CN102519449B - Fiber optic gyro (FOG) signal denoising method based on overlap M-band discrete wavelet transform (OMDWT) - Google Patents

Abstract

The invention relates to a fiber optic gyro (FOG) signal denoising method based on overlap M-band discrete wavelet transform (OMDWT). The FOG signal denoising method comprises the following steps of: establishing an FOG output signal model at first; carrying out OMDWT wavelet decomposition on an FOG output signal; then carrying out threshold processing on an OMDWT wavelet coefficient; and finally carrying out OMDWT wavelet reconstruction on the FOG output signal to obtain a denoised gyro signal. According to the invention, in the event of denoising the FOG output signal by utilizing the OMDWT, the wavelet coefficient and the scale coefficient of the OMDWT circularly move for corresponding beats along with circular motion of the FOG signal; in the conversion process, the gyro signal is decomposed according to a plurality of channels; the FOG signal denoising method has rapider decomposition speed according to different bands, more detailed band division on the gyro signal and a denoising effect prior to the traditional wavelet denoising effect; and the FOG signal denoising method disclosed by the invention has a important meaning for increasing the navigation performance of an inertial navigation system.

Description

A kind of based on overlapping M the signal of fiber optical gyroscope denoising method with wavelet transform

Technical field

The present invention relates to a kind of signal of fiber optical gyroscope denoising method based on overlapping M band wavelet transform (Overlap M-band Discrete Wavelet Transform, OMDWT), belong to inertial navigation technology field.

Background technology

Optical fibre gyro is taking Sagnac effect as the novel all solid state gyroscope that basis grows up, and is subject to the great attention of countries in the world, has become the desirable inertia device in low-accuracy strapdown inertial navigation, guidance system in a new generation.A gordian technique in Methods of Strapdown Inertial Navigation System is how completely independently to realize fast initial alignment, independently determines fast initial orientation angle and the horizontal attitude angle of carrier.The principal element that affects alignment of orientation (seeking north) precision is gyroscopic drift, and effectively eliminating gyroscopic drift is the key of guarantor's bit alignment precision.

Optical fibre gyro drift can be divided into two types of systematicness drift and random drifts.Because random drift is small nonlinearity, becomes when slow, be subject to the impact of the uncertain factors such as external environment condition simultaneously, cannot set up its accurate system model, in inertial navigation system, can not be compensated by simple method, therefore random drift becomes the important indicator of weighing gyroscope precision.In order to improve initial alignment precision, must adopt effective signal processing method to gyroscope signal process, suppress these random drifts.At present the processing of gyro signal is had to two kinds of thoughts: (1) sets up Modelling of Random Drift of Gyroscopes model, use the methods such as Kalman filtering, Wiener filtering to compensate; (2) directly gyro output signal is carried out to denoising Processing.Common method has digital low-pass filtering, auto adapted filtering and wavelet threshold-value filter etc.In view of the characteristic of random drift, can not obtain in advance accurate statistical property, need to adopt direct filtering method to carry out denoising to gyro signal.

Small echo has good time-frequency resolution characteristic, is therefore applied in the denoising of signal of fiber optical gyroscope.In the existing analysis and research of the signal of fiber optical gyroscope based on wavelet theory, be all with small echo based on 2, denoising result has certain limitation, major embodiment is both ways: on the one hand, along with the carrying out of decomposing, the length of wavelet coefficient is successively decreased with 2 times of relations, and decomposition rate is slow; On the other hand, after the certain beat of signal of fiber optical gyroscope loopy moving, its wavelet transform (Discrete Wavelet Transform, DWT) wavelet coefficient and scale coefficient can not the same beats of loopy moving, and denoising effect is poor.

Summary of the invention

Technology of the present invention is dealt with problems and is: technology of the present invention is for the deficiency in existing signal of fiber optical gyroscope analytical approach, and overlapping M band wavelet transform is introduced to Gyro Sigal Denoising.On the one hand, overcome the signal of fiber optical gyroscope with small echo based on 2 and processed the slow deficiency of decomposition rate, what M was wavelet basis with wavelet theory chooses provides choice widely; Decomposing under sub band number the same terms, in M band wavelet transform (M-band Discrete Wavelet Transform, MDWT), signal decomposes by hyperchannel; On the other hand, overcome while carrying out signal of fiber optical gyroscope denoising based on 2 band small echos, after the certain beat of signal of fiber optical gyroscope loopy moving, the deficiency that DWT small echo and scale coefficient can not the same beats of loopy moving.

Technical solution of the present invention is: the present invention proposes a kind of based on overlapping M the signal of fiber optical gyroscope denoising method with wavelet transform, provided and calculated that effective signal of fiber optical gyroscope decomposes, threshold value is processed and restructing algorithm.Concrete steps are as follows:

(1) set up Optical Fiber Gyroscope model

Wherein, X _tfor Optical Fiber Gyroscope; T=0 ..., N-1, N represents the length of Optical Fiber Gyroscope; ω _iefor earth rotation angular speed, ω _ie=7.27 × 10 ^-5rad/s;

for the geographic latitude of test point; ε _tfor gyroscopic drift, gyroscopic drift forms by being often worth component, periodic component and white noise, that is:

ε _t＝ε _d+Ω _dsin(2πf _d+θ ₀)+W _t

Wherein, ε _dfor normal value component, 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 _tfor zero-mean white Gaussian noise.Ω in formula _dsin (2 π f _d+ θ ₀) and W _ttwo random drift items that form optical fibre gyro output.

(2) Optical Fiber Gyroscope is made to OMDWT wavelet decomposition

The Optical Fiber Gyroscope X of the length N that step (1) is obtained _tdo OMDWT conversion, the OMDWT wavelet coefficient and the scale coefficient that OMDWT are converted to the j yardstick obtaining are used respectively N n dimensional vector n

with

represent,

corresponding element

with

corresponding element

be respectively:

${\underset{\‾}{\overset{~}{W}}}_{j,t}^i\≡\underset{l=0}{\overset{L_j-1}{\mathrm{\Σ}}}{\tilde{h}}_{j,l}^i{X}_{t-l\mathrm{mod}N},$ ${\tilde{V}}_{j,t}\≡\underset{l=0}{\overset{L_j-1}{\mathrm{\Σ}}}{\tilde{g}}_{j,l}{X}_{t-l\mathrm{mod}N}$

In formula, t=0 ..., N-1, N represents the length of signal of fiber optical gyroscope; L=1 ..., L, L=2M represents J ₀the length of MDWT wave filter on yardstick, M represents small echo band number, i.e. M band small echo; I=1 ..., M-1; J=J ₀, J ₀+ 1 ..., J, J ₀the initial gauges that represents wavelet transformation, J represents the termination yardstick of wavelet transformation;

with

be respectively i wavelet filter coefficient and the scaling filter coefficient of OMDWT on j yardstick; LmodN represents that l is to N remainder.

${\tilde{h}}_{j,l}^i\≡h_{j,l}^i/M^{j/2},$ ${\tilde{g}}_{j,l}\≡g_{j,l}/M^{j/2}$

In formula,

{ g _{j, l}represent respectively i wavelet filter coefficient and the scaling filter coefficient of MDWT on j yardstick.M ^j/2represent the j/2 power of M; Wave filter on j yardstick

length be L _j≡ (M ^j-1) (L-1)+1.

To signal of fiber optical gyroscope X _tcarry out filtering by Periodic filter respectively, can utilize the scale coefficient vector of signal of fiber optical gyroscope on j-1 yardstick

calculate the wavelet coefficient vector of signal of fiber optical gyroscope on j yardstick

with scale coefficient vector

element.

with

corresponding element is used respectively with

represent:

${\underset{\‾}{\overset{~}{W}}}_{j,t}^i\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{\tilde{h}}_l^i{\tilde{V}}_{j-1,t-M^{j-1}\mathrm{mod}N},t=\mathrm{0,1},...,N-1$

${\tilde{V}}_{j,t}=\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{\tilde{g}}_l{\tilde{V}}_{j-1,t-M^{j-1}\mathrm{mod}N},t=\mathrm{0,1},...,N-1$

In formula,

with

represent respectively i wavelet filter coefficient and the scaling filter coefficient of OMDWT;

represent t-M ^j-1the scale coefficient of lmodN moment j-1 yardstick, j=J ₀, J ₀+ 1 ..., J.

In above-mentioned conversion, OMDWT wavelet filter coefficient with scaling filter coefficient

solve as follows:

${\tilde{h}}_l^i\≡h_l^i/\sqrt{M},$ ${\tilde{g}}_l\≡g_l/\sqrt{M}$

In formula, l=1 ..., L;

{ g _lbe respectively i wavelet filter and the scaling filter coefficient of MDWT.

When step (2) is made OMDWT wavelet decomposition to signal of fiber optical gyroscope, thereby decompose speed by different frequency bands, and signal of fiber optical gyroscope is had to thinner frequency band division; After signal of fiber optical gyroscope loopy moving, its OMDWT wavelet coefficient and scale coefficient are understood the corresponding beat of loopy moving, are conducive to the signal denoising of optical fibre gyro.

(3) OMDWT wavelet coefficient is done to threshold value processing

The wavelet coefficient obtaining after signal of fiber optical gyroscope in step (2) is decomposed

do threshold value processing.Utilize threshold value processing, absolute value is less than to the wavelet coefficient zero setting of threshold value, but the wavelet coefficient that absolute value is greater than threshold value has been done to contraction.

${\tilde{W}}_{j,t}^i({\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i,T_s)=\left\{\begin{array}{cc}{\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i-T_s,& {\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i\&GreaterEqual;T_s\\ 0& \left|{\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i\right|<T_s\\ {\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i+T_s& {\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i\&le;-T_s\end{array}\right.$

In formula, T _sthreshold value, 10 ^-5< T _s< 10 ^-3;

be illustrated in yardstick j upper through threshold value i wavelet coefficient after treatment.

(4) Optical Fiber Gyroscope after thresholding threshold process is carried out to OMDWT wavelet reconstruction

${\tilde{V}}_{j-1,t}=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{M-1}{\mathrm{\&Sigma;}}}{\tilde{h}}_l^i{\tilde{W}}_{j,t+M^{j-1}l\mathrm{mod}N}^i+\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\tilde{g}}_l{\tilde{V}}_{j,t+M^{j-1}l\mathrm{mod}N}$

In formula,

represent the scale coefficient of t moment j-1 yardstick; with

represent respectively t+M ^j-1the scale coefficient of scale j and threshold value i wavelet coefficient after treatment when lmodN.

Utilize above formula through calculating, finally at J ₀on yardstick, obtain the signal of fiber optical gyroscope after the denoising of reconstruct $\tilde{X}={\tilde{V}}_{J_0,t}.$

The present invention's advantage is compared with prior art: the present invention in the time carrying out denoising, thereby decompose speed by different frequency bands, and signal of fiber optical gyroscope is had to thinner frequency band division; (2) after signal of fiber optical gyroscope loopy moving, its OMDWT wavelet coefficient and scale coefficient are understood the corresponding beat of loopy moving, are conducive to the signal denoising of optical fibre gyro.

Brief description of the drawings

Fig. 1 is calculation flow chart of the present invention.

Embodiment

As shown in Figure 1, implementation method of the present invention is as follows:

1, set up Optical Fiber Gyroscope model

Wherein, X _tfor Optical Fiber Gyroscope; T=0 ..., N-1, N represents the length of Optical Fiber Gyroscope; ω _iefor earth rotation angular speed, ω _ie=7.27 × 10 ^-5rad/s;

for the geographic latitude of test point; ε _tfor gyroscopic drift, gyroscopic drift forms by being often worth component, periodic component and white noise,

ε _t＝ε _d+Ω _dsin(2πf _d+θ ₀)+W _t (2)

In formula, ε _dfor normal value component, 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 _tfor zero-mean white Gaussian noise.Ω in formula _dsin (2 π f _d+ θ ₀) and W _ttwo random drift items that form optical fibre gyro output.

2, Optical Fiber Gyroscope is made to OMDWT wavelet decomposition

A. Optical Fiber Gyroscope being made to OMDWT mono-step decomposes

Order

$X_t=\left[\begin{array}{c}{X}_0\\ X_1\\ .\\ .\\ .\\ X_{N-3}\\ X_{N-2}\\ X_{N-1}\end{array}\right]$

Definition

One step decomposable process of OMDWT algorithm is: use wavelet coefficient

respectively to X _t,

carry out MDWT decomposition, obtain

and V ₁, and arrange by formula (5).That is to say, carry out, after M MDWT decomposition, M group coefficient being lined up,

Wherein,

in subscript i represent that this matrix is made up of with i wavelet coefficient of wavelet transformation M.

For example, work as M=3, when L=6

Wavelet filter coefficient in wushu (6) replace with g _l, obtain

and V ₁element can be expressed as:

$W_1^i={[M^{1/M}{\tilde{W}}_{1,M-1}^i,M^{1/M}{\tilde{W}}_{\mathrm{1,2}M-1}^i,M^{1/M}{\tilde{W}}_{\mathrm{1,3}M-1}^i,...,M^{1/M}{\tilde{W}}_{1,N-1}^i]}^T---\left(8\right)$

$V_1={[M^{1/M}{\tilde{V}}_{1,M-1},M^{1/M}{\tilde{V}}_{\mathrm{1,2}M-1},M^{1/M}{\tilde{V}}_{\mathrm{1,3}M-1},...,M^{1/M}{\tilde{V}}_{1,N-1}]}^T---\left(9\right)$

Can find out, use wavelet filter

and scaling filter { g _land time series X _tcyclic convolution, obtains

and V ₁.

and V ₁the sequence that is N by length respectively

with

m-1,2M-1 ..., N-1 element composition.

X in wushu (5) _treplace with loopy moving vector

with

have

Definition

For example, work as M=3, when L=6, have

replace with g _l, can obtain

with

element can be expressed as:

element can be expressed as:

Equally,

element can be expressed as:

element can be expressed as:

Definition

${\tilde{W}}_1^i\&equiv;{[{\tilde{W}}_{\mathrm{1,0}}^i,{\tilde{W}}_{\mathrm{1,1}}^i,{\tilde{W}}_{\mathrm{1,2}}^i,...,{\tilde{W}}_{1,N-1}^i]}^T---\left(21\right)$

${\tilde{V}}_1\&equiv;{[{\tilde{V}}_{\mathrm{1,0}},{\tilde{V}}_{\mathrm{1,1}},{\tilde{V}}_{\mathrm{1,2}},...,{\tilde{V}}_{1,N-1}]}^T---\left(22\right)$

Will with

element divided by coefficient M ^1/M, and they are arranged by formula (21), can obtain by similar approach by V ₁,

with

obtain.Here,

with

element be actually the wave filter with OMDWT

with

to X _tafter filtering, the output obtaining

with

by matrix

with

in each

replace with

and the row in these matrixes is arranged by formula (23), obtain N × N matrix

For example, work as M=3, when L=6

Therefore

In wushu (23) replace with

can obtain

finally, a step exploded representation of OMDWT algorithm be:

wherein

By this process, when signal of fiber optical gyroscope is made to OMDWT wavelet decomposition, thereby decompose speed by different frequency bands, and signal of fiber optical gyroscope is had to thinner frequency band division; After signal of fiber optical gyroscope loopy moving, its OMDWT wavelet coefficient and scale coefficient can the corresponding beats of loopy moving.

B. ask signal of fiber optical gyroscope X _toMDWT conversion on j yardstick

The signal of fiber optical gyroscope X of the length N that step 1 is obtained _tdo OMDWT conversion, the OMDWT wavelet coefficient of j yardstick and scale coefficient are used respectively to N n dimensional vector n

with

represent,

corresponding element

with

corresponding element

be respectively:

${\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i\&equiv;\underset{l=0}{\overset{L_j-1}{\mathrm{\&Sigma;}}}{\tilde{h}}_{j,l}^i{X}_{t-l\mathrm{mod}N},$ ${\tilde{V}}_{j,t}\&equiv;\underset{l=0}{\overset{L_j-1}{\mathrm{\&Sigma;}}}{\tilde{g}}_{j,l}{X}_{t-l\mathrm{mod}N},i=1,...,M-1---\left(27\right)$

In formula, t=0 ..., N-1, N represents the length of signal of fiber optical gyroscope; L=1 ..., L, j=J ₀, J ₀+ 1 ..., J, J ₀the initial gauges that represents wavelet transformation, J represents the termination yardstick of wavelet transformation; with

be respectively i wavelet filter coefficient and the scaling filter coefficient of OMDWT on j yardstick; LmodN represents that l is to N remainder.

${\tilde{h}}_{j,l}^i\&equiv;h_{j,l}^i/M^{j/2},$ ${\tilde{g}}_{j,l}\&equiv;g_{j,l}/M^{j/2}---\left(28\right)$

{ g _{j, l}represent respectively i wavelet filter coefficient and the scaling filter coefficient of MDWT on j yardstick.Can push away, wave filter

length be L _j≡ (M ^j-1) (L-1)+1.

Utilize the scale coefficient vector of signal of fiber optical gyroscope on j-1 yardstick

calculate the wavelet coefficient vector of signal of fiber optical gyroscope on j yardstick

with scale coefficient vector

element.

with

corresponding element is used respectively

with

represent:

${\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\tilde{h}}_l^i{\tilde{V}}_{j-1,t-M^{j-1}\mathrm{mod}N},t=\mathrm{0,1},...,N-1---\left(29\right)$

${\tilde{V}}_{j,t}=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\tilde{g}}_l{\tilde{V}}_{j-1,t-M^{j-1}\mathrm{mod}N},t=\mathrm{0,1},...,N-1---\left(30\right)$

In formula,

with

represent respectively i wavelet filter coefficient and the scaling filter coefficient of OMDWT; represent t-M ^j-1the scale coefficient of lmodN moment j-1 yardstick, j=J ₀, J ₀+ 1 ..., J.

C. ask OMDWT wavelet filter coefficient

with scaling filter coefficient

${\tilde{h}}_l^i\&equiv;h_l^i/\sqrt{M},$ ${\tilde{g}}_l\&equiv;g_l/\sqrt{M}---\left(31\right)$

In formula, l=1 ..., L; I=1 ..., M-1;

{ g _lbe respectively i wavelet filter and the scaling filter coefficient of MDWT.

3, OMDWT wavelet coefficient is done to threshold value processing

The wavelet coefficient obtaining after signal of fiber optical gyroscope in step 2 is decomposed

do threshold value processing.Utilize threshold value processing, absolute value is less than to the wavelet coefficient zero setting of threshold value, but the wavelet coefficient that absolute value is greater than threshold value has been done to contraction.

${\tilde{W}}_{j,t}^i({\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i,T_s)=\left\{\begin{array}{cc}{\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i-T_s,& {\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i\&GreaterEqual;T_s\\ 0& \left|{\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i\right|<T_s\\ {\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i+T_s& {\underset{\&OverBar;}{\overset{~}{W}}}_{j,t}^i\&le;-T_s\end{array}\right.,t=\mathrm{0,1},...,N-1---\left(32\right)$

In formula, T _sthreshold value, 10 ^-5< T _s< 10 ^-3;

be illustrated in yardstick j upper through threshold value i wavelet coefficient after treatment.

4, the OMDWT restructing algorithm following formula that the Optical Fiber Gyroscope after thresholding threshold process is carried out to OMDWT wavelet reconstruction Optical Fiber Gyroscope is described:

${\tilde{V}}_{j-1,t}^i=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{M-1}{\mathrm{\&Sigma;}}}{\tilde{h}}_l^i{\tilde{W}}_{j,t+M^{j-1}l\mathrm{mod}N}^i+\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\tilde{g}}_l{\tilde{V}}_{j,t+M^{j-1}l\mathrm{mod}N}---\left(33\right)$

In formula, t=0,1 ..., N-1;

with represent respectively t+M ^j-1the scale coefficient of scale j and threshold value i wavelet coefficient after treatment when lmodN.

Utilize above formula through calculating, finally at J ₀on yardstick, obtain the signal of fiber optical gyroscope after the denoising of reconstruct $\tilde{X}={\tilde{V}}_{J_0,t}.$

The present invention is based on OMDWT signal of fiber optical gyroscope is carried out to denoising, compared with the signal of fiber optical gyroscope denoising method with small echo based on 2, computing velocity is fast, and noise ratio of compression is large.

The content not being described in detail in instructions of the present invention belongs to the known prior art of professional and technical personnel in the field.

Claims (3)

1. the signal of fiber optical gyroscope denoising method with wavelet transform based on overlapping M, is characterized in that performing step is as follows:

(1) set up Optical Fiber Gyroscope model

Wherein, X _tfor Optical Fiber Gyroscope; T=0 ..., N-1, N represents the length of Optical Fiber Gyroscope; ω _iefor earth rotation angular speed, ω _ie=7.27 × 10 ^-5rad/s;

for the geographic latitude of test point; ε _tfor gyroscopic drift;

(2) Optical Fiber Gyroscope is made to OMDWT wavelet decomposition

First, use with

respectively to Optical Fiber Gyroscope X _tcarry out filtering, obtain J ₀wavelet coefficient on yardstick and scale coefficient; Then, obtained scale coefficient is used with carry out filtering, obtain wavelet coefficient and the scale coefficient of OMDWT on j yardstick, the OMDWT wavelet coefficient of the j yardstick obtaining and scale coefficient are used respectively to N n dimensional vector n

with

represent,

corresponding element

with corresponding element

be respectively:

${\underset{\&OverBar;}{\tilde{W}}}_{j,t}^i\&equiv;\underset{l=0}{\overset{L_j-1}{\mathrm{\&Sigma;}}}{\tilde{h}}_{j,l}^i{X}_{t-l\mathrm{mod}N},{\tilde{V}}_{j,t}\&equiv;\underset{l=0}{\overset{L_j-1}{\mathrm{\&Sigma;}}}{\tilde{g}}_{j,l}{X}_{t-l\mathrm{mod}N};$

In formula, t=0 ..., N-1, N represents the length of signal of fiber optical gyroscope; L=1 ..., L, L=2M represents J ₀the length of MDWT wave filter on yardstick, M represents small echo band number, i.e. M band small echo; I=1 ..., M-1; J=J ₀, J ₀+ 1 ..., J, J ₀the initial gauges that represents wavelet transformation, J represents the termination yardstick of wavelet transformation; LmodN represents that l is to N remainder;

Calculate successively, to yardstick J,

Wherein, with be respectively J ₀i wavelet filter coefficient of OMDWT and scaling filter coefficient on yardstick,

with

be respectively i wavelet filter coefficient and the scaling filter coefficient of OMDWT on j yardstick;

${\tilde{h}}_{j,l}^i\&equiv;h_{j,l}^i/M^{j/2},{\tilde{g}}_{j,l}\&equiv;g_{j,l}/M^{j/2}---\left(2\right)$

In formula,

with

represent respectively i wavelet filter coefficient and the scaling filter coefficient of MDWT on j yardstick; M ^j/2represent the j/2 power of M; Wave filter on j yardstick

length be L _j≡ (M ^j-1) (L-1)+1;

(3) OMDWT wavelet coefficient is done to threshold value processing

The wavelet coefficient obtaining after signal of fiber optical gyroscope in step (2) is decomposed

do threshold value processing, utilize threshold value processing, absolute value is less than to the wavelet coefficient zero setting of threshold value, but the wavelet coefficient that absolute value is greater than threshold value has been done to contraction:

${\tilde{W}}_{j,t}^i({\underset{\&OverBar;}{\tilde{W}}}_{j,t}^i,T_s)=\left\{\begin{array}{cc}{\underset{\&OverBar;}{\tilde{W}}}_{j,t}^i-T_s,& {\underset{\&OverBar;}{\tilde{W}}}_{j,t}^i\&GreaterEqual;T_s\\ 0& \left|{\underset{\&OverBar;}{\tilde{W}}}_{j,t}^i\right|<T_s\\ {\underset{\&OverBar;}{\tilde{W}}}_{j,t}^i+T_s,& {\underset{\&OverBar;}{\tilde{W}}}_{j,t}^i\&le;-T_s\end{array}\right.---\left(3\right)$

In formula, t=0,1 ..., N-1, T _sit is threshold value;

be illustrated in yardstick j upper through threshold value i wavelet coefficient after treatment;

(4) Optical Fiber Gyroscope after thresholding threshold process is carried out to OMDWT wavelet reconstruction:

${\tilde{V}}_{j-1,t}=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{M-1}{\mathrm{\&Sigma;}}}{{\tilde{h}}_l}^i{\tilde{W}}_{j,t+M^{j-1}l\mathrm{mod}N}^i+\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\tilde{g}}_l{\tilde{V}}_{j,t+M^{j-1}l\mathrm{mod}N}---\left(4\right)$

In formula, j=J ₀, J ₀+ 1 ..., J; L=1 ..., L, L=2M represents J ₀the length of MDWT wave filter on yardstick, M represents small echo band number, i.e. M band small echo;

with

represent respectively i wavelet filter coefficient and the scaling filter coefficient of OMDWT;

represent the scale coefficient of t moment j-1 yardstick;

with

represent respectively t+M ^j-1i wavelet coefficient when lmodN after scale j Upper threshold threshold process and scale coefficient;

(5) utilize formula (4) through calculating, finally at J ₀on yardstick, obtain the signal of fiber optical gyroscope after the denoising of reconstruct

According to claim 1 a kind of based on overlapping M the signal of fiber optical gyroscope denoising method with wavelet transform, it is characterized in that: when described step (2) is made OMDWT wavelet decomposition to signal of fiber optical gyroscope, obtain the scale coefficient of OMDWT on j yardstick

and wavelet coefficient

implementation procedure as follows:

wherein

Wherein:

In wushu (7)

replace with

obtain

with

be respectively i wavelet filter coefficient and the scaling filter coefficient of OMDWT.

According to claim 1 based on overlapping M the signal of fiber optical gyroscope denoising method with wavelet transform, it is characterized in that: described T _svalue is 10 ^-5< T _s< 10 ^-3.

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