CN105759264A - Micro-motion target defect echo high-resolution imaging method based on time-frequency dictionary - Google Patents

Abstract

The invention discloses a high-resolution imaging method of micro-moving target defect echo based on a time-frequency dictionary, which mainly solves the problem in the prior art that it is difficult to perform high-resolution imaging on complex micro-moving targets and targets with data defects. The implementation scheme is as follows: firstly, the distance compression processing is performed on the micro-moving target defect echo data received by the inverse synthetic aperture radar; then, the short-time Fourier transform matrix of the echo is generated; and then, the modified augmented Lager The Langer algorithm calculates the time-instantaneous Doppler distribution of the defect echo signal of each range unit; finally, stacks the time-instantaneous Doppler distribution of all range units into a three-dimensional matrix, and selects two-dimensional matrices at different times to generate targets The range of the instantaneous Doppler image sequence. The invention can obtain well-focused imaging results under relatively low computing load, and can be used for target recognition and radar target detection.

Description

High-resolution imaging method of micro-moving target defect echo based on time-frequency dictionary

technical field

The invention belongs to the field of radar technology, and further relates to a high-resolution two-dimensional ISAR imaging method for micro-moving targets, which can be used for target recognition and radar target detection.

Background technique

With the rapid development of inverse synthetic aperture radar (ISAR), high-resolution ISAR imaging of micro-moving targets has become a new research direction in the field of radar imaging in recent years. For example, the engine blades of fixed-wing aircraft, the propellers of helicopters, the arms that swing when pedestrians walk, etc. Target fretting will produce sideband frequency modulations in addition to the subject Doppler frequency, known as micro-Doppler. Micro-Doppler is an inherent essential feature of a micro-moving target, which contains the structure and motion information of the target. When it is described by time-frequency analysis method, this complex frequency modulation will be used as an important feature in radar automatic target recognition and radar target detection. In recent years, high-resolution radar imaging of micro-moving targets has attracted extensive attention in the field of radar imaging.

Xidian University disclosed a two-dimensional ISAR imaging method for micro-moving rotating targets in the air in its patent application "Two-dimensional ISAR imaging method for micro-moving rotating targets in the air" (publication number: CN102426360A, application number: 201110257606.X) Imaging method. The specific steps of the method are as follows: perform translational compensation on the ISAR echoes collected by the radar, draw a time-frequency distribution map, determine the micro-Doppler range unit, and then separate the echoes for each range unit respectively, and finally use the range-multiple The Puler method is used to image the echo of the rigid body and the real number inverse Radon transform I-Radon transform algorithm is used to image the echo of the rotating part. This method has the advantages of simple implementation and high efficiency, but the disadvantage of this method in the implementation process is that this method cannot accurately image the micro-moving target in the case of micro-moving targets with echo defects and complex micro-movement forms.

Xidian University disclosed a sparse-aperture-based maneuvering target inverse synthetic aperture radar in its invention patent "Sparse Aperture-Based Maneuvering Target Inverse Synthetic Aperture Radar Imaging Method" (publication number: CN103901429A, application number: 201410140123.5) Imaging method. The specific steps of the method are as follows: performing range compression and envelope alignment processing on the received raw echo data of the inverse synthetic aperture radar with sparse aperture, and performing precise phase correction, then reconstructing the sparse aperture echo signal, and finally using Fast Fourier transform for range-Doppler imaging. Although the invention can achieve accurate phase compensation and data reconstruction in the case of maneuvering targets and sparse apertures, this method cannot achieve good focused imaging of complex micro-moving targets due to the traditional range-Doppler imaging method.

Contents of the invention

The purpose of the present invention is to propose a high-resolution imaging method for micro-moving target defect echoes based on a time-frequency dictionary, so as to realize accurate imaging of micro-moving targets under the condition of serious echo defects and complicated micro-movement forms of micro-moving targets, and obtain focus Good 2D ISAR image.

The basic idea of the present invention is: by using the defect echo information of the micro-moving target, constructing a non-parametric dictionary in the time-frequency domain, and using the modified augmented Lagrangian method to obtain the target range-instantaneous Doppler image, the implementation scheme includes as follows:

(1) Record the defect echo signal S ₀ of the micro-moving target through the inverse synthetic aperture radar, and perform distance compression on the defect echo data S ₀ of the micro-moving target, and obtain the echo signal S after the distance compression;

(2) Randomly generate short-time Fourier transform matrix W, and calculate the pseudo-inverse matrix of W

(3) Randomly generate a unit diagonal matrix T ₀ , and generate a data defect matrix T according to T ₀ ;

(4) Calculate the time-instantaneous Doppler distribution of the target defect echo signal in each range unit:

(4a) According to the data defect matrix T and the pseudo-inverse matrix G, calculate the inverse short-time Fourier transform matrix G ₁ =TG of the defect echo;

(4b) set splitting variable u=v-d, wherein d is an auxiliary vector, and v is the variable that adopts variable splitting method to separate from the time-instantaneous Doppler image f; Make the first sequence number m=1 of the distance unit;

(4c) Take the vector s _m corresponding to the mth distance unit from the echo signal S after range compression, set the initial value of the iteration step k as k=0, the regularization coefficient λ=0.03, and the auxiliary coefficient μ=0.2 ; Let the initial value d ₀ of the auxiliary vector d be an all-zero vector, and the initial value f ₀ of the time-instantaneous Doppler image = G ₁ s _m , where G ₁ is the inverse short-time Fourier transform matrix of the defect echo ;

(4d) Find the kth iteration result u _k of the splitting variable u according to the following formula:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}$

Among them, f _k is the kth iteration result of the time-instantaneous Doppler image f, d _k is the kth iteration result of the auxiliary vector d, soft is the contraction function, f _k +d _k is the sum vector, is the ratio of the regularization coefficient to the auxiliary coefficient;

When the corresponding element of f _k +d _k is greater than , the contraction function soft takes the element value corresponding to f _k +d _k , otherwise it takes zero;

(4e) Find the k+1 iteration result d _k+1 of the auxiliary vector d according to the following formula:

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; c</span>}$

in, is the conjugate transposition matrix of the inverse short-time Fourier transform matrix G ₁ of the defect echo, c is the coefficient vector, when s _m corresponds to the element defect, the corresponding element of the coefficient vector c is 1+μ, when s _m corresponds to the element When known, the corresponding element of the coefficient vector c is μ;

(4f) Calculate the k+1 iteration result f _k+1 of the time-instantaneous Doppler image f according to the following formula:

f _k+1 =u _k +d _k+1 ;

(4g) Set the threshold value ε=10 ^-3 , judge whether the stop condition is satisfied according to the following formula:

$\frac{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}$

If the condition is met, then stop the iteration, and stack the vector f _k+1 into a time-instantaneous Doppler matrix by columns, and perform step (4h);

When not satisfying this condition, update iteration step number k=k+1, and return to step (4d);

(4h) Update the range unit serial number m=m+1, when the updated range unit serial number is greater than the range unit number M, then stop the search for the range unit, obtain the time-instantaneous Doppler matrix corresponding to all range units, and execute Step (5); Otherwise, return to step (4c);

(5) Stack the time-instantaneous Doppler matrices corresponding to the echoes of all range units into a three-dimensional matrix, and extract two-dimensional matrices at different times from the three-dimensional matrix to generate the range-instantaneous Doppler image sequence of the target.

The present invention has the following advantages:

1. The present invention uses a non-parametric dictionary to realize range-instantaneous Doppler imaging, which can maintain robustness to complex micro-movements, avoid high computational complexity caused by estimating multiple parameters, and have high computational efficiency.

2. The present invention utilizes the defect echo information of the micro-moving target, and adopts the modified augmented Lagrangian method to solve the range-instantaneous Doppler image of the target. This method does not require the inverse of the matrix, and has high calculation efficiency. In the case of data defects, the false peaks caused by the defect echo are avoided, and a well-focused high-resolution two-dimensional ISAR image sequence can be obtained.

The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Description of drawings

Fig. 1 is the realization flowchart of the present invention;

Figure 2 is a distance-time diagram of randomly generated defect echo signals;

Figure 3 is the original range-instantaneous Doppler diagram of the complete echo signal;

Fig. 4 is the original range-instantaneous Doppler diagram of the defect echo signal;

Fig. 5 is the range-instantaneous Doppler diagram reconstructed from the defect echo signal by the present invention.

Embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.

detailed description

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

Step 1, the inverse synthetic aperture radar records the defect echo S ₀ of the micro-moving target.

Micro-movement refers to the small non-uniform motion or motion component of the target or target components in the radial direction relative to the radar.

Micro-motion targets, including pedestrians with wobbling hands and legs, vibrating wings of an airplane, tank tracks, helicopter rotors, rotating radomes on warships and armored vehicles, and ballistic missile warheads.

The defect echo of the micro-moving target is recorded by the inverse synthetic aperture radar, which means that the electromagnetic wave emitted by the inverse synthetic aperture radar encounters the micro-moving target during the propagation process, the micro-moving target reflects the electromagnetic wave, and the reflected echo is received by the radar receiver , the defect echo S ₀ of the micro-moving target is displayed on the radar display.

Step 2, performing range compression processing on the defect echo S ₀ of the micro-moving target received by the inverse synthetic aperture radar, to obtain the echo signal S after the range compression processing.

2a) Perform coherent detection processing on the defect echo S ₀ of the micro-moving target received by the inverse synthetic aperture radar, and obtain the echo signal after coherent detection processing

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>$

in, is the fast time of distance, t _m is the slow time of azimuth, S _r ( ) is the reference signal whose center frequency and modulation frequency are the same as the transmitted signal of inverse SAR, and * represents the conjugate operation;

2b) Perform Fourier transform on the echo signal processed by coherent detection to obtain the echo signal processed by range compression $S={\mathrm{\&Sigma;}}_i{\mathrm{\&rho;}}_i\&CenterDot;\sin c\&lsqb;\frac{2B}{c}(r-{\mathrm{\&Delta;R}}_i(t_m\left)\right)\&rsqb;\&Center\; Dot;\exp \&lsqb;-j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{\&Delta;R}}_i\left(t_m\right)\&rsqb;,$ Where i is the serial number of the target scattering point, ρ _i is the echo amplitude of the i-th scattering point of the micro-moving target, B is the bandwidth of the radar transmitting signal, c is the speed of light, r is the distance variable, λ is the wavelength, ΔR _i (t _m ) is the difference between the instantaneous slant distance and the reference distance of the i-th scattering point of the micro-moving target at time _tm .

Step 3, randomly generate short-time Fourier transform matrix W, and calculate the pseudo-inverse matrix of W

3a) Generate a discrete Fourier transform matrix F with e ^{-j2 π (k-1)(n-1)/N} as an element, where k is the row number, ranging from 1 to N, and n is the column number, ranging from 1 to N, where N is the number of target echo pulses;

3b) Select time l, retain the elements in the lth to l+h columns of the discrete Fourier transform matrix F, and set other elements to zero to obtain the short-time Fourier transform matrix W _{l at time l} , where h=N /4 is the window length of short-time Fourier transform;

3c) Make the time l change from 1 to Nh, repeat step (2b), stack the short-time Fourier transform matrix W _l of all moments, and obtain the short-time Fourier transform matrix W;

3d) Find the pseudo-inverse matrix of the short-time Fourier transform matrix W The dimension of the matrix is N ² ×N, where N is the number of target echo pulses.

Step 4, generate a data defect matrix T.

4a) Generate a unit diagonal matrix The dimension of T ₀ is N×N;

4b) Find the column number corresponding to the missing signal column vector from the defect echo signal S ₀ , and set the diagonal element corresponding to the column number of the diagonal matrix T ₀ to zero to obtain the data defect matrix T.

Step 5, calculating the time-instantaneous Doppler distribution of the target defect echo signal for each range unit.

5a) According to the data defect matrix T and the pseudo-inverse matrix G, calculate the inverse short-time Fourier transform matrix G ₁ =TG of the defect echo;

5b) Set the splitting variable u=v-d, where d is an auxiliary vector, and v is a variable separated from the time-instantaneous Doppler image f by using the variable splitting method; make the first serial number m=1 of the distance unit;

5c) Take the vector s _m corresponding to the mth distance unit from the range-compressed echo signal S, set the initial value of the iteration step k as k=0, the regularization coefficient λ=0.03, and the auxiliary coefficient μ=0.2; Let the initial value d ₀ of the auxiliary vector d be an all-zero vector, and the initial value f ₀ of the time-instantaneous Doppler image = G ₁ s _m , where G ₁ is the inverse short-time Fourier transform matrix of the defect echo;

5d) Calculate the kth iteration result u _k of the splitting variable u according to the following formula:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}$

Among them, f _k is the kth iteration result of the time-instantaneous Doppler image f, d _k is the kth iteration result of the auxiliary vector d, soft is the contraction function, f _k +d _k is the sum vector, is the ratio of the regularization coefficient to the auxiliary coefficient; when the corresponding element of f _k +d _k is greater than , the contraction function soft takes the element value corresponding to f _k +d _k , otherwise it takes zero;

5e) Find the k+1 iteration result d _k+1 of the auxiliary vector d according to the following formula:

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; c</span>}$

in, is the conjugate transposition matrix of the inverse short-time Fourier transform matrix G ₁ of the defect echo, c is the coefficient vector, when s _m corresponds to the element defect, the corresponding element of the coefficient vector c is 1+μ, when s _m corresponds to the element When known, the corresponding element of the coefficient vector c is μ;

5f) Find the k+1 iteration result f _k+1 of the time-instantaneous Doppler image f according to the following formula:

f _k+1 =u _k +d _k+1 ;

5g) Set the threshold value ε=10 ^-3 , and judge whether the stop condition is satisfied according to the following formula:

$\frac{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}$

If the condition is met, then stop the iteration, and rearrange the vector f _k+1 into a time-instantaneous Doppler matrix by column, and perform step (5h);

When not satisfying this condition, update iteration step number k=k+1, and return to step (5d);

5h) update the range unit serial number m=m+1, when the updated range unit serial number is greater than the range unit number M, then stop the search for the range unit, obtain the time-instantaneous Doppler matrix corresponding to all range units, and perform the steps (6); otherwise, return to step (5c).

Step 6: Construct the range-instantaneous Doppler image sequence of the micro-moving target.

6a) Arranging all the time-instantaneous Doppler two-dimensional matrices obtained in step (4) according to the serial number of the range unit to form a distance-time-instantaneous Doppler three-dimensional matrix;

6b) Select multiple time points in the time dimension of the range-time-instantaneous Doppler three-dimensional matrix, extract the two-dimensional matrices corresponding to these time points and arrange them in sequence to form the range-instantaneous Doppler image of the micro-moving target sequence.

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

1. Simulation parameters

Using a broadband radar operating in the X-band, the length of the micro-moving target is 6.4 meters, the wingspan width is 3.4 meters, the target rotation angle is 0° to 360° during the observation time, and the defect rate of the echo signal is 40%.

2. Simulation content

Simulation 1: Use 128 continuous echo signals to generate complete echo signal data, and then randomly generate 40% of the defect position, fill the defect position with zero, then generate defect echo signal data, draw its distance-slow time echo, and the result Figure 2.

Simulation 2: Perform short-time Fourier transform on the complete echo signal, and draw its original range-instantaneous Doppler image, the result is shown in Figure 3.

Simulation 3: Short-time Fourier transform is performed on the defect echo signal, and its original range-instantaneous Doppler image is drawn. The result is shown in Figure 4.

Simulation 4: Using the present invention to reconstruct the defect echo signal shown in FIG. 2 to obtain its range-instantaneous Doppler image, and the result is shown in FIG. 5 .

From the comparison between Fig. 5 and Fig. 3, it can be seen that the reconstructed range-instantaneous Doppler image of the defect echo signal has a narrower main lobe and Doppler Le resolution has been improved;

From the comparison between Figure 5 and Figure 4, it can be seen that the reconstructed range-instantaneous Doppler image of the defect echo signal is compared with the original range-instantaneous Doppler image of the defect echo signal, most of the false peaks are effectively suppressed, And the image focus effect is better.

The simulation results show that the present invention uses the defect echo information of the micro-moving target to construct a non-parametric dictionary in the joint time-frequency domain, and uses the modified augmented Lagrangian method to obtain the range-instantaneous Doppler image of the micro-moving target, which can The main lobe is narrower, the Doppler resolution is higher, and the image with good focusing effect is obtained.

Claims (5)

1. The micro-motion target defect echo high-resolution imaging method based on the time-frequency dictionary comprises the following steps:

(1) method for recording defect echo signal S of micro-motion target by inverse synthetic aperture radar₀And for the micro-motion target defect echo data S₀Performing distance compression to obtain an echo signal S after the distance compression;

(2) randomly generating a short-time Fourier transform matrix W and calculating a pseudo-inverse of W

(3) Randomly generating unit diagonal matrix T₀According to T₀Generating a data defect matrix T;

(4) calculating the time-instantaneous Doppler distribution of the target defect echo signal of each range cell:

(4a) calculating an inverse short-time Fourier transform matrix G of the defect echo according to the data defect matrix T and the pseudo inverse matrix G₁＝TG；

(4b) Setting a splitting variable u as v-d, wherein d is an auxiliary vector, and v is a variable separated from a time-instantaneous Doppler image f by adopting a variable splitting method; making the first serial number m of the distance unit equal to 1;

(4c) obtaining a vector S corresponding to the mth range unit from the echo signal S after range compression_mSetting the initial value of the iteration step number k as 0, the regularization coefficient lambda as 0.03 and the auxiliary coefficient mu as 0.2; setting an initial value d of an auxiliary vector d₀As initial values f of all-zero vector, time-instantaneous Doppler images₀＝G₁s_mWherein G is₁An inverse short-time Fourier transform matrix of the defect echo;

(4d) solving the kth iteration result u of the splitting variable u according to the formula_k：

Wherein f is_kAs a result of the k-th iteration of the time-instantaneous Doppler image f, d_kAs a result of the k-th iteration of the auxiliary vector d, soft is the contraction function, f_k+d_kIn order to sum the vectors, the vector is,the ratio of the regularization coefficient to the auxiliary coefficient;

when f is_k+d_kIs greater thanWhen it is, the shrinking function soft is taken as f_k+d_kCorresponding element valueOtherwise, zero is taken;

(4e) solving the (k + 1) th iteration result d of the auxiliary vector d according to the following formula_k+1：

Wherein,inverse short-time Fourier transform matrix G for defective echoes₁C is a coefficient vector when s is_mWhen the corresponding element is defective, the coefficient vector c has a corresponding element of 1+ mu, when s is_mWhen the corresponding element is known, the corresponding element of the coefficient vector c is mu;

(4f) solving the k +1 th iteration result f of the time-instantaneous Doppler image f according to the following formula_k+1：

f_k+1＝u_k+d_k+1；

(4g) Set threshold value of 10^-3Whether the stop condition is satisfied is determined according to the following formula:

if the condition is met, the iteration is stopped and the vector f is added_k+1Rearranging the Doppler frequency signals into a time-instantaneous Doppler matrix according to columns, and executing the step (4 h);

if the condition is not met, updating the iteration step number k to k +1, and returning to the step (4 d);

(4h) updating the sequence number M of the range units to be M +1, stopping searching the range units when the sequence number of the updated range units is greater than the number M of the range units, obtaining time-instantaneous Doppler matrixes corresponding to all the range units, and executing the step (5); otherwise, returning to the step (4 c);

(5) and stacking the time-instantaneous Doppler matrixes corresponding to all range cell echoes into a three-dimensional matrix, and extracting two-dimensional matrixes at different moments from the three-dimensional matrix to generate a range-instantaneous Doppler image sequence of the target.

2. The time-frequency dictionary-based micro-motion target defect echo high-resolution imaging method according to claim 1, wherein the short-time Fourier transform matrix W is randomly generated in the step (2) and is performed according to the following steps:

(2a) with e^{-j2 π (k-1)(n-1)/N}Generating a discrete Fourier transform matrix F for the elements, wherein k is a row number and ranges from 1 to N, N is a column number and ranges from 1 to N, and N is the number of target echo pulses;

(2b) selecting time l, reserving the elements from the l th row to the l + h th row of the discrete Fourier transform matrix F, and setting other elements to zero to obtain a short-time Fourier transform matrix W at the time l_lWherein h is N/4 is the window length of the short-time fourier transform;

(2c) changing the time l from 1 to N-h, repeatedly executing the step (2b), and transforming the short-time Fourier transform matrix W at all the time_lStacked to obtain a short-time fourier transform matrix W.

3. The time-frequency dictionary-based micro-motion target defect echo high-resolution imaging method according to claim 1, wherein the step (3) is performed according to the following steps:

(3a) generating unit diagonal matrixT₀Is N × N;

(3b) from defect echo signal S₀Finding out the column serial number corresponding to the defective signal column vector, and converting the diagonal array T into a diagonal array₀And setting the diagonal line element corresponding to the column sequence number to zero to obtain a data defect matrix T.

4. The time-frequency dictionary-based micro-motion target defect echo high-resolution imaging method according to claim 1, wherein in the step (5), time-instantaneous Doppler matrixes corresponding to echoes of all range cells are stacked into a three-dimensional matrix, and all the time-instantaneous Doppler two-dimensional matrixes obtained in the step (4) are sequentially arranged according to the sequence numbers of the range cells to form a distance-time-instantaneous Doppler three-dimensional matrix.

5. The time-frequency dictionary-based micro-motion target defect echo high-resolution imaging method according to claim 1, wherein in step (5), two-dimensional matrices at different moments are extracted from a three-dimensional matrix to generate a range-instantaneous Doppler image sequence of a target, a plurality of time points are selected in a time dimension of the range-time-instantaneous Doppler three-dimensional matrix, and two-dimensional matrices corresponding to the time points are extracted and sequentially arranged to form the range-instantaneous Doppler image sequence of the micro-motion target.