1. An NLCS imaging method of a curvilinear motion bistatic SAR is characterized in that aiming at the requirement of observing a target scene from multiple angles, a slope function expression of the curvilinear motion bistatic SAR is constructed, and a curvilinear motion bistatic SAR echo model is established; for the constructed slope function expression, a Chebyshev orthogonal polynomial is approximated to be a fourth-order series form related to azimuth time; the rest steps are as follows:

1) completing distance compression of the point target in a distance frequency domain, an azimuth time domain, and effectively correcting and compensating the LRCM and the Doppler linear phase;

2) after the pretreatment of the distance direction, carrying out Fourier inverse transformation of the distance direction, and transforming the distance direction into a two-dimensional time domain;

3) a nonlinear scaling function is provided, and is multiplied by the two-dimensional time domain echo signals after distance direction preprocessing, so that the Doppler frequency modulation of targets at different points is balanced;

4) and performing azimuth Fourier transform, performing azimuth matched filtering in a range-Doppler domain, and finally performing azimuth Fourier inverse transform to obtain a point target focused image of the bistatic SAR.

2. The NLCS imaging method of curved motion bistatic SAR of claim 1, wherein said slope function expression is represented as follows:

R_A(t)＝R_T(t)+R_R(t)

in the region of a sceneThe central point is A (x)₀,y₀0), T and R respectively represent a transmitting platform and a receiving platform, which respectively follow different paths and at different three-dimensional velocities (v)_Tx,v_Ty,v_Tz) And (v)_Rx,v_Ry,v_Rz) Flying, and having different three-dimensional accelerations (a)_Tx,a_Ty,a_Tz) And (a)_Rx,a_Ry,a_Rz) (ii) a After the time t, the position coordinate of the transmitting platform is (x)_T,y_T,z_T) Wherein x is_T＝v_Txt+a_Txt²/2，y_T＝v_Tyt+a_Tyt²/2，z_T＝v_Tzt+a_Tzt²/2+H_TThe position coordinate of the receiving platform is (x)_R,y_R,z_R) Wherein x is_R＝v_Rxt+a_Rxt²/2，y_R＝v_Ryt+a_Ryt²/2，z_R＝v_Rzt+a_Rzt²/2+H_R，a_i0＝x₀+y₀+H_i，a_i1＝-x₀v_ix-y₀v_iy+H_iv_iz，a_i3＝v_ixa_ix+v_iya_iy+v_iza_iz，a_i4＝(a_ix+a_iy+a_iz)²/4,i＝T,R。

3. The NLCS imaging method of curvilinear motion bistatic SAR of claim 1, wherein said curvilinear motion bistatic SAR echo model is represented as

Wherein A is₀Is the backscattering coefficient of the point object, tau and T ∈ [ -T [ - ]_s/2,T_s/2]Are respectively provided withFor fast time in range and slow time in azimuth, T_sIs the synthetic pore size time; omega_r(. and ω)_az(. h) are a distance window function and an orientation window function, respectively; c is the speed of light; λ is the carrier wavelength; k_rFrequency modulation for the transmitted signal; r_AAnd (t) is the instantaneous slope distance total course of the central point target A.

4. The NLCS imaging method of curvilinear motion bistatic SAR according to claim 2, wherein for the constructed slope function expression, the step of approximating a Chebyshev orthogonal polynomial into a fourth order series form with respect to azimuth time specifically comprises:

normalizing the azimuth time t, i.e. orderingT_sRepresenting the synthetic aperture time, the pitch function is expressed as:

are respectively to R_T(x) And R_R(x) Performing Chebyshev orthogonal decomposition, and arranging the solution according to the power series of x as follows:

R_T(x)＝α_T0+α_T1x+α_T2x²+α_T3x³+α_T4x⁴

R_R(x)＝α_R0+α_R1x+α_R2x²+α_R3x³+α_R4x⁴

wherein the decomposition coefficientα_i1＝C_i1-3C_i3，α_i2＝2C_i2-8C_i4，α_i3＝4C_i3,α_i4＝8C_i4In the formula C_ijIs a Chebyshev coefficient, j is 0,1,2,3,4, i means T orR is and has

Wherein, T_j(x) Is a Chebyshev polynomial recursion and has T₀(x)＝1，T₁(x)＝x，...，T_j(x)＝2xT_j-1(x)-T_j-2(x)，Is a variable node, n-4 is the expansion order,

will be provided withSubstituting into the normalized slant range function expression, and sorting according to the fourth power series of t to obtain the Chebyshev decomposition formula of bistatic SAR slant range under the action of constant acceleration

R(t)＝λ₀+λ₁t+λ₂t²+λ₃t³+λ₄t⁴+…

Wherein λ is₀＝α_T0+α_R0，

5. The NLCS imaging method of the curvilinear motion bistatic SAR according to claim 4, wherein the step 1) specifically comprises the following steps:

the bidirectional distance offset is calculated assuming t is 0:

LRCMC and distance compression correspond to a compensation function of where f_τRepresents the distance-wise frequency:

the pitch function of the center point a at this time is:

R_A1(t)＝λ₀+λ₂t²+λ₃t³+λ₄t⁴+…

selecting reference point C for subsequent analysis, where t_CPosition time representing reference point C:

R_C1(t)＝λ₀+λ₂(t-t_C)²+λ₃(t-t_C)³+λ₄(t-t_C)⁴+…

linear phase removal the corresponding compensation function:

6. the NLCS imaging method of curved motion bistatic SAR according to claim 4, wherein the step 2) specifically comprises the following steps:

the signal after LRCMC and linear phase removal is, wherein f_cCarrier frequency:

performing range-wise IFFT on the signals preprocessed by the point A and the point C to obtain a time domain echo signal, wherein t is_aAzimuth time representing point a:

7. the NLCS imaging method of curved motion bistatic SAR according to claim 6, wherein step 3) specifically comprises the following steps: a perturbation function exp { j pi alpha t is provided³The disturbance function is multiplied by the time domain echo signal so as to realize the aim of balancing the target frequency regulation of different points; multiplying the time domain echo signal of the point A by a disturbance function, and neglecting a constant term of the slope distance and a coefficient higher than a quadratic term to obtain:

also, multiplying the echo signal of the reference point C by the perturbation function and ignoring the constant term of the slope distance and the coefficients higher than the quadratic term yields:

solve the coefficient of the disturbance function to

8. The NLCS imaging method of curved motion bistatic SAR according to claim 7, wherein step 4) specifically comprises the following steps:

the higher order terms of target a may be processed by performing an azimuth FFT:

and (3) solving a resident phase point by utilizing a resident phase principle, substituting the resident phase point into the azimuth phase, and obtaining an azimuth compensation function as follows:

wherein the content of the first and second substances,representing the phase of the orientation compensation function, t (f)_a) Dwell phase point, f, representing azimuth_aAnd representing azimuth frequency, and transforming the echo signals to a two-dimensional time domain after azimuth phase matching filtering to obtain a point target focused image of the bistatic SAR.

Background

Bistatic Synthetic Aperture Radar (bistar) refers to a Radar imaging system in which a transmitting platform and a receiving platform operate separately. Compared with the traditional single-base SAR, the method has the advantages of higher flexibility in application, longer acting distance and capability of acquiring richer information. However, the structure with separate transceiving platforms also brings some technical challenges, and the bistatic SAR slant range function is the sum of two hyperbolas, which makes the solution of the frequency spectrum function more difficult and increases the complexity of the imaging algorithm.

When special scene requirements such as multi-angle observation of targets are needed in practical application scenes, a carrier platform of the bistatic SAR usually moves in a curve track due to the existence of three-dimensional speed and acceleration, and the special configuration of the bistatic SAR in the curve track has higher flexibility, autonomy and mobility. The three-dimensional speed and the acceleration not only reduce the precision of the slant range of the bistatic SAR, but also increase the requirement on an imaging algorithm. The Zhanneli et al in China approximate the slope function by using Taylor series, and compared with the method of orthogonal polynomial, the method has larger error of slope; the Yuhai et al is an NLCS algorithm for bistatic SAR, but only considers the three-dimensional speed of the platform, and ignores the error influence caused by three-dimensional acceleration due to atmospheric turbulence and the like; wujunjie et al apply KT (Keystone transform) transform to NLCS algorithm, correct LRCM of moving target in bistatic SAR static scene, but neglect residual RCM, make focusing effect have relatively large attenuation in azimuth and distance direction; li Zhong et al, the university of electronic technology, proposed a self-adaptive NLCS technique that corrects the high-order RCM and balances the space-variant of Doppler parameters, but this method is only applicable to the moving target mode of forward-looking SAR and has a limited application range. Plum rain et al expand the slant range by Taylor series, and the azimuth equalizes the frequency modulation rates of different point targets through an NLCS algorithm, but has constraints on synthetic aperture time, and the phenomenon of spectrum aliasing can occur in large synthetic aperture time.

Based on the existing problems, overcoming the defects of the existing method is a problem to be solved urgently in the technical field.

Disclosure of Invention

The invention aims to overcome the defects of the prior art, provides an NLCS (non line of sight) imaging method of a curve motion bistatic SAR (synthetic aperture radar) aiming at the requirements of special scenes such as a target needing to be observed from multiple angles in practical application scenes, effectively solves the problem of the azimuth space-variant of Doppler frequency modulation caused by three-dimensional speed and acceleration, and improves the focusing performance and the imaging quality of a point target.

The technical scheme of the invention is as follows:

an NLCS imaging method of a curvilinear motion bistatic SAR is characterized in that aiming at special scene requirements such as a target needing multi-angle observation and the like, a slope function expression of the curvilinear motion bistatic SAR is constructed, and a curvilinear motion bistatic SAR echo model is established; for the constructed slope function expression, a Chebyshev orthogonal polynomial is approximated to be a fourth-order series form related to azimuth time; other steps include the following:

1) completing distance compression of the point target in a distance frequency domain, an azimuth time domain, and effectively correcting and compensating the LRCM and the Doppler linear phase;

2) after the pretreatment of the distance direction, carrying out Fourier inverse transformation of the distance direction, and transforming the distance direction into a two-dimensional time domain;

3) a nonlinear scaling function is provided, and is multiplied by the two-dimensional time domain echo signals after distance direction preprocessing, so that the Doppler frequency modulation of targets at different points is balanced;

4) and performing azimuth Fourier transform, performing azimuth matched filtering in a range-Doppler domain, and finally performing azimuth Fourier inverse transform to obtain a point target focused image of the bistatic SAR.

Preferably, aiming at special scene requirements such as the need of observing a target from multiple angles, constructing a slope function expression of the curvilinear motion bistatic SAR, and establishing a curvilinear motion bistatic SAR echo model, wherein the slope function expression is expressed as follows:

R_A(t)＝R_T(t)+R_R(t)

the central point of the scene area is A (x)₀,y₀0), T and R respectively represent a transmitting platform and a receiving platform, which respectively follow different paths and at different three-dimensional velocities (v)_Tx,v_Ty,v_Tz) And (v)_Rx,v_Ry,v_Rz) Flying, and having different three-dimensional accelerations (a)_Tx,a_Ty,a_Tz) And (a)_Rx,a_Ry,a_Rz). After the time t, the position coordinate of the transmitting platform is (x)_T,y_T,z_T) Wherein x is_T＝v_Txt+a_Txt²/2，y_T＝v_Tyt+a_Tyt²/2，z_T＝v_Tzt+a_Tzt²/2+H_TThe position coordinate of the receiving platform is (x)_R,y_R,z_R) Wherein x is_R＝v_Rxt+a_Rxt²/2，y_R＝v_Ryt+a_Ryt²/2，z_R＝v_Rzt+a_Rzt²/2+H_R。a_i0＝x₀+y₀+H_i，a_i1＝-x₀v_ix-y₀v_iy+H_iv_iz，a_i3＝v_ixa_ix+v_iya_iy+v_iza_iz，a_i4＝(a_ix+a_iy+a_iz)²/4。

The curvilinear motion bistatic SAR echo signal is expressed as

In the formula A₀Is the backscattering coefficient of the point object, tau and T ∈ [ -T [ - ]_s/2,T_s/2]Respectively, the fast time of the distance direction and the slow time of the azimuth direction, T_sIs the synthetic pore size time; omega_r(. and ω)_az(. h) are a distance window function and an orientation window function, respectively; c is the electromagnetic wave propagation speed; f. of_cIs the carrier frequency; k_rFrequency modulation for the transmitted signal; r_AAnd (t) is the instantaneous slope distance total course of the central point target A. .

Preferably, for the constructed slope function expression, the step of approximating the constructed slope function expression into a fourth-order series form with respect to azimuth time by using a Chebyshev orthogonal polynomial specifically includes:

normalizing the azimuth time t, i.e. orderingx∈[-1,1]The pitch function is expressed as:

are respectively to R_T(x) And R_R(x) Performing Chebyshev orthogonal decomposition, and arranging the solution according to the power series of x as follows:

R_T(x)＝α_T0+α_T1x+α_T2x²+α_T3x³+α_T4x⁴

R_R(x)＝α_R0+α_R1x+α_R2x²+α_R3x³+α_R4x⁴

wherein the decomposition coefficientα_i1＝C_i1-3C_i3，α_i2＝2C_i2-8C_i4，α_i3＝4C_i3,α_i4＝8C_i4(in the formula C_ijIs a Chebyshev coefficient, j is 0,1,2,3,4, i means T or R), and has

Wherein, T_j(x) Is a Chebyshev polynomial recursion and has T₀(x)＝1，T₁(x)＝x，...，T_j(x)＝2xT_j-1(x)-T_j-2(x)，Is a variable node, n-4 is the expansion order,

will be provided withSubstituting into the normalized slant range function expression, and sorting according to the fourth power series of t to obtain the Chebyshev decomposition formula of bistatic SAR slant range under the action of constant acceleration

R(t)＝λ₀+λ₁t+λ₂t²+λ₃t³+λ₄t⁴+…

Wherein λ is₀＝α_T0+α_R0，

In the formula

λ₀＝[(C_T0/2-C_T2+C_T4)+(C_R0/2-C_R2+C_R4)]

Wherein λ₀Is a constant term; lambda [ alpha ]₁Is a range migration term coefficient for linear phase removal; lambda [ alpha ]₂Is a distance warping term coefficient used for controlling the azimuth Frequency Modulation (FM) rate and can also be used for the derivation of a disturbance function; lambda [ alpha ]₃And λ₄Are high order term coefficients used to derive the two-bit spectrum using series inversion and define an azimuthal matched filter.

Preferably, the step of performing distance compression in the distance frequency domain, azimuth time domain, and effective correction and compensation of the LRCM and the doppler linear phase specifically includes:

the bidirectional distance offset is calculated assuming t is 0:

LRCMC and distance compression correspond to the compensation function:

the pitch function of the center point a at this time is:

R_A1(t)＝λ₀+λ₂t²+λ₃t³+λ₄t⁴+…

reference point C was selected for subsequent analysis:

R_C1(t)＝λ₀+λ₂(t-t_C)²+λ₃(t-t_C)³+λ₄(t-t_C)⁴+…

linear phase removal the corresponding compensation function:

preferably, after the preprocessing in the distance direction, performing inverse Fourier transform in the distance direction, and transforming to the two-dimensional time domain, specifically includes:

the signal after LRCMC and linear phase removal is:

performing range-wise IFFT on the signals preprocessed by the point A and the point C to obtain time domain echo signals, wherein the time domain echo signals are as follows:

preferably, the step of providing a nonlinear scaling function, multiplying the nonlinear scaling function by the two-dimensional time domain echo signal after the distance direction preprocessing, and equalizing the doppler frequency modulation of the targets at different points specifically includes:

a perturbation function exp { j pi alpha t is provided³And multiplying the disturbance function and the echo signal by each other to realize the aim of balancing the target frequency adjustment of different points.

Multiplying the echo signal of the point A by the disturbance function, and neglecting a constant term of the slope distance and a coefficient higher than a quadratic term to obtain:

also, multiplying the echo signal of the reference point C by the perturbation function and ignoring the constant term of the slope distance and the coefficients higher than the quadratic term yields:

solve the coefficient of the disturbance function to

Preferably, the method specifically includes the steps of performing azimuth Fourier transform, performing azimuth matched filtering in a range-doppler domain, and finally performing azimuth Fourier inverse transform to obtain a bistatic SAR focused image:

the higher order terms of target a can be processed by performing an azimuthal FFT (ignoring constant terms):

and (3) solving a resident phase point by utilizing a resident phase principle, substituting the resident phase point into the azimuth phase, and obtaining an azimuth compensation function as follows:

and after azimuth phase matching filtering, converting the echo signals into a two-dimensional time domain to obtain a point target focused image of the bistatic SAR.

By adopting the scheme, the invention has the beneficial effects that:

in special application scenes such as a target needing to be observed in multiple angles, the BiSAR carrier platform often has three-dimensional speed and acceleration to do curve track motion, and the three-dimensional speed and the acceleration not only reduce the precision of the slant range of the BiSAR, but also increase the requirement on an imaging algorithm. The invention provides an NLCS imaging method of a curve motion bistatic SAR, which utilizes a Chebyshev polynomial to decompose a pitch function under three-dimensional speed and acceleration, and greatly improves the approximation precision of the pitch function compared with a Taylor approximate pitch method; the linear distance walking item and the linear phase are compensated through the LRCMC, so that large strabismus is equivalent to small strabismus or front side view imaging, the processing process of a later algorithm is simplified, and distance-azimuth coupling is reduced; the method is characterized in that an azimuth nonlinear scaling algorithm is provided for the azimuth time space-variant problem caused by three-dimensional speed and acceleration, and the azimuth space-variant problem of Doppler frequency modulation is solved by using a disturbance function, so that the same azimuth compensation function can be adopted for matched filtering of the targets at the same distance unit point.

The NLCS algorithm is a time-frequency domain hybrid algorithm, only comprises FFT and complex multiplication operation, and does not relate to interpolation processing, so that the NLCS algorithm is easy to apply in real time in engineering. The disturbance function is a cubic function related to azimuth time, the disturbance function is multiplied by an echo signal in a time domain, point-by-point processing is needed, and the operation efficiency is lower than that of a frequency domain algorithm. Simulation experiments prove that the NLCS algorithm not only can well image a central point, but also can realize a high-resolution imaging effect on edge points, and the algorithm can well improve the imaging quality of edge point targets; and the Chebyshev decomposition-based NLCS algorithm of the BiSAR is not only suitable for the curvilinear motion BiSAR, but also can realize high-resolution imaging in a linear motion mode. In conclusion, the Chebyshev decomposition-based NLCS algorithm has wide application scenes and high imaging quality, and is an imaging algorithm which is worthy of wide popularization.

Drawings

FIG. 1 is a diagram of bistatic SAR geometry employed in accordance with an embodiment of the present invention;

FIG. 2 is a flow chart of the NLCS imaging method of bistatic SAR of the present invention;

FIG. 3 is a schematic of LRCMC and linear phase removal;

FIG. 4 is a schematic diagram of the equalization tuning of the perturbation function;

FIG. 5 is a multi-point imaging diagram of the method of the present invention;

FIG. 6 is a contour plot of center and edge points for the method of the present invention;

FIG. 7 is a graph of distance responses to center and edge points for the method of the present invention;

FIG. 8 is a graph of the azimuthal impulse response of the center and edge points for the method of the present invention.

Detailed Description

The invention mainly adopts a simulation experiment method for verification, and all steps and conclusions are verified to be correct on Matlab2016 a. The invention is described in further detail below with reference to the figures and the detailed description of the invention.

As shown in FIG. 2, the invention relates to a Chebyshev orthogonal decomposition-based NLCS (Non-Linear Chirp Scaling) imaging method of a curvilinear motion bistatic SAR, which constructs a slope function expression of the curvilinear motion bistatic SAR and establishes a curvilinear motion bistatic SAR echo model aiming at special scene requirements such as a target needing multi-angle observation and the like.

Specifically, the bistatic SAR geometry used in embodiments of the present invention is shown in fig. 1, wherein:

the central point of the scene area is A (x)₀,y₀0), T and R respectively represent a transmitting platform and a receiving platform, which respectively follow different paths and at different three-dimensional velocities (v)_Tx,v_Ty,v_Tz) And (v)_Rx,v_Ry,v_Rz) Flying, and having different three-dimensional accelerations (a)_Tx,a_Ty,a_Tz) And (a)_Rx,a_Ry,a_Rz). After the time t, the position coordinate of the transmitting platform is (x)_T,y_T,z_T) Wherein x is_T＝v_Txt+a_Txt²/2，y_T＝v_Tyt+a_Tyt²/2，z_T＝v_Tzt+a_Tzt²/2+H_TThe position coordinate of the receiving platform is (x)_R,y_R,z_R) Wherein x is_R＝v_Rxt+a_Rxt²/2，y_R＝v_Ryt+a_Ryt²/2，z_R＝v_Rzt+a_Rzt²/2+H_R。

The curve motion trajectory bistatic SAR slant range function expression is as follows:

R_A(t)＝R_T(t)+R_R(t)

in the formula a_i0＝x₀+y₀+H_i，a_i1＝-x₀v_ix-y₀v_iy+H_iv_iz，a_i2＝v_i2_x+v_i2_y+v_i2_z-x₀a_ix-y₀a_iy+H_ia_iz，a_i3＝v_ixa_ix+v_iya_iy+v_iza_iz，a_i4＝(a_ix+a_iy+a_iz)²/4。

The curvilinear motion bistatic SAR echo signal is expressed as

Wherein A is₀Is the backscattering coefficient of the point object, tau and T ∈ [ -T [ - ]_s/2,T_s/2]Respectively, the fast time of the distance direction and the slow time of the azimuth direction, T_sIs the synthetic pore size time; omega_r(. and ω)_az(. h) are a distance window function and an orientation window function, respectively; λ is the carrier wavelength; c represents the speed of light; k_rFrequency modulation for the transmitted signal; r_AAnd (t) is the instantaneous slope distance total course of the central point target A.

Further, for the constructed slope function expression, a Chebyshev orthogonal polynomial is used to approximate a fourth order series form related to the azimuth time.

Specifically, the Chebyshev polynomial is applied to the curvilinear motion bistatic SAR slant range function, and the azimuth time t is normalized first, namely the Chebyshev polynomial is orderedx∈[-1,1]The pitch function is expressed as:

then separately to R_T(x) And R_R(x) Performing Chebyshev orthogonal decomposition, and arranging the solution according to the power series of x as follows:

R_T(x)＝α_T0+α_T1x+α_T2x²+α_T3x³+α_T4x⁴

R_R(x)＝α_R0+α_R1x+α_R2x²+α_R3x³+α_R4x⁴

wherein the decomposition coefficientα_i1＝C_i1-3C_i3，α_i2＝2C_i2-8C_i4，α_i3＝4C_i3,α_i4＝8C_i4(in the formula C_ijIs a Chebyshev coefficient, j is 0,1,2,3,4, i means T or R), and has

Wherein, T_j(x) Is a Chebyshev polynomial recursion and has T₀(x)＝1，T₁(x)＝x，...，T_j(x)＝2xT_j-1(x)-T_j-2(x)，Is a variable node, n-4 is the expansion order,

will be provided withSubstituting into the normalized slant range function expression, and sorting according to the fourth power series of t to obtain the Chebyshev decomposition formula of the curvilinear motion bistatic SAR slant range under the action of three-dimensional acceleration

R(t)＝λ₀+λ₁t+λ₂t²+λ₃t³+λ₄t⁴+…

Wherein λ is₀＝α_T0+α_R0，

Other steps of the invention include the following:

1) and the distance compression of the point target in the distance frequency domain, the azimuth time domain is completed, and the LRCM and the Doppler linear phase are effectively corrected and compensated.

Specifically, since the slant range locus of the point target generally includes a linear range migration component (LRCM) and a nonlinear range migration component, when the composite antenna beam is obliquely viewed, the linear component appears, and most of the range-doppler coupling comes from the linear component, the LRCM component needs to be removed through the LRCMC operation, so that the target locus is aligned with the azimuth coordinate axis, so as to facilitate azimuth compression.

Performing range direction FFT on the original echo signal to obtain a range frequency domain-azimuth time domain signal as follows:

the slope of the LRCM varies with distance because the squint angle varies with the target distance, and in the case of azimuthally varying bistatic, the squint angle also varies with azimuth. To solve this problem, it is necessary to perform the LRCMC in the invariant region to keep the variation of the squint angle small. The bidirectional distance offset is calculated assuming t is 0:

LRCMC and distance compression correspond to a compensation function of where f_τRepresents the distance-wise frequency:

the pitch function of the center point a at this time is:

R_A1(t)＝λ₀+λ₂t²+λ₃t³+λ₄t⁴+…

reference point C was selected for subsequent analysis:

R_C1(t)＝λ₀+λ₂(t-t_C)²+λ₃(t-t_C)³+λ₄(t-t_C)⁴+…

wherein t is_CIndicating the azimuth time of the reference point C.

The LRCMC removes only the linear translational component of the slant-range function, and the linear phase term due to doppler shift still exists, so this linear phase term should be removed to facilitate the application of MSR to eliminate the coupling of range and azimuth.

Linear phase removal the corresponding compensation function:

the signal after LRCMC and linear phase removal is, wherein f_cRepresents the carrier frequency:

2) after the preprocessing of the distance direction, the Fourier inverse transformation of the distance direction is carried out, and the distance direction is transformed to a two-dimensional time domain.

Specifically, distance IFFT is performed on the signal preprocessed at point a and point C, and the obtained time domain echo signal is:

wherein t is_aThe azimuth time of point a is shown.

3) And (4) providing a nonlinear scaling function, and multiplying the nonlinear scaling function by the two-dimensional time domain echo signal after the distance direction preprocessing to balance the Doppler frequency modulation of the targets at different points.

Specifically, after LRCMC and range compression, point targets with different azimuth tuning frequencies are located in the same range unit. In order to realize azimuth compression in a Doppler frequency domain, an NLCS algorithm is applied in a time domain to balance the modulation frequencies of targets at different points, and a disturbance function exp { j pi alpha t is provided³And the disturbance function is multiplied by the signal, so that the aim of balancing the target frequency adjustment of different points is fulfilled.

Multiplying the echo signal of the point A by the disturbance function, and neglecting a constant term of the slope distance and a coefficient higher than a quadratic term to obtain:

since the approximation in the above equation only includes the second order phase term, the NLCS algorithm only equalizes the chirp component of the target.

Also, multiplying the echo signal of the reference point C by the perturbation function and ignoring the constant term of the slope distance and the coefficients higher than the quadratic term yields:

let t_n＝t-t_CAnd carry over into s_pertC(τ,t_a) And (4) obtaining:

to find the disturbance factor α, let t_CIs 0 while makingAndadding to zero, i.e.The disturbance coefficient can be solved

In the formula

R_T(0)+R_R(0)＝λ₁t_C＝2[(C_T1-3C_T3)+(C_R1-3C_R3)]t_C/T_s

Then

s_pertC(τ,t_n) The first phase term in (1) is due to the perturbation process, the second term is a small doppler shift, the third term is a constant term, depending on the position of the target, which has no effect on the focusing process, and the fourth term is a chirp modulation term, which is the same for all targets. Therefore, the final azimuth phase modulation is contained in the first and fourth exponential terms, and this modulation is the same for all targets in the same range bin.

5) And performing azimuth Fourier transform, performing azimuth matched filtering in a range-Doppler domain, and finally performing azimuth Fourier inverse transform to obtain a point target focused image of the bistatic SAR.

Specifically, the higher order terms of target a may be processed by performing an azimuthal FFT (ignoring constant terms):

and (3) solving a dwell phase point by using a dwell phase principle and a series inversion method:

order to

To obtain f_aThe relation with the azimuth time t is as follows:

the resident phase point is obtained by using a series inversion method as follows:

wherein the content of the first and second substances,

substituting the resident phase point into the azimuth phase to obtain an azimuth compensation function as follows:

and performing azimuth IFFT after azimuth phase matching and filtering to obtain a point target focusing image.

The method of the present invention will be described below by experimental simulation.

Fig. 2 is a flow chart of the NLCS algorithm of the present invention. Firstly, preprocessing a point target, removing LRCMC and linear phases in a distance frequency domain, providing a disturbance function in order to balance the frequency modulation of different point targets, multiplying a preprocessed point target echo signal by the disturbance function to realize the purpose of balancing the frequency modulation of different point targets, and finally compensating azimuth phases in an azimuth frequency domain to realize high-resolution imaging of the point target.

Fig. 3 is a schematic of LRCMC and linear phase removal. As shown in fig. 3(a), C has the same closest slant distance as E, B has the same closest slant distance as D, and B and E have the same beam center. After LRCMC and linear phase removal, as shown in fig. 3(b), a, C, and D are located in the same range bin and have the same slope, and the LRCMC operates to move point targets with different azimuth tuning frequencies into the same range bin, so as to equalize the tuning frequencies of different point targets by using a perturbation function, thereby compensating for the azimuth null deformation of the doppler tuning frequency.

Fig. 4 is a schematic diagram of equalizing the tuning frequency using a perturbation function. The amount of doppler shift caused by squint is not shown in the figure to simplify the schematic diagram. In fig. 4, (a) is the real part of the azimuth frequency modulation signal of the three point targets, and (b) is the phase corresponding to each azimuth signal. As can be seen, the three curves have different azimuthal frequency modulation, where frequency modulation refers to the second derivative of the curve of the real part of the signal, which varies with the original range position of the target. In order to equalize the tuning frequency of the target, a perturbation function to the third power of azimuth time is proposed, and its graph is shown in (c). This cubic phase is added to the phase of plot (b) resulting in the three target phases of plot (d), the phase of the point target being changed and having the same tuning frequency according to the nature of the exponential function. Graph (e) is the real part of the point target signal after perturbation.

In order to verify the effectiveness and feasibility of the NLCS algorithm in the BiSAR system, experimental simulation was performed using the data in table 1. The three-dimensional velocities and accelerations of the launch and receive platforms are listed in table 2.

TABLE 1 simulation parameters

TABLE 2 speed and acceleration

Fig. 5 is a 25-point target contour map of NLCS algorithm based on Chebyshev approximation, and it can be seen from the map that good imaging effect can be achieved regardless of the scene center point or the scene edge point, and it can be seen that the algorithm can improve the focusing effect of the edge point. Meanwhile, a rule can be found, the imaging effect of point targets located in the same distance unit is the same, because linear distance migration correction is firstly carried out, the point targets of different distance units are corrected in the same distance unit, and finally the same azimuth matched filter is applied in the distance unit, so that high-resolution imaging of the NLCS algorithm is realized.

FIG. 6 is a center point P₁₃Near end point P₂₃And edge point P₂₅Is imaged on the contour map. It can be seen from the figure that the center point and the edge point have good imaging quality and focusing effect even under the action of three-dimensional speed and acceleration.

FIG. 7 is a center point P₁₃Near end point P₂₃And edge point P₂₅Towards the impulse response diagram. As can be seen from the figure, the distances between the center point and the edge point are close to the ideal impulse response towards the impulse response; FIG. 8 is a center point P₁₃Near end point P₂₃And edge point P₂₅The azimuth impulse response map of (3). As can be seen from the figure, the center points and the edge pointsHas ideal azimuth impulse response and a central point P₁₃The main lobe width of (a) is narrower, indicating that the azimuth resolution is higher. In conclusion, the invention can realize good focusing effect on the distance direction and the azimuth direction of the target based on the NLCS algorithm of Chebyshev orthogonal decomposition.

To evaluate the imaging performance of the Chebyshev polynomial-based NLCS algorithm of the present invention, the center point P was calculated separately₁₃Near end point P₂₃And edge point P₂₅Integrated Sidelobe Ratio (ISLR) and Peak Sidelobe Ratio (PSLR) of the range and azimuth, and resolution. As shown in table 3, through numerical analysis and comparison, the PSLR and ISLR measured values of the algorithm of the present invention are close to the theoretical values, the distance-wise resolutions of the center point and the edge points are similar, and the azimuth-wise resolution of the center point is the highest.

TABLE 3 two methods of imaging quality assessment under curvilinear motion mode

In conclusion, the method utilizes the Chebyshev polynomial to decompose the slope function under the three-dimensional speed and the acceleration, and compared with a method for approximating the slope by Taylor, the method greatly improves the approximation precision of the slope function; the linear distance walking item and the linear phase are compensated through the LRCMC, so that large strabismus is equivalent to small strabismus or front side view imaging, the processing process of a later algorithm is simplified, and distance-azimuth coupling is reduced; the method is characterized in that an azimuth nonlinear scaling algorithm is provided for the azimuth time space-variant problem caused by three-dimensional speed and acceleration, and the azimuth space-variant problem of Doppler frequency modulation is solved by using a disturbance function, so that the same azimuth compensation function can be adopted for matched filtering of the targets at the same distance unit point. The simulation verification proves that the NLCS algorithm can well image the central point and can realize the high-resolution imaging effect on the edge point, the algorithm can well improve the imaging quality of the edge point target, and the application range is wide.

The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.