CN103885050B - Echo signal parameter estimation method based on scaled-down dictionary - Google Patents

Abstract

The invention belongs to the technical field of radar target echo signal parameter estimation, and discloses an echo signal parameter estimation method based on a scaled-down dictionary. The echo signal parameter estimation method based on the scaled-down dictionary comprises the following steps that 1, an initial parameter set {theta ＜(1)＞} is obtained according to all unknown parameters corresponding to scattering centers in an echo signal model, the dictionary A (theta ＜(1)＞) is formed through the initial parameter set {theta ＜(1)＞}, and the number m of iteration times is set to be one; 2, a new parameter set {theta' ＜(m)＞} is obtained by carrying out Bayes learning for the mth time according to the A (theta ＜(m)＞); 3, if m is equal to M, the step 5 is carried out, or, the value of m increases by one and the step 4 is carried out; 4, a new parameter set {theta ＜(m)＞} is obtained according to a refinement method for a parameter set {theta ＜(m-1)＞}, a dictionary A (theta ＜(m)＞) is formed through the parameter set {theta ＜(m)＞}, and then the step 2 is carried out; 5, the number m* of iteration times meets the set condition and is found out; 6, weighting and clustering are carried out on{theta' ＜(m*)＞} according to a K-means clustering method.

Description

Echo-signal method for parameter estimation based on scaling dictionary

Technical field

The invention belongs to radar target Signal parameter estimation technical field, particularly to the echo based on scaling dictionary Modulated parameter estimating method.

Background technology

When radar is to an objective emission electromagnetic signal, electromagnetic signal by target acquisition and is back to radar.From radar The information obtaining in echo can reflect the feature of target, and some information can directly with the parameter in echo signal model Lai Represent.Therefore, by the parameter of estimate echo signal model, we can obtain the information of target and target is analyzed. Such as, the line spectrum observing data with unknown white noise estimates that the target characteristic being widely used in synthetic aperture radar image-forming carries Take；The time delay of the aliasing signal of known form and amplitude Estimation are also very common in Radar Signal Processing；Target fine motion causes The frequency modulation(PFM) of echo-signal be called micro-Doppler effect, by the estimation to target micro-doppler parameter, we can obtain Geometry and size to target；The ISAR of super-resolution and synthetic aperture radar image-forming technology can be used to retouch State the scattering geometry characteristic of target.

Matched filtering is simplest method for parameter estimation, and it easily operates, and is widely used in Radar Signal Processing.But It is that the major defect of matched filtering is exactly the parameter that can estimate many falsenesses, and be difficult to differentiate the target being within close proximity. Relax is one of conventional method for parameter estimation, and it estimates multicomponent multiple sinusoidal signal by minimizing error energy Amplitude and frequency.Compressed sensing (compressive sensing, cs) theory thinks if a signal is under certain dictionary Sparse, then it just accurately can be reconstructed out with a small amount of accidental projection observation data.In recent years, because having good surpassing Differentiate and parameter estimation capabilities, compressed sensing is widely used in Radar Signal Processing.Three kinds are generally had to solve sparse approximately to ask The computational methods of topic: 1) greedy tracing algorithm: this kind of method is progressively forced by selecting a locally optimal solution during each iteration Nearly primary signal, these algorithms include match tracing (matching pursuit, mp), orthogonal matching pursuit (orthogonal Matching pursuit, omp) etc.；2) convex method of relaxation: this kind of method is looked for by non-convex problem is converted into convex problem solution Approaching to signal；3) Bayesian frame: to unknown parameter, this kind of method is by assuming that a prior distribution obtains parameter Sparse expression.

Method mentioned above, generally using one group of initiation parameter covering parameter to be estimated as far as possible, generates a ginseng The dictionary of numberization is realizing parameter estimation.Although they can estimate the parameter in echo to a certain extent, they are adopted It is the fixing dictionary that restricted parameter set generates, and the redundancy (i.e. the traversal degree of parameter) of dictionary directly influences parameter The accuracy estimated, namely when construction dictionary, the setting interval of parameter is a problem needing emphasis to consider.If just The setting interval of beginning parameter is too big, then be difficult to find the parameter of the atom of optimum and true echo-signal accordingly；If initial The setting of parameter is spaced too little (i.e. super complete dictionary), and the operand of parameter estimation can be very big, and might not can guarantee that word The corresponding atom of actual parameter is comprised in allusion quotation.

Content of the invention

It is an object of the invention to proposing the echo-signal method for parameter estimation based on scaling dictionary.The present invention proposes one Plant the method for parameter estimation that multilamellar is approached, that is, using sparse Bayesian expression (the sparse bayesian of scaling dictionary Representation with zoom-dictionary, sbrzd) method, can fast and accurately estimate parameter.

For realizing above-mentioned technical purpose, the present invention adopts the following technical scheme that and is achieved.

Comprised the following steps based on the echo-signal method for parameter estimation of scaling dictionary:

S1: receive echo-signal using radar, in setting echo signal model, the corresponding γ of each scattering center is individual not Know the initial value interval δ θ of parameter_γ, γ takes 1 to c, and c is the corresponding unknown parameter of each scattering center in echo signal model Number；For the corresponding all unknown parameters of each scattering center in echo signal model, travel through taking of each unknown parameter Value, draws parameter group intersection { θ⁽¹⁾, described parameter group intersection { θ⁽¹⁾Including g parameter combination, described g parameter combination represents ForExtremelyUsing parameter group intersection { θ⁽¹⁾Form dictionary a (θ⁽¹⁾)；Set iterationses m, m takes 1,2,3 ...；When m takes 1 When, if

S2: according to a (θ^(m)), by carrying out the m time management loading, reduce { θ^(m)In parameter combination number, Draw new parameter group intersection { θ '^(m)}；Draw dump energy e after the m time management loading_m；

S3: if m is equal with maximum iteration time m setting, go to step s5；Otherwise, m value Jia 1, go to step s4；

S4: for parameter group intersection { θ '^(m-1), by the value interval of corresponding for each scattering center γ unknown parameterReplace with New parameter group intersection { θ is drawn by the method becoming more meticulous^(m)}； Using parameter group intersection { θ^(m)Form dictionary a (θ^(m)), then go to step s2；

S5: find out the iterationses m meeting following condition^*: m^*Dump energy after secondary management loadingFor e₁To e_mIn minima；

S6: using k-means clustering method pairIt is weighted clustering, draw corresponding c of each scattering center The estimated result of unknown parameter.

The invention has the benefit that 1) present invention is applied to any known multiple echo-signal (real signal can be used as one Individual special case) simulated target parameter estimation.It would be desirable to the parameter estimated is embodied in letter when known to multiple echo signal model In number model, constitute the atom of dictionary with the different corresponding signal models of parameter value, with parameter estimation later.2) this Bright using fewer initial parameter, the method approached using multilamellar, gradually become more meticulous parameter, until realize accurate parameter estimating Meter.So operand can not only be reduced moreover it is possible to ensure the accuracy of parameter estimation.3) present invention is in each iteration using dilute Thin Bayesian learning method, has the two-valued variable that value is 0 or 1 in the method, therefore can adaptive sparse selection Parameter combination, and the method can provide the Posterior distrbutionp of each variable, rather than obtain simple point estimation, in addition, the party Method has stronger noise removal capability it is adaptable to relatively low state of signal-to-noise.4) present invention is obtaining the parameter of multilamellar approximation timates Afterwards, employ k-means clustering method parameter to be weighted cluster, to obtain more accurate parameter estimation again.

Brief description

Fig. 1 is the flow chart of the echo-signal method for parameter estimation based on scaling dictionary of the present invention；

Fig. 2 is the directed acyclic graph of the probability explanation of signal model in the present invention；

Fig. 3 is to become more meticulous the schematic flow sheet of parameter combination；

Fig. 4 is the present invention and other method parameter estimation comparative result to multiple sinusoidal signal under being not added with noise situations； Wherein, Fig. 4 a is the contrast of the parameter estimation result to multiple sinusoidal signal under being not added with noise situations for the convex optimization and actual parameter Schematic diagram；Fig. 4 b be orthogonal matching pursuit method under being not added with noise situations to the parameter estimation result of multiple sinusoidal signal with true The contrast schematic diagram of parameter；Fig. 4 c is the Bayes's compression sense based on variation Bayes (variational bayesian, vb) The contrast schematic diagram of the perception method parameter estimation result to multiple sinusoidal signal and actual parameter under being not added with noise situations；Fig. 4 d is The present invention is before cluster to the contrast schematic diagram being not added with the parameter estimation result of multiple sinusoidal signal and actual parameter under noise situations； Fig. 4 e be the present invention after cluster to being not added with noise situations the parameter estimation result of multiple sinusoidal signal and the contrast of actual parameter Schematic diagram；

Fig. 5 is the present invention and other method compares knot to the parameter estimation of multiple sinusoidal signal in the case of signal to noise ratio is for 10db Really；Wherein, Fig. 5 a is that convex optimization is joined with true to the parameter estimation result of multiple sinusoidal signal in the case of signal to noise ratio is for 10db The contrast schematic diagram of number；Fig. 5 b estimates to the parameter of multiple sinusoidal signal in the case of signal to noise ratio is for 10db for orthogonal matching pursuit method Meter result and the contrast schematic diagram of actual parameter；Fig. 5 c is the Bayes's compression sensing method based on vb is 10db feelings in signal to noise ratio To the parameter estimation result of multiple sinusoidal signal and the contrast schematic diagram of actual parameter under condition；Fig. 5 d be the present invention before cluster to letter Make an uproar than for answering the parameter estimation result of sinusoidal signal and the contrast schematic diagram of actual parameter in the case of 10db；Fig. 5 e exists for the present invention To signal to noise ratio for answering the parameter estimation result of sinusoidal signal and the contrast schematic diagram of actual parameter in the case of 10db after cluster；

Fig. 6 is the present invention and other method compares knot to the parameter estimation of multiple sinusoidal signal in the case of signal to noise ratio is for 5db Really；Wherein, Fig. 6 a is the parameter estimation result to multiple sinusoidal signal in the case of signal to noise ratio is for 5db for the convex optimization and actual parameter Contrast schematic diagram；Fig. 6 b is orthogonal matching pursuit method parameter estimation to multiple sinusoidal signal in the case of signal to noise ratio is for 5db Result and the contrast schematic diagram of actual parameter；Fig. 6 c is the Bayes's compression sensing method based on vb is 5db situation in signal to noise ratio Under contrast schematic diagram to the parameter estimation result of multiple sinusoidal signal and actual parameter；Fig. 6 d be the present invention before cluster to noise Than for answering the parameter estimation result of sinusoidal signal and the contrast schematic diagram of actual parameter in the case of 5db；Fig. 6 e is the present invention poly- To signal to noise ratio for answering the parameter estimation result of sinusoidal signal and the contrast schematic diagram of actual parameter in the case of 5db after class；

Fig. 7 is the present invention and other method is estimated to the parameter of the micro-doppler signal that spin causes under being not added with noise situations Meter comparative result；Wherein, Fig. 7 a is the parameter to the micro-doppler signal that spin causes under being not added with noise situations for the convex optimization Estimated result and the 3-dimensional contrast schematic diagram of actual parameter；The convex optimization of Fig. 7 b causes to spin under being not added with noise situations The parameter estimation result of micro-doppler signal ties up contrast schematic diagrams with the 2 of actual parameter；Fig. 7 c exists for orthogonal matching pursuit method It is not added with noise situations, the parameter estimation result of the micro-doppler signal that spin causes being illustrated with the 3-dimensional contrast of actual parameter Figure；Fig. 7 d is the parameter estimation knot to the micro-doppler signal that spin causes under being not added with noise situations for the orthogonal matching pursuit method Fruit ties up contrast schematic diagrams with the 2 of actual parameter；Fig. 7 e is that the Bayes's compression sensing method based on vb is being not added with noise situations Parameter estimation result to the micro-doppler signal that spin causes and the 3-dimensional contrast schematic diagram of actual parameter；Fig. 7 f is based on vb The parameter estimation result of micro-doppler signal that under being not added with noise situations, spin caused of Bayes's compression sensing method with 2 dimension contrast schematic diagrams of actual parameter；Fig. 7 g be the present invention before cluster under being not added with noise situations to spin cause micro- many The general parameter estimation result strangling signal and the 3-dimensional contrast schematic diagram of actual parameter；Fig. 7 h is being not added with making an uproar before cluster for the present invention In the case of sound, with the 2 of actual parameter, contrast schematic diagrams are tieed up to the parameter estimation result of the micro-doppler signal that spin causes；Fig. 7 i For the present invention before cluster be not added with the parameter estimation result of micro-doppler signal under noise situations, spin is caused with true The 3-dimensional contrast schematic diagram of parameter；Fig. 7 j is the micro-doppler that the present invention causes to spin before cluster under being not added with noise situations The parameter estimation result of signal ties up contrast schematic diagrams with the 2 of actual parameter；

Fig. 8 is the present invention and other method ginseng to the micro-doppler signal that spin causes in the case of signal to noise ratio is for 10db Number estimates comparative result；Wherein, Fig. 8 a is the micro-doppler letter that convex optimization causes to spin in the case of signal to noise ratio is for 10db Number parameter estimation result and actual parameter 3-dimensional contrast schematic diagram；Fig. 8 b is convex optimization in the case of signal to noise ratio is for 10db With the 2 of actual parameter, contrast schematic diagrams are tieed up to the parameter estimation result of the micro-doppler signal that spin causes；Fig. 8 c is orthogonal Join method for tracing in the case of signal to noise ratio is for 10db, the parameter estimation result of the micro-doppler signal that spin causes to be joined with true The 3-dimensional contrast schematic diagram of number；Fig. 8 d be orthogonal matching pursuit method in the case of signal to noise ratio is for 10db to spin cause micro- many The general parameter estimation result strangling signal and 2 dimension contrast schematic diagrams of actual parameter；Fig. 8 e is the Bayes's compressed sensing based on vb The 3-dimensional of the method parameter estimation result to the micro-doppler signal that spin causes and actual parameter in the case of signal to noise ratio is for 10db Contrast schematic diagram；Fig. 8 f be Bayes's compression sensing method based on vb in the case of signal to noise ratio is for 10db, spin is caused micro- The parameter estimation result of Doppler signal ties up contrast schematic diagrams with the 2 of actual parameter；Fig. 8 g be the present invention before cluster in noise Than for illustrating with the 3-dimensional contrast of actual parameter to the parameter estimation result of the micro-doppler signal that spin causes in the case of 10db Figure；Fig. 8 h is present invention parameter estimation to the micro-doppler signal that spin causes in the case of signal to noise ratio is for 10db before cluster Result ties up contrast schematic diagrams with the 2 of actual parameter；Fig. 8 i be the present invention before cluster in the case of signal to noise ratio is for 10db to spin The parameter estimation result of micro-doppler signal causing and the 3-dimensional contrast schematic diagram of actual parameter；Fig. 8 j is the present invention in cluster Front right to the parameter estimation result of the micro-doppler signal that spin causes and 2 dimensions of actual parameter in the case of signal to noise ratio is for 10db Compare schematic diagram；

Fig. 9 is the present invention and other method ginseng to the micro-doppler signal that spin causes in the case of signal to noise ratio is for 5db Number estimates comparative result；Wherein, Fig. 9 a is the micro-doppler signal that convex optimization causes to spin in the case of signal to noise ratio is for 5db Parameter estimation result and actual parameter 3-dimensional contrast schematic diagram；Fig. 9 b be convex optimization in the case of signal to noise ratio is for 5db to from Revolve 2 dimension contrast schematic diagrams of the parameter estimation result of micro-doppler signal causing and actual parameter；Fig. 9 c chases after for orthogonal coupling Track method parameter estimation result and the 3 of actual parameter to the micro-doppler signal that spin causes in the case of signal to noise ratio is for 5db Dimension contrast schematic diagram；Fig. 9 d is the micro-doppler letter that orthogonal matching pursuit method causes to spin in the case of signal to noise ratio is for 5db Number parameter estimation result and actual parameter 2 dimension contrast schematic diagrams；Fig. 9 e is to be existed based on Bayes's compression sensing method of vb Signal to noise ratio is for showing with the 3-dimensional contrast of actual parameter to the parameter estimation result of the micro-doppler signal that spin causes in the case of 5db It is intended to；Fig. 9 f is the micro-doppler that the Bayes's compression sensing method based on vb causes to spin in the case of signal to noise ratio is for 5db The parameter estimation result of signal ties up contrast schematic diagrams with the 2 of actual parameter；Fig. 9 g is the present invention is 5db in signal to noise ratio before cluster In the case of the parameter estimation result of micro-doppler signal that spin is caused and actual parameter 3-dimensional contrast schematic diagram；Fig. 9 h is The parameter estimation result of micro-doppler signal that the present invention causes to spin before cluster in the case of signal to noise ratio is for 5db with true 2 dimension contrast schematic diagrams of parameter；Fig. 9 i be the present invention before cluster in the case of signal to noise ratio is for 5db to spin cause micro- how general Strangle the parameter estimation result of signal and the 3-dimensional contrast schematic diagram of actual parameter；Fig. 9 j for the present invention in signal to noise ratio is before cluster In the case of 5db, with the 2 of actual parameter, contrast schematic diagrams are tieed up to the parameter estimation result of the micro-doppler signal that spin causes；

Specific embodiment

The invention will be further described below in conjunction with the accompanying drawings:

With reference to Fig. 1, it is the flow chart of the echo-signal method for parameter estimation based on scaling dictionary of the present invention.Should be based on contracting The echo-signal method for parameter estimation putting dictionary comprises the following steps:

S1: initial dictionary is generated according to target echo signal model.It is described as follows:

It is assumed that the multiple echo-signal of target is s (t), it is broken down into the weighted sum of one group of echo-signal function:

$s\left(t\right)=\underset{k=1}{\overset{f}{\mathrm{\σ}}}{g}_{k}f(r_k,t)+\mathrm{\ϵ}\left(t\right)$

Wherein, t is the time serieses that length is n；K takes 1 to f, f to represent the number of scattering center；g_kRepresent k-th scattering center Unknown magnitude；f(r_k, t) represent the parameterized echo signal model of k-th scattering center； r_kIt is that k-th signal model (refers to f (r_k, t)) in unknown parameter, c represents that k-th signal model (refers to f (r_k, t)) in unknown ginseng The number of number；For example this c unknown parameter includes: the Doppler frequency of target, range information of scattering center etc., and ε (t) represents Noise.In above formula, signal model can be written as vector-matrix form:

s=d(r)·g+ε

Wherein, s=[s₁,…,s_n,…s_n]^t, r=[r₁,…,r_k,…,r_f]^t, g=[g₁,…,g_k,…,g_f]^t, ε=[ε₁,…, ε_n,…,ε_n]^t, and d (r)=[f (r₁),…,f(r_k),…,f(r_f)].Wherein, the transposition of t representing matrix or vector, f (r_k) With f (r_k, t) there is identical implication, ε and ε (t) has identical implication.s_nRepresent in s that n-th time series are corresponding to answer back Ripple signal, ε_nRepresent the corresponding noise of n-th time series in ε.

By above description, it is understood that signal s can be by f atom (f (r₁) to f (r_f)) carry out rarefaction representation.In advance We are not aware that parameter r in s_kConcrete value, but according to actual priori, draw corresponding with arbitrary scattering center γ unknown parameter r^γSpan, arrange r^γValue be spaced apart δ θ_γ, now, δ θ_γThe ratio that can arrange is larger.According to r^γ Span and δ θ_γ, determine r^γMultiple initial values；Traversal combines c unknown parameterInitial value, draw Parameter group intersection { θ (1) }；Wherein, Represent { θ⁽¹⁾In p-th parameter combination, p takes 1 to g；Wherein,Represent r^γAn initial value；G is { θ⁽¹⁾In The number of parameter combination.It should be noted that r here_kWithRepresent the different values of same parameter combination, our target It is exactly from { θ⁽¹⁾In estimate r_k.Finally we utilize parameter group intersection { θ⁽¹⁾Generate an initialized dictionary a (θ⁽¹⁾), $a\left({\mathrm{\θ}}^{\left(1\right)}\right)=[f\left({\mathrm{\θ}}_1^{\left(1\right)}\right),\·\·\·,f\left({\mathrm{\θ}}_p^{\left(1\right)}\right),\·\·\·,f\left({\mathrm{\θ}}_g^{\left(1\right)}\right)];$ Represent withCorresponding parameterized signal model. For example when signal model is multiple sinusoidal model, that is, $s\left(t\right)=\underset{k=1}{\overset{f}{\mathrm{\σ}}}{g}_k\exp \left(j2\mathrm{\π}{f}_{k}t\right)+\mathrm{\ϵ}\left(t\right),$ Now, parameter to be estimated For f_k, thenForThen set iterationses m, m takes 1,2,3 ...；When m takes 1,

S2: according to a (θ^(m)), by carrying out the m time management loading (i.e. sparse Bayesian method for parameter estimation), Reduce { θ^(m)In parameter combination number, draw new parameter group intersection { θ '^(m)}；After drawing the m time management loading Dump energy e_m.It is described as follows: according to the description in step s1, we are rewritten as signal model:

s=a(θ^(m))×(w^(m)⊙z^(m))+ε^(m)

Wherein, ⊙ represents that hadamard amasss；w^(m)For echo-signal in dictionary a (θ^(m)) coefficient vector； $a\left({\mathrm{\θ}}^{\left(m\right)}\right)=[f\left({\mathrm{\θ}}_1^{\left(m\right)}\right),\·\·\·,f\left({\mathrm{\θ}}_{p^{\left(m\right)}}^{\left(m\right)}\right),\·\·\·,f\left({\mathrm{\θ}}_{g^{\left(m\right)}}^{\left(m\right)}\right)],$ Represent withCorresponding parameterized letter Number model.{θ^(m)Represent the parameter group intersection carrying out being used during the m time management loading,p^(m)Take 1 to g^(m), as m=1, p^(m)=p, g^(m)=g；Wherein,Represent w^(m)Pth^(m)Individual element；g^(m)For { θ^(m)Middle ginseng The number that array is closed.z^(m)For column vector,z^(m)Element number be { θ^(m)In The number of parameter combination, z^(m)In each element take 0 or 1, that is,Therefore, z^(m)Can be used to realize sparse, Dictionary a (θ can sparsely be selected^(m)) in corresponding to actual parameter combination column vector.

In the present invention, the process of parameter estimation may be considered: based on the signal model in step s2 from echo-signal s Study sparse vector z^(m).Learning z^(m)Afterwards, by finding z^(m)The corresponding parameterized atom of middle nonzero element, you can To realize parameter estimation.In the signal model of step s2, ε^(m)For carrying out the noise setting during the m time management loading. Set ε^(m)Obeying average is zero, and variance isGauss distribution, τ_mFor variable, represent noise degree of accuracy, i_nRepresent dimension The likelihood function of the signal model of the unit matrix for n, therefore step s2 is:

Wherein, cn () represents multiple Gaussian probability-density function, the conjugate transpose of h representing matrix.

We give w first^(m)Defining an average is zero, and variance is(α_mFor variable,Expression dimension is g^(m)Unit matrix) multiple Gauss prior distribution

$p\left(w^{\left(m\right)}\right|{\mathrm{\α}}_m)=\mathrm{cn}\left(w^{\left(m\right)}\right|0,{\mathrm{\α}}_m^{-1}{i}_{g^m})$

In order that parameter learning is more flexible, to α_mWith noise degree of accuracy τ_mDefinition is advanced and is tested respectively, suitably super prior distribution For gamma distribution, then α_mAnd τ_mSuper prior distribution be respectively as follows:

$p\left({\mathrm{\α}}_m\right)=\mathrm{gamma}\left({\mathrm{\α}}_m\right|a_0,b_0)=\mathrm{\γ}{\left(a_0\right)}^{-1}{b_0}^{a_0}{{\mathrm{\α}}_m}^{a_0-1}{e}^{-b_0{\mathrm{\α}}_m}$

$p\left({\mathrm{\τ}}_m\right)=\mathrm{gamma}\left({\mathrm{\τ}}_m\right|c_0,d_0)$

Wherein gamma () represents gamma distribution,Represent gamma function.In order that hyper parameter Do not there is provided information to posteriority study, make posteriority depend entirely on data, we define a₀=b₀=c₀=d₀=10^-6.

Due to z^(m)It is a binary vector (i.e. element therein only takes 0 or 1) it is clear that working asWhen, just It is equivalent to from dictionary a (θ^(m)) in directly delete pth^(m)Individual atom, namely pth^(m)Individual parameter combination.To binary vector z^(m), We adopt Bernoulli Jacob-beta (bernoulli-beta) priori, and it is the limited approximate of beta (beta) process, then have:

$p\left(z^{\left(m\right)}\right|u^{\left(m\right)})=\underset{p^{\left(m\right)}=1}{\overset{g^m}{\mathrm{\π}}}\mathrm{bernoulli}\left(z_{p^{\left(m\right)}}^{\left(m\right)}\right|u_{p^{\left(m\right)}}^{\left(m\right)})=\underset{p^{\left(m\right)}=1}{\overset{g^{\left(m\right)}}{\mathrm{\π}}}{u}_{p^{\left(m\right)}}^{{\left(m\right)}^{z_{p^{\left(m\right)}}^{\left(m\right)}}}{(1-u_{p^{\left(m\right)}}^{\left(m\right)})}^{1-z_{p^{\left(m\right)}}^{\left(m\right)}}$

$p\left(u^{\left(m\right)}\right)=\underset{p^{\left(m\right)}=1}{\overset{g^{\left(m\right)}}{\mathrm{\π}}}\mathrm{beta}\left(u_{p^{\left(m\right)}}^{\left(m\right)}\right|\frac{e_0}{d},\frac{f_0(d-1)}{d})$

Wherein, bernoulli () represents bernoulli probability density function, and beta () represents beta probability density function；u^(m) For the parameter in bernoulli probability density function and beta probability density function, Represent u^(m)In pth^(m)Individual element, e₀And f₀It is the hyper parameter more than zero.Generally, we set d be one big but Limited number, the present invention sets d=1000, thereforeExpectationFor:

$\⟨u_{p^{\left(m\right)}}^{\left(m\right)}\⟩=\frac{e_0/d}{e_0/d+f_0(d-1)/d}$

Wherein,<>represents expectation；Understand according to the above description,Level off to zero, also imply that z^(m)In non- The number of neutral element is considerably less, it is achieved thereby that z^(m)Sparse (most element is zero).So far, for this model Through there being a complete probability explanation, the directed acyclic graph of this probabilistic model is as shown in Figure 2.

We are solved to model above using variational Bayesian method in the present invention.Variational Bayesian method Process is: in the case of given observation data η and hyper parameter γ, estimates the Posterior distrbutionp of hidden variable ψ in model.

In variational Bayesian method, we are with distribution q (the ψ)=∏ of a variation_ρq(ψ_ρ) go the true of approximate hidden variable Real Posterior distrbutionp p (ψ | h, γ), ψ_ρRepresent the ρ element in ψ, then have:

lnp(h|γ)=ln∫p(h,ψ|γ)dψ=ln∫q(ψ)p(h,ψ|γ)/q(ψ)dψ

≥∫q(ψ)ln(p(h,ψ|γ)/q(ψ))dψ

=lnp(h|γ)-∫q(ψ)ln(q(ψ)/p(ψ|h,γ))dψ

=lnp (h | γ)-κ l (q (ψ) | p (ψ | h, γ))

=l(q(ψ))

Wherein, κ l (q (ψ) | p (ψ | h, γ)) represents the approximate q of variation (ψ) and real jointly posteriority p (ψ | h, γ) Kullback-leibler distance.(q (ψ) | p (ψ | h, γ)) >=0 because κ l, that is, mean l (q (ψ)) be lnp (h | Strict lower bound γ).Therefore, by minimizing κ l (q (ψ) | p (ψ | h, γ)), we can obtain q (ψ_f) optimum Solution.

In the present invention, h is s, and ψ isγ is { a₀,b₀,c₀,d₀,e₀,f₀}. In order to allow l (q (ψ)) approach lnp (h | γ), variational Bayesian method needs iteration to update { q (ψ_ρ) until its convergence.According to {p(ψ_ρ| h, γ) } conjugate property, we can analytically estimate { q (ψ_ρ)}.The renewal that each hidden variable is given below pushes away Lead formula:

1) w^(m)Renewal, w^(m)Posterior distrbutionp q (w^(m)) meet:

q(w^(m))∝p(s|w^(m),z^(m),τ_m)p(w^(m)|α_m)

Wherein, ∝ represents and is proportional to.Therefore w^(m)Posterior distrbutionp q (w^(m)) it is multivariable multiple Gauss distribution:

$q\left(w^{\left(m\right)}\right)=\mathrm{cn}({\mathrm{\&mu;}}_{w^{\left(m\right)}},{\mathrm{\&sigma;}}_{w^{\left(m\right)}})$

Represent that average isCovariance isMultiple Gauss distribution,With It is respectively as follows:

Wherein,<>represents expectation,Expression dimension is g^(m)Unit matrix, diag () represent diagonalization operation, diag(z^(m)) represent with z^(m)In the diagonal matrix that builds for the elements in a main diagonal of element；And

$\&lang;w^{\left(m\right)}{\left(w^{\left(m\right)}\right)}^h\&rang;={\mathrm{\&sigma;}}_{w^{\left(m\right)}}+{\mathrm{\&mu;}}_{w^{\left(m\right)}}{\mathrm{\&mu;}}_{w^{\left(m\right)}}^h.$

2) α_mRenewal, α_mPosterior distrbutionp q (α_m) meet:

q(α_m)∝p(w^(m)|α_m)p(α_m|a₀,b₀)

Therefore α_mPosterior distrbutionp be gamma distributionWherein,

$\tilde{a}=a_0+g^{\left(m\right)},\tilde{b}=b_0+\underset{p^{\left(m\right)}=1}{\overset{g^{\left(m\right)}}{\mathrm{\&sigma;}}}\&lang;{\left(w_{p^{\left(m\right)}}^{\left(m\right)}\right)}^2\&rang;$

Then < α_m> be expressed as

3) τ_mRenewal, τ_mPosterior distrbutionp q (τ_m) meet:

q(τ_m)∝p(s|w^(m),z^(m),τ_m)p(τ_m|c₀,d₀)

Therefore, τ_mPosterior distrbutionp be gamma distributionWherein,

$\tilde{c}=c_0+n$

Wherein, diaf () represents the elements in a main diagonal taking matrix as column vector, and sum () represents summation operation, Then < τ_m> be expressed as $\tilde{c}/\tilde{d}.$

4)Renewal, z^(m)Posterior distrbutionp q (z^(m)) meet:

$q\left(z^{\left(m\right)}\right)\&proportional;p\left(s\right|w^{\left(m\right)},z^{\left(m\right)},{\mathrm{\&tau;}}_m)p\left(z_{p^{\left(m\right)}}^{\left(m\right)}\right|u_{p^{\left(m\right)}}^{\left(m\right)})$

Therefore,Posterior distrbutionp be $\mathrm{bernoulli}\left(\frac{p(z_{p^{\left(m\right)}}^{\left(m\right)}=1)}{p(z_{p^{\left(m\right)}}^{\left(m\right)}=0)+p(z_{p^{\left(m\right)}}^{\left(m\right)}=1)}\right),$ Wherein, $p(z_{p^{\left(m\right)}}^{\left(m\right)}=1)$ Represent $z_{p^{\left(m\right)}}^{\left(m\right)}=1$ Probability, $p(z_{p^{\left(m\right)}}^{\left(m\right)}=0)$ Represent $z_{p^{\left(m\right)}}^{\left(m\right)}=0$ Probability, wherein, $p(z_{p^{\left(m\right)}}^{\left(m\right)}=1)$ With under Formula is directly proportional: $\exp (\&lang;\ln \left(u_{p^{\left(m\right)}}^{\left(m\right)}\right)\&rang;)\&times;\exp (\&lang;{\mathrm{\&tau;}}_m\&rang;(2\&lang;{\left(w_{p^{\left(m\right)}}^{\left(m\right)}\right)}^h\&rang;a{\left({\mathrm{\&theta;}}^m\right)}_{p^{\left(m\right)}}^h(s-{\mathrm{\&xi;}}^{\left(m\right)})-\&lang;{\left(w_{p^{\left(m\right)}}^{\left(m\right)}\right)}^2{a}^h\left({\mathrm{\&theta;}}^{\left(m\right)}\right)a\left({\mathrm{\&theta;}}^{\left(m\right)}\right)))$ Wherein, ${\mathrm{\&xi;}}^{\left(m\right)}=\underset{h^{\left(m\right)}\&notequal;p^{\left(m\right)}}{\mathrm{\&sigma;}}{z}_{h^{\left(m\right)}}^{\left(m\right)}\&lang;w_{h^{\left(m\right)}}^{\left(m\right)}\&rang;a{\left({\mathrm{\&theta;}}^{\left(m\right)}\right)}_{h^{\left(m\right)}},$ Represent a (θ^(m)) pth^(m)Row,RepresentConjugate transpose,Represent a (θ^(m)) h^(m)Row, h^(m)≠p^(m).

$p(z_{p^{\left(m\right)}}^{\left(m\right)}=0)$ With $\exp (\&lang;\ln (1-u_{p^{\left(m\right)}}^{\left(m\right)})\&rang;)$ It is directly proportional, with regard to $\&lang;\mathrm{lm}\left(u_{p^{\left(m\right)}}^{\left(m\right)}\right)\&rang;$ With $\&lang;\ln (1-u_{p^{\left(m\right)}}^{\left(m\right)})\&rang;$ 's Result of calculation, is being carried outRenewal when be given.In addition,

<z^(m)(z^(m))^t>=<z^(m)><z^(m)>^t+diag<z^(m)>-(diag<z^(m)>)².

5)Renewal,Posterior distrbutionpMeet:

$q\left(u_{p^{\left(m\right)}}^{\left(m\right)}\right)\&proportional;p\left(z_{p^{\left(m\right)}}^{\left(m\right)}\right|u_{p^{\left(m\right)}}^{\left(m\right)})p\left(u_{p^{\left(m\right)}}^{\left(m\right)}\right|e_0,f_0)$

Therefore,Posterior distrbutionp be beta distributionWherein,

${\tilde{e}}_{p^{\left(m\right)}}=e_0+d\&lang;z_{p^{\left(m\right)}}^{\left(m\right)}\&rang;$

${\tilde{f}}_{p^{\left(m\right)}}=f_0+\frac{d}{d-1}(1-\&lang;z_{p^{\left(m\right)}}^{\left(m\right)}\&rang;)$

Then have:

$\&lang;\ln \left(u_{p^{\left(m\right)}}^{\left(m\right)}\right)\&rang;=\mathrm{\&psi;}\left({}_{}\frac{{\tilde{e}}_{p^{\left(m\right)}}}{d}\right)-\mathrm{\&psi;}\left(\frac{{\tilde{e}}_{p^{\left(m\right)}}+{\tilde{f}}_{p^{\left(m\right)}}(d-1)}{d}\right)$

$\&lang;\ln (1-u_{p^{\left(m\right)}}^{\left(m\right)})\&rang;=\mathrm{\&psi;}\left(\frac{{\tilde{f}}_{p^{\left(m\right)}}(d-1)}{d}\right)-\mathrm{\&psi;}\left(\frac{{\tilde{e}}_{p^{\left(m\right)}}+{\tilde{f}}_{p^{\left(m\right)}}(d-1)}{d}\right)$

Wherein ψ () represents digamma function.

When parameter estimation restrains, we can obtain posterior error < z^(m)>and<w^(m)>.The present invention passes throughValue Determine: a (θ^(m)) pth^(m)Arrange whether corresponding parameter combination is chosen, that is, determine parameter group intersection { θ^(m)In pth^(m) Individual parameter combinationWhether it is chosen.IfPosterior probability be more than or equal to 0.5, then illustrate parameter group intersection {θ^(m)In pth^(m)Individual parameter combinationAnd w^(m)Pth^(m)Individual elementIt is chosen；Otherwise,With It is removed, now, obtained new parameter group intersection { θ '^(m)} $\left(\right\{{\mathrm{\&theta;}}^{\&prime;\left(m\right)}\}=[{\mathrm{\&theta;}}_1^{\&prime;\left(m\right)},\&centerdot;\&centerdot;\&centerdot;,{\mathrm{\&theta;}}_{l^{\left(m\right)}}^{\&prime;\left(m\right)},\&centerdot;\&centerdot;\&centerdot;,{\mathrm{\&theta;}}_{l^{\left(m\right)}}^{\&prime;\left(m\right)}],$ Wherein, ${\mathrm{\&theta;}}_{l^{\left(m\right)}}^{\&prime;\left(m\right)}=\{{{\mathrm{\&theta;}}_{l^{\left(m\right)}}}^{\left(m\right)1},\&centerdot;\&centerdot;\&centerdot;,{{\mathrm{\&theta;}}_{l^{\left(m\right)}}}^{\left(m\right)\mathrm{\&gamma;}},\&centerdot;\&centerdot;\&centerdot;,{{\mathrm{\&theta;}}_{l^{\left(m\right)}}}^{\left(m\right)\mathrm{ac}}\})$ And echo-signal is in dictionary a (θ '^(m)) coefficient vector w'^(m) $\left(\right\{w^{\&prime;\left(m\right)}\}=[w_1^{\&prime;\left(m\right)},\&centerdot;\&centerdot;\&centerdot;,w_{l^{\left(m\right)}}^{\&prime;\left(m\right)},\&centerdot;\&centerdot;\&centerdot;,w_{l^{\left(m\right)}}^{\&prime;\left(m\right)}\left]\right).$

Understand l according to the above description^(m)≤g^(m).According to the above description, the present invention can also obtain τ simultaneously_m(the i.e. essence of noise Exactness) Posterior distrbutionp, therefore can be obtained by out noise component(s), realize the function of denoising.It would be desirable to protect in this step Stay the dump energy after the m time management loading (dump energy after restraining) e_m, e_m=(norm(s-a(θ^(m))·(<w^(m)>⊙<z^(m)>)))², wherein norm () represent seek 2- norm.

S3: if m is equal with maximum iteration time m setting, go to step s5；Otherwise, m value Jia 1, now, turn To step s4.

S4: obtain the parameter combination becoming more meticulous using the method for scaling, then utilize new parameter combination to produce new ginseng Numberization dictionary.It is described as follows: for parameter group intersection { θ '^(m-1), by corresponding for each scattering center γ unknown ginseng The value interval of numberReplace with $\mathrm{\&delta;}{\mathrm{\&theta;}}_{\mathrm{\&gamma;}}^{\left(m\right)}=\mathrm{\&delta;}{\mathrm{\&theta;}}_{\mathrm{\&gamma;}}^{(m-1)}/2;$ Now, { θ '^(m-1)InAround Produce two new values, then travel through all existing value of each parameter, draw new parameter group intersection { θ^(m)}.Using Parameter group intersection { θ^(m)Form dictionary a (θ^(m)), then go to step s2.

It is exemplified below, in this example, c=2, m=8, now, parameter group intersection { θ '⁽⁷⁾In l-th parameter combination IncludingWithL takes 1 to l⁽⁷⁾.According to formula $\mathrm{\&delta;}{\mathrm{\&theta;}}_{\mathrm{\&gamma;}}^{\left(m\right)}=\mathrm{\&delta;}{\mathrm{\&theta;}}_{\mathrm{\&gamma;}}^{(m-1)}/2,$ Draw $\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)}=\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(7\right)}/2$ , andThe change being spaced according to value, thenValue can be changed into three below: ${\mathrm{\&theta;}}_l^{\left(7\right)1}-\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)},{\mathrm{\&theta;}}_l^{\left(7\right)1},{\mathrm{\&theta;}}_l^{\left(7\right)1}+\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)}.$ Value can be changed into three below: Then parameter group intersection { θ⁽⁸⁾The following parameter combination of inclusion: $\{{\mathrm{\&theta;}}_l^{\left(7\right)1}-\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)},{\mathrm{\&theta;}}_l^{\left(7\right)2}-\mathrm{\&delta;}{\mathrm{\&theta;}}_2^{\left(8\right)}\},$ $\{{\mathrm{\&theta;}}_l^{\left(7\right)1}-\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)},{\mathrm{\&theta;}}_l^{\left(7\right)2}\},$ $\{{\mathrm{\&theta;}}_l^{\left(7\right)1}-\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)},{\mathrm{\&theta;}}_l^{\left(7\right)2}+\mathrm{\&delta;}{\mathrm{\&theta;}}_2^{\left(8\right)}\},$ $\{{\mathrm{\&theta;}}_l^{\left(7\right)1},{\mathrm{\&theta;}}_l^{\left(7\right)2}-\mathrm{\&delta;}{\mathrm{\&theta;}}_2^{\left(8\right)}\},$ $\{{\mathrm{\&theta;}}_l^{\left(7\right)1},{\mathrm{\&theta;}}_l^{\left(7\right)2}\},$ $\{{\mathrm{\&theta;}}_l^{\left(7\right)1},{\mathrm{\&theta;}}_l^{\left(7\right)2}+\mathrm{\&delta;}{\mathrm{\&theta;}}_2^{\left(8\right)}\},$ $\{{\mathrm{\&theta;}}_l^{\left(7\right)1}+\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)},{\mathrm{\&theta;}}_l^{\left(7\right)2}-\mathrm{\&delta;}{\mathrm{\&theta;}}_2^{\left(8\right)}\},$ $\{{\mathrm{\&theta;}}_l^{\left(7\right)1}+\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)},{\mathrm{\&theta;}}_l^{\left(7\right)2}\},$ $\{{\mathrm{\&theta;}}_l^{\left(7\right)1}+\mathrm{\&delta;}{\mathrm{\&theta;}}_1^{\left(8\right)},{\mathrm{\&theta;}}_l^{\left(7\right)2}+\mathrm{\&delta;}{\mathrm{\&theta;}}_2^{\left(8\right)}\}.$ Fig. 3 gives the schematic diagram of the parameter combination that becomes more meticulous.When c ≠ 2, we Carry out parameter combination process of refinement using the method similar to c=2, draw parameter group intersection { θ^(m)}.Using parameter group intersection {θ^(m)Form dictionary a (θ^(m)), then go to step s2.

S5: find out the iterationses m meeting following condition^*: m^*Dump energy after secondary management loadingFor e₁To e_mIn minima.It is described as follows:

After completing m management loading, the present invention is using following criterion come it is determined that selected which time The result of iteration is as final parameter estimation result: the residual energy after each management loading retaining in step s2 Amount, in these dump energies, finds out least residue energy corresponding iterationses m^*.Then m^*After secondary management loading Draw parameter group intersection { θ '^(m)For the present invention select parameter estimation result.Foundation using such criterion is that noise can not be by Rarefaction representation, if not having noise in signal s, minimum dump energy is 0, if there being noise in s, least residue energy It should be noise energy.Determine optimum iteration m^*Afterwards, we extract preservation from step s2With $w^{\&prime;\left(m^{*}\right)}.$

S6: using k-means clustering method pairIt is weighted clustering, draw corresponding c of each scattering center The estimated result of unknown parameter.It is described as follows:

Although having carried out process of refinement to parameter combination in step s4, it is still difficult to zoom to exactly really Parameter combination position, actual result is to estimate some approximate parameter combinations around real parameter combination.In order to Obtain as accurate as possible parameter estimation result, in the present invention, we are to the approximation parameters combination around these real parameter combinations Using k-means clustering method weighted cluster.

In the embodiment of the present invention, using k-means clustering method to the parameter group intersection obtaining in step s5Enter Row weighted cluster.It is known for requiring f in k-means clustering method.If in embodiments of the present invention, f is known, then k- Means clustering method exports the cluster index of each point (parameter combination before cluster) and the center (ginseng after cluster of cluster Array is closed).But, the present invention not using k-means clustering method output cluster centre as final parameter estimation result, and Obtain using in step s5The cluster index put with each calculates the cluster centre of weighting, so can be fully sharp Realize cluster with the physical characteristics of signal.

Specifically, when known to number f of scattering center, using k-means clustering method pairIn all ginsengs Array is closed and is clustered, and gathers for f class；Gathering the parameter combination for kth class isWithCorresponding coefficient isThen after corresponding weighting, parameter combination is:

${\mathrm{\&theta;}}_k=\frac{\mathrm{\&sigma;}\left|w_{l^{\left(m^{*}\right)}}^{\&prime;\left(m^{*}\right)\left(k\right)}\right|{\mathrm{\&theta;}}_{l\left(m^{*}\right)}^{\&prime;\left(m^{*}\right)\left(k\right)}}{\mathrm{\&sigma;}\left|w_{l^{\left(m^{*}\right)}}^{\&prime;\left(m^{*}\right)\left(k\right)}\right|}.$

Management loading method in recycle step s2 or orthogonal matching pursuit method reevaluate each and add The corresponding coefficient of parameter combination after power.

If in embodiments of the present invention, f is unknown it is necessary to realize drawing the value of f, the present invention is by following criterion Go to set the value of f: first it is known that dump energy before clusterIf clustering successfully, by weighted cluster Dump energy e that rear parameter combination and coefficient obtain_aShould be not more thanOr it is closeFor exampleBased on this it is assumed that the present invention using it as determine scattering center number end condition.In addition, If we are it should be noted that the scattering center number selecting is more than real scattering center number f, supposition above according to So set up, therefore, we allow scattering center number begin stepping through trial (i.e. from the beginning of 1) from small to large here, once select Scattering center number meet above it is assumed that we can terminate searching for, the as real scattering center number of f value now.

The effect of the present invention is further illustrated by following emulation experiment:

1) emulation experiment scene: set radar target and obey scatter times, we provide two kinds of echo-signal moulds here Type.

The first echo signal model in emulation experiment is simplest scatter times: multiple sinusoidal model, that is,Wherein f is the number of scattering center, f_kIt is unknown parameter r_k,N represents the length of data sample.Here t can be fast time or slow time.In Narrow-band Radar In, t is the slow time, namely residence time, and wherein n represents pulse number, f_*It is pulse recurrence frequency, f_kRepresent the how general of target Strangle frequency.In wideband radar, not only one-dimensional High Range Resolution, and the synthetic aperture radar of two dimension and retrosynthesis aperture Radar can use this model representation.In one-dimensional High Range Resolution, t is the fast time of distance dimension, and wherein n is sampled point Number, f_*It is sample frequency, in this case, f_kCharacterize the range information of scattering center.In synthetic aperture radar and retrosynthesis In aperture radar, t both can be the fast time of distance dimension or the slow time of azimuth dimension.According to priori, Wo Menzhi Road f_kScope be [- f_*/2,f_*/2].In this experiment, it is assumed that n=64, f_*The value model of=150hz, f=6, therefore parameter Enclose for θ_p∈ [- 75,75], the amplitude of six scattering centers is respectively 0.5,0.4,0.2,0.3,0.25, and 0.6, corresponding f_k It is respectively -50.74, -43.73, -5.48,7.92,9.34, and 30.35.The method for parameter estimation that the present invention is introduced, sets Initial parameter interval δ θ is f_*/ 64, that is, initial dictionary dimension is 64, and in additive method: convex optimization (cvx), orthogonal Join method for tracing and Bayes's compressed sensing (the bayesian compressive sensing based on based on vb Vb, abbreviation bcs-vb method) in, set initial parameter and be spaced apart f_*/ 512, that is, initial dictionary dimension is 512, and it is us 8 times of method, operand is bigger than the present invention.

Second echo signal model in emulation experiment is the micro-doppler model that spin causes: $s\left(t\right)=\underset{k=1}{\overset{f}{\mathrm{\&sigma;}}}{g}_k\exp \left({\mathrm{jb}}_k\sin (w_{s}t+e_k)\right)+\mathrm{\&epsiv;}\left(t\right),$ Wherein f is the number of scattering center, It it is the slow time, wherein n represents the number of pulse, f_*Represent pulse recurrence frequency, g_kRepresent the amplitude of k-th scattering center, b_kIt is One variable relevant with radius of turn, w_sRepresent speed, e_kRepresent initial phase.In this experiment, w_s=10rad/s, n =1000,f_*The corresponding amplitude of=500hz, f=4, four scattering center is respectively 2,1.6,1.4, and 1.8, its corresponding parameter r_k= {b_k,e_kIt is respectively { 35.85, -2.5133 }, { 14.24,0 }, { 28.56,2.0944 }, and { 5.61,1.3464 }, therefore join Array closes r_k={b_k,e_kAnd corresponding amplitude g_kIt is exactly the parameter that we want to estimate.According to priori it can be appreciated that Parameter value scope to be estimated is respectively(corresponding parameter b_k) and(corresponding parameter e_k).Right The method for parameter estimation that the present invention introduces, sets initial parameter interval δ θ₁=2.5, δ θ₂=0.2, then initial dictionary dimension is 608, and in additive method: convex optimization (cvx), orthogonal matching pursuit method and the Bayes compressed sensing side based on vb In method (bayesian compressive sensing based on vb, abbreviation bcs-vb method), the initial parameter of setting It is spaced apart δ θ₁=2.5/3, δ θ₂=0.2/3, that is, initial dictionary dimension is 5415, essentially the 9 of the present invention times.

2) emulation content:

For both echo models, we all provide three kinds of experimental conditions: noiseless, plus signal to noise ratio is making an uproar of 10db Sound, and add the noise that signal to noise ratio is 5db, set noise as white Gaussian noise.For noisy situation, introduce in the present invention Method and bcs-vb method because they can adaptive estimation noise, in emulation experiment suppose noise known to.

With reference to Fig. 4, it is that the present invention compares to the parameter estimation of multiple sinusoidal signal under being not added with noise situations with other methods Result.With reference to Fig. 5, it is that the present invention compares to the parameter estimation of multiple sinusoidal signal in the case of signal to noise ratio is for 10db with other methods Result.With reference to Fig. 6, it is that the present invention compares to the parameter estimation of multiple sinusoidal signal in the case of signal to noise ratio is for 5db with other methods Result.

Table 1 be the present invention and other methods under three kinds of experimental conditions to the parameter estimation of the first echo signal model when Central processing unit (central processing unit, cpu) expends time comparative result.

Table 1

Time/second	cvx	omp	bcs-vb	The present invention
					Noiseless	3.9125	0.1459	9.2683	1.6270
Signal to noise ratio is 10db	3.8604	0.0171	9.2123	1.6890
					Signal to noise ratio is 5db	3.9096	0.0171	9.1721	1.4400

With reference to Fig. 7, it is the micro-doppler signal that the present invention and other method cause to spin under being not added with noise situations Parameter estimation comparative result.In Fig. 7 a to Fig. 7 j, parameter 1 is b_k, parameter 2 is e_k.With reference to Fig. 8, it is the present invention and other method The parameter estimation comparative result to the micro-doppler signal that spin causes in the case of signal to noise ratio is for 10db.In Fig. 8 a to Fig. 8 j In, parameter 1 is b_k, parameter 2 is e_k.With reference to Fig. 9, it is that the present invention causes to spin in the case of signal to noise ratio is for 5db with other methods Micro-doppler signal parameter estimation comparative result.In Fig. 9 a to Fig. 9 j, parameter 1 is b_k, parameter 2 is e_k.Table 2 is this Bright and other method expends the time to cpu during the parameter estimation of second echo signal model under three kinds of experimental conditions and compares knot Really.

Table 2

Time/second	cvx	omp	bcs-vb	The present invention
					Noiseless	164.0029	1.7200	6.4436e+03	57.9071
Signal to noise ratio is 10db	185.3225	0.0950	6.3315e+03	19.3530

Signal to noise ratio is 5db

226.3316

0.0929

6.5689e+03

15.0968

3) analysis of simulation result:

Figure 4, it is seen that in Fig. 4 e the present invention parameter estimation result than other methods parameter estimation result Accurately many, some False Intersection Points, Fig. 4 a and Fig. 4 c convexity optimization are had by the parameter that orthogonal matching pursuit method estimates With the result of the parameter estimation of the Bayes's compression sensing method based on vb similar to parameter before cluster for the present invention in Fig. 4 d Estimated result, this also demonstrates the present invention from another point of view in the analysis in step s6: occurs near around real parameter As parameter.It is to be noted, however, that the dimension of the initial dictionary of convex optimization and the Bayes's compression sensing method based on vb Degree is far longer than the dimension of the initial dictionary of the present invention, even if so, the parameter estimated in Fig. 4 d is than estimation in Fig. 4 a and 4c Parameter is more concentrated, and indicates the effectiveness of scaling dictionary.In addition, comparing with actual parameter, the ginseng that the present invention estimates after cluster Number difference, this effectiveness that also show weighted cluster and necessity only slightly.It is several that Fig. 5 and Fig. 6 sets forth this Method for parameter estimation parameter estimation result to the first signal model in the case of signal to noise ratio is for 10db and 5db.As can be seen that No matter being to be 10db or 5db in signal to noise ratio, with respect to other parameters method of estimation, the present invention can obtain more accurately parameter and estimate Meter result, also illustrate that the preferable noise removal capability of the present invention, i.e. the parameter estimation capabilities to Low SNR signal.Similar to Fig. 4, In fig. 5 and fig., the parameter being estimated by orthogonal matching pursuit method still has False Intersection Points, convex optimization and based on vb's Bayes's compression sensing method carries out having estimated approximation parameters around real parameter during parameter estimation, estimates simultaneously Some slight False Intersection Points.It should also be noted that Fig. 6 d is the same with the estimation number of parameters in Fig. 6 e, but their amplitude is slightly There is difference, the amplitude in Fig. 6 e is more accurate, this is the result that the amplitude to parameter combination in step s6 relearns.Compare After this four method for parameter estimation are to the parameter estimation accuracy of the first signal model, we have been given in Table 1 these four The time-consuming comparison of cpu in method.From table 1 it follows that the Bayes's compression sense with respect to convex optimization with based on vb Perception method, the present invention is less to the parameter estimation used time of the first signal model under three kinds of experimental conditions, then ratio of the present invention Orthogonal matching pursuit method is more time-consuming, and this is to determine, orthogonal matching pursuit method belongs to greedy by the realization mechanism of two kinds of algorithms Greedy algorithm is it is commonly known that its computing is very fast.Even so, with respect to other parameters method of estimation, we still it may be said that this Invention has accurate parameter estimation capabilities and relative high arithmetic speed.

It is micro- how general with what other methods caused to spin under three kinds of experimental conditions that Fig. 7, Fig. 8 and Fig. 9 are respectively the present invention Strangle the parameter estimation comparative result of signal.Because this signal model parameter to be estimated has three: parameter 1b_k, parameter 2e_k, and Their corresponding amplitudes g_k, therefore to each method for parameter estimation, we all provide 3-dimensional Parameter Map and 2 dimension Parameter Map.In addition In order that 3-dimensional Parameter Map becomes apparent from, we are to convex optimization with the atom that estimated based on Bayes's compression sensing method of vb Amplitude arranges a thresholding (being 0.02 here), more than the corresponding parameter of the amplitude of this thresholding as the parameter estimating.From this No matter it is that the parameter that the present invention estimates will be than in addition in noiseless or under having noise situations that three in figures can be seen that The parameter that three kinds of methods estimate is accurately many.The parameter estimation result of convex optimization and orthogonal matching pursuit method makes us discontented Meaning, they have all estimated some False Intersection Points, although the parameter estimation result of the Bayes's compression sensing method based on vb is than convex Optimization and orthogonal matching pursuit method are a shade better, but still can not meet our expectation.The time-consuming ratio for cpu Relatively, it can be seen from Table 2 that, similar to table 1, the present invention will be slower than orthogonal matching pursuit method, but is faster than convex optimization and base In Bayes's compression sensing method of vb, the Bayes's compression sensing method being based particularly on vb is the most time-consuming.Generally, Bayes method, the Bayes's compression sensing method including the present invention with based on vb, need when calculating weights covariance matrix Inversion operation, when dictionary dimension is big, inversion operation can consume many times, and in addition variational Bayesian method needs many times Iteration just can restrain, and this is also why to consume a lot of times based on Bayes's compression sensing method of vb.Therefore we can To say for the bayes method derived with vb, multilamellar approximation technique is a good selection.

Obviously, those skilled in the art can carry out the various changes and modification essence without deviating from the present invention to the present invention God and scope.So, if these modifications of the present invention and modification belong to the scope of the claims in the present invention and its equivalent technologies Within, then the present invention is also intended to comprise these changes and modification.

Claims (4)

1. the echo-signal method for parameter estimation based on scaling dictionary is it is characterised in that comprise the following steps:

S1: receive echo-signal using radar, the corresponding γ unknown ginseng of each scattering center in setting echo signal model The initial value interval △ θ of number_γ, γ takes 1 to c, c be in echo signal model the corresponding unknown parameter of each scattering center Number, draws some initial values of the corresponding γ unknown parameter of each scattering center；For in echo signal model each The corresponding all unknown parameters of scattering center, travel through the value of each unknown parameter, draw parameter group intersection { θ⁽¹⁾, described ginseng Array intersection { θ⁽¹⁾Including g parameter combination, described g parameter combination is expressed asExtremelyUsing parameter group intersection {θ⁽¹⁾Form dictionary a (θ⁽¹⁾)；Set iterationses as m；When m takes 1, if the corresponding γ unknown ginseng of each scattering center The value interval of number

S2: according to a (θ^(m)), by carrying out the m time management loading, reduce { θ^(m)In parameter combination number, draw New parameter group intersection { θ^'(m)}；Draw dump energy e after the m time management loading_m:

e_m=(norm (s-a (θ^(m))·(<w^(m)>⊙<z^(m)>)))²,

Wherein,<>represents expectation, and s represents echo signal model, w^(m)For echo-signal in dictionary a (θ^(m)) coefficient vector；z^(m)For column vector, its element number is { θ^(m)In parameter combination number, z^(m)In each element take 0 or 1, norm () table Show and seek 2- norm, ⊙ represents that hadamard amasss；

S3: if m is equal with maximum iteration time m setting, go to step s5；Otherwise, m value Jia 1, go to step s4；

S4: for parameter group intersection { θ^'(m-1), orderNew parameter is drawn by the method becoming more meticulous Combination of sets { θ^(m)}；Using parameter group intersection { θ^(m)Form dictionary a (θ^(m)), then go to step s2；

S5: find out the iterationses m meeting following condition^*: m^*Dump energy after secondary management loadingFor e₁To e_m In minima；

S6: using k-means clustering method pairIt is weighted clustering, show that the corresponding c of each scattering center is individual unknown The estimated result of parameter.

2. the echo-signal method for parameter estimation based on scaling dictionary as claimed in claim 1 is it is characterised in that in step s1 In, receive echo-signal using radar, echo signal model s is expressed as:

S=d g+ ε

Wherein, d=[f (r₁),…,f(r_k),…,f(r_f)],K takes 1 to f, f to represent the individual of scattering center Number；f(r_k) represent k-th scattering center parameterized echo signal model；Represent f (r_k) in k-th scattering center Corresponding the γ unknown parameter；G=[g₁,…,g_k,…,g_f]^t, g_kIt is the unknown width of the echo-signal of k-th scattering center Degree；ε represents noise；

The γ unknown parameter r corresponding with arbitrary scattering center is drawn by priori^γSpan, arrange r^γTake Value is spaced apart △ θ_γ, according to r^γSpan and △ θ_γ, determine r^γMultiple initial value；

Traversal combines c unknown parameterInitial value, draw parameter group intersection { θ⁽¹⁾}；

$\left\{{\mathrm{\&theta;}}^{\left(1\right)}\right\}=\&lsqb;{\mathrm{\&theta;}}_1^{\left(1\right)},\mathrm{...},{\mathrm{\&theta;}}_p^{\left(1\right)},\mathrm{...},{\mathrm{\&theta;}}_g^{\left(1\right)}\&rsqb;,$

Wherein,Represent { θ⁽¹⁾In p-th parameter combination, p takes 1 to g；

Wherein,Represent r^γAn initial value；

Using parameter group intersection { θ⁽¹⁾Form dictionary a (θ⁽¹⁾),

$a\left({\mathrm{\&theta;}}^{\left(1\right)}\right)=\&lsqb;f\left({\mathrm{\&theta;}}_1^{\left(1\right)}\right),\mathrm{...},f\left({\mathrm{\&theta;}}_p^{\left(1\right)}\right),\mathrm{...},f\left({\mathrm{\&theta;}}_g^{\left(1\right)}\right)\&rsqb;;$

Wherein,Represent withCorresponding parameterized signal model.

3. the echo-signal method for parameter estimation based on scaling dictionary as claimed in claim 2 is it is characterised in that in step s2 In, echo signal model s is rewritten as following form:

S=a (θ^(m))×(w^(m)⊙z^(m))+ε^(m)

Wherein, ⊙ represents that hadamard amasss；w^(m)For echo-signal in dictionary a (θ^(m)) coefficient vector；z^(m)For column vector, its Element number is { θ^(m)In parameter combination number, z^(m)In each element take 0 or 1；ε^(m)For carrying out the m time sparse pattra leaves The noise setting during this study；

When carrying out the m time management loading, using variational Bayesian method from a (θ^(m)) in select one or several Atom；In parameter group intersection { θ^(m)In, will be with a (θ^(m)) in the corresponding parameter combination of each atom selected retain, by it He removes parameter combination, draws parameter group intersection { θ^'(m)}；In w^(m)In, will be with a (θ^(m)) in each atom pair of selecting should Element retain, other elements are removed, draw echo-signal in dictionary a (θ^'(m)) coefficient vector w^'(m).

4. the echo-signal method for parameter estimation based on scaling dictionary as claimed in claim 3 is it is characterised in that in step s6 In, when known to number f of scattering center, using k-means clustering method pairIn all parameter combinations gathered Class, gathers for f class；From coefficient vectorIn find out and the corresponding coefficient of parameter combination gathering for kth class；Using gathering for kth class Parameter combination and corresponding coefficient, be weighted sue for peace, obtain corresponding weighting after parameter combination；Reevaluate weighting more poly- The corresponding coefficient of each parameter combination after class；

When number f of scattering center is unknown, scattering center number is attempted from 1 traversal proceeding by from small to large, until Meet the first end condition or the second end condition, then f is the current value of scattering center number；Described first end condition For:Wherein, e_aBe by weighted cluster after parameter combination and the dump energy that obtains of corresponding coefficient；Second eventually Only condition is:And