CN104459657A - Extension factorization space-time two-dimensional self-adaptive processing method based on data fitting - Google Patents

Abstract

The invention discloses an extension factorization space-time two-dimensional self-adaptive processing method based on data fitting and relates to radar technology. The method comprises the specific steps that 1, dimensionality reduction echo data and space-time guide vectors are obtained; 2, a data basis matrix of a distance unit to be detected is constructed; 3, a data basis matrix with targets blocked is obtained; 4, the fitting coefficient of auxiliary echo data is obtained; 5, the minimum fitting error of data of the distance unit to be detected is obtained; 6, unit average constant false alarm rate detection is carried out on the minimum fitting error of the data of the distance unit to be detected. The extension factorization space-time two-dimensional self-adaptive processing method mainly solves the problem that a traditional STAP method is huge in computation burden and strict in sample requirement, and has the good application prospect in measured data processing and STAP performance improvement.

Description

Based on the spreading factor space-time adaptive processing method of data fitting

Technical field

The invention belongs to communication technical field, relate to Radar Technology, particularly a kind of spreading factor space-time adaptive processing method based on data fitting, for airborne early warn ing radar signal transacting.

Background technology

The main task of airborne early warn ing radar is the detection of a target in complex clutter background, and positions tracking to it, and carries out effectively suppressing being the core means improving airborne early warn ing radar serviceability to clutter.Space-time adaptive process (space-time adaptive processing, STAP) technology makes full use of spatial domain and time-domain information, while coherent accumulation is carried out to echo signal, by space-time adaptive process filtering ground clutter, realize the effective detection of airborne early warn ing radar to target, the E2-D airborne early warn ing radar as the U.S. just adopts this technology.

In actual applications, mainly there are following two aspect problems in STAP technology: on the one hand, in clutter environment heterogeneous, obtain the abundant independent same distribution for estimate covariance matrix (independent and identically distributed, IID) training sample very difficult; On the other hand, even if the demand of training sample is met, the excessive problem of full space time processing calculated amount can cause real-time to be difficult to ensure.

For solving the problem, promoting STAP technology more practical, there has been proposed many innovative approachs or method.The patent of invention " space-time adaptive processing method under non-homogeneous clutter environment " (number of patent application 201010129723.3, publication No. CN101819269A) of Tsing-Hua University's application discloses a kind of overcomplete sparse representation method of super-resolution estimation clutter space-time two-dimensional spectrum in non-homogeneous clutter environment.The method achieve when independent same distribution sample number deficiency, utilize single frames training sample to estimate clutter covariance matrix, thus avoid strong non-homogeneous clutter environment on the impact of self-adaptive processing effect.But, still there is following main deficiency in the method: one is the problem that operand is large, super complete radix order clutter spectrum being carried out to rarefaction representation is uncertain, but much larger than degree of freedom in system, and degree of freedom in system is usually thousands of in reality, operand required in the covariance matrix restructuring procedure of each range unit sample is like this very large, is unfavorable for real-time process, thus has influence on the effect in practical engineering application.Two is base mismatch problems, and the base used in the method is actually one group of interpolation discrete fourier DFT vector, and the echo data of reality is because exist the non-ideal factors such as error, can not use given base vector rarefaction representation; In addition, the method needs to carry out discretize expression to plane during sky, the signal not being positioned at discrete grid block dot center can be made like this to reveal to all net points, thus destroy the openness of echo data.

Summary of the invention

For the deficiency of the overcomplete sparse representation method of above-mentioned super-resolution estimation clutter space-time two-dimensional spectrum in non-homogeneous clutter environment, the present invention proposes a kind of spreading factor space-time adaptive processing based on data fitting (ExtendedFactored Approach STAP, EFA-STAP) method, the detection to echo signal can be realized, and solve the problem of the huge and base mismatch of operand in prior art, simultaneously relative to conventional Extension factorization EFA-STAP method, the detection probability of moving-target can be improved, reduce the false alarm rate of detection.

For achieving the above object, the present invention is pre-to realize by the following technical solutions.

Based on a spreading factor space-time adaptive processing method for data fitting, it is characterized in that, comprise the following steps:

Step 1, utilizes airborne early warn ing radar aerial receiver to carry the space-time two-dimensional echo data x of early warning radar, carries out spreading factor EFA dimensionality reduction to space-time two-dimensional echo data x, obtains dimensionality reduction echo data z and steering vector s time empty _z-EFA;

Step 2, constructs the Data Base matrix Φ of range unit to be detected _k;

Step 3, steering vector s when utilizing empty _z-EFAderive blocking matrix B; Utilize the data z of blocking matrix B and range unit to be detected _k, obtain target and block later auxiliary echo data the data z of this range unit to be detected _ktake from the dimensionality reduction echo data z in step 1 successively; Utilize the Data Base matrix Φ of blocking matrix B and range unit to be detected _kobtain target and block later Data Base matrix

Step 4, utilizes target to block later Data Base matrix to auxiliary echo data carry out data fitting, obtain auxiliary echo data fitting coefficient

Step 5, utilizes the Data Base matrix Φ of range unit to be detected _kwith auxiliary echo data fitting coefficient treat the data z of detecting distance unit _kcarry out data fitting, obtain the data z of range unit to be detected _kminimum error of fitting y _k; The data z of this range unit to be detected _ktake from the dimensionality reduction echo data z in step 1 successively;

Step 6, treats the minimum error of fitting y of the data of detecting distance unit _kcarry out CA-CFAR detection, and there is target or there is not target in output.

Feature and further improvement of technique scheme are:

(1) step 1 specifically comprises following sub-step:

1a) utilize airborne early warn ing radar antenna, within the coherent accumulation time, receive the space-time two-dimensional echo data x of ground return; Space-time two-dimensional echo data x is MN dimension, wherein M indicating impulse number, and N represents the array number of airborne early warn ing radar antenna;

1b) be expanded according to following formula the dimensionality reduction transition matrix P of factorization EFA dimensionality reduction _eFA:

$P_{\mathrm{EFA}}=P_t(f_{i-1},f_i,f_{i+1})\⊗I_N$

Wherein, P _t(f _i-1, f _i, f _i+1) represent the time domain transition matrix become by three Doppler filter group closed on, f _irepresent the normalization Doppler frequency of target, f _i-1, f _i+1represent two the normalization Doppler frequencies adjacent with target, i be less than or equal to M and be more than or equal to 1 natural number, M indicating impulse number, I _nrepresent the unit matrix of N × N, represent Kronecker product, N represents the array number of airborne early warn ing radar antenna, dimensionality reduction transition matrix P _eFAdimension be MN × 3N dimension;

1c) according to dimensionality reduction transition matrix P _eFAbe expanded the dimensionality reduction echo data z after factorization EFA dimensionality reduction, is expressed as following formula:

$z=P_{\mathrm{EFA}}^{H}x$

Wherein, () ^hrepresent conjugate transposition operation, according to dimensionality reduction transition matrix P _eFAdimension be MN × 3N dimension and space-time two-dimensional echo data x be the dimension that MN dimension can obtain dimensionality reduction echo data z be 3N dimension;

Steering vector s during empty after spreading factor EFA dimensionality reduction _z-EFA, be expressed as following formula:

$s_{z-\mathrm{EFA}}={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^T\⊗s_s\left(f_s\right)$

s _s(f _s)＝[1 exp(j2πf _s) exp(j2πf _s2) … exp(j2πf _s(N-1))] ^T

Wherein, () ^trepresent matrix transpose operation, s _s(f _s) represent the spatial domain steering vector of target, f _srepresent the normalization spatial frequency of target, N represents the array number of airborne early warn ing radar antenna.

(2) step 2 specifically comprises following sub-step:

Data Base matrix Φ _kbe expressed as following formula:

Φ _k＝[z ₁z ₂… z _L]∈C ^D×L

Wherein, Φ _krepresent the Data Base matrix of a kth range unit to be detected; K represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; D represents the dimension of dimensionality reduction echo data z, and L represents the number of the data of closing on range unit, C ^{d × L}represent the complex matrix space of D × L dimension, z _l(l=1,2 ..., L) represent and close on the data of range unit, close on range unit and represent and range unit near range unit to be detected do not comprise two range units for the protection of target.

(3) step 3 specifically comprises following sub-step:

3a) to steering vector s during sky _z-EFAtransposed form carry out svd, obtain left singular matrix U, right singular matrix V and singular value matrix Λ; Decomposition formula as shown in the formula:

$s_{z-\mathrm{EFA}}^T=U\·\mathrm{\Λ}\·V^H$

Wherein, U represents left singular matrix, and V represents right singular matrix, and Λ represents singular value matrix, () ^trepresent matrix transpose operation, () ^hrepresent conjugate transposition operation;

3b) blocking matrix B is made up of to the arrangement of N row order the 2nd of right singular matrix V, derives blocking matrix B by right singular matrix V and following formula;

B＝[V(:,2:N)] ^T

Wherein, V (:, 2:N) represent that all row, the 2nd of right singular matrix V are to N column matrix element; () ^trepresent matrix transpose operation;

3c) obtain auxiliary echo data according to following formula later Data Base matrix is blocked with target

${\stackrel{\‾}{z}}_k=B{z}_k,{\stackrel{\‾}{\mathrm{\Φ}}}_k=B{\mathrm{\Φ}}_k$

Wherein, z _krepresent the data of a kth range unit to be detected, the data of this range unit to be detected take from the dimensionality reduction echo data z in step 1 successively, and k represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; represent that target blocks later auxiliary echo data, represent that target blocks later Data Base matrix, B is blocking matrix.

(4) step 4 specifically comprises following sub-step:

4a) block later Data Base matrix by target later auxiliary echo data is blocked to target carry out least square fitting expression, be expressed as following formula:

$\underset{{\stackrel{\‾}{\mathrm{\α}}}_k}{\min }{\left|\right|{\stackrel{\‾}{z}}_k-{\stackrel{\‾}{\mathrm{\Φ}}}_k{\stackrel{\‾}{\mathrm{\α}}}_k\left|\right|}_2$

Wherein, || || ₂represent 2 norms solving vector, represent auxiliary echo data fitting coefficient;

4b) according to step 4a) in least square fitting represent, solve auxiliary echo data fitting coefficient least square solution be expressed as following formula:

${\stackrel{\‾}{\mathrm{\α}}}_k^{*}={\stackrel{\‾}{\mathrm{\Φ}}}_k^H{\left({\stackrel{\‾}{\mathrm{\Φ}}}_k{\stackrel{\‾}{\mathrm{\Φ}}}_k^H\right)}^{-1}{\stackrel{\‾}{z}}_k$

Wherein, () ^-1representing matrix inversion operation, () ^hrepresent conjugate transposition operation, represent that target blocks later Data Base matrix, represent that target blocks later auxiliary echo data.

(5) step 5 specifically comprises following sub-step:

5a) with the Data Base matrix Φ of range unit to be detected _k, treat the data z of detecting distance unit _kcarry out least square fitting; With the auxiliary echo data of solution fitting coefficient least square solution calculate and optimize restrained boundary η _k, realize especially by following formula:

$\underset{{\mathrm{\α}}_k}{\min }{\left|\right|z_k-{\mathrm{\Φ}}_k{\mathrm{\α}}_k\left|\right|}_2,\mathrm{subjectto}{\left|\right|{\mathrm{\α}}_k\left|\right|}_2\≤{\mathrm{\η}}_k$

Wherein, α _krepresent the fitting coefficient of the data of range unit to be detected, y _krepresent 2 norms of minimum error of fitting vector, η _krepresent and optimize restrained boundary,

The optimal fitting coefficient of the data of range unit to be detected 5b) is obtained by solving above formula

According to the optimal fitting coefficient of the data of range unit to be detected obtain the minimum error of fitting y of the data of range unit to be detected _k, obtained by following formula:

$y_k={\left|\right|z_k-{\mathrm{\Φ}}_k{\mathrm{\α}}_k^{*}\left|\right|}_2$

Wherein, z _krepresent the data of a kth range unit to be detected, the data of this range unit to be detected take from the dimensionality reduction echo data z in step 1 successively, and k represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; Φ _krepresent the Data Base matrix of range unit to be detected; represent the optimal fitting coefficient of the data of range unit to be detected; || || ₂represent 2 norms solving vector.

Compared with prior art, the present invention has outstanding substantive distinguishing features and significant progress.The present invention has the following advantages compared with STAP method with existing sparse recovery:

(1) for the problem of operand, the super complete radix order that existing sparse restoration methods carries out rarefaction representation to clutter spectrum is uncertain, but much larger than degree of freedom in system, and degree of freedom in system is usually thousands of in reality, operand required in the covariance matrix restructuring procedure of each range unit sample is like this very large, be unfavorable for real-time process, thus have influence on its practical engineering application effect.STAP method combines with EFA by the present invention, and the little optimization problem optimization problem that original MN ties up being decomposed into M 3N dimension solves, and greatly reduces the computation complexity of algorithm, solves the problem that in sparse recovery STAP method, operand is large.

(2) for base mismatch problems, the expression base used in existing sparse restoration methods is actually one group of interpolated DFT vector, and because there is the non-ideal factors such as error in real data, can not with give base vector rarefaction representation, in addition, the method needs to carry out discretize expression to plane during sky, the signal not being positioned at discrete grid block dot center can be made like this to reveal to all net points, thus destroy the openness of data.The present invention directly uses real data sample as basis matrix, instead of the ideal flowing pattern adopting certain to determine, thus has evaded the problem of base mismatch in above-mentioned sparse recovery STAP method.

Visible, in prior art, STAP carries out airborne radar signal transacting usually in high-dimensional data space, greatly will increase the problem of computational complexity and required training sample number like this, in order to obtain better performance, the data sample utilizing range unit to be detected to close on range unit carrys out Optimal Fitting range unit clutter data to be detected, thus improve the clutter recognition performance of Adaptive Signal Processing, improve the detection probability of target.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, the present invention will be further described.

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is general pulse doppler processing result figure;

Fig. 3 is the change curve of detection probability with border compensation rate;

Fig. 4 is the change curve of detection probability with sample number;

Fig. 5 is the Output rusults figure of the minimum error of fitting of the data of target proximity range unit; Fig. 5 (a) is the Output rusults of the minimum error of fitting of a segment distance unit scope after conventional EFA method; Fig. 5 (c) is the Output rusults through the minimum error of fitting of a segment distance unit scope after the inventive method process; Fig. 5 (b) is the Output rusults of the minimum error of fitting of another segment distance unit scope after conventional EFA method; Fig. 5 (d) is the Output rusults of the minimum error of fitting of another segment distance unit scope after the inventive method;

Fig. 6 is the change curve of detection probability with target power;

Fig. 7 is the change curve graph of a relation of detection probability with false alarm rate.

Embodiment

With reference to Fig. 1, a kind of spreading factor space-time adaptive processing method based on data fitting of the present invention is described, the present invention is used for airborne early warn ing radar signal transacting, and its concrete implementation step is as follows:

Step 1, utilizes airborne early warn ing radar aerial receiver to carry the space-time two-dimensional echo data x of early warning radar, carries out spreading factor EFA dimensionality reduction to space-time two-dimensional echo data x, obtains dimensionality reduction echo data z and steering vector s time empty _z-EFA;

Step 1 specifically comprises following sub-step:

1a) utilize airborne early warn ing radar antenna, within the coherent accumulation time, receive the space-time two-dimensional echo data x of ground return; Space-time two-dimensional echo data x is MN dimension, wherein M indicating impulse number, and N represents the array number of airborne early warn ing radar antenna;

1b) be expanded according to following formula the dimensionality reduction transition matrix P of factorization EFA dimensionality reduction _eFA:

$P_{\mathrm{EFA}}=P_t(f_{i-1},f_i,f_{i+1})\⊗I_N$

Wherein, P _t(f _i-1, f _i, f _i+1) represent the time domain transition matrix become by three Doppler filter group closed on, f _irepresent the normalization Doppler frequency of target, f _i-1, f _i+1represent two the normalization Doppler frequencies adjacent with target, i be less than or equal to M and be more than or equal to 1 natural number, M indicating impulse number, I _nrepresent the unit matrix of N × N, represent Kronecker product, N represents the array number of airborne early warn ing radar antenna, dimensionality reduction transition matrix P _eFAdimension be MN × 3N dimension;

1c) according to dimensionality reduction transition matrix P _eFAbe expanded the dimensionality reduction echo data z after factorization EFA dimensionality reduction, is expressed as following formula:

$z=P_{\mathrm{EFA}}^{H}x$

Wherein, () ^hrepresent conjugate transposition operation, according to dimensionality reduction transition matrix P _eFAdimension be MN × 3N dimension and space-time two-dimensional echo data x be the dimension that MN dimension can obtain dimensionality reduction echo data z be 3N dimension;

Steering vector s during empty after spreading factor EFA dimensionality reduction _z-EFA, be expressed as following formula:

$s_{z-\mathrm{EFA}}={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^T\⊗s_s\left(f_s\right)$

s _s(f _s)＝[1 exp(j2πf _s) exp(j2πf _s2) … exp(j2πf _s(N-1))] ^T

Wherein, () ^trepresent matrix transpose operation, s _s(f _s) represent the spatial domain steering vector of target, f _srepresent the normalization spatial frequency of target, N represents the array number of airborne early warn ing radar antenna.

During general sky, steering vector s can be expressed as the Kronecker product form of time domain steering vector and spatial domain steering vector, namely f _dand f _srepresent normalized Doppler frequency and spatial frequency respectively, time domain and spatial domain steering vector can be expressed as respectively $\begin{array}{c}{s}_t\left(f_d\right)={\left[\begin{array}{cccc}1& \exp \left(j2\mathrm{\π}{f}_d\right)& ...& \mathrm{e\; xp}(j2\mathrm{\π}(M-1)f_d)\end{array}\right]}^T\\ s_s=\left(f_s\right)={\left[\begin{array}{cccc}1& \exp \left(j2\mathrm{\π}{f}_s\right)& ...& \exp \left(j2\mathrm{\π}(N-1)f_s\right)\end{array}\right]}^T\end{array}.$

Step 2, constructs the Data Base matrix Φ of range unit to be detected _k;

Data Base matrix Φ _kbe expressed as following formula:

Φ _k＝[z ₁z ₂… z _L]∈C ^D×L

Wherein, Φ _krepresent the Data Base matrix of a kth range unit to be detected; K represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; D represents the dimension of dimensionality reduction echo data z, and L represents the number of the data of closing on range unit, C ^{d × L}represent the complex matrix space of D × L dimension, z _l(l=1,2 ..., L) represent and close on the data of range unit, close on range unit and represent and range unit near range unit to be detected do not comprise two range units for the protection of target.

Step 3, steering vector s when utilizing empty _z-EFAderive blocking matrix B; Utilize the data z of blocking matrix B and range unit to be detected _k, obtain target and block later auxiliary echo data the data z of this range unit to be detected _ktake from the dimensionality reduction echo data z in step 1 successively; Utilize the Data Base matrix Φ of blocking matrix B and range unit to be detected _kobtain target and block later Data Base matrix

Step 3 specifically comprises following sub-step:

3a) to steering vector s during sky _z-EFAtransposed form carry out svd, obtain left singular matrix U, right singular matrix V and singular value matrix Λ; Decomposition formula as shown in the formula:

$s_{z-\mathrm{EFA}}^T=U\·\mathrm{\Λ}\·V^H$

Wherein, U represents left singular matrix, and V represents right singular matrix, and Λ represents singular value matrix, () ^trepresent matrix transpose operation, () ^hrepresent conjugate transposition operation;

3b) blocking matrix B is made up of to the arrangement of N row order the 2nd of right singular matrix V, derives blocking matrix B by right singular matrix V and following formula;

B＝[V(:,2:N)] ^T

Wherein, V (:, 2:N) represent that all row, the 2nd of right singular matrix V are to N column matrix element; () ^trepresent matrix transpose operation;

3c) obtain auxiliary echo data according to following formula later Data Base matrix is blocked with target

${\stackrel{\‾}{z}}_k=B{z}_k,{\stackrel{\‾}{\mathrm{\Φ}}}_k=B{\mathrm{\Φ}}_k$

Wherein, z _krepresent the data of a kth range unit to be detected, the data of this range unit to be detected take from the dimensionality reduction echo data z in step 1 successively, and k represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; represent that target blocks later auxiliary echo data, represent that target blocks later Data Base matrix, B is blocking matrix.

Step 4, utilizes target to block later Data Base matrix to auxiliary echo data carry out data fitting, obtain auxiliary echo data fitting coefficient

Step 4 specifically comprises following sub-step:

4a) block later Data Base matrix by target later auxiliary echo data is blocked to target carry out least square fitting expression, be expressed as following formula:

$\underset{{\stackrel{\‾}{\mathrm{\α}}}_k}{\min }{\left|\right|{\stackrel{\‾}{z}}_k-{\stackrel{\‾}{\mathrm{\Φ}}}_k{\stackrel{\‾}{\mathrm{\α}}}_k\left|\right|}_2$

Wherein, || || ₂represent 2 norms solving vector, represent auxiliary echo data fitting coefficient;

4b) according to step 4a) in least square fitting represent, solve auxiliary echo data fitting coefficient least square solution be expressed as following formula:

${\stackrel{\‾}{\mathrm{\α}}}_k^{*}={\stackrel{\‾}{\mathrm{\Φ}}}_k^H{\left({\stackrel{\‾}{\mathrm{\Φ}}}_k{\stackrel{\‾}{\mathrm{\Φ}}}_k^H\right)}^{-1}{\stackrel{\‾}{z}}_k$

Wherein, () ^-1representing matrix inversion operation, () ^hrepresent conjugate transposition operation, represent that target blocks later Data Base matrix, represent that target blocks later auxiliary echo data.

Step 5, utilizes the Data Base matrix Φ of range unit to be detected _kwith auxiliary echo data fitting coefficient treat the data z of detecting distance unit _kcarry out data fitting, obtain the data z of range unit to be detected _kminimum error of fitting y _k; The data z of this range unit to be detected _ktake from the dimensionality reduction echo data z in step 1 successively;

Step 5 specifically comprises following sub-step:

5a) with the Data Base matrix Φ of range unit to be detected _k, treat the data z of detecting distance unit _kcarry out least square fitting; With the auxiliary echo data of solution fitting coefficient least square solution calculate and optimize restrained boundary η _k, realize especially by following formula:

$\underset{{\mathrm{\α}}_k}{\min }{\left|\right|z_k-{\mathrm{\Φ}}_k{\mathrm{\α}}_k\left|\right|}_2,\mathrm{subjectto}{\left|\right|{\mathrm{\α}}_k\left|\right|}_2\≤{\mathrm{\η}}_k$

Wherein, α _krepresent the fitting coefficient of the data of range unit to be detected, y _krepresent 2 norms of minimum error of fitting vector, η _krepresent and optimize restrained boundary

The optimal fitting coefficient of the data of range unit to be detected 5b) is obtained by solving above formula

According to the optimal fitting coefficient of the data of range unit to be detected obtain the minimum error of fitting y of the data of range unit to be detected _k, obtained by following formula:

$y_k={\left|\right|z_k-{\mathrm{\Φ}}_k{\mathrm{\α}}_k^{*}\left|\right|}_2$

Wherein, z _krepresent the data of a kth range unit to be detected, the data of this range unit to be detected take from the dimensionality reduction echo data z in step 1 successively, and k represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; Φ _krepresent the Data Base matrix of range unit to be detected; represent the optimal fitting coefficient of the data of range unit to be detected; || || ₂represent 2 norms solving vector.

Step 6, treats the minimum error of fitting y of the data of detecting distance unit _kcarry out CA-CFAR detection, and there is target or there is not target in output.

Treat the minimum error of fitting y of the data of detecting distance unit _kcarry out CA-CFAR detection (Cell-averaging constant false alarm rate, CA-CFAR), by minimum error of fitting y _kcompare with the mean value of the minimum error of fitting of the data of the range unit of the surrounding of range unit to be detected, according to minimum error of fitting y _kjudge whether to there is target with toaverage ratio size, finally will there is target or there is not target output.

Below in conjunction with emulation experiment, effect of the present invention is described further.

(1) experiment condition:

Experiment of the present invention is carried out under MATLAB7.11 software.In experimental design of the present invention, in order to check the inventive method validity in actual applications, process data are from the measured data MCARM data set of external admission, under its radar is operated in positive side battle array pattern, the spatial domain array element that can be used for Adaptive Signal Processing that front is arranged by 2 row 11 forms, and its part system parameter is with reference to table 1.In order to test conveniently, the present invention extracts the first row 11 array elements in MCARM data, the echo data of front 32 pulses is verified.

Table 1

(2) Comparison of experiment results

Accompanying drawing 2 is general pulse doppler processing result figure, is also range Doppler figure.Transverse axis represents Doppler's channel position, and the longitudinal axis represents range unit sequence number.Range unit also claims range gate in the present invention.Under as can be seen from Figure 2 although this radar is operated in positive side battle array situation, the strong clutter component in space-time two-dimensional echo data, is subject to the existence of various false target in the different modulation of landform reflectivity and actual environment, has certain heterogeneity.

Accompanying drawing 3 is the change curve of detection probability with border compensation rate.Transverse axis represents boundary compensation, and the longitudinal axis represents detection probability.Boundary compensation is the additional compensation rate in the optimization upper bound showing in solution procedure 5 gained when optimizing restrained boundary.As can be seen from Figure 3, substantially near 0 compensation rate, detection probability can obtain maximal value, and this also just describes step 5 calculation optimization restrained boundary in the present invention is effective and optimum.

Accompanying drawing 4 is the change curve of detection probability with sample number.Sample number refers to the number of the data of closing on range unit in the present invention.Transverse axis represents sample number, and the longitudinal axis represents detection probability.In the present invention after data EFA dimension-reduction treatment, data dimension (i.e. degree of freedom) reduces to 3N, and wherein N is array number, in this experiment 3N=33.As can be seen from the figure, detection probability reaches maximal value substantially when sample number is more than 100, this just illustrates, the data that in the present invention, Data Base matrix can close on range unit by 3 times of number of degrees of freedom, objects near range unit to be detected are formed, and obtain optimum detection perform.

Fig. 5 is the Output rusults figure of the minimum error of fitting of the data of target proximity range unit.In the present invention, the data of target proximity range unit comprise the data of many groups range unit to be detected.Transverse axis represents the sequence number of range unit, and the longitudinal axis represents power, represents with dB.In Fig. 5, curve represents the Output rusults of the minimum error of fitting of a segment distance unit scope in target Doppler passage, horizontal linear represents the average output value of the minimum error of fitting of this segment distance unit scope, circle represents the minimum error of fitting output valve of target range unit, and in Fig. 5, " difference " represents the difference between the average output value of the minimum error of fitting output valve of target range unit and the minimum error of fitting of this segment distance unit scope.As can be seen from Figure 5, after process of the present invention, target exports more obvious, Fig. 5 (a) compared with 5 (c) when range unit is 150 power improve more than 15dB, Fig. 5 (b) compared with 5 (d) when range unit is 200 power improve more than 25dB, thus more can be conducive to the detection of echo signal.

Fig. 6 is the change curve of detection probability with target power.Transverse axis represents the artificial target power arranged, and the longitudinal axis represents the detection probability of this target.The spreading factor method (DF-EFA) based on data fitting that the sparse restoration methods of direct data domain (D3SR), conventional Extension factorization method (EFA) and the present invention propose is compared in Fig. 6.As can be seen from Figure 6, the detection perform of the inventive method is much better than other two kinds of methods.

Fig. 7 is the change curve graph of a relation of detection probability with false alarm rate.Transverse axis represents false alarm rate, and the longitudinal axis represents detection probability.The spreading factor method (DF-EFA) based on data fitting of conventional Extension factorization method (EFA) and the present invention's proposition is compared in Fig. 7.As can be seen from Figure 7, the inventive method, relative to traditional E FA method, has higher detection probability, and have lower false alarm rate under identical detection probability under certain false alarm rate.

Claims (6)

1., based on a spreading factor space-time adaptive processing method for data fitting, it is characterized in that, comprise the following steps:

Step 1, utilizes airborne early warn ing radar aerial receiver to carry the space-time two-dimensional echo data x of early warning radar, carries out spreading factor EFA dimensionality reduction to space-time two-dimensional echo data x, obtains dimensionality reduction echo data z and steering vector s time empty _z-EFA;

Step 2, constructs the Data Base matrix Φ of range unit to be detected _k;

Step 3, steering vector s when utilizing empty _z-EFAderive blocking matrix B; Utilize the data z of blocking matrix B and range unit to be detected _k, obtain target and block later auxiliary echo data the data z of this range unit to be detected _ktake from the dimensionality reduction echo data z in step 1 successively; Utilize the Data Base matrix Φ of blocking matrix B and range unit to be detected _kobtain target and block later Data Base matrix

Step 4, utilizes target to block later Data Base matrix to auxiliary echo data carry out data fitting, obtain auxiliary echo data fitting coefficient

Step 5, utilizes the Data Base matrix Φ of range unit to be detected _kwith auxiliary echo data fitting coefficient treat the data z of detecting distance unit _kcarry out data fitting, obtain the data z of range unit to be detected _kminimum error of fitting y _k; The data z of this range unit to be detected _ktake from the dimensionality reduction echo data z in step 1 successively;

Step 6, treats the minimum error of fitting y of the data of detecting distance unit _kcarry out CA-CFAR detection, and there is target or there is not target in output.

2. the spreading factor space-time adaptive processing method based on data fitting according to claim 1, it is characterized in that, step 1 specifically comprises following sub-step:

1a) utilize airborne early warn ing radar antenna, within the coherent accumulation time, receive the space-time two-dimensional echo data x of ground return; Space-time two-dimensional echo data x is MN dimension, wherein M indicating impulse number, and N represents the array number of airborne early warn ing radar antenna;

1b) be expanded according to following formula the dimensionality reduction transition matrix P of factorization EFA dimensionality reduction _eFA:

$P_{\mathrm{EFA}}=P_t(f_{i-1},f_i,f_{i+1})\⊗I_N$

Wherein, P _t(f _i-1, f _i, f _i+1) represent the time domain transition matrix become by three Doppler filter group closed on, f _irepresent the normalization Doppler frequency of target, f _i-1, f _i+1represent two the normalization Doppler frequencies adjacent with target, i be less than or equal to M and be more than or equal to 1 natural number, M indicating impulse number, I _nrepresent the unit matrix of N × N, represent Kronecker product, N represents the array number of airborne early warn ing radar antenna, dimensionality reduction transition matrix P _eFAdimension be MN × 3N dimension;

1c) according to dimensionality reduction transition matrix P _eFAbe expanded the dimensionality reduction echo data z after factorization EFA dimensionality reduction, is expressed as following formula:

$z=P_{\mathrm{EFA}}^{H}x$

Wherein, () ^hrepresent conjugate transposition operation, according to dimensionality reduction transition matrix P _eFAdimension be MN × 3N dimension and space-time two-dimensional echo data x be the dimension that MN dimension can obtain dimensionality reduction echo data z be 3N dimension;

Steering vector s during empty after spreading factor EFA dimensionality reduction _z-EFA, be expressed as following formula:

$s_{z-\mathrm{EFA}}={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^T\⊗s_s\left(f_s\right)$

s _s(f _s)＝[1 exp(j2πf _s) exp(j2πf _s2) … exp(j2πf _s(N-1))] ^T

Wherein, () ^trepresent matrix transpose operation, s _s(f _s) represent the spatial domain steering vector of target, f _srepresent the normalization spatial frequency of target, N represents the array number of airborne early warn ing radar antenna.

3. the spreading factor space-time adaptive processing method based on data fitting according to claim 1, it is characterized in that, step 2 specifically comprises:

Data Base matrix Φ _kbe expressed as following formula:

Φ _k＝[z ₁z ₂…z _L]∈C ^D×L

Wherein, Φ _krepresent the Data Base matrix of a kth range unit to be detected, k represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; D represents the dimension of dimensionality reduction echo data z, and L represents the number of the data of closing on range unit, C ^{d × L}represent the complex matrix space of D × L dimension, z _l(l=1,2 ..., L) represent and close on the data of range unit, close on range unit and represent and range unit near range unit to be detected do not comprise two range units for the protection of target.

4. the spreading factor space-time adaptive processing method based on data fitting according to claim 1, it is characterized in that, step 3 specifically comprises following sub-step:

3a) to steering vector s during sky _z-EFAtransposed form carry out svd, obtain left singular matrix U, right singular matrix V and singular value matrix Λ; Decomposition formula as shown in the formula:

$s_{z-\mathrm{EFA}}^T=U\·\mathrm{\Λ}\·V^H$

Wherein, U represents left singular matrix, and V represents right singular matrix, and Λ represents singular value matrix, () ^trepresent matrix transpose operation, () ^hrepresent conjugate transposition operation;

3b) blocking matrix B is made up of to the arrangement of N row order the 2nd of right singular matrix V, derives blocking matrix B by right singular matrix V and following formula;

B＝[V(:,2:N)] ^T

Wherein, V (:, 2:N) represent that all row, the 2nd of right singular matrix V are to N column matrix element; () ^trepresent matrix transpose operation;

3c) obtain auxiliary echo data according to following formula later Data Base matrix is blocked with target

${\stackrel{\‾}{z}}_k=B{z}_k,{\stackrel{\‾}{\mathrm{\Φ}}}_k=B{\mathrm{\Φ}}_k$

Wherein, z _krepresent the data of a kth range unit to be detected, the data of this range unit to be detected take from the dimensionality reduction echo data z in step 1 successively, and k represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; represent that target blocks later auxiliary echo data, represent that target blocks later Data Base matrix, B is blocking matrix.

5. the spreading factor space-time adaptive processing method based on data fitting according to claim 1, it is characterized in that, step 4 specifically comprises following sub-step:

4a) block later Data Base matrix by target later auxiliary echo data is blocked to target carry out least square fitting expression, be expressed as following formula:

$\underset{{\stackrel{\‾}{\mathrm{\α}}}_k}{\min }{\left|\right|{\stackrel{\‾}{z}}_k-{\stackrel{\‾}{\mathrm{\Φ}}}_k{\stackrel{\‾}{\mathrm{\α}}}_k\left|\right|}_2$

Wherein, || || ²represent 2 norms solving vector, represent auxiliary echo data fitting coefficient;

4b) according to step 4a) in least square fitting represent, solve auxiliary echo data fitting coefficient least square solution be expressed as following formula:

${\stackrel{\‾}{\mathrm{\α}}}_k^{*}={\stackrel{\‾}{\mathrm{\Φ}}}_k^H{\left({\stackrel{\‾}{\mathrm{\Φ}}}_k{\stackrel{\‾}{\mathrm{\Φ}}}_k^H\right)}^{-1}{\stackrel{\‾}{z}}_k$

Wherein, () ^-1representing matrix inversion operation, () ^hrepresent conjugate transposition operation represent that target blocks later Data Base matrix, represent that target blocks later auxiliary echo data.

6. the spreading factor space-time adaptive processing method based on data fitting according to claim 1, it is characterized in that, step 5 specifically comprises following sub-step:

5a) with the Data Base matrix Φ of range unit to be detected _k, treat the data z of detecting distance unit _kcarry out least square fitting; With the auxiliary echo data of solution fitting coefficient least square solution calculate and optimize restrained boundary η _k, realize especially by following formula:

$\underset{{\mathrm{\α}}_k}{\min }{\left|\right|z_k-{\mathrm{\Φ}}_k{\mathrm{\α}}_k\left|\right|}_2,\mathrm{subjectto}{\left|\right|{\mathrm{\α}}_k\left|\right|}_2\≤{\mathrm{\η}}_k$

Wherein, α _krepresent the fitting coefficient of the data of range unit to be detected, y _krepresent 2 norms of minimum error of fitting vector, η _krepresent and optimize restrained boundary,

The optimal fitting coefficient of the data of range unit to be detected 5b) is obtained by solving above formula

According to the optimal fitting coefficient of the data of range unit to be detected k obtains the minimum error of fitting y of the data of range unit to be detected _k, obtained by following formula:

$y_k={\left|\right|z_k-{\mathrm{\Φ}}_k{\mathrm{\α}}_k^{*}\left|\right|}_2$

Wherein, z _krepresent the data of a kth range unit to be detected, the data of this range unit to be detected take from the dimensionality reduction echo data z in step 1 successively, and k represents the sequence number of the data of range unit to be detected, for being no more than the natural number of all range unit sums to be detected; Φ _krepresent the Data Base matrix of range unit to be detected; represent the optimal fitting coefficient of the data of range unit to be detected; || || ²represent 2 norms solving vector.