comprises the following steps:

Step 1: the noisy output signal of original fiber gyro is carried out to convergent-divergent, its amplitude is zoomed in certain interval range, avoid coded signal to cause aliasing;

Wherein, the noisy output signal of original fiber gyro is expressed as:

y(t)=x(t)+ε(t)

Wherein, wherein, t is the time, and y (t) is the noisy output signal of optical fibre gyro, and x (t) is the useful signal of gyro output, and ε (t) is gyro noise;

Signal indication after convergent-divergent is:

$y_c\left(t\right)=0.5*\frac{y\left(t\right)-\min \left[y\left(t\right)\right]}{\max \left[y\left(t\right)\right]-\min \left[y\left(t\right)\right]}$

Wherein, max[y (t)] and min[y (t)] maximal value and the minimum value function of y (t) represented respectively;

Step 2: the noisy output signal of proportion modulation system coding original fiber gyro is the frequency modulation (PFM) analytic signal that an amplitude is constant by Signal coding, is expressed as:

$z_y\left(t\right)={\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000417097930000012.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$

Wherein, λ is integration variable, and μ is scale parameter;

Step 3: adopt the pseudo-Wigner-Ville distribution window function that adaptive approach is coded signal to select optimum window long;

Step 4: according to optimum window function length, optimize signal transient Frequency Estimation scope;

Step 5: in the Signal estimation frequency range of optimizing in step 4, adopt the instantaneous frequency of pseudo-this frequency modulated signal of Wigner-Ville distribution peak estimation;

Step 6: the instantaneous Frequency Estimation peak value of modulation signal is separated to the anti-convergent-divergent of mediation, recover to obtain the Optical Fiber Gyroscope after denoising.

In step 3, the pseudo-Wigner-Ville distribution of signal window function is defined as:

${\mathrm{PWVD}}_x(t,\mathrm{\&omega;})={\&Integral;}_{-\&infin;}^{+\&infin;}x(t+\mathrm{\&tau;}/2)x^{*}(t-\mathrm{\&tau;}/2)h\left(\mathrm{\&tau;}\right)e^{-\mathrm{j\&omega;\&tau;}}\mathrm{d\&tau;}=W_x(t,\mathrm{\&omega;})*H\left(\mathrm{\&omega;}\right)$

Wherein, h (τ) is window function, and H (ω) is the Fourier transform of h (τ);

For coded signal z _y(t) peak value, distributing by its pseudo-Wigner-Ville can estimated signal instantaneous frequency be:

${\widehat{\mathrm{\&omega;}}}_h\left(t\right)=\arg \underset{\mathrm{\&omega;}}{\max }\left[W_x(t,\mathrm{\&omega;})\right]$

In formula, W _x(t, ω) is that the pseudo-Wigner-Ville of coded signal distributes, and ω is angular frequency,

represent W _xthe value of ω when (t, ω) reaches maximal value;

The exact value ω (t) of described instantaneous frequency is positioned at a fiducial interval, is expressed as:

$D_k\left(t\right)=[L_k\left(t\right),U_k\left(t\right)]=[{\widehat{\mathrm{\&omega;}}}_h\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_h,{\widehat{\mathrm{\&omega;}}}_h\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_h]$

In formula, L _kand U (t) _k(t) represent respectively the bound of fiducial interval, the estimated value that represents instantaneous frequency, κ σ _hrepresent random component;

For a long sequence H={h of the window increasing progressively ₁<h ₂< ... <h _j, h wherein _jbe not more than data sampling points N, definition

$O_k\left(t\right)=\frac{|D_k\left(t\right)\&cap;D_{k-1}\left(t\right)|}{\left|D_k\left(t\right)\right|}$

K=2 wherein, 3 ..., j, D _k(t), D _k-1(t) be that length of window is respectively h _k, h _k-1time instantaneous frequency exact value fiducial interval;

Ask for respectively the long corresponding fiducial interval registration O of each window in the long sequence H of window _k(t), set a certain threshold value O _thr, work as h ^*meet O _k(t)>=O _thr, and be maximal window wherein when long, h ^*for best window long.

In step 4, obtaining the long h of optimum window ^*basis on, ask for and be less than or equal to h ^*the long h of window _ithe frequency range of corresponding coded signal:

$D_{k_i}\left(t\right)=[L_{k_i}\left(t\right),U_{k_i}\left(t\right)]=[{\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i},{\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i}]$

In formula,

that length of window is h _itime instantaneous frequency exact value fiducial interval, with

the bound that represents respectively this fiducial interval,

represent the long h of window _ithe estimated value of corresponding instantaneous frequency, represent the long h of window _icorresponding random component;

According to above-mentioned fiducial interval

obtain new frequency range

${\widehat{\mathrm{\&omega;}}}_d\left(t\right)=\max ({\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i})$

${\widehat{\mathrm{\&omega;}}}_u\left(t\right)=\min ({\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i})$

In formula

with

represent respectively the bound of the instantaneous frequency fiducial interval of renewal.

In step 5, be less than or equal to the long long h of window of optimum window _iin choose minimum value h _m, obtaining window long is h _mtime pseudo-Wigner-Ville Distribution Value, and

in interval, select maximal value as the estimated value of signal frequency, that is:

${\widehat{\mathrm{\&omega;}}}_x\left(t\right)=\underset{\mathrm{\&omega;}\&Subset;[{\widehat{\mathrm{\&omega;}}}_d\left(t\right),{\widehat{\mathrm{\&omega;}}}_u\left(t\right)]}{\arg \max }\left[W_x(t,\mathrm{\&omega;})\right]$

In formula ${\widehat{\mathrm{\&omega;}}}_x\left(t\right)=\underset{\mathrm{\&omega;}\&Subset;[{\widehat{\mathrm{\&omega;}}}_d\left(t\right),{\widehat{\mathrm{\&omega;}}}_u\left(t\right)]}{\arg \max }\left[W_x(t,\mathrm{\&omega;})\right]$ Represent that ω exists $[{\widehat{\mathrm{\&omega;}}}_d\left(t\right),{\widehat{\mathrm{\&omega;}}}_u\left(t\right)]$ In scope, make W _xvalue when (t, ω) reaches maximal value.

In step 6, known coded signal z _y(t) instantaneous frequency, can recover original signal x (t), and original useful signal x (t) can recover by following formula:

${\hat{x}}_c\left(t\right)=\frac{{\widehat{\mathrm{\&omega;}}}_x\left(t\right)}{2\mathrm{\&pi;\&mu;}}$

In formula,

original noisy scale signal y _c(t) by the signal obtaining after time-frequency peak filtering,

The echo signal of estimating

can obtain by anti-zoom operations, after the denoising obtaining, Optical Fiber Gyroscope is:

$\hat{x}\left(t\right)=\frac{\max \left[x_c\left(t\right)\right]-\min \left[x_c\left(t\right)\right]}{0.5}{\hat{x}}_c\left(t\right)+\min \left[x_c\left(t\right)\right].$

Beneficial effect

The inventive method is the optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering, can be used for the signal denoising of the inertial equipments such as optical fibre gyro.Compare with existing gyro denoising method, the method realizes flexibly, for Dynamic Signal, can effectively follow the tracks of original signal, and life period does not postpone.The inventive method adopt to strengthen self-adaptation time-frequency peak filtering method, can optimization frequency estimation range, obtain more excellent coded signal frequency estimation.

Accompanying drawing explanation

Fig. 1 is the overall flow figure of the inventive method;

Fig. 2 is optimum window selection course schematic diagram in the step 3 of the inventive method;

The signal transient frequency estimating methods schematic diagram of Fig. 3 for strengthening.

Embodiment

Below in conjunction with accompanying drawing, the technical scheme of invention is elaborated:

The overall flow figure of the present embodiment method as shown in Figure 1, gyro signal modulation is become to the instantaneous frequency of a frequency modulated signal, the instantaneous frequency of the peak estimation coded signal distributing by pseudo-Wigner-Ville, and then reduction useful signal, realize the removal of optical fibre gyro noise.Concrete steps are as follows:

1. signal convergent-divergent

If containing noisy signal of fiber optical gyroscope model be:

y(t)=x(t)+ε(t) (1)

Wherein, t is the time, and y (t) is the noisy output signal of optical fibre gyro, and x (t) is the useful signal of gyro output, and ε (t) is gyro noise.

For avoiding coded signal to cause aliasing, need to carry out convergent-divergent to original signal.Signal y after convergent-divergent _c(t) can obtain by following formula:

$y_c\left(t\right)=0.5*\frac{y\left(t\right)-\min \left[y\left(t\right)\right]}{\max \left[y\left(t\right)\right]-\min \left[y\left(t\right)\right]}---\left(2\right)$

In formula, max[] and min[] maximal value and minimum value function represented respectively.

2. signal modulating-coding

By the noisy output signal of optical fibre gyro after frequency modulation (PFM) coding convergent-divergent, by signals and associated noises y _c(t) be encoded to a warbled analytic signal of normal amplitude:

$z_y\left(t\right)={\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000417097930000012.png"\; state="\{\{state\}\}">e</figure-callout>}}^j---\left(3\right)$

Wherein λ is integration variable, and μ is scale parameter, is similar to usually said frequency modulation (PFM) index.

3. pseudo-Wigner-Ville distributes

Time-frequency peak filtering need adopt Time-Frequency Analysis Method to analyze modulation signals, and in the various time-frequency distributions that proposed, time-frequency aggregation that Wigner-Ville distributes is best and form is simple, Wigner-Ville distribution theory is done to simple introduction below.

For signal x (t), its Wigner-Ville distributes and is defined as:

$W_x(t,\mathrm{\&omega;})={\&Integral;}_{-\&infin;}^{+\&infin;}x(t+\mathrm{\&tau;}/2)x^{*}(t-\mathrm{\&tau;}/2)e^{-\mathrm{j\&omega;\&tau;}}\mathrm{d\&tau;}---\left(4\right)$

In formula, τ is time variable, and ω is angular frequency.As can be seen from the above equation, the Wigner-Ville of signal distribution is its time autocorrelation function R (t, τ)=x (t+ τ 2) x ^*the Fourier transform of (t-τ 2), that is:

$W_x(t,\mathrm{\&omega;})={\&Integral;}_{-\&infin;}^{+\&infin;}x(t+\mathrm{\&tau;}/2)x^{*}(t-\mathrm{\&tau;}/2)e^{-\mathrm{j\&omega;\&tau;}}\mathrm{d\&tau;}={\&Integral;}_{-\&infin;}^{+\&infin;}R(t,\mathrm{\&tau;})e^{-\mathrm{j\&omega;\&tau;}}\mathrm{d\&tau;}---\left(5\right)$

When the instantaneous frequency of signal is a constant or the linear function of time, its Wigner-Ville is distributed as the impulse function of peak value respective signal instantaneous frequency, adopts the time-frequency peak filtering distributing based on Wigner-Ville can obtain without inclined to one side estimated signal.When the instantaneous frequency of signal is the nonlinear function of time, although its Wigner-Ville distribution energy concentrates on around instantaneous frequency, shape is no longer impulse function, causes time-frequency peak value to depart from instantaneous frequency, causes the deviation of estimation.For reducing estimated bias, conventionally use windowing Wigner-Ville to distribute, pseudo-Wigner-Ville distributes and replaces Wigner-Ville to distribute, by signal local linearization, to improve Frequency Estimation precision.For pseudo-Wigner-Ville, distribute, it is defined as follows:

${\mathrm{PWVD}}_x(t,\mathrm{\&omega;})={\&Integral;}_{-\&infin;}^{+\&infin;}x(t+\mathrm{\&tau;}/2)x^{*}(t-\mathrm{\&tau;}/2)h\left(\mathrm{\&tau;}\right)e^{-\mathrm{j\&omega;\&tau;}}\mathrm{d\&tau;}=W_x(t,\mathrm{\&omega;})*H\left(\mathrm{\&omega;}\right)---\left(6\right)$

Wherein, h (τ) is window function, and H (ω) is the Fourier transform of h (τ).

Because Wigner-Ville distributes, be defined in (∞ <t< ∞) on full-time countershaft, by energy distribution, represent the temporal properties of signal.In actual applications, the data of need analyzing are to have limit for length, therefore need in practice signal to add the window function sliding in time, and window function can make the Wigner-Ville of signal be distributed in to obtain in frequency direction level and smooth.

4. the optimum window of self-adaptation time-frequency peak value is selected

For improving the filter effect of time-frequency peak filtering, adopt pseudo-Wigner-Ville to distribute Optical Fiber Gyroscope is processed, the length of window that wherein How to choose is suitable is the problem that needs solution to obtain optimum filtering performance.When length of window is chosen when longer, in window, the statistical property of noise is just close to the zero mean characteristic of true white Gaussian noise, and time-frequency peak filtering strengthens the compacting ability of noise, but can cause the deviation increase of instantaneous Frequency Estimation; When length of window is chosen more in short-term, although can reduce the deviation of instantaneous Frequency Estimation, it can decline to the ability of noise compacting at frequency domain.When signal fluctuation is larger, the removal of selecting the long time-frequency peak filtering of fixed window to carry out random noise can not do the trick.So adopt self-adaptation time-frequency peak filtering.

For strengthening self-adaptation time-frequency peak filtering, its key is optimum length of window h ^*selection.

To coded signal z _y(t) peak value, distributing by its pseudo-Wigner-Ville can estimated signal instantaneous frequency be:

$\widehat{\mathrm{\&omega;}}\left(t\right)=\arg \underset{\mathrm{\&omega;}}{\max }\left[W_x(t,\mathrm{\&omega;})\right]---\left(7\right)$

For each moment t, the deviation chart of instantaneous Frequency Estimation is shown:

$\mathrm{\&Delta;}{\widehat{\mathrm{\&omega;}}}_h\left(t\right)=\mathrm{\&omega;}\left(t\right)-{\widehat{\mathrm{\&omega;}}}_h\left(t\right)---\left(8\right)$

Wherein, ω (t) represents instantaneous frequency value accurately,

the estimated value that represents instantaneous frequency.

Work as evaluated error

when smaller, error can be expressed as a definite component and random component and, that is:

$|\mathrm{\&omega;}\left(t\right)-{\widehat{\mathrm{\&omega;}}}_h\left(t\right)|\&le;\left|\mathrm{bias}(t,h)\right|+\mathrm{\&kappa;}{\mathrm{\&sigma;}}_h---\left(9\right)$

Wherein, | bias (t, h) | represent to determine component, κ σ _hrepresent random component; κ is the fractional bits of standard Gaussian distribution, along with the increase of κ, and probability P (κ) → 1; σ _hthat window length is the evaluated error of h

standard variance, for rectangular window, σ _hcan be expressed as:

${\mathrm{\&sigma;}}_h=\sqrt{\frac{6{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2}{{\left|A\right|}^2}(1+\frac{{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2}{2{\left|A\right|}^2})\frac{T}{h^3}}---\left(10\right)$

In formula,

for noise variance, A is signal amplitude, and T is signal sampling period, and h is length of window.

Wherein,

${\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2=({\mathrm{\&sigma;}}_{\mathrm{\&epsiv;<figure-callout\; id="2"\; label="r"\; filenames="HDA0000417097930000012.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;i}}^2)/2---\left(11\right)$

${\mathrm{\&sigma;}}_{\mathrm{\&epsiv;r}}=\frac{\{\mathrm{median}\left(\right|y_r\left(\mathrm{nT}\right)-y_r\left((n-1)T\right)\left|\right):n=2,...,N\}}{0.6745}---\left(12\right)$

${\mathrm{\&sigma;}}_{\mathrm{\&epsiv;i}}=\frac{\{\mathrm{median}\left(\right|y_i\left(\mathrm{nT}\right)-y_i\left((n-1)T\right)\left|\right):n=2,...,N\}}{0.6745}---\left(13\right)$

Wherein, σ _{ε r}and σ _{ε i}respectively σ _εreal part and imaginary part, y _rand y (nT) _i(nT) be respectively real part and the imaginary part of optical fibre gyro signals and associated noises y (nT), N is that signal sampling is counted.

And

$A^2+{\mathrm{\&sigma;}}_{\mathrm{\&epsiv;}}^2=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left|y\left(\mathrm{nT}\right)\right|}^2---\left(14\right)$

So, can calculate σ by formula (10)-Shi (14) _h.

When choosing fenestella length, determine that component can be expressed as:

|bias(t,h)|≤κσ _h (15)

Formula (9) can be expressed as:

$|\mathrm{\&omega;}\left(t\right)-{\widehat{\mathrm{\&omega;}}}_h\left(t\right)|\&le;2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_h---\left(16\right)$

From above formula, can see, the exact value ω (t) of instantaneous frequency is positioned at a fiducial interval, is expressed as:

$D_k\left(t\right)=[L_k\left(t\right),U_k\left(t\right)]=[{\widehat{\mathrm{\&omega;}}}_h\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_h,{\widehat{\mathrm{\&omega;}}}_h\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_h]---\left(17\right)$

In formula, L _kand U (t) _k(t) represent respectively the bound of fiducial interval.

For a long sequence H={h of the window increasing progressively ₁<h ₂< ... <h _j, h wherein _jbe not more than data sampling points N.Definition

$O_k\left(t\right)=\frac{|D_k\left(t\right)\&cap;D_{k-1}\left(t\right)|}{\left|D_k\left(t\right)\right|}---\left(18\right)$

K=2 wherein, 3 ..., j, D _k(t), D _k-1(t) be that length of window is respectively h _k, h _k-1time instantaneous frequency exact value fiducial interval.

O _k(t) value is as follows:

(1) work as D _k(t) be D _k-1(t) during subset, O _k(t)=1;

(2) work as D _k(t) ∩ D _k-1(t)=and during Φ, O _k(t)=0;

(3) in other situations, O _k(t) ∈ (0,1).

As shown in Figure 2, [L _k(t), U _k(t)] be the exact value ω of instantaneous frequency _k(t) residing fiducial interval, according to above-mentioned O _k(t) value criterion, calculates respectively the long corresponding fiducial interval registration O of each window in H _k(t).As long in window is h ₂time, D ₂(t) be D ₁(t) subset, O ₂(t)=1; Window is long is h ₃time, O ₃(t)=0.9.Set a certain threshold value O _thr, work as h ^*meet O _k(t)>=O _thr, and be maximal window wherein when long, h ^*for best window long.So move in circles, can calculate the optimum window that each sampled point of input signal is corresponding long.

5. the signal transient frequency estimating methods strengthening

Obtaining the long h of optimum window ^*basis on, calculate and to be less than or equal to h ^*the long h of window _ithe frequency range of corresponding coded signal:

$D_{k_i}\left(t\right)=[L_{k_i}\left(t\right),U_{k_i}\left(t\right)]=[{\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i},{\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i}]---\left(19\right)$

In formula, subscript i represents that window length is less than or equal to the long h of optimum window ^*correlation parameter.

To above-mentioned fiducial interval

do and calculate as follows new frequency range

${\widehat{\mathrm{\&omega;}}}_d\left(t\right)=\max ({\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i})---\left(20\right)$

${\widehat{\mathrm{\&omega;}}}_u\left(t\right)=\min ({\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i})---\left(21\right)$

Obtain

arrive

the common interval of a plurality of frequency ranges, as shown in Figure 3.For avoiding

be the situation that new frequency range is empty set, the long h of window _iby minimum value order, increased progressively, work as appearance

time, increasing process stops.

Be less than or equal to the long long h of window of optimum window _iin choose minimum value h _m, calculating window long is h _mtime pseudo-Wigner-Ville Distribution Value, and

in interval, select maximal value as the estimated value of signal frequency, that is:

${\widehat{\mathrm{\&omega;}}}_x\left(t\right)=\underset{\mathrm{\&omega;}\&Subset;[{\widehat{\mathrm{\&omega;}}}_d\left(t\right),{\widehat{\mathrm{\&omega;}}}_u\left(t\right)]}{\arg \max }\left[W_x(t,\mathrm{\&omega;})\right]---\left(22\right)$

Thus, can adopt the instantaneous frequency of the frequency estimating methods estimated coding signal of enhancing.

6. signal recovers

Known coded signal z _y(t) instantaneous frequency, can recover original signal x (t).Original useful signal x (t) can recover by following formula:

${\hat{x}}_c\left(t\right)=\frac{{\widehat{\mathrm{\&omega;}}}_x\left(t\right)}{2\mathrm{\&pi;\&mu;}}---\left(23\right)$

In formula,

original signals and associated noises y _c(t) by the signal obtaining after time-frequency peak filtering.

The echo signal of estimating

can obtain by anti-zoom operations, also:

$\hat{x}\left(t\right)=\frac{\max \left[x_c\left(t\right)\right]-\min \left[x_c\left(t\right)\right]}{0.5}{\hat{x}}_c\left(t\right)+\min \left[x_c\left(t\right)\right]---\left(24\right)$

By above-mentioned steps, can obtain filtered final signal.

According to signal characteristic, regulate in real time optimum length of window to carry out the calculating of time-frequency peak filtering, finally realize the elimination of signal of fiber optical gyroscope noise.So far, the idiographic flow based on strengthening self-adaptation time-frequency peak filtering method elimination optical fibre gyro noise finishes.

Claims (5)

1. the optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering, is characterized in that, comprises the following steps:

Step 1: the noisy output signal of original fiber gyro is carried out to convergent-divergent, its amplitude is zoomed in certain interval range, avoid coded signal to cause aliasing;

Wherein, the noisy output signal of original fiber gyro is expressed as:

y(t)＝x(t)+ε(t)

Wherein, t is the time, and y (t) is the noisy output signal of optical fibre gyro, and x (t) is the useful signal of gyro output, and ε (t) is gyro noise;

Signal indication after convergent-divergent is:

$y_c\left(t\right)=0.5*\frac{y\left(t\right)-\min \left[y\left(t\right)\right]}{\max \left[y\left(t\right)\right]-\min \left[y\left(t\right)\right]}$

Wherein, max[y (t)] and min[y (t)] maximal value and the minimum value function of y (t) represented respectively;

Step 2: the noisy output signal of proportion modulation system coding original fiber gyro is the frequency modulation (PFM) analytic signal that an amplitude is constant by Signal coding, is expressed as:

$z_y\left(t\right)=e^{j2\mathrm{\&pi;\&mu;}{\&Integral;}_0^t{y}_c\left(\mathrm{\&lambda;}\right)\mathrm{d\&lambda;}}$

Wherein, λ is integration variable, and μ is scale parameter;

Step 3: adopt the pseudo-Wigner-Ville distribution window function that adaptive approach is coded signal to select optimum window long;

Step 4: according to optimum window function length, optimize signal transient Frequency Estimation scope;

Step 5: in the Signal estimation frequency range of optimizing in step 4, adopt the instantaneous frequency of pseudo-this frequency modulated signal of Wigner-Ville distribution peak estimation;

Step 6: the instantaneous Frequency Estimation peak value of modulation signal is separated to the anti-convergent-divergent of mediation, recover to obtain the Optical Fiber Gyroscope after denoising.

2. the optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering as claimed in claim 1, is characterized in that, in step 3, the pseudo-Wigner-Ville distribution of signal window function is defined as:

${\mathrm{PWVD}}_x(t,\mathrm{\&omega;})={\&Integral;}_{-\&infin;}^{+\&infin;}x(t+\mathrm{\&tau;}/2)x^{*}(t-\mathrm{\&tau;}/2)h\left(\mathrm{\&tau;}\right)e^{-\mathrm{j\&omega;\&tau;}}\mathrm{d\&tau;}=W_x(t,\mathrm{\&omega;})*H\left(\mathrm{\&omega;}\right)$

Wherein, h (τ) is window function, and H (ω) is the Fourier transform of h (τ);

For coded signal z _y(t) peak value, distributing by its pseudo-Wigner-Ville can estimated signal instantaneous frequency be:

${\widehat{\mathrm{\&omega;}}}_h\left(t\right)=\arg \underset{\mathrm{\&omega;}}{\max }\left[W_x(t,\mathrm{\&omega;})\right]$

In formula, W _x(t, ω) is that the pseudo-Wigner-Ville of coded signal distributes, and ω is angular frequency,

represent W _xthe value of ω when (t, ω) reaches maximal value;

The exact value ω (t) of described instantaneous frequency is positioned at a fiducial interval, is expressed as:

$D_k\left(t\right)=[L_k\left(t\right),U_k\left(t\right)]=[{\widehat{\mathrm{\&omega;}}}_h\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_h,{\widehat{\mathrm{\&omega;}}}_h\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_h]$

In formula, L _kand U (t) _k(t) represent respectively the bound of fiducial interval,

the estimated value that represents instantaneous frequency, κ σ _hrepresent random component;

For a long sequence H={h of the window increasing progressively ₁< h ₂< ... < h _j, h wherein _jbe not more than data sampling points N, definition

$O_k\left(t\right)=\frac{|D_k\left(t\right)\&cap;D_{k-1}\left(t\right)|}{\left|D_k\left(t\right)\right|}$

K=2 wherein, 3 ..., j, D _k(t), D _k-1(t) be that length of window is respectively h _k, h _k-1time instantaneous frequency exact value fiducial interval;

Ask for respectively the long corresponding fiducial interval registration O of each window in the long sequence H of window _k(t), set a certain threshold value O _thr, work as h ^*meet O _k(t)>=O _thr, and be maximal window wherein when long, h ^*for best window long.

3. the optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering as claimed in claim 2, is characterized in that, in step 4, is obtaining the long h of optimum window ^*basis on, ask for and be less than or equal to h ^*the long h of window _ithe frequency range of corresponding coded signal:

$D_{k_i}\left(t\right)=[L_{k_i}\left(t\right),U_{k_i}\left(t\right)]=[{\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i},{\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i}]$

In formula,

that length of window is h _itime instantaneous frequency exact value fiducial interval,

with

the bound that represents respectively this fiducial interval,

represent the long h of window _ithe estimated value of corresponding instantaneous frequency,

represent the long h of window _icorresponding random component;

According to above-mentioned fiducial interval obtain new frequency range

${\widehat{\mathrm{\&omega;}}}_d\left(t\right)=\max ({\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)-2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i})$

${\widehat{\mathrm{\&omega;}}}_u\left(t\right)=\min ({\widehat{\mathrm{\&omega;}}}_{h_i}\left(t\right)+2\mathrm{\&kappa;}{\mathrm{\&sigma;}}_{h_i})$

In formula

with

represent respectively the bound of the instantaneous frequency fiducial interval of renewal.

4. the optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering as claimed in claim 3, is characterized in that, in step 5, is being less than or equal to the long long h of window of optimum window _iin choose minimum value h _m, obtaining window long is h _mtime pseudo-Wigner-Ville Distribution Value, and

in interval, select maximal value as the estimated value of signal frequency, that is:

${\widehat{\mathrm{\&omega;}}}_x\left(t\right)=\underset{\mathrm{\&omega;}\&Subset;[{\widehat{\mathrm{\&omega;}}}_d\left(t\right),{\widehat{\mathrm{\&omega;}}}_u\left(t\right)]}{\arg \max }\left[W_x(t,\mathrm{\&omega;})\right]$

In formula ${\widehat{\mathrm{\&omega;}}}_x\left(t\right)=\underset{\mathrm{\&omega;}\&Subset;[{\widehat{\mathrm{\&omega;}}}_d\left(t\right),{\widehat{\mathrm{\&omega;}}}_u\left(t\right)]}{\arg \max }\left[W_x(t,\mathrm{\&omega;})\right]$ Represent that ω exists $[{\widehat{\mathrm{\&omega;}}}_d\left(t\right),{\widehat{\mathrm{\&omega;}}}_u\left(t\right)]$ In scope, make W _xvalue when (t, ω) reaches maximal value.

5. the optical fibre gyro denoising method based on strengthening self-adaptation time-frequency peak filtering as claimed in claim 4, is characterized in that, in step 6, and known coded signal z _y(t) instantaneous frequency, can recover original signal x (t), and original useful signal x (t) can recover by following formula:

${\hat{x}}_c\left(t\right)=\frac{{\widehat{\mathrm{\&omega;}}}_x\left(t\right)}{2\mathrm{\&pi;\&mu;}}$

In formula,

original noisy scale signal y _c(t) by the signal obtaining after time-frequency peak filtering,

The echo signal of estimating

can obtain by anti-zoom operations, after the denoising obtaining, Optical Fiber Gyroscope is:

$\hat{x}\left(t\right)=\frac{\max \left[x_c\left(t\right)\right]-\min \left[x_c\left(t\right)\right]}{0.5}{\hat{x}}_c\left(t\right)+\min \left[x_c\left(t\right)\right].$

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