CN102608598A - Method for imaging actual aperture foresight on basis of subspace projection - Google Patents

Abstract

The invention discloses a real-aperture forward-looking imaging method based on subspace projection, which mainly solves the problem of high-resolution imaging of a target directly in front of a flight track. The detection process is as follows: 1) Emitting radar beams at equal intervals, sequentially overlapping scanning of the ground surveillance area, and obtaining radar echo data; 2) Extracting the intensity vector of the echo data through modulo calculation; 3) Obtaining the echo intensity Vector autocorrelation matrix; 4) Eigendecompose the autocorrelation matrix; 5) Construct the noise subspace with the eigenvector corresponding to the small eigenvalue; 6) Define the pattern search vector; 7) Project the pattern search vector to the noise subspace In space; 8) calculating the peak value of the spatial spectral function; 9) determining the number of signals according to the peak value of the spatial spectral function to realize forward-looking imaging. The invention has the advantage of improving the resolution accuracy of the adjacent targets in the main lobe, and can be used in the imaging field of the airborne radar monitoring system to realize the detection and identification of the target in the track line direction.

Description

Real Aperture Front-Look Imaging Method Based on Subspace Projection

technical field

The invention relates to the field of imaging, in particular to the problem of high-resolution imaging of a target directly in front of a flight track, which can be used in an airborne radar monitoring system to detect and identify targets along the direction of the flight track.

Background technique

In the ever-changing modern high-tech warfare environment in the future, battlefield information is complex and changeable, and fighters are fleeting. Timely and correct battlefield detection and tactical reconnaissance are related to the success or failure of the war. Therefore, it is necessary to require the radar imaging system to have a certain imaging accuracy and imaging range. However, when the antenna beam is close to coincident with the track line, since the ground targets distributed on both sides of the track have the same Doppler history, aliasing is likely to occur, and the Doppler change rate of the target is very small, the azimuth resolution will be reduced. Rapid decline, forming a forward-looking "blind zone", and the existing synthetic aperture radar system cannot solve this problem. Therefore, how to better use the radar system to carry out effective detection of the target in front to obtain the forward-looking image has become one of the hotspots in the radar field.

For the forward-looking imaging problem, typical solutions include: bistatic SAR forward-looking imaging method, single-pulse forward-looking imaging method, real-aperture deconvolution forward-looking imaging method, etc., among which:

1. Bistatic SAR forward-looking imaging method. It is carried out through the bistatic SAR system. This system refers to the synthetic aperture radar with the transmitter and receiver installed on different platforms. The transmitter and receiver can have different spatial positions and movement speeds. The transmitter transmits the chirp signal to the observation area; the receiver receives the ground echo signal and performs imaging processing. Due to its special receiving mode, the bistatic SAR system can only achieve forward-looking imaging in certain specific modes. For example, the transmitter and receiver have their own independent flight paths and cannot overlap. The target point is on the track of the receiver. Along the projection line on the ground; motion errors will greatly affect the forward-looking imaging results of bistatic SAR, and motion compensation must be performed. However, the analysis of motion compensation for bistatic SAR forward-looking imaging is complicated, and the corresponding compensation techniques and schemes are very difficult to implement. Large; in the existing algorithms, the geometric correction of the bistatic SAR forward-looking imaging results is not perfect, and there is no complete theoretical analysis of the type and amount of geometric deformation; since the receiver and the transmitter are placed on different platforms , leading to the separation of transceivers. Therefore, bistatic SAR forward-looking imaging faces a series of synchronization problems of transceiver systems, including time synchronization, space synchronization and frequency synchronization.

2. Single-pulse forward-looking imaging method. The basic idea of monopulse imaging is to use sufficiently high distance resolution to distinguish the main scatterers on the target, and then use monopulse goniometric technology to obtain the angle of the scattering point away from the center of the beam, and then use it for target positioning. Although monopulse angle measurement has high measurement accuracy in theory, in practical applications, there are often the following limitations: when a complex-shaped target moves relative to the radar, it will cause the deviation between the apparent center of the target and the actual center of the target, Angular flicker phenomenon occurs, which restricts the imaging quality; the single-pulse forward-looking imaging technology cannot measure the angles of different scattering centers in the same range unit, and can only obtain the positions of equivalent scattering points, which reduces the accuracy of angle measurement; when the same beam memory When there are many targets, the angle measurement accuracy will drop sharply and even the position of the target cannot be detected accurately, especially when there are two or more targets with similar energy in the beam azimuth range within a certain distance unit, the angle measurement accuracy is especially Low: In monopulse forward-looking imaging, two independent receiving branches are usually used for each angle measurement coordinate plane, that is, two branches in the azimuth plane and two branches in the elevation plane, and the system is complex.

3. Real-aperture deconvolution forward-looking imaging method. It regards the echo signal output by the radar sensor as the convolution of the transmitted signal and the target angle information in the azimuth domain, and as the convolution of the transmitted signal and the target range information in the distance domain, so in theory it can be deconvolution method Accurate location information of the target is obtained. This method is simple to operate, does not require motion compensation, and has little difficulty in system calculation and analysis. However, there are also certain problems in the deconvolution process: single-channel deconvolution is prone to produce ill-conditioned solutions, and the algorithm requires a high signal-to-noise ratio. When the signal-to-noise ratio is less than 30dB, the target resolution effect is poor; To reduce the influence of ill-conditioned effects, Berenstein et al. developed multi-channel deconvolution technology for information reconstruction of linear shift invariant systems, which can transform part of the deconvolution problem into a good state, but not all convolution sets Satisfying the strong coprime condition, when the multi-channel cannot satisfy the strong coprime condition, the signal-to-noise ratio will still be greatly reduced after deconvolution. Therefore, the use of multi-channel deconvolution technology also has great limitations.

Contents of the invention

The purpose of the present invention is to address the shortcomings of the above-mentioned existing forward-looking imaging problems, and propose a real-aperture forward-looking imaging method based on subspace projection, so as to realize airborne radar forward-looking high-resolution imaging, reduce noise interference, and improve main Resolution accuracy of nearby targets within the lobe.

The technical scheme of the present invention is as follows: firstly, sequential overlapping scanning is performed on the ground monitoring area to obtain radar echo data; then the intensity vector of the echo data is extracted; finally, an array high-resolution method based on subspace projection is used to analyze the echo intensity vector Processing is carried out to realize airborne radar forward-looking high-resolution imaging, and its specific steps include the following:

(1) Sequential overlapping scanning of the ground surveillance area is carried out by transmitting radar beams at equal intervals to obtain radar echo data Y;

(2) Perform a modulo operation on the echo data Y to extract its intensity vector X:

X=|Y(k)|,

Wherein, |·| represents the modulus operation, k=1, 2, ..., K, K represents the length of the echo data;

(3) Obtain the autocorrelation matrix R _X of the echo intensity vector X:

R _X =E[XX ^H ],

Among them, X represents the echo intensity vector, (·) ^H represents the conjugate transpose, E[·] represents the expected value;

(4) Carry out eigendecomposition on the autocorrelation matrix R _X , and decompose it into the form of multiplication and accumulation of eigenvalues and eigenvectors:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ,</span>$

Wherein, λ _j represents the j eigenvalue, v _j represents the j eigenvector, ( ) ^H represents the conjugate transpose, j=1, 2, ..., N, N represents the number of eigenvalues;

(5) Arrange the eigenvalues λ _j in ascending order λ ₁ =λ ₂ =...=λ _Np ≤λ _N-p+1 ≤...≤λ _N , and adjust the order of the eigenvectors accordingly: v ₁ , v ₂ ,...,v _Np , v _N-p+1 ,...,v _N , use the eigenvectors corresponding to the first NP small eigenvalues to form the noise subspace E _N :

E _N = [v ₁ , v ₂ , . . . , v _Np ],

Among them, p represents the number of signals, and N represents the number of eigenvalues;

(6) Define the direction map search vector set a:

a=[a _i ],

Wherein, a _i represents the i-th pattern search vector, i=1, 2, ..., 2M, and M represents the length of the pattern search vector;

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; M\&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; M\&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span>$

b_width表示主瓣宽度，d为一个变化的参数；Among them, ( ) ^T represents the transpose, δ _i represents the displacement of the i-th pattern search vector, n is a fixed parameter, which controls the main lobe width of the pattern, and τ represents the scanning density,

b_width represents the width of the main lobe, and d is a variable parameter;

(7) Project the i-th direction map search vector a _i onto the noise subspace E _N to obtain the projection of the search vector on the noise subspace:

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>$

Among them, v _j represents the eigenvector corresponding to the small eigenvalue, ( ) ^H represents the conjugate transpose, p represents the number of signals, and N represents the number of eigenvalues;

(8) Calculate the spatial spectral function:

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$

where E _N represents the noise subspace, a _i represents the search vector, Represents the square of the two-norm;

(9) Determine the number of signals according to the number of peaks of the spatial spectrum function to distinguish adjacent targets in the main lobe, complete the detection and identification of targets along the track line, and realize forward-looking high-resolution imaging.

Compared with the prior art, the present invention has the following advantages:

(1) The present invention performs imaging processing on the intensity extraction vector of the echo data, which does not produce angular flicker phenomenon, can separate multiple targets in the same main lobe, and can even detect two objects with similar energy in the same beam. target, effectively improving the detection accuracy and imaging quality;

(2) The present invention only needs one channel to receive echo data, which is beneficial to system realization;

(3) The present invention can alleviate the influence of noise on the signal through the method of constructing the noise subspace, and will not generate ill-conditioned solutions.

Description of drawings

Fig. 1 is the general flow chart of the forward vision imaging of the present invention;

Fig. 2 is a schematic diagram of sequential overlapping scanning in the present invention;

Fig. 3 is the forward vision imaging result of the present invention;

Fig. 4 is the target resolution probability after scanning with four side lobe patterns in the present invention;

Fig. 5 is the target resolution probability after scanning with no sidelobe pattern in the present invention;

Fig. 6 is the relationship diagram of the resolution probability and the signal-to-noise ratio under the target interval 1/4 main lobe width of the present invention;

FIG. 7 is a graph showing the relationship between the scanning interval and the minimum target interval when the signal-to-noise ratio is 10 dB in the present invention.

Detailed ways

With reference to Fig. 1, the implementation steps of the present invention are as follows:

Step 1: Sequential overlapping scanning of the ground monitoring area is carried out by transmitting radar beams at equal intervals to obtain radar echo data Y;

Referring to Figure 2, in this step, the airborne radar sequentially overlaps and scans the ground surveillance area, that is, the radar echo data is regarded as the convolution of the antenna beam and the target information, and the echo data Y is obtained by emitting radar beams at equal intervals.

Step 2: Perform a modulo operation on the echo data Y to extract its intensity vector X:

X＝|Y(k)|, 1)

Wherein, |·| represents a modulo operation, k=1, 2, . . . , K, K represents the length of the echo data.

Express the intensity vector X as a multiply-accumulate form of the signal amplitude value and the pattern vector:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Wherein, N represents the noise vector, s _t represents the amplitude value of the t-th signal, _at represents the pattern vector corresponding to the t-th signal, t=1, ..., p, p represents the number of signals.

Step 3: Obtain the autocorrelation matrix R _X of the echo intensity vector X:

R _x =E[XX ^H ], 3)

Among them, X represents the echo intensity vector, (·) ^H represents the conjugate transpose, and E[·] represents the expected value.

Step 4: Carry out eigendecomposition on the autocorrelation matrix R _X , and decompose it into the form of multiplication and accumulation of eigenvalues and eigenvectors:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, λ _j represents the jth eigenvalue, v _j represents the jth eigenvector, (·) ^H represents the conjugate transpose, j=1, 2, ..., N, N represents the number of eigenvalues.

Step 5: Arrange the eigenvalues λ _j in ascending order λ ₁ =λ ₂ =...=λ _Np ≤λ _N-p+1 ≤...≤λ _N , and adjust the order of the eigenvectors accordingly: v ₁ , v ₂ ,...,v _Np , v _N-p+1 ,...,v _N , use the eigenvectors corresponding to the first NP small eigenvalues to form the noise subspace E _N :

E _N = [v ₁ , v ₂ , . . . , v _Np ], 5)

Among them, p represents the number of signals, and N represents the number of eigenvalues.

Step 6: Define the direction map search vector set a:

a=[a _i ], 6)

Wherein, a _i represents the i-th pattern search vector, i=1, 2, ..., 2M, and M represents the length of the pattern search vector;

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; M\&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; M\&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

b_width表示主瓣宽度，d为一个变化的参数。Among them, ( ) ^T represents the transpose, δ _i represents the displacement of the i-th pattern search vector, n is a fixed parameter, which controls the main lobe width of the pattern, and τ represents the scanning density,

b_width represents the width of the main lobe, and d is a variable parameter.

Step 7: Project the i-th direction map search vector a _i onto the noise subspace E _N to get the projection of the search vector on the noise subspace:

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Among them, v _j represents the eigenvector corresponding to the small eigenvalue, ( ) ^H represents the conjugate transpose, p represents the number of signals, and N represents the number of eigenvalues.

Step 8: Calculate the spatial spectral function:

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

where E _N represents the noise subspace, a _i represents i pattern search vectors, Represents the square of the binorm.

Step 9: Determine the number of signals according to the number of peaks of the spatial spectrum function to distinguish adjacent targets in the main lobe, complete the detection and identification of targets along the track line, and realize forward-looking high-resolution imaging.

Due to the orthogonality of the signal subspace and the noise subspace, the projection of the direction diagram vector a _i corresponding to the signal on the noise subspace E _N is the smallest, forming the peak of the spatial spectral function P(i), so the number of spatial spectral function peaks That is, the number of signals, so as to complete the detection and identification of targets along the flight path, and realize forward-looking high-resolution imaging.

Effect of the present invention can be further illustrated by following simulation:

Simulation 1, to verify the imaging results of the method proposed in the present invention.

Sequentially overlap and scan the ground point targets under the pattern interval of 1/4 the main lobe width, the distance between the two point targets is 1/4 the main lobe width, the signal-to-noise ratio is 10dB, and snapshots are taken 500 times. The forward-looking imaging results are shown in Figure 3 shown.

Observing FIG. 3, it can be found that the method proposed in the present invention can distinguish two adjacent targets in the main lobe. This is because the array high-resolution imaging method based on subspace projection can reduce the influence of noise and improve the detection accuracy of the target by constructing the noise subspace.

Simulation 2, to verify the impact of side lobes on target resolution probability.

Sequentially overlap and scan the ground point targets at a pattern interval of 1/4 the main lobe width, the distance between two point targets is 1/4 the main lobe width, the signal-to-noise ratio is 10dB, take 500 snapshots, and conduct Monte Carlo experiments 200 times , the target resolution probabilities obtained after scanning with four sidelobe patterns are shown in Fig. 4, and the target resolution probabilities after scanning with no sidelobe pattern are shown in Fig. 5.

Observing Figure 4 and Figure 5, it can be found that the number of side lobes has little effect on the target resolution probability. This is because the energy of the side lobes is very small and can be ignored in practical applications.

Simulation 3, to verify the influence of signal-to-noise ratio on target resolution probability.

The point targets on the ground are overlapped and scanned sequentially under the interval of 1/4 of the main lobe width of the pattern, the distance between two point targets is 1/4 of the main lobe width, snapshots are taken 500 times, and Monte Carlo experiments are carried out 500 times, and the resolution probability and signal are obtained. The relationship between the noise ratio is shown in Figure 6.

Observing Figure 6, it can be found that the smaller the signal-to-noise ratio, the lower the target resolution probability. This is because at a low SNR, the signal will be buried in the noise, and the correct signal subspace and noise subspace cannot be obtained, resulting in a decrease in the target resolution probability.

Simulation 4, to verify the resolvable minimum target interval under different scan intervals.

Under the condition that the threshold of resolution probability is 90% and the signal-to-noise is 10dB, 500 snapshots and 100 Monte Carlo experiments are performed, and the relationship between the scan interval and the minimum target interval is shown in Figure 7.

Observing Figure 7, it can be found that when the signal-to-noise ratio is 10dB, the limit value of the target interval is 1/5 of the main lobe width, that is, only when the target interval is greater than or equal to 1/5 of the main lobe width, forward-looking high-resolution imaging can be performed.

Claims (1)

1. the real aperture forward sight formation method based on subspace projection comprises the steps:

(1) through the equidistant emission of radar beam, the order overlapping scan is carried out in the surface surveillance zone, obtains the radar return data Y;

(2) echo data Y is carried out modulo operation, extracts its strength vector X:

X＝|Y(k)|，

Wherein, || the expression modulo operation, k=1,2 ..., K, K represent the length of echo data;

(3) ask for the autocorrelation matrix R of echo strength vector X _X:

R _X＝E[XX ^H]，

Wherein, X representes echo strength vector, () ^HThe expression conjugate transpose, E [] representes expectation value;

(4) to autocorrelation matrix R _XCarry out feature decomposition, it be decomposed into the multiply accumulating form of eigenwert and proper vector:

$R_X=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j{v}_j{v}_j^H,$

Wherein, λ _jRepresent j eigenwert, v _jRepresent j proper vector, () ^HThe expression conjugate transpose, j=1,2 ..., N, the number of N representation feature value;

(5) with eigenvalue _jArrange λ by ascending order ₁=λ ₂=...=λ _N-p≤λ _N-p+1≤...≤λ _N, and correspondingly adjust proper vector and be in proper order: v ₁, v ₂..., v _N-p, v _N-p+1..., v _N, constitute noise subspace E with preceding N-P little eigenwert characteristic of correspondence vector _N:

E _N＝[v ₁，v ₂，...，v _N-p]，

Wherein, the number of p expression signal, the number of N representation feature value;

(6) definition directional diagram search vector set a:

a＝[a _i]，

Wherein, a _iRepresent i directional diagram search vector, i=1,2 ..., 2M, M represent the length of directional diagram search vector;

$a_i={[\frac{\sin \left[n(\mathrm{M\&tau;}+{\mathrm{\&delta;}}_i)\right]}{n(\mathrm{M\&tau;}+{\mathrm{\&delta;}}_i)},\frac{\sin \left[\left(n((M-1)\mathrm{\&tau;}+{\mathrm{\&delta;}}_i\right)\right]}{n[(M-1)\mathrm{\&tau;}+{\mathrm{\&delta;}}_i]},...,\frac{\sin \left[n((-M)\mathrm{\&tau;}+{\mathrm{\&delta;}}_i)\right]}{n[(-M)\mathrm{\&tau;}+{\mathrm{\&delta;}}_i]}]}^T,$

Wherein, () ^TThe expression transposition, δ _iRepresent the displacement of i directional diagram search vector, n is a fixing parameter, the main lobe width of control directional diagram, and τ has represented the scanning dense degree,

B_width representes main lobe width, and d is the parameter of a variation;

(7) with i directional diagram search vector a _iProject to noise subspace E _NOn, obtain the projection of search vector on noise subspace:

$E_N{a}_i=\left[\underset{j=1}{\overset{N-p}{\mathrm{\&Sigma;}}}{v}_j{v}_j^H\right]a_i,$

Wherein, v _jRepresent little eigenwert characteristic of correspondence vector, () ^HThe expression conjugate transpose, the number of p expression signal, the number of N representation feature value;

(8) computer memory spectral function:

$P\left(i\right)=1/{\left|\right|E_N{a}_i\left|\right|}_2^2,$

Wherein, E _NThe expression noise subspace, a _iThe expression search vector,

Represent two norms square;

(9) confirm the number of signal according to the number of spatial spectrum peak of function,, accomplish detection and identification, realize the forward sight high-resolution imaging along track line direction target to differentiate the adjacent objects in the main lobe.

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