CN102645649A - Radar target recognition method based on radar target range profile time-frequency feature extraction - Google Patents

Abstract

The invention provides a radar target recognition method based on radar target range profile time-frequency feature extraction. The method comprises the steps that firstly a matching pursuit time-frequency analysis method is used for calculation to obtain a time-frequency distribution matrix of a radar target range profile; then a nonnegative matrix decomposition technique is used for decomposing the time-frequency distribution matrix to obtain the time-frequency features of a time-frequency coherent structure in the high resolution range profile (HRRP) of a radar target; and finally the radar target is recognized according to a time-frequency feature extraction scheme for the radar target range profile. The radar target recognition method based on the radar target range profile time-frequency feature extraction has the advantages that the method can be executed through computer operation, the workload of observers for radar target recognition is reduced, the improvement of radar target recognition efficiency is facilitated, the nonnegative matrix decomposition technique used in the method effectively realizes the dimension reduction of the target range profile time-frequency matrix, the time phase structure scatted by the radar target is obtained through decomposition and the operational performance and the accuracy of radar target recognition can be further improved.

Description

The radar target identification method extracted based on Radar Target Using Range Profiles time-frequency characteristics

Technical field

The invention belongs to Technology of Radar Target Identification field, more particularly to a kind of radar target identification method extracted based on Radar Target Using Range Profiles time-frequency characteristics.

Background technology

Radar target recognition is the important subject in science and techniques of defence field.It is main path to carry out radar target recognition using Radar Target Using Range Profiles, and key therein is that the validity feature of Radar Target Using Range Profiles is extracted.

Radar target recognition is the important subject in science and techniques of defence field, and carries out the main realization means that radar target recognition is radar target recognition using Radar Target Using Range Profiles.The specific method for carrying out radar target recognition using Radar Target Using Range Profiles is generally divided into two big steps：Step one, the target's feature-extraction scheme of Radar Target Using Range Profiles is determined, that is, selectes a class in Radar Target Using Range Profiles and can recognize that feature as target signature, and set up the extraction scheme of the target signature；Step 2, it regard the target signature for the Radar Target Using Range Profiles extracted according to aforementioned schemes as radar target recognition feature, carry out radar target recognition, gather the Radar Target Using Range Profiles of known radar target, the corresponding target signature of Radar Target Using Range Profiles for extracting known radar target using the extraction scheme of the target signature described in step one is as the corresponding target signature template of known radar target, then target signature to be identified is extracted to the Radar Target Using Range Profiles of radar target to be measured using the extraction scheme of the target signature described in step one again, then the target signature to be identified is matched with each target signature template, if there is the target signature template matched in the target signature to be identified, then judge that radar target to be measured known radar target corresponding with the target signature template matched belongs to similar radar target, complete radar target recognition.It can be seen that by above-mentioned radar target recognition process, how the target's feature-extraction scheme of Radar Target Using Range Profiles is determined, it is to influence a key factor of radar target recognition accuracy, if target signature itself selection is inaccurate, or target's feature-extraction process make it that extraction result is not accurate enough, can all influence the accuracy of radar target recognition.

At present, the target's feature-extraction method of common Radar Target Using Range Profiles has：(1) target signature is used as using the power spectrum of Radar Target Using Range Profiles, but power spectrum can only reflect the global information of Radar Target Using Range Profiles frequency spectrum, the local frequencies characteristic of Radar Target Using Range Profiles can not be described, cause the classification capacity of radar target recognition limited, limit the scope and accuracy of radar target recognition.(2) the scattering center amplitude of target distance image, location parameter are extracted using Relax methods and is used as target signature, but this target signature is all very sensitive to noise and radar target flicker, and noise and radar target flicker then easily influence the accuracy of radar target recognition.(3) time-frequency characteristics for extracting Radar Target Using Range Profiles using time frequency analysis are used as target signature, because Radar Target Using Range Profiles reflect the Physical Mechanism of target scattering, and the scattering physical mechanism of complex target is complex, for example in target the scattering of some parts is not limited on some time zone, and echo may be caused apart from upward extension, it is inadequate that these scattering phenomenons are described only from scattering center, and the time-frequency characteristics for taking Radar Target Using Range Profiles that Time-Frequency Analysis is extracted can effectively disclose and describe these complicated Electromagnetic Scattering Characteristics information, it is favorably improved the accuracy of radar target recognition, therefore it is particularly suitable for the target signature as Radar Target Using Range Profiles.But, the classification that the time-frequency plane distributed data of Radar Target Using Range Profiles is used for radar target recognition directly as target signature is more difficult, because the dimension of the time-frequency distributions data matrix of Radar Target Using Range Profiles is very high, directly as target signature data dimension will be caused too big, data processing is excessively complicated, and the characteristic information that wherein can be used in effectively recognizing only is distributed in a small number of local locations on time-frequency plane, and other considerable data elements are useless to target identification, therefore also need to carry out further time-frequency characteristics extraction to the time-frequency plane distributed data of Radar Target Using Range Profiles, on the one hand the characteristic information that can be used in effectively recognizing therefrom is extracted, on the other hand to reduce data dimension, from can more effectively carry out the identification of radar target.But in the prior art, extracted for the time-frequency characteristics of Radar Target Using Range Profiles, generally all by manually being extracted from being carried out on time-frequency collection of illustrative plates after identification, this manual observation identification extracting method not only takes very much, and due to the cognitive difference of different observation technology personnel, it recognizes that extraction standard is uneven, causes that the time-frequency characteristics extraction efficiency of Radar Target Using Range Profiles is low, radar target recognition accuracy is difficult to ensure that.

The content of the invention

For the above-mentioned problems in the prior art, in order to solve the problem of radar target recognition efficiency is low, accuracy is not high in the prior art, the invention provides a kind of radar target identification method extracted based on Radar Target Using Range Profiles time-frequency characteristics, the radar target identification method can be run by computer and be performed, help to reduce the workload that radar target recognition observes personnel, improve recognition efficiency, it is often more important that this method can effectively improve the accuracy of radar target recognition.

To achieve the above object, present invention employs following technological means：

The radar target identification method extracted based on Radar Target Using Range Profiles time-frequency characteristics, is comprised the following steps：

A）Set up the basic function storehouse G for including X basic function_D；Wherein any x-th of basic function G_x(t)∈G_D, its expression formula is：

$G_x\left(t\right)=\frac{1}{\sqrt{s_x}}g\left(\frac{t-p_x}{s_x}\right)\exp \left[j2(\mathrm{\π}{f}_{x}t+{\mathrm{\φ}}_x)\right];$

Wherein, t represents the time；s_x、p_x、f_xAnd φ_xX-th of basic function G is represented respectively_x(t) ratio control parameter, time-domain position control parameter, frequency parameter and phase angular dimensions；

For Gaussian function g (t) time-shifted function；

B）Extract the time-frequency characteristics of Radar Target Using Range Profiles；The step is specially：

b1）With basic function storehouse G_DIn basic function to Radar Target Using Range Profiles Θ (t) carry out match tracing decomposition, obtain its decompose expression formula：

$\mathrm{\Θ}\left(t\right)=\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{a}_i{G}_i\left(t\right)+R_I;$

Wherein, I represents the series that match tracing is decomposed, and I ＜ X, i ∈ { 1,2 ..., I }；R_IRepresent residue signals of the Radar Target Using Range Profiles Θ (t) after I grades of match tracings are decomposed；G_i(t) represent that i-stage decomposes matched basic function, and G_i(t)∈G_D；a_iRepresent the compensating factor that i-stage is decomposed, and a_i=|<R_i-1, G_i(t)>|, wherein R_i-1Residue signals of the Radar Target Using Range Profiles Θ (t) after the decomposition of (i-1) level match tracing, |<R_i-1, G_i(t)>| expression takes R_i-1With G_i(t) absolute value after inner product operation is carried out；

b2）The match tracing for taking Radar Target Using Range Profiles Θ (t) to decompose expression formula decomposes partAs the corresponding time-frequency function gammas (t) of Radar Target Using Range Profiles Θ (t), even

Ask for the time-frequency distributions function Ω (t, f) of the time-frequency function gamma (t)：

$\mathrm{\&Omega;}(t,f)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2\mathrm{WV}{G}_i(t,f)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2{\hat{g}}^2\left(s_i(f-f_i)\right)g^2\left(\frac{t-p_i}{s_i}\right);$

Wherein, f represents frequency；WVG_i(t, f) represents basic function G_i(t) Eugene Wigner-Willie distribution function；s_i、p_iAnd f_iBasic function G is represented respectively_i(t) ratio control parameter, time-domain position control parameter and frequency parameter；

For Gaussian function g (t) time-shifted function；For the time-shifted function

It is fourier transformed obtained frequency-domain function；

b3）According to Radar Target Using Range Profiles Θ (t) time domain sampling point sum N and presetting frequency domain sample point sum M, N≤M≤2N, time-frequency distributions matrix V of the corresponding dimensions of time-frequency distributions function Ω (t, f) for M rows × N row is tried to achieve_Ω(n,m)：

$V_{\mathrm{\&Omega;}}(n,m)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2\left[\begin{array}{c}{\hat{g}}^2\left(s_i(f_1-f_i)\right)\\ {\hat{g}}^2\left(s_i(f_2-f_i)\right)\\ .\\ .\\ .\\ {\hat{g}}^2\left(s_i(f_m-f_i)\right)\\ .\\ .\\ .\\ {\hat{g}}^2\left(s_i(f_M-f_i)\right)\end{array}\right]\&CenterDot;\left[\begin{array}{cccccc}{g}^2\left(\frac{t_1-p_i}{s_i}\right)& g^2\left(\frac{t_2-p_i}{s_i}\right)& ...& g^2\left(\frac{t_n-p_i}{s_i}\right)& ...& g^2\left(\frac{t_N-p_i}{s_i}\right)\end{array}\right];$

Wherein, t_nTime-frequency distributions function Ω (t, f) n-th of sampled point corresponding time in time domain of expression, n ∈ { 1,2 ..., N }；f_mRepresent time-frequency distributions function Ω (t, f) corresponding frequency of m-th of sampled point on frequency domain, m ∈ { 1,2 ..., M }；

b4）According to presetting decomposition dimension K and decomposition threshold value ε, K ＜ N, 0<ε≤10^-2, to the time-frequency distributions matrix V_Ω(n, m) carries out Non-negative Matrix Factorization, and acquisition dimension is the primitive matrix W of M rows × K row_Ω(k, m) and dimension are the coefficient matrix H of K rows × N row_Ω(n, k), makes it meet Euclidean distance square value E (W_Ω,H_Ω)<ε；The Euclidean distance square value E (W_Ω,H_Ω) represent time-frequency distributions matrix V_Ω(n, m) and matrix product W_Ω(k,m)·H_ΩSquare of Euclidean distance between (n, k), i.e.,：

E(W_Ω,H_Ω)=||V_Ω(n,m)-W_Ω(k,m)·H_Ω(n,k)||²；

Wherein, primitive matrix W_Ω(k, m) and coefficient matrix H_Ω(n, k) is nonnegative matrix；k∈{1,2,…,K}；b5）Obtain primitive matrix W_ΩEach column vector of (k, m)

And coefficient matrix H_ΩEach row vector of (n, k)k∈{1,2,…,K}；

${\stackrel{\&RightArrow;}{w}}_k\left(m\right)=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00001637365800022.png,HDA00001637365800031.png"\; state="\{\{state\}\}">w</figure-callout>}}_{1,\mathrm{<figure-callout\; id="2"\; label="k\; w"\; filenames="HDA00001637365800022.png,HDA00001637365800032.png"\; state="\{\{state\}\}">k</figure-callout>}}& \\ w_{}{}_{2,k}\\ .\\ .\\ .\\ w_{m,k}\\ .\\ .\\ .\\ w_{M,k}\end{array}\right];$

${\stackrel{\&RightArrow;}{h}}_k\left(n\right)=\left[\begin{array}{cccccc}{h}_{k,1}& h_{k,2}& ...& h_{k,n}& ...& h_{k,N}\end{array}\right];$

Wherein, w_{M, k}Represent primitive matrix W_ΩThe element that m rows kth is arranged in (k, m)；h_k,nRepresent coefficient matrix H_ΩThe element that row k n-th is arranged in (n, k)；

b6）According to presetting frequency domain character exponent number Q and temporal signatures exponent number P, primitive matrix W is calculated_Ω(k, m) each column vector

Corresponding frequency-domain sparse feature

With each rank frequency domain vector square

And coefficient matrix H_Ω(n, k) each row vector

Corresponding time domain sparse featuresWith each rank time-domain vector square

${\mathrm{SF}}_{{\stackrel{\&RightArrow;}{w}}_k}=\frac{\sqrt{M}-[\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{m,k}\right)/\sqrt{\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{w_{m,k}}^2}]}{\sqrt{M}-1};$

$W{F}_{{\stackrel{\&RightArrow;}{w}}_k}\left(q\right)=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{(m-{\mathrm{\&mu;}}_{{\stackrel{\&RightArrow;}{w}}_k})}^q{w}_{m,k};$

${\mathrm{ST}}_{{\stackrel{\&RightArrow;}{h}}_k}=\frac{\sqrt{N}-[\left(\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{h}_{k,n}\right)/\sqrt{\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{w_{k,n}}^2}]}{\sqrt{N}-1};$

$M{T}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{(n-{\mathrm{\&mu;}}_{{\stackrel{\&RightArrow;}{h}}_k})}^p{w}_{k,n}$

Wherein, k ∈ { 1,2 ..., K }；

Represent primitive matrix W_ΩThe column vector that kth is arranged in (k, m)

The frequency domain vector square of corresponding q ranks, q ∈ { 1,2 ..., Q }；Represent column vector

In each element average, i.e.,

Represent coefficient matrix H_ΩThe row vector of row k in (n, k)

The time-domain vector square of corresponding pth rank, p ∈ { 1,2 ..., P }；

Represent row vector

In each element average, i.e.,

b7）By primitive matrix W_ΩThe column vector that kth is arranged in (k, m)

Corresponding frequency-domain sparse featureWith each rank frequency domain vector square

And coefficient matrix H_ΩThe row vector of row k in (n, k)

Corresponding time domain sparse features

With each rank time-domain vector square

Set as Radar Target Using Range Profiles Θ (t) k-th of time-frequency characteristics vector ξ_k, i.e.,：

${\mathrm{\&xi;}}_k=[{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(1\right),{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(2\right),...,{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right),...,{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right),$

${\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(1\right),{\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(2\right),...,{\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(q\right),...,{\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(Q\right),;$

${\mathrm{ST}}_{{\stackrel{\&RightArrow;}{h}}_k},{\mathrm{SF}}_{{\stackrel{\&RightArrow;}{w}}_k}]$

Thus, Radar Target Using Range Profiles Θ (t) time-frequency characteristics vector sequence ζ={ ξ is obtained₁,ξ₂,…,ξ_k,…,ξ_K, and it regard the time-frequency characteristics vector sequence ζ as the time-frequency characteristics extracted from Radar Target Using Range Profiles Θ (t)；

C）Will be according to step B）The time-frequency characteristics for the Radar Target Using Range Profiles that the scheme is extracted carry out radar target recognition as radar target recognition feature.

In above-mentioned radar target identification method, further, the span for the series I that the match tracing is decomposed is 20≤I≤100.

In above-mentioned radar target identification method, further, the span for decomposing dimension K is 0.05N≤K≤0.5N.

In above-mentioned radar target identification method, further, the span of the frequency domain character exponent number Q is 1≤Q≤6；The span of the temporal signatures exponent number P is 1≤P≤6.

Compared to prior art, the present invention has the advantages that：

1st, the invention provides a kind of radar target identification method extracted based on Radar Target Using Range Profiles time-frequency characteristics, this method can be run by computer and be performed, reduce radar target recognition and observe the workload of personnel, and be favorably improved radar target recognition efficiency.

2nd, in the radar target identification method that the present invention is extracted based on Radar Target Using Range Profiles time-frequency characteristics, the Radar Target Using Range Profiles time-frequency matrix computations based on rarefaction representation have the advantages that no cross term interference, time frequency resolution are high.

3rd, in the radar target identification method that the present invention is extracted based on Radar Target Using Range Profiles time-frequency characteristics, the dimensionality reduction of target distance image time-frequency matrix is effectively realized using Non-negative Matrix Factorization, to improve operational performance；In addition, decompose the obtained basic matrix characterization vector spectrum structure of target scattering, decompose the obtained coefficient matrix characterization vector when phase structure of Radar Target Scatter, it so can effectively extract the notable feature in time-frequency matrix, the description of time-frequency characteristics and the identification of radar target are more conducive to, the accuracy of radar target recognition can be further improved.

Brief description of the drawings

The FB(flow block) for the radar target identification method that Fig. 1 is extracted for the present invention based on Radar Target Using Range Profiles time-frequency characteristics；

Fig. 2 is the optical imagery of five class radar targets in the embodiment of the present invention；

Fig. 3 is the 1st Radar Target Using Range Profiles figure in the Radar Target Using Range Profiles sequence data of a BMP2 radar target signal pattern in the embodiment of the present invention；

Fig. 4 is the 50th Radar Target Using Range Profiles figure in the Radar Target Using Range Profiles sequence data of a BMP2 radar target signal pattern in the embodiment of the present invention；

Fig. 5 is the 100th Radar Target Using Range Profiles figure in the Radar Target Using Range Profiles sequence data of a BMP2 radar target signal pattern in the embodiment of the present invention；

Fig. 6 is the time-frequency distributions Matrix Pattern of the Radar Target Using Range Profiles shown in Fig. 3；

Fig. 7 is the primitive matrix W that time-frequency distributions matrix shown in Fig. 6 is obtained through Non-negative Matrix Factorization _Ω10 column vector figures of (k, m)；

Fig. 8 is the coefficient matrix H that time-frequency distributions matrix shown in Fig. 6 is obtained through Non-negative Matrix Factorization _Ω10 row vector figures of (n, k)；

Fig. 9 is the Radar Target Using Range Profiles time-frequency characteristics distribution map of five class radar targets in the embodiment of the present invention.

Embodiment

Technical scheme is further described with reference to the accompanying drawings and examples.

The present invention proposes a kind of radar target identification method extracted based on Radar Target Using Range Profiles time-frequency characteristics, and this method is calculated using match tracing Time-Frequency Analysis Method obtain radar target HRRP first（High Resolution Range Profile, often referred to simply as radar HRRP, Radar Target Using Range Profiles）Time-frequency distributions matrix, then application Non-negative Matrix Factorization technology decompose time-frequency distributions matrix, obtain effectively reflecting the time-frequency characteristics of time-frequency coherent structure inside radar target HRRP；Finally, the time-frequency characteristics extraction scheme further according to radar target HRRP carries out radar target recognition.The radar target identification method that the present invention is extracted based on Radar Target Using Range Profiles time-frequency characteristics, the flow of this method is as shown in figure 1, specifically include following steps：

A）Set up the basic function storehouse G for including X basic function_D；Wherein any x-th of basic function G_x(t)∈G_D, its expression formula is：

$G_x\left(t\right)=\frac{1}{\sqrt{s_x}}g\left(\frac{t-p_x}{s_x}\right)\exp \left[j2(\mathrm{\&pi;}{f}_{x}t+{\mathrm{\&phi;}}_x)\right];$

Wherein, t represents the time；s_x、p_x、f_xAnd φ_xX-th of basic function G is represented respectively_x(t) ratio control parameter, time-domain position control parameter, frequency parameter and phase angular dimensions；

For Gaussian function g (t) time-shifted function.

The step is used to set up basic function storehouse, and the purpose for setting up basic function storehouse is, using the basic function in basic function storehouse, Radar Target Using Range Profiles are carried out with match tracing decomposition, is reached with the breakdown completed to Radar Target Using Range Profiles.In actual applications, basic function storehouse should be the set of complete and redundancy a basic function；Here " complete and redundancy " is it is to be understood that basic function storehouse G_DIncluded in basic function number X, from far away be more than can complete Radar Target Using Range Profiles breakdown reach required basic function number；Therefore, the foundation in basic function storehouse can constantly accumulate that the basic function included in completion, basic function storehouse is more in actual applications, be more conducive to reach the breakdown of Radar Target Using Range Profiles, should include ten hundreds of basic functions in usual basic function storehouse.And basic function is based on Gaussian function g (t), it is therefore intended that utilize the characteristics exhibit time-frequency characteristics of Gaussian function.

B）Extract the time-frequency characteristics of Radar Target Using Range Profiles.The processing procedure of the step is the important inventive point of the present invention, and its processing procedure is specially：

b1）With basic function storehouse G_DIn basic function to Radar Target Using Range Profiles Θ (t) carry out match tracing decomposition, obtain its decompose expression formula：

$\mathrm{\&Theta;}\left(t\right)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{a}_i{G}_i\left(t\right)+R_I;$

Wherein, I represents the series that match tracing is decomposed, and I ＜ X, i ∈ { 1,2 ..., I }；R_IRepresent residue signals of the Radar Target Using Range Profiles Θ (t) after I grades of match tracings are decomposed；G_i(t) represent that i-stage decomposes matched basic function, and G_i(t)∈g_D；a_iRepresent the compensating factor that i-stage is decomposed, and a_i=|<R_i-1,G_i(t)>|, wherein R_i-1Residue signals of the Radar Target Using Range Profiles Θ (t) after the decomposition of (i-1) level match tracing, |<R_i-1, G_i(t)>| expression takes R_i-1With G_i(t) absolute value after inner product operation is carried out.

The step is that the breakdown for decomposing completion Radar Target Using Range Profiles Θ (t) by match tracing reaches, and obtaining decomposition expression formula includes two parts, i.e. match tracing decomposition partWith residual signal section R_IAs long as the series I that match tracing is decomposed is sufficiently large, it becomes possible to the main time-frequency coherent structure in Radar Target Using Range Profiles is decomposed into match tracing and decomposes part

In, and residue signal R_IRandom noise or clutter can then be regarded as, wherein enough time-frequency localization properties are not embodied, can be in follow-up time-frequency sign extraction process residue signal R_IIgnore.In order to obtain such discomposing effect, the series I that match tracing is decomposed should be at least 20 grades, and the series more at most discomposing effect that match tracing is decomposed is better；But if the series that match tracing is decomposed is excessive, such as more than 100 grades after, the decomposition technique that the lifting of discomposing effect is just less obvious and excessive can increase data processing amount；Therefore, the preferred span for the series I that match tracing is decomposed is 20≤I≤100.It is existing ripe algorithm as match tracing decomposition method, its detailed process is just repeated no more herein.

b2）The match tracing for taking Radar Target Using Range Profiles Θ (t) to decompose expression formula decomposes part

As the corresponding time-frequency function gammas (t) of Radar Target Using Range Profiles Θ (t), even

Ask for the time-frequency distributions function Ω (t, f) of the time-frequency function gamma (t)：

$\mathrm{\&Omega;}(t,f)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2\mathrm{WV}{G}_i(t,f)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2{\hat{g}}^2\left(s_i(f-f_i)\right)g^2\left(\frac{t-p_i}{s_i}\right);$

Wherein, f represents frequency；WVG_i(t, f) represents basic function G_i(t) Eugene Wigner-Willie distribution function；s_i、p_iAnd f_iBasic function G is represented respectively_i(t) ratio control parameter, time-domain position control parameter and frequency parameter；

For Gaussian function g (t) time-shifted function；

For the time-shifted functionIt is fourier transformed obtained frequency-domain function.

In the step, because the match tracing that Radar Target Using Range Profiles decompose expression formula decomposes part

Contain the main time-frequency coherent structure in Radar Target Using Range Profiles, therefore using the part is as time-frequency function gamma (t) and carries out Eugene Wigner-Willie and is distributed, to obtain time-frequency distributions function Ω (t, f).The characteristic being distributed according to Eugene Wigner-Willie, is distributed WVg (t, f) for Gaussian function g (t) Eugene Wigner-Willie, is a two-dimensional Gaussian function, i.e.,

It is therein

For Gaussian function g (t) Fourier transform function；It can thus be concluded that, basic function G_i(t) Eugene Wigner-Willie distribution function WVG_i(t,f)：

${\mathrm{WVG}}_i(t,f)={\hat{g}}^2\left(s_i(f-f_i)\right)g^2\left(\frac{1-p_i}{s_i}\right);$

And then, thus obtain time-frequency distributions function Ω (t, f) expression formula.

b3）According to Radar Target Using Range Profiles Θ (t) time domain sampling point sum N and presetting frequency domain sample point sum M, N≤M≤2N, time-frequency distributions matrix V of the corresponding dimensions of time-frequency distributions function Ω (t, f) for M rows × N row is tried to achieve_Ω(n,m)：

$V_{\mathrm{\&Omega;}}(n,m)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2\left[\begin{array}{c}{\hat{g}}^2\left(s_i(f_1-f_i)\right)\\ {\hat{g}}^2\left(s_i(f_2-f_i)\right)\\ .\\ .\\ .\\ {\hat{g}}^2\left(s_i(f_m-f_i)\right)\\ .\\ .\\ .\\ {\hat{g}}^2\left(s_i(f_M-f_i)\right)\end{array}\right]\&CenterDot;\left[\begin{array}{cccccc}{g}^2\left(\frac{t_1-p_i}{s_i}\right)& g^2\left(\frac{t_2-p_i}{s_i}\right)& ...& g^2\left(\frac{t_n-p_i}{s_i}\right)& ...& g^2\left(\frac{t_N-p_i}{s_i}\right)\end{array}\right];$

Wherein, t_nTime-frequency distributions function Ω (t, f) n-th of sampled point corresponding time in time domain of expression, n ∈ { 1,2 ..., N }；f_mRepresent time-frequency distributions function Ω (t, f) corresponding frequency of m-th of sampled point on frequency domain, m ∈ { 1,2 ..., M }.

In theory, Radar Target Using Range Profiles Θ (t) can be considered as the continuous function using time t as variable, but when being gathered by using instrument and obtaining Radar Target Using Range Profiles, the Radar Target Using Range Profiles data obtained are actually the discrete function in time-domain sampling, therefore under conditions of the fixation of time-domain sampling frequency, the Radar Target Using Range Profiles Θ (t) in certain time has its certain time domain sampling point sum N.Correspondingly, frequency domain sample is also such, it is therefore desirable to presetting frequency domain sample point sum M, it is desirable to N≤M≤2N, to obtain time-frequency distributions matrix V of the corresponding dimensions of time-frequency distributions function Ω (t, f) as M rows × N row_Ω(n,m).Certainly, if in order to reduce time-frequency distributions matrix V_ΩThe data volume of (n, m) so that computing is easier, can take minimum M=N of frequency domain sample point sum.

b4）According to presetting decomposition dimension K and decomposition threshold value ε, K ＜ N, 0<ε≤10^-2, to the time-frequency distributions matrix V_Ω(n, m) carries out Non-negative Matrix Factorization, and acquisition dimension is the primitive matrix W of M rows × K row_Ω(k, m) and dimension are the coefficient matrix H of K rows × N row_Ω(n, k), makes it meet Euclidean distance square value E (W_Ω,H_Ω)<ε；The Euclidean distance square value E (W_Ω,H_Ω) represent time-frequency distributions matrix V_Ω(n, m) and matrix product W_Ω(k,m)·H_ΩSquare of Euclidean distance between (n, k), i.e.,：

E(W_Ω,H_Ω)=||V_Ω(n,m)-W_Ω(k,m)·H_Ω(n,k)||²；

Wherein, primitive matrix W_Ω(k, m) and coefficient matrix H_Ω(n, k) is nonnegative matrix；k∈{1,2,…,K}.

The step uses the processing mode of Non-negative Matrix Factorization, to reduce time-frequency distributions matrix V_ΩThe dimension of (n, m).The dreamboat of Non-negative Matrix Factorization is by time-frequency distributions matrix V_Ω(n, m) is decomposed into the product of two nonnegative matrixes, that is, reaches：

V_Ω(n,m)=W′(k,m)·H′(n,k)；

Wherein, matrix W ' (k, m) it is the nonnegative matrix of M rows × K row, matrix H ' (n, k) it is the nonnegative matrix of K rows × N row, mathematical expression that thus then can be by dimension using N as radix is converted into mathematical expression of the dimension using K as radix, and K ＜ N, so as to reach the purpose of dimensionality reduction, to improve the operational performance of the inventive method.Meanwhile, the matrix decomposition process is also the decomposable process of time-frequency coherent structure；Matrix W ' (k, m) of M rows × K row obtained by decomposition can be expressed as column vector set, and matrix H ' (n, k) of K rows × N row can be expressed as row vector set, i.e.,：

$W^{\&prime;\&prime;}(k,m)=[{\stackrel{\&RightArrow;}{w}}_1^{\&prime;}\left(m\right),{\stackrel{\&RightArrow;}{w}}_2^{\&prime;}\left(m\right),...,{\stackrel{\&RightArrow;}{w}}_k^{\&prime;}\left(m\right),...,{\stackrel{\&RightArrow;}{w}}_K^{\&prime;}\left(m\right)];$

$H^{\&prime;}(n,k)==\left[\begin{array}{c}{\stackrel{\&RightArrow;}{h}}_1^{\&prime;}\left(n\right)\\ {\stackrel{\&RightArrow;}{h}}_2^{\&prime;}\left(n\right)\\ .\\ .\\ .\\ {\stackrel{\&RightArrow;}{h}}_k^{\&prime;}\left(n\right)\\ .\\ .\\ .\\ {\stackrel{\&RightArrow;}{h}}_K^{\&prime;}\left(n\right)\end{array}\right];$

Wherein,

The column vector that kth is arranged in representing matrix W ' (k, m),

The row vector of row k in representing matrix H ' (n, k), k ∈ { 1,2 ..., K }；Matrix W ' (k, m) each column vector

Then illustrate time-frequency distributions matrix V_ΩThe frequency structure feature of a time-frequency component in (n, m), and each row vector in matrix H ' (n, k)

Then illustrate time-frequency distributions matrix V_ΩThe time structure feature of a time-frequency component in (n, m), therefore matrix W ' (k, m) can be referred to as primitive matrix, matrix H ' (n, k) is referred to as coefficient matrix；And time-frequency component is divided into K, the more big then time-frequency component of value for decomposing dimension K divides thinner, therefore the expression of time-frequency coherent structure is also more careful, is more conducive to the description of time-frequency characteristics and the identification of radar target, but decomposition dimension K value is excessive, does not reach obvious dimensionality reduction purpose；Therefore composite factor considers, it is 0.05N≤K≤0.5N to decompose the preferred spans of dimension K.However, in actual applications, it is difficult to find the dreamboat V that two nonnegative matrixes meet Non-negative Matrix Factorization_Ω(n, m)=W ' (k, m) H ' (n, k), is merely able to ask for primitive matrix W of the dimension for M rows × K row as far as possible_Ω(k, m) and dimension are the coefficient matrix H of K rows × N row_Ω(n, k), primitive matrix W_Ω(k, m) and coefficient matrix H_Ω(n, k) is nonnegative matrix, is allowed to meet V_Ω(n,m)≈W_Ω(k,m)·H_Ω(n, k), the criterion being approximately equal to for satisfaction, present invention employs Euclidean distance square value E (W_Ω,H_Ω) judge, the Euclidean distance square value E (W_Ω,H_Ω) represent time-frequency distributions matrix V_Ω(n, m) and matrix product W_Ω(k,m)·H_ΩSquare of Euclidean distance between (n, k), if Euclidean distance square value E (W_Ω,H_Ω) sufficiently small, so that less than presetting decomposition threshold value ε, 0<ε<10^-2, that is, meet E (W_Ω,H_Ω)<ε, then it is assumed that the primitive matrix W now obtained_Ω(k, m) and coefficient matrix H_Ω(n, k) meets the requirement of Non-negative Matrix Factorization；So as to obtain primitive matrix W_ΩThe column vector aggregate expression and coefficient matrix H of (k, m)_ΩThe row vector aggregate expression of (n, k)：

$W_{\mathrm{\&Omega;}}(k,m)=[{\stackrel{\&RightArrow;}{w}}_1\left(m\right),{\stackrel{\&RightArrow;}{w}}_2\left(m\right),...,{\stackrel{\&RightArrow;}{w}}_k\left(m\right),...,{\stackrel{\&RightArrow;}{w}}_K\left(m\right)];$

$H_{\mathrm{\&Omega;}}(n,k)==\left[\begin{array}{c}{\stackrel{\&RightArrow;}{h}}_1^{\&prime;}\left(n\right)\\ {\stackrel{\&RightArrow;}{h}}_2^{\&prime;}\left(n\right)\\ .\\ .\\ .\\ {\stackrel{\&RightArrow;}{h}}_k^{\&prime;}\left(n\right)\\ .\\ .\\ .\\ {\stackrel{\&RightArrow;}{h}}_K^{\&prime;}\left(n\right)\end{array}\right].$

Wherein,

Represent primitive matrix W_ΩThe column vector that kth is arranged in (k, m),

Represent coefficient matrix H_ΩThe row vector of row k in (n, k), k ∈ { 1,2 ..., K }.As for primitive matrix W_Ω(k, m) and coefficient matrix H_ΩThe Non-negative Matrix Factorization acquiring method of (n, k), primitive matrix W can be generally set at random_Ω(k, m) and coefficient matrix H_ΩThe initial value of (n, k) is iterated computing（Also can be according to the self-defined setting initial value of data characteristicses, to improve iteration efficiency）, the Projected bound constrained optimization algorithm that iterative process can be proposed using Lin（Refer to document " Lin C J.Projected gradient methods for non-negative matrix factorization [J] .Neural Computing, 2007,19 (10):2756-2779.”）, each iteration judges whether to meet E (W_Ω,H_Ω)<ε, continues iteration if being unsatisfactory for, until terminating iteration when meeting, obtains primitive matrix W_Ω(k, m) and coefficient matrix H_ΩThe decomposition result of (n, k)；It is ripe prior art between Non-negative Matrix Factorization, the concrete operation process and its iterative process no longer to Non-negative Matrix Factorization are described in detail herein.

b5）Obtain primitive matrix W_ΩEach column vector of (k, m)

And coefficient matrix H_ΩEach row vector of (n, k)k∈{1,2,…,K}；

${\stackrel{\&RightArrow;}{w}}_k\left(m\right)=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00001637365800022.png,HDA00001637365800031.png"\; state="\{\{state\}\}">w</figure-callout>}}_{1,\mathrm{<figure-callout\; id="2"\; label="k\; w"\; filenames="HDA00001637365800022.png,HDA00001637365800032.png"\; state="\{\{state\}\}">k</figure-callout>}}& \\ w_{}{}_{2,k}\\ .\\ .\\ .\\ w_{m,k}\\ .\\ .\\ .\\ w_{M,k}\end{array}\right];$

${\stackrel{\&RightArrow;}{h}}_k\left(n\right)=\left[\begin{array}{cccccc}{h}_{k,1}& h_{k,2}& ...& h_{k,n}& ...& h_{k,N}\end{array}\right];$

Wherein, w_{M, k}Represent primitive matrix W_ΩThe element that m rows kth is arranged in (k, m)；h_k,nRepresent coefficient matrix H_ΩThe element that row k n-th is arranged in (n, k).

In the step, primitive matrix W is obtained_ΩEach column vector of (k, m)And coefficient matrix H_ΩEach row vector of (n, k)

That is, obtaining time-frequency distributions matrix V_ΩThe frequency structure feature and time structure feature of the time-frequency component of each in (n, m), therefore can be by primitive matrix W_ΩEach column vector in (k, m)

Regard a frequency domain character vector as, by coefficient matrix H_ΩEach row vector in (n, k)Regard a temporal signatures vector as.And the transient components and continuous component that the moment of a vector of frequency domain character vector sum temporal signatures vector then then can be used in discriminating Radar Target Using Range Profiles containing the information for being described joint time-frequency plane square, the vectorial sparse features of frequency domain character vector sum temporal signatures.Therefore, primitive matrix W is next asked for_Ω(k, m) each column vector

And coefficient matrix H_Ω(n, k) each row vector

Corresponding sparse features and multistage moment of a vector, and in this, as the time-frequency characteristics that extraction is obtained from Radar Target Using Range Profiles Θ (t).

b6）According to presetting frequency domain character exponent number Q and temporal signatures exponent number P, primitive matrix W is calculated_Ω(k, m) each column vector

Corresponding frequency-domain sparse feature

With each rank frequency domain vector square

And coefficient matrix H_Ω(n, k) each row vector

Corresponding time domain sparse features

With each rank time-domain vector square

${\mathrm{SF}}_{{\stackrel{\&RightArrow;}{w}}_k}=\frac{\sqrt{M}-[\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{m,k}\right)/\sqrt{\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{w_{m,k}}^2}]}{\sqrt{M}-1};$

$M{F}_{{\stackrel{\&RightArrow;}{w}}_k}\left(q\right)=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{(m-{\mathrm{\&mu;}}_{{\stackrel{\&RightArrow;}{w}}_k})}^q{w}_{m,k};$

${\mathrm{ST}}_{{\stackrel{\&RightArrow;}{h}}_k}=\frac{\sqrt{N}-[\left(\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{h}_{k,n}\right)/\sqrt{\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{w_{k,n}}^2}]}{\sqrt{N}-1};$

$M{T}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{(n-{\mathrm{\&mu;}}_{{\stackrel{\&RightArrow;}{h}}_k})}^p{h}_{k,n}$

Wherein, k ∈ { 1,2 ..., K }；

Represent primitive matrix W_ΩThe column vector that kth is arranged in (k, m)

The frequency domain vector square of corresponding q ranks, q ∈ { 1,2 ..., Q }；Represent column vectorIn each element average, i.e.,

Represent coefficient matrix H_ΩThe row vector of row k in (n, k)

The time-domain vector square of corresponding pth rank, p ∈ { 1,2 ..., P }；

Represent row vectorIn each element average, i.e.,

Frequency domain character exponent number Q and temporal signatures exponent number P is set in the step, primarily to improving time-frequency characteristics identification composition using multistage moment of a vector to a certain extent, therefore frequency domain character exponent number Q and temporal signatures exponent number P value is all unsuitable excessive, to avoid blindly increasing time-frequency characteristics data dimension；Under normal circumstances, frequency domain character exponent number Q preferred span is 1≤Q≤6, and temporal signatures exponent number P preferred span is 1≤P≤6, and the two can respective independent value.

b7）By primitive matrix W_ΩThe column vector that kth is arranged in (k, m)

Corresponding frequency-domain sparse featureWith each rank frequency domain vector square

And coefficient matrix H_ΩThe row vector of row k in (n, k)

Corresponding time domain sparse features

With each rank time-domain vector square

Set as Radar Target Using Range Profiles Θ (t) k-th of time-frequency characteristics vector ξ_k, i.e.,：

${\mathrm{\&xi;}}_k=[{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(1\right),{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(2\right),...,{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right),...{,\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right),$

${\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(1\right),{\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(2\right),...,{\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(q\right),...,{\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(Q\right),;$

${\mathrm{ST}}_{{\stackrel{\&RightArrow;}{h}}_k}{\mathrm{SF}}_{{\stackrel{\&RightArrow;}{w}}_k}]$

Thus, Radar Target Using Range Profiles Θ (t) time-frequency characteristics vector sequence ζ={ ξ is obtained₁,ξ₂,…,ξ_k,…,ξ_K, and it regard the time-frequency characteristics vector sequence ζ as the time-frequency characteristics extracted from Radar Target Using Range Profiles Θ (t).

So far, step B）Processing procedure be to be accomplished, the time-frequency characteristics extraction scheme of Radar Target Using Range Profiles has been thereby determined that, also that is, establishing the corresponding time-frequency characteristics model of Radar Target Using Range Profiles.

C）Will be according to step B）The time-frequency characteristics for the Radar Target Using Range Profiles that the scheme is extracted carry out radar target recognition as radar target recognition feature.Specifically, the common handling process of the step is the Radar Target Using Range Profiles of known radar target to be gathered, using step B）The scheme extracts the time-frequency characteristics of the Radar Target Using Range Profiles of known radar target and in this, as the corresponding time-frequency characteristics template of known radar target；Then for the Radar Target Using Range Profiles of radar target to be measured, also using using step B）The scheme extracts the time-frequency characteristics to be identified of the Radar Target Using Range Profiles of radar target to be measured, then the time-frequency characteristics to be identified are matched with each time-frequency characteristics template, if there is the time-frequency characteristics template matched in the time-frequency characteristics to be identified, then judge that radar target to be measured known radar target corresponding with the time-frequency characteristics template matched belongs to similar radar target, that is, complete radar target recognition.It is then very many in the adoptable existing ripe algorithm of computer match cognization process, it will not enumerate herein.

Thus, the invention provides a kind of radar target identification method extracted based on Radar Target Using Range Profiles time-frequency characteristics, this method can be run by computer and be performed, and reduce radar target recognition and observe the workload of personnel, and be favorably improved radar target recognition efficiency.

Technical scheme is further described below by embodiment.

Embodiment：

The present embodiment is using radar target identification method of the invention, and the five class radar targets published to MSTAR companies are identified.This five classes radar target is ground military vehicle, and its radar target code name is respectively BMP2_SN9563, BTR70_SNC71, T72_SN132, D7, ZSU23_4（Hereinafter for sake of convenience, this radar target code name is referred to as BMP2, BTR70, T72, D7, ZSU23 respectively）, the optical imagery of five class radar targets is respectively as in Fig. 2（2a）~（2e）Shown, wherein BMP2 is infantry fighting vehicles, and BTR70 is armored personnel carrier, and T72 is tank, and D7 is bull-dozer, and ZSU23 is ack-ack.Radar target signal is a kind of complex image data for containing amplitude and phase, Radar Target Using Range Profiles sequence data can be converted into by a series of filtering transformation calculation process, include in each Radar Target Using Range Profiles sequence data by several evenly distributed Radar Target Using Range Profiles of the order of azimuth size, the quantity of included Radar Target Using Range Profiles determines that each Radar Target Using Range Profiles characterize distance feature of the radar target on an azimuth position according to filtering transformation calculation process process.For example, BMP2 radar targets signal and image processing is comprising 100 azimuthal Radar Target Using Range Profiles sequence datas, the 1st, the 50th and the 100th Radar Target Using Range Profiles are respectively as shown in Fig. 3~Fig. 5 in the Radar Target Using Range Profiles sequence data.Feature extraction is carried out to these Radar Target Using Range Profiles, you can radar target is identified according to the feature of extraction.Below by the present embodiment, concrete application process and technique effect to radar target identification method of the present invention are further detailed.

A）Set up the basic function storehouse G for including X basic function_D。

The basic function storehouse G for including 66612 basic functions is constructed in the present embodiment_D（That is X=66612）, it is constituted complete and redundancy a basic function storehouse.

B）Extract the time-frequency characteristics of Radar Target Using Range Profiles.

The time-frequency characteristics of Radar Target Using Range Profiles are extracted using the inventive method.By taking the Radar Target Using Range Profiles shown in Fig. 3 as an example, the process for extracting its time-frequency characteristics is as follows：By step b1）, with basic function storehouse G_DIn basic function to shown in Fig. 3 Radar Target Using Range Profiles carry out match tracing decomposition, decomposed class be 100 grades（Take I=100）, obtain it and decompose expression formula；Then step b2 is pressed）, the match tracing for taking the Radar Target Using Range Profiles to decompose expression formula decomposes part as the corresponding time-frequency function of the Radar Target Using Range Profiles, and asks for the time-frequency distributions function Ω (t, f) of the time-frequency function；Because the sampling number of the Radar Target Using Range Profiles shown in Fig. 3 is 100（That is N=100）, presetting frequency domain sample point sum M=100 in the present embodiment, therefore by step b3）, try to achieve the time-frequency distributions matrix V that the corresponding dimension of above-mentioned time-frequency distributions function Ω (t, f) arranges for 100 rows × 100_Ω(n, m), its time-frequency distributions matrix V_ΩThe figure of (n, m) is as shown in Figure 6；Presetting decomposition dimension K=10 and decomposition threshold value ε=10 in the present embodiment^-2, therefore step b4 is pressed again）, to the time-frequency distributions matrix V_Ω(n, m) carries out Non-negative Matrix Factorization, and acquisition dimension is the primitive matrix W that 100 rows × 10 are arranged_Ω(k, m) and dimension are the coefficient matrix H that 10 rows × 100 are arranged_Ω(n, k), and by step b5）Obtain primitive matrix W_Ω10 column vectors of (k, m)And coefficient matrix H_Ω10 row vectors of (n, k)

Wherein primitive matrix W_Ω10 column vectors of (k, m) are as shown in fig. 7, coefficient matrix H_Ω10 row vector figures of (n, k) are as shown in Figure 8；Presetting frequency domain character exponent number Q=6 and temporal signatures exponent number P=6 in the present embodiment, therefore by step b6）Calculate primitive matrix W_Ω(k, m) each column vector

Corresponding frequency-domain sparse feature

With 6 rank frequency domain vector squaresAnd coefficient matrix H_Ω(n, k) each row vectorCorresponding time domain sparse features

With 6 rank time-domain vector squares

So as to by step b7）The time-frequency characteristics vector sequence of the Radar Target Using Range Profiles shown in Fig. 3 is obtained, and regard it as the time-frequency characteristics extracted from the Radar Target Using Range Profiles shown in Fig. 3.

According to step B in the present invention）The method for extracting the time-frequency characteristics of Radar Target Using Range Profiles, the Radar Target Using Range Profiles time-frequency characteristics of the class radar target of BMP2, BTR70, T72, D7, ZSU23 five in the present embodiment are extracted respectively, and the Radar Target Using Range Profiles time-frequency characteristics distribution situation for finally obtaining the five classes radar target is as shown in Figure 9；As it can be seen in figure 9 that according to step B in the present invention）The time-frequency characteristics of extraction, its similar clarification of objective aggregation and inhomogeneity clarification of objective separation property are all very good, can be good at the identification for radar target.

C）Will be according to step B）The time-frequency characteristics for the Radar Target Using Range Profiles that the scheme is extracted carry out radar target recognition as radar target recognition feature.

The present embodiment is in identification process, for the class radar target of BMP2, BTR70, T72, D7, ZSU23 five, 233 BMP2 training samples, 233 BTR70 training samples, 232 T72 training samples, 233 D7 training samples, 234ZSU23 training sample are acquired respectively as five class known radar target unions and obtains its Radar Target Using Range Profiles, and use step B of the present invention）Scheme be extracted the time-frequency characteristics of these known radar target distance images and in this, as the corresponding time-frequency characteristics template of known radar target；Then, each class for above-mentioned five classes radar target acquires 196 test samples as radar target union to be measured and obtains its Radar Target Using Range Profiles, using step B of the present invention）Scheme extract radar target to be measured Radar Target Using Range Profiles time-frequency characteristics to be identified；Then, the present embodiment uses HMM classification and identification algorithm, the HMM of each time-frequency characteristics template and time-frequency characteristics to be identified is set up respectively, then time-frequency characteristics to be identified and each time-frequency characteristics template are carried out matching Classification and Identification, hidden status number is 120 in each HMM, and Gaussian mixture number is 6；If the class radar target of BMP2, BTR70, T72, D7, ZSU23 five is referred to as into the 1st class, the 2nd class, the 3rd class, the 4th class, the 5th class radar target, d is made_{I, j}Represent the number that the i-th class testing specimen discerning is jth class radar target, i ∈ { 1,2,3,4,5 }, j ∈ { 1,2,3,4,5 }；Make P_ciRepresent the correct recognition rata of the i-th class radar target, P_ci=d_ii/(d_i1+d_i2+…+d_i5)×100%；Separately

Represent average recognition rate,

Thus, the recognition result for obtaining all kinds of radar target test samples is as shown in table 1：

Table 1

It can see, radar target recognized from the recognition result shown in table 1 using the inventive method combination HMM classification and identification algorithm, correct recognition rata has most preferably reached 98.47%, and average recognition rate can reach 97.55%, and recognition effect is very good.

In order to be contrasted, the present embodiment additionally uses another radar target identification method and respective 196 test samples of above-mentioned five kinds of radar targets is identified, in the radar target identification method as a comparison, using Principal Component Analysis Algorithm（Principal Component Analysis Algorithm is statement algorithm of the prior art, refer to document " Behnaz G.; Sridhar K.Quantifcation and localization of features in time-frequency plane [C] .Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering; May 4-7,2008. "）The time-frequency characteristics of Radar Target Using Range Profiles are extracted, then equally carrying out hidden status number in radar target recognition, each HMM according to the time-frequency characteristics of extraction using HMM classification and identification algorithm again is similarly 120, and Gaussian mixture number is similarly 6；The radar target identification method as a comparison, its time-frequency feature extraction scheme is different from the present invention, and classification and identification algorithm is identical with the embodiment that above-mentioned use the present invention program in the present embodiment carries out radar target recognition, thus influence of the more different frequency feature extraction schemes to radar target recognition result.Above-mentioned 233 BMP2 training samples, 233 BTR70 training samples, 232 T72 training samples, 233 D7 training samples, 234ZSU23 training sample is equally respectively adopted as five class known radar target unions and obtains its Radar Target Using Range Profiles, 196 test samples respective to five kinds of radar targets are identified, and the recognition result of the radar target identification method as a comparison is as shown in table 2：

Table 2

Contrast is carried out by table 2 and table 1 it can be seen that, in classification and identification algorithm under the same conditions, the correct recognition rata most preferably 86.22% of the radar target identification method as a comparison is low compared with the method for the present invention by 12.25%；It is low compared with the method for the present invention by 13.78% and average recognition rate is 83.77%.Because the principal component analysis feature of time-frequency plane is merely with Global Information, and obtained time-frequency characteristics are extracted based on the inventive method and have then fully excavated the time partial structurtes and frequency spectrum partial structurtes characteristic information of signal, therefore can further improve the accuracy of radar target recognition.

What is finally illustrated is, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although the present invention is described in detail with reference to preferred embodiment, it will be understood by those within the art that, technical scheme can be modified or equivalent substitution, without departing from the objective and scope of technical solution of the present invention, it all should cover among scope of the presently claimed invention.

Claims (4)

1. the radar target identification method extracted based on Radar Target Using Range Profiles time-frequency characteristics, it is characterised in that comprise the following steps：

A）Set up the basic function storehouse G for including X basic function_D；Wherein any x-th of basic function G_x(t)∈G_D, its expression formula is：

$G_x\left(t\right)=\frac{1}{\sqrt{s_x}}g\left(\frac{t-p_x}{s_x}\right)\exp \left[j2(\mathrm{\&pi;}{f}_{x}t+{\mathrm{\&phi;}}_x)\right];$

Wherein, t represents the time；s_x、p_x、f_xAnd φ_xX-th of basic function G is represented respectively_x(t) ratio control parameter, time-domain position control parameter, frequency parameter and phase angular dimensions；For Gaussian function g (t) time-shifted function；

B）Extract the time-frequency characteristics of Radar Target Using Range Profiles；The step is specially：

b1）With basic function storehouse G_DIn basic function to Radar Target Using Range Profiles Θ (t) carry out match tracing decomposition, obtain its decompose expression formula：

$\mathrm{\&Theta;}\left(t\right)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{a}_i{G}_i\left(t\right)+R_I;$

Wherein, I represents the series that match tracing is decomposed, and I ＜ X, i ∈ { 1,2 ..., I }；R_IRepresent residue signals of the Radar Target Using Range Profiles Θ (t) after I grades of match tracings are decomposed；G_i(t) represent that i-stage decomposes matched basic function, and G_i(t)∈G_D；a_iRepresent the compensating factor that i-stage is decomposed, and a_i=|<R_i-1,G_i(t)>|, wherein R_i-1Residue signals of the Radar Target Using Range Profiles Θ (t) after the decomposition of (i-1) level match tracing, |<R_i-1, G_i(t)>| expression takes R_i-1With G_i(t) absolute value after inner product operation is carried out；

b2）The match tracing for taking Radar Target Using Range Profiles Θ (t) to decompose expression formula decomposes partAs the corresponding time-frequency function gammas (t) of Radar Target Using Range Profiles Θ (t), even

Ask for the time-frequency distributions function Ω (t, f) of the time-frequency function gamma (t)：

$\mathrm{\&Omega;}(t,f)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2\mathrm{WV}{G}_i(t,f)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2{\hat{g}}^2\left(s_i(f-f_i)\right)g^2\left(\frac{t-p_i}{s_i}\right);$

Wherein, f represents frequency；WVG_i(t, f) represents basic function G_i(t) Eugene Wigner-Willie distribution function；s_i、p_iAnd f_iBasic function G is represented respectively_i(t) ratio control parameter, time-domain position control parameter and frequency parameter；

For Gaussian function g (t) time-shifted function；

For the time-shifted function

It is fourier transformed obtained frequency-domain function；

b3）According to Radar Target Using Range Profiles Θ (t) time domain sampling point sum N and presetting frequency domain sample point sum M, N≤M≤2N, time-frequency distributions matrix V of the corresponding dimensions of time-frequency distributions function Ω (t, f) for M rows × N row is tried to achieve_Ω(n,m)：

$V_{\mathrm{\&Omega;}}(n,m)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\left|a_i\right|}^2\left[\begin{array}{c}{\hat{g}}^2\left(s_i(f_1-f_i)\right)\\ {\hat{g}}^2\left(s_i(f_2-f_i)\right)\\ .\\ .\\ .\\ {\hat{g}}^2\left(s_i(f_m-f_i)\right)\\ .\\ .\\ .\\ {\hat{g}}^2\left(s_i(f_M-f_i)\right)\end{array}\right]\&CenterDot;\left[\begin{array}{cccccc}{g}^2\left(\frac{t_1-p_i}{s_i}\right)& g^2\left(\frac{t_2-p_i}{s_i}\right)& ...& g^2\left(\frac{t_n-p_i}{s_i}\right)& ...& g^2\left(\frac{t_N-p_i}{s_i}\right)\end{array}\right];$

Wherein, t_nTime-frequency distributions function Ω (t, f) n-th of sampled point corresponding time in time domain of expression, n ∈ { 1,2 ..., N }；f_mRepresent time-frequency distributions function Ω (t, f) corresponding frequency of m-th of sampled point on frequency domain, m ∈ { 1,2 ..., M }；

b4）According to presetting decomposition dimension K and decomposition threshold value ε, K ＜ N, 0<ε≤10^-2, to the time-frequency distributions matrix V_Ω(n, m) carries out Non-negative Matrix Factorization, and acquisition dimension is the primitive matrix W of M rows × K row_Ω(k, m) and dimension are the coefficient matrix H of K rows × N row_Ω(n, k), makes it meet Euclidean distance square value E (W_Ω,H_Ω)<ε；The Euclidean distance square value E (W_Ω,H_Ω) represent time-frequency distributions matrix V_Ω(n, m) and matrix product W_Ω(k,m)·H_ΩSquare of Euclidean distance between (n, k), i.e.,：

E(W_Ω,H_Ω)=||V_Ω(n,m)-W_Ω(k,m)·H_Ω(n,k)||²；

Wherein, primitive matrix W_Ω(k, m) and coefficient matrix H_Ω(n, k) is nonnegative matrix；k∈{1,2,…,K}；

b5）Obtain primitive matrix W_ΩEach column vector of (k, m)

And coefficient matrix H_ΩEach row vector of (n, k)

k∈{1,2,…,K}；

${\stackrel{\&RightArrow;}{w}}_k\left(m\right)=\left[\begin{array}{c}{w}_{1,k}\\ w_{2,k}\\ .\\ .\\ .\\ w_{m,k}\\ .\\ .\\ .\\ w_{M,k}\end{array}\right];$

${\stackrel{\&RightArrow;}{h}}_k\left(n\right)=\left[\begin{array}{cccccc}{h}_{k,1}& h_{k,2}& ...& h_{k,n}& ...& h_{k,N}\end{array}\right];$

Wherein, w_{M, k}Represent primitive matrix W_ΩThe element that m rows kth is arranged in (k, m)；h_k,nRepresent coefficient matrix H_ΩThe element that row k n-th is arranged in (n, k)；

B6) according to presetting frequency domain character exponent number Q and temporal signatures exponent number P, primitive matrix W is calculated_Ω(k, m) each column vectorCorresponding frequency-domain sparse featureWith each rank frequency domain vector square

And coefficient matrix H_Ω(n, k) each row vector

Corresponding time domain sparse features

With each rank time-domain vector square

${\mathrm{SF}}_{{\stackrel{\&RightArrow;}{w}}_k}=\frac{\sqrt{M}-[\left(\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{m,k}\right)/\sqrt{\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{w_{m,k}}^2}]}{\sqrt{M}-1};$

$W{F}_{{\stackrel{\&RightArrow;}{w}}_k}\left(q\right)=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{(m-{\mathrm{\&mu;}}_{{\stackrel{\&RightArrow;}{w}}_k})}^q{w}_{m,k};$

${\mathrm{ST}}_{{\stackrel{\&RightArrow;}{h}}_k}=\frac{\sqrt{N}-[\left(\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{h}_{k,n}\right)/\sqrt{\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{w_{k,n}}^2}]}{\sqrt{N}-1};$

$M{T}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{(n-{\mathrm{\&mu;}}_{{\stackrel{\&RightArrow;}{h}}_k})}^p{w}_{k,n};$

Wherein, k ∈ { 1,2 ..., K }；

Represent primitive matrix W_ΩThe column vector that kth is arranged in (k, m)

The frequency domain vector square of corresponding q ranks, q ∈ { 1,2 ..., Q }；

Represent column vector

In each element average, i.e.,

Represent coefficient matrix H_ΩThe row vector of row k in (n, k)

The time-domain vector square of corresponding pth rank, p ∈ { 1,2 ..., P }；Represent row vector

In each element average, i.e.,

B7) by primitive matrix W_ΩThe column vector that kth is arranged in (k, m)

Corresponding frequency-domain sparse feature

With each rank frequency domain vector square

And coefficient matrix H_ΩThe row vector of row k in (n, k)

Corresponding time domain sparse features

With each rank time-domain vector square

Set as Radar Target Using Range Profiles Θ (t) k-th of time-frequency characteristics vector ξ_k, i.e.,：

${\mathrm{\&xi;}}_k=[{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(1\right),{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(2\right),...,{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right),...,{\mathrm{MT}}_{{\stackrel{\&RightArrow;}{h}}_k}\left(p\right),$

${\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(1\right),{\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(2\right),...{,\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(q\right),...,{\mathrm{MF}}_{{\stackrel{\&RightArrow;}{w}}_k}\left(Q\right),;$

${\mathrm{ST}}_{{\stackrel{\&RightArrow;}{h}}_k}{,\mathrm{SF}}_{{\stackrel{\&RightArrow;}{w}}_k}]$

Thus, Radar Target Using Range Profiles Θ (t) time-frequency characteristics vector sequence f={ ξ are obtained₁, ξ₂..., ξ_k..., ξ_K), and it regard the time-frequency characteristics vector sequence ζ as the time-frequency characteristics extracted from Radar Target Using Range Profiles Θ (t)；

C) will be according to step B) time-frequency characteristics of Radar Target Using Range Profiles that extract of the scheme are used as radar target recognition feature, carry out radar target recognition.

2. radar target identification method according to claim 1, it is characterised in that the span for the series I that the match tracing is decomposed is 20≤I≤100.

3. radar target identification method according to claim 1, it is characterised in that the span of the decomposition dimension K is 0.05N≤K≤0.5N.

4. radar target identification method according to claim 1, it is characterised in that the span of the frequency domain character exponent number Q is 1≤Q≤6；The span of the temporal signatures exponent number P is 1≤P≤6.

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