CN102252669A - Forward linear prediction (FLP) denoising method based on lifting wavelet reconstruction layer - Google Patents
Forward linear prediction (FLP) denoising method based on lifting wavelet reconstruction layer Download PDFInfo
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Abstract
The invention discloses a forward linear prediction (FLP) denoising method based on a lifting wavelet reconstruction layer. The method comprises the following steps of: performing multi-scale decomposition on an optical fiber gyro output signal by utilizing lifting wavelet; performing single branch reconstruction on decomposed approximate signals and detailed signals to acquire reconstructed approximate signals and detailed signals; denoising the decomposed approximate signals and detailed signals layer by layer by an FLP method respectively; and reconstructing the signals which are denoised layer by layer so as to obtain a final denoising result. Due to the processing method, the received signal spectrums are split into different sub-bands, denoising is performed according to different performance characteristics of available signals and noise in the sub-bands by utilizing an FLP algorithm, and a denoising accuracy can be effectively improved so as to fulfill the aim of improving a signal to noise ratio.
Description
Technical field
The invention belongs to the signal Processing in the inertial technology field, relate to a kind of optical fibre gyro signal antinoise method, be particularly related to a kind of forward direction linear prediction (FLP) denoise algorithm-LWT-FLP algorithm, be applicable to various fibre optic gyroscopes based on Lifting Wavelet (LWT) reconstruction of layer.
Background technology
Optical fibre gyro is a kind of novel angular rate sensor, with respect to traditional electro-mechanical gyro, optical fibre gyro movement-less part and wearing terrain, therefore have the reliability height, the life-span is long, volume is little, light weight, low in energy consumption, advantage such as dynamic range is big, toggle speed is fast and frequency band range is wide, therefore is widely used in fields such as Aeronautics and Astronautics, navigation.
Because often there are a large amount of random noises in the influence of principle of work, design feature, production technology and the environment for use of optical fibre gyro self in the output signal, these random noises can have a strong impact on the precision of optical fibre gyro signal.The random noise of optical fibre gyro mainly comprises two parts, and the one, white noise, this is a kind of high frequency noise, is generally caused by environment for use; The 2nd, fractal noise, fractal noise mainly is to be caused by the instability that the light path fluctuation causes setovering, in addition, the error that the phase error that the Rayleigh back scattering brings, Faraday effect cause, the undesirable error that causes of polarizer also are the main causes that fractal noise produces.1/f
rThe class fractal noise is a class important in the fractal noise, and it is a kind of long-range correlativity that has, self-similarity and 1/f
rA kind of non-stationary random noise of type spectral density characteristics.1/f
rThe class fractal noise is at first found in electron tube by Johnmson, is considered to a kind of ultralow frequency noise.How effectively to eliminate this two kinds of noises, significant for the precision that improves the optical fibre gyro signal.
Traditional denoising method is based on the signal and the nonoverlapping viewpoint of noise spectrum of classical filtering theory, comes stripping filter frequency band noise in addition by wave filters such as low pass, high pass are set.But overlapping seriously the time when signal and noise spectrum, be difficult to reach the good denoising effect, as 1/f
rNoise is a kind of ultralow frequency noise, tend to be entrained in the optical fibre gyro signal of low frequency, so traditional filtering method can't effectively be removed this noise like.In order to address this problem, the present invention is incorporated into denoise algorithm with lifting wavelet transform, utilize Lifting Wavelet that the optical fibre gyro signal is carried out multiple dimensioned decomposition, obtain the signal under the different frequency range, and the signal of each frequency range carried out the FLP denoising, to reach the purpose of effective removal white noise and fractal noise.
Summary of the invention
Technology of the present invention is dealt with problems: overcome the deficiencies in the prior art, a kind of forward direction linear prediction (FLP) denoise algorithm-LWT-FLP algorithm based on Lifting Wavelet (LWT) reconstruction of layer has been proposed, this method with the advantages of lifting wavelet transform and FLP algorithm together, can effectively remove white noise and fractal noise in the optical fibre gyro signal, and be easy to realize.
Technical solution of the present invention: a kind of forward direction linear prediction denoising method based on the Lifting Wavelet reconstruction of layer comprises the steps:
(1): utilize Lifting Wavelet that the optical fibre gyro signal is carried out multiple dimensioned decomposition
The optical fibre gyro signal that utilizes Lifting Wavelet that the data acquisition system is collected carries out the wavelet coefficient that multiple dimensioned decomposition obtains decomposing each layer of back, comprises approximation coefficient and detail coefficients, and the decomposition number of plies is n;
(2): to decomposition obtain approach coefficient and detail coefficients is carried out single reconstruct
To decomposition obtain approach coefficient and detail coefficients is carried out single reconstruct, obtain the approximate signal a after the reconstruct
nWith detail signal d
i(i=1,2, Λ, n);
(3): approximation signal after the reconstruct and detail signal are successively carried out the denoising of forward direction linear prediction FLP algorithm respectively
To the approximation signal a that carries out in the step (2) obtaining after single the reconstruct
nWith detail signal d '
i(i=1,2, Λ n) utilizes the FLP algorithm to carry out denoising respectively;
(4): the signal after the denoising successively that obtains in the step (3) is reconstructed
Approximate signal a ' after the FLP denoising that obtains in the reconstruction step (3)
nWith detail signal d '
i(i=1,2, Λ n), thereby obtains optical fibre gyro signal after the denoising.
Utilize Lifting Wavelet that signal is carried out multiple dimensioned decomposition in the described step (1), its wavelet basis is the haar small echo, promptly the haar small echo is promoted the decomposition wavelet basis that is used as the optical fibre gyro signal; The analytic method of Haar small echo is as follows:
Pairing approximation signal and detail signal carry out single reconstruct in the described step (2), and its wavelet basis is elected the haar small echo as, promptly the haar small echo is promoted, be used as approximate signal and detail signal the reconstruct wavelet basis.
Utilize the FLP algorithm to carry out denoising in the described step (3), its denoising process is to carry out in the reconstruction of layer of signal, the approximation signal and the detail signal that obtain after promptly at first Lifting Wavelet being decomposed carry out single reconstruct, then the signal after single the reconstruct are carried out the FLP denoising.
Approximation signal that in the described step (3) multiple dimensioned decomposition is obtained and detail signal successively carry out the FLP denoising respectively, and its FLP wave filter prediction order elects 30 as.
Approximation signal that in the described step (3) multiple dimensioned decomposition is obtained and detail signal successively carry out the FLP denoising respectively, and the step-length in its FLP wave filter selects to follow following formula:
E
j=E[|e
n(n) |].μ wherein
jBe the step-length under the different frequency range, j=1,2, Λ, n, E
jIt is the average of FLP absolute error in the j frequency range.
In the described step (4) to the approximate signal a ' after the FLP denoising
nWith detail signal d '
i(i=1,2, Λ n) is reconstructed, and its reconstructing method is approximation signal a
nWith detail signal d '
i(i=1,2, Λ, n) directly addition, addition result is the optical fibre gyro signal that utilizes after the denoising of LWT-FLP algorithm.
The present invention's advantage compared with prior art is:
(1) Lifting Wavelet can be carried out multiple dimensioned decomposition to signal, thereby obtains the signal under the different frequency range, can reduce the dispersion degree of the autocorrelation function feature in each frequency range like this, has improved the speed of convergence of FLP denoising process.
(2) owing to the advantage of Lifting Wavelet self, make that the operand of whole algorithm is less, can handle boundary problem easily, and can carry out original position and calculate.
(3) because the advantage of FLP algorithm self makes whole algorithm have characteristics such as real-time, time delay is little, initial procedure is short.
(4) this algorithm merges the advantage of Lifting Wavelet and FLP algorithm, has solved the problem that traditional denoise algorithm can't effectively be removed fractal noise, can effectively eliminate the influence to the optical fibre gyro signal of white noise and fractal noise, improves the precision of optical fibre gyro.
Description of drawings
Fig. 1 is the synoptic diagram of LWT-FLP algorithm denoising implementation procedure;
Fig. 2 is based on the forward wavelet transform process flow diagram that promotes;
Fig. 3 is based on the reverse wavelet transform shift process figure that promotes.
Embodiment
The implementation procedure of optical fibre gyro signal antinoise method of the present invention mainly comprises following four steps as shown in Figure 1:
(1): utilize Lifting Wavelet that the optical fibre gyro signal is carried out multiple dimensioned decomposition
As shown in Figure 2, x (n) is the output signal under the optical fibre gyro static state that obtains by data acquisition system (DAS).From figure we as can be seen, the decomposable process of x (n) can be divided into following three steps:
One, division: original signal x (n) is split into two mutually disjoint subclass, and common way is that an ordered series of numbers is divided into even number sequence x
eWith odd number sequence x
0, that is:
x
e(n)＝x(2n)，x
o(n)＝x(2n+1)
Two, prediction: produce wavelet coefficient d (n) with predictive operator P, be and use x
e(n) remove to predict x
o(n) error of Chan Shenging, its expression formula is:
d(n)＝x
o(n)-P(x
e(n))
Three, upgrade: produce a better subdata collection by operator U, make it to keep legacy data collection x
e(n) some characteristics.The expression formula of renewal process is:
a(n)＝x
e(n)+U(d(n))
Just finished the once lifting of signal by above three steps, this also is equivalent to wavelet decomposition one time, approaches coefficient a (n) and detail coefficients d (n) after having obtained once decomposing.Repeat above three steps, approach coefficient and detail coefficients after just obtaining multilayer and decomposing.
(2): to decomposition obtain approach coefficient and detail coefficients is carried out single reconstruct
The restructuring procedure of Lifting Wavelet is opposite with decomposable process, and at first contrary the renewal recovers the even number sequence, and inverse prediction recovers the odd number sequence then, at last odd number sequence and even number sequence is intersected placement, reconstructs original signal.We only prop up the list that obtains after decomposing and approach coefficient and detail coefficients is reconstructed at this, and obtain the approximation signal a after the reconstruct
nWith detail signal d
i(i=1,2, Λ, n).
(3): the essence that the approximation signal after the reconstruct and detail signal are successively carried out FLP denoising forward direction linear prediction (FLP) algorithm respectively is to utilize in the past the sampled value in N data prediction future.Wherein, the most frequently used have the linear one-step prediction that certain exponent number postpones structure.Its main thought is that the gyro signal of previous time output be multiply by the gyro signal that corresponding weights is predicted current time, and the acquisition of its optimal weight needs an iterative process.In this process, at first needing to set the weight initial value is zero, calculate the difference between current gyro signal and the predicted value then, minimize this difference, and utilize this difference constantly to adjust and upgrade weight and the final weighted value that obtains a stable convergence according to the LMS least mean square theory.Can utilize the gyro output of previous time to try to achieve the estimated value of current time gyro signal x (n) by following formula:
Wherein, X (n-1)=x (n-1), x (n-2) ..., x (n-N) }
TBe the vector that the output of previous time gyro is formed, x (n-p) is the gyro signal of previous time, α
pBe weight; N is an exponent number.Wherein the exponent number of N is chosen for the key factor that influences this algorithm application, exponent number is big more, and filter effect is good more, but the excessive calculating that can strengthen filtering again of exponent number in addition and influence the real-time of filtering, through repetition test repeatedly, choose N=30 as the exponent number of FLP wave filter herein.Step-length in the FLP wave filter selects to follow following formula:
μ wherein
jBe the step-length under the different frequency range, j=1,2, Λ, n, E
jIt is the average of FLP absolute error in the j frequency range.
(4): the signal after the denoising successively that obtains in the step (3) is reconstructed
As shown in figure one, the signal after the denoising successively that obtains in the step (3) is reconstructed, reconstructing method is the direct addition of each layer signal, addition result is the optical fibre gyro signal after the denoising of LWT-FLP algorithm.
In a word, the present invention combines the advantage of lifting wavelet transform and FLP denoise algorithm, by lifting wavelet transform white noise in the optical fibre gyro signal and fractal noise are extracted respectively, utilize the FLP algorithm respectively it to be carried out denoising again, so just effectively removed the noise of different frequency range, obtained the good denoising effect, for improving the optical fibre gyro signal accuracy, and then it is significant to improve the precision of whole inertial navigation system.
Claims (7)
1. the forward direction linear prediction denoising method based on the Lifting Wavelet reconstruction of layer is characterized in that comprising the steps:
(1): utilize Lifting Wavelet that the optical fibre gyro signal is carried out multiple dimensioned decomposition
The optical fibre gyro signal that utilizes Lifting Wavelet that the data acquisition system is collected carries out the wavelet coefficient that multiple dimensioned decomposition obtains decomposing each layer of back, comprises approximation coefficient and detail coefficients, and the decomposition number of plies is n;
(2): to decomposition obtain approach coefficient and detail coefficients is carried out single reconstruct
To decomposition obtain approach coefficient and detail coefficients is carried out single reconstruct, obtain the approximate signal a after the reconstruct
nWith detail signal d
i(i=1,2, Λ, n);
(3): approximation signal after the reconstruct and detail signal are successively carried out the denoising of forward direction linear prediction FLP algorithm respectively
To the approximation signal a that carries out in the step (2) obtaining after single the reconstruct
nWith detail signal d
i(i=1,2, Λ n) utilizes the FLP algorithm to carry out denoising respectively;
(4): the signal after the denoising successively that obtains in the step (3) is reconstructed
Approximate signal a ' after the FLP denoising that obtains in the reconstruction step (3)
nWith detail signal d '
i(i=1,2, Λ n), thereby obtains optical fibre gyro signal after the denoising.
2. according to a kind of forward direction linear prediction denoising method according to claim 1 based on the Lifting Wavelet reconstruction of layer, it is characterized in that, utilize Lifting Wavelet that signal is carried out multiple dimensioned decomposition in the described step (1), its wavelet basis is the haar small echo, promptly the haar small echo is promoted the decomposition wavelet basis that is used as the optical fibre gyro signal; The analytic method of Haar small echo is as follows:
3. a kind of forward direction linear prediction denoising method according to claim 1 based on the Lifting Wavelet reconstruction of layer, it is characterized in that, pairing approximation signal and detail signal carry out single reconstruct in the described step (2), its wavelet basis is elected the haar small echo as, promptly the haar small echo is promoted, be used as approximate signal and detail signal the reconstruct wavelet basis.
4. a kind of forward direction linear prediction denoising method according to claim 1 based on the Lifting Wavelet reconstruction of layer, it is characterized in that, utilize the FLP algorithm to carry out denoising in the described step (3), its denoising process is to carry out in the reconstruction of layer of signal, the approximation signal and the detail signal that obtain after promptly at first Lifting Wavelet being decomposed carry out single reconstruct, then the signal after single the reconstruct are carried out the FLP denoising.
5. a kind of forward direction linear prediction denoising method according to claim 1 based on the Lifting Wavelet reconstruction of layer, it is characterized in that, approximation signal that in the described step (3) multiple dimensioned decomposition is obtained and detail signal successively carry out the FLP denoising respectively, and its FLP wave filter prediction order elects 30 as.
6. a kind of forward direction linear prediction denoising method according to claim 1 based on the Lifting Wavelet reconstruction of layer, it is characterized in that, approximation signal that in the described step (3) multiple dimensioned decomposition is obtained and detail signal successively carry out the FLP denoising respectively, and the step-length in its FLP wave filter selects to follow following formula:
E
j=E[|e
n(n) |].μ wherein
jBe the step-length under the different frequency range, j=1,2, Λ, n, E
jIt is the average of FLP absolute error in the j frequency range.
7. a kind of forward direction linear prediction denoising method based on the Lifting Wavelet reconstruction of layer according to claim 1 is characterized in that, in the described step (4) to the approximate signal a ' after the FLP denoising
nWith detail signal d '
i(i=1,2, Λ n) is reconstructed, and its reconstructing method is approximation signal a '
nWith detail signal d '
i(i=1,2, Λ, n) directly addition, addition result is the optical fibre gyro signal that utilizes after the denoising of LWT-FLP algorithm.
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| CN102494680A (en) * | 2011-11-11 | 2012-06-13 | 东南大学 | Self-adaptive FLP (forward linear prediction) denoising method based on the grey theory |
| CN103557856A (en) * | 2013-10-25 | 2014-02-05 | 哈尔滨工程大学 | Random drift real-time filtering method for fiber-optic gyroscope |
| CN103630808A (en) * | 2013-11-11 | 2014-03-12 | 华南理工大学 | Partial discharge signal denoising method based on lifting wavelet transform |
| CN103900610A (en) * | 2014-03-28 | 2014-07-02 | 哈尔滨工程大学 | MEMS (Micro-electromechanical Systems) gyroscope random error predication method based on grey wavelet neural network |
| CN107766793A (en) * | 2017-09-20 | 2018-03-06 | 天津大学 | MEMS gyroscope signal denoising processing method based on mixed method |
| CN108390398A (en) * | 2018-03-14 | 2018-08-10 | 中南大学 | The potential sub-synchronous oscillation recognition methods of wind power plant based on noise-like signal |
| CN109766787A (en) * | 2018-12-21 | 2019-05-17 | 哈尔滨工程大学 | A kind of single axis fiber gyro disturbance rejection seeks northern calculation method |
| CN111640519A (en) * | 2020-05-07 | 2020-09-08 | 中国工程物理研究院核物理与化学研究所 | Reactor neutron noise spectrum analysis method based on improved wavelet fractal algorithm |
| CN112084845A (en) * | 2020-07-30 | 2020-12-15 | 中国人民解放军63892部队 | Low-frequency 1/f noise elimination method based on multi-scale wavelet coefficient autocorrelation |
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| CN102494680A (en) * | 2011-11-11 | 2012-06-13 | 东南大学 | Self-adaptive FLP (forward linear prediction) denoising method based on the grey theory |
| CN103557856A (en) * | 2013-10-25 | 2014-02-05 | 哈尔滨工程大学 | Random drift real-time filtering method for fiber-optic gyroscope |
| CN103630808A (en) * | 2013-11-11 | 2014-03-12 | 华南理工大学 | Partial discharge signal denoising method based on lifting wavelet transform |
| CN103900610A (en) * | 2014-03-28 | 2014-07-02 | 哈尔滨工程大学 | MEMS (Micro-electromechanical Systems) gyroscope random error predication method based on grey wavelet neural network |
| CN107766793A (en) * | 2017-09-20 | 2018-03-06 | 天津大学 | MEMS gyroscope signal denoising processing method based on mixed method |
| CN108390398A (en) * | 2018-03-14 | 2018-08-10 | 中南大学 | The potential sub-synchronous oscillation recognition methods of wind power plant based on noise-like signal |
| CN108390398B (en) * | 2018-03-14 | 2021-04-16 | 中南大学 | Wind power plant potential subsynchronous oscillation identification method based on noise-like signals |
| CN109766787A (en) * | 2018-12-21 | 2019-05-17 | 哈尔滨工程大学 | A kind of single axis fiber gyro disturbance rejection seeks northern calculation method |
| CN111640519A (en) * | 2020-05-07 | 2020-09-08 | 中国工程物理研究院核物理与化学研究所 | Reactor neutron noise spectrum analysis method based on improved wavelet fractal algorithm |
| CN111640519B (en) * | 2020-05-07 | 2022-04-05 | 中国工程物理研究院核物理与化学研究所 | Reactor neutron noise spectrum analysis method based on improved wavelet fractal algorithm |
| CN112084845A (en) * | 2020-07-30 | 2020-12-15 | 中国人民解放军63892部队 | Low-frequency 1/f noise elimination method based on multi-scale wavelet coefficient autocorrelation |
| CN112084845B (en) * | 2020-07-30 | 2023-05-02 | 中国人民解放军63892部队 | Low-frequency 1/f noise elimination method based on multi-scale wavelet coefficient autocorrelation |
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Application publication date: 20111123 |