CN104459658B - Unite-domain positioning space-time two-dimensional self-adaptive processing method based on data fitting - Google Patents

Abstract

The invention discloses a unite-domain positioning space-time two-dimensional self-adaptive processing method based on data fitting, and relates to radar technology. The method comprises the steps that 1, JDL 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 unite-domain positioning 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, reduces the false alarm rate, improves movable target detection probability, and has the good application prospect in measured data processing and STAP performance improvement.

Description

Joint domain based on data matching positions space-time adaptive processing method

Technical field

The invention belongs to communication technical field, it is related to Radar Technology, particularly to a kind of joint domain based on data matching Positioning space-time adaptive processing method, for airborne early warning Radar Signal Processing.

Background technology

The main task of airborne early warning radar is detection target in complex clutter background, and carries out locating and tracking to it, And it is the core means improving airborne early warning radar service behaviour that clutter is effectively suppressed.Space-time adaptive is processed (space-time adaptive processing, stap) technology makes full use of spatially and temporally information, to echo signal While carrying out coherent accumulation, processed by space-time adaptive and filter ground clutter, realizing airborne early warning radar has to target Effect detection, such as the e2-d airborne early warning radar of the U.S. just adopt this technology.

In actual applications, stap technology is primarily present following two aspect problems: on the one hand, in clutter environment heterogeneous In, enough independent same distribution (independent and identically for estimate covariance matrix will be obtained Distributed, iid) training sample is extremely difficult；On the other hand, even if the demand of training sample is met, at full space-time The excessive problem of reason amount of calculation can lead to real-time to be difficult to ensure that.

For solving the above problems, promote stap technology more practical, there has been proposed many corrective measures or method.Clearly Patent of invention " the space-time adaptive processing method under non-homogeneous clutter environment " (number of patent application of Hua Da application 201010129723.3, publication No. cn101819269a) and disclose a kind of super-resolution estimation clutter in non-homogeneous clutter environment The overcomplete sparse representation method of space-time two-dimensional spectrum.The method achieve in the case of independent same distribution sample number deficiency, profit Estimate clutter covariance matrix with single frames training sample, thus avoiding the shadow to self-adaptive processing effect for the strong non-homogeneous clutter environment Ring.But, the method yet suffers from following main deficiency is: one is the big problem of operand, carries out rarefaction representation to clutter spectrum Super complete radix mesh uncertain, but be much larger than degree of freedom in system, and degree of freedom in system is generally thousands of in practice, so every In the covariance matrix restructuring procedure of one range cell sample, required operand is very big, is unfavorable for real-time processing, thus Have influence on the effect in practical engineering application.Two is base mismatch problems, and used in the method, base is actually one group of interpolation Discrete fourier dft vector, and the echo data of reality because there is the non-ideal factors such as error it is impossible to base vector Rarefaction representation；In addition, the method needs to carry out discretization expression to space-time plane, such that not being located in discrete grid block point The signal of the heart is revealed to all mesh points, thus destroying the openness of echo data.

Content of the invention

Overcomplete sparse representation side for above-mentioned super-resolution estimation clutter space-time two-dimensional spectrum in non-homogeneous clutter environment The deficiency of method, the present invention proposes a kind of positioning space-time adaptive processing (joint- of the joint domain based on data matching Domain localized stap, jdl-stap) method, it is capable of the detection to echo signal, and solve above-mentioned sparse extensive In multiple stap method, the huge problem with base mismatch of operand, positions jdl-stap method with respect to classical joint domain simultaneously, carries The detection probability of high moving-target, reduces the false alarm rate of detection.

For reaching above-mentioned purpose, the present invention employ the following technical solutions pre- with realize.

A kind of based on data matching joint domain positioning space-time adaptive processing method it is characterised in that include with Lower step:

Step 1, receives the space-time two-dimensional echo data x of airborne early warning radar, to space-time using airborne early warning radar antenna Two-dimentional echo data x carries out joint domain positioning jdl dimensionality reduction, obtains dimensionality reduction echo data z and space-time steering vector s_z-jdl；

Step 2, constructs the data basic matrix φ of range cell to be detected_k；

Step 3, using space-time steering vector s_z-jdlDerive blocking matrix b；Using blocking matrix b and range cell to be detected Data z_k, obtain target and block later auxiliary echo dataData z of this range cell to be detected_kTake from step successively Dimensionality reduction echo data z in 1；Data basic matrix φ using blocking matrix b and range cell to be detected_kObtain target block with Data basic matrix afterwards

Step 4, blocks later data basic matrix using targetTo auxiliary echo dataCarry out data matching, obtain Auxiliary echo dataFitting coefficient

Step 5, using the data basic matrix φ of range cell to be detected_kWith auxiliary echo dataFitting coefficientRight Range cell data z to be detected_kCarry out data matching, obtain data z of range cell to be detected_kMinimum error of fitting y_k；Should Data z of range cell to be detected_kTake from the dimensionality reduction echo data z in step 1 successively；

Step 6, treats 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.

The feature of technique scheme and further improvement is that:

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

1a) utilize airborne early warning radar antenna, receive the space-time two-dimensional number of echoes of ground return within the coherent accumulation time According to x, this space-time two-dimensional echo data x ties up for mn, and wherein m represents umber of pulse, and n represents the array number of airborne early warning radar antenna；

1b) the dimensionality reduction transition matrix p that joint domain positions jdl dimensionality reduction is obtained according to following formula_jdl:

$p_{\mathrm{jdl}}=p_t(f_{i-1},f_i,f_{i+1})\&circletimes;p_s(g_{j-1},g_j,g_{j+1})$

Wherein, p_t(f_i-1,f_i,f_i+1) represent the time domain transition matrix being made up of three Doppler filters closing on, f_iTable Show the normalization Doppler frequency of target, f_i-1,f_i+1Represent the two normalization Doppler frequencies adjacent with target；I be less than Natural number equal to m and more than or equal to 1, m represents umber of pulse, p_s(g_j-1,g_j,g_j+1) represent be made up of three spatial filters Spatial domain transition matrix, the wave filter in the middle of these three spatial filters is the spatial domain steering vector of target, g_jReturning for target One change spatial frequency, g_j-1,g_j+1Be neighbouring two normalization spatial frequency, j be less than or equal to m and more than or equal to 1 from So count；Represent Kronecker product；Dimensionality reduction transition matrix p_jdlDimension be mn × 9 tie up；

1c) according to dimensionality reduction transition matrix p_jdlObtain the dimensionality reduction echo data z after joint domain positions jdl dimensionality reduction, be expressed as down Formula:

$z=p_{\mathrm{jdl}}^{h}x$

Wherein, ()^hRepresent conjugate transposition operation, according to dimensionality reduction transition matrix p_jdlDimension be mn × 9 dimension and space-time The dimension that two-dimentional echo data x can obtain dimensionality reduction echo data z for mn dimension is 9 dimensions；

Joint domain positions the space-time steering vector s after jdl dimensionality reduction_z-jdl, it is expressed as following formula:

$s_{z-\mathrm{jdl}}={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^t\&circletimes;{\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^t$

Wherein, ()^tRepresent transposition operation, s_z-jdlFor the space-time steering vector after dimensionality reduction.

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

Data basic matrix φ_kIt is expressed as following formula:

φ_k=[z₁z₂…z_l]∈c^d×l

Wherein, φ_kRepresent the data basic matrix of k-th range cell to be detected, k represents the data of range cell to be detected Sequence number, be less than the natural number needing all range cells to be detected sums to be processed；D represents dimensionality reduction echo data z's Dimension, l represents the number of the data closing on range cell, c^d×lRepresent the complex matrix space of d × l dimension, z_l(l=1,2 ..., l) Represent and close on the data of range cell, close on range cell and represent range cell near range cell to be detected, do not comprise two The individual range cell for protecting target.

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

3a) to space-time steering vector s_z-jdlTransposed form carry out singular value decomposition, obtain left singular matrix u, right unusual Matrix v and singular value matrix λ；Decomposition formula such as following formula:

$s_{z-\mathrm{jdl}}^t=u\·\mathrm{\λ}\·v^h$

Wherein, u represents that left singular matrix, v represent that right singular matrix, λ represent singular value matrix；(·)^tRepresent transposition behaviour Make, ()^hRepresent conjugate transposition operation；

3b) blocking matrix b is arranged to make up by the 2nd to n row order of right singular matrix, by right singular matrix v and following formula Derive blocking matrix b；

B=[v (:, 2:n)]^t

Wherein, v (:, 2:n) represents all row of right singular matrix v, the 2nd arrives n column matrix element；(·)^tRepresent transposition behaviour Make；

3c) auxiliary echo data is obtained according to blocking matrix bBlock later data basic matrix with targetAs following formula Shown:

${\stackrel{\&overbar;}{z}}_k={\mathrm{bz}}_k,{\stackrel{\&overbar;}{\mathrm{\φ}}}_k={\mathrm{b\φ}}_k$

Wherein, z_kRepresent the data of k-th range cell to be detected, the data of this range cell to be detected takes from step successively Dimensionality reduction echo data z in rapid 1, k represent the sequence number of the data of range cell to be detected, are needed by be processed less than need The natural number of detecting distance unit sum；Represent that target blocks later auxiliary echo data,After representing that target is blocked Data basic matrix, b be blocking matrix.

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

4a) block later data basic matrix with targetLater auxiliary echo data is blocked to targetCarry out A young waiter in a wineshop or an inn takes advantage of matching to represent, is expressed as following formula:

$\underset{{\stackrel{\&overbar;}{\mathrm{\α}}}_k}{\min }{\left|\right|{\stackrel{\&overbar;}{z}}_k-{\stackrel{\&overbar;}{\mathrm{\φ}}}_k{\stackrel{\&overbar;}{\mathrm{\α}}}_k\left|\right|}_2$

Wherein, | | | |₂Represent 2 norms solving vector,Represent auxiliary echo dataFitting coefficient；

4b) according to step 4a) in least square fitting represent, solve auxiliary echo dataFitting coefficient? A young waiter in a wineshop or an inn takes advantage of solutionIt is expressed as following formula:

${\stackrel{\&overbar;}{\mathrm{\α}}}_k^{*}={\stackrel{\&overbar;}{\mathrm{\φ}}}_k^h{\left({\stackrel{\&overbar;}{\mathrm{\φ}}}_k{\stackrel{\&overbar;}{\mathrm{\φ}}}_k^h\right)}^{-1}{\stackrel{\&overbar;}{z}}_k$

Wherein, ()^-1Representing matrix inversion operation, ()^hRepresent conjugate transposition operation,After representing that target is blocked Data basic matrix,Represent that target blocks later auxiliary echo data.

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

5a) with the data basic matrix φ of range cell to be detected_k, treat data z of detecting distance unit_kCarry out a young waiter in a wineshop or an inn Take advantage of matching；And with assisting echo dataFitting coefficientLeast square solutionIt is calculated optimization restrained boundary η_k, tool Body is realized by following formula:

$y_k=\underset{{\mathrm{\α}}_k}{\min }{|{|z}_k-{\mathrm{\φ}}_k{\mathrm{\α}}_k||}_2,\mathrm{subject\; to}{\left|\right|{\mathrm{\α}}_k\left|\right|}_2\≤{\mathrm{\η}}_k$

Wherein, α_kRepresent the fitting coefficient of the data of range cell to be detected, y_kThe 2 of the minimum error of fitting vector of expression Norm, η_kRepresent and optimize restrained boundary,

5b) by solving the optimal fitting coefficient that above formula obtains the data of range cell to be detected

The optimal fitting coefficient of the data according to range cell to be detectedObtain the data of range cell to be detected Little error of fitting y_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 k-th range cell to be detected, the data of this range cell to be detected takes from step successively Dimensionality reduction echo data z in rapid 1, k represent the sequence number of the data of range cell to be detected, are needed by be processed less than need The natural number of detecting distance unit sum；φ_kRepresent the data basic matrix of range cell to be detected；Represent that distance to be detected is single The optimal fitting coefficient of the data of unit；||·||₂Represent 2 norms solving vector.

Compared with prior art, the present invention has prominent substantive distinguishing features and significantly improves, and the present invention is dilute with existing Dredge recovery stap method to compare, the invention has the advantages that

(1) it is directed to the problem of operand, sparse restoration methods carry out the super complete radix mesh of rarefaction representation not to clutter spectrum Fixed, but it is much larger than degree of freedom in system, and degree of freedom in system is generally thousands of in practice, so in each range cell sample In covariance matrix restructuring procedure, required operand is very big, is unfavorable for real-time processing, thus having influence on its actual work Journey application effect.The present invention, by combining with dimensionality reduction stap method jdl, the optimization problem of original mn dimension is decomposed into m 9 dimension Little optimization problem to solve, greatly reduce the computation complexity of algorithm, solve operand in sparse recovery stap method Big problem.

(2) it is directed to base mismatch problems, used in sparse restoration methods, represent that base is actually one group of interpolation dft vector, And real data because there is the non-ideal factors such as error it is impossible to use given base vector rarefaction representation, in addition, the method needs right Space-time plane carries out discretization expression, such that the signal not being located at discrete grid block dot center is revealed to all mesh points, Thus destroying the openness of data.The present invention is directly used real data sample as basic matrix, rather than true using certain Fixed ideal flowing pattern, thus evaded the problem of base mismatch in above-mentioned sparse recovery stap method.

It can be seen that, in prior art, stap carries out airborne radar signal processing generally in high-dimensional data space, thus can Greatly increase computational complexity and required training sample number, in order to obtain better performance, the present invention is directed to above-mentioned asking Topic, closes on the data sample of range cell come Optimal Fitting range cell to be detected clutter data using range cell to be detected, Thus improving the clutter recognition performance of Adaptive Signal Processing, improve the detection probability of target.

Brief description

The present invention will be further described with reference to the accompanying drawings and detailed description.

Fig. 1 is flow chart of the present invention；

Fig. 2 is general pulse doppler processing result figure；

Fig. 3 is the change curve with border compensation dosage for the detection probability；

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

Fig. 5 is the output result figure of the minimum error of fitting of data of target proximity range cell；Fig. 5 (a) is through normal The output result of the minimum error of fitting of a segment distance unit scope after rule jdl method；Fig. 5 (c) is through transmission from one meridian to another side of the present invention The output result of the minimum error of fitting of a segment distance unit scope after method process；Fig. 5 (b) be through conventional jdl method it The output result of the minimum error of fitting of another segment distance unit scope afterwards；Fig. 5 (d) is another section after the inventive method The output result of the minimum error of fitting of range cell scope；

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

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

Specific embodiment

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

With reference to Fig. 1, a kind of joint domain positioning space-time adaptive processing method based on data matching of the present invention is described, The present invention is used for airborne early warning Radar Signal Processing, and its specific implementation step is as follows:

Step 1, receives the space-time two-dimensional echo data x of airborne early warning radar, to space-time using airborne early warning radar antenna Two-dimentional echo data x carries out joint domain positioning jdl dimensionality reduction, obtains dimensionality reduction echo data z and space-time steering vector s_z-jdl；

Step 1 specifically includes following sub-step:

1a) utilize airborne early warning radar antenna, receive the space-time two-dimensional number of echoes of ground return within the coherent accumulation time According to x, this space-time two-dimensional echo data x ties up for mn, and wherein m represents umber of pulse, and n represents the array number of airborne early warning radar antenna；

1b) the dimensionality reduction transition matrix p that joint domain positions jdl dimensionality reduction is obtained according to following formula_jdl:

$p_{\mathrm{jdl}}=p_t(f_{i-1},f_i,f_{i+1})\&circletimes;p_s(g_{j-1},g_j,g_{j+1})$

Wherein, p_t(f_i-1,f_i,f_i+1) represent the time domain transition matrix being made up of three Doppler filters closing on, f_iTable Show the normalization Doppler frequency of target, f_i-1,f_i+1Represent the two normalization Doppler frequencies adjacent with target；I be less than Natural number equal to m and more than or equal to 1, m represents umber of pulse, p_s(g_j-1,g_j,g_j+1) represent be made up of three spatial filters Spatial domain transition matrix, the wave filter in the middle of these three spatial filters is the spatial domain steering vector of target, g_jReturning for target One change spatial frequency, g_j-1,g_j+1Be neighbouring two normalization spatial frequency, j be less than or equal to m and more than or equal to 1 from So count；Represent Kronecker product；Dimensionality reduction transition matrix p_jdlDimension be mn × 9 tie up；

1c) according to dimensionality reduction transition matrix p_jdlObtain the dimensionality reduction echo data z after joint domain positions jdl dimensionality reduction, be expressed as down Formula:

$z=p_{\mathrm{jdl}}^{h}x$

Wherein, ()^hRepresent conjugate transposition operation, according to dimensionality reduction transition matrix p_jdlDimension be mn × 9 dimension and space-time The dimension that two-dimentional echo data x can obtain dimensionality reduction echo data z for mn dimension is 9 dimensions；

Joint domain positions the space-time steering vector s after jdl dimensionality reduction_z-jdl, it is expressed as following formula:

$s_{z-\mathrm{jdl}}={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^t\&circletimes;{\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^t$

Wherein, ()^tRepresent transposition operation, s_z-jdlFor the space-time steering vector after dimensionality reduction.

General space-time steering vector s is represented by the Kronecker product form of time domain steering vector and spatial domain steering vector, I.e.f_dAnd f_sRepresent normalized Doppler frequency and spatial frequency respectively；Time domain and spatial domain guiding arrow Amount is represented by respectively $\begin{array}{c}{s}_t\left(f_d\right)={\left[\begin{array}{cccc}1& \exp \left(j2\mathrm{\π}{f}_d\right)& ...& \exp \left(j2\mathrm{\π}(m-1)f_d\right)\end{array}\right]}^t\\ s_s\left(f_s\right)={\left[\begin{array}{cccc}1& \exp \left(j2\mathrm{\π}{f}_s\right)& ...& \exp \left(j2\mathrm{\π}(n-1)f_s\right)\end{array}\right]}^t\end{array}.$

Step 2, constructs the data basic matrix φ of range cell to be detected_k；

Data basic matrix φ_kIt is expressed as following formula:

φ_k=[z₁z₂… z_l]∈c^d×l

Wherein, φ_kRepresent the data basic matrix of k-th range cell to be detected, k represents the data of range cell to be detected Sequence number, be less than the natural number needing all range cells to be detected sums to be processed；D represents dimensionality reduction echo data z's Dimension, l represents the number of the data closing on range cell, c^d×lRepresent the complex matrix space of d × l dimension, z_l(l=1,2 ..., l) Represent and close on the data of range cell, close on range cell and represent range cell near range cell to be detected, do not comprise two The individual range cell for protecting target.

Step 3, using space-time steering vector s_z-jdlDerive blocking matrix b；Using blocking matrix b and range cell to be detected Data z_k, obtain target and block later auxiliary echo dataData z of this range cell to be detected_kTake from step successively Dimensionality reduction echo data z in 1；Data basic matrix φ using blocking matrix b and range cell to be detected_kObtain target block with Data basic matrix afterwards

Step 3 specifically includes following sub-step:

3a) to space-time steering vector s_z-jdlTransposed form carry out singular value decomposition, obtain left singular matrix u, right unusual Matrix v and singular value matrix λ；Decomposition formula such as following formula:

$s_{z-\mathrm{jdl}}^t=u\·\mathrm{\λ}\·v^h$

Wherein, u represents that left singular matrix, v represent that right singular matrix, λ represent singular value matrix；(·)^tRepresent transposition behaviour Make, ()^hRepresent conjugate transposition operation；

3b) blocking matrix b is arranged to make up by the 2nd to n row order of right singular matrix, by right singular matrix v and following formula Derive blocking matrix b；

B=[v (:, 2:n)]^t

Wherein, v (:, 2:n) represents all row of right singular matrix v, the 2nd arrives n column matrix element；(·)^tRepresent transposition behaviour Make；

3c) auxiliary echo data is obtained according to blocking matrix bBlock later data basic matrix with targetAs follows Shown in formula:

${\stackrel{\&overbar;}{z}}_k={\mathrm{bz}}_k,{\stackrel{\&overbar;}{\mathrm{\φ}}}_k={\mathrm{b\φ}}_k$

Wherein, z_kRepresent the data of k-th range cell to be detected, the data of this range cell to be detected takes from step successively Dimensionality reduction echo data z in rapid 1, k represent the sequence number of the data of range cell to be detected, are needed by be processed less than need The natural number of detecting distance unit sum；Represent that target blocks later auxiliary echo data,Represent target block with Data basic matrix afterwards, b is blocking matrix.

Step 4, blocks later data basic matrix using targetTo auxiliary echo dataCarry out data matching, obtain Take auxiliary echo dataFitting coefficient

Step 4 specifically includes following sub-step:

4a) block later data basic matrix with targetLater auxiliary echo data is blocked to targetCarry out A young waiter in a wineshop or an inn takes advantage of matching to represent, is expressed as following formula:

$\underset{{\stackrel{\&overbar;}{\mathrm{\α}}}_k}{\min }{\left|\right|{\stackrel{\&overbar;}{z}}_k-{\stackrel{\&overbar;}{\mathrm{\φ}}}_k{\stackrel{\&overbar;}{\mathrm{\α}}}_k\left|\right|}_2$

Wherein, | | | |₂Represent 2 norms solving vector,Represent auxiliary echo dataFitting coefficient；

4b) according to step 4a) in least square fitting represent, solve auxiliary echo dataFitting coefficient? A young waiter in a wineshop or an inn takes advantage of solutionIt is expressed as following formula:

${\stackrel{\&overbar;}{\mathrm{\α}}}_k^{*}={\stackrel{\&overbar;}{\mathrm{\φ}}}_k^h{\left({\stackrel{\&overbar;}{\mathrm{\φ}}}_k{\stackrel{\&overbar;}{\mathrm{\φ}}}_k^h\right)}^{-1}{\stackrel{\&overbar;}{z}}_k$

Wherein, ()^-1Representing matrix inversion operation, ()^hRepresent conjugate transposition operation,After representing that target is blocked Data basic matrix,Represent that target blocks later auxiliary echo data.

Step 5, using the data basic matrix φ of range cell to be detected_kWith auxiliary echo dataFitting coefficientRight Range cell data z to be detected_kCarry out data matching, obtain data z of range cell to be detected_kMinimum error of fitting y_k；Should Data z of range cell to be detected_kTake from the dimensionality reduction echo data z in step 1 successively；

Step 5 specifically includes following sub-step:

5a) with the data basic matrix φ of range cell to be detected_k, treat data z of detecting distance unit_kCarry out a young waiter in a wineshop or an inn Take advantage of matching；And with assisting echo dataFitting coefficientLeast square solutionIt is calculated optimization restrained boundary η_k, tool Body is realized by following formula:

$y_k=\underset{{\mathrm{\α}}_k}{\min }{|{|z}_k-{\mathrm{\φ}}_k{\mathrm{\α}}_k||}_2,\mathrm{subject\; to}{\left|\right|{\mathrm{\α}}_k\left|\right|}_2\≤{\mathrm{\η}}_k$

Wherein, α_kRepresent the fitting coefficient of the data of range cell to be detected, y_kThe 2 of the minimum error of fitting vector of expression Norm, η_kRepresent and optimize restrained boundary,

5b) by solving the optimal fitting coefficient that above formula obtains the data of range cell to be detected

The optimal fitting coefficient of the data according to range cell to be detectedObtain the data of range cell to be detected Little error of fitting y_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 k-th range cell to be detected, the data of this range cell to be detected takes from step successively Dimensionality reduction echo data z in rapid 1, k represent the sequence number of the data of range cell to be detected, are needed by be processed less than need The natural number of detecting distance unit sum；φ_kRepresent the data basic matrix of range cell to be detected；Represent that distance to be detected is single The optimal fitting coefficient of the data of unit；||·||₂Represent 2 norms solving vector.

Step 6, treats 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 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), will minimum error of fitting y_kSingle with distance to be detected The meansigma methodss of the minimum error of fitting of the data of the range cell of surrounding of unit compare, according to minimum error of fitting y_kWith meansigma methodss Ratio size, to determine whether there is target, finally there will be target or there is not target output.

With reference to emulation experiment, the effect of the present invention is described further.

(1) experiment condition:

The experiment of the present invention is carried out under matlab7.11 software.In the experimental design of the present invention, in order to check this Inventive method effectiveness in actual applications, processing data is derived from the measured data mcarm data set of external admission, its radar It is operated under positive side battle array pattern, front is made up of the spatial domain array element that can be used for Adaptive Signal Processing that 2 row 11 arrange, its part system System parameter is with reference to table 1.In order to test conveniently, the present invention extracts 11 array elements of the first row in mcarm data, front 32 pulses Echo data is verified.

Table 1

(2) Comparison of experiment results

Accompanying drawing 2 is general pulse doppler processing result figure.Transverse axis represents Doppler's channel position, and the longitudinal axis represents that distance is single First sequence number.Range cell is also referred to as range gate in the present invention.Although as can be seen from Figure 2 this radar is operated in positive side battle array situation Under, but the strong clutter component in space-time two-dimensional echo data, by various in the different modulation of landform reflectance and actual environment The presence of false target, has certain heterogeneity.

Accompanying drawing 3 is the change curve with border compensation dosage for the detection probability.Transverse axis represents boundary compensation, and the longitudinal axis represents detection Probability.When boundary compensation refers to optimize restrained boundary in solution procedure 5, the optimization upper bound of gained adds a compensation dosage.From Fig. 3 In as can be seen that basic near 0 compensation dosage, detection probability can obtain maximum, and this also just illustrates step 5 in the present invention Calculation optimization restrained boundary is effective and optimum.

Accompanying drawing 4 is the change curve with sample number for the detection probability.Sample number refers to close on range cell in the present invention The number of data.Transverse axis represents sample number, and the longitudinal axis represents detection probability.In the present invention after the dimension-reduction treatment of data jdl, data Dimension (i.e. degree of freedom) is reduced to 9.Figure 4, it is seen that detection probability basically reaches maximum when sample number is more than 36, this Just illustrate, in the present invention, data basic matrix can nearby 4 times of number of degrees of freedom, purposes close on range cell by range cell to be detected Data, to constitute, obtains the detection performance of optimum.

Fig. 5 is the output result figure of the minimum error of fitting of the data of target proximity range cell.In the present invention, target Nearby the data of range cell includes the data of multigroup range cell to be detected.Transverse axis represents the sequence number of range cell, longitudinal axis table Show power, represented with db.In Fig. 5, curve represents the minimum error of fitting of a segment distance unit scope in target Doppler passage Output result, horizontal linear represents the average output value of the minimum error of fitting of this segment distance unit scope, and circle represents target The minimum error of fitting output valve of range cell, in Fig. 5, " difference " represents the minimum error of fitting output valve of target range unit Difference and between the average output value of minimum error of fitting of this segment distance unit scope.From figure 5 it can be seen that through the present invention After process, target output becomes apparent from, and Fig. 5 (a) power when range cell is 150 compared with Fig. 5 (c) improves 11.9db, Fig. 5 (b) power when range cell is 200 compared with Fig. 5 (d) improves 11.1db, such that it is able to be more beneficial for echo signal Detection.

Fig. 6 is the change curve with target power for the detection probability.Transverse axis represents the target power of artificial setting, longitudinal axis table Show the detection probability of this target.The sparse restoration methods of direct data domain (d3sr), classical joint domain localization method is compared in Fig. 6 And joint domain localization method (df-jdl) based on data matching proposed by the present invention (jdl).From fig. 6 it can be seen that this The detection performance of bright method is much better than other two methods.

Fig. 7 is the change curve graph of a relation with false alarm rate for the detection probability.Transverse axis represents false alarm rate, and the longitudinal axis represents that detection is general Rate.Classical joint domain localization method (jdl) and the joint domain positioning side based on data matching proposed by the present invention is compared in Fig. 7 Method (df-jdl).It can be seen from figure 7 that the inventive method, with respect to traditional jdl method, has higher under certain false alarm rate Detection probability, and there is under identical detection probability lower false alarm rate.

Claims (5)

1. a kind of joint domain positioning space-time adaptive processing method based on data matching is it is characterised in that include following Step:

Step 1, receives the space-time two-dimensional echo data x of airborne early warning radar, to space-time two-dimensional using airborne early warning radar antenna Echo data x carries out joint domain positioning jdl dimensionality reduction, obtains dimensionality reduction echo data z and space-time steering vector s_z-jdl；

Step 2, constructs the data basic matrix φ of range cell to be detected_k；

Step 3, using space-time steering vector s_z-jdlDerive blocking matrix b；Number using blocking matrix b and range cell to be detected According to z_k, obtain target and block later auxiliary echo dataData z of this range cell to be detected_kTake from successively in step 1 Dimensionality reduction echo data z；Data basic matrix φ using blocking matrix b and range cell to be detected_kAfter obtaining target obstruction Data basic matrix

Step 3 specifically includes following sub-step:

3a) to space-time steering vector s_z-jdlTransposed form carry out singular value decomposition, obtain left singular matrix u, right singular matrix v With singular value matrix a；Decomposition formula such as following formula:

$s_{z-jdl}^t=u\·\mathrm{\λ}\·v^h$

Wherein, u represents that left singular matrix, v represent that right singular matrix, λ represent singular value matrix；(·)^tRepresent transposition operation, (·)^hRepresent conjugate transposition operation；

3b) blocking matrix b is arranged to make up by the 2nd to n row order of right singular matrix, is derived by right singular matrix v and following formula Blocking matrix b；

B=[v (:, 2:n)]^t

Wherein, v (:, 2:n) represents all row of right singular matrix v, the 2nd arrives n column matrix element；(·)^tRepresent transposition operation；

3c) auxiliary echo data is obtained according to blocking matrix bBlock later data basic matrix with targetIt is shown below:

${\stackrel{\&overbar;}{z}}_k={\mathrm{bz}}_k,{\stackrel{\&overbar;}{\mathrm{\φ}}}_k={\mathrm{b\φ}}_k$

Wherein, z_kRepresent the data of k-th range cell to be detected, the data of this range cell to be detected is taken from step 1 successively Dimensionality reduction echo data z, k represents the sequence number of the data of range cell to be detected, is to be processed all to be detected less than needing The natural number of range cell sum；Represent that target blocks later auxiliary echo data,Represent that target blocks later number According to basic matrix, b is blocking matrix；

Step 4, blocks later data basic matrix using targetTo auxiliary echo dataCarry out data matching, obtain auxiliary Echo dataFitting coefficient

Step 5, using the data basic matrix φ of range cell to be detected_kWith auxiliary echo dataFitting coefficientTo be checked Find range from cell data z_kCarry out data matching, obtain data z of range cell to be detected_kMinimum error of fitting y_k；This is to be checked Survey data z of range cell_kTake from the dimensionality reduction echo data z in step 1 successively；

Step 6, treats minimum error of fitting y of the data of detecting distance unit_kCarry out CA-CFAR detection, and export There is target or there is not target.

2. the joint domain positioning space-time adaptive processing method based on data matching according to claim 1, it is special Levy and be, step 1 specifically includes following sub-step:

1a) utilize airborne early warning radar antenna, receive the space-time two-dimensional echo data x of ground return within the coherent accumulation time, This space-time two-dimensional echo data x ties up for mn, and wherein m represents umber of pulse, and n represents the array number of airborne early warning radar antenna；

1b) the dimensionality reduction transition matrix p that joint domain positions jdl dimensionality reduction is obtained according to following formula_jdl:

$p_{jdl}=p_t(f_{i-1},f_i,f_{i+1})\&circletimes;p_s(g_{j-1},g_j,g_{j+1})$

Wherein, p_t(f_i-1, f_i, f_i+1) represent the time domain transition matrix being made up of three Doppler filters closing on, f_iRepresent mesh Target normalization Doppler frequency, f_i-1, f_i+1Represent the two normalization Doppler frequencies adjacent with target；I is less than or equal to m And the natural number more than or equal to 1, m represents umber of pulse, ps (g_j-1, g_j, g_j+1) represent the sky being made up of three spatial filters Domain transition matrix, the wave filter in the middle of these three spatial filters is the spatial domain steering vector of target, g_iNormalization for target Spatial frequency, g_j-1, g_j+1Be neighbouring two normalization spatial frequency, j be less than or equal to m and more than or equal to 1 natural number；Represent Kronecker product；Dimensionality reduction transition matrix p_jdlDimension be mn × 9 tie up；

1c) according to dimensionality reduction transition matrix p_jdlObtain the dimensionality reduction echo data z after joint domain positions jdl dimensionality reduction, be expressed as following formula:

$z=p_{jdl}^{h}x$

Wherein, ()^hRepresent conjugate transposition operation, according to dimensionality reduction transition matrix p_jdlDimension be mn × 9 dimension and space-time two-dimensional The dimension that echo data x can obtain dimensionality reduction echo data z for mn dimension is 9 dimensions；

Joint domain positions the space-time steering vector s after jdl dimensionality reduction_z-jdl, it is expressed as following formula:

$s_{z-jdl}={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^t\&circletimes;{\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^t$

Wherein, (.)^tRepresent transposition operation, s_z-jdlFor the space-time steering vector after dimensionality reduction.

3. the joint domain positioning space-time adaptive processing method based on data matching according to claim 1, it is special Levy and be, step 2 specifically includes:

Data basic matrix φ_kIt is expressed as following formula:

φ_k=[z₁z₂… z_l]∈c^d×l

Wherein, φ_kRepresent the data basic matrix of k-th range cell to be detected, k represents the sequence of the data of range cell to be detected Number, it is less than the natural number needing all range cell sums to be detected to be processed；D represents the dimension of dimensionality reduction echo data z, L represents the number of the data closing on range cell, c^d×lRepresent the complex matrix space of d × l dimension, z_l(l=1,2 ..., l) represent and face The closely data of unit, closes on range cell and represents range cell near range cell to be detected, do not comprise two and be used for The range cell of protection target.

4. the joint domain positioning space-time adaptive processing method based on data matching according to claim 1, it is special Levy and be, step 4 specifically includes following sub-step:

4a) block later data basic matrix with targetLater auxiliary echo data is blocked to targetCarry out least square Matching represents, is expressed as following formula:

$\begin{array}{cc}\underset{{\stackrel{\&overbar;}{\mathrm{\α}}}_k}{min}& \left|\right|{\stackrel{\&overbar;}{z}}_k-{\stackrel{\&overbar;}{\mathrm{\φ}}}_k{\stackrel{\&overbar;}{\mathrm{\α}}}_k|{|}_2\end{array}$

Wherein, | | | |₂Represent 2 norms solving vector,Represent auxiliary echo dataFitting coefficient；

4b) according to step 4a) in least square fitting represent, solve auxiliary echo dataFitting coefficientA young waiter in a wineshop or an inn Take advantage of solutionIt is expressed as following formula:

${\stackrel{\&overbar;}{\mathrm{\α}}}_k^{*}={\stackrel{\&overbar;}{\mathrm{\φ}}}_k^h{\left({\stackrel{\&overbar;}{\mathrm{\φ}}}_k{\stackrel{\&overbar;}{\mathrm{\φ}}}_k^h\right)}^{-1}{\stackrel{\&overbar;}{z}}_k$

Wherein, ()^-1Representing matrix inversion operation, ()^hRepresent conjugate transposition operation,Represent that target blocks later data Basic matrix,Represent that target blocks later auxiliary echo data.

5. the joint domain positioning space-time adaptive processing method based on data matching according to claim 1, it is special Levy and be, step 5 specifically includes following sub-step:

5a) with the data basic matrix φ of range cell to be detected_k, treat data z of detecting distance unit_kCarry out least square plan Close；And with assisting echo dataFitting coefficientLeast square solutionIt is calculated optimization restrained boundary η_k, especially by Following formula is realized:

$\begin{array}{cc}{y}_k=\underset{{\mathrm{\α}}_k}{min}\left|\right|z_k-{\mathrm{\φ}}_k{\mathrm{\α}}_k|{|}_2,& subjectto\left|\right|{\mathrm{\α}}_k|{|}_2\≤{\mathrm{\η}}_k\end{array}$

Wherein, α_kRepresent the fitting coefficient of the data of range cell to be detected, y_kRepresent 2 norms of minimum error of fitting vector, η_kRepresent and optimize restrained boundary,

5b) by solving the optimal fitting coefficient that above formula obtains the data of range cell to be detected

The optimal fitting coefficient of the data according to range cell to be detectedObtain the minimum matching of the data of range cell to be detected Error y_k, obtained by following formula:

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

Wherein, z_kRepresent the data of k-th range cell to be detected, the data of this range cell to be detected is taken from step 1 successively Dimensionality reduction echo data z, k represents the sequence number of the data of range cell to be detected, is to be processed all to be detected less than needing The natural number of range cell sum；φ_kRepresent the data basic matrix of range cell to be detected；Represent range cell to be detected The optimal fitting coefficient of data；||·||₂Represent 2 norms solving vector.