CN102288961B - Imaging method for synthetic aperture radar nonlinear frequency modulation label change - Google Patents

Abstract

The invention belongs to an imaging method for nonlinear frequency modulation label change in the synthetic aperture radar imaging technology, which comprises the steps of two-dimensional frequency domain unfolding, filtering processing, nonlinear frequency modulation label change, distance compression, distance migration correction, rest phase compensation and position compression. In the method of the invention, the characteristics of orthogonality and minimum square error of the Legendre polynomials are utilized for carrying out three-order unfolding on the two-dimensional frequency domain signals of the obtained echo signals according to the Legendre orthogonality polynomials, and then, the focusing imaging on targets is realized through carrying out filtering processing and the like on three-order phase items in echo signal two-dimensional frequency domain expression. When the method of the invention is adopted, the maximum phase error under the same condition is less than 0.2 percent of the maximum phase error in the prior art, so the assurance is provided for the high-precision imaging under the large-inclination view angle condition. Therefore, the method of the invention has the characteristics that the phase error in the imaging process can be effectively reduced, the imaging processing of the large-inclination view angle is realized, in addition, the imaging effect is good, the imaging processing efficiency and the precision are high, and the like.

Description

Imaging method of synthetic aperture radar nonlinear frequency modulation and scaling

Technical Field

The invention belongs to the technical field of Synthetic Aperture Radar (SAR) imaging, and particularly relates to an imaging processing method for performing three-order expansion on a two-dimensional frequency domain signal in a Synthetic Aperture Radar Nonlinear frequency modulation scaling (NCS) method by using Legendre (Legendre) orthogonal polynomial.

Background

The synthetic aperture radar is an imaging radar with high resolution, and the principle is that an equivalent antenna aperture is formed through the movement of a platform, so that higher azimuth resolution is obtained; high range-wise resolution is obtained by transmitting a broadband signal. Compared with an optical sensor, the SAR has the all-weather working capacity and is widely applied to the fields of earth remote sensing, ocean research, resource exploration, disaster prediction, military reconnaissance and the like.

The basic principle of SAR imaging is to complete pulse compression of a range-direction signal by performing range-direction matched filtering on an echo signal, and then to perform azimuth-direction matched filtering to obtain a focused SAR image. Common imaging processing methods include Range-Doppler (R-D) imaging methods, linear Scaling (CS) imaging methods, wave-domain imaging methods, and nonlinear Scaling methods. The R-D imaging processing method is widely applied due to high efficiency, but becomes complicated or even ineffective for processing with a certain squint angle; the wave number domain imaging processing method is accurate and can adapt to the conditions of large squint angle and large Range Cell Migration (Range Cell Migration), but due to the fact that interpolation processing is needed in the imaging processing process, the calculated amount is increased and the imaging accuracy is reduced; the imaging processing method of the linear frequency modulation and scaling does not need interpolation processing, can realize imaging processing only by complex multiplication and Fast Fourier Transform (FFT), and has high imaging precision, but the traditional imaging processing method of the linear frequency modulation and scaling cannot realize focusing imaging with a larger oblique angle.

The NCS imaging processing method considers the secondary distance compression which linearly changes along with the distance, so the method is suitable for a larger squint angle and is an ideal SAR imaging processing method for larger squint angle imaging. In the processing process of the NCS imaging method, a strand of two-dimensional frequency domain signals of echo signals are subjected to Taylor (Taylor) polynomial three-order expansion, approximate processing is adopted in the expansion process, the phase error is large, and the imaging precision is not high; if the processing precision of imaging is to be improved and the target is imaged under a large oblique angle, the two-dimensional frequency domain signal of the echo signal must be subjected to taylor polynomial expansion of fourth order or higher, at this time, although the requirement of imaging precision can be met, the defects of complex imaging processing method, low imaging efficiency and precision and the like exist.

Disclosure of Invention

The invention aims to improve and design an imaging method of a synthetic aperture radar nonlinear frequency modulation and scaling aiming at the defects in the background technology, and aims to reduce the complexity of imaging processing, improve the efficiency of imaging processing and the like on the premise of effectively improving the accuracy of imaging processing and meeting the imaging requirement of a large squint angle by adopting high-resolution SAR nonlinear frequency modulation and scaling processing based on Legendre orthogonal polynomial third-order expansion.

Firstly, fast Fourier transform in distance direction and azimuth direction is respectively carried out on echo signals received by a radar, the echo signals are transformed into two-dimensional frequency domain signals, and third-order expansion is carried out on the two-dimensional frequency domain signals under Legendre orthogonal polynomials; then, multiplying the two-dimensional frequency domain expression of the echo signal obtained by Fourier transform by a nonlinear frequency modulation function to complete the filtering processing of a cubic phase item in the two-dimensional frequency domain signal expression of the echo signal; then the signal after filtering processing is transformed to a Doppler frequency domain-distance time domain, and is multiplied by the signal of the Doppler frequency domain-distance time domain through a nonlinear frequency modulation scaling function so as to complete nonlinear frequency modulation scaling processing; then, Fourier transform is carried out on the signal subjected to the nonlinear frequency modulation and scaling processing along the distance direction to obtain a two-dimensional frequency domain signal subjected to the nonlinear frequency modulation and scaling processing, and the two-dimensional frequency domain signal is multiplied by a distance direction reference function to finish distance compression and distance migration correction; then the signals after the distance compression and the distance migration correction are converted to a Doppler frequency domain-distance time domain, and are multiplied by the signals of the distance time domain-Doppler frequency domain through an azimuth reference function so as to complete azimuth compression and residual phase compensation; and finally, performing Fourier inverse transformation on the signal subjected to azimuth compression and residual phase compensation along the azimuth direction, thereby completing the imaging processing of the target. Thus, the method of the invention comprises:

A. and (3) two-dimensional frequency domain expansion: fourier transform and transformation are respectively carried out on the received echo signals in the distance direction and the azimuth direction to a two-dimensional frequency domain, and three-order expansion is carried out on the two-dimensional frequency domain signals of the obtained echo signals through Legendre orthogonal polynomials, so that the decoupling processing of the azimuth direction and the distance direction of the echo signals is completed;

B. and (3) filtering treatment: multiplying the signal subjected to decoupling processing obtained in the step A by a non-linear frequency modulation function, and filtering a cubic phase term of the signal obtained in the step A to eliminate the influence of the cubic phase term on imaging;

C. nonlinear frequency modulation scaling: transforming the signal obtained in the step B into a Doppler frequency domain-distance time domain through Inverse distance Fourier transform (Inverse Fourier transform), and multiplying the signal of the Doppler frequency domain-distance time domain by a nonlinear frequency modulation scaling function to perform nonlinear frequency modulation scaling processing;

D. distance compression and distance migration correction: transforming the signal obtained in the step C into a two-dimensional frequency domain through distance Fourier transform; then multiplying the two-dimensional frequency domain signal by a distance direction reference function to carry out distance compression and distance migration correction processing;

E. residual phase compensation and azimuth compression: d, performing inverse Fourier transform on the signal obtained in the step D through the distance, and transforming the signal into a distance time domain-Doppler frequency domain; then multiplying the distance time domain-Doppler frequency domain signal with an azimuth reference function to finish azimuth compression and residual phase compensation processing; and finally, performing azimuth-direction inverse Fourier transform on the signal subjected to the azimuth compression and the residual phase compensation so as to finish the imaging processing of the target.

The invention relates to a three-order expansion processing of Legendre orthogonal polynomial to a two-dimensional frequency domain signal of an echo signal, which adopts the following expansion formula:

$\mathrm{\φ}(f_{\mathrm{\τ}},f_{\mathrm{\η}})\≈\frac{4\mathrm{\π}{R}_b}{\mathrm{\λ}}[a_0\left(f_n\right)+a_1\left(f_n\right)f_{\mathrm{\τ}}+a_2\left(f_n\right)f_{\mathrm{\τ}}^2+a_3\left(f_{\mathrm{\η}}\right)f_{\mathrm{\τ}}^3]$

in the formula: phi (f)_τ，f_η) For a two-dimensional spectral representation of the echo signal to be unfolded, f_τIs the range frequency, f_ηIs the azimuth frequency, R_bThe distance from the radar to the target at the moment of the center of the synthetic aperture, lambda is the wavelength of the signal emitted by the radar, a₀(f_η)，a₁(f_η)，a₂(f_η)，a₃(f_η) Coefficient of zero-order term, first-order term, second-order term and third-order term which are respectively Legendre polynomial expansion.

And B, performing filtering processing on the cubic phase term of the signal obtained in the step A, wherein the filtering processing is performed by:

S_2Y(f_τ，f_η)＝S₂(f_τ，f_η)H₁(f_τ，f_η)

wherein: s_2Y(f_τ，f_η) For filtering the processed signal, S₂(f_τ，f_η) For two-dimensional frequency-domain signals developed three-order by Legendre orthogonal polynomials, H₁(f_τ，f_η) Is a non-chirp function.

The processing method of the nonlinear frequency modulation and scaling processing is carried out according to the following formula:

S_2Ya(τ，f_η)＝S_2Y(τ，f_η)H₂(τ，f_η)

wherein S is_2Ya(τ，f_η) For the signal after the nonlinear frequency modulation and scaling treatment, S_2Y(τ，f_η) Is S_2Y(f_τ，f_η) Signal obtained by inverse Fourier transform along the distance direction, H₂(τ，f_η) Is a non-chirp scaling function.

The distance compression and distance migration correction processing is carried out according to the following processing method:

S_YR(f_τ，f_η)＝S_2Ya(f_τ，f_η)H₃(f_τ，f_η)

wherein S is_YR(f_τ，f_η) Is a distance-compressed and range migration-corrected signal, S_2Ya(f_τ，f_η) Is S_2Ya(τ，f_η) Signals obtained by Fourier transformation along the distance direction, H₃(f_τ，f_η) Is a distance-to-reference function. The processing method for completing the residual phase compensation and the azimuth compression processing is carried out according to the following formula:

S_YA(τ，f_η)＝S_YR(τ，f_η)H₄(τ，f_η)

wherein S is_YA(τ，f_η) For the residual phase-compensated and azimuth-compressed signal, S_YR(τ，f_η) Is S_YR(f_τ，f_η) Signal obtained by inverse Fourier transform along the distance direction, H₄(τ，f_η) Is an azimuth reference function.

The method utilizes the characteristic that the Legendre polynomial has the minimum orthogonality and the minimum square error, carries out third-order expansion on the two-dimensional frequency spectrum of the obtained echo signal according to the Legendre orthogonal polynomial, and then carries out filtering processing, nonlinear frequency modulation and scaling, distance compression, range migration correction, residual phase compensation and azimuth compression on a third-order phase term in a two-dimensional frequency domain expression of the echo signal to finish focusing imaging on a target. Maximum phase error (6 x 10) under the same conditions by adopting the method of the invention^-3rad) is less than two thousandth of the maximum phase error (3.5rad) expanded by a Taylor polynomial in the background technology, so that high-precision imaging under the condition of large oblique angle is guaranteed; therefore, the invention has the characteristics of effectively reducing the phase error in the imaging process, realizing the imaging processing of a large oblique angle, having good imaging effect, high imaging processing efficiency and precision and the like.

Drawings

FIG. 1 is a schematic diagram of a geometric configuration of an embodiment of the present invention;

fig. 2 is a phase error coordinate diagram of two-dimensional frequency spectrums of echo signals respectively obtained by simulation operation under the same conditions in the embodiment of the present invention and the background art at an oblique angle of 50 °, wherein:

(a) for a phase error plot of the two-dimensional spectrum of an echo signal developed using the legendre orthogonal polynomial of the present invention,

(b) a phase error coordinate graph of a two-dimensional frequency spectrum of an echo signal expanded by a Taylor polynomial in the background technology is adopted;

fig. 3 is a target imaging result (gray scale) obtained by the embodiment of the present invention.

Detailed Description

FIG. 1 is a schematic diagram of a geometrical configuration of an embodiment of the present invention, wherein a radar transmitter transmits a chirp signal with a wavelength λ of 0.03m and a pulse width T_p10us, the chirp rate K is 7.5 × 10¹²Hz/s; then, after coherent demodulation, the target echo signal received by the radar is represented as:

$s_r(\mathrm{\τ},\mathrm{\η})=\mathrm{rect}\left(\frac{\mathrm{\τ}-\frac{2R\left(\mathrm{\η}\right)}{c}}{T_p}\right)\exp \left[\mathrm{j\πK}{(\mathrm{\τ}-\frac{2R\left(\mathrm{\η}\right)}{c})}^2\right]\exp \left[\frac{-j4\mathrm{\πR}\left(\mathrm{\η}\right)}{\mathrm{\λ}}\right]$

wherein tau represents the distance fast time and the variation range is [ 010 ]]Microsecond; eta is azimuth time and the variation range is [ 07.94 ]]Second, and η is 3.97 seconds, which is the time when the beam center irradiates the target; c is the speed of light and c is 3 × 10⁸m/s, rect () is a rectangular window function, exp (-) is an exponential function, and R (η) is the distance from the radar to the target, expressed as:

$\mathrm{rect}\left(u\right)=\left\{\begin{array}{cc}1& \left|u\right|\≤1/2\\ 0& \left|u\right|>1/2\end{array}\right.$

exp(u)＝e^u

$R\left(\mathrm{\η}\right)=\sqrt{R_b^2+{(\mathrm{v\η}-X_n)}^2-2R_b(\mathrm{v\η}-X_n)\sin {\mathrm{\θ}}_s}$

wherein R is_b28.284km is the distance from the radar to the target at the moment of the center of the synthetic aperture, the platform speed v is 200m/s, and theta_sIs a squint angle and theta_s＝50°，X_nIs the coordinate of the target in the X direction and X_n0km, the target coordinate is Y in the Y direction_n＝20km。

The specific imaging processing steps of the embodiment are as follows:

A. two-dimensional frequency domain expansion

Firstly, an echo signal is respectively transformed to a two-dimensional frequency domain through distance direction FFT and azimuth direction FFT, and then the method comprises the following steps:

S₂(f_τ，f_η)＝P(f_τ)exp[jφ(f_η，f_τ)]

in the formula (f)_τIs the range frequency, f_ηIs the azimuth frequency, and:

$P\left(f_{\mathrm{\τ}}\right)=M\left(f_{\mathrm{\τ}}\right)\exp (-\mathrm{j\π}\frac{{f_{\mathrm{\τ}}}^2}{K})$

$\mathrm{\φ}(f_{\mathrm{\τ}},f_{\mathrm{\η}})=-\frac{4\mathrm{\π}{R}_b}{\mathrm{\λ}}\sqrt{D^2\left(f_{\mathrm{\η}}\right)+\frac{2f_{\mathrm{\τ}}}{f_c}+\frac{f_{\mathrm{\τ}}^2}{f_c^2}}$

wherein,

f_ccarrier frequency of signal transmitted for radar and f_c＝10GHz，M(f_τ) Is a frequency domain expression of the rectangular window function;

due to the phase phi (f) of the echo signal_τ，f_η) There is coupling of distance and orientation and changes with distance, and the embodiment adopts Legendre polynomial to carry out third-order expansion, and the third-order expansion of Legendre polynomial is:

$\mathrm{\φ}(f_{\mathrm{\τ}},f_{\mathrm{\η}})\≈\frac{4\mathrm{\π}{R}_b}{\mathrm{\λ}}[a_0\left(f_{\mathrm{\η}}\right)+a_1\left(f_{\mathrm{\η}}\right)f_{\mathrm{\τ}}+a_2\left(f_{\mathrm{\η}}\right)f_{\mathrm{\τ}}^2+a_3\left(f_{\mathrm{\η}}\right)f_{\mathrm{\τ}}^3]$

wherein, a₀(f_η)，a₁(f_η)，a₂(f_η)，a₃(f_η) Coefficients of the zero-order term, the primary term, the secondary term and the tertiary term for Legendre polynomial expansion are specifically derived below;

order to

Br is the bandwidth of the transmitted signal, x is ∈ [ -1, 1]Substituting the above equation yields a function for the variable x, denoted as μ (x):

$\mathrm{\μ}\left(x\right)=\sqrt{D^2\left(f_{\mathrm{\η}}\right)+\frac{B_r}{f_c}x+\frac{{B_r}^2}{4f_c^2}{x}^2}$

a legendre polynomial third order approximation expansion is performed on μ (x) as:

$\mathrm{\&mu;}\left(x\right)\&ap;\frac{1}{2}<\mathrm{\&mu;},{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA0000074330490000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_0>+\frac{3}{2}<\mathrm{\&mu;},p_1>x+\frac{5}{2}<\mathrm{\&mu;},p_2>\left(\frac{1}{2}(3x^2-1)\right)+\frac{7}{2}<\mathrm{\&mu;},{\mathrm{<figure-callout\; id="3"\; label="p"\; filenames="HDA0000074330490000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_3>\left(\frac{1}{2}(5x^3-3x)\right)$

wherein p is₀，p₁，p₂，p₃The meaning of (a) is as above,

and m is 0, 1, 2 and 3. Then, a₀(f_η)，a₁(f_η)，a₂(f_η)，a₃(f_η) Can be expressed as:

$a_0\left(f_{\mathrm{\&eta;}}\right)=\frac{1}{2}<\mathrm{\&mu;},{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA0000074330490000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_0>-\frac{5}{4}<\mathrm{\&mu;},p_2>$

$a_1\left(f_{\mathrm{\&eta;}}\right)=\frac{3}{B_r}<\mathrm{\&mu;},p_1>-\frac{21}{2B_r}<\mathrm{\&mu;},{\mathrm{<figure-callout\; id="3"\; label="p"\; filenames="HDA0000074330490000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_3>$

$a_2\left(f_{\mathrm{\&eta;}}\right)=\frac{15}{{B_r}^2}<\mathrm{\&mu;},p_2>$

$a_3\left(f_{\mathrm{\&eta;}}\right)=\frac{70}{{{\mathrm{<figure-callout\; id="3"\; label="B\; r"\; filenames="HDA0000074330490000012.png"\; state="\{\{state\}\}">B</figure-callout>}}_r}^3}<\mathrm{\&mu;},{\mathrm{<figure-callout\; id="3"\; label="p"\; filenames="HDA0000074330490000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_3>$

therefore, the two-dimensional spectrum of the echo signal after orthogonal expansion by the legendre polynomial is:

$S_2(f_{\mathrm{\&tau;}},f_{\mathrm{\&eta;}})=M\left(f_{\mathrm{\&tau;}}\right)\exp (-\mathrm{j\&pi;}\frac{{f_{\mathrm{\&tau;}}}^2}{K})$

$\&times;\exp [-j\frac{4\mathrm{\&pi;}{R}_b}{\mathrm{\&lambda;}}[a_0\left(f_{\mathrm{\&eta;}}\right)+a_1\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}+a_2\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}^2+a_3\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}^3\left]\right]$

B. filtering process

In order to eliminate the influence of the cubic phase term on the imaging, the signal S obtained in the step A is used₂(f_τ，f_η) And the chirp slope is Y (f)_η) Non-linear frequency modulation function H₁(f_τ，f_η) And (4) multiplying, and finishing the filtering of the cubic phase term of the signal obtained in the step A. The filtering process is performed by the following equation:

S_2Y(f_τ，f_η)＝S₂(f_τ，f_η)H₁(f_τ，f_η)

wherein S is_2Y(f_τ，f_η) For the filtered signal, H₁(f_τ，f_η) Is a non-chirp function expressed as:

$H_1(f_{\mathrm{\&tau;}},f_{\mathrm{\&eta;}})=\exp \left[j\frac{2\mathrm{\&pi;}}{3}Y\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}^3\right]$

C. non-linear frequency modulation scaling

The signal S obtained in the step B_2Y(f_τ，f_η) Transforming to Doppler frequency domain-distance time domain by inverse range-to-Fourier transform, and converting the Doppler frequency domain-distance time domain signal S_2Y(τ，f_η) And nonlinear frequency modulation scaling function H₂(τ，f_η) The multiplication is carried out with a nonlinear frequency modulation and scaling operation. The nonlinear frequency modulation scaling operation is performed by the following formula:

S_2Ya(τ，f_η)＝S_2Y(τ，f_η)H₂(τ，f_η)

wherein S is_2Ya(τ，f_η) For the signal after the nonlinear frequency modulation and scaling treatment, H₂(τ，f_η) For the nonlinear frequency modulation scaling operation function, the expression is:

$H_2(\mathrm{\&tau;},f_{\mathrm{\&eta;}})=\exp [\mathrm{j\&pi;}{q}_2\left(f_{\mathrm{\&eta;}}\right){(\mathrm{\&tau;}-{\mathrm{\&tau;}}_{\mathrm{ref}})}^2-j\frac{2\mathrm{\&pi;}}{3}{q}_3\left(f_{\mathrm{\&eta;}}\right){(\mathrm{\&tau;}-{\mathrm{\&tau;}}_{\mathrm{ref}})}^3]$

wherein q is₂＝K_mrefL(f_η)[α(f_η)-1]In the form of a chirp slope, the chirp rate,

is the nonlinear chirp slope, and:

K_mL＝1/[1/K-4R_ba₂(f_η)f_c/c]

$K_{\mathrm{mrefL}}\left(f_{\mathrm{\&eta;}}\right)=\frac{-1+\sqrt{1+2K_{\mathrm{mL}}\left(f_{\mathrm{\&eta;}}\right)\mathrm{\&Delta;\&tau;}\left(f_{\mathrm{\&eta;}}\right)a_2\left(f_{\mathrm{\&eta;}}\right)/a_1\left(f_{\mathrm{\&eta;}}\right)}}{4\mathrm{\&Delta;\&tau;}\left(f_{\mathrm{\&eta;}}\right)a_2\left(f_{\mathrm{\&eta;}}\right)/a_1\left(f_{\mathrm{\&eta;}}\right)}$

K_sL(f_η)＝2K² _mrefL(f_η)a₂(f_η)/a₁(f_η)

1/α(f_η)＝-2π{[K_mrefL(f_η)+K_sL(f_η)τ_ref]/[K_mrefL(f_η)+q₂(f_η)]}

Δτ(f_η)＝τ_d-τ_ref

${\mathrm{\&tau;}}_d=2R_b/(c\&times;\sqrt{1-(f_{\mathrm{\&eta;}}/f_{\mathrm{\&eta;M}})})$

${\mathrm{\&tau;}}_{\mathrm{ref}}=\frac{2R_s}{c}$

wherein f is_ηM2v/λ is the maximum Doppler frequency, R_sIs the distance from the center of the scene to the radar platform and R_s＝44.003km；

D. Distance compression and distance migration correction:

the signal S obtained in step C_2Ya(τ，f_η) Transforming the two-dimensional frequency domain signal into a two-dimensional frequency domain signal by distance Fourier transform, and comparing the two-dimensional frequency domain signal with a distance reference function H₃(f_τ，f_η) Multiplying to carry out distance compression and distance migration correction; the correction method is carried out according to the following formula:

S_YR(f_τ，f_η)＝S_2Ya(f_τ，f_η)H₃(f_τ，f_η)

wherein S is_YR(f_τ，f_η) Is a distance-compressed and range-migration-corrected signal, H₃(f_τ，f_η) For the distance reference function, the expression is:

$H_3(f_{\mathrm{\&tau;}},f_{\mathrm{\&eta;}})=\exp \left[l\frac{4\mathrm{\&pi;}}{\mathrm{\&alpha;}\left(f_{\mathrm{\&eta;}}\right)}\mathrm{\&Delta;\&tau;}\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}\right]$

$\&times;\exp (-j\frac{\mathrm{\&pi;}{f_{\mathrm{\&tau;}}}^2}{K_{\mathrm{mref}}\left(f_{\mathrm{\&eta;}}\right)\mathrm{\&alpha;}\left(f_{\mathrm{\&eta;}}\right)}-j\frac{2\mathrm{\&pi;}}{3}\frac{Y_m\left(f_{\mathrm{\&eta;}}\right)K_{\mathrm{mrefL}}^3\left(f_{\mathrm{\&eta;}}\right)+q_3\left(f_{\mathrm{\&eta;}}\right)}{K_{\mathrm{mrefL}}^3\left(f_{\mathrm{\&eta;}}\right){\mathrm{\&alpha;}}^3\left(f_{\mathrm{\&eta;}}\right)}{f_{\mathrm{\&tau;}}}^3)$

E. residual phase compensation and azimuth compression

The signal S obtained in the step D_YR(f_τ，f_η) Is transformed into a range time domain-Doppler frequency domain by inverse range-to-Fourier transform, andthe distance time domain-Doppler frequency domain signal and the azimuth reference function H are compared₄(τ，f_η) The multiplication is used for residual phase compensation and azimuth compression. Residual phase compensation and azimuth compression are performed by:

S_YA(τ，f_η)＝S_YR(τ，f_η)H₄(τ，f_η)

wherein S is_YA(τ，f_η) For the signal after residual phase compensation and azimuth compression, H₄(τ，f_η) For the azimuth reference function, the expression is:

$H_4(\mathrm{\&tau;},f_{\mathrm{\&eta;}})=\exp \left[j\frac{4\mathrm{\&pi;}{R}_b}{\mathrm{\&lambda;}}{a}_0\left(f_{\mathrm{\&eta;}}\right)\right]\exp [-\mathrm{j\&Delta;\&phi;}\left(f_{\mathrm{\&eta;}}\right)]$

wherein, Δ φ (f)_η) Is the residual phase, expressed as:

$\mathrm{\&Delta;\&phi;}\left(f_{\mathrm{\&eta;}}\right)=-\mathrm{\&pi;}\frac{K_{\mathrm{mrefL}}[\mathrm{\&alpha;}\left(f_{\mathrm{\&eta;}}\right)-1]}{\mathrm{\&alpha;}\left(f_{\mathrm{\&eta;}}\right)}\mathrm{\&Delta;}{\mathrm{\&tau;}}^2-\mathrm{\&pi;}\frac{K_{\mathrm{sL}}[{\mathrm{\&alpha;}}^2\left(f_{\mathrm{\&eta;}}\right)+5\mathrm{\&alpha;}\left(f_{\mathrm{\&eta;}}\right)-6]}{3{\mathrm{\&alpha;}}^2\left(f_{\mathrm{\&eta;}}\right)}\mathrm{\&Delta;}{\mathrm{\&tau;}}^3\left(f_{\mathrm{\&eta;}}\right)$

and finally, performing azimuth-direction Fourier inverse transformation on the signal subjected to the azimuth compression and the residual phase compensation, and finishing the imaging processing.

Fig. 2 is a phase error coordinate diagram of two-dimensional frequency spectrums of echo signals respectively obtained by performing comparison simulation operation under the same conditions according to the embodiment of the present invention and the background art at an oblique angle of 50 °, wherein:

(a) the phase error coordinate diagram of the echo signal two-dimensional frequency spectrum expanded by adopting the Legendre orthogonal polynomial is shown; the maximum phase error shown in the figure is about 2.1 × 10^-3rad；

(b) A phase error coordinate graph of a two-dimensional frequency spectrum of an echo signal expanded by a Taylor polynomial in the background technology is adopted; the maximum phase error shown in the figure is about 1.16 rad;

as can be seen from a comparison of fig. 2(a) and 2 (b): the phase error obtained by the embodiment is far smaller than the phase error expanded by the Taylor polynomial, so that the high-precision imaging under the condition of large oblique angle is guaranteed;

fig. 3 is a final target imaging result graph (gray scale graph) obtained in a simulation run by the embodiment of the invention at an oblique angle of 50 ° and a dynamic range of 40 dB.

Thus, from the simulation run results, it can be seen that: according to the method, three-order expansion processing is carried out on the two-dimensional frequency of the echo signal according to the Legendre orthogonal polynomial, so that the phase error of subsequent imaging processing is reduced, imaging processing with a large oblique angle is realized, the imaging effect is good, and the imaging processing efficiency and precision are high.

Claims (6)

1. An imaging method of a synthetic aperture radar nonlinear frequency modulation and scaling comprises the following steps:

A. and (3) two-dimensional frequency domain expansion: fourier transform and transformation are respectively carried out on the received echo signals in the distance direction and the azimuth direction to a two-dimensional frequency domain, and three-order expansion is carried out on the two-dimensional frequency domain signals of the obtained echo signals through Legendre orthogonal polynomials, so that the decoupling processing of the azimuth direction and the distance direction of the echo signals is completed;

B. and (3) filtering treatment: multiplying the signal subjected to decoupling processing obtained in the step A by a non-linear frequency modulation function, and filtering a cubic phase term of the signal obtained in the step A to eliminate the influence of the cubic phase term on imaging; wherein the non-chirp function is:

$H_1(f_{\mathrm{\&tau;}},f_{\mathrm{\&eta;}})=\exp \left[j\frac{2\mathrm{\&pi;}}{3}Y\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}^3\right]$

in the formula: f. of_τIs the range frequency, f_ηFor azimuthal frequency, exp (-) is an exponential function, Y (f)_η) Is the frequency modulation slope;

C. nonlinear frequency modulation scaling: b, the signal obtained in the step B is subjected to inverse Fourier transform through the distance, and is transformed to a Doppler frequency domain-distance time domain, and then the signal of the Doppler frequency domain-distance time domain is multiplied by a nonlinear frequency modulation scaling function to carry out nonlinear frequency modulation scaling processing; the nonlinear chirp scaling function is:

$H_2(\mathrm{\&tau;},f_{\mathrm{\&eta;}})=\exp [\mathrm{j\&pi;}{q}_2\left(f_{\mathrm{\&eta;}}\right){(\mathrm{\&tau;}-{\mathrm{\&tau;}}_{\mathrm{ref}})}^2-j\frac{2\mathrm{\&pi;}}{3}{q}_3\left(f_{\mathrm{\&eta;}}\right){(\mathrm{\&tau;}-{\mathrm{\&tau;}}_{\mathrm{ref}})}^3]$

wherein: τ denotes the distance fast time, q₂Is the chirp slope, q₃Is a non-linear chirp slope;

R_sthe distance from the center of the scene to the radar platform and the speed of light c are shown;

D. distance compression and distance migration correction: transforming the signal obtained in the step C into a two-dimensional frequency domain through distance Fourier transform; then multiplying the two-dimensional frequency domain signal by a distance direction reference function to carry out distance compression and distance migration correction processing;

E. residual phase compensation and azimuth compression: d, performing inverse Fourier transform on the signal obtained in the step D through the distance, and transforming the signal into a distance time domain-Doppler frequency domain; then multiplying the distance time domain-Doppler frequency domain signal with an azimuth reference function to finish azimuth compression and residual phase compensation processing; and finally, performing azimuth-direction inverse Fourier transform on the signal subjected to the azimuth compression and the residual phase compensation so as to finish the imaging processing of the target.

2. The method for imaging a non-linear frequency modulation beacon of a synthetic aperture radar as claimed in claim 1, wherein the three-order expansion of the legendre orthogonal polynomial is performed on the two-dimensional frequency domain signal of the echo signal, and the expansion is performed by:

$\mathrm{\&phi;}(f_{\mathrm{\&tau;}},f_{\mathrm{\&eta;}})\&ap;-\frac{4\mathrm{\&pi;}{R}_b}{\mathrm{\&lambda;}}[a_0\left(f_{\mathrm{\&eta;}}\right)+a_1\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}+a_2\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}^2+a_3\left(f_{\mathrm{\&eta;}}\right)f_{\mathrm{\&tau;}}^3]$

in the formula: phi (f)_τ,f_η) For a two-dimensional spectral representation of the echo signal to be unfolded, f_τIs a distanceOff-directional frequency, f_ηIs the azimuth frequency, R_bThe distance from the radar to the target at the moment of the center of the synthetic aperture, lambda is the wavelength of the signal emitted by the radar, a₀(f_η),a₁(f_η),a₂(f_η),a₃(f_η) Coefficient of zero-order term, first-order term, second-order term and third-order term which are respectively Legendre polynomial expansion.

3. The method of imaging a synthetic aperture radar nonlinear frequency modulation scale according to claim 1, wherein said filtering of the cubic phase term of the signal obtained in step a is performed by:

S_2Y(f_τ,f_η)=S₂(f_τ,f_η)H₁(f_τ,f_η)

wherein: s_2Y(f_τ,f_η) For filtering the processed signal, S₂(f_τ,f_η) For two-dimensional frequency-domain signals developed three-order by Legendre orthogonal polynomials, H₁(f_τ,f_η) Is a non-linear frequency modulation function, f_τIs the range frequency, f_ηIs the azimuth frequency.

4. The method of imaging a synthetic aperture radar nonlinear frequency modulation scale according to claim 1, wherein said nonlinear frequency modulation scale is processed by the following formula:

S_2Ya(τ,f_η)=S_2Y(τ,f_η)H₂(τ,f_η)

wherein S is_2Ya(τ,f_η) For the signal after the nonlinear frequency modulation and scaling treatment, S_2Y(τ,f_η) Is S_2Y(f_τ,f_η) Signal obtained by inverse Fourier transform along the distance direction, H₂(τ,f_η) As a function of the non-linear FM scaling, f_τIs the range frequency, f_ητ represents the range fast time for the azimuth frequency.

5. The method for imaging a synthetic aperture radar nonlinear frequency modulation scale according to claim 1, wherein the distance compression and distance migration correction are performed according to the following formula:

S_YR(f_τ,f_η)=S_2Ya(f_τ,f_η)H₃(f_τ,f_η)

wherein S is_YR(f_τ,f_η) Is a distance-compressed and range migration-corrected signal, S_2Ya(f_τ,f_η) Is S_2Ya(τ,f_η) Signals obtained by Fourier transformation along the distance direction, H₃(f_τ,f_η) As a distance-wise reference function, f_τIs the range frequency, f_ητ represents the range fast time for the azimuth frequency.

6. The method of claim 1 wherein the residual phase compensation and azimuth compression processing is performed by the following equation:

S_YA(τ,f_η)=S_YR(τ,f_η)H₄(τ,f_η)

wherein S is_YA(τ,f_η) For the residual phase-compensated and azimuth-compressed signal, S_YR(τ,f_η) Is S_YR(f_τ,f_η) Signal obtained by inverse Fourier transform along the distance direction, H₄(τ,f_η) As an azimuth reference function, f_τIs the range frequency, f_ητ represents the range fast time for the azimuth frequency.

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