CN102998674A - Method and device for detecting multi-channel SAR (synthetic aperture radar) slow ground moving target - Google Patents

Abstract

The invention discloses a method and a device for detecting a multi-channel SAR (synthetic aperture radar) slow ground moving target. The implementation mode of the method for deducing an interferogram amplitude statistical distribution model group specifically includes steps of on the basis of multiplex Wishart distribution, combining a product model by introducing scene environment types, and deducing the interferogram amplitude distribution model group by means of inverse square root Gamma distribution and generalized inverse Gauss square root distribution; the implementation mode of deducing a parameter estimator of each distribution model specifically includes deducing the parameter estimator of each novel distribution model on the basis of Mellin conversion. By building the new interferogram amplitude distribution model group, accurate modeling of interferogram amplitude data corresponding to a broad area under the condition of changing uniformity is achieved.

Description

Hyperchannel SAR ground slow motion object detection method and device

Technical field

The present invention relates to synthetic-aperture radar (Synthetic Aperture Radar, SAR) technical field, relate in particular to a kind of hyperchannel SAR ground slow motion target (Slow Ground Moving Target) detection method and device.

Background technology

SAR is a kind of novel radar system grown up early 1950s.It belongs to active microwave remote sensing equipment, has the characteristics of round-the-clock, round-the-clock and remote imaging, can greatly improve the information obtaining ability, particularly battlefield perception of radar, to dual-use important using value is all arranged.Ground moving target indication (Ground Moving Target Indication, GMTI) is the prerequisite basic function of military SAR system as the part of tactical reconnaissance, is also a major issue during the SAR signal is processed.Traditional single-channel SAR system can only detect all or part of moving target dropped on outside clutter spectrum of frequency spectrum.Be submerged in the detection of the slow motion target within clutter spectrum for frequency spectrum, the single-channel SAR system generally is difficult to realize.With respect to the single-channel SAR system, hyperchannel SAR system has increased the spatial degrees of freedom of system, thereby can utilize a plurality of spatial degrees of freedom to suppress the main-lobe clutter of broadening, and the signal to noise ratio of raising slow motion moving target, obtain and detect preferably performance.

Hyperchannel SAR ground slow motion target Automatic Measurement Technique based on interferogram (interferogram) is a kind of technology of being devoted to fast and effeciently to detect the vehicle target travelled at a slow speed on ground from the significantly SAR image of complexity.This technology is the basic advanced subject of SAR to the ground observation application, has important science and using value, has novelty.

Generally speaking, hyperchannel SAR ground slow motion object detection method comprises the following steps: step 1: determine interferogram amplitude and phase place; Step 2: derive the statistical distribution pattern of interferogram according to determined interferogram amplitude and phase place, and derive the parameter estimator of each distributed model; Step 3: according to the statistical distribution pattern of deriving and parameter estimator, realize the automatic detection of slow motion target.

Above-mentioned steps 2 is links of whole scheme outbalance, how to derive quickly and accurately statistical distribution pattern and parameter estimator, is the problem received much concern.

Interferogram is a kind of main mode of multi-channel information, because the method for statistics can reach the theoretic Bayes(Bayes of information extraction) optimum solution, therefore the statistical modeling of interferogram particularly the interferogram amplitude statistics be modeled as one of study hotspot for hyperchannel SAR, it all has wide practical use at aspects such as polarization, interference, moving-target indications, is the general character fundamental research problem of hyperchannel SAR decipher and application.

The multiple Wishart proposed with Goodman is distributed as basis, and at first the people such as Lee derive and obtained the distributed model of interferogram amplitude under the homogeneous area environment.On this basis, Gierull, Sikaneta, the people such as Abdelfattah have carried out comparatively deep research to the interferogram Amplitude Distributed Model, wherein, the most famous and performance is best is the interferogram Amplitude Distributed Model that the people such as Gierull proposes, its advantage is that integrality is better, the corresponding interferogram amplitude data of non-uniform areas is had to certain modeling ability, its shortcoming is owing to still comprising the correction Bessel(Bessel of Second Type in distributed model corresponding under the homogeneous area environment) special function such as function, but the difficulty that causes threshold value to solve the scope that has greatly limited fitted area, and for complex environment (as city etc.), the modeling ability wretched insufficiency of this model.Therefore, urgently seek more perfect, as to there is the extensive region modeling ability under the uniformity coefficient variation new interferogram Amplitude Distributed Model.

Summary of the invention

The present invention proposes a kind of hyperchannel SAR ground slow motion object detection method and device based on interferogram, and method wherein comprises the following steps:

Determine interferogram amplitude and phase place; Derivation interferogram amplitude statistical distribution model family, and derive the parameter estimator of each distributed model; According to described statistical distribution pattern and parameter estimator, realize the automatic detection of slow motion target.Wherein, the specific implementation of described derivation interferogram amplitude statistical distribution model family is: with multiple Wishart, be distributed as basis, by introducing the scene environment classification, in conjunction with product model, utilize contrary root Gamma to distribute and the distribution of generalized inverse Gauss root, derive interferogram Amplitude Distributed Model family; The described specific implementation of deriving the parameter estimator of each distributed model is: based on Mellin, the parameter estimator of each new distributed model is derived in conversion.

In scheme provided by the invention, by setting up new interferogram Amplitude Distributed Model family, solved the Accurate Model problem of interferogram amplitude data corresponding to the extensive region of uniformity coefficient under changing, and expand to the hyperchannel field take coherent spot model and product model as the single-channel SAR image statistics modeling family that base growth comes, realized theoretical expansion and the unification of arriving the modeling of hyperchannel SAR interferogram amplitude of single-channel SAR image modeling.Parameter estimator corresponding to each distributed model based on Mellin conversion iteration quickly and accurately goes out the estimated value of each distributions containing parameter, thereby guaranteed the practicality of new distributed model family.

The accompanying drawing explanation

Fig. 1 is the hyperchannel SAR ground slow motion object detection method process flow diagram that the present invention is based on interferogram;

Fig. 2 illustrates the relation between each distribution of interferogram amplitude under homogeneous area of the present invention, non-uniform areas and extreme non-uniform areas environment.

Embodiment

The present invention proposes a kind of brand-new hyperchannel SAR ground slow motion target detection scheme based on interferogram.Wherein, new interferogram Amplitude Distributed Model family and corresponding parameter estimator have been proposed especially.At first, under the product model framework, be distributed as basis with multiple Wishart, by introducing the thought of scene environment classification, utilization possesses true atural object RCS(Radar Cross Section, RCS) the contrary root Gamma of component Accurate Model ability distributes and the distribution of generalized inverse Gauss root, derives and has set up theoretical perfect new interferogram Amplitude Distributed Model family: Extended Gamma distributes, expansion G ⁰distribute and expansion G distribution, i.e. E-Gamma distribution, E-G ⁰distribute and E-G distributes, solved the Accurate Model problem that uniformity coefficient changes interferogram amplitude data corresponding to lower extensive region, realized that single-channel SAR image modeling theory arrives expansion and the unification of the modeling of hyperchannel SAR interferogram amplitude.Secondly, convert the parameter estimator of having derived each new distributed model based on Mellin: E-Gamma MoLC, E-G ⁰moLC and E-G MoLC.New estimator iteration quickly and accurately goes out the estimated value of each distribution parameter.With KL tolerance, MSE(Mean Square Error, square error) tolerance and K-S check are as the qualitative assessment criterion, interferogram corresponding to star-carrying multichannel SAR measured data tested, and result has proved the validity of model family and the corresponding parameter estimator put forward.

Referring to Fig. 1, the hyperchannel SAR ground slow motion object detection method based on interferogram for the present invention proposes specifically comprises:

S101: derivation interferogram amplitude statistical distribution model family, and derive the parameter estimator of each distributed model;

Particularly: the specific implementation of derivation interferogram amplitude statistical distribution model family is: under the product model framework, be distributed as basis with multiple Wishart, by introducing the scene environment classification, the contrary root Gamma that utilization possesses true atural object RCS component Accurate Model ability distributes and the distribution of generalized inverse Gauss root, derives and sets up new interferogram Amplitude Distributed Model family: E-Gamma distribution, E-G ⁰distribute and the E-G distribution; The specific implementation of deriving the parameter estimator of each distributed model is: based on Mellin, the parameter estimator of each new distributed model has been derived in conversion: E-Gamma MoLC, E-G ⁰moLC and E-G MoLC.

S102: according to described statistical distribution pattern and parameter estimator, realize the automatic detection of slow motion target.

Visible, the present invention is distributed as basis with multiple Wishart, the people such as introducing Frery are divided into the real image scene thought of three classes such as homogeneous area, non-uniform areas and extreme non-uniform areas, in conjunction with product model, the contrary root Gamma that utilization possesses true atural object RCS range weight Accurate Model ability distributes and the distribution of generalized inverse Gauss root, has derived interferogram Amplitude Distributed Model family new under the different images scene.On this basis, utilize the Mellin conversion to derive the new parameter estimator that respectively distributes.

Below introduce in detail.

1 new interferogram amplitude statistical distribution model family

According to central limit theorem, when the RCS component of image scene is constant, the homophase of coherent speckle noise component (In-phase) and quadrature (Quadrature) passage are separate and all obey the Gauss distribution of zero-mean, have possessed the precondition that multiple Wishart distributes.Suppose that binary channels n looks sample covariance matrix and is

$\hat{R}=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}Z\left(k\right)Z{\left(k\right)}^H=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}\left[\begin{array}{cc}{\left|z_1\left(k\right)\right|}^2& z_1\left(k\right)z_2{\left(k\right)}^{*}\\ z_1{\left(k\right)}^{*}{z}_2\left(k\right)& {\left|z_2\left(k\right)\right|}^2\end{array}\right]---\left(1\right)$

Wherein, n means to look number, Z (k)=[z ₁(k), z ₂(k)] ^tbe the k time single-view picture, * means complex conjugate, and H means complex-conjugate transpose.

the counter-diagonal element be called multiple n and look interferogram, the mould value of interferogram is the interferogram amplitude.

Those skilled in the art are known, stochastic matrix

obeying multiple Wishart distributes.The elements in a main diagonal is carried out to the joint distribution that integration can obtain standardized interferogram amplitude ξ and interferogram phase place ψ is:

$p=(\mathrm{\ξ},\mathrm{\ψ})=\frac{{2n}^{n+1}{\mathrm{\ξ}}^n}{\mathrm{\π\Γ}\left(n\right)(1-{\mathrm{\ρ}}^2)}\exp \left(\frac{2\mathrm{n\ρ\ξ}\cos (\mathrm{\ψ}-\mathrm{\θ})}{1-{\mathrm{\ρ}}^2}\right)K_{n-1}\left(\frac{2\mathrm{n\ξ}}{1-{\mathrm{\ρ}}^2}\right)---\left(2\right)$

Wherein, K _n-1() is n-1) the Second Type modified Bessel function on rank, ρ e ^{j θ}be the multiple correlation coefficient of two passage outputs, ρ is called the degree of correlation, and standardized interferogram amplitude ξ is:

$\mathrm{\&xi;}=\frac{\left|(1/n){\mathrm{\&Sigma;}}_{k=1}^n{z}_1\left(k\right)z_2{\left(k\right)}^{*}\right|}{\sqrt{E\left({\left|{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002320172500021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\right|}^2\right)E\left({\left|{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HDA00002320172500021.png"\; state="\{\{state\}\}">z</figure-callout>}}_2\right|}^2\right)}}=\frac{\left|(1/n){\mathrm{\&Sigma;}}_{k=1}^n{z}_1\left(k\right)z_2{\left(k\right)}^{*}\right|}{\sqrt{C_{11}{C}_{22}}}---\left(3\right)$

1.1E-Gamma distribute

In order to obtain the probability distribution of interferogram amplitude under even environment, need carry out integration to the interferogram phase variant in (2) formula, the marginal distribution that obtains standardization interferogram amplitude is:

$p\left(\mathrm{\&xi;}\right)=\frac{{4n}^{n+1}{\mathrm{\&xi;}}^n}{\mathrm{\&Gamma;}\left(n\right)(1-{\mathrm{\&rho;}}^2)}{I}_0\left(\frac{2\mathrm{n\&rho;\&xi;}}{1-{\mathrm{\&rho;}}^2}\right)K_{n-1}\left(\frac{2\mathrm{n\&xi;}}{1-{\mathrm{\&rho;}}^2}\right)---\left(4\right)$

Wherein, I ₀the first kind modified Bessel function that () is zeroth order.

(4) formula of analysis, due to its modified Bessel function that comprises two types, this capability of fitting to this distribution is brought larger restriction.Particularly, the special character (this function can promptly trend towards infinite) according to modified Bessel function, when independent variable x value hour, Equations of The Second Kind modified Bessel function K _v(x) value can be very large, and when the independent variable value is larger, first kind modified Bessel function I _v(x) value again will be very large, so, when the probability distribution of the modified Bessel function that comprises two types when utilization is carried out the Fitting Calculation, accuracy can be poor usually, more obvious when particularly the precision of data layout is low.Moreover, under actual conditions, the n ξ in (4) formula can be again a larger value usually.For this reason, can be according to the asymptotic expansion expression formula of the first kind and Equations of The Second Kind modified Bessel function, push away:

$p\left(\mathrm{\&xi;}\right)=\frac{{\mathrm{\&alpha;}}_0{n}^n\mathrm{\&xi;}}{\mathrm{\&Gamma;}\left(n\right)}{\left({\mathrm{\&alpha;}}_0\mathrm{\&xi;}\right)}^{n-1}\exp \left({-\mathrm{n\&alpha;}}_0\mathrm{\&xi;}\right),$ α ₀,n,ξ＞0 (5)

Wherein, a ₀=2/ (1+ ρ).(5) formula is the distribution that under the homogeneous area environment, the interferogram amplitude is obeyed, and is referred to as Extended Gamma and distributes, and notes the distribution into E-Gamma by abridging.

1.2E-G ⁰distribute

These class non-uniform areas such as farmland for forest, farming, their RCS has certain fluctuating, if now utilize the interferogram amplitude distribution (being that E-Gamma distributes) of homogeneous area when the amplitude data of non-uniform areas is carried out to matching, can show larger deviation.For this reason, introduce product model, i.e. Y _i=A _ix _i, i=1.Wherein, A _irepresent atural object back scattering RCS range weight, X _i~ N ^□(0,1), mean the speckle noise component, and i is i independent receiving cable.

In reality, for whole non-uniform areas, RCS rises and falls, but the RCS of adjacent several resolution elements usually can think and have steady state value.That is to say, when utilizing the neighborhood window to construct sample covariance matrix, can suppose that the RCS fluctuating length of scene is more than or equal to the width of neighborhood window, scene has relatively long correlativity, thereby the atural object back scattering RCS in the neighborhood window can think constant.Simultaneously, suppose two channel energy balances, thereby under inhomogeneous environment, the interferogram amplitude can be expressed as Ξ=A ²ξ=W ξ.In view of the extensive modeling ability that contrary root Gamma distributes, suppose that A obeys contrary root Gamma and distributes.

So far, under the product model framework, with the E-Gamma under even environment, be distributed as basis, distribute in conjunction with contrary Gamma, the probability distribution that obtains interferogram amplitude Ξ under the non-uniform areas environment is

$p\left(\mathrm{\&Xi;}\right)=\frac{{\mathrm{\&alpha;}}_0{n}^n{\mathrm{\&gamma;}}^{-\mathrm{\&alpha;}}\mathrm{\&Gamma;}(n-\mathrm{\&alpha;})}{\mathrm{\&Gamma;}\left(n\right)\mathrm{\&Gamma;}(-\mathrm{\&alpha;})}\&CenterDot;\frac{{\left({\mathrm{\&alpha;}}_0\mathrm{\&Xi;}\right)}^{n-1}}{{(\mathrm{\&gamma;}+{\mathrm{n\&alpha;}}_0\mathrm{\&Xi;})}^{n-\mathrm{\&alpha;}}},$ α ₀,-α,γ,n,Ξ＞0(6)

(6) formula is called to expansion G ⁰distribute, note by abridging as E-G ⁰distribute.Wherein, α is form parameter, has reflected in essence the uniformity coefficient in tested zone, and-α ∈ (0, ∞) show that this distribution can cover the modeling problem of the extensive region under the uniformity coefficient variation; γ is scale parameter, relevant with the average energy in tested zone.

1.3E-G distribute

For inhomogeneous scenes of extreme such as cities, it contains multiple heterogeneous composition, and the histogram hangover is serious.Now in theory, if remove the influence factor of estimation of distribution parameters, even utilize the E-G that modeling ability is stronger ⁰distribute and also can't realize the high precision matching of interferogram amplitude data under this condition.For this reason, by sacrificing certain computation complexity, introduce the RCS range weight that generalized inverse Gauss root that modeling ability is stronger distributes to the extreme non-uniform areas and carry out modeling.Viewpoint according to people such as scholar Muller, " general significance; the backscatter intensity that characterizes atural object RCS fluctuation characteristic should be comprised of two parts; form by obeying the regular scattered portion that Gamma distributes and obeying the unusual scattered portion that contrary Gamma distributes ", this explanation generalized inverse Gauss distributes and can carry out effective modeling to the RCS component of the extreme non-uniform areas that consists of regular scattered portion and unusual scattered portion.

Same E-G ⁰the derivation distributed is similar, and under the product model framework, associating E-Gamma distributes and generalized inverse Gauss distributes, and that derives and obtain that under extreme non-uniform areas environment, the interferogram amplitude is obeyed is distributed as:

$p\left(\mathrm{\&Xi;}\right)=\frac{{\mathrm{\&alpha;}}_0{n}^n{(\mathrm{\&lambda;}/\mathrm{\&gamma;})}^{\mathrm{\&alpha;}/2}}{\mathrm{\&Gamma;}\left(n\right)K_{\mathrm{\&alpha;}}\left(2\sqrt{\mathrm{\&lambda;\&gamma;}}\right)}{\left({\mathrm{\&alpha;}}_0\mathrm{\&Xi;}\right)}^{n-1}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&gamma;}+{\mathrm{n\&alpha;}}_0\mathrm{\&Xi;}}\right)}^{(n-\mathrm{\&alpha;})/2}$

(7)

$\&CenterDot;K_{n-\mathrm{\&alpha;}}\left(2\sqrt{\mathrm{\&lambda;}(\mathrm{\&gamma;}+n{\mathrm{\&alpha;}}_0\mathrm{\&Xi;})}\right),$ α ₀,-α,λ，γ,n,Ξ＞0

(7) formula is referred to as to expand G and distributes, note the distribution into E-G by abridging.Its parameter space is:

$\left\{\begin{array}{cc}\mathrm{\&gamma;}>0,\mathrm{\&lambda;}\&GreaterEqual;0& \mathrm{if\&alpha;}<0\\ \mathrm{\&gamma;}>0,\mathrm{\&lambda;}>0& \mathrm{if\&alpha;}=0\\ \mathrm{\&gamma;}\&GreaterEqual;0,\mathrm{\&lambda;}>0& \mathrm{if\&alpha;}>0\end{array}\right.---\left(8\right)$

1.4 the relation between each distribution

Fig. 2 shows the relation between each distribution of interferogram amplitude new under the different images scene, can draw thus following some conclusion.

(1) there is " downward compatibility " between each distribution of new interferogram amplitude

From the derivation of front, for E-G, distribute, when its containing parameter-alpha, gamma>0 and λ → 0, this distribution convergence in distribution is in E-G ⁰distribute; E-G ⁰distribute and convergence in distribution distributes in E-Gamma.That is to say, extremely the interferogram Amplitude Distributed Model under the non-uniform areas environment comprises the corresponding modeling ability distributed under homogeneous area, non-uniform areas environment, distributed model under the non-uniform areas environment comprises again the corresponding modeling ability distributed of homogeneous area simultaneously, and new interferogram Amplitude Distributed Model family has " downward compatibility ".

(2) new interferogram amplitude distribution has " passage compatibility "

" passage compatibility " herein refers to " for for describing the distributed model of hyperchannel SAR interferogram amplitude, the distributed model that it comprises single passage SAR intensity image ".For hyperchannel SAR complex pattern, any two channel datas wherein all can obtain corresponding interferogram, at homogeneous area, non-uniform areas with under the scene that extremely non-uniform areas etc. is different, the amplitude distribution of this interferogram can utilize respectively that E-Gamma distributes, E-G ⁰distribution and E-G distribute and carry out Accurate Model.When two channel image complete dependences, i.e. corresponding degree of correlation parameter ρ=1 o'clock, the interferogram amplitude becomes the SAR intensity image of single passage, and corresponding E-Gamma distributes, E-G ⁰distribution and E-G distribute and also are reduced to respectively Gamma distribution, G ⁰distribute and the G distribution, most widely used distributed model when these three distributions are carried out modeling to the single-channel SAR image exactly.This has not only confirmed the correctness that new interferogram Amplitude Distributed Model is derived, and the more important thing is, shows that new interferogram amplitude distribution has " passage compatibility ".

The 2 new model parameter estimation that convert based on Mellin

After completing the modeling of interferogram amplitude, the accurate estimation that realizes each distributed model parameter becomes new model and successfully is generalized to the key problem in practical application.

For this reason, by analyzing, E-Gamma distributes, E-G ⁰the modeling principle that distribution and E-G distribute, " though be to be distributed as basis with Wishart, in conjunction with product model, develop, but also can be considered in essence under the product model framework, from the coherent spot model, by single channel expansion, obtained " characteristics, find to adopt this model family parameter of Mellin transfer pair to estimate to have unique advantage, because when the RCS of atural object component has certain fluctuating, be transformed to basic Second Type statistic with Mellin and can the coherent speckle noise component be considered as to " Mellin convolution ", can greatly simplify new interferogram Amplitude Distributed Model family parameter estimation procedure, and can obtain the parameter estimation performance consistent with optimum maximal possibility estimation.

2.1 the estimation of degree of correlation parameter

Utilizing before the Second Type statistic estimated parameter n, α, γ, λ, at first will distribute to E-Gamma, E-G ⁰distribution and the total degree of correlation parameter ρ of E-G distributions are estimated.This is mainly that its estimated value does not change along with the difference of distributed model because the degree of correlation means is a kind of intrinsic relation between two channel image.Get:

$\widehat{\mathrm{\&rho;}}=\frac{1}{N}\underset{m=1}{\overset{n}{\mathrm{\&Sigma;}}}[(1/n){\mathrm{\&Sigma;}}_{k=1}^n{z}_1\left(k\right)z_2{\left(k\right)}^{*}/\sqrt{E\left({\left|{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002320172500021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\right|}^2\right)E\left({\left|{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HDA00002320172500021.png"\; state="\{\{state\}\}">z</figure-callout>}}_2\right|}^2\right)}]---\left(9\right)$

This estimator is the unbiased estimator of ρ, thereby, utilize standardized interferogram just can realize estimating without inclined to one side of the degree of correlation.

(9) formula is derived and is obtained under the homogeneous area environment, for non-uniform areas and extreme non-uniform areas, two passages by the prerequisite of accurate calibration under, because atural object back scattering RCS in the neighborhood window is constant, thereby atural object back scattering component is cancelled, now the degree of correlation estimator of the homogeneous area shown in (9) formula remains effective for non-uniform areas and extreme non-uniform areas.

2.2E-Gamma_MoLC

The fundamental function of first that utilizes Mellin conversion to obtain that E-Gamma distributes corresponding, second Second Type is respectively:

$\left\{\begin{array}{c}{\mathrm{\&phi;}}_{\mathrm{E\&Gamma;}}\left(s\right)={\left(\frac{1}{{\mathrm{\&alpha;}}_{0}n}\right)}^{s-1}\frac{\mathrm{\&Gamma;}(n+s-1)}{\mathrm{\&Gamma;}\left(n\right)}\\ {\mathrm{\&zeta;}}_{\mathrm{E\&Gamma;}}\left(s\right)=(s-1)\ln \left(\frac{1}{{\mathrm{\&alpha;}}_{0}n}\right)+\ln (n+s-1)-\ln \mathrm{\&Gamma;}\left(n\right)\end{array}\right.---\left(10\right)$

To ζ _{e Γ}(s) ask its all-order derivative at the s=1 place, obtain the logarithm semi-invariant that E-Gamma distributes corresponding and be:

$\left\{\begin{array}{c}{\tilde{c}}_1=-\ln \left({\mathrm{\&alpha;}}_{0}n\right)+\mathrm{\&Psi;}\left(n\right)\\ {\tilde{c}}_k=\mathrm{\&Psi;}(k-1,n),k\&GreaterEqual;2\end{array}\right.---\left(11\right)$

Wherein, ψ () means general western function (being called again the Digamma function, i.e. logarithm Gamma function derivative), ψ (k) (k=1,2, ...) mean (k) to mean the k order derivative by k rank Polygamma functions (being the k order derivative of Digamma function).

If x ₁, x ₂..., x _nfor N sample observation, sample logarithm cumulative scale is shown:

$\left\{\begin{array}{c}{\hat{\tilde{c}}}_1=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[\ln \right]\left(x_i\right)\\ {\hat{\tilde{c}}}_k=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[{(\ln \left(x_i\right)-{\hat{\tilde{c}}}_1)}^k\right],k\&GreaterEqual;2\end{array}\right.---\left(12\right)$

The estimation expression formula that is easily obtained parameter n in the E-Gamma distribution by (12), (11) formula is

this formula is referred to as to the logarithm semi-invariant estimator of E-Gamma distribution parameter, notes by abridging as E-Gamma_MoLC.

2.3E-G ⁰_MoLC

E-G ⁰the corresponding logarithm semi-invariant that distributes is:

$\left\{\begin{array}{c}{\tilde{c}}_1=\ln \left(\frac{\mathrm{\&gamma;}}{{\mathrm{\&alpha;}}_{0}n}\right)+\mathrm{\&Psi;}\left(n\right)-\mathrm{\&Psi;}(-\mathrm{\&alpha;})\\ {\tilde{c}}_k=\mathrm{\&Psi;}(k-1,n)+{(-1)}^k\mathrm{\&Psi;}(k-1,-\mathrm{\&alpha;}),k\&GreaterEqual;2\end{array}\right.---\left(13\right)$

Associating (12), (13) formula, try to achieve E-G ⁰the estimation expression formula of profile parameter, γ, n is:

$\left\{\begin{array}{c}\ln (\widehat{\mathrm{\&gamma;}}/\left({\mathrm{\&alpha;}}_0\hat{n}\right))+\mathrm{\&Psi;}\left(\hat{n}\right)-\mathrm{\&Psi;}(-\widehat{\mathrm{\&alpha;}})=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[\ln \left(x_i\right)\right]\\ \mathrm{\&Psi;}(1,\hat{n})+\mathrm{\&Psi;}(1,-\widehat{\mathrm{\&alpha;}})=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[{(\ln \left(x_i\right)-{\hat{\tilde{c}}}_1)}^2\right]\\ \mathrm{\&Psi;}(2,\hat{n})-\mathrm{\&Psi;}(2,\widehat{-\mathrm{\&alpha;}})=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[{(\ln \left(x_i\right)-{\hat{\tilde{c}}}_1)}^3\right]\end{array}\right.---\left(14\right)$

(14) formula is called to E-G ⁰the logarithm semi-invariant estimator of distribution parameter, note by abridging as E-G ⁰_ MoLC.

2.4E-G_MoLC

The fundamental function of first of E-G distribution correspondence, second Second Type is respectively:

$\left\{\begin{array}{c}{\mathrm{\&phi;}}_{\mathrm{EG}}\left(s\right)={\left[\frac{\mathrm{\&gamma;}}{{\left({\mathrm{\&alpha;}}_{0}n\right)}^2\mathrm{\&lambda;}}\right]}^{(s-1)/2}.\frac{K_{\mathrm{\&alpha;}+s-1}\left(2\sqrt{\mathrm{\&gamma;\&lambda;}}\right)\mathrm{\&Gamma;}(n+s-1)}{K_{\mathrm{\&alpha;}}\left(2\sqrt{\mathrm{\&gamma;\&lambda;}}\right)\mathrm{\&Gamma;}\left(n\right)}\\ {\mathrm{\&zeta;}}_{\mathrm{EG}}\left(s\right)=\frac{(s-1)}{2}\ln \left(\frac{\mathrm{\&gamma;}}{{\left({\mathrm{\&alpha;}}_{0}n\right)}^2\mathrm{\&lambda;}}\right)+\ln K_{\mathrm{\&alpha;}+s-1}\left(2\sqrt{\mathrm{\&gamma;\&lambda;}}\right)\\ +\ln \mathrm{\&Gamma;}(n+s-1)-\ln K_{\mathrm{\&alpha;}}\left(2\sqrt{\mathrm{\&gamma;\&lambda;}}\right)-\ln \mathrm{\&Gamma;}\left(n\right)\end{array}\right.---\left(15\right)$

Order $W={\&Integral;}_0^{\&infin;}{x}^{\mathrm{\&alpha;}+s-2}\mathrm{esp}(-\frac{\mathrm{\&gamma;}}{x}-\mathrm{\&lambda;x})\mathrm{dx},$ Definition:

$\mathrm{\&Omega;}(k;\mathrm{\&alpha;},\mathrm{\&gamma;},\mathrm{\&lambda;})={\frac{{\&PartialD;}^{k}W\left(s\right)}{{\&PartialD;s}^k}|}_{s=1}$

(16)

$={\&Integral;}_0^{\&infin;}{\left(\ln x\right)}^k{x}^{\mathrm{\&alpha;}-1}\exp (-\frac{\mathrm{\&gamma;}}{x}-\mathrm{\&lambda;x})\mathrm{dx},$ k＝0,1，2,.

Brief note is Ω (k).Especially, $\mathrm{\&Omega;}\left(0\right)=2{(\mathrm{\&gamma;}/\mathrm{\&lambda;})}^{\mathrm{\&alpha;}/2}{K}_{\mathrm{\&alpha;}}\left(2\sqrt{\mathrm{\&gamma;\&lambda;}}\right).$

Simultaneously, the Derivative Definition of Ω (k) is:

${\left[\mathrm{\&Omega;}\left(k\right)\right]}^{\&prime;}={\frac{{\&PartialD;}^{k+1}W}{{\&PartialD;s}^{k+1}}|}_{s=1}$

(17)

$={\&Integral;}_0^{\&infin;}{\left(\ln x\right)}^{k+1}{x}^{\mathrm{\&alpha;}-1}\exp (-\frac{\mathrm{\&gamma;}}{x}-\mathrm{\&lambda;x})\mathrm{dx},$ k＝0,1，2,...

Easily prove, meet following relation between Ω (k) and Ω (k+1):

$\left\{\begin{array}{c}\mathrm{\&Omega;}(k+1)={\left[\mathrm{\&Omega;}\left(k\right)\right]}^{\&prime;}\\ {\left[\frac{\mathrm{\&Omega;}(k+1)}{\mathrm{\&Omega;}\left(k\right)}\right]}^{\&prime;}=\frac{\mathrm{\&Omega;}\left(k\right)\mathrm{\&Omega;}(k+2)-{\mathrm{\&Omega;}}^2(k+1)}{{\mathrm{\&Omega;}}^2\left(k\right)}\end{array}\right.,k=\mathrm{0,1,2},...---\left(18\right)$

Thereby the recurrence relation of the Ω (k) provided according to (18) formula obtains the logarithm cumulative amount that E-G distributes corresponding and is:

$\left\{\begin{array}{c}{\tilde{c}}_1=-\ln \left({\mathrm{\&alpha;}}_{0}n\right)+\mathrm{\&Omega;}\left(1\right){\mathrm{\&Omega;}}^{-1}\left(0\right)+\mathrm{\&Psi;}\left(n\right)\\ {\tilde{c}}_k={\left[\mathrm{\&Omega;}\left(1\right){\mathrm{\&Omega;}}^{-1}\left(0\right)\right]}^{k-1}+\mathrm{\&Psi;}(k-1,n)\end{array}\right.,k=\mathrm{2,3},...\left(19\right)$

The estimation expression formula that finally obtains E-G profile parameter, λ, γ, n in conjunction with (12) and (19) formula is:

$\left\{\begin{array}{c}-\ln \left({\mathrm{\&alpha;}}_{0}n\right)+\mathrm{\&Omega;}\left(1\right){\mathrm{\&Omega;}}^{-1}\left(0\right)+\mathrm{\&Psi;}\left(n\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[\ln \left(x_i\right)\right]\\ {\left[\mathrm{\&Omega;}\left(1\right){\mathrm{\&Omega;}}^{-1}\left(0\right)\right]}^{\&prime;}+\mathrm{\&Psi;}(1,n)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[{(\ln \left(x_i\right)-{\hat{\tilde{c}}}_1)}^2\right]\\ {\left[\mathrm{\&Omega;}\left(1\right){\mathrm{\&Omega;}}^{-1}\left(0\right)\right]}^{\&prime;\&prime;}+\mathrm{\&Psi;}(2,n)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[{(\ln \left(x_i\right)-{\hat{\tilde{c}}}_1)}^3\right]\\ {\left[\mathrm{\&Omega;}\left(1\right){\mathrm{\&Omega;}}^{-1}\left(0\right)\right]}^{\&prime;\&prime;\&prime;}+\mathrm{\&Psi;}(3,n)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left[{(\ln \left(x_i\right)-{\hat{\tilde{c}}}_1)}^4\right]\end{array}\right.---\left(20\right)$

(20) formula is called to the logarithm semi-invariant estimator of E-G distribution parameter, note by abridging as E-G_MoLC.

E-Gamma_MoLC, E-G ⁰the Estimation Performance Analysis of _ MoLC and E-G MoLC is those skilled in the art's known technology, does not repeat them here.

Thus, pass through the present invention program, the foundation of new interferogram Amplitude Distributed Model family, solved the Accurate Model problem of interferogram amplitude data corresponding to the extensive region of uniformity coefficient under changing, and expand to the hyperchannel field take coherent spot model and product model as the single-channel SAR image statistics modeling family that base growth comes, realized theoretical expansion and the unification of arriving the modeling of hyperchannel SAR interferogram amplitude of single-channel SAR image modeling.Parameter estimator corresponding to each distributed model based on Mellin conversion iteration quickly and accurately goes out the estimated value of each distributions containing parameter, thereby guaranteed the practicality of new distributed model family.

Above provide specific descriptions of the present invention with for being set forth and illustrating.But do not really want exhaustive or limit the invention to disclosed precise forms.According to above instruction, can realize a lot of the modification and modification.Above-described embodiment is selected for explaining best principle of the present invention and practical application thereof, thereby makes those skilled in the art and to utilize the different modification that are suitable for the particular desired purposes to utilize best the present invention with different embodiment.Scope of the present invention will be defined by claims.

Claims (10)

1. a hyperchannel SAR ground slow motion object detection method, is characterized in that, comprising:

Derivation interferogram amplitude statistical distribution model family, and derive the parameter estimator of each distributed model;

According to described statistical distribution pattern and parameter estimator, realize the automatic detection of slow motion target;

Wherein:

The specific implementation of described derivation interferogram amplitude statistical distribution model family is: with multiple Wishart, be distributed as basis, by introducing the scene environment classification, in conjunction with product model, utilize contrary root Gamma to distribute and the distribution of generalized inverse Gauss root, derive interferogram Amplitude Distributed Model family;

The described specific implementation of deriving the parameter estimator of each distributed model is: based on Mellin, the parameter estimator of each new distributed model is derived in conversion.

2. method according to claim 1, is characterized in that, with multiple Wishart, is distributed as the joint distribution that basis obtains standardized interferogram amplitude and interferogram phase place, particularly:

Determine that hyperchannel n looks sample covariance matrix and is

Will the counter-diagonal element be defined as multiple n and look interferogram;

Determine and obey the stochastic matrix that multiple Wishart distributes the elements in a main diagonal is carried out to the joint distribution that integration can obtain standardized interferogram amplitude ξ and interferogram phase place ψ.

3. method according to claim 1 and 2, is characterized in that, described interferogram Amplitude Distributed Model family comprises that Extended Gamma distributes, expansion G ⁰distribute and expansion G distribution.

4. method according to claim 3, is characterized in that, described Extended Gamma distributes and means interferogram amplitude under the homogeneous area environment, and its process of establishing is:

Described interferogram phase place is carried out to integration, obtain the marginal distribution of standardization interferogram amplitude;

According to the asymptotic expansion expression formula of the first kind and Equations of The Second Kind modified Bessel function, from the marginal distribution of described standardization interferogram amplitude, infer that described Extended Gamma distributes.

5. method according to claim 3, is characterized in that, described expansion G ⁰distribute and mean interferogram amplitude under the non-uniform areas environment, its process of establishing is:

Under the product model framework, be distributed as basis with the Extended Gamma under even environment, in conjunction with contrary Gamma, distribute, obtain the probability distribution of interferogram amplitude under the non-uniform areas environment.

6. method according to claim 3, is characterized in that, described expansion G distributes and means interferogram amplitude under extreme non-uniform areas environment, and its process of establishing is:

Under the product model framework, the associating Extended Gamma distributes and generalized inverse Gauss distributes, and derives and obtains the distribution that under extreme non-uniform areas environment, the interferogram amplitude is obeyed.

7. method according to claim 3, is characterized in that, between described Extended Gamma distributes, expansion G0 distributes and expansion G distributes, has downward compatibility and passage compatibility.

8. method according to claim 3, is characterized in that, the detailed process of the described parameter estimator based on each new distributed model of Mellin conversion derivation is:

Extended Gamma is distributed, expands G ⁰distribute and expand the total degree of correlation parameter ρ of G distributions and estimated;

Determine the logarithm semi-invariant estimator of Extended Gamma distribution parameter;

Determine expansion G ⁰the logarithm semi-invariant estimator of distribution parameter;

Determine the logarithm accumulation estimator of expansion G distribution parameter.

9. method according to claim 8, is characterized in that, determines Extended Gamma distribution parameter, expansion G ⁰the detailed process of the logarithm semi-invariant estimator of distribution parameter or expansion G distribution parameter is:

Gamma distributes, expansion G to utilize the Mellin conversion to be expanded respectively ⁰the fundamental function of first of distribution and expansion G distribution correspondence, second Second Type;

Ask the all-order derivative of fundamental function, the Gamma that is expanded respectively distributes, expansion G ⁰distribute and expand the logarithm semi-invariant that G distributes corresponding.

10. a hyperchannel SAR ground slow motion object detecting device, is characterized in that, this device can be carried out method as described as claim 1-9.

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