CS imaging method based on ultra-high resolution sliding aggregation SAR high-order slope distance model

Abstract

The invention relates to the technical field of synthetic aperture radar signal processing, and discloses a CS imaging method based on an ultrahigh-resolution slip SAR high-order slope distance model, and the method comprises the steps: building a high-order slope distance model based on the ephemeris parameters of a synthetic aperture radar satellite and the position information of an imaging target; determining a first expression of an original echo signal of a synthetic aperture radar satellite in a two-dimensional frequency domain and a second expression of the original echo signal in a distance Doppler domain based on a high-order slant-range model, and constructing a phase compensation function based on the first expression and the second expression; and performing range compression, range migration correction, secondary range compression and azimuth compression based on the phase compensation function to generate a focused synthetic aperture radar image. According to the method, universality description can be carried out on the slant range process of the SAR satellites running in different eccentricity rate orbits, and high precision can be kept.

Description

Technical Field

[0001] The present invention relates to the technical field of synthetic aperture radar signal processing, and specifically relates to a CS imaging method based on a high-order slant range model of ultra-high resolution sliding spotlight SAR. Background Art

[0002] Spaceborne synthetic aperture radar (SAR for short) is a high-resolution imaging radar carried on a satellite, which can observe the earth's surface under all-weather and all-day conditions and generate high-resolution radar images.

[0003] The sliding spotlight mode is one of the common operating modes of spaceborne SAR. In the sliding spotlight mode, the coherent integration time of the target echo can be increased by controlling the pointing of the antenna beam to the virtual point of the scene, thereby achieving ultra-high resolution.

[0004] The chirp scaling (CS for short) imaging algorithm uses the hyperbolic equivalent squint range model (ESRM for short), which is established based on the "go-stop-go" geometric configuration. Its two-dimensional spatial variation in the azimuth and range directions lacks sufficient accuracy and flexibility. As the coherent integration time of the echo increases, ESRM can no longer meet the description accuracy of the radar slant range history. Summary of the Invention

[0005] In view of this, the present invention provides a CS imaging method based on a high-order slant range model of ultra-high resolution sliding spotlight SAR to solve the problem that ESRM cannot meet the description accuracy of the radar slant range history.

[0006] In a first aspect, the present invention provides a CS imaging method based on a high-order slant range model of ultra-high resolution sliding spotlight SAR, the method comprising: constructing a high-order slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target; determining a first expression of the original echo signal of the synthetic aperture radar satellite in the two-dimensional frequency domain and a second expression of the original echo signal in the range-Doppler domain based on the high-order slant range model, and constructing a phase compensation function based on the first expression and the second expression; performing range compression, range migration correction, second range compression and azimuth compression based on the phase compensation function to generate a focused synthetic aperture radar image.

[0007] In an alternative embodiment, constructing a high-order slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target includes: calculating the relative position, relative velocity, relative acceleration, the first derivative of the relative acceleration, and the second derivative of the relative acceleration between the synthetic aperture radar satellite and the imaging target based on the position information and the ephemeris parameters; constructing a fourth-order slant range vector expression based on the relative position, the relative velocity, the relative acceleration, the first derivative, and the second derivative; performing a fourth-order Taylor expansion based on the azimuth time in the fourth-order slant range vector expression to obtain an expansion; and determining the coefficients of each order variable in the fourth-order slant range vector expression based on the expansion to determine the high-order slant range model.

[0008] In an alternative embodiment, determining the second expression of the original echo signal in the range-Doppler domain includes characterizing the second expression S rd (τ, f η ):

[0009]

[0010] where A0 is used to characterize a complex constant, W r (·) is used to characterize the range envelope, W α (·) is used to characterize the azimuth envelope, f ηc is used to characterize the Doppler center frequency of the reference point, τ is used to characterize the fast time in the range direction, f η is used to characterize the azimuth frequency, φ1(f η ; R0; α) is used to characterize the range migration term, φ0(f η ; R0; α) is used to characterize the azimuth modulation term, φ2(f η ; R0; α) is used to characterize the second-order range compression term, R rd (·) is used to characterize the expression of the high-order slant range model corresponding to the center point of the scene in the range-Doppler domain, R0 is used to characterize the slant range corresponding to the azimuth center time η c corresponding to different range gates, α is used to characterize the coefficient set of each term in the slant range model, c is used to characterize the speed of light, and j is used to characterize the imaginary unit.

[0011] In an alternative embodiment, performing range compression, range migration correction, second-order range compression, and azimuth compression based on the phase compensation function to generate a focused synthetic aperture radar image includes: constructing a chirp scaling compensation factor based on the second expression, multiplying the chirp scaling compensation factor by the second expression to obtain a scaled range-Doppler domain signal; converting the scaled range-Doppler domain signal to a two-dimensional frequency domain to obtain a two-dimensional frequency domain conversion signal, constructing a compensation function, and generating a corrected two-dimensional frequency domain signal based on the compensation function and the two-dimensional frequency domain conversion signal; converting the corrected two-dimensional frequency domain signal to the range-Doppler domain to obtain a range-Doppler domain signal, constructing an azimuth compression factor, and generating a focused synthetic aperture radar image based on the range-Doppler domain signal and the azimuth compression factor.

[0012] In an alternative embodiment, constructing the chirp scaling compensation factor includes constructing the chirp scaling compensation factor H through the following formula sc (τ, f η ):

[0013]

[0014] where τ is used to represent the fast time in the range direction, η is used to represent the slow time in the azimuth direction, R ref is used to represent the slant range at the scene center reference point, α ref is used to represent the coefficient set of each term in the slant range model corresponding to the scene center point, φ1(f η ; R0; α) is used to represent the range migration term, R0 is used to represent the slant range corresponding to the azimuth center time η c of different range gates, α is used to represent the coefficient set of each term in the slant range model, c is used to represent the speed of light, j is used to represent the imaginary unit, f η is used to represent the azimuth frequency, f ηc is used to represent the Doppler center frequency of the reference point, φ2(f η ; R ref ; α ref ) is used to represent the second-order range compression term under the slant range parameters corresponding to the scene center point, R rd (·) is used to represent the expression of the slant range model corresponding to the scene center point in the range-Doppler domain.

[0015] In an alternative embodiment, constructing the high-order slant range model includes representing the high-order slant range model R(η) through the following formula:

[0016] R(η) = R + c1η + c2η 2 + c3η3 +c4η 4

[0017] Wherein, R is used to represent the relative distance between the imaging target and the satellite, and η is used to represent the azimuth slow time. V st is used to represent the velocity vector of the satellite relative to the imaging target, and R st is used to represent the relative position vector of the satellite relative to the imaging target, and A st is used to represent the acceleration vector of the satellite relative to the imaging target, and dA st is used to represent the first derivative of the relative acceleration of the satellite relative to the imaging target, and ddA st is used to represent the second derivative of the relative acceleration of the satellite relative to the imaging target.

[0018] In an alternative embodiment, the first expression S of the original echo signal in the two-dimensional frequency domain is represented by the following formula 2df (f τ , f η ):

[0019]

[0020] Wherein, f τ is used to represent the range frequency, f η is used to represent the azimuth frequency, A0 is used to represent a complex constant, and W r (·) is used to represent the range envelope, and W α (·) is used to represent the azimuth envelope, and f ηc is used to represent the Doppler center frequency of the reference point, K r is used to represent the range chirp rate of the signal, f0 is used to represent the signal center frequency, c is used to represent the speed of light, and R 2d is used to represent the expression of the slant range model in the two-dimensional frequency domain, η is used to represent the azimuth slow time, and φ0(f η ; R0; α) is used to represent the azimuth modulation term; φ1(f η ; R0; α) is used to represent the range migration term; φ2(f η ; R0; α) is used to represent the second range compression term; φ3(f η ; R0; α) is used to represent the high-order perturbation term.

[0021] In a second aspect, the present invention provides a CS imaging device based on a high-order slant range model of ultra-high resolution sliding spotlight SAR. The device includes: a slant range model construction module, configured to construct a high-order slant range model based on the ephemeris parameters of a synthetic aperture radar satellite and the position information of an imaging target; a compensation function construction module, configured to determine a first expression of the original echo signal of the synthetic aperture radar satellite in the two-dimensional frequency domain and a second expression of the original echo signal in the range-Doppler domain based on the high-order slant range model, and construct a phase compensation function based on the first expression and the second expression; and an imaging module, configured to perform phase compensation for range compression, range migration correction, second-order range compression, and azimuth compression based on the phase compensation function, and generate a focused synthetic aperture radar image.

[0022] In a third aspect, the present invention provides a computer device, including: a memory and a processor, which are communicatively connected to each other. The memory stores computer instructions, and the processor executes the computer instructions to execute the CS imaging method based on the high-order slant range model of ultra-high resolution sliding spotlight SAR according to the first aspect or any corresponding embodiment thereof.

[0023] In a fourth aspect, the present invention provides a computer-readable storage medium, on which computer instructions are stored. The computer instructions are used to cause a computer to execute the CS imaging method based on the high-order slant range model of ultra-high resolution sliding spotlight SAR according to the first aspect or any corresponding embodiment thereof.

[0024] In a fifth aspect, the present invention provides a computer program product, including computer instructions, which are used to cause a computer to execute the CS imaging method based on the high-order slant range model of ultra-high resolution sliding spotlight SAR according to the first aspect or any corresponding embodiment thereof.

[0025] Based on the ephemeris parameters of a synthetic aperture radar satellite and the position information of an imaging target, a slant range model is established, which can provide a general description of the slant range history of an SAR satellite operating in orbits with different eccentricities and maintain a high accuracy. At the same time, range compression, range migration correction, second-order range compression, and azimuth compression are performed through the phase compensation function to complete the imaging processing and focusing of spaceborne sliding spotlight SAR, and ultra-high resolution imaging can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in related technologies, the following will briefly introduce the drawings required for use in the description of the specific embodiments or related technologies. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0027] Figure 1 Shows the schematic flow chart of the CS imaging method based on the high-order slant range model of ultra-high resolution sliding spotlight SAR according to the embodiment of the present invention;

[0028] Figure 2 Shows the schematic algorithm flow chart of the de-aliasing processing of the original echo signal of the synthetic aperture radar satellite according to the embodiment of the present invention;

[0029] Figure 3 Shows the schematic diagram of the echo amplitude of point targets with a resolution of 0.1 m in sliding spotlight SAR according to the embodiment of the present invention;

[0030] Figure 4 Shows the schematic contour map of the focusing result of the extended CS imaging processing of the echo data of point targets at the center of the SAR scene based on the high-precision fourth-order polynomial slant range model;

[0031] Figure 5 Shows the schematic azimuth profile of the focusing result of point targets at the center of the scene according to the embodiment of the present invention;

[0032] Figure 6 Shows the schematic range profile of the focusing result of point targets at the center of the scene according to the embodiment of the present invention;

[0033] Figure 7 Shows the schematic structural diagram of the CS imaging device based on the high-order slant range model of ultra-high resolution sliding spotlight SAR according to the embodiment of the present invention;

[0034] Figure 8 Is the schematic hardware structure diagram of the computer device according to the embodiment of the present invention. Detailed implementation manners

[0035] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0036] In the process of SAR imaging processing, the establishment of the distance history model between the target and the SAR platform plays a crucial role in the SAR imaging focusing result. An accurate slant range model is the basis of the imaging algorithm. The error between the slant range model and the real distance history will cause an error in the compensated phase in the imaging algorithm, and thus result in the phenomenon of azimuth defocusing.

[0037] In the related art, the slant range model of spaceborne SAR in near-circular orbits is generally established in a flat imaging geometry, and the expansion terms generally go up to the second order, which can meet the engineering requirements for low-orbit SAR. However, the flight trajectories of spaceborne SAR in large elliptical orbits and medium-high orbits are different from those of traditional near-circular SAR. Affected by large eccentricities, the bending effect of the orbit increases significantly. If the equivalent slant range model in the related art is still used for approximation, the phase error introduced in the imaging process will cause the focusing result to defocus.

[0038] Therefore, establishing a high-precision slant range model for ultra-high-resolution spaceborne SAR applicable to different orbital eccentricities is of great significance for applications such as SAR imaging processing and remote sensing observations.

[0039] In the related art, the improved equivalent squint range model (MESRM for short) improves the accuracy of the slant range model by introducing the third- and fourth-order Doppler modulation frequencies. However, since this slant range model is established based on the concept of equivalent velocity, when the spaceborne SAR operates at some positions with a large orbital bending curvature and in the apogee orbital segment of a large elliptical orbit, its Doppler modulation frequency is negative, resulting in the failure of the equivalent velocity concept and the inability to establish a slant range model based on equivalent velocity and equivalent acceleration.

[0040] Therefore, there is an urgent need to establish a high-precision SAR slant range model to accurately describe the slant range history of signals in the full orbital period of spaceborne SAR, thereby characterizing the two-dimensional space-variant slant range history characteristics of signals, and proposing a SAR extended Chirp Scaling imaging processing method based on this high-precision slant range model.

[0041] According to an embodiment of the present invention, there is provided an embodiment of a CS imaging method based on a high-order slant range model of ultra-high-resolution sliding focusing SAR. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0042] In this embodiment, a CS imaging method based on a high-order slant range model of ultra-high-resolution sliding focusing SAR is provided, which can be used for satellites, especially SAR satellites operating at positions with large curvature orbits or on large elliptical orbits. Figure 1 The flowchart of the CS imaging method based on the high-order slant range model of ultra-high-resolution sliding focusing SAR according to the embodiment of the present invention is shown, as Figure 1 shown, the process includes the following steps:

[0043] Step S101: construct a high-order slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target.

[0044] In this step, a fourth-order slant range polynomial model can be established by calculating the relative motion vector and position parameters between the SAR satellite and the imaging target, such as acceleration, velocity or position vector.

[0045] By expanding the simultaneous equations through Taylor series, the slant range model coefficients are solved, providing a mathematical basis for subsequent frequency domain compensation. In this way, by establishing a high-order slant range model, the changes in the slant range history between the SAR and the target can be described.

[0046] Step S102, based on the high-order slant range model, determine a first expression of the original echo signal of the synthetic aperture radar satellite in the two-dimensional frequency domain and a second expression of the original echo signal in the range Doppler domain, and construct a phase compensation function based on the first expression and the second expression.

[0047] In this step, the original sliding spotlight SAR echo signal is subjected to azimuth Deramp de-aliasing in the azimuth time domain, and the de-aliasing result is converted to the two-dimensional frequency domain by performing a two-dimensional Fast Fourier Transform (FFT) on the de-aliasing result.

[0048] The slant range equation is expanded according to the high-order slant range model, and the frequency domain expression of the range history is solved through Taylor series inversion. Based on the stationary phase principle, the two-dimensional frequency domain integral operation is simplified, the signal phase dominant term is extracted, the high-order phase error is eliminated, and the coupling effect between the range and azimuth directions is eliminated. According to the two-dimensional frequency domain model of the signal, a high-order disturbance phase compensation factor is constructed to perform phase compensation on the two-dimensional frequency domain model.

[0049] In this way, the image resolution can be significantly improved by suppressing spectrum aliasing through dealiasing, combining phase compensation and eliminating range-azimuth coupling. At the same time, the frequency domain integral operation can be simplified based on the stationary phase principle, and the series inversion method can reduce the number of iterations, thereby improving the processing efficiency.

[0050] Step S103, based on the phase compensation function, range compression, range migration correction, secondary range compression and azimuth compression are performed to generate a focused synthetic aperture radar image.

[0051] In this step, perform a range IFFT on the phase compensation function and multiply it by the extended chirp scaling factor in the range-Doppler domain. Perform a range FFT on the scaled signal to achieve range compression, second-order range compression, and azimuth coarse focusing in the two-dimensional frequency domain. Perform a range IFFT on the coarsely focused signal, multiply it by the extended azimuth compression factor in the Doppler domain, and perform residual range migration correction. Perform an azimuth IFFT on the corrected signal to complete imaging focusing in the azimuth time domain.

[0052] The CS imaging method based on the high-order slant range model of ultra-high resolution sliding spotlight SAR provided by this embodiment can establish a slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target, and can perform a general description of the slant range history of the SAR satellite operating in orbits with different eccentricities, and can maintain a high accuracy. At the same time, through the phase compensation function for range compression, range migration correction, second-order range compression, and azimuth compression, the imaging processing and focusing of the spaceborne sliding spotlight SAR are completed, and ultra-high resolution imaging can be achieved.

[0053] In some optional embodiments, based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target, a high-order slant range model is constructed, including: calculating the relative position R st , relative velocity V st , relative acceleration A st , first derivative dA of the relative acceleration st and second derivative ddA of the relative acceleration st ; based on the relative position R st , relative velocity V st , relative acceleration A st , first derivative dA st and second derivative ddA st , construct a fourth-order slant range vector expression; based on the azimuth time in the fourth-order slant range vector expression, perform a fourth-order Taylor expansion to obtain an expansion; based on the expansion, determine the coefficients of each order variable in the fourth-order slant range vector expression to determine the high-order slant range model.

[0054] In this embodiment, based on the relative position R st , relative velocity V st , relative acceleration A st , first derivative dA st and second derivative ddA st , construct a fourth-order slant range vector expression R(t a ), as follows:

[0055]

[0056] Among them, R is used to represent the distance between the satellite and the imaging target, η is used to represent the azimuth slow time, and x is used to represent the distance from R. st For each item to be multiplied, x can be set to:

[0057] x=x1η+x2η 2 +x3η 3 +x4η 4

[0058] Based on the fourth-order slant distance vector expression, a fourth-order Taylor expansion about x is performed to obtain the expansion R(η) as shown below:

[0059]

[0060] By combining x and R(η), we can solve x1, x2, x3 and x4 respectively, and the solution is:

[0061]

[0062] Assume that the high-order slant range model R(η) to be established, that is, the mathematical expression of the SAR high-precision fourth-order polynomial slant range model is as follows:

[0063] R(η)=R+c1η+c2η 2 +c3η 3 +c4η 4

[0064] The calculation expressions of c1, c2, c3 and c4 are as follows:

[0065]

[0066] In order to derive the accurate analytical expression of the SAR signal based on the fourth-order slant range vector expression model in the two-dimensional frequency domain, and to construct the phase compensation function in each algorithm step of the extended CS imaging algorithm, firstly, the two-dimensional frequency domain expression s0(τ, η) of the baseband signal of a single point target after demodulation, that is, the original echo signal of the synthetic aperture radar satellite, is assumed to be:

[0067]

[0068] Among them, A0 is used to represent the complex constant, W r (·) is used to characterize the distance envelope, W α (·) is used to characterize the azimuthal envelope, K r It is used to characterize the signal range modulation frequency, R(η) is used to characterize the target one-way slant range history, τ is used to characterize the fast time in range, η is used to characterize the slow time in azimuth, η c It is used to characterize the central moment of the azimuth reference, c is used to characterize the speed of light, and λ is used to characterize the signal wavelength.

[0069] Based on the stationary phase principle, the expression of S0(f) after the range Fourier transform of s0(τ, η) is derived as follows: τ :

[0070]

[0071] where f0 is used to characterize the signal center frequency, f0 = c / λ, and f τ is used to characterize the range frequency, and W r (·) is used to characterize the range envelope.

[0072] To obtain the exact expression of s0(τ, η) in the two-dimensional frequency domain, the azimuth Fourier transform is performed on S0(f τ , η). Let the expression of the signal after the azimuth Fourier transform be S 2df (f τ , f η ) as follows:

[0073]

[0074] Let the phase θ 2df (f τ , f η ) in the Fourier integral of S 2d (f τ , f η ) be:

[0075]

[0076] Take the derivative of θ 2d (f τ , f η ) with respect to η, and set the derivative to 0. Combine it with the high-order slant range model R(η) and organize to obtain the following equation:

[0077]

[0078] Use the series inversion method to solve this equation. Let Then its direct function Y(f τ , f η ) and inverse function η are as follows:

[0079]

[0080] where A i (i = 1, 2, 3, 4) are the coefficients of each term in the polynomial expression in the inverse function. Substitute η into Y(f τ , f η ) and organize to obtain the following formula:

[0081] Y(f τ,f η )=(2A1c2)Y(f τ ,f η )+(3A1 2 c3+2A2c2)Y(f τ ,f η ) 2

[0082] +(4A1 3 c4+6A2A1c3+2A3c2)Y(f τ ,f η ) 3

[0083] Using the undetermined coefficient method, Y(f τ ,f η ) is configured as 1, and the coefficients of the other higher-order terms are all 0, then A1, A2 and A3 can be solved in sequence, as shown below:

[0084]

[0085] Thus, the stationary phase point η(f τ ,f η ) is expressed in the frequency domain as follows:

[0086] η(f τ ,f η )=A1Y(f τ ,f η )+A2Y(f τ ,f η ) 2 +A3Y(f τ ,f η ) 3

[0087] Therefore, S 2df (f τ , f η ) is the phase θ of the Fourier integral 2d (f τ , f η The two-dimensional frequency domain expression of R(η) in ) is:

[0088]

[0089] Among them, R0 is used to represent the azimuth center time η of different range gates. c The corresponding slope distance, c i Used to characterize the center time η c Corresponding to the coefficients of each order of the fourth-order polynomial slope range model.

[0090] Simultaneous θ2d (f τ ,f η )、η(f τ ,f η ) and R 2d (f τ ,f η ), the first expression S 2df (f τ ,f η ) of the original echo signal in the two-dimensional frequency domain can be obtained as follows:

[0091]

[0092] From the expression of the two-dimensional frequency domain model S 2df (f τ ,f η ), it can be known that the range frequency f τ and the azimuth frequency f η are closely coupled in the two-dimensional frequency domain. Directly applying the stationary phase principle to solve the range fast inverse Fourier transform (Inverse Fast Fourier Transform, abbreviated as IFFT) of the two-dimensional frequency domain model S 2df (f τ ,f η ) will result in extremely cumbersome and complex results.

[0093] The range frequency f τ and the azimuth frequency f η can be separated. First, expand the stationary phase point η(f τ ,f η ) further into a polynomial about f τ to obtain:

[0094] η(f τ ,f η )≈b0(f η )+b1(f η )f τ +b2(f η )f τ 2

[0095] Let The expressions of b0(f η ), b1(f η ) and b2(f η ) can be obtained as follows respectively:

[0096]

[0097] Among them, A1, A2, and A3 are used to represent the coefficients of each term in the frequency-domain expression obtained by using the series inversion method and the method of undetermined coefficients to solve the stationary phase point η(F τ , F η ). Specifically, the expressions of A1, A2, and A3 are as follows:

[0098]

[0099] Let φ 2d (f τ , f η ) be the signal phase in the first expression S 2df (f τ , f η ). Expand φ 2d (f τ , f η ) further into a polynomial of f τ up to the third order, which can be written as:

[0100]

[0101] Among them, α is used to represent the set of coefficients of each term in the high-order slant range model, that is, α =

[0102] {c1, c2, c3, c4}. Substitute η(f τ , f η ), b0(f η ), b1(f η ), b2(f η ), and R 2d (f τ , f η ) into the expression of φ 2d (f τ , f η ), and the terms in φ 2d (f τ , f η ) can be obtained respectively. Among them, φ0(f η ; R0; α) is used to represent the azimuth modulation term; φ1(f η ; R0; α) is used to represent the range migration term;

[0103] φ2(f η ; R0; α) is used to represent the Secondary Range Compressing (SRC) term; φ3(f η ; R0; α) is used to represent the high-order perturbation term.

[0104] The analytical expressions of each term are given below. The expression of φ0(f η ; R0; α) is as follows:

[0105]

[0106] φ1(f η ; R0; α) is expressed as follows:

[0107]

[0108] φ2(f η ; R0; α) is expressed as follows:

[0109]

[0110] φ3(f η ; R0; α) is expressed as follows:

[0111]

[0112] In this way, the accurate analytical derivation of the SAR signal based on the high-order slant range model in the two-dimensional frequency domain is completed. Based on the expression of s0(τ, η) in the two-dimensional frequency domain, the compensation function can be further decomposed and constructed, and the extended CS scaling factor can be configured to realize the extended CS imaging processing.

[0113] Ultra-high resolution generally refers to a resolution less than 0.2 meters. Most of the SAR equivalent slant range models in related technologies are based on concepts such as Doppler parameters or equivalent velocity. For SAR satellites operating at large curvature orbit positions or on large elliptical orbits, these slant range models cannot describe the accurate slant range history because the large curvature of the operating orbit will cause the Doppler modulation frequency to be negative, and the square of the equivalent velocity is the Doppler modulation frequency. Therefore, this means that the equivalent velocity is a complex number and has lost the meaning of its own velocity. Therefore, the method of establishing the slant range model in related technologies cannot be used anymore.

[0114] In the embodiments of the present invention, the method of establishing a slant range model based on the concept of equivalent velocity and Doppler parameters in related technologies is abandoned. The present invention first establishes a fourth-order slant range vector expression model based on ephemeris parameters, that is, calculates the relative position vector, velocity vector, acceleration vector, first derivative vector of acceleration, and second derivative vector of acceleration between the satellite and the target, and then constructs a new fourth-order polynomial slant range model through the Taylor series expansion method, and solves the coefficients of each term in the fourth-order polynomial slant range model through the series inversion method to complete the establishment of a high-precision fourth-order polynomial slant range model. This fourth-order polynomial slant range model is universal for describing the slant range history of SAR satellites on orbits with different eccentricities and maintains a high accuracy.

[0115] In the embodiments of the present invention, the extended CS imaging algorithm includes: azimuth spectrum dealiasing processing; high-order phase and additional phase compensation introduced by dealiasing; derivation of the extended Chirp Scaling factor based on a high-precision fourth-order polynomial slant range model; signal expression form of the signal in the two-dimensional frequency domain after scaling; construction of compensation functions for range compression, second-order range compression, and consistent range cell migration (RCM) compensation; and, construction methods for the residual range cell migration correction function and the extended azimuth compression factor.

[0116] In some alternative embodiments, a phase compensation function is constructed based on the first expression and the second expression.

[0117] In this embodiment, the construction of the dealiasing factor for convolution with the original echo signal of the synthetic aperture radar satellite includes the first dealiasing factor H1(f r_ref , η) and the second dealiasing factor H2(f r_ref , η), and the expressions of the first dealiasing factor H1(f r_ref , η) and the second dealiasing factor H2(f r_ref , η) are as follows:

[0118]

[0119] Wherein, f ηc is used to represent the Doppler center frequency of the reference point, and f r_ref is used to represent the Doppler frequency modulation rate of the reference point. The convolution processing based on the dealiasing factor and the echo signal can be expressed as:

[0120]

[0121] The last exponential term in the above integral formula can be regarded as the transform kernel of the discrete azimuth Fourier transform. The above convolution processing process can be regarded as three steps. It should be noted that since the convolution processing process is equivalent to the Fourier transform through variable substitution, the output interval of the azimuth time has changed. The new azimuth time interval of the signal after dealiasing processing is as follows:

[0122]

[0123] Wherein, N a is used to represent the number of azimuth sampling points of the signal, and PRF is used to represent the pulse repetition frequency of the original signal. After dealiasing processing, the expression of the new pulse repetition frequency PRF dep of the signal is as follows:

[0124]

[0125] Figure 2 The figure shows a schematic diagram of the algorithm process for the anti-aliasing processing of the original echo signal of a synthetic aperture radar satellite in an embodiment of the present invention. As Figure 2 shown, s(η) is multiplied by the first anti-aliasing factor , and the multiplication result is Fourier-transformed. The obtained Fourier-transform result is multiplied by the second anti-aliasing factor to obtain the anti-aliasing processing result s * (η1).

[0126] After the above-mentioned anti-aliasing processing steps, the aliasing in the Doppler domain of the sliding spotlight SAR has been removed, and the anti-aliasing processing result can be obtained.

[0127] After the anti-aliasing processed echo signal is subjected to azimuth FFT, a compensation function H dep (f η ) for adding phase can be introduced in the azimuth frequency domain to compensate for the additional phase introduced by the anti-aliasing processing. Among them, the compensation function H dep (f η ) is as follows:

[0128]

[0129] After being compensated by the compensation function for adding phase, the signal is subjected to range FFT and enters the two-dimensional frequency domain. From the expression of φ 2d (f τ , f η ), it can be seen that in the phase of the two-dimensional frequency domain signal of the SAR signal derived based on the proposed high-precision fourth-order polynomial slant range model, there is a high-order perturbation term φ3(f η ; R0; c η ) containing a cubic term about f i . Therefore, before the imaging processing, a high-order perturbation compensation factor H3(f τ , f η ) can be constructed. The expression of the high-order perturbation compensation factor H3(f τ , f η ) is as follows:

[0130] H3(f τ , f η ) = exp{-jπφ3(f η ; R0; c i )f τ 3}

[0131] After the foregoing steps, the original echo signal of the synthetic aperture radar is subjected to de-aliasing processing, and the high-order perturbation terms and the additional phase introduced by de-aliasing are compensated by the high-order perturbation compensation factor and the compensation function of the additional phase in the two-dimensional frequency domain, as follows:

[0132] S0(f τ ,f η )=A0W r (f r )W a (f η -f ηc )

[0133] ×exp{φ0(f η ;R0;c i )+φ1(f η ;R0;c i )f τ +φ2(f η ;R0;c i )f τ 2}

[0134] In this way, based on the high-order perturbation compensation factor, the high-order phase errors ignored in the related art, such as the quadratic phase error caused by acceleration or the non-linear phase perturbation caused by atmospheric refraction, can be analyzed and compensated, significantly reducing the residual phase error. In the device equipped with the synthetic aperture radar or in a complex electromagnetic environment, the imaging resolution and the image signal-to-noise ratio can be improved. At the same time, the Chirp Scaling factor is extended, and the Doppler frequency aliasing in the signal frequency modulation component is eliminated through frequency domain filtering, avoiding the image blurring caused by range-azimuth coupling. In the wide beam or large squint angle SAR, the sidelobe level can be effectively suppressed, and the target edge sharpness and geometric fidelity can be improved. In addition, through the joint compensation factor and the de-chirp operation, the phase distortion caused by multipath scattering and noise interference can be suppressed, and the imaging consistency of the complex scene can be improved.

[0135] In some alternative embodiments, based on the phase compensation function, range compression, range migration correction, second range compression, and azimuth compression are performed to generate a focused synthetic aperture radar image, including: constructing an extended frequency modulation scaling compensation factor based on the second expression, multiplying the extended frequency modulation scaling compensation factor by the second expression to obtain a scaled range-Doppler domain signal; converting the scaled range-Doppler domain signal to the two-dimensional frequency domain to obtain a two-dimensional frequency domain conversion signal, constructing a compensation function, and generating a corrected two-dimensional frequency domain signal based on the compensation function and the two-dimensional frequency domain conversion signal; converting the corrected two-dimensional frequency domain signal to the range-Doppler domain to obtain a range-Doppler domain signal, constructing an azimuth compression factor, and generating a focused synthetic aperture radar image based on the range-Doppler domain signal and the azimuth compression factor.

[0136] In this embodiment, the derivation of the extended Chirp Scaling factor based on the high-precision fourth-order polynomial slant range model includes performing a range IFFT on S0(f τ , f η ) to obtain S rd (τ, f η ). The expression of S rd (τ, f η ) is as follows:

[0137]

[0138] Let the integrated phase in the expression of S rd (τ, f η ) be θ RD (f τ , f η ). The expression of the obtained θ RD (f τ , f η ) is as follows:

[0139] θ RD (f τ , f η ) = πφ0(f η ; R0; α) + πφ1(f η ; R0; α)f τ + πφ2(f η ; R0; α)f τ 2 + 2πf τ τ

[0140] Take the derivative of the phase in θ RD (f τ , f η ) with respect to f τ and set the derivative to 0, we can get:

[0141]

[0142] Among them, when f τ satisfies , the derivative in is 0.

[0143] Substitute f τ into the expression of θ RD (f τ , f η ), we can get the second expression S rd (τ, f η ) of the signal in the range-Doppler domain as follows:

[0144]

[0145] The expression of the range migration term included in the above formula is as follows:

[0146]

[0147] The function of the scaling equation is to enable the imaging target to compensate for the remaining phase of each range bin after the consistent RCM correction. Therefore, in order to achieve complementary translation, at the range R rd (f η ; R0; α), the Scaling equation frequency at the azimuth frequency f η is as follows:

[0148] F scl (f η ; R0; α) = K sc Δτ

[0149] where, Δτ is used to characterize the time translation amount corresponding to the phase complementarity, and the expression of Δτ is as follows:

[0150]

[0151] where, β sc is used to characterize the scaling at the reference azimuth frequency, R ref is used to characterize the slant range at the scene center reference point, and α is used to characterize the coefficient set of each term in the fourth-order polynomial slant range model, that is, α = {c1, c2, c3, c4}.

[0152] Based on the second expression of the original echo signal in the range-Doppler domain, construct the extended chirp scaling compensation factor H sc (τ, f η ), and complement the range migration based on the extended chirp scaling compensation factor H sc (v, f η ), adjust the range migration trajectory corresponding to each target in the Range-Doppler (RD) domain. The expression of the extended chirp scaling compensation factor H sc (τ, f η ) is as follows:

[0153]

[0154] where, τ is used to characterize the fast time in the range direction, η is used to characterize the slow time in the azimuth direction, R ref is used to characterize the slant range at the scene center reference point, α refA set of coefficients for each term in the slant range model corresponding to the scene center point, φ1(f η ; R0; α) is used to represent the range migration term, R0 is used to represent the azimuth center time η of different range gates c corresponding slant range, α is used to represent a set of coefficients for each term in the high-order slant range model, c is used to represent the speed of light, j is used to represent the imaginary unit, f η is used to represent the azimuth frequency, f ηc is used to represent the Doppler center frequency of the reference point, φ2(f η ; R ref ; α ref ) is used to represent the second-order range compression term under the slant range parameters corresponding to the scene center point, R rd (·) is used to represent the expression of the slant range model corresponding to the scene center point in the range-Doppler domain.

[0155] By multiplying the extended frequency modulation scaling compensation factor with the first range-Doppler domain signal, the scaled range-Doppler domain signal is obtained. Through the scaled range-Doppler domain signal, the adjustment of the range migration trajectories corresponding to each target in the range-Doppler domain is realized.

[0156] In this way, by introducing a high-order phase compensation term, the extended Chirp Scaling factor can correct the non-linear range migration that is difficult to handle by traditional methods, eliminate the trajectory divergence caused by range-azimuth coupling, ensure the alignment of the migration trajectories of targets in different range cells, improve the geometric consistency of imaging, reduce the residual phase error, and avoid image defocusing; at the same time, the extended frequency modulation scaling compensation factor can adapt to the migration slope differences of different range cells by dynamically adjusting the phase modulation frequency, avoiding the problem of insufficient edge scene correction caused by the fixed modulation frequency assumption in the Chirp Scaling algorithm in related technologies.

[0157] Performing a range FFT transform on the aforementioned scaled range-Doppler signal to the two-dimensional frequency domain, obtaining a two-dimensional frequency domain conversion signal, and constructing a range compression, second-order range compression, and consistency range migration correction compensation function to multiply with the two-dimensional frequency domain conversion signal to realize range compression, second-order range compression, and azimuth rough focusing.

[0158] Specifically, in the range-Doppler domain, multiplying H sc (τ, f η ) with S rd (τ, f η ), then performing a range FFT, and through the stationary phase principle, the two-dimensional frequency domain conversion signal S2(f τ , f η ) can be obtained. To make the variables in the formula more concise, it can be set:

[0159]

[0160] In this way, the obtained two-dimensional frequency domain conversion signal S2(f τ , f η ) has the following expression:

[0161]

[0162] Based on the expression of the two-dimensional frequency domain conversion signal S2(f τ , f η ), a compensation function H rcm (f τ , f η ) for range compression, secondary range compression, and range migration correction can be constructed. Based on the compensation function H rcm (f τ , f η ), the second, third, and fourth exponential terms in the expression of S2(f τ , f η ) are compensated. The compensation function H rcm (f τ , f η ) is characterized by the following formula:

[0163]

[0164] After multiplying S2(f τ , f η ) by H rcm (f τ , f η ) in the two-dimensional frequency domain, a corrected two-dimensional frequency domain signal is generated. The corrected two-dimensional frequency domain signal is subjected to range IFFT, and the corrected two-dimensional frequency domain signal is converted to the range-Doppler domain to obtain a second range-Doppler domain signal. By constructing an azimuth compression factor H az (τ, f η ), precise focusing of the imaging target is achieved.

[0165] The expression of the azimuth compression factor H az (τ, f η ) is as follows:

[0166]

[0167] In this way, the derivation and analysis of the steps of the extended CS imaging algorithm for the ultra-high resolution spaceborne sliding spotlight SAR based on the high-precision fourth-order polynomial slant range model are completed. Based on the high-precision fourth-order polynomial slant range model provided by the embodiments of the present invention, an extended Chirp Scaling imaging processing method is further proposed. The present invention gives the exact analytical expressions and detailed derivation processes of the sliding spotlight SAR signal in the two-dimensional frequency domain and the range-Doppler domain, and gives the construction method of the general extended Chirp Scaling factor compensation function. By using the extended Chirp Scaling imaging algorithm proposed by the present invention, the precise focusing and imaging of the ultra-high resolution sliding spotlight SAR echo data can be realized, and the evaluation of its imaging indexes meets the theoretical requirements.

[0168] Table 1 shows the simulation parameters of the point target echo of the ultra-high resolution spaceborne sliding spotlight SAR in the embodiments of the present invention.

[0169] Table 1 Simulation Parameters of Point Target Echo of Ultra-High Resolution Spaceborne Sliding Spotlight SAR

[0170] Orbit semi-major axis (m) 6887315.0 Orbit inclination (°) 97.6399 Argument of perigee (°) 90 Right ascension of ascending node (°) 120 Orbit eccentricity 0.0011 Signal wavelength (m) 0.0196 Signal band Ku Antenna center viewing angle (°) 33.13 Antenna length (m) 3.6 Antenna width (m) 2.08 Signal sampling rate (MHz) 360 Signal bandwidth (MHz) 300 Pulse repetition frequency (Hz) 4000 Pulse width (s) 0.00003 Number of azimuth points 40000 Number of range points 16384

[0171] Figure 3 shows the schematic diagram of the amplitude of the point target echo with a resolution of 0.1 m in the sliding spotlight SAR in the embodiments of the present invention. As Figure 3 shown, due to the long illumination time of the 0.1 m sliding spotlight beam, the range migration curve of the point target echo is obvious.

[0172] Table 2 shows the imaging parameters of the sliding spotlight SAR calculated based on the ephemeris parameters, etc. and the parameters in the fourth-order polynomial slant range model.

[0173] Table 2

[0174]

[0175] Figure 4 shows the schematic diagram of the contour map of the focusing result of the extended CS imaging processing of the point target echo at the center of the SAR scene based on the high-precision fourth-order polynomial slant range model. Figure 4 The abscissa in it is used to represent the sampling points in the range direction, and the ordinate is used to represent the sampling points in the azimuth direction.

[0176] Figure 5 shows the schematic diagram of the azimuth profile of the focusing result of the point target at the center of the scene in the embodiments of the present invention. Figure 5 The abscissa in it is used to represent the azimuth direction, and the ordinate is used to represent the azimuth amplitude, with the unit of dB.

[0177] Figure 6 shows the schematic diagram of the range profile of the focusing result of the point target at the center of the scene in the embodiments of the present invention. Figure 6The horizontal axis is used to represent the distance direction, and the vertical axis is used to represent the amplitude of the distance direction, and the unit is dB.

[0178] In order to fully demonstrate the accuracy of the fourth-order polynomial slant range model proposed in the present invention and the performance of the extended CS imaging algorithm, Table 3 shows the index evaluation and resolution evaluation of the mid-field scenic spot target focusing results after the extended CS imaging processing of the ultra-high resolution sliding SAR simulation echo. It can be seen that its peak sidelobe ratio can reach -13.147dB, the integrated sidelobe ratio can reach -9.968dB, and the azimuth resolution is 0.0889m, which is almost the same as the theoretical expected indicators, which strongly proves the good performance and feasibility of the present invention.

[0179] Table 3. Evaluation of imaging indicators of scene center point targets

[0180]

[0181] The scheme for establishing the ultra-high resolution SAR slant range model in the related art does not take into account the description of the slant range course between the SAR satellite and the target in the large elliptical orbit or the large curvature orbit. Most of the slant range models are based on Doppler parameters or equivalent speeds, etc., and for SAR satellites running at large curvature orbit positions or on large elliptical orbits, these slant range models cannot achieve the description of the accurate slant range course. This is because the curvature of the running orbit is large, which will cause the Doppler modulation frequency to be negative, and the square of the equivalent speed is the Doppler modulation frequency, so this means that the equivalent speed is a complex number, which has lost the meaning of its own speed. It is impossible to accurately express the slant range course between the satellite and the target at these special positions. The present invention proposes a universal high-precision slant range model for different eccentricity orbits, regardless of the size of the orbital curvature. At the same time, the present invention provides a detailed derivation method and coefficient definition of each coefficient in the high-order slant range model.

[0182] In this embodiment, a CS imaging device based on an ultra-high resolution SAR high-order slant range model is also provided, and the device is used to implement the above-mentioned embodiments and preferred implementation modes, and the descriptions that have been made will not be repeated. As used below, the term "module" can be a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, the implementation of hardware, or a combination of software and hardware, is also possible and conceivable.

[0183] This embodiment provides a CS imaging device based on an ultra-high resolution sliding focusing SAR high-order slant range model. Figure 7 FIG. 4 is a schematic diagram showing the structure of a CS imaging device based on an ultra-high resolution sliding focusing SAR high-order slant range model according to an embodiment of the present invention. Figure 7 As shown, including:

[0184] The slant range model construction module 701 is used to construct a high-order slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target.

[0185] The compensation function construction module 702 is used to determine the first expression of the original echo signal of the synthetic aperture radar satellite in the two-dimensional frequency domain and the second expression of the original echo signal in the range-Doppler domain based on the high-order slant range model, and construct a phase compensation function based on the first expression and the second expression.

[0186] The imaging module 703 is used to perform phase compensation for range compression, range migration correction, second-order range compression, and azimuth compression based on the compensation function, and generate a focused synthetic aperture radar image.

[0187] In some alternative embodiments, the slant range model construction module 701 includes:

[0188] The first model construction unit is used to construct a high-order slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target, including: calculating the relative position, relative velocity, relative acceleration, first derivative of the relative acceleration, and second derivative of the relative acceleration between the synthetic aperture radar satellite and the imaging target based on the position information and the ephemeris parameters; constructing a fourth-order slant range vector expression based on the relative position, relative velocity, relative acceleration, first derivative, and second derivative; performing fourth-order Taylor expansion based on the azimuth time in the fourth-order slant range vector expression to obtain an expansion; and determining the coefficients of each order variable in the fourth-order slant range vector expression and determining the high-order slant range model.

[0189] In some alternative embodiments, the compensation function construction module 702 includes:

[0190] The first unit of the compensation function construction module is used to construct a high-order perturbation compensation factor and a de-chirp factor, compensate the phase error in the two-dimensional frequency domain model based on the high-order perturbation compensation factor and the de-chirp factor to generate a compensated two-dimensional frequency domain signal, construct a scaling factor and a high-order perturbation compensation factor according to the two-dimensional frequency domain model of the signal, and deduce the expression of the signal in the range-Doppler domain, and then construct an azimuth compression factor.

[0191] In some alternative embodiments, the imaging module 703 includes:

[0192] The first unit of the imaging module is used to perform range compression, range migration correction, second range compression, and azimuth compression based on a phase compensation function to generate a focused synthetic aperture radar image, including: constructing an extended frequency modulation scaling compensation factor based on a second expression, multiplying the extended frequency modulation scaling compensation factor by the second expression to obtain a scaled range-Doppler domain signal; converting the scaled range-Doppler domain signal to a two-dimensional frequency domain to obtain a two-dimensional frequency domain conversion signal, constructing a compensation function, and generating a corrected two-dimensional frequency domain signal based on the compensation function and the two-dimensional frequency domain conversion signal; converting the corrected two-dimensional frequency domain signal to the range-Doppler domain to obtain a range-Doppler domain signal, constructing an azimuth compression factor, and generating a focused synthetic aperture radar image based on the range-Doppler domain signal and the azimuth compression factor.

[0193] The further functional descriptions of the above-mentioned modules and units are the same as those in the corresponding embodiments above, and will not be elaborated here.

[0194] The CS imaging device based on the high-resolution sliding focusing SAR high-order slant range model in this embodiment is presented in the form of functional units. Here, the unit refers to an application specific integrated circuit (ASIC) circuit, a processor and a memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.

[0195] The embodiment of the present invention also provides a computer device having the above-mentioned Figure 7 CS imaging device based on the high-resolution sliding focusing SAR high-order slant range model as shown.

[0196] Please refer to Figure 8 , Figure 8 which is a schematic structural diagram of a computer device provided by an optional embodiment of the present invention. As shown in Figure 8 , the computer device includes: one or more processors 10, a memory 20, and interfaces for connecting various components, including a high-speed interface and a low-speed interface. Each component communicates with each other using different buses and can be installed on a common motherboard or in other ways as needed. The processor can process instructions executed within the computer device, including instructions stored in the memory or on the memory to display graphic information of a graphical user interface on an external input / output device (such as a display device coupled to the interface). In some optional embodiments, if necessary, multiple processors and / or multiple buses can be used together with multiple memories and multiple memories. Similarly, multiple computer devices can be connected, and each device provides some necessary operations (such as an array of servers, a set of blade servers, or a multi-processor system). Figure 8 In

[0197] The processor 10 can be a central processing unit, a network processor, or a combination thereof. Among them, the processor 10 can further include a hardware chip. The above-mentioned hardware chip can be an application-specific integrated circuit, a programmable logic device, or a combination thereof. The above-mentioned programmable logic device can be a complex programmable logic device, a field-programmable gate array, a generic array logic, or any combination thereof.

[0198] Among them, the aforementioned memory 20 stores instructions executable by at least one processor 10, so that the aforementioned at least one processor 10 executes the method shown in the above embodiments.

[0199] The memory 20 can include a program storage area and a data storage area. Among them, the program storage area can store an operating system and application programs required for at least one function; the data storage area can store data created according to the use of the computer device, etc. In addition, the memory 20 can include a high-speed random access memory, and can also include a non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state storage devices. In some alternative embodiments, the memory 20 can optionally include a memory remotely set relative to the processor 10, and these remote memories can be connected to the computer device through a network. Examples of the above-mentioned network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0200] The memory 20 can include a volatile memory, such as a random access memory; the memory can also include a non-volatile memory, such as a flash memory, a hard disk, or a solid-state drive; the memory 20 can also include a combination of the above types of memories.

[0201] The computer device further includes an input device 30 and an output device 40. The processor 10, the memory 20, the input device 30, and the output device 40 can be connected through a bus or other means, Figure 8 Taking the connection through the bus as an example.

[0202] The input device 30 can receive input digital or character information, and generate key signal inputs related to the user settings and function control of the computer device, such as a touch screen, a keypad, a mouse, a trackpad, a touchpad, a pointing stick, one or more mouse buttons, a trackball, a joystick, etc. The output device 40 can include a display device, an auxiliary lighting device (such as a light-emitting diode), and a tactile feedback device (such as a vibration motor), etc. The above-mentioned display device includes but is not limited to a liquid crystal display, a light-emitting diode, a display, and a plasma display. In some alternative embodiments, the display device can be a touch screen.

[0203] Embodiments of the present invention also provide a computer-readable storage medium. The method according to the embodiments of the present invention can be implemented in hardware, firmware, or be implemented as computer code that can be recorded on a storage medium, or be implemented as computer code that is originally stored in a remote storage medium or a non-transitory machine-readable storage medium and downloaded through a network and will be stored in a local storage medium, so that the method described herein can be stored in such software processing on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. Among them, the storage medium can be a magnetic disk, an optical disc, a read-only memory, a random access memory, a flash memory, a hard disk, or a solid-state drive, etc.; further, the storage medium can also include a combination of the above types of memories. It can be understood that a computer, a processor, a microprocessor controller, or programmable hardware includes a storage component that can store or receive software or computer code, and when the software or computer code is accessed and executed by the computer, the processor, or the hardware, the method shown in the above embodiments is implemented.

[0204] A part of the present invention can be applied as a computer program product, such as computer program instructions, which when executed by a computer, can call or provide the method and / or technical solution according to the present invention through the operation of the computer. Those skilled in the art should understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executes the instruction, or the computer compiles the instruction and then executes the corresponding compiled program, or the computer reads and executes the instruction, or the computer reads and installs the instruction and then executes the corresponding installed program. Herein, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible by the computer.

[0205] Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A CS imaging method based on a high-order slant range model of ultra-high resolution sliding spotlight SAR, characterized in that, The method includes: Constructing a high-order slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target; Based on the high-order slant range model, determining a first expression of the original echo signal of the synthetic aperture radar satellite in the two-dimensional frequency domain and a second expression of the original echo signal in the range-Doppler domain, and constructing a phase compensation function based on the first expression and the second expression; Based on the phase compensation function, performing range compression, range migration correction, second-order range compression, and azimuth compression to generate a focused synthetic aperture radar image.

2. The method according to claim 1, characterized in that, The constructing of the high-order slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target includes: Based on the position information and the ephemeris parameters, calculating the relative position, relative velocity, relative acceleration, the first derivative of the relative acceleration, and the second derivative of the relative acceleration between the synthetic aperture radar satellite and the imaging target; Constructing a fourth-order slant range vector expression based on the relative position, the relative velocity, the relative acceleration, the first derivative, and the second derivative; Performing a fourth-order Taylor expansion based on the azimuth time in the fourth-order slant range vector expression to obtain an expansion; Based on the expansion, determining the coefficients of each order variable in the fourth-order slant range vector expression and determining the high-order slant range model.

3. The method according to claim 1 or 2, characterized in that, Determining the second expression of the original echo signal in the range-Doppler domain includes characterizing the second expression S by the following formula rd (τ, f η ): wherein, A0 is used to represent a complex constant, W r (·) is used to represent the range envelope, W α (·) is used to represent the azimuth envelope, f ηc is used to represent the Doppler center frequency of the reference point, τ is used to represent the fast time in the range direction, f η is used to represent the azimuth frequency, φ1(f η ; R0; α) is used to represent the range migration term, φ0(f η ; R0; α) is used to represent the azimuth modulation term, φ2(f η ; R0; α) is used to represent the second range compression term, R rd (·) is used to represent the expression of the high-order slant range model corresponding to the center point of the scene in the range-Doppler domain, R0 is used to represent the slant range corresponding to the azimuth center time η c of different range gates, α is used to represent the coefficient set of each term in the slant range model, c is used to represent the speed of light, and j is used to represent the imaginary unit.

4. The method according to claim 1, characterized in that, The performing of range compression, range migration correction, second-order range compression, and azimuth compression based on the phase compensation function to generate a focused synthetic aperture radar image includes: Constructing an extended frequency modulation scaling compensation factor based on the second expression, and multiplying the extended frequency modulation scaling compensation factor and the second expression to obtain a scaled range-Doppler domain signal; Converting the scaled range-Doppler domain signal to the two-dimensional frequency domain to obtain a two-dimensional frequency domain conversion signal, constructing a compensation function, and generating a corrected two-dimensional frequency domain signal based on the compensation function and the two-dimensional frequency domain conversion signal; Converting the corrected two-dimensional frequency domain signal to the range-Doppler domain to obtain a range-Doppler domain signal, constructing an azimuth compression factor, and generating a focused synthetic aperture radar image based on the range-Doppler domain signal and the azimuth compression factor.

5. The method according to claim 4, wherein The described construction extends the chirp scaling compensation factor, including constructing the extended chirp scaling compensation factor H through the following formula sc (τ, f η ): Among them, τ is used to represent the fast time in the range direction, η is used to represent the slow time in the azimuth direction, and R ref is used to represent the slant range at the reference point of the scene center, and α ref is used to represent the coefficient set of each term in the slant range model corresponding to the scene center point. φ1(f η ; R0; α) is used to represent the range migration term, R0 is used to represent the slant range corresponding to the azimuth center time η of different range gates c , α is used to represent the coefficient set of each term in the slant range model, c is used to represent the speed of light, j is used to represent the imaginary unit, and f η is used to represent the azimuth frequency, and f ηc is used to represent the Doppler center frequency of the reference point, and φ2(f η ; R ref ; α ref ) is used to represent the second-order range compression term under the slant range parameters corresponding to the scene center point, and R rd (·) is used to represent the expression of the slant range model corresponding to the scene center point in the range-Doppler domain.

6. The method according to claim 1 or 2, characterized in that, The constructing of the high-order slant range model includes characterizing the high-order slant range model R(η) by the following formula: R(η) = R + c1η + c2η 2 + c3η 3 + c4η 4 Among them, R is used to represent the relative distance between the imaging target and the satellite, and η is used to represent the azimuth slow time, V st is used to represent the velocity vector of the satellite relative to the imaging target, R st is used to represent the relative position vector of the satellite relative to the imaging target, Ast is used to represent the acceleration vector of the satellite relative to the imaging target, dAst is used to represent the first derivative of the relative acceleration of the satellite relative to the imaging target, ddA st is used to represent the second derivative of the relative acceleration of the satellite relative to the imaging target.

7. The method according to claim 1, characterized in that, The first expression S of the original echo signal in the two-dimensional frequency domain is characterized by the following formula 2df (f τ , f η ): Among them, fτ is used to represent the range frequency, fη is used to represent the azimuth frequency, A0 is used to represent the complex constant, W r (·) is used to represent the range envelope, W α (·) is used to represent the azimuth envelope, f ηc is used to represent the Doppler center frequency of the reference point, K r is used to represent the range chirp rate of the signal, f0 is used to represent the signal center frequency, c is used to represent the speed of light, R 2d is used to represent the expression of the high-order slant range model in the two-dimensional frequency domain, η is used to represent the azimuth slow time, φ0(f η ; R0; α) is used to represent the azimuth modulation term; φ1(f η ; R0; α) is used to represent the range migration term; φ2(f η ; R0; α) is used to represent the second-order range compression term; φ3(f η ; R0; α) is used to represent the high-order perturbation term.

8. A CS imaging device based on a high-order slant range model of ultra-high resolution sliding spotlight SAR, characterized in that, The apparatus includes: A slant range model construction module for constructing a high-order slant range model based on the ephemeris parameters of the synthetic aperture radar satellite and the position information of the imaging target; A compensation function construction module for determining a first expression of the original echo signal of the synthetic aperture radar satellite in the two-dimensional frequency domain and a second expression of the original echo signal in the range-Doppler domain based on the high-order slant range model, and constructing a phase compensation function based on the first expression and the second expression; An imaging module for performing phase compensation of range compression, range migration correction, second-order range compression, and azimuth compression based on the phase compensation function to generate a focused synthetic aperture radar image.

9. A computer device, characterized in that, Including: A memory and a processor, which are communicatively connected to each other. Computer instructions are stored in the memory, and the processor executes the computer instructions to perform the CS imaging method based on the high-order slant range model of ultra-high resolution sliding spotlight SAR according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Computer instructions are stored on the computer-readable storage medium, and the computer instructions are used to cause a computer to perform the CS imaging method based on the high-order slant range model of ultra-high resolution sliding spotlight SAR according to any one of claims 1 to 7.

Images