CN104331583A - Multi-fractal modelling method based on actually measured sea clutter data - Google Patents

Multi-fractal modelling method based on actually measured sea clutter data Download PDF

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CN104331583A
CN104331583A CN201410697188.XA CN201410697188A CN104331583A CN 104331583 A CN104331583 A CN 104331583A CN 201410697188 A CN201410697188 A CN 201410697188A CN 104331583 A CN104331583 A CN 104331583A
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sea clutter
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鹿浩
鲍星星
马林冲
汪飞
胡居荣
曹宁
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Hohai University HHU
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Abstract

The invention discloses a multi-fractal modelling method based on actually measured sea clutter data. The problem that the stimulation flow needs repeated judgment optimizing when high-frequency sea clutter with multi-fractal feature is produced through a weighted array method is solved. The method comprises the following steps: performing wavelet denoising on the actually measured sea clutter containing noise; computing a multi-fractal parameter of the de-noised actually measured sea clutter by using MF-DFA; determining a minimum section, and producing a parameter qnew again by the minimum section; computing the modified multi-fractal parameter by using a box-counting method; producing a corresponding single fractal sub-set according to the modified Hurst index Hnew (qnew); computing number li=n.fnew(anew) of element in a fractal sub-set Fi through the fnew(qnew); and computing according to a stimulation module (FORMULA) to obtain simulating data Fnn. The method disclosed by the invention is simple to operate, high in accuracy, and suitable for signal modelling with multi-fractal feature under any complex backgrounds.

Description

A kind of Multifractal Modeling method based on Observed sea clutter
Technical field
The present invention relates to a kind of modeling method, be specifically related to a kind of Multifractal Modeling method based on Observed sea clutter, belong to Radar Technology field.
Background technology
Radar sea clutter, refers to that radar transmitted pulse is irradiated to the backscattering echo on sea, local.Research shows: a point dimension characteristic for scattering surface will be carried in scattered signal.On this basis, within 1993, fractal theory is introduced in the input of complex background by researchist, and obtains and develop rapidly.Many literature research fractal theory is applied in Radar Targets'Detection.These researchs all to be verified Theories and methods with measured data and are illustrated, there is very strong cogency, but not there is ubiquity, and measured data most of scientific research personnel is difficult to obtain, is unfavorable for the further further investigation of fractal theory in Radar Signal Detection field and popularization.Therefore, apply fractal theory to set up sea clutter model and seem particularly necessary.
Based on the sea clutter modeling of fractal theory, be divided into based on scattering mechanism model and simple Model in Time Domain 2 class.The calculated amount of the sea clutter scattering mechanism model in the past provided is all very huge, compared to scattering mechanism modeling, simple time domain modeling can produce complicated noise signal with a fairly simple iterated function system (Iterated Function System, IFS) and less parameter.On the fractal property had in known clutter background and the basis of fractal parameter, the time series of sea clutter can be finally inversed by.
Research shows: sea clutter background often has multifractal property, the sea clutter multifractal time domain modeling method of conventional is mainly divided into two classes: one is create the sea clutter with multi-fractal features by the method for weighted array, its simulation flow is complicated, needs repeatedly to differentiate certainly excellent; But the emulated data that this modeling method produces is very similar at fractal property to measured data, emulation hangover data and to survey data of trailing also very similar in statistical property.Two is the stochastic processes producing an approximate multifractal based on the Fractional Brownian Motion of compound, its simulation flow is simple, without the need to adjudicating optimizing, but the emulated data that this modeling method produces is only very similar at fractal property to measured data, in statistical property, emulation hangover data are with to survey data similarity of trailing very poor.
Summary of the invention
The object of the invention is to overcome deficiency of the prior art, a kind of Multifractal Modeling method based on Observed sea clutter is provided, solve by the method for weighted array produce there is the ANTENNA OF HF SEA clutter of multi-fractal features time, its simulation flow needs the problem of repeatedly adjudicating optimizing.
For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of Multifractal Modeling method based on Observed sea clutter, comprises the steps:
Step one: carry out Wavelet Denoising Method to containing noisy actual measurement sea clutter;
Step 2: the multifractal parameter adopting the actual measurement sea clutter after MF-DFA calculating denoising: generalized Hurst index h (q), scaling exponent α (q) and multifractal spectrum f (α), wherein: parameter q is interval [a, b] on a systematic sampling sequence, a ∈ R -, b ∈ R +;
Step 3: determine the smallest interval that in MF-DFA, parameter q is required under completely can describing the prerequisite of actual measurement sea clutter, and regenerate parameter q by smallest interval new;
Step 4: based on parameter q new, adopt box-counting method to calculate revised multifractal parameter: generalized Hurst index H new(q new), scaling exponent α new(q new) and multifractal spectrum f new(α new);
Step 5: according to Hurst index H after correction new(q new) produce corresponding single fractal subset: F i={ f iji=1,2 ... n; J=1,2 ... M;
Step 6: by f new(α new) calculate fractal subset F ithe number l of middle element i=nf new(α new), wherein: f new(α new) value normalization, n is the zonule number that fractal is divided;
Step 7: the time domain multiple Fractal-Based Simulation model setting up sea clutter emulated data F is calculated according to this realistic model nn.
Survey the multifractal parameter of sea clutter after adopting MF-DFA to calculate denoising described in step 2, concrete operation step is as follows:
2.1) MF-DFA is adopted to calculate the q rank wave function F of actual measurement sea clutter q(r);
2.2) according to wave function F qpower law relation F between (r) and time scale r q(r) ∝ r h (q), to logarithmic graph in (F q(r)) point on-ln (r) carries out matching and obtains generalized Hurst index h (q);
2.3) according to the relation of generalized Hurst index h (q) with multifractal spectra f (α) ~ α: α ( q ) = h ( q ) + qh ′ ( q ) f ( α ) = q · ( α ( q ) - h ( q ) ) + 1 Calculate scaling exponent α (q) and multifractal spectra f (α) ~ α.
Determine in step 3 that the concrete operation step of smallest interval is as follows:
3.1) find out the index value of f (α) for q corresponding during negative value, and these index values are preserved;
3.2) as q<0, manipulative indexing is worth maximal value to be just q from adding 1 again newcorresponding interval minimum value; As q>0, manipulative indexing is worth minimum value to be just q from subtracting 1 again newcorresponding interval maximal value.
The concrete operation step producing single fractal subset in step 5 is as follows:
4.1) by H new(q new) produce n fractal subset F i={ f ij, wherein: n=length (q new);
4.2) producing Hurst index by Weiestrass function method is H new(q new(i)) a simple fbm signal ff i;
4.3) to ff icarry out piecewise acquisition and obtain f ij, every section of signal length gathered is M, wherein: M is the length of emulated data.
Compared with prior art, the beneficial effect that the present invention reaches is:
(1) " having the single fractal subset of identical fractal dimension " is adopted to replace tradition " the single fractal weighted array according to probability distribution ", the fractal dimension of its single fractal subset is determined by revised generalized Hurst index, the determination of corresponding weight coefficient only need be determined, without the need to repeatedly adjudicating optimizing by revised multifractal spectrum f (α) and the zonule number n dividing fractal jointly;
(2) problem of negative value is there is for the multifractal spectrum f (α) of the actual sea clutter calculated, analyze the reason producing this problem, and propose amendment scheme on this basis, a kind of simple and smallest interval that the new method determination parameter q that degree of accuracy is higher is required under completely can describing the prerequisite of actual measurement sea clutter is devised, the parameter q regenerated by this smallest interval in this amendment scheme newrevise the multifractal parameter of measured data;
(3) in the present invention, the fractal parameter of measured data, based on multifractal parameter, is stablized than original fractal parameter calculated based on single fractal theory.
The inventive method has the signal modeling of multifractal property under being applicable to any complex background.
Accompanying drawing explanation
Fig. 1 is operational flowchart of the present invention.
Fig. 2 is time domain beamformer and the corresponding power spectral density figure of measured data in the present invention.
Fig. 3 is performance figure τ (q) comparison diagram of measured data and emulated data in the present invention.
Fig. 4 is multifractal spectra f (α) comparison diagram of measured data and emulated data in the present invention.
Fig. 5 is cumulative distribution function (CDF) comparison diagram of measured data and emulated data in the present invention.
Fig. 6 is cumulative distribution function (CDF) comparison diagram of actual measurement hangover data and emulation hangover data in the present invention.
Fig. 7 is Observed sea clutter and the power spectrum density comparison diagram emulating sea clutter data in the present invention.
Embodiment
The present invention, according to the scope of application of all kinds of multifractal Analysis method and relative merits, adopts " multifractal detrend fluctuation analysis method (MF-DFA) " to carry out multiple characteristic analysis to actual measurement sea clutter, and calculates its multifractal parameter.For the problem that there is negative value in actual measurement sea clutter normalization multifractal spectrum f (α) calculated, analyze the possible cause that there is negative value in f (α): because in actual measurement sea clutter, noise does not possess fractal property, then in measured data, the existence of noise may result in f (α) and there is negative value; In addition, analyze the multifractal property of sea clutter based on MF-DFA: as q>0, large variance is occupied an leading position in fluctuating function, the scale feature that the large sequence (i.e. sea clutter) of main reflection rises and falls; As q<0, little variance is occupied an leading position in fluctuating function, the scale feature that the little sequence (i.e. noise) of main reflection rises and falls, then, when the burst length of the parameter q set is excessive, also may cause there is negative value in f (α).Consider the possible cause that there is negative value in actual measurement sea clutter normalization f (α) calculated, the present invention also proposes amendment scheme: first, when initial modeling, adopt and to actual measurement sea clutter, denoising is carried out to chaotic signal denoising effect good " Wavelet-denoising Method ", then, adopt the normalization multifractal spectrum f (α) of the measured signal after MF-DFA calculating Wavelet Denoising Method again, if now still there is negative value in f (α), then can think that the main cause caused is that the burst length of parameter q is excessive, reverse thinking is considered, propose a kind of new method to determine the saturation interval of parameter q: we can be contained in interval [0 according to the scope of the normalization multifractal spectrum f (α) of sea clutter in theory, 1] smallest interval that parameter q is required under completely can describing the prerequisite of actual measurement sea clutter is determined, and regenerate parameter q by smallest interval new, now q newlength should be far longer than the length of q.More much larger than the operand of box-counting method in calculating multifractal parameter according to MF-DFA, consider q again newlength be far longer than again former q, now adopt box-counting method calculate based on q newmeasured data multifractal parameter; According to fractional Brownian motion (fbm), this existing conclusion of sea clutter can be described well, simultaneously identical in order to ensure each the single fractal sequences fractal dimension forming same fractal subset again, we carry out piecewise acquisition to the fractional Brownian motion produced by Weiestrass function method (fbm) and are formed a fractal subset to obtain one group of fbm signal, and the fractal dimension of different fractal subset is by H new(q new) determine.Can regarding as measuring the multiple dimensioned according to probability distribution of actual measurement sea clutter according to multifractal spectra, adopting f new(α new) determine that each fracton concentrates the number of element.
Below in conjunction with accompanying drawing, the invention will be further described.
As shown in Figure 1, be operational flowchart of the present invention, a kind of Multifractal Modeling method based on Observed sea clutter, comprises the steps:
Step one: adopt and to containing noisy actual measurement sea clutter, denoising is carried out to chaotic signal denoising effect good " Wavelet-denoising Method ";
Step 2: the multifractal parameter adopting the actual measurement sea clutter after MF-DFA calculating denoising: generalized Hurst index h (q), scaling exponent α (q) and multifractal spectrum f (α), wherein: parameter q is interval [a, b] on a systematic sampling sequence, a ∈ R -, b ∈ R +.
Concrete operation step is as follows:
2.1) MF-DFA is adopted to calculate the q rank wave function F of actual measurement sea clutter q(r);
2.2) according to wave function F qpower law relation F between (r) and time scale r q(r) ∝ r h (q), to logarithmic graph ln (F q(r)) point on-ln (r) carries out matching and obtains generalized Hurst index h (q);
2.3) according to the relation of generalized Hurst index h (q) with multifractal spectra f (α) ~ α: &alpha; ( q ) = h ( q ) + qh &prime; ( q ) f ( &alpha; ) = q &CenterDot; ( &alpha; ( q ) - h ( q ) ) + 1 Calculate scaling exponent α (q) and multifractal spectra f (α) ~ α.
Step 3: the scope according to the normalization multifractal spectrum f (α) of sea clutter is in theory contained in interval [0,1] determine the smallest interval that in MF-DFA, parameter q is required under completely can describing the prerequisite of actual measurement sea clutter, and regenerate parameter q by smallest interval new, now q newlength should be far longer than the length of q.Determine that the concrete operation step of smallest interval is as follows:
3.1) find out the index value of f (α) for q corresponding during negative value, and these index values are preserved;
3.2) as q<0, manipulative indexing is worth maximal value to be just q from adding 1 again newcorresponding interval minimum value; As q>0, manipulative indexing is worth minimum value to be just q from subtracting 1 again newcorresponding interval maximal value.
Step 4: based on parameter q new, adopt box-counting method to calculate revised multifractal parameter: generalized Hurst index H new(q new), scaling exponent α new(q new) and multifractal spectrum f new(α new).
Step 5: according to Hurst index H after correction new(q new) produce corresponding single fractal subset: F i={ f iji=1,2 ... n; J=1,2 ... M:
4.1) by H new(q new) produce n fractal subset F i={ f ij, wherein: n=length (q new);
4.2) producing Hurst index by Weiestrass function method is H new(q new(i)) a simple fbm signal ff i;
4.3) to ff icarry out piecewise acquisition and obtain f ij, every section of signal length gathered is M, wherein: M is the length of emulated data.
Step 6: by f new(α new) calculate fractal subset F ithe number l of middle element i=nf new(α new), wherein: f new(α new) value normalization, n is the zonule number that fractal is divided;
Step 7: the time domain multiple Fractal-Based Simulation model setting up sea clutter emulated data F is calculated according to this realistic model nn.
In order to statistical property and the fractal property of emulated data and measured data can well be compared, to F nndo simple data processing: first, by F nnamplitude normalizes to interval [min (X deno), max (X deno)] obtain sequence and be designated as Z deno, then, obtain emulation sea clutter Z=Z deno+ N z.
Below in conjunction with concrete the simulation results and Figure of description, the beneficial effect that the present invention produces is described further.Following examples only for technical scheme of the present invention is clearly described, and can not limit the scope of the invention with this.
Total simulated conditions: the present invention selects the IPIX radar data from X-band, the data " hi.dat " by name of measured data, it comes from #269 file, range unit is 3, adopt HH polarization.Hi.dat is the exemplary of high sea condition data, and done the pre-service (being namely ASCII character) of data, have two column datas in hi.dat, it is respectively I, Q two paths of data, and the length of two paths of data is 2^17.
The initialization of parameter: obtain its multiple quantities received hi according to I, Q two paths of data, range weight hi is obtained to hi amp, get hi ampfront N=2^12 data as experiment emulated data X; Emulated data is designated as Z, the length M=N of Z; Assuming that initial parameter q=-20:0.1:20; The complexity of program is by revised parameter q newdetermine, be n=length (q new).
Emulation content 1: the frequency district characteristic analysis of actual measurement sea clutter
Simulated conditions: under the experiment parameter same with total simulation and condition.
Simulation result: Fig. 2 middle and upper part is divided into the time domain beamformer of measured data, bottom is divided into the power spectral density plot of Observed sea clutter corresponding with it.Concentrate in zero-frequency environs by the power spectral density plot visible sea clutter energy overwhelming majority, be mainly noise in remaining frequency range, and noise is stationary signal, then tackle removal/segmentation modeling that whole actual measurement sea clutter carries out noise.
Emulation content 2: measured data compares emulation with the multifractal property of emulated data.
Simulated conditions: adopt the multiple characteristic of multifractal detrend fluctuation analysis method (MF-DFA) to actual measurement sea clutter and emulated data to carry out com-parison and analysis.
Simulation result: Fig. 3 gives performance figure τ (the q) ~ q comparison diagram of measured data and emulated data, obvious non-linear relation between τ (q) and q as seen from the figure, namely measured data is relevant with q with the performance figure τ (q) of emulated data, illustrates that measured data and emulated data all have multifractal property.Fig. 4 gives the comparison diagram of multifractal spectra f (the α) ~ α of measured data and emulated data, multifractal spectra f (the α) ~ α figure goodness of fit of measured data and emulated data is higher as seen from the figure, shows that measured data is similar to the multifractal property of emulated data.
Emulation content 3: measured data compares emulation with the statistical property of emulated data.
Simulated conditions: under the experiment parameter same with total simulation and condition.
Simulation result: Fig. 5 gives theoretical cumulative distribution function (CDF) comparison diagram of measured data and emulated data, the goodness of fit of measured data and emulated data CDF curve is better as seen from the figure, show that emulated data is similar to the statistical property of measured data, further demonstrate rationality and the validity of this multifractal model.
Emulation content 4: actual measurement hangover data with emulate the statistical property of data of trailing and compare emulation.
Simulated conditions: under the experiment parameter same with total simulation and condition.
Simulation result: Fig. 6 gives cumulative distribution function (CDF) comparison diagram of actual measurement hangover data and emulation hangover data, actual measurement hangover data are better with the goodness of fit emulating the data CDF curve that trails as seen from the figure, show that emulated data is similar to the statistical property of measured data.And utilize the K-S method of inspection checking measured data and emulated data revised whether with distribution, and we examine level of signifiance α=0.2, and 0.1,0.05, when 0.01, null hypothesis is still set up.The goodness of fit of trailing portion data in statistical property of visible measured data and emulated data is fairly good, and such advantage is conducive to the detection technique applied to by this multifractal model radar target.
Emulation content 5: measured data compares with the frequency domain characteristic of emulated data
Simulated conditions: under the experiment parameter same with total simulation and condition.
Simulation result: Fig. 7 gives the power spectrum density comparison diagram of Observed sea clutter with emulation sea clutter data, according to the goodness of fit of the power spectrum density of measured data and emulated data, can find out that the frequency domain characteristic similarity of emulated data and measured data is better, and all in level of signifiance α=0.2,0.1,0.05, the K-S statistical test carried out for 0.01 time, its hypothesis is all set up, and the goodness of fit of this modeling hangover data in statistical property is very good as seen.
The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and distortion, these improve and distortion also should be considered as protection scope of the present invention.

Claims (4)

1., based on a Multifractal Modeling method for Observed sea clutter, it is characterized in that: comprise the steps:
Step one: carry out Wavelet Denoising Method to containing noisy actual measurement sea clutter;
Step 2: the multifractal parameter adopting the actual measurement sea clutter after MF-DFA calculating denoising: generalized Hurst index h (q), scaling exponent α (q) and multifractal spectrum f (α), wherein: parameter q is interval [a, b] on a systematic sampling sequence, a ∈ R -, b ∈ R +;
Step 3: determine the smallest interval that in MF-DFA, parameter q is required under completely can describing the prerequisite of actual measurement sea clutter, and regenerate parameter q by smallest interval new;
Step 4: based on parameter q new, adopt box-counting method to calculate revised multifractal parameter: generalized Hurst index H new(q new), scaling exponent α new(q new) and multifractal spectrum f new(α new);
Step 5: according to Hurst index H after correction new(q new) produce corresponding single fractal subset: F i={ f iji=1,2 ... n; J=1,2 ... M;
Step 6: by f new(α new) calculate fractal subset F ithe number l of middle element i=nf new(α new), wherein: f new(α new) value normalization, n is the zonule number that fractal is divided;
Step 7: the time domain multiple Fractal-Based Simulation model setting up sea clutter emulated data F is calculated according to this realistic model nn.
2. the Multifractal Modeling method based on Observed sea clutter according to claim 1, is characterized in that: the multifractal parameter of surveying sea clutter after adopting MF-DFA to calculate denoising described in step 2, and concrete operation step is as follows:
2.1) MF-DFA is adopted to calculate the q rank wave function F of actual measurement sea clutter q(r);
2.2) according to wave function F qpower law relation F between (r) and time scale r q(r) ∝ r h (q), to logarithmic graph ln (F q(r)) point on-ln (r) carries out matching and obtains generalized Hurst index h (q);
2.3) according to the relation of generalized Hurst index h (q) with multifractal spectra f (α)-α: &alpha; ( q ) = h ( q ) + q h &prime; ( q ) f ( &alpha; ) = q &CenterDot; ( &alpha; ( q ) - h ( q ) ) + 1 Calculate scaling exponent α (q) and multifractal spectra f (α)-α.
3. the Multifractal Modeling method based on Observed sea clutter according to claim 1, is characterized in that: determine in step 3 that the concrete operation step of smallest interval is as follows:
3.1) f (α) is found out for corresponding during negative value xindex value, and these index values to be preserved;
3.2) as q<0, manipulative indexing is worth maximal value to be just q from adding 1 again newcorresponding interval minimum value; As q>0, manipulative indexing is worth minimum value to be just q from subtracting 1 again newcorresponding interval maximal value.
4. the Multifractal Modeling method based on Observed sea clutter according to claim 1, is characterized in that: the concrete operation step producing single fractal subset in step 5 is as follows:
4.1) by H new(q new) produce n fractal subset F i={ f ij, wherein: n=length (q new);
4.2) producing Hurst index by Weiestrass function method is H new(q new(i)) a simple fbm signal ff i;
4.3) to ff icarry out piecewise acquisition and obtain f ij, every section of signal length gathered is M, wherein: M is the length of emulated data.
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CN112763999B (en) * 2020-11-13 2023-10-03 河海大学 Sea clutter space correlation analysis method

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