CN106125073A - The scattering mechanism identification expressed based on adaptive Gauss and extracting method - Google Patents

Abstract

A kind of scattering mechanism identification expressed based on adaptive Gauss and extracting method, obtain the wideband angular scanning scattering data of target, at range direction or azimuth direction, signal is carried out AGR calculating, the adaptive spectrum figure of signal calculated energy is carried out according to AGR result of calculation, it is finally separating component of signal that in AGR, Gaussian bases width is big and the little component of signal of width, carry out ISAR imaging respectively, it is achieved the location of scattering mechanism and separation.Present invention achieves the identification that complex target colocalization and delocalization scattering mechanism are produced position, and the separation to different scattering mechanisms can be realized by extracting different Gaussian bases, can be used for electromagnetism stealth design, can also be used for SAR/ISAR image understanding and process, solve delocalization in SAR/ISAR image and scatter the problem of image blurring brought, be that a kind of tool is widely used the basic analysis method of future.

Description

The scattering mechanism identification expressed based on adaptive Gauss and extracting method

Technical field

The present invention relates to electromagnetic characteristic of scattering research field, particularly relate to a kind of based on adaptive Gauss expression The scattering mechanism identification of (Adaptive Gaussion Representation, AGR) and extracting method.

Background technology

Artificial complex target is made up of scattering sources such as plane, edge, dihedral angle, trihedral angle, cavitys, and every kind of scattering source has not Same back scattering mechanism, and the back scattering mechanism of complex target is often difficult to prediction.Change if over frequency, scattered field Having fixing amplitude and the change of linear phase place, such scattering properties is referred to as on-dispersive scattering mechanism, available point scattering mould Type simulated.Scattering phenomenon in reality, its amplitude is typically all weak frequency dependence, and phase place is also the nonlinear function of frequency. This dispersion phenomenon occurs in the structures such as non-ideal metallic object, wave conductor so that receive echo deformation, and Energy distribution spreads, It is difficult to be explained from time domain echo, can be collectively referred to as delocalization scattering mechanism.Broadband backscatter data is carried out high score Distinguish time frequency analysis, identify and extract localization and delocalization scattering mechanism, can be that understanding target scattering mechanism provides one to have The instrument of effect, and provide important means for SAR/ISAR image understanding and process.

In the document that the openest and limited range retrieved is delivered, there is foreign language works that time frequency analysis is discussed specially Algorithm application in Electromagnetic Scattering, compared for several linear and non-linear time frequency analysis algorithm on time-frequency surface Resolution capability；There is again document to use adaptive Time Frequency Analysis instrument that ISAR image is processed, reject non-office in ISAR image Portion's scattering center signal, extracts local scattering center accurately；Patent (patent No.: 201110344673) is had to utilize time frequency analysis Carry out InISAR multi-target imaging and movement locus is rebuild.In sum, foreign study mechanism has been noted that time frequency analysis exists Electromagnetic Scattering Characteristics research in effect, but do not find can self adaptation differentiate local with non local scattering mechanism time Frequency analysis algorithm；And studies in China person only utilizes time frequency analysis to carry out Radar Imaging Processing, do not carry out Electromagnetic Scattering of Target special Property analyze.

Summary of the invention

The present invention provides a kind of scattering mechanism identification expressed based on adaptive Gauss and extracting method, it is achieved that to complexity Target colocalization and delocalization scattering mechanism produce the identification of position, and can by extract different Gaussian bases realize right The separation of different scattering mechanisms, can be used for electromagnetism stealth and designs it can also be used to SAR/ISAR image understanding and process, solve In SAR/ISAR image, delocalization scatters the problem of image blurring brought, is that a kind of tool is widely used basic point of future Analysis method.

In order to achieve the above object, the present invention provides a kind of scattering mechanism identification expressed based on adaptive Gauss and extraction Method, comprises the steps of

Step S1, the broadband-angle scanning scattering data of acquisition target；

Step S2, at range direction or azimuth direction, signal is carried out AGR calculating；

Step S3, carry out the adaptive spectrum figure of signal calculated energy according to AGR result of calculation；

Step S4, separate Gaussian bases width is big in AGR component of signal and the little component of signal of width, carry out respectively ISAR imaging, it is achieved the location of scattering mechanism and separation；

Gaussian bases width a_pBig part represents frequency dependence scattering center, a_pLittle part represents point scattering center.

In described step S2, the step that signal carries out AGR calculating specifically comprises the steps of

Step S2.1, determine iteration initial value；

As p=0, determine iteration initial value k₀And a₀, and give initial signal assignment s₀(t)=s (t)；

Step S2.2, begin look for the local maximum of basic function:

Wherein, subscript p represents pth Gaussian bases, and s (t) is signal, basic function h_pT () is normalization Gaussian function, B_pIt it is its coefficient；

Step S2.3, calculating s_pT () projects to h_pSurplus s after (t)_p+1(t):

s_p+1(t)=s_p(t)-B_ph_p(t) (8)

Step S2.4, calculating dump energy:

||s_p+1(t)||²=| | s_p(t)||²-||B_p||² (9)

Step S2.5, calculating reconstructed error SNR_q；

After q time is decomposed, original signal is:

$s\left(t\right)={\mathrm{\Σ}}_{p=0}^q{B}_p{h}_p\left(t\right)+s_{q+1}\left(t\right)---\left(10\right)$

According to preservation of energy:

$\left|\right|s_t\left(t\right)|{|}^2={\mathrm{\Σ}}_{p=0}^q|B_p{|}^2+\left|\right|s_{q+1}\left(t\right)|{|}^2---\left(11\right)$

Along with q increases, error s_q+1T () is dull reduces, when increasing new basic function h_q+1After (t), do not select before impact During the parameter selected, it is believed that iteration stopping, now reconstructed error is:

${\mathrm{SNR}}_q=10\log \left\{\frac{|s_t\left(t\right){|}^2}{|s_{q+1}\left(t\right){|}^2}\right\}dB---\left(12\right)$

Step S2.6, judging whether reconstructed error meets iteration stopping condition the most then iteration and terminate, record is now a_p,t_p,f_pNumerical value, if it is not, then make p=p+1, proceeds step S2.2；

Arranging iteration stopping condition is reconstructed error SNR_qLess than certain little value ε, or reach certain ultimate value for iterations；

SNR_q+1≤R (13)

If p → ∞, then reconstruction signal energy is identical with original signal, i.e.

In described step S2.1,

Choosing of each step a is carried out in the way of two points:

$a_k=\left(\frac{4}{\mathrm{\π}}\right)2^{2(k_0-k)},k=0,1,2,...,k_0---\left(5\right)$

The time step of kth step is:

${\mathrm{\ΔT}}_k=\sqrt{0.5a_k}=2^{k_0-k}\sqrt{\frac{2}{\mathrm{\π}}}---\left(6\right)$

AGR calculating, then initial value k is carried out if in range direction₀Determine by known signal time step delta T:

$k_0={\log }_2\left(\mathrm{\Δ}T\sqrt{\frac{\mathrm{\π}}{2}}\right)---\left(7\right)$

AGR calculating, then initial value k is carried out if in azimuth direction₀Walk to angular samples by the orientation of known signal Length determines.

In described step S2, for meeting the Electromagnetic Scattering of Target data that sampling density requires, range direction makes Processing with AGR algorithm, the frequency that can identify and separate this group scattering data relies on and frequency unrelated scattering mechanism component, Use AGR algorithm to process in the azimuth direction, then can identify and separate orientation coupling and orientation independence scattering mechanism is divided Amount.

In described step S1, the method for test or accurately calculating is used to obtain the broadband-angle scanning scattering number of target According to, bandwidth and angle scanning scope and interval is chosen relevant with the initial step length of AGR iteration.

In described step S1, according to radiation reflective model, scattering object being regarded radiant body as, spread speed is true in medium The half of real speed, i.e. target image F is the Fourier transformation of scattered field E, and two corresponding Fourier transform pairs areWith D:

$F\left(d_n\right)~\underset{m=1}{\overset{M}{\mathrm{\Σ}}}E\left(f_m\right)e^{j2\mathrm{\π}\left(\frac{f_m}{c/2}\right)d_n}---\left(15\right)$

If carrying out AGR calculating in time domain, according to formula (6), time step corresponding to kth=0 step should be less than equal to total Time-domain sampling width, it may be assumed that

${\mathrm{\Δd}}_0\≥2^{k_0}\sqrt{\frac{2}{\mathrm{\π}}}---\left(16\right)$

k₀It it is variance a_pThe number of times of iteration, at least 1, i.e.Distance should be greater than 1.6m to imaging width, enters And obtain frequency domain sample interval and be to the maximum

Same, if carrying out AGR calculating at frequency domain, Ying You:

$\frac{{\mathrm{\Δf}}_0}{c/2}\≥2\sqrt{\frac{2}{\mathrm{\π}}}---\left(17\right)$

I.e. frequency domain sample bandwidth should be greater than

In described step S3, utilize the adaptive spectrum figure of following formula signal calculated energy:

$ADS(t,f)=2\underset{p=0}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}|B_p{|}^2{e}^{-\frac{{(t-t_p)}^2}{a_p}-{\left(2\mathrm{\π}\right)}^2{a}_p{(f-f_p)}^2}{a}_p\∈R^{+},t_p\∈R,f_p\∈\[0,\mathrm{\∞})---\left(18\right).$

Present invention achieves the identification that complex target colocalization and delocalization scattering mechanism are produced position, and can lead to Cross and extract different Gaussian bases and realize the separation to different scattering mechanisms, can be used for electromagnetism stealth design it can also be used to SAR/ ISAR image understanding and process, solve delocalization in SAR/ISAR image and scatter the problem of image blurring brought, be a kind of Has the basic analysis method of the future that is widely used.

Accompanying drawing explanation

Fig. 1 is a kind of based on adaptive Gauss expression the scattering mechanism identification and the flow process of extracting method that the present invention provides Figure.

Fig. 2 is the flow chart that signal carries out in the present invention AGR calculating.

Detailed description of the invention

Below according to Fig. 1 and Fig. 2, illustrate presently preferred embodiments of the present invention.

As it is shown in figure 1, the present invention provides a kind of scattering mechanism identification expressed based on adaptive Gauss and extracting method, bag Containing following steps:

Step S1, the broadband-angle scanning scattering data of acquisition target；

Step S2, at range direction or azimuth direction, signal is carried out AGR calculating；

Step S3, adaptive spectrum figure (Adaptive according to AGR result of calculation signal calculated energy Spectrogram, ADS)；Adaptive spectrum figure i.e. signal energy is at the scattergram of time-frequency domain；

Step S4, separate Gaussian bases width is big in AGR component of signal and the little component of signal of width, carry out respectively ISAR imaging, it is achieved the location of scattering mechanism and separation；

Gaussian bases width a_pBig part represents frequency dependence scattering center, a_pLittle part represents point scattering center.

In described step S2, for meeting the Electromagnetic Scattering of Target data that sampling density requires, range direction makes Processing with AGR algorithm, the frequency that can identify and separate this group scattering data relies on and frequency unrelated scattering mechanism component, Use AGR algorithm to process in the azimuth direction, then can identify and separate orientation coupling and orientation independence scattering mechanism is divided Amount.

AGR is a kind of non-linear time frequency analyzing tool, be characterized in using flexibly basic function to adapt to different signals Component.AGR algorithm can be extended by basic function, automatic distinguishing frequency dependence and the contribution of frequency incoherent scattering.AGR algorithm will Signal s (t) weighted accumulation of Gaussian bases is expressed:

$s\left(t\right)=\underset{p=0}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}{B}_p{h}_p\left(t\right)---\left(1\right)$

Wherein, subscript p represents pth Gaussian bases, basic function h_pT () is normalization Gaussian function, B_pIt it is its coefficient.

Basic function h_pT () has adjustable width variance a_pWith time-frequency center { t_p,f_p, expression formula is:

$h_p\left(t\right)=g_p(t-t_p)e^{j2{\mathrm{\πf}}_{p}t}---\left(2\right)$

$g_p\left(t\right)={\left({\mathrm{\πa}}_p\right)}^{-0.25}{e}^{-\frac{t^2}{2a_p}}---\left(3\right)$

Wherein, a_p∈R⁺, t_p,f_p∈R。

Gaussian function g_pT () is compressed the most over time or over frequency, it has the time-bandwidth product of minimum, thus has Good T/F resolution.

The purpose of AGR algorithm chooses suitable a exactly_p,t_p,f_pSo that basic function h_pT () approaches letter the most best Number s (t), it may be assumed that

$|B_p{|}^2=\underset{a_p,t_p,f_p}{\max }|{\mathrm{\Γ}}_p{|}^2=\underset{a_p,t_p,f_p}{\max }|\∫s_p\left(t\right)h_p^{*}\left(t\right)dt{|}^2---\left(4\right)$

Target scattering signal decomposition is become one group of width a by AGR algorithm_pThe combination of different Gaussian bases, in point scattering The heart has the narrowest time span, can use a_pThe least basic function represents, diffusibility scattering center then uses width a_pBigger height This basic function represents.If only using width a_pLittle Gaussian bases reconstruct ISAR image, then obtain is point scattering center Set, width a_pBig Gaussian bases represents frequency resonance and chromatic dispersion structure naturally, and the ISAR image that its reconstruct obtains can To reach to identify resonance and the purpose of frequency dependence scattering phenomenon.This AGR algorithmic stability, time frequency resolution is high.

As in figure 2 it is shown, in described step S2, to signal range direction carry out the step of AGR calculating specifically comprise with Lower step:

Step S2.1, determine iteration initial value；

As p=0, determine iteration initial value k₀And a₀, and give initial signal assignment s₀(t)=s (t)；

Choosing of each step a is carried out in the way of two points:

$a_k=\left(\frac{4}{\mathrm{\π}}\right)2^{2(k_0-k)},k=0,1,2,...,k_0---\left(5\right)$

The time step of kth step is:

${\mathrm{\ΔT}}_k=\sqrt{0.5a_k}=2^{k_0-k}\sqrt{\frac{2}{\mathrm{\π}}}---\left(6\right)$

AGR calculating, then initial value k is carried out if in range direction₀Determine by known signal time step delta T:

$k_0={\log }_2\left(\mathrm{\Δ}T\sqrt{\frac{\mathrm{\π}}{2}}\right)---\left(7\right)$

AGR calculating, then initial value k is carried out if in azimuth direction₀Walk to angular samples by the orientation of known signal Length determines；

Step S2.2, begin look for the local maximum of basic function:

$|B_p{|}^2=\underset{a_p,t_p,f_p}{\max }|\∫s_p\left(t\right)h_p^{*}\left(t\right)dt{|}^2;$

Step S2.3, calculating s_pT () projects to h_pSurplus s after (t)_p+1(t):

s_p+1(t)=s_p(t)-B_ph_p(t) (8)

Step S2.4, calculating dump energy:

||s_p+1(t)||²=| | s_p(t)||²-||B_p||² (9)

Step S2.5, calculating reconstructed error SNR_q；

After q time is decomposed, original signal is:

$s\left(t\right)={\mathrm{\Σ}}_{p=0}^q{B}_p{h}_p\left(t\right)+s_{q+1}\left(t\right)---\left(10\right)$

According to preservation of energy:

$\left|\right|s_t\left(t\right)|{|}^2={\mathrm{\Σ}}_{p=0}^q|B_p{|}^2+\left|\right|s_{q+1}\left(t\right)|{|}^2---\left(11\right)$

Along with q increases, error s_q+1T () is dull reduces, when increasing new basic function h_q+1After (t), do not select before impact During the parameter selected, it is believed that iteration stopping, now reconstructed error is:

${\mathrm{SNR}}_q=10\log \left\{\frac{|s_t\left(t\right){|}^2}{|s_{q+1}\left(t\right){|}^2}\right\}dB---\left(12\right)$

Step S2.6, judging whether reconstructed error meets iteration stopping condition the most then iteration and terminate, record is now a_p,t_p,f_pNumerical value, if it is not, then make p=p+1, proceeds step S2.2；

Arranging iteration stopping condition is reconstructed error SNR_qLess than certain little value ε, or reach certain ultimate value for iterations；

SNR_q+1≤ε (13)

Judge SNR_q+1Reason be, if after increasing new basic function, do not have impact before select parameter time, permissible Think iteration stopping, so calculating the q+1 time iteration；

If p → ∞, then reconstruction signal energy is identical with original signal, i.e.

The process that realizes of AGR algorithm can be regarded as Gaussian bases and constantly adapts to the iteration of signal to be expressed at time-frequency domain Process, frequency division when this is a kind of self-adaptation nonlinear with advantages such as high time frequency resolution, absolute convergence, explicit physical meaning Analysis algorithm.Gaussian bases width a_pAccording to two divider rule classifications shown in formula (5), add up the individual of every grade of Gaussian bases Number, can analyze the localization property of signal, width a_pLittle basic function occupy ratio many if, illustrate that signal has well Locality, otherwise illustrates that non local component is more.Extract different Gaussian bases components, different signal processing can be reached Purpose, such as rejects a_pBig component, can reach the purpose of SAR/ISAR image noise reduction, improves image quality.

In described step S1, the method for test or accurately calculating is used to obtain the broadband-angle scanning scattering number of target According to, bandwidth and angle scanning scope and interval is chosen relevant with the initial step length of AGR iteration.

According to radiation reflective model, scattering object being regarded radiant body as, spread speed is the half of true velocity in medium, i.e. Target image F is the Fourier transformation of scattered field E, and two corresponding Fourier transform pairs areWith d:

$F\left(d_n\right)~\underset{m=1}{\overset{M}{\mathrm{\Σ}}}E\left(f_m\right)e^{j2\mathrm{\π}\left(\frac{f_m}{c/2}\right)d_n}---\left(15\right)$

If in time domain, (spatial domain d) carries out AGR calculating, and according to formula (6), time step corresponding to kth=0 step should be less than Equal to total time-domain sampling width, it may be assumed that

${\mathrm{\Δd}}_0\≥2^{k_0}\sqrt{\frac{2}{\mathrm{\π}}}---\left(16\right)$

k₀It it is variance a_pThe number of times of iteration, at least 1, i.e.Distance should be greater than 1.6m to imaging width, enters And obtain frequency domain sample interval and be to the maximum

Same, if carrying out AGR calculating at frequency domain, Ying You:

$\frac{{\mathrm{\Δf}}_0}{c/2}\≥2\sqrt{\frac{2}{\mathrm{\π}}}---\left(17\right)$

I.e. frequency domain sample bandwidth should be greater than

In described step S3, utilize the adaptive spectrum figure of following formula signal calculated energy:

$ADS(t,f)=2\underset{p=0}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}|B_p{|}^2{e}^{-\frac{{(t-t_p)}^2}{a_p}-{\left(2\mathrm{\π}\right)}^2{a}_p{(f-f_p)}^2}{a}_p\∈R^{+},t_p\∈R,f_p\∈\[0,\mathrm{\∞})---\left(18\right)$

Above formula has non-negative, does not has cross term, resolution advantages of higher.

In described step S4, separate Gaussian bases width a in AGR_pBig component of signal and width a_pLittle signal divides Amount, carries out ISAR imaging respectively, and the former represents the image that delocalization scattering component generates, and tends not to relative with realistic objective Should, the latter is then the image that localized scatter component generates, and can be used for target recognition with target realistic model one_to_one corresponding Deng application.

The present invention proposes scattering mechanism identification and the extracting method expressed based on adaptive Gauss, it is achieved that to complex target Colocalization and delocalization scattering mechanism produce the identification of position, and can realize difference by extracting different Gaussian bases The separation of scattering mechanism, can be used for electromagnetism stealth and designs it can also be used to SAR/ISAR image understanding and process, solve SAR/ In ISAR image, delocalization scatters the problem of image blurring brought, is that a kind of tool is widely used the basic analysis side of future Method.

Although present disclosure has been made to be discussed in detail by above preferred embodiment, but it should be appreciated that above-mentioned Description is not considered as limitation of the present invention.After those skilled in the art have read foregoing, for the present invention's Multiple amendment and replacement all will be apparent from.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (7)

1. the scattering mechanism identification expressed based on adaptive Gauss and extracting method, it is characterised in that comprise the steps of

Step S1, the broadband-angle scanning scattering data of acquisition target；

Step S2, at range direction or azimuth direction, signal is carried out AGR calculating；

Step S3, carry out the adaptive spectrum figure of signal calculated energy according to AGR result of calculation；

Step S4, separate Gaussian bases width is big in AGR component of signal and the little component of signal of width, carry out ISAR respectively Imaging, it is achieved the location of scattering mechanism and separation；

Gaussian bases width a_pBig part represents frequency dependence scattering center, a_pLittle part represents point scattering center.

2. the scattering mechanism identification expressed based on adaptive Gauss as claimed in claim 1 and extracting method, it is characterised in that In described step S2, the step that signal carries out AGR calculating specifically comprises the steps of

Step S2.1, determine iteration initial value；

As p=0, determine iteration initial value k₀And a₀, and give initial signal assignment s₀(t)=s (t)；

Step S2.2, begin look for the local maximum of basic function:

Wherein, subscript p represents pth Gaussian bases, and s (t) is signal, basic function h_pT () is normalization Gaussian function, B_pIt is Its coefficient；

Step S2.3, calculating s_pT () projects to h_pSurplus s after (t)_p+1(t):

s_p+1(t)=s_p(t)-B_ph_p(t) (8)

Step S2.4, calculating dump energy:

||s_p+1(t)||²=| | s_p(t)||²-||B_p||² (9)

Step S2.5, calculating reconstructed error SNR_q；

After q time is decomposed, original signal is:

According to preservation of energy:

Along with q increases, error s_q+1T () is dull reduces, when increasing new basic function h_q+1After (t), do not select before impact During parameter, it is believed that iteration stopping, now reconstructed error is:

Step S2.6, judge whether reconstructed error meets iteration stopping condition the most then iteration and terminate, record a now_p,t_p, f_pNumerical value, if it is not, then make p=p+1, proceeds step S2.2；

Arranging iteration stopping condition is reconstructed error SNR_qLess than certain little value ε, or reach certain ultimate value for iterations；

SNR_q+1≤R (13)

If p → ∞, then reconstruction signal energy is identical with original signal, i.e.

。

3. the scattering mechanism identification expressed based on adaptive Gauss as claimed in claim 2 and extracting method, it is characterised in that In described step S2.1,

Choosing of each step a is carried out in the way of two points:

The time step of kth step is:

AGR calculating, then initial value k is carried out if in range direction₀Determine by known signal time step delta T:

AGR calculating, then initial value k is carried out if in azimuth direction₀True to angular samples step-length by the orientation of known signal Fixed.

4. the scattering mechanism identification expressed based on adaptive Gauss as claimed in claim 3 and extracting method, it is characterised in that In described step S2, for meeting the Electromagnetic Scattering of Target data that sampling density requires, range direction uses AGR algorithm Processing, the frequency that can identify and separate this group scattering data relies on and frequency unrelated scattering mechanism component, in orientation side It is used up AGR algorithm to process, then can identify and separate orientation coupling and orientation independence scattering mechanism component.

5. the scattering mechanism identification expressed based on adaptive Gauss as claimed in claim 4 and extracting method, it is characterised in that In described step S1, use test or the method that accurately calculates to obtain the broadband-angle scanning scattering data of target, bandwidth and Angle scanning scope and interval are chosen relevant with the initial step length of AGR iteration.

6. the scattering mechanism identification expressed based on adaptive Gauss as claimed in claim 5 and extracting method, it is characterised in that In described step S1, according to radiation reflective model, scattering object being regarded radiant body as, spread speed is true velocity in medium Half, i.e. target image F are the Fourier transformations of scattered field E, and two corresponding Fourier transform pairs areWith d:

If carrying out AGR calculating in time domain, according to formula (6), time step corresponding to kth=0 step should be less than equal to time total Territory sampling width, it may be assumed that

k₀It it is variance a_pThe number of times of iteration, at least 1, i.e.Distance should be greater than 1.6m to imaging width, and then obtains It is to the maximum to frequency domain sample interval

Same, if carrying out AGR calculating at frequency domain, Ying You:

I.e. frequency domain sample bandwidth should be greater than

7. the scattering mechanism identification expressed based on adaptive Gauss as claimed in claim 6 and extracting method, it is characterised in that In described step S3, utilize the adaptive spectrum figure of following formula signal calculated energy: