CN106199602A - A kind of Staggered SAR echo signal method for reconstructing - Google Patents

Abstract

The invention discloses a Staggered-SAR echo signal reconstruction method, which uses conformal Fourier transform to process the radar signal after range compression. The method fully considers the echo characteristics of the Staggered-SAR, and can obtain a uniform image suitable for high-quality radar imaging. Azimuth spectrum. The spectrum obtained by this method can accurately reflect the spectral characteristics of the azimuth echo under data loss and non-uniform sampling conditions, and finally can be used for high-quality imaging of the Staggered-SAR system. Compared with the existing method, the method of the present invention can obtain uniform azimuth frequency spectrum, is suitable for classical frequency domain algorithms and the like, and can obtain high-quality imaging results.

Description

A Staggered-SAR Echo Signal Reconstruction Method

technical field

The invention belongs to the field of radar technology, and in particular relates to the imaging technology of High-Resolution Wide-Swath (HRWS) Synthetic Aperture Radar (SAR).

Background technique

Staggered-SAR is a new radar mode for high resolution wide swath imaging. Compared with traditional SAR, Staggered-SAR lies in the pulse repetition frequency (Pulse Repetition Frequency, PRF for short). Due to the agile PRF, the Staggered-SAR system can improve the blind area distribution in the radar echo of the traditional SAR system, and can realize the High-resolution wide-swath imaging of targets. Therefore, the Staggered-SAR system can be applied to fields such as all-day and all-weather spaceborne SAR rapid and large-scale map mapping, and plays an important role in the development of the national economy and national security. The Institute for Microwave and Radar Technology of the German Aerospace Agency (DLR) conducted research on Staggered-SAR in 2012.

The complete echo spectrum of the Staggered-SAR system is the necessary premise and basis for constructing the frequency domain imaging algorithm. Compared with the echoes of traditional SAR, the echoes obtained by the Staggered-SAR system have changed the distribution of blind areas. Under the condition of rapid PRF changes, there will be no continuous loss of large segments, but the phenomenon of blind area distribution still exists. In actual imaging processing These blind areas will seriously affect the imaging quality during the imaging process, so it is necessary to reconstruct the echo data before imaging processing. In addition, since Staggered-SAR adopts agile PRF technology, the result is non-uniform sampling in the azimuth of the radar echo. When using the traditional frequency domain algorithm, non-uniform sampling will also affect the imaging quality. Therefore, reconstructing the echo data and obtaining the echo spectrum is the key link in Staggered-SAR signal processing.

In the currently published Staggered-SAR echo signal reconstruction literature, representative methods include two-point linear interpolation, multi-channel reconstruction, optimal linear interpolation and other methods adopted by Italy Villano and other scholars (see literature 1: VillanoM, Krieger G , Moreira A. Staggered SAR: High-resolution wide-swath imaging by continuous PRI variation [J]. Geoscience and Remote Sensing, IEEE Transactionson, 2014, 52(7): 4462-4479.). However, in the reconstruction process of radar echoes, these methods have the disadvantages of unsatisfactory two-point linear interpolation results, narrow application conditions for multi-channel reconstruction, and large amount of calculation for optimal linear interpolation. Therefore, a new reconstruction method is proposed very important.

Contents of the invention

In order to overcome the above-mentioned technical problems, the present invention proposes a Staggered-SAR echo signal reconstruction method, by adopting conformal Fourier transform to process the radar signal after range compression; obtaining a uniform azimuth spectrum suitable for high-quality radar imaging, which can Accurately reflect the spectral characteristics of the azimuth echo under data loss and non-uniform sampling conditions.

The technical scheme adopted in the present invention is: a Staggered-SAR echo signal reconstruction method, comprising the following steps:

S1. Initialize the parameters of the Staggered-SAR imaging system, including: the wavelength of the radar emission signal, denoted as λ; the pulse width of the radar system emission, denoted as T _p ; the bandwidth of the radar system emission signal, denoted as B; the radar system platform speed, denoted as V _s ; the beam velocity of the radar system, denoted as V _g ; the pulse repetition frequency of the radar system changes periodically, and it increases or decreases linearly in each cycle, among which the maximum pulse repetition frequency is denoted as PRF _max ; the minimum pulse repetition frequency is denoted as PRF _min ; the number of pulses transmitted in a pulse repetition frequency change period, denoted as M;

Staggered-SAR original echo data matrix, denoted as S, where S is a matrix of N _a rows and N _r columns, each column of data is the sampling of the azimuth echo signal, and the data of each row is the single pulse range echo one by one Signal sampling, N _a is the number of sampling points in the azimuth direction, N _r is the number of sampling points in the range direction;

S2, distance compression, according to the parameters in step S1, use the traditional frequency domain distance compression method to perform distance compression on the Staggered-SAR original echo data matrix S, and obtain the data matrix S _r , where S _r is the number of N _a rows and N _r columns matrix;

S3. Calculate the data loss location record matrix blind;

Wherein, the blind dimension of the data loss position record matrix is N _target row N _a column, the value blind(k,j) of the jth column element in the kth row in the matrix is 0 or 1, and the blind(k,j) value is determined by Delay T(k,j) is determined; T(k,j) is the delay when the kth point target receives the jth transmit pulse, k=1,2...N _target , j=1,2...N _a , N _target is the number of targets in the scene;

S4, preprocessing the distance compressed data, according to the lost position record matrix blind calculated in S3, removing each row of data corresponding to the position of 0 in the blind matrix in the matrix S _r , and obtaining the preprocessed data matrix S _c ;

Among them, S _c is N _c row N _r column matrix, N _c is the number of received pulses;

S5. Conformal Fourier transform. Conformal Fourier transform is performed column by column on the preprocessed data matrix S _c obtained in S4 to obtain a uniform azimuth spectrum matrix F _cft with N _a rows and N _r columns;

Among them, the segment length of conformal Fourier transform processing is MM _miss + 1, M is the number of pulses transmitted by the radar system in one cycle, M _miss is the number of pulses lost in one cycle, and M _miss uses the blind matrix to calculate a pulse The number of lost pulses in the repetition period, get M _miss ;

S6, two-dimensional spectral conjugate compensation, fast Fourier transform is performed on each row of the azimuth spectral matrix F _cft obtained in S5, to obtain a two-dimensional spectral matrix B _cft with N _a rows and N _r columns, and the two-dimensional spectral matrix B _cft is compared with the reference The spectrum matrix θ _2df is conjugated and multiplied to obtain a two-dimensional data matrix S _2df with N _a rows and N _r columns, namely Then perform two-dimensional fast Fourier inverse transform on S _2df to obtain the imaging result;

in, is the reference spectrum, R _min is the shortest slant distance, c is the speed of light, V _r is the equivalent velocity of the platform, f _ττ is the spectrum equalization vector in the range direction, and f _ηη is the frequency equalization vector in the azimuth direction;

The range-to-frequency decile vector f _{ττ is} specifically obtained by dividing [-B, B) into N _r parts, B is the bandwidth of the transmitted signal, and N _r is the number of sampling points in the range direction; the azimuth-to-frequency decile vector f _ηη specifically by It is obtained by equally dividing into N _a parts, T _SAR is the synthetic aperture time, and N _a is the number of azimuth sampling points.

Further, the calculation formula of the time delay T(k, j) in step S3 is as follows:

T(k,j)=(R _t (k,j)+R _r (k,j))/c;

Among them, R _t (k, j) represents the slant distance between the platform and the k-th point target when the j-th pulse is transmitted; R _r (k, j) represents the slant distance between the platform and the k-th point target when the j-th pulse is received the slope distance between.

Furthermore, the value of blind(k,j) in step S3 is determined by the time delay T(k,j), specifically: if T(k,j) satisfies the condition |T(k,j)-trans(j )|<T _p , then blind(k,j)=0, otherwise blind(k,j)=1;

Among them, trans(j)=Trans(j+ii)-Trans(j) represents the time interval between the jth transmission pulse and the j+ii transmission pulse, and the value of ii is a natural number; Trans(j) is jth pulse transmission moment; T _p is the pulse width of the radar system transmission.

Further, the angle α _k,j between R _t (k,j), R _r (k,j) and the direction of radar movement and the target direction from the jth pulse to the kth point from the platform satisfies:

${\mathrm{<span\; class="notranslate">\; cos\&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span>$

Furthermore, R _t (k,j) is determined according to the following formula:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; ;</span>$

in, Indicates the coordinates when the platform emits the jth pulse, Indicates the coordinates of the kth point target.

Further, cosα _k,j is determined according to the following formula:

${\mathrm{<span\; class="notranslate">\; cos\&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; ></span><span\; class="notranslate">\; ;</span>$

in, is the coordinate when the platform emits the jth pulse, is the coordinate of the kth point target, is the flight direction of the platform, V _r is the equivalent velocity of the platform, express and angle between.

Beneficial effects of the present invention: the present invention discloses a Staggered-SAR echo signal reconstruction method, which utilizes conformal Fourier transform to process the range-compressed radar signal. This method fully considers the echo characteristics of Staggered-SAR, and can obtain Uniform azimuth spectrum of high-quality radar imaging; the spectrum obtained by the method of this application can accurately reflect the spectral characteristics of the azimuth echo under data loss and non-uniform sampling conditions, and finally can be used for high-quality imaging of the Staggered-SAR system. Compared with the existing method, the method of the present invention can obtain uniform azimuth frequency spectrum, is suitable for classical frequency domain algorithms and the like, and can obtain high-quality imaging results.

Description of drawings

Fig. 1 is the workflow block diagram of the present invention.

detailed description

In order to facilitate those skilled in the art to understand the technical content of the present invention, the content of the present invention will be further explained below in conjunction with the accompanying drawings.

In order to describe content of the present invention conveniently, at first do following term definition:

Definition 1. Lagrange interpolation

It is known that a function f(t) has M+1 different time points t _k in its domain [p ₀ , p ₁ ], k=1,...,M+1, then it can be obtained by Lagrangian The M-order interpolation polynomial P ^M (t) of interpolation construction f(t) is:

${\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Among them, f(t _k ) is the function value when the corresponding time is t _k , L _k (t) is the Lagrangian interpolation basis function of point t _k , which can be expressed as For details, please refer to the reference: Zhu Chunhui, Research on Conformal Fourier Transform Algorithms. Harbin: Harbin Institute of Technology, 2012, Chapter 3.

Definition 2. Conformal Fourier transform

The function f(x) is continuous in the finite interval [p ₀ ,p ₁ ], and the function value is always zero outside the interval [p ₀ ,p ₁ ], then the conformal Fourier transform F( u) is:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}^{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>$

Wherein, L is the segment number of [p ₀ ,p ₁ ], starting point x ₁ =p ₀ , x _l =x ₁ +(l-1)Δ, l=1,2,...,L+ 1, segment interval It is the Lagrangian interpolation polynomial of f(x). For the specific implementation steps of CFT, please refer to the reference: Zhu Chunhui, Research on Conformal Fourier Transform Algorithm. Harbin: Harbin Institute of Technology, 2012, Chapter 3.

Definition 3. Traditional frequency domain distance compression method

Set the emission signal Where T is the pulse width of the transmitted signal, μ is the frequency modulation slope of the transmitted signal, is a rectangular window, The target echo signal is where τ ₀ is the echo delay. The distance compression algorithm is:

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Among them, S _RC (f) is the result of the Fourier transform of the signal after range compression, and S(f) is the result of the Fourier transform of the target echo signal s(τ), is the complex conjugate of the transmitted signal s ₀ (τ) after Fourier transform. For details, please refer to references: Bao Zheng, Xing Mengdao, Wang Tong, etc., Radar Imaging Technology, Electronic Industry Press, 2004.

The present invention mainly adopts the method of simulation experiment to verify, and all steps and conclusions are verified correctly on MATLAB (R2013b). As shown in Figure 1, it is the workflow of the present invention, comprising the following steps:

S1, initialization parameters

The initial Staggered-SAR system parameters include: the wavelength of the radar transmission signal, denoted as λ; the pulse width of the radar system transmission, denoted as T _p ; the bandwidth of the radar system transmission signal, denoted as B; the radar system platform speed, denoted as V _s ; The beam velocity is denoted as V _g ; the pulse repetition frequency of the radar system changes periodically, and it increases or decreases linearly in each period, among which the maximum pulse repetition frequency is denoted as PRF _max ; the minimum pulse repetition frequency is denoted as PRF _min ; The number of pulse transmissions within the pulse repetition frequency change period is denoted as M; the number of sampling points in the range direction of the radar system is denoted as N _r ; the number of sampling points in the azimuth direction of the radar system is denoted as N _a . The specific initialization parameter values are shown in Table 1, the initial position of the platform Pt _init =[0,622661,750000], and the target position of the scene point P _target =[0,0,0].

Table 1 initialization parameters

parameter symbol value Carrier wavelength(m) lambda 0.2384 Transmit pulse width (s) T _p 30e-6 Transmit signal bandwidth (MHz) B 20 Platform speed (m/s) V _s 7473 Beam speed (m/s) V _g 6645 Maximum Pulse Repetition Frequency (Hz) _PRFmax 1800 Minimum pulse repetition frequency (Hz) _PRFmin 1500 Number of pulses per cycle m 20 The number of sampling points in the distance direction N _r 2000 Azimuth sampling points _Na 3000 Platform initial position (m) Pt _init [0,622661,750000] Scene point target position (m) P _target [0,0,0]

Staggered-SAR original echo data matrix, denoted as S, where S is a matrix of N _a rows and N _r columns, each column of data is the sampling of the azimuth echo signal, and the data of each row is the single pulse range echo signal one by one , N _a is the number of sampling points in the azimuth direction, and N _r is the number of sampling points in the range direction.

S2, distance compression

According to the parameters in step S1, the traditional frequency domain distance compression method is used to perform distance compression on the Staggered-SAR original echo data matrix S to obtain a data matrix S _r , wherein S _r is a matrix with N _a rows and N _r columns;

S3. Calculate the data loss location record matrix and initial offset

First, the blind dimension of the data loss location record matrix is N _target rows and N _a columns, and the blind(k,j) value of the k-th row and j-column element in the matrix is 0 or 1; the blind(k,j) value is determined by The time delay T(k, j) is determined; the calculation formula of the time delay T(k, j) is as follows:

T(k,j)=(R _t (k,j)+R _r (k,j))/c,

Among them, R _t (k, j), R _r (k, j) are the slant distances between the platform and the k-th point target when transmitting and receiving the j-th pulse respectively; R _t (k, j), R _r (k ,j) and the angle α _k,j between the radar motion direction and the target direction from the jth pulse to the kth point when the platform launches:

${\mathrm{<span\; class="notranslate">\; cos\&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$

And R _t (k,j) can be obtained by the formula Obtained, cosα _k,j can be obtained by the formula get, is the coordinate when the platform emits the jth pulse, is the coordinate of the kth point target, is the flight direction of the platform, V _r is the equivalent velocity of the platform, used to represent vectors the angle between representation vector and the angle between

Finally, the value of blind(k,j) can be judged according to the calculated T(k,j); specifically: if T(k,j) satisfies the condition |T(k,j)-trans(j)|<T _p , then blind(k,j)=0, otherwise blind(k,j)=1.

Among them, trans(j)=Trans(j+ii)-Trans(j) represents the time interval between the jth transmission pulse and the j+ii transmission pulse, and the value of ii is a natural number; Trans(j) is the first j pulse transmission time; T _p is the transmission pulse width, T(k,j) is the delay when the kth point target receives the jth transmission pulse, k=1,2...N _target , j=1,2 ...N _a , N _target is the number of targets in the scene.

S4, preprocessing distance compression data

According to the lost position record matrix blind calculated by S3, remove the data of each row corresponding to the position of 0 in the blind matrix in the matrix S _r , and obtain the preprocessed data matrix S _c , where S _c is a matrix of N _c rows and N _r columns , N _c is the number of received pulses.

S5. Conformal Fourier transform

Conformal Fourier transform is performed column by column on the preprocessed data matrix S _c obtained in S4 to obtain a uniform azimuth spectrum matrix F _cft with N _a rows and N _r columns. Among them, the subsection length during conformal Fourier transform processing is MM _miss + 1 = 18, M is the number of pulses transmitted in one cycle of the radar system, and M _miss is the number of missing point pulses in one cycle. M _miss uses the blind matrix to calculate a The number of lost pulses in the pulse repetition period, get M _miss .

S6. Two-dimensional spectrum conjugate compensation

Perform fast Fourier transform on each row of the azimuth spectrum matrix F _cft obtained in S5 to obtain a two-dimensional spectrum matrix B _cft with N _a rows and N _r columns, and carry out conjugate complex multiplication of the two-dimensional spectrum matrix B _cft and the reference spectrum matrix θ _2df , to obtain a two-dimensional data matrix S _2df with N _a rows and N _r columns, namely Then perform two-dimensional fast Fourier inverse transform on S _2df to obtain the imaging result;

in, For the reference spectrum, R _min is the shortest slant distance, c is the speed of light, V _r is the equivalent velocity of the platform, f _ττ is the distance-to-frequency equipartition vector, and [-B,B) is divided into N _r equal parts to obtain f _ττ , B is the bandwidth of the transmitted signal, f _ηη is the azimuth direction frequency equalization vector, the Equally divided into N _a parts, f _ηη can be obtained, and T _SAR is the synthetic aperture time.

Under the above parameter conditions, the missing point positions appear at three positions 9, 11, and 12 within a pulse repetition period, and are distributed in the middle of a pulse repetition period. Table 2 shows the imaging performance evaluation parameters obtained through the above steps S1 to S6. Table 2 lists two parameters, ISLR (Integral Side Lobe Ratio) and PSLR (Peak Side Lobe Ratio). From the data in Table 2, it can be seen that this The processing effect of the method is better than lagrange interpolation. In terms of algorithm calculation amount, the calculation amount of this method is regarded as O(NlogN), N is the number of sampling points in azimuth direction, and the calculation amount of direct lagrange interpolation processing is O(Q·NlogN), Q is the order of lagrange interpolation, in the algorithm In terms of calculation amount, this method is also smaller than lagrange interpolation in terms of calculation amount. Therefore, when the missing point appears in the middle of the segment period, this method has certain advantages.

Table 2 Comparison of performance parameters between this method and different methods

Conformal Fourier Transform Lagrange interpolation unprocessed ISLR(dB) -7.3241 -6.1923 -6.0859 PSLR(dB) -12.5976 -12.0439 -12.4863

Those skilled in the art will appreciate that the embodiments described here are to help readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Various modifications and variations of the present invention will occur to those skilled in the art. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of the claims of the present invention.

Claims (6)

1. A Staggered-SAR echo signal reconstruction method, characterized in that, comprising: S1. Initialize the parameters of the Staggered-SAR imaging system, including: the wavelength of the radar emission signal, denoted as λ; the pulse width of the radar system emission, denoted as T _p ; the bandwidth of the radar system emission signal, denoted as B; the radar system platform speed, denoted as V _s ; the beam velocity of the radar system, denoted as V _g ; the pulse repetition frequency of the radar system changes periodically, and it increases or decreases linearly in each cycle, among which the maximum pulse repetition frequency is denoted as PRF _max ; the minimum pulse repetition frequency is denoted as PRF _min ; the number of pulses transmitted in a pulse repetition frequency change period, denoted as M; Staggered-SAR original echo data matrix, denoted as S, where S is a matrix of N _a rows and N _r columns, each column of data is the sampling of the azimuth echo signal, and the data of each row is the single pulse range echo one by one Signal sampling, N _a is the number of sampling points in the azimuth direction, N _r is the number of sampling points in the range direction; S2, distance compression, according to the parameters in step S1, use the traditional frequency domain distance compression method to perform distance compression on the Staggered-SAR original echo data matrix S, and obtain the data matrix S _r , where S _r is the number of N _a rows and N _r columns matrix; S3. Calculate the data loss location record matrix blind; Wherein, the blind dimension of the data loss position record matrix is N _target row N _a column, the value blind(k,j) of the jth column element in the kth row in the matrix is 0 or 1, and the blind(k,j) value is determined by Delay T(k,j) is determined; T(k,j) is the delay when the kth point target receives the jth transmit pulse, k=1,2...N _target , j=1,2...N _a , N _target is the number of targets in the scene; S4, preprocessing the distance compressed data, according to the lost position record matrix blind calculated in S3, removing each row of data corresponding to the position of 0 in the blind matrix in the matrix S _r , and obtaining the preprocessed data matrix S _c ; Among them, S _c is N _c row N _r column matrix, N _c is the number of received pulses; S5. Conformal Fourier transform. Conformal Fourier transform is performed column by column on the preprocessed data matrix S _c obtained in S4 to obtain a uniform azimuth spectrum matrix F _cft with N _a rows and N _r columns; Among them, the segment length of conformal Fourier transform processing is MM _miss + 1, M is the number of pulses transmitted by the radar system in one cycle, M _miss is the number of pulses lost in one cycle, and M _miss uses the blind matrix to calculate a pulse The number of lost pulses in the repetition period, get M _miss ; S6, two-dimensional spectral conjugate compensation, fast Fourier transform is performed on each row of the azimuth spectral matrix F _cft obtained in S5, to obtain a two-dimensional spectral matrix B _cft with N _a rows and N _r columns, and the two-dimensional spectral matrix B _cft is compared with the reference The spectrum matrix θ _2df is conjugated and multiplied to obtain a two-dimensional data matrix S _2df with N _a rows and N _r columns, namely Then perform two-dimensional fast Fourier inverse transform on S _2df to obtain the imaging result; in, is the reference spectrum, R _min is the shortest slant distance, c is the speed of light, V _r is the equivalent velocity of the platform, f _ττ is the spectrum equalization vector in the range direction, and f _ηη is the frequency equalization vector in the azimuth direction; The range-to-frequency decile vector f _{ττ is} specifically obtained by dividing [-B, B) into N _r parts, B is the bandwidth of the transmitted signal, and N _r is the number of sampling points in the range direction; the azimuth-to-frequency decile vector f _ηη specifically by It is obtained by equally dividing into N _a parts, T _SAR is the synthetic aperture time, and N _a is the number of azimuth sampling points. 2. a kind of Staggered-SAR echo signal reconstruction method according to claim 1, is characterized in that, the time delay T (k, j) calculation formula described in step S3 is as follows: T(k,j)=(R _t (k,j)+R _r (k,j))/c; Among them, R _t (k, j) represents the slant distance between the platform and the k-th point target when the j-th pulse is transmitted; R _r (k, j) represents the slant distance between the platform and the k-th point target when the j-th pulse is received the slope distance between. 3. A Staggered-SAR echo signal reconstruction method according to claim 2, wherein the value of blind (k, j) in step S3 is determined by time delay T (k, j), specifically: If T(k,j) satisfies the condition |T(k,j)-trans(j)|<T _p , then blind(k,j)=0, otherwise blind(k,j)=1; Among them, trans(j)=Trans(j+ii)-Trans(j) represents the time interval between the jth transmission pulse and the j+ii transmission pulse, and the value of ii is a natural number; Trans(j) is jth pulse transmission moment; T _p is the pulse width of the radar system transmission. 4. a kind of Staggered-SAR echo signal reconstruction method according to claim 2, is characterized in that, R _t (k, j), R _r (k, j) and radar motion direction and platform launch jth pulse The angle α _{k, j} between the target direction to the kth point satisfies: ${\mathrm{<span\; class="notranslate">\; cos\&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span>$ 5. a kind of Staggered-SAR echo signal reconstruction method according to claim 4, is characterized in that, R _t (k, j) is determined according to the following formula: ${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; ;</span>$ in, Indicates the coordinates when the platform emits the jth pulse, Indicates the coordinates of the kth point target. 6. a kind of Staggered-SAR echo signal reconstruction method according to claim 4, is characterized in that, cosα _{k, j} is determined according to the following formula: ${\mathrm{<span\; class="notranslate">\; cos\&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; ></span><span\; class="notranslate">\; ;</span>$ in, is the coordinate when the platform emits the jth pulse, is the coordinate of the kth point target, is the flight direction of the platform, V _r is the equivalent velocity of the platform, express and angle between.