CN103675787A - One-dimension range profile optimal orthogonal nolinear subspace identification method for radar targets - Google Patents

Abstract

The invention belongs to the technical field of radar target identification and provides a one-dimension range profile optimal orthogonal nolinear subspace identification method for radar targets. Nonlinear transformation is conducted on a one-dimension range profile of each category of targets, the one-dimension range profile is mapped to high-dimensional linear characteristic space, an optimal orthogonal nolinear transformational matrix is established in the high-dimensional linear characteristic space, characteristic extraction is conducted, a nearest neighbor rule is adopted for classification, and the category of an input target is finally determined. The method comprises the steps of utilizing a kernel function and the one-dimension range profile of the radar target to train a vector to determine matrixes of Ui, Vrj, (K)ij, W alpha and B alpha; determining a vector alpha i (i=1, 2, ..., n) in optimal orthogonal nolinear subspace, determining the transformational matrix A of the optimal orthogonal nolinear subspace, wherein the A ranges from alpha 1 to alpha n; determining a base template vector of the target; determining an optimal orthogonal nolinear projection vector of the one-dimension range profile xt of the input target; determining the Euclidean distance between the optimal orthogonal nolinear projection vector and the base template vector of the target and determining the category of the one-dimension range profile of the input target. The one-dimension range profile optimal orthogonal nolinear subspace identification method for radar targets can effectively improve target identification performance.

Description

The optimum Nonlinear Orthogonal subspace recognition methods of a kind of radar target-range image

Technical field

The invention belongs to Technology of Radar Target Identification field, relate to the optimum Nonlinear Orthogonal subspace recognition methods of a kind of radar target-range image.

Background technology

High-resolution radar can obtain the one-dimensional range profile information of target, and one-dimensional range profile has reflected the distribution situation of target scattering point on radar line of sight, the target RCS that low resolution radar is obtained is relatively long-pending, it is more about information such as object construction and shapes that one-dimensional range profile can provide, and these information are very beneficial for the classification of target.

Sorting technique based on subspace is widely used in the fields such as image recognition, recognition of face, has also obtained good recognition effect in radar target recognition, and wherein more representational method has proper subspace method and Canonical sub-space method.But within the scope of great-attitude angle and under complicated electromagnetic environment, the distribution of one-dimensional range profile occurs significantly non-linear, the recognition performance of the linear subspaces recognition methodss such as Canonical sub-space method can decline greatly.

For this reason, introduce kernel function and solve the nonlinear problem occurring in one-dimensional range profile, many identification of nonlinearity methods have been proposed thereupon, as the proper subspace method based on kernel function, Canonical sub-space method based on kernel function etc., owing to correctly having processed non-linear in one-dimensional range profile, therefore, the recognition performance of these nonlinear methods has had certain improvement.

But the dimension of the Canonical sub-space based on kernel function is subject to the restriction of target classification number, for the very high one-dimensional range profile of dimension, can cause the length of extraction feature too short, there is the loss of classified information.In addition, the axes of coordinates of the Canonical sub-space based on kernel function is not quadrature, in the feature that makes to extract, comprises redundant information.These factors are by limiting the recognition performance of the Canonical sub-space method based on kernel function, so the recognition performance of the Canonical sub-space method based on kernel function still has further room for improvement above.

Summary of the invention

In order to overcome defect of the prior art, the invention provides the optimum Nonlinear Orthogonal subspace recognition methods of a kind radar target-range image, effectively improve the recognition performance to radar target, its technical scheme is,

The optimum Nonlinear Orthogonal subspace recognition methods of a kind of radar target-range image, first the one-dimensional range profile of target is carried out to nonlinear transformation, be mapped to High-dimensional Linear feature space, then at high-dimensional feature space, set up an optimum Nonlinear Orthogonal transformation matrix, carry out feature extraction, adopt nearest neighbor classifier to classify, the classification under final decision input target, comprises the following steps:

1) utilize kernel function and radar target-range image trained vector to determine matrix U _i, V _rj(K) _ij,

2) according to matrix U _i, V _rj(K) _ijdetermine matrix W _α;

3) according to matrix U _idetermine matrix B _α;

4) according to matrix W _αand B _αdetermine a vector α in subspace ₁;

5) according to matrix W _α, B _αand α ₁determine other the vector α in subspace _i(i=2,3 ..., n);

6) utilize vector α _idetermine subspace matrix A=[α ₁α ₂α _n];

7) determine the library template vector of target;

8) determine the target one-dimensional range profile x of input _toptimum Nonlinear Orthogonal projection vector;

9) determine the Euclidean distance between optimum Nonlinear Orthogonal projection vector and the library template vector of target;

10) determine the affiliated classification of target one-dimensional range profile of input.

Further preferably, using the average library template vector as such target of the non-linear projection vector of optimum quadrature of every classification target one-dimensional range profile training sample, determine after optimum Nonlinear Orthogonal projection vector and Euclidean distance, by arest neighbors criterion, judge target classification.

Further preferably, judge that other concrete grammar of target class is: by

eigenvalue of maximum characteristic of correspondence vector determine first vector of subspace, by matrix

eigenvalue of maximum characteristic of correspondence vector determine other vector of subspace, finally determine that optimum Nonlinear Orthogonal subspace is A=[α ₁α ₂α _n], the one-dimensional range profile of training objective is by formula

to optimum Nonlinear Orthogonal subspace projection, using the average library template vector as such target of the optimum Nonlinear Orthogonal projection vector of every classification target one-dimensional range profile training sample, total library template vector is

wherein

be that i classification target is trained optimum Nonlinear Orthogonal projection average vector; One-dimensional range profile x to input target _t, by formula

calculate optimum Nonlinear Orthogonal projection vector y _t, and calculate following Euclidean distance:

$d_i=\left|\right|y_t-{\stackrel{\‾}{y}}_i\left|\right|i=\mathrm{1,2},...,g$

If

sentencing input target is k class.

Beneficial effect of the present invention:

The present invention extracts target signature by set up optimum Nonlinear Orthogonal subspace at high-dimensional feature space, the dimension of this nonlinear subspace is not subject to the restriction of number of targets on the one hand, solved the problem of the classified information loss existing while extracting low dimensional feature from high dimensional data, simultaneously, the axis of projection of this nonlinear subspace is mutually orthogonal, reduced and extracted the redundant information in feature, thereby improved the recognition performance to radar target.By four classification target emulation experiments having been verified to the validity of the method.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described.

Optimum Nonlinear Orthogonal subspace

If n dimension column vector x _ij(i=1,2 ..., g; J=1,2 ..., N _i) be j one-dimensional range profile of i classification target, wherein g is target classification number, N _iit is i classification target number of training.

One-dimensional range profile is carried out to nonlinear transformation

y _ij＝φ(xi _j) (1)

Wherein φ () is Nonlinear Mapping function.Above formula is mapped to high-dimensional feature space by one-dimensional range profile, y _ijfor x _ijat picture corresponding to high-dimensional feature space, its dimension is made as n', can be for large or infinitely great arbitrarily.

At high-dimensional feature space, scatter matrix B between class _swith scatter matrix W in class _sbe respectively

$B_S=\underset{i=1}{\overset{g}{\mathrm{\Σ}}}{N}_i({\stackrel{\‾}{y}}_i-\stackrel{\‾}{y}){({\stackrel{\‾}{y}}_i-\stackrel{\‾}{y})}^T---\left(2\right)$

$W_S=\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Σ}}}(y_{\mathrm{ij}}-{\stackrel{\‾}{y}}_i){(y_{\mathrm{ij}}-{\stackrel{\‾}{y}}_i)}^T---\left(3\right)$

N=N wherein ₁+ N ₂+ ... + N _gfor total number of training,

${\stackrel{\‾}{y}}_i=\frac{1}{N_i}\underset{i=1}{\overset{g}{\mathrm{\Σ}}}{y}_{\mathrm{ij}}---\left(4\right)$

$\stackrel{\‾}{y}=\frac{1}{N}\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_g}{\mathrm{\Σ}}}{y}_{\mathrm{ij}}---\left(5\right)$

i＝1,2,…,g。

Be constructed as follows ratio

$F=\frac{s^T{B}_{S}s}{s^T{W}_{S}s}---\left(6\right)$

Wherein F is ratio, and s is any one column vector in n' dimensional feature space.

Can not make the vector s of F maximum from formula (6) direct solution, because do not know the concrete functional form of Nonlinear Mapping φ, but can solve by the following method.

Introduce following kernel function k (x _k, x _l)=φ ^t(x _k) φ (x _l), and order

$s=\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{ij}}\mathrm{\φ}\left(x_{\mathrm{ij}}\right)---\left(7\right)$

Combined type (4), formula (5) abbreviation can obtain

$s^T{\stackrel{\‾}{z}}_i=\frac{1}{N_i}\underset{r=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_1}{\mathrm{\Σ}}}\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{rj}}k(x_{\mathrm{rj}},x_{\mathrm{ik}})={\mathrm{\α}}^T{U}_i---\left(8\right)$

$s^T\stackrel{\‾}{z}=\frac{1}{N}\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\left\{\frac{1}{N_i}\underset{r=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Σ}}}\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{rj}}k(x_{\mathrm{rj}},x_{\mathrm{ik}})\right\}={\mathrm{\α}}^{T}V---\left(9\right)$

$s^T{z}_{\mathrm{ij}}=\underset{r=1}{\overset{g}{\mathrm{\Σ}}}\underset{k=1}{\overset{N_r}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{rk}}k(x_{\mathrm{rk}},x_{\mathrm{ij}})={\mathrm{\α}}^T{\left(K\right)}_{\mathrm{ij}}---\left(10\right)$

Wherein $\mathrm{\α}={[{\mathrm{\α}}_{11}{\mathrm{\α}}_{12}\·\·\·{\mathrm{\α}}_{g{H}_g}]}^T,$

$V_{\mathrm{rj}}=\frac{1}{N}\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\frac{1}{N_i}\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}k(x_{\mathrm{rj}},x_{\mathrm{ik}})---\left(12\right)$

(K) _ij,rk＝k(x _rk,x _ij) (13)

r＝1,2,…,g;k＝1,2,…,N _r。

Therefore, can be calculated by formula (7), formula (8) and formula (9)

s ^TB _Ss＝α ^TB _αα (14)

s ^TWs＝α ^TW _αα (15)

Wherein,

$B_{\mathrm{\α}}=\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1,i\≠j}{\overset{g}{\mathrm{\Σ}}}\frac{N_i{N}_j}{N}(U_i-U_j){(U_i-U_j)}^T---\left(16\right)$

$W_{\mathrm{\α}}=\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Σ}}}({\left(K\right)}_{\mathrm{ij}}-V_i){({\left(K\right)}_{\mathrm{ij}}-V_i)}^T---\left(17\right)$

By formula (14) and formula (15) substitution formula (4), can obtain

$F=\frac{{\mathrm{\α}}^T{B}_{\mathrm{\α}}\mathrm{\α}}{{\mathrm{\α}}^T{W}_{\mathrm{\α}}\mathrm{\α}}---\left(18\right)$

F is got to maximum value, and formula (18) the right to α differentiate and make it equal zero, can obtain

$W_{\mathrm{\α}}^{-1}{B}_{\mathrm{\α}}\mathrm{\α}=\mathrm{\λ\α}---\left(19\right)$

Wherein λ and α are respectively eigenwert and characteristic of correspondence vector.If the vector of the eigenvalue of maximum characteristic of correspondence in formula (19) is α ₁.

By vector α ₁substitution formula (7), can make the vector of F maximum in formula (6) be

$s_1={\mathrm{\α}}_1^T\left[\begin{array}{c}\mathrm{\φ}\left(x_{11}\right)\\ \mathrm{\φ}\left(x_{12}\right)\\ .\\ .\\ .\\ \mathrm{\φ}\left(x_{{2N}_2}\right)\end{array}\right]---\left(20\right)$

If s _i(i=2,3 ..., g) be in feature space with s ₁vertical n' dimension column vector, and meet

$F_{\max }=\underset{\left\{a_i\right\}}{\max }\frac{s_i^{T}B{s}_i}{s_i^{T}W{s}_i}---\left(21\right)$

Structure

$\frac{s_i^{T}B{s}_i}{s_i^{T}W{s}_i}-{\mathrm{\β}}_1{s}_i^T{s}_1-{\mathrm{\β}}_2{s}_i^T{s}_2-...-{\mathrm{\β}}_{i-1}{s}_i^T{s}_{i-1}---\left(22\right)$

β wherein ₁, β ₂, β _i-1for Lagrange constant.Application solves with same above Kernel-Based Methods, order

$s_i=\underset{r=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_r}{\mathrm{\Σ}}}{\mathrm{\α}}_{i,\mathrm{rj}}\mathrm{\φ}\left(x_{\mathrm{rj}}\right)---\left(23\right)$

Formula (22) can abbreviation be

$\frac{{\mathrm{\α}}_i^T{B}_{\mathrm{\α}}{\mathrm{\α}}_i}{{\mathrm{\α}}_i^T{W}_{\mathrm{\α}}{\mathrm{\α}}_i}-{\mathrm{\β}}_1{\mathrm{\α}}_i^{T}K{\mathrm{\α}}_1-{\mathrm{\β}}_2{\mathrm{\α}}_i^{T}K{\mathrm{\α}}_2...-{\mathrm{\β}}_{i-1}{\mathrm{\α}}_i^{T}K{\mathrm{\α}}_{i-1}---\left(24\right)$

Wherein

k=[k (x _rk, x _ij)] _{n * N}for nuclear matrix (r, i=1,2 ... g; K, j=1,2 ..., N _i).To the α in formula (24) _idifferentiate to make it be zero, abbreviation can obtain

A ^(i-1)＝[α ₁α ₂…α _i-1] (26)

From formula (25), α _iproper vector for equation in formula (25), makes α _ifor eigenvalue of maximum characteristic of correspondence vector, and by its substitution formula (23), can obtain

$s_i={\mathrm{\α}}_i^T\left[\begin{array}{c}\mathrm{\φ}\left(x_{11}\right)\\ \mathrm{\φ}\left(x_{12}\right)\\ .\\ .\\ .\\ \mathrm{\φ}\left(x_{{2N}_2}\right)\end{array}\right]---\left(27\right)$

From above derivation, vector s ₁, s ₂..., s _nall make formula (6) reach greatly, and s _iand s _r(i ≠ r) is mutually orthogonal.At high-dimensional feature space, by s ₁, s ₂s _ncan form a sub spaces

S＝[s ₁s ₂…s _n] (28)

Claim that S is projection subspace.One-dimensional range profile x is Nonlinear Mapping being projected as in this subspace of high-dimensional feature space arbitrarily

z＝S ^Tφ(x) (29)

Claim the optimum Nonlinear Orthogonal projection vector that z is x.

By formula (20), formula (27) and formula (28) substitution formula (29), abbreviation can obtain

Wherein

A＝[α ₁α ₂…α _n] (31)

A is called optimum Nonlinear Orthogonal subspace.

Radar target recognition based on optimum Nonlinear Orthogonal subspace

Suppose to have g class target, can utilize kernel function and every classification target one-dimensional range profile training sample set to set up optimum Nonlinear Orthogonal subspace by formula (19), formula (27) and formula (31), the one-dimensional range profile of training objective is pressed formula (30) to optimum Nonlinear Orthogonal subspace projection, using the average library template vector as such target of the optimum Nonlinear Orthogonal projection vector of every classification target one-dimensional range profile training sample, total library template vector is

$\{{\stackrel{\‾}{z}}_1{\stackrel{\‾}{z}}_2...{\stackrel{\‾}{z}}_g\}---\left(32\right)$

Wherein

be that i classification target is trained optimum Nonlinear Orthogonal projection average vector.

One-dimensional range profile x to input target _t, can calculate optimum Nonlinear Orthogonal projection vector by formula (30) is z _t, and calculate following Euclidean distance

$d_i=\left|\right|z_t-{\stackrel{\‾}{z}}_i\left|\right|i=\mathrm{1,2},...g---\left(33\right)$

If

$k=\arg \underset{\left\{i\right\}}{\min }\left\{d_i\right\}---\left(34\right)$

Sentencing input target is k class.

Fig. 1 illustrates the process flow diagram of the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image of the present invention.Flow process starts from step 201.

In step 202, by g class training objective one-dimensional range profile training one-dimensional range profile vector x _ijdetermine following matrix:

${\left(U_i\right)}_{\mathrm{rj}}=\frac{1}{N_i}\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}k(x_{\mathrm{rj}},x_{\mathrm{ik}})---\left(35\right)$

$V_{\mathrm{rj}}=\frac{1}{N}\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\frac{1}{N_i}\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}k(x_{\mathrm{rj}},x_{\mathrm{ik}})---\left(36\right)$

(K)i _j,rk＝k(x _rk,x _ij) (37)

I=1 wherein, 2 ... g, j=1,2 ... N _i, r=1,2 ... g, g is target classification sum, N _iit is i classification target one-dimensional range profile number of training.

In step 2031, determine matrix:

$W_{\mathrm{\α}}=\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Σ}}}({\left(K\right)}_{\mathrm{ij}}-U_i){({\left(K\right)}_{\mathrm{ij}}-U_i)}^T---\left(38\right)$

$B_{\mathrm{\α}}=\underset{i=1}{\overset{g}{\mathrm{\Σ}}}\underset{j=1,i\≠j}{\overset{g}{\mathrm{\Σ}}}\frac{N_i{N}_j}{N}(V_i-V_j){(V_i-V_j)}^T---\left(39\right)$

In step 2032, determine first vector in subspace:

α ₁for matrix

middle eigenvalue of maximum characteristic of correspondence vector

In step 2033, determine other vector in subspace:

eigenvalue of maximum characteristic of correspondence vector

In step 2034, true optimum Nonlinear Orthogonal subspace is:

A＝[α ₁α ₂…α _n] (40)

In step 204, determine that the library template vector of target is

$\{{\stackrel{\‾}{y}}_1{\stackrel{\‾}{y}}_2...{\stackrel{\‾}{y}}_g\}---\left(41\right)$

Wherein

it is the mean vector of the optimum Nonlinear Orthogonal projection vector of i classification target one-dimensional range profile training sample.

In step 2051, determine the target one-dimensional range profile x of input _toptimum Nonlinear Orthogonal projection vector be:

In step 2052, determine that the Euclidean distance between optimum Nonlinear Orthogonal projection vector and the library template vector of target is:

$d_i=\left|\right|y_t-\stackrel{\‾}{y_i}\left|\right|i=\mathrm{1,2},...g---\left(43\right)$

In step 2053, determine the affiliated classification of target one-dimensional range profile of input.

$k=\arg \underset{\left\{i\right\}}{\min }\left\{d_i\right\}---\left(44\right)$

According to the flow process of the optimum Nonlinear Orthogonal subspace recognition methods of radar target picture of the present invention, end at step 206.

Emulation experiment

The validity of extracting method in order to verify, carries out following emulation experiment.

Design four kinds of point targets: " | " font, " V " font, " doing " font and " little " font target.The bandwidth of radar transmitted pulse is 150MHZ (range resolution is 1m, and radar radially sample interval is 0.5m), and target is set to even scattering point target, " | " scattering point of target is 5, the scattering of its excess-three target is counted and is 9.Object attitude angle be within the scope of 0 °～70 ° in the one-dimensional range profile of 1 °, get object attitude angle and be 0 °, 2 °, 4 °, 6 ° ..., the one-dimensional range profile of 70 ° trains, the one-dimensional range profile of all the other attitude angle is as test data, and every classification indicates 35 test sample books.In experiment, kernel function is gaussian kernel function σ wherein ²=6.2.Experiment shows, to other kernel function, radar target-range image non-linear projection recognition method is herein applicable equally.

To four kinds of targets (" | " font target, " V " font target, " doing " font target and " little " font target), within the scope of 0 °～70 ° of attitude angle, utilize the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image herein and the Canonical sub-space method based on kernel function to carry out identification experiment, result as shown in Table 1.

As seen from Table 1, to target " | ", the discrimination of the Canonical sub-space method based on kernel function is 81%, and the discrimination of the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image is herein 98%; To target " V ", the discrimination of the Canonical sub-space method based on kernel function is 80%, and the discrimination of the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image is herein 87%; Target " is done ", and the discrimination of the Canonical sub-space method based on kernel function is 76%, and the discrimination of the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image is herein 82%; To target " little ", the discrimination of the Canonical sub-space method based on kernel function is 80%, and the discrimination of the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image is herein 87%.On average, to four class targets, the correct recognition rata of the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image herein, higher than the Canonical sub-space method based on kernel function, illustrates that the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image herein can improve the recognition performance of multi-class targets really.

The recognition result of two kinds of methods of table 1

The optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image that the present invention can be proposed is applied to radar target-range image recognition system, meets radar target-range image recognition system to improving the requirement of the recognition performance of multi-class targets.

The above; it is only preferably embodiment of the present invention; protection scope of the present invention is not limited to this; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses, the simple change of the technical scheme that can obtain apparently or equivalence are replaced and are all fallen within the scope of protection of the present invention.

Claims (3)

1. the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image, it is characterized in that, first the one-dimensional range profile of target is carried out to nonlinear transformation, be mapped to High-dimensional Linear feature space, then at high-dimensional feature space, set up an optimum Nonlinear Orthogonal transformation matrix, carry out feature extraction, adopt nearest neighbor classifier to classify, classification under final decision input target, comprises the following steps:

1) utilize kernel function and radar target-range image trained vector to determine matrix U _i, V _rj(K) _ij;

2) according to matrix U _i, V _rj(K) _ijdetermine matrix W _α;

3) according to matrix U _idetermine matrix B _α;

4) according to matrix W _αand B _αdetermine a vector α in subspace ₁;

5) according to matrix W _α, B _αand α ₁determine other the vector α in subspace _i(i=2,3 ..., n);

6) utilize vector α _idetermine subspace matrix A=[α ₁α ₂α _n];

7) determine the library template vector of target;

8) determine the target one-dimensional range profile x of input _toptimum Nonlinear Orthogonal projection vector;

9) determine the Euclidean distance between optimum Nonlinear Orthogonal projection vector and the library template vector of target;

10) determine the affiliated classification of target one-dimensional range profile of input.

2. the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image according to claim 1, it is characterized in that, using the average library template vector as such target of the non-linear projection vector of optimum quadrature of every classification target one-dimensional range profile training sample, determine after optimum Nonlinear Orthogonal projection vector and Euclidean distance, by arest neighbors criterion, judge target classification.

3. the optimum Nonlinear Orthogonal subspace recognition methods of radar target-range image as claimed in claim 2, is characterized in that: judge that other concrete grammar of target class is: by eigenvalue of maximum characteristic of correspondence vector determine first vector of subspace, by matrix

eigenvalue of maximum characteristic of correspondence vector determine other vector of subspace, finally determine that optimum Nonlinear Orthogonal subspace is A=[α ₁α ₂α _n], the one-dimensional range profile of training objective is by formula

to optimum Nonlinear Orthogonal subspace projection, using the average library template vector as such target of the optimum Nonlinear Orthogonal projection vector of every classification target one-dimensional range profile training sample, total library template vector is

wherein

be that i classification target is trained optimum Nonlinear Orthogonal projection average vector; One-dimensional range profile x to input target _t, by formula

calculate optimum Nonlinear Orthogonal projection vector y _t, and calculate following Euclidean distance:

$d_i=\left|\right|y_t-{\stackrel{\‾}{y}}_i\left|\right|i=\mathrm{1,2},...,g$

If

sentencing input target is k class.

Images