CN101819269A - Space-time adaptive processing method under non-homogeneous clutter environment - Google Patents

Abstract

Space-time adaptive processing method under non-homogeneous clutter environment belongs to airborne radar clutter suppression technology field. Along distance to a snap training sample xl is extracted, clutter space-time two-dimensional spectrum is solved, by sparse solution The clutter covariance matrix for bringing into estimate; Clutter covariance matrix weighting to estimating; According to the covariance matrix of estimation, calculate corresponding space-time adaptive filter, and output end do moving-target whether there is or not judgement. The IID training sample that the present invention occurs for non-homogeneous clutter environment lacks, and is composed with the method super-resolution estimation clutter space-time two-dimensional of overcomplete sparse representation, and then realize that single frames training sample estimates clutter covariance matrix. The present invention can effectively avoid becoming influence fastly because of discrete noise source, landform, while the also more robust of the space-time spectrum diffusion caused by the factors such as clutter internal motion and channel be inconsistent. Mountaintop real data demonstrates the method and is able to maintain fine clutter recognition performance, is highly suitable for strong non-homogeneous clutter environment.

Description

Space-time adaptive processing method under non-homogeneous clutter environment

Technical field

The present invention relates to space-time adaptive under the non-homogeneous clutter environment (STAP) disposal route, be a kind of STAP framework CS-STAP that estimates based on sparse property clutter, utilize the sparse priori of clutter distribution, super-resolution estimation clutter space-time two-dimensional spectrum (space-time spectrum), and then realize that a small amount of training sample can estimate the clutter covariance matrix method, improve the purpose of estimating speed of convergence thereby reach, belong to airborne radar clutter and suppress technical field.

Background technology

The present invention is directed to the problem that independent same distribution in the actual non-homogeneous clutter environment (IID) training sample lacks, spectrum when proposition utilizes a small amount of training sample of method reality of overcomplete sparse representation (Sparse Overcomplete Representations) to get final product high-resolution estimation clutter sky, and then the purpose of estimation clutter covariance matrix, improve the speed of convergence of estimating greatly, solved the problem that the IID sample lacks in the actual non-homogeneous clutter environment well.

Following article and patent documentation have covered the main background technology in this field substantially.In order to present the evolution of technology, allow their time sequencings arrange, and introduce the main contribution and the shortcoming of document one by one.

1、Haimovich?A.，Bar?Y.，An?eigenanalysis?interference?canceler，IEEETransactions?on?Signal?Processing?1992，39，1，76-84.

The clutter autocorrelation matrix of estimating is carried out characteristic value decomposition, think that the contribution of clutter is mainly by estimating some big components (clutter subspace) contribution in the clutter autocorrelation matrix, so with the orthogonal intersection space projection of signal to the clutter subspace, reaching the purpose of clutter reduction principal component, and this moment, needed IID training also was reduced to 2 times of clutter subspace sizes.Shortcoming is that not enough robust is revealed in the clutter subspace, in actual STAP system when having clutter internal motion and STAP systematic error poor-performing.

2、Guerci?J.R.，Theory?and?application?of?covariance?matrix?tapers?for?robustadaptive?beamforming，IEEE?Transactions?on?Signal?Processing，1999，47，4，977-985.

The phenomenon of revealing at the clutter subspace of causing such as factors such as clutter internal motion, channel errors that exists in the actual environment, adopt the method for autocorrelation matrix weighting that the influence of these factors is brought in the estimation of clutter covariance matrix, improved the robustness that the clutter subspace is revealed.Shortcoming is to utilize the prior estimate weighting of systematic error comparatively complicated in the reality.

3、Sarkar?T.，Wang?H.，Park?S.，Adve?R.，Koh?J.，Kim?K.，Zhang?Y.，Wicks?M.，BrownR.D.，A?deterministic?least?squares?approach?to?space-time?adaptive?processing(STAP)，IEEE?Transactions?on?Antennas?Propagation，2001，49，1，91-103.

At the discrete noise source that only in detecting unit, occurs, the target component that may exist in the method filtering detecting unit that at first adopts empty time domain to offset, when the two dimension that does not contain target is empty, slide in the sampling afterwards, obtain a plurality of the sub-aperture training units that contain clutter, at last clutter in the sub-aperture of wave filter filtering of the low dimension of design.Shortcoming is to even clutter restraint relatively poor (the wave filter degree of freedom is low), secondly is that the acquisition hardware spending of subspace training sample is big.

4、Roman?J.，Rangaswamy?M.，Davis?D.，Zhang?Q.，Himed?B.，and?Michels?J.，Parametric?adaptive?matched?filter?for?airborne?radar?applications，IEEETransactions?on?Aerospace?and?Electronic?Systems.，2000，36，2，677-692.

Cascade time domain and spatial domain whitening filtering, wherein relativity of time domain AR (P) model formulation, parametric method significantly reduces required training sample, significantly accelerates speed of convergence, to containing comparatively robust of target in the training sample.Shortcoming is comparatively difficulty of AR (P) problem of determining the order, CFAR poor-performing simultaneously.

5、Goldstein?J.，Scharf?L.，and?Reed?I.，A?multistage?representation?of?the?Wienerfilter?based?on?orthogonal?projections，IEEE?Transactions?on?Information?Theory，1998，44，7，2943-2959.

Multistage wiener filter is split as multilevel hierarchy with the traditional integral Wiener filtering, all design every grade subspace and ask optimal filter in each level by maximizing simple crosscorrelation and minimizing MSE (square error), so just avoid asking the clutter autocorrelation matrix of desirable full rank, but progressively select basic filtering clutter component, each so remaining clutter degree of freedom is all reducing gradually, thereby has reduced the requirement of training sample.Shortcoming is that operand is big, complex structure.

6、Wicks?M.C.，Rangaswamy?M.，Adve?R.，and?Hale?T.B.，Space-time?adaptiveprocessing，IEEE?Signal?Processing?Magazine，2006，23，51-65.

Proposition is based on the STAP framework of knowledge, mainly be by the selective power of associating priori (as other sensing datas such as topomap, SAR images) raising to the IID training sample, simultaneously data are carried out prewhitening, reduce clutter residue degree of freedom, improve convergence speed.Shortcoming is that the additional system expense is big, and the difficult assurance of the accurate use of priori.

By can finding out at the summary and the comparison of actual non-homogeneous clutter environment STAP technology existing, existing STAP technology is by to the clutter modeling or utilize the priori prewhitening on the one hand, reduces the clutter degree of freedom to reach, and improves the purpose of convergence speed.But in fact priori obtains with accurately registration is all comparatively difficult.Be the selectivity of strengthening training sample on the other hand, reject nonuniform sample, to reduce such as the influence that exists target to detecting unit in the training sample.And existing non-homogeneous detecting device (NHD) also all needs the clutter covariance matrix pre-estimation, also can't avoid the clutter statistical information and estimate this problem, and if the clutter covariance of estimating have error, also can the judgement of non-homogeneous detecting device be exerted an influence.

Summary of the invention

After the in-depth analysis to the clutter echo model, we find the motion of airborne radar just, have coupling during land clutter empty, promptly

$f_d=\frac{2v}{\mathrm{\λ}}\sin {\mathrm{\θ}}_s=\mathrm{\β}\sin {\mathrm{\θ}}_s,---\left(1\right)$

Wherein, f _dBe the space angle of the relative airborne radar of the static noise source in ground, θ _sBe the Doppler frequency that is had owing to airborne motion clutter, v is the speed of airborne platform, and λ is corresponding wavelength.Therefore at (f _d, θ _s) clutter distributes and mainly concentrates near the diagonal line zone on the space-time two-dimensional plane, so have near sparse property (main energy all concentrates on the diagonal line) in the spectrum when clutter two dimension is empty.And state theory with sparse sampling according to super complete base table, if in case signal has sparse property, distribute in the time of then just might only estimating that by a small amount of sample clutter is empty, and then under the situation that does not increase system overhead, spectrum when the super-resolution estimation clutter is empty so just provides new approaches for estimating clutter covariance matrix and reducing the clutter degree of freedom.

The sparse recovery that the present invention is based on super complete base is theoretical, with the fast beat of data (snapshot) of vectorization as input, distribute when utilizing the estimation clutter of the method super-resolution that overcomplete sparse recovers empty, and then realize that a small amount of sample estimates the purpose of clutter covariance matrix, effectively avoid traditional STAP method because discrete strong noise source, landform become soon, contain the influence of non-homogeneous clutter environments such as target in the training sample, improved clutter rejection under the non-homogeneous clutter environment significantly.

Space-time adaptive processing method under non-homogeneous clutter environment, this method step is as follows:

Step 1: spectrum is estimated when empty based on the clutter of sparse property

(1.1) single frames model (SMV)

At first STAP three-dimensional data (array element dimension N, M and distance dimension L are tieed up in pulse) is turned to x along distance to fast beat of data of extraction and with its vector, all the noise source echo summations on the expression respective distances unit, promptly the clutter echo model is:

$x=\underset{i=1}{\overset{Q_c}{\mathrm{\Σ}}}{\mathrm{\γ}}_i\·\mathrm{\φ}({\mathrm{\θ}}_{s,i},f_{d,i}),---\left(2\right)$

Wherein dimension is the fast beat of data after the x of NM * 1 represents vectorization, Q _cRepresent separate noise source number, γ _i, θ _{S, i}And f _{D, i}Represented i the pairing complex magnitude of noise source, space angle and Doppler frequency respectively, and φ (θ _{S, i}, f _{D, i}) guiding vector when the expression dimension is NM * 1 empty; To Doppler and space angle discretize, then (2) formula can be rewritten matrix form

$x=\underset{n=1}{\overset{N_s{N}_d}{\mathrm{\Σ}}}\mathrm{\α}\left(n\right)\·\mathrm{\φ}\left(n\right)=\mathrm{\Ψ\α},---\left(3\right)$

Here N _s, N _dThe quantifying unit number (grid number) of angle and Doppler frequency is divided in representative respectively, wherein

$\mathrm{\Ψ}=[\mathrm{\φ}\left(1\right),...\mathrm{\φ}\left(N_s\right),...\mathrm{\φ}\left(N_s{N}_d\right)],---\left(4\right)$

$\mathrm{\α}={[{\mathrm{\γ}}_1,...{\mathrm{\γ}}_{N_s}...,{\mathrm{\γ}}_{N_d{N}_s}]}^T,---\left(5\right)$

Represent all noise sources pairing guiding set of vectors and corresponding noise source complex magnitude when empty respectively;

According to the theory that super complete base recovers and sparse sampling recovers, when finding the solution underdetermined equation, add the sparse constraint of priori, obtain separating of approximate actual distribution, i.e. the true space-time two-dimensional amplitude distribution of clutter scene, formula is as follows

$\widehat{\mathrm{\α}}=\arg \min \left|\right|\mathrm{\α}{\left|\right|}_1\mathrm{subjecttox}=\mathrm{\Ψ\α},---\left(6\right)$

Ideally degree of rarefication is defined as || || ₀Norm (being nonzero element number in the vector), use || || ₁Come approximate || || ₀The norm optimum solution; Owing to The noise, the ideal model in (3) formula is revised as in actual scene

x＝Ψα+e， (7)

Wherein e represents noise, establishes || e|| ₂≤ ε, ε represents noise power; With || || ₁Norm is approached actual sparse solution, promptly

$\left|\right|\widehat{\mathrm{\α}}-{\mathrm{\α}}_0{\left|\right|}_2\≤\mathrm{\Λ}(Q,S)\·\mathrm{\ϵ},---\left(8\right)$

Wherein Be the minimum of (7) formula || || ₁Norm is separated, α ₀Be the desirable sparse solution that does not contain noise, (Q S) is stability parameter to Λ;

(1.2) multiframe model (MMV)

When having the independent identically distributed training sample of multiframe, introduce multiframe model (MMV) model:

X＝[x ₁，…x _r]＝Ψ[α ₁，…α _r] (9)

Wherein, r is the frame number (fast umber of beats) of multiframe model, and dimension is N _sN _dThe X of * r represents the fast beat of data after the multiframe vectorization, and dimension is NM * N _sN _d(NM＜＜N _sN _d) super complete basic Ψ guiding vector when covering all noise source correspondences empty, dimension is N _sN _d[the α of * r ₁... α _r] represent multiframe clutter distribution estimating;

The observation data X that to dimension is NM * r is by randomly drawing to such an extent that single frames mixes observation x _Extract, former like this problem just is reduced to single frames model (SMV) promptly

x _extract＝Ψα _extract (10)

Then utilize formula (6) to ask to mixed SMV model || || ₁The minimum corresponding sparse solution of norm

Utilize the similar priori of sparsity structure, the sparsity structure that the definable clutter distributes is

$\mathrm{\Γ}=\mathrm{Supp}\left({\widehat{\mathrm{\α}}}_{\mathrm{extract}}\right)---\left(11\right)$

Wherein Γ represents

The subscript of nonzero element; Alternative sparsity structure has been arranged like this, former problem from owe to decide problem reduction be overdetermined problem (S≤r, wherein S=|| α here || ₀Degree of rarefication for desirable problem), solve promptly by minimizing variance

min||X-Ψ _Γα|| ₂ (12)

Spectrum diffusion influence when (1.3) empty

When having empty time error in (3) formula echo model be revised as

T wherein _S-i(θ _{S, i}, f _{D, i}) be corresponding empty time error weighting, further expand into

$t_{s-t}({\mathrm{\θ}}_{s,i},f_{d,i})=t_s({\mathrm{\θ}}_{s,i},f_{d,i})\⊗t_t({\mathrm{\θ}}_{s,i},f_{d,i})---\left(14\right)$

T wherein _s(θ _{S, i}, f _{D, i}) and t _t(θ _{S, i}, f _{D, i}) stochastic error of representing the inconsistent and clutter internal motion of passage to be caused respectively; Spectrum diffusion to some extent when clutter is empty, so desirable degree of rarefication || α || ₀(number of nonzero element) will become greatly, and we define relative degree of rarefication here, i.e. the number of remarkable component;

Step 2: wave filter when estimating clutter covariance matrix and design sky

In case obtain high-resolution clutter when empty spectrum distribute, the estimation formulas of clutter covariance further is reduced to

${\hat{R}}_{\mathrm{cs}}=E\left[{\mathrm{xx}}^H\right]=E\left(\left(\mathrm{\Ψ}\widehat{\mathrm{\α}}\right){\left(\mathrm{\Ψ}\widehat{\mathrm{\α}}\right)}^H\right)$

$=\underset{p}{\mathrm{\Σ}}\underset{q}{\mathrm{\Σ}}E\left(\widehat{\mathrm{\α}}\left(p\right){\widehat{\mathrm{\α}}}^{*}\left(q\right)\right)\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(q\right)}^H,---\left(15\right)$

1≤p≤N wherein _sN _d, 1≤q≤N _sN _dRepresent the resolution element subscript, guiding vector when Ψ (p) represents p noise source correspondence empty; If it is uncorrelated mutually between each noise source,

$E\left(\widehat{\mathrm{\α}}\left(p\right)\stackrel{\‾}{\widehat{\mathrm{\α}}\left(q\right)}\right)=0,p\≠q.---\left(16\right)$

The clutter covariance matrix of estimating like this is reduced to

${\hat{R}}_{\mathrm{cs}}=\underset{p}{\mathrm{\Σ}}E\left({\left|\widehat{\mathrm{\α}}\left(p\right)\right|}^2\right)\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(p\right)}^H,---\left(17\right)$

Wherein on behalf of multiframe, E () ask expectation; If have only the single frames training sample, then utilize instantaneous sample to replace expectation (the multiframe scene can similarly be handled)

${\hat{R}}_{\mathrm{cs}}=\underset{p}{\mathrm{\Σ}}{\left|\widehat{\mathrm{\α}}\left(p\right)\right|}^2\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(p\right)}^H,---\left(18\right)$

Because small component is estimated to have error in the sparse recovery of underdetermined equation, so need screen the subscript p in (18) here, ignores

The contribution that middle small component distributes to clutter; In order to improve the numerical stability of estimating autocorrelation matrix, it is carried out the diagonal angle load, promptly at last

${\hat{R}}_{\mathrm{cs}}={\hat{R}}_{\mathrm{cs}}+\mathrm{\βI},---\left(19\right)$

Here β represents the size that the diagonal angle loads, and can provide according to the noise power of estimating in advance; So just obtained the estimation of alternative clutter autocorrelation matrix; Be brought into the optimal filter form at last

$w=\mathrm{\γ}{\hat{R}}_{\mathrm{cs}}^{-1}{v}_t---\left(20\right).$

The present invention is directed to the IID training sample shortage problem that non-homogeneous clutter environment occurs, proposition utilizes the method super-resolution estimation clutter space-time two-dimensional spectrum (space-time spectrum) of overcomplete sparse representation, and then realization single frames training sample is estimated the purpose of clutter covariance matrix, the method can have been avoided effectively because of influences such as discrete noise source, fast change of landform, simultaneously to factors such as clutter internal motion and passage be inconsistent cause empty the time spectrum spread also comparatively robust.The Mountaintop real data has proved that the method can keep fine clutter rejection, is highly suitable for strong non-homogeneous clutter environment.

Description of drawings

Fig. 1 is that SATP receives three-dimensional data to clutter space-time two-dimensional spectrum conversion synoptic diagram.

Fig. 2 is an associating multiframe method of estimation process flow diagram.

Fig. 3 is a process flow diagram of the present invention.

Fig. 4 be the high-resolution clutter of CS-STAP and Capon when empty spectrum estimate synoptic diagram

High-resolution spectrum Capon and CS-STAP contrast when Fig. 5 is sky, Δ _ε=0.02, Δ _φ=2 °.

Fig. 6 is the response synoptic diagram of CS-STAP wave filter along space angle.

Fig. 7 is signal to noise ratio improvement factor (improvement factor) curve synoptic diagram of CS-STAP and DL.

Embodiment

Further specify the present invention below in conjunction with accompanying drawing.

Space-time adaptive processing method under non-homogeneous clutter environment, this method step is as follows:

Step 1: spectrum is estimated when empty based on the clutter of sparse property

● single frames model (SMV)

Fig. 1 receives three-dimensional data to clutter space-time two-dimensional spectrum conversion synoptic diagram for SATP.As shown in Figure 1, at first (array element is tieed up N with the STAP three-dimensional data among the figure, M and distance dimension L are tieed up in pulse) turn to x along distance to an extraction fast beat of data (snapshot) and with its vector, all the noise source echo summations on the expression respective distances unit, promptly the clutter echo model is

$x=\underset{i=1}{\overset{Q_c}{\mathrm{\Σ}}}{\mathrm{\γ}}_i\·\mathrm{\φ}({\mathrm{\θ}}_{s,i},f_{d,i}),---\left(21\right)$

Wherein dimension is the fast beat of data after the x of NM * 1 represents vectorization, Q _cRepresent separate noise source number, γ _i, θ _{S, i}And f _{D, i}Represented i the pairing complex magnitude of noise source, space angle and Doppler frequency respectively, and φ (θ _{S, i}, f _{D, i}) guiding vector when the expression dimension is NM * 1 empty.To Doppler and space angle discretize, then (2) formula can be rewritten matrix form

$x=\underset{n=1}{\overset{N_s{N}_d}{\mathrm{\Σ}}}\mathrm{\α}\left(n\right)\·\mathrm{\φ}\left(n\right)=\mathrm{\Ψ\α},---\left(22\right)$

Here N _s, N _dThe quantifying unit number (grid number) of angle and Doppler frequency is divided in representative respectively, wherein

Ψ＝[φ(1)，…φ(N _s)，…φ(N _sN _d)]， (23)

$\mathrm{\α}={[{\mathrm{\γ}}_1,...{\mathrm{\γ}}_{N_s}...,{\mathrm{\γ}}_{N_d{N}_s}]}^T,---\left(24\right)$

Represent all noise sources pairing guiding set of vectors and corresponding noise source complex magnitude when empty (Ψ for example respectively _iGuiding vector when just representing i empty that noise source had, and α _iRepresent its corresponding complex magnitude).As previously mentioned, so coupling during just because of sky is actual noise source number Q _cCount N much smaller than the space-time two-dimensional plane lattice _sN _d, clutter space-time two-dimensional plane presents sparse property.As shown in Figure 1, in (3) formula, estimating that the clutter space-time two-dimension distributes just is equivalent at alternative known observation data x and find the solution the inverse problem of α among guiding set of vectors Ψ when empty, and since the purpose that high-resolution is estimated or super complete base table is stated, the dimension NM of matrix Ψ * N _sN _dIn usually choose NM＜＜N _sN _dSo this problem owes fixed, countless a plurality of separating are arranged usually.But because coupling during land clutter empty, the main energy of the empty time-frequency spectrum of desirable clutter two dimension only can distribute along diagonal line, whole relatively plane, frequency spectrum is comparatively sparse, be that the priori of the actual α of separating own has sparse property and (has only minority element non-zero in the α component in the equation (3), and other elements are all very little or approach 0), so according to the theory that super complete base recovers and sparse sampling recovers, when finding the solution underdetermined equation, add the sparse constraint of priori, just might obtain separating of approximate actual distribution, be the space-time two-dimensional amplitude distribution of true clutter scene, concrete formula is as follows

$\widehat{\mathrm{\α}}=\arg \min \left|\right|\mathrm{\α}{\left|\right|}_1\mathrm{subjecttox}=\mathrm{\Ψ\α},---\left(25\right)$

Ideally degree of rarefication is defined as || || ₀Norm (being nonzero element number in the vector), but || || ₀The computation optimization amount is huge, so use usually in the reality || || ₁Come approximate || || ₀The norm optimum solution, wherein ask || || ₁The norm minimum value is protruding optimization problem, and degree of stability is higher, about L ₁/ L ₀The condition and the proof of equivalence, see list of references [D.L.Donoho for details, M.Elad, and V.N.Temlyakov. " Stable recovery of sparse overcomplete representations in the presenceof noise, " IEEE Transactions on Information Theory, vol.52, no.1, pp.6-18, Jan.2006.], just deeply do not introduce here.Secondly, in actual scene, certainly exist The noise, so the ideal model in (3) formula need be revised as

x＝Ψα+e， (26)

Wherein e represents noise, and miscellaneous noise ratio (CNR) is bigger in the general echo, so but here simple hypothesis be || e|| ₂≤ ε, ε represents noise power.Just because of the existence of noise e, original model can only be similar to sparse, and then has influence on the stability of restoration methods.Have The noise even people such as Donoho proved in 2005, use || || ₁Norm also can well be approached actual sparse solution, promptly

$\widehat{\mathrm{\α}}-{\mathrm{\α}}_0{\left|\right|}_2\≤\mathrm{\Λ}(Q,S)\·\mathrm{\ϵ},---\left(27\right)$

Wherein Be the minimum of (7) formula || || ₁Norm is separated, α ₀Be the desirable sparse solution that does not contain noise, (Q S) is stability parameter to Λ, maximum correlation Q is relevant between each row of it and priori degree of rarefication S and super complete basic Ψ, can find out under the sparse prerequisite of priori, from (8) formula if the degree of correlation is very little between the less and super complete base of noise level, then || || ₁The degree of stability of approaching actual optimum is still good.

● multiframe model (MMV)

Traditional overcomplete sparse representation method all is based on single frames model (SMV) basically, and when we had the independent identically distributed training sample of multiframe, we can further improve estimated performance by introducing multiframe model (MMV) model, and model is as follows

X＝[x ₁，…x _r]＝Ψ[α ₁，…α _r] (28)

Wherein r is the frame number (fast umber of beats) of multiframe model, and dimension is N _sN _dThe X of * r represents the fast beat of data after the multiframe vectorization, and dimension is NM * N _sN _d(NM＜＜N _sN _d) super complete basic Ψ guiding vector when covering all noise source correspondences empty, dimension is N _sN _d[the α of * r ₁... α _r] represent multiframe clutter distribution estimating, though in general slightly rise and fall with the noise source amplitude between different samples that distributes, pairing when empty guiding vector (space angle and Doppler frequency) should remain unchanged in theory, promptly equation (9) separates α _i, i=1 ... the sparsity structure of r should unanimity (be α _iThe row of nonzero element number should be consistent or similar), the method of intuitively utilizing multiframe information is that the clutter of separately the fast beat of data of each range unit being done based on sparse property recovers, utilize multiframe to ask expectation E () afterwards, but so just not using multiframe separates the similar priori of sparsity structure, here we use for reference the multi-frame joint estimation model, make full use of priori α _i, i=1 ... the similar characteristic of sparsity structure between r improves estimation performance, and concrete multi-frame joint estimation approach flow process as shown in Figure 2.Fig. 2 is an associating multiframe method of estimation process flow diagram.At first, be that the observation data X of NM * r is by randomly drawing to such an extent that single frames mixes observation x to dimension _Extract, former like this problem just is reduced to single frames model (SMV) promptly

x _extract＝Ψα _extract (29)

Then utilize formula (6) to ask to mixed SMV model || || ₁The minimum corresponding sparse solution of norm

Utilize the similar priori of sparsity structure, the sparsity structure that the definable clutter distributes is

$\mathrm{\Γ}=\mathrm{Supp}\left({\widehat{\mathrm{\α}}}_{\mathrm{extract}}\right)---\left(30\right)$

Wherein Γ represents

The subscript of nonzero element.Alternative sparsity structure has been arranged like this, and we just can simplify corresponding super complete base (extracting some row of Γ correspondence among the super complete basic Ψ) greatly, former like this problem just can from owe to decide problem reduction be overdetermined problem (S≤r, wherein S=|| α here || ₀Degree of rarefication for desirable problem), solve preferably promptly by minimizing variance

min||X-Ψ _Γα|| ₂ (31)

● spectrum diffusion influence when empty

CS-STAP only uses seldom the IID training sample just can well estimate the clutter covariance battle array, thereby can avoid effectively that classic method needs that a large amount of training sample introduces such as discrete strong noise source, sample power is non-homogeneous, contain the influence of non-homogeneous clutter environments such as target in the training sample, even but in fact only use single sample to estimate clutter covariance matrix, still can exist because the problem that clutter internal motion (ICM) or channel characteristic inconsistent (Channel Mismatch) cause desirable clutter subspace to be revealed, when having empty time error in (3) formula echo model need be revised as

T wherein _S-t(θ _{S, i}, f _{D, i}) be corresponding empty time error weighting, can further expand into

$t_{s-t}({\mathrm{\θ}}_{s,i},f_{d,i})=t_s({\mathrm{\θ}}_{s,i},f_{d,i})\⊗t_t({\mathrm{\θ}}_{s,i},f_{d,i})---\left(33\right)$

T wherein _s(θ _{S, i}, f _{D, i}) and tx (θ _{S, i}, f _{D, i}) stochastic error of representing the inconsistent and clutter internal motion of passage to be caused respectively.Just because of the existence of empty time error, spectrum diffusion to some extent when causing clutter empty, so desirable degree of rarefication || α || ₀(number of nonzero element) will become big, similar and the scene of handling noise, here we define relative degree of rarefication, i.e. the remarkable number of component, and the The Realization of Simulation proof CS-STAP method by our back has robustness preferably to the echoed signal that has empty time error.

Step 2: wave filter when estimating clutter covariance matrix and design sky

In case we have obtained high-resolution clutter spectrum (the separating of equation (6) that distribute when empty

), the estimation formulas of clutter covariance can further be reduced to

${\hat{R}}_{\mathrm{cs}}=E\left[{\mathrm{xx}}^H\right]=E\left(\left(\mathrm{\Ψ}\widehat{\mathrm{\α}}\right){\left(\mathrm{\Ψ}\widehat{\mathrm{\α}}\right)}^H\right)$

$\underset{p}{\mathrm{\Σ}}\underset{q}{\mathrm{\Σ}}E\left(\widehat{\mathrm{\α}}\left(p\right){\widehat{\mathrm{\α}}}^{*}\left(q\right)\right)\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(q\right)}^H,---\left(34\right)$

1≤p≤N wherein _sN _d, 1≤q≤N _sN _dRepresent the resolution element subscript, guiding vector when Ψ (p) represents p noise source correspondence empty.Further can suppose between each noise source uncorrelated mutually

$E\left(\widehat{\mathrm{\α}}\left(p\right)\stackrel{\‾}{\widehat{\mathrm{\α}}\left(q\right)}\right)=0,p\≠q.---\left(35\right)$

The clutter covariance matrix of estimating like this can be reduced to

${\hat{R}}_{\mathrm{cs}}=\underset{p}{\mathrm{\Σ}}E\left(\right|\widehat{\mathrm{\α}}\left(p\right){|}^2)\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(p\right)}^H,---\left(36\right)$

Wherein on behalf of multiframe, E () ask expectation.If have only the single frames training sample, can utilize instantaneous sample to replace expectation (the multiframe scene can similarly be handled)

${\hat{R}}_{\mathrm{cs}}=\underset{p}{\mathrm{\Σ}}|\widehat{\mathrm{\α}}\left(p\right){|}^2\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(p\right)}^H,---\left(37\right)$

Here note,,,, ignore so need screen the subscript p in (18) here because small component is estimated to have error in the sparse recovery of underdetermined equation as last argumentation the in the step 1

The contribution that middle small component distributes to clutter.In order to improve the numerical stability of estimating autocorrelation matrix, it is carried out the diagonal angle load, promptly at last

${\hat{R}}_{\mathrm{cs}}={\hat{R}}_{\mathrm{cs}}+\mathrm{\βI},---\left(38\right)$

Here β represents the size that the diagonal angle loads, and can provide according to the noise power of estimating in advance.We have just obtained the estimation of alternative clutter autocorrelation matrix like this.Be brought into the optimal filter form at last

$w=\mathrm{\γ}{\hat{R}}_{\mathrm{cs}}^{-1}{v}_t---\left(39\right)$

Design corresponding when empty wave filter come clutter reduction component effectively.

Process flow diagram of the present invention as shown in Figure 3.As shown in Figure 3,

A) at first to the STAP three-dimensional data that receives along distance to the training sample x that extracts a snap _l, design the super complete basic Ψ that guides vector when covering empty that noise source had, bring formula (6) into, find the solution L ₁The sparse solution of norm minimum value correspondence

It is clutter space-time two-dimensional spectrum.

B) with sparse solution

Be brought into the clutter covariance matrix that formula (18) can be estimated, diagonal line loads and improves numerical stability.

C) estimate the clutter diffusion according to priori (as average channel error, clutter internal motion speed etc.), to the clutter covariance matrix weighting of estimating.

D) according to the covariance matrix of estimating, calculate corresponding space-time adaptive wave filter, and do the judgement that moving-target has or not at output terminal.

We use the Mountaintop real data to verify based on sparse property clutter the validity of spectrum restoration methods when empty, the Mountaintop project is that MIT Lincoln laboratory is in order to verify the experimental project of STAP performance development, major parameter is 14 array elements, 16 pulses, distance is to 403 sampled points, and [http://spib.rice.edu/spib/mtn_top.html] seen in concrete detailed parameter introduction.The data scene of using concentrates on angle-15 degree as the main clutter district, the position of Doppler 156Bz, and true moving-target is positioned at apart from 152km, angle 15 degree, the position of Doppler 156Hz.

● step 1: spectrum is estimated when empty

At first the estimated performance of spectrum when verifying that clutter is empty uses the Capon spectrum as reference.Notice that the Capon spectrum used sufficient IID training sample (60 frame) to estimate noise performance, and based on sparse property clutter when empty spectrum recover CS-STAP and only use single frames information, find the solution sparse clutter according to (6) formula and distribute.Here we use the protruding majorized function bag cvx of people such as Boyd exploitation to realize || || 1 minimized finding the solution obtains among the cvx function Bao Kecong [http://www.stanford.edu/～boyd/cvx].Fig. 4 be the high-resolution clutter of CS-STAP and Capon when empty spectrum estimate synoptic diagram, X-axis is the wave beam territory among the figure, Y-axis is represented the Doppler territory, image intensity is represented the amplitude (the red more explanation amplitude of color is big more, and the blue more explanation amplitude of color is low more) of corresponding empty time-frequency spectrum.But described in (8) formula, because equation itself owes fixed, we can only guarantee to utilize || || ₁Norm is minimized separate and actual sparse solution between evaluated error can be retrained by noise level, be presented as to occur the pseudo-peaks of some small components in the estimated result, shown in Fig. 4 (b).Inevitably exist in the simultaneously actual STAP system such as clutter internal motion and the inconsistent factor of passage, thus here we also emulation testing CS-STAP have the stability that clutter recovers under the empty time error situation.Simulation parameter: the STAP system architecture is 8 of array numbers, 8 of umber of pulses, noise source number Q _c=60, and along the normalization space-time-frequency

Evenly distribute.Only consider channel error (influence of clutter internal motion is similar), random weighting is during empty in the formula (13)

Here we suppose ε _iAnd φ _iAll satisfy evenly distribution, represent relevant amplitude and phase error respectively, concrete form is as follows

$-\frac{{\mathrm{\Δ}}_{\mathrm{\φ}}}{2}\≤{\mathrm{\φ}}_i\≤\frac{{\mathrm{\Δ}}_{\mathrm{\φ}}}{2}---\left(41\right)$

Wherein

Similar range error is distributed as

$1-\frac{{\mathrm{\Δ}}_{\mathrm{\ϵ}}}{2}\≤{\mathrm{\ϵ}}_i\≤1+\frac{{\mathrm{\Δ}}_{\mathrm{\ϵ}}}{2}---\left(43\right)$

Wherein

High-resolution spectrum Capon and CS-STAP contrast when Fig. 5 is sky, the channel error parameter is taken as Δ here _ε=0.02, Δ _φIn the time of=2 °, the Capon spectrum is selected 60 frame IID training samples for use, and CS-STAP only uses single frames.X-axis is represented Doppler among Fig. 5, Y-axis representation space angle.As can be seen from Figure, the Capon spectrum is because the frequency spectrum of channel error is even more serious along the diffusion of angle dimension, and the relative Capon of CS-STAP spectrum is to channel error robust more, and the energy distribution centrality is better, so estimate that by the high-resolution of CS-STAP the actual clutter that recovers of robust distributes.

● step 2: filtering performance when empty

Spectrum is estimated during according to high-resolution clutter sky

Construct corresponding wave filter according to formula (18)-(20), and the 152km frame data that Mountaintop contains moving-target are carried out filtering.Fig. 6 has provided the response of CS-STAP wave filter along space angle.In order to simulate the non-homogeneous influence that causes of clutter, the training sample of DL method is got the training sample (interval is far away more on the distance, and clutter distribution independent same distribution is difficult to guarantee more) apart from test sample book 7.5-12km and 13.5-18km place respectively here.X-axis is represented angle domain among the figure, the output power (dB of unit) when Y-axis is represented sky behind the wave filter.As can be seen from Figure, when training sample is non-homogeneous, need the DL method performance of multiframe IID training sample to descend greatly, cause the main clutter district clutter that is arranged in angle-15 degree to suppress poor ability (shown in last upper thread of figure and the medium line), and CS-STAP is owing to only need the single frames sample can realize the high-resolution estimation, avoided clutter influence heterogeneous to a great extent, so can form very dark clutter depression in actual main clutter district, clutter reduction makes the moving-target that is arranged in about 15 degree distinguish (shown in the figure trough minimum rate of accumulation) from clutter on every side simultaneously effectively.

● step 3: signal to noise ratio is improved performance

Keep above-mentioned test parameters constant, investigate signal to noise ratio improvement factor (improvement factor) curve of CS-STAP and DL, Fig. 7 is signal to noise ratio improvement factor (improvement factor) curve synoptic diagram of CS-STAP and DL.As shown in Figure 7, X-axis is represented Doppler frequency, and Y-axis is represented the signal to noise ratio improvement factor.Just as shown in FIG., the DL method is owing to lack enough IID training samples, can't accurately estimate noise performance, cause position and all obviously decline (shown in red line among the figure and purple line) of depth performance of IF curve clutter depression, and training unit distance detecting unit is far away more, noise performance is inconsistent more, signal to noise ratio is improved just poor more, but simultaneously, because CS-STAP only uses the single frames training sample just to estimate the clutter distribution and then accurately estimate the clutter covariance battle array by high-resolution, so greatly reduce the non-homogeneous influence that the STAP signal to noise ratio is improved of clutter environment, keep good signal to noise ratio to improve performance (shown in the top curve among the figure).

The present invention is directed to the IID training sample shortage problem that non-homogeneous clutter environment occurs, proposition utilizes the method super-resolution estimation clutter space-time two-dimensional spectrum (space-time spectrum) of overcomplete sparse representation, and then realization single frames training sample is estimated clutter covariance matrix, the present invention can avoid effectively because of influences such as discrete noise source, fast change of landform, simultaneously to factors such as clutter internal motion and passage be inconsistent cause empty the time spectrum spread also comparatively robust.Real data has proved that the method can keep fine clutter rejection, is applicable to strong non-homogeneous clutter environment.

Claims (2)

1. space-time adaptive processing method under non-homogeneous clutter environment is characterized in that, this method step is as follows:

Step 1: spectrum is estimated when empty based on the clutter of sparse property

(1.1) single frames model (SMV)

At first STAP three-dimensional data (array element dimension N, M and distance dimension L are tieed up in pulse) is turned to x along distance to fast beat of data of extraction and with its vector, all the noise source echo summations on the expression respective distances unit, promptly the clutter echo model is:

$x=\underset{i=1}{\overset{Q_c}{\mathrm{\Σ}}}{\mathrm{\γ}}_i\·\mathrm{\φ}({\mathrm{\θ}}_{s,i},f_{d,i}),---\left(1\right)$

Wherein dimension is the fast beat of data after the x of NM * 1 represents vectorization, Q _cRepresent separate noise source number, γ _i, θ _{S, i}And f _{D, i}Represented i the pairing complex magnitude of noise source, space angle and Doppler frequency respectively, and φ (θ _{S, i}, f _{D, i}) guiding vector when the expression dimension is NM * 1 empty; To Doppler and space angle discretize, then (2) formula can be rewritten matrix form

$x=\underset{n=1}{\overset{N_s{N}_d}{\mathrm{\Σ}}}\mathrm{\α}\left(n\right)\·\mathrm{\φ}\left(n\right)=\mathrm{\Ψ\α},---\left(2\right)$

Here N _s, N _dThe quantifying unit number (grid number) of angle and Doppler frequency is divided in representative respectively, wherein

Ψ＝[φ(1)，…φ(N _s)，…φ(N _sN _d)]，(3)

$\mathrm{\α}={[{\mathrm{\γ}}_1,...{\mathrm{\γ}}_{N_s}...,{\mathrm{\γ}}_{N_d{N}_s}]}^T,---\left(4\right)$

Represent all noise sources pairing guiding set of vectors and corresponding noise source complex magnitude when empty respectively;

According to the theory that super complete base recovers and sparse sampling recovers, when finding the solution underdetermined equation, add the sparse constraint of priori, obtain separating of approximate actual distribution, i.e. the true space-time two-dimensional amplitude distribution of clutter scene, formula is as follows

$\widehat{\mathrm{\α}}=\arg \min {\left|\right|\mathrm{\α}\left|\right|}_1\mathrm{subject\; to\; x}=\mathrm{\Ψ\α},---\left(5\right)$

Ideally degree of rarefication is defined as || || ₀Norm (being nonzero element number in the vector), use || || ₁Come approximate || || ₀The norm optimum solution; Owing to The noise, the ideal model in (3) formula is revised as in actual scene

x＝Ψα+e，(6)

Wherein e represents noise, establishes || e|| ₂≤ ε, ε represents noise power; With || || ₁Norm is approached actual sparse solution, promptly

${\left|\right|\widehat{\mathrm{\α}}-{\mathrm{\α}}_0\left|\right|}_2\≤\mathrm{\Λ}(Q,S)\·\mathrm{\ϵ},---\left(7\right)$

Wherein,

Be the minimum of (7) formula || || ₁Norm is separated, α ₀Be the desirable sparse solution that does not contain noise, (Q S) is stability parameter to Λ;

Spectrum diffusion influence when (1.2) empty

When having empty time error in (3) formula echo model be revised as

T wherein _S-t(θ _{S, i}, f _{D, i}) be corresponding empty time error weighting, further expand into

$t_{s-t}({\mathrm{\θ}}_{s,i},f_{d,i})=t_s({\mathrm{\θ}}_{s,i},f_{d,i})\⊗t_i({\mathrm{\θ}}_{s,i},f_{d,i})---\left(9\right)$

T wherein _s(θ _{S, i}, f _{D, i}) and t _t(θ _{S, i}, f _{D, i}) stochastic error of representing the inconsistent and clutter internal motion of passage to be caused respectively; Spectrum diffusion to some extent when clutter is empty, so desirable degree of rarefication || α || ₀(number of nonzero element) will become greatly, and we define relative degree of rarefication here, i.e. the number of remarkable component;

Step 2: wave filter when estimating clutter covariance matrix and design sky

In case obtain high-resolution clutter when empty spectrum distribute, the estimation formulas of clutter covariance further is reduced to

${\hat{R}}_{\mathrm{CS}}=E\left[{\mathrm{xx}}^H\right]=E\left(\left(\mathrm{\Ψ}\widehat{\mathrm{\α}}\right){\left(\mathrm{\Ψ}\widehat{\mathrm{\α}}\right)}^H\right)$

$=\underset{p}{\mathrm{\Σ}}\underset{q}{\mathrm{\Σ}}E{\left(\widehat{\mathrm{\α}}\left(p\right){\widehat{\mathrm{\α}}}^{*}\left(q\right)\right)\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}\left(q\right)}^H,---\left(10\right)$

1≤p≤N wherein _sN _d, 1≤q≤N _sN _dRepresent the resolution element subscript, guiding vector when Ψ (p) represents p noise source correspondence empty; If it is uncorrelated mutually between each noise source,

$E\left(\widehat{\mathrm{\α}}\left(p\right)\stackrel{\‾}{\widehat{\mathrm{\α}}\left(q\right)}\right)=0,p\≠q.---\left(11\right)$

The clutter covariance matrix of estimating like this is reduced to

${\hat{R}}_{\mathrm{CS}}=\underset{p}{\mathrm{\Σ}}E\left({\left|\widehat{\mathrm{\α}}\left(p\right)\right|}^2\right)\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(p\right)}^H,---\left(12\right)$

Wherein on behalf of multiframe, E () ask expectation; If have only the single frames training sample, then utilize instantaneous sample to replace expectation (the multiframe scene can similarly be handled)

${\hat{R}}_{\mathrm{CS}}=\underset{p}{\mathrm{\Σ}}{\left|\widehat{\mathrm{\α}}\left(p\right)\right|}^2\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(p\right)}^H,---\left(13\right)$

Because small component is estimated to have error in the sparse recovery of underdetermined equation, so need screen the subscript p in (18) here, ignores The contribution that middle small component distributes to clutter; In order to improve the numerical stability of estimating autocorrelation matrix, it is carried out the diagonal angle load, promptly at last

${\hat{R}}_{\mathrm{CS}}={\hat{R}}_{\mathrm{CS}}+\mathrm{\βI},--\left(14\right)$

Here β represents the size that the diagonal angle loads, and can provide according to the noise power of estimating in advance; So just obtained the estimation of alternative clutter autocorrelation matrix; Be brought into the optimal filter form at last

$w=\mathrm{\γ}{\hat{R}}_{\mathrm{CS}}^{-1}{v}_t---\left(15\right).$

2. space-time adaptive processing method under non-homogeneous clutter environment is characterized in that, this method step is as follows:

Step 1: spectrum is estimated when empty based on the clutter of sparse property

(1.1) multiframe model (MMV)

When having the independent identically distributed training sample of multiframe, introduce multiframe model (MMV) model:

X＝[x ₁，…x _r]＝Ψ[α ₁，…α _r](16)

Wherein, r is the frame number (fast umber of beats) of multiframe model, and dimension is N _sN _dThe X of * r represents the fast beat of data after the multiframe vectorization, and dimension is NM * N _sN _d(NM＜＜N _sN _d) super complete basic Ψ guiding vector when covering all noise source correspondences empty, dimension is N _sN _d[the α of * r ₁... α _r] represent multiframe clutter distribution estimating;

The observation data X that to dimension is NM * r is by randomly drawing to such an extent that single frames mixes observation x _Extract, former like this problem just is reduced to single frames model (SMV) promptly

x _extract＝Ψα _extract(17)

Then utilize following formula (6) to ask to mixed SMV model || || ₁The minimum corresponding sparse solution of norm

$\widehat{\mathrm{\α}}=\arg \min {\left|\right|\mathrm{\α}\left|\right|}_1\mathrm{subject\; to\; x}=\mathrm{\Ψ\α},---\left(18\right)$

Utilize the similar priori of sparsity structure, the sparsity structure that the definable clutter distributes is

$\mathrm{\Γ}=\mathrm{Supp}\left({\widehat{\mathrm{\α}}}_{\mathrm{extract}}\right)---\left(19\right)$

Wherein Γ represents

The subscript of nonzero element; Alternative sparsity structure has been arranged like this, former problem from owe to decide problem reduction be overdetermined problem (S≤r, wherein S=|| α here || ₀Degree of rarefication for desirable problem), solve promptly by minimizing variance

min||X-Ψ _Γα|| ₂(20)

Spectrum diffusion influence when (1.2) empty

When having empty time error in (3) formula echo model be revised as

T wherein _S-t(θ _{S, i}, f _{D, i}) be corresponding empty time error weighting, further expand into

$t_{s-t}({\mathrm{\θ}}_{s,i},f_{d,i})=t_s({\mathrm{\θ}}_{s,i},f_{d,i})\⊗t_i({\mathrm{\θ}}_{s,i},f_{d,i})---\left(22\right)$

T wherein _s(θ _{S, i}, f _{D, i}) and t _t(θ _{S, i}, f _{D, i}) stochastic error of representing the inconsistent and clutter internal motion of passage to be caused respectively; Spectrum diffusion to some extent when clutter is empty, so desirable degree of rarefication || α || ₀(number of nonzero element) will become greatly, and we define relative degree of rarefication here, i.e. the number of remarkable component;

Step 2: wave filter when estimating clutter covariance matrix and design sky

In case obtain high-resolution clutter when empty spectrum distribute, the estimation formulas of clutter covariance further is reduced to

${\hat{R}}_{\mathrm{CS}}=E\left[{\mathrm{xx}}^H\right]=E\left(\left(\mathrm{\Ψ}\widehat{\mathrm{\α}}\right){\left(\mathrm{\Ψ}\widehat{\mathrm{\α}}\right)}^H\right)$

$=\underset{p}{\mathrm{\Σ}}\underset{q}{\mathrm{\Σ}}E\left(\widehat{\mathrm{\α}}\left(p\right){\widehat{\mathrm{\α}}}^{*}\left(q\right)\right)\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(q\right)}^H,---\left(23\right)$

1≤p≤N wherein _sN _d, 1≤q≤N _sN _dRepresent the resolution element subscript, guiding vector when Ψ (p) represents p noise source correspondence empty; If it is uncorrelated mutually between each noise source,

$E\left(\widehat{\mathrm{\α}}\left(p\right)\stackrel{\‾}{\widehat{\mathrm{\α}}\left(q\right)}\right)=0,p\≠q.---\left(24\right)$

The clutter covariance matrix of estimating like this is reduced to

${\hat{R}}_{\mathrm{CS}}=\underset{p}{\mathrm{\Σ}}E\left({\left|\widehat{\mathrm{\α}}\left(p\right)\right|}^2\right)\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(p\right)}^H,---\left(25\right)$

Wherein on behalf of multiframe, E () ask expectation; If have only the single frames training sample, then utilize instantaneous sample to replace expectation (the multiframe scene can similarly be handled)

${\hat{R}}_{\mathrm{CS}}=\underset{p}{\mathrm{\Σ}}{\left|\widehat{\mathrm{\α}}\left(p\right)\right|}^2\mathrm{\Ψ}\left(p\right)\mathrm{\Ψ}{\left(p\right)}^H,---\left(26\right)$

Because small component is estimated to have error in the sparse recovery of underdetermined equation, so need screen the subscript p in (18) here, ignores

The contribution that middle small component distributes to clutter; In order to improve the numerical stability of estimating autocorrelation matrix, it is carried out the diagonal angle load, promptly at last

${\hat{R}}_{\mathrm{CS}}={\hat{R}}_{\mathrm{CS}}+\mathrm{\βI},---\left(27\right)$

Here β represents the size that the diagonal angle loads, and can provide according to the noise power of estimating in advance; So just obtained the estimation of alternative clutter autocorrelation matrix; Be brought into the optimal filter form at last

$w=\mathrm{\γ}{\hat{R}}_{\mathrm{CS}}^{-1}{v}_t---\left(28\right).$

Images