A high-speed large-angle squint curve trajectory SAR imaging method combining omega-k and fnCS

Abstract

The application discloses a high-speed large-oblique-view curve trajectory SAR imaging method combined with Omega-K and FNCS, and comprises the following steps: obtaining a polynomial slant range model by extending a Taylor series to the fifth order to a momentary slant range history; performing linear distance walk correction, distance pulse compression and acceleration de-slope preprocessing in an echo signal distance wave number domain; performing distance block on a two-dimensional time domain signal, introducing a reference function in a two-dimensional wave number domain of a sub-block, and performing distance cell migration correction by using an improved Stolt mapping; introducing an alignment function to the signal after the distance cell migration correction, and realizing distance focusing by using two-dimensional IFFT; when performing azimuth processing, introducing a fifth-order disturbance function in an azimuth time domain, introducing a fifth-order NCS function in an azimuth frequency domain, performing unified azimuth compression in the azimuth time domain, and finally obtaining a two-dimensional SAR image by using azimuth FFT. The application can be directly applied to a high-speed large-oblique-view SAR system under a curve trajectory, and high-precision curve trajectory SAR imaging can be realized under a high-speed large-oblique-view angle scene.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to a high-speed large-slant-look curve trajectory SAR imaging method that combines Omega-K and frequency nonlinear frequency modulated scaling (FNCS). Background Technology

[0002] As the core technology of SAR systems on high-speed mobile platforms, SAR imaging algorithms typically need to consider many unique characteristics, including large oblique angles, azimuth spatial variability of Doppler parameters, real-time processing, and curved trajectories.

[0003] SAR imaging algorithms can be broadly categorized into two types: time-domain algorithms and hybrid-domain algorithms. Time-domain algorithms, such as Backward Projection (BPA) and Fast Factorization BPA (FFBPA), are suitable for scenarios with large oblique angles and curved trajectories, but their enormous computational complexity makes them difficult to apply in real-time. In contrast, hybrid-domain algorithms have lower computational complexity and are easier to process in real-time. Therefore, it is necessary to design a hybrid-domain imaging method for high-speed, large oblique-angle SAR with curved motion trajectories. Fundamentally, hybrid-domain algorithms can be viewed as a large class of algorithms that process data in the time, frequency, or wavenumber domains to achieve high-resolution SAR imaging. Their imaging process typically involves range focusing and azimuth compression.

[0004] For high-speed, large-slant-look curved trajectory SAR imaging, Taylor series approximation and Stolt mapping (SM) are two main methods for achieving range focusing. First, the accuracy of the slant range model essentially determines the range focusing accuracy of Taylor series approximation and Stolt mapping. Classical slant range models include polynomial models and equivalent hyperbolic models. Due to the presence of multidimensional velocity and acceleration, the parameters of the polynomial model become extremely complex. Through velocity and acceleration vector synthesis, the equivalent hyperbolic model can convert the instantaneous slant range model into the form of the traditional hyperbolic model. However, when the acceleration is too large, the error of the aforementioned classical slant range models becomes intolerable. Simultaneously, the range focusing accuracy of Taylor series approximation also depends on the order of the two-dimensional spectral expansion, and the phase of the two-dimensional spectral expansion is decoupled by the Taylor series expansion. Although the third-order two-dimensional spectral expansion can satisfy most complex cases, it still performs unnecessary approximations. Furthermore, due to the large error of the interpolation kernel, and considering the influence of curved dive trajectory errors, traditional SM processing is not suitable for the equivalent hyperbolic model, and naturally, it cannot be applied to the polynomial slant range model.

[0005] Azimuth compression refers to the unified processing of signals in the azimuth dimension to obtain a two-dimensional high-resolution SAR image. For high-speed, large-look curved trajectory SAR imaging, linear range travel correction (LRWC) and acceleration deskewing are important methods for decoupling the severely decoupled range-azimuth coupling (RAC). However, these methods often violate the azimuth translation invariance after range focusing, making azimuth compression unable to uniformly address this issue. Some studies have used azimuth resampling methods to address this problem, but their approximation conditions fail in large-look imaging scenarios. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a hybrid domain imaging method for high-speed, large-slant-look-out SAR, which combines Omega-K and FNCS to solve the serious two-dimensional coupling problem introduced by high speed, large slant-out, and acceleration, thereby improving imaging accuracy.

[0007] Technical Solution: To achieve the above-mentioned objectives, this invention provides a high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS, comprising the following steps:

[0008] Step 1: Based on the SAR imaging geometric model of the high-speed large-slant-sight-zone curve trajectory, the instantaneous slant range history is extended to the fifth order using Taylor series to obtain a polynomial slant range model.

[0009] Step 2: The SAR system transmits a linear frequency modulated signal and receives the corresponding echo signal. In the range wavenumber domain of the echo signal, linear range travel correction, range pulse compression, and acceleration deskewing preprocessing are performed.

[0010] Step 3: Divide the preprocessed signal into two-dimensional time-domain distance blocks, introduce a reference function in the two-dimensional wavenumber domain of the sub-block data, and use the improved Stolt mapping to implement the improved Omega-K algorithm for distance cell migration correction.

[0011] Step 4: An alignment function is introduced into the signal after range cell migration correction. Two-dimensional IFFT is used to realize range-focused sub-block data. The sub-block data is stitched together one by one to obtain the azimuth signal to be processed.

[0012] Step 5: For the azimuth signal to be processed, introduce a fifth-order perturbation function in the azimuth time domain, introduce a fifth-order NCS function in the azimuth frequency domain, perform uniform azimuth compression in the azimuth time domain, and finally use azimuth FFT to obtain a two-dimensional SAR image.

[0013] Preferably, in step 1, a fifth-order Taylor expansion is performed on the instantaneous slant range history of the extended slant range model:

[0014]

[0015] Where R0 represents the reference slant distance, v = (v x ,v y ,v z ) T and a=(a x ,a y ,a z ) T For the three-dimensional velocity and three-dimensional acceleration of the SAR platform, X = v e t a Indicates location, x n =v e t n Indicates the target signal position, t a For the direction of slow time, t n For the target zero Doppler moment, v e For the equivalent velocity, κ i ε is the Taylor expansion coefficient related to the reference slant distance R0 in the model. i (R0,t n ) is in R0 and t n The Taylor expansion coefficients related to velocity and acceleration in the model below.

[0016] Preferably, the distance pulse compression function H used in step 2 is... RC (K r ), linear distance travel correction function H LRWC (K r X), acceleration deslope function H AD (K r X and X are respectively:

[0017]

[0018] H LRWC (K r ,X)=exp(-jK r sinθ e X)

[0019]

[0020] in, K represents the second-order Taylor expansion coefficients related to velocity and acceleration in the model at the reference slant distance R0 and the zero Doppler moment. r K is the distance to the full wave number. rc Where γ is the distance reference wavenumber, c is the speed of light, γ is the signal modulation frequency, and θ is the reference wavenumber. e This is the equivalent oblique angle.

[0021] Preferably, the sub-block data reference function H used in step 3 is... ref (K r ,K x)for:

[0022]

[0023] Among them, K x =2πf a / v e f is the azimuth wave number. a R is the Doppler frequency. ref Z represents the reference distance corresponding to the center of different sub-blocks of the scene. i These are the expansion coefficients of the signal's remaining range-azimuth coupling. Is the signal in R ref The remaining range-azimuth coupling expansion coefficients are calculated; each sub-block data is uniformly compensated according to the sub-block data reference function; the improved Stolt mapping (MSM) interpolation kernel is obtained.

[0024]

[0025] Wherein, K′ r Let ΔR represent the new total range number, and ΔR0 represent the spatially invariant range value for each sub-block of data. Let ΔR = R0 - R ref Indicates the range of the focusing position, ΔZ i =Z i -Z i ref ΔZ represents the expansion coefficient of the residual range-azimuth coupling of the signal at different focusing positions. ip (p=1,2,3) represents ΔZ i (i=2,3,4,5) Taylor expansion coefficients with respect to ΔR when ΔR=0; Stolt interpolation is performed on the signal after unified compensation of the reference function using the interpolation kernel of MSM to realize the range cell migration correction.

[0026] Preferably, the alignment function H used in step 4 is... align (K x )for:

[0027]

[0028] Phase compensation is performed on the distance cell migration-corrected signal using an alignment function to obtain range-focused sub-block data.

[0029] Preferably, the orientation signal to be processed in step 5 is:

[0030]

[0031] Where A represents the signal amplitude, w a (·) represents the signal's azimuth time-domain envelope, sinc[·] represents the sinc function, Br It is the distance bandwidth, R is the distance cell index, and x is the distance bandwidth. n Indicates the location of the target signal. This is the slant range information for distance focusing, which is used to replace R0. ζ represents the second-order Taylor expansion coefficients related to velocity and acceleration in the model at the reference slant range R0 and zero Doppler moment. i This indicates that after focusing at distance, at X=x n The Taylor expansion coefficients are given.

[0032] Preferably, the fifth-order perturbation function H introduced in the azimuth time domain in step 5 is... PF (X) is:

[0033]

[0034] Among them, A i (η) represents the coefficients of the 3rd to 5th order azimuth time-domain perturbation functions related to the slant range information η of range focusing; the time-domain perturbation functions are introduced into the azimuth signal to be processed to obtain the azimuth time-domain perturbation signal, the signal form of which is:

[0035]

[0036] in,

[0037]

[0038] Preferably, the fifth-order NCS function H introduced in the azimuth frequency domain in step 5 is... NCS (K x )for:

[0039]

[0040] Among them, B i (η) represents the coefficients of the 2nd to 5th order frequency domain NCS functions related to the slant range information η of the range focusing; the signal before NCS processing is obtained by performing an azimuth FFT on the azimuth time-domain perturbation signal, and its signal form is as follows:

[0041]

[0042] in,

[0043] Δ d (η,x n ) = K rc ι1

[0044]

[0045] Introducing a fifth-order NCS function into the signal before NCS processing yields an azimuth frequency domain NCS signal, the signal form of which is:

[0046]

[0047] in,

[0048]

[0049] Preferably, the uniform orientation compression function H used in step 5 is AC (X) is:

[0050] H AC (X)=exp[-jK rc A(X)]

[0051] in, It is the azimuth compression coefficient. The azimuth compression factor in x n =0;

[0052]

[0053] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the aforementioned high-speed large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS.

[0054] Beneficial Effects: Compared with existing technologies, this invention designs a hybrid domain imaging method for high-speed, large-slant-look SAR with curved motion trajectories. By establishing a fifth-order polynomial extended slant-range model, the accuracy of instantaneous slant-range history is improved. For high-speed, large-slant-look SAR imaging with curved trajectories, this invention proposes an improved Stolt mapping (Modified-SM, MSM) processing method, which can improve the accuracy of range focusing. Furthermore, by increasing the NCS order and handling complex derivation processes, imaging accuracy can be enhanced, and this method can be further extended to higher orders. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0057] Figure 2 A geometric model diagram of high-speed, large-slant-look SAR imaging with curved motion trajectory;

[0058] Figure 3The image shows the simulation imaging result of the algorithm proposed in the embodiment of the present invention;

[0059] Figure 4 Two-dimensional contour maps after processing with different algorithms are shown; (a)-(c) are two-dimensional contour maps of targets T1, T2, and T3 after processing with the MFNCSA algorithm; (d)-(f) are two-dimensional contour maps of targets T1, T2, and T3 after processing with the EOKA algorithm; (g)-(i) are two-dimensional contour maps of targets T1, T2, and T3 after processing with the algorithm of this embodiment of the invention.

[0060] Figure 5 The following are azimuth profiles after processing with different algorithms: (a)-(c) are azimuth profiles of targets T1, T2, and T3 after processing with the MFNCSA algorithm; (d)-(f) are azimuth profiles of targets T1, T2, and T3 after processing with the EOKA algorithm; (g)-(i) are azimuth profiles of targets T1, T2, and T3 after processing with the algorithm of the present invention.

[0061] Figure 6 The images show the results of real data processed by different algorithms; where (a) is the result of real data processed by the MFNCSA algorithm; (b) is the result of real data processed by the EOKA algorithm; and (c) is the result of real data processed by the algorithm of the present invention. Detailed Implementation

[0062] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0063] This invention discloses a high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS. The specific flowchart of this method is shown below. Figure 1 Specifically, it includes the following steps:

[0064] Step 1: Based on the SAR imaging geometric model of the high-speed large slant range curve trajectory, the instantaneous slant range history is extended to the fifth order using Taylor series to obtain a polynomial slant range model.

[0065] In this step, a SAR geometric model of a high-speed, large-slant-look trajectory is established. Under this geometric model, an isolated point Q is randomly selected at an arbitrary location in the imaging region S, and the instantaneous slant range R(t) from the SAR carrier to the isolated point target Q is calculated. a ;R0,t n The instantaneous slant range history information of the extended slant range model is obtained by extending the instantaneous distance to the fifth order using Taylor series (v, a).

[0066] The system transmits a linear frequency modulated (LFM) signal and obtains a baseband echo signal Ss(K) in the range wavenumber domain from the target Q.r (,X), where K r The range full-wave number represents the large-slant-look SAR under a curved trajectory, and X represents the azimuth spatial position of the SAR aircraft; specifically including:

[0067] (1.a) Refer to Figure 2 This invention establishes a geometric model diagram of a high-speed, large-slant-look SAR based on a curved motion trajectory: wherein the SAR carrier platform moves along a curved trajectory in the spatial rectangular coordinate system O-XYZ. With a three-dimensional velocity v=(v x ,v y ,v z ) T and three-dimensional acceleration a=(a x ,a y ,a z ) T Movement; direction, slow time t a When =0, vector Where h represents the aircraft's flight altitude, and point C is the curve trajectory. Any position on; vector Let R0 be the reference slant range vector of the imaging region S in the ground coordinate system O-XY, and let α be the azimuth angle, β be the dive angle, and θ be the equivalent residual angle of the zero Doppler angle of view.

[0068] (1.b) Select any isolated point Q in the imaging region S of the ground coordinate system. The instantaneous slant range history information |CQ| of the extended slant range model can be expressed as:

[0069]

[0070] Where v is the three-dimensional velocity of the airborne platform, t a For the direction of slow time, t n For the target zero Doppler moment; R e (t a ;R0,t n ,v) represents the slant range model under the equivalent dive model:

[0071]

[0072] in, For the equivalent speed, v e sinθ e =v T r0, θ e For the equivalent angle of inclination, r0 = (sinβcosα, sinβsinα, -cosβ) T The beam direction is indicated by α and β, which represent the azimuth and elevation angles of the beam, respectively.

[0073] ΔR(t a ;R0,t n ,v,a) represents the error term introduced by three-dimensional acceleration, at t a =t n Expanding the expression using a fifth-order Taylor series, we get:

[0074]

[0075]

[0076] Let X = v e t a Indicates location, x n =v e t n Representing the target signal position, the slant range model under the equivalent dive model is in the case of X = x. n Performing a fifth-order Taylor expansion at that point, we obtain:

[0077]

[0078] Among them, κ i These are the Taylor expansion coefficients in the model that are related to the reference slant distance R0;

[0079]

[0080] Therefore, the instantaneous slope range history information of the extended slope range model is written as:

[0081]

[0082] Where, ε i (R0,t n ) is in R0 and t n The Taylor expansion coefficients related to velocity and acceleration in the model below, ε i =k i / v e i Indicates location dependence, v e R0 is the equivalent velocity and R0 is the reference slant distance.

[0083] Step 2: The system transmits a linear frequency modulated (LFM) signal to obtain a baseband echo signal in the range-wavenumber domain. The echo signal undergoes linear range travel correction, range compression filtering, and acceleration de-chirping processing. After obtaining the echo signal with linear range travel correction, range compression filtering, and acceleration de-chirping, an azimuth Fourier transform is performed to obtain a two-dimensional spectrum echo signal. Specifically, this includes:

[0084] (2.a) The SAR carrier platform transmits a linear frequency modulated (LFM) signal, and performs range FFT on the echo signal to obtain a range wavenumber domain signal, the signal form of which is:

[0085]

[0086] Among them, W r (·) denotes the distance envelope in the wavenumber domain, w a (·) represents the azimuth envelope in the time domain, A is the signal amplitude, γ is the signal modulation frequency, c is the speed of light, and f c and f r These are the carrier frequency and the range frequency, respectively; K r and K rc These represent the total range wavenumber and the reference range wavenumber, respectively.

[0087] (2.b) Obtain the distance pulse compression function H RC (K r ), linear distance travel correction function H LRWC (K r X), acceleration deslope function H AD (K r ,X):

[0088]

[0089] H LRWC (K r ,X)=exp(-jK r sinθ e X) (11)

[0090]

[0091] Among them, K r and K rc These represent the total range wavenumber and the reference range wavenumber, respectively. That is, the second-order Taylor expansion coefficients related to velocity and acceleration in the distance model at the reference slant range R0 and zero Doppler moment, where X represents the azimuth position and θ e This is the equivalent oblique angle.

[0092] (2.c) After range pulse compression, linear range travel correction, and acceleration deskewing, the signal undergoes an azimuth-directed Fourier transform to convert it to the two-dimensional wavenumber domain. The signal is written as:

[0093]

[0094] Among them, K x =2πf a / v e Indicates the azimuth wave number.

[0095] Step 3 involves dividing the echo signal after linear range migration correction, range compression filtering, and acceleration de-chirping into range blocks in the range time domain, performing a range Fourier transform to obtain the echo signal in the two-dimensional wavenumber domain, introducing a reference function (RFM) into the sub-block data for consistent SRC, and using an improved Stolt mapping for range cell migration correction; specifically including:

[0096] (3.a) Perform distance IFFT on the preprocessed signal to obtain a two-dimensional time domain signal, and then divide it into distance blocks;

[0097] (3.b) Obtaining the sub-block data reference function H ref (K r ,K x Write it as:

[0098]

[0099] in, Is the signal in R ref The expansion coefficient of the remaining range azimuth coupling; K x =2πf a / v e f is the azimuth wave number. a R is the Doppler frequency. ref This represents the reference distance corresponding to the center of different sub-block scenes; each sub-block data is compensated uniformly according to the sub-block data reference function in turn;

[0100] The signal after introducing the reference function is written as:

[0101]

[0102] In the formula: ΔR=R0-R ref Indicates the range of the focus position. The expansion coefficients representing the residual range-azimuth coupling of the signal at different focusing positions are approximated by a second-order Taylor expansion for ΔZ. i , written as:

[0103] ΔZ i ≈(ΔZ i1 +ΔZ i2 ΔR+ΔZ i3 ΔR 2 )ΔR (17)

[0104] Where, ΔZ i1 ,ΔZ i2 ,ΔZ i3 The coefficients of Taylor's expansion when ΔR = 0 are represented, and the signal can be re-expressed as:

[0105]

[0106] (3.c) Obtain the interpolation kernel of the improved Stolt mapping (MSM):

[0107]

[0108] Among them, K' r The new range full-wave number is represented by ΔR0, which represents the spatially invariant range value for each sub-block of data. Stolt interpolation is performed on the signal after unified compensation of the reference function using the MSM interpolation kernel to achieve range cell migration correction; the signal after MSM is represented as follows:

[0109]

[0110] Step 4 involves introducing an alignment function into the range cell migration-corrected signal, using two-dimensional IFFT to achieve range-focused sub-block data, and then stitching the sub-block data together one by one to obtain the azimuth signal to be processed; specifically including:

[0111] (4.a) Obtain the alignment function H align (K x ):

[0112] Phase compensation is performed on the range cell migration-corrected signal using an alignment function to obtain range-focused sub-block data; the signal is written as:

[0113]

[0114] Among them, B r Represents distance bandwidth. This represents the slant range information after focusing, and is used to replace the reference slant range R0.

[0115] (4.b) Perform a two-dimensional IFFT on the distance-focused sub-block data to obtain two-dimensional time-domain data, and stitch the sub-block data one by one to obtain the azimuth signal to be processed.

[0116] Step 5: For the azimuth signal to be processed, a fifth-order perturbation function is introduced in the azimuth time domain, and a fifth-order nonlinear frequency scaling (NCS) function is introduced in the azimuth frequency domain. Uniform azimuth compression is then performed in the azimuth time domain, and finally, a two-dimensional SAR image is obtained using azimuth FFT. In this embodiment, both the perturbation function and the NCS function are increased to the fifth order, improving the focusing effect and enhancing imaging accuracy. Details are as follows:

[0117] (5.a) The azimuth signal to be processed is represented as follows:

[0118]

[0119] Where, ζ i This indicates that after focusing at distance, at X=x n Taylor expansion coefficients;

[0120]

[0121] Where sinc[·] represents the sinc function, and R is the distance cell index. For subsequent processing, R0 is replaced by η after distance focusing, and the replacement relationship is:

[0122]

[0123] (5.b) Obtain the azimuth time-domain perturbation function (PF) for subsequent homogenization processing. The perturbation function (PF) can be expressed as:

[0124]

[0125] Among them, A i (η) represents the coefficients of the 3rd to 5th order azimuth time-domain perturbation functions, τ = 2δ-1, where δ is the NCS scaling factor and τ is the adjustment parameter of the scaling factor.

[0126]

[0127] η r =η+R ref It is the actual distance to the focal point, A 4i It is the fourth-order distance factor term of the perturbation function coefficients, A 5i It is the fifth-order distance factor term of the perturbation function coefficients. A 4i and A 5i The specific expression is given in the formula appendix. Introducing the time-domain perturbation function into the azimuth signal to be processed yields the azimuth time-domain perturbation signal, whose signal form is:

[0128]

[0129] in,

[0130]

[0131] (5.c) After applying the azimuth time-domain perturbation, obtain the azimuth frequency-domain NCS function H. NCS (K x ):

[0132]

[0133] Among them, B i (η) is a factor of the second to fifth order frequency domain NCS function;

[0134]

[0135] B 3i B 4i and B 5i These are the 3rd, 4th, and 5th order distance factor terms of the NCS function coefficients, respectively. B 3i B 4i and B 5i The specific expression is given in the formula appendix. An azimuth FFT is performed on the azimuth time-domain perturbation signal to obtain the signal before NCS processing, and its signal form is as follows:

[0136]

[0137] Among them, W a (·) represents the frequency domain envelope of the signal orientation.

[0138]

[0139] Introducing the NCS function into the signal before NCS processing yields the azimuth frequency domain NCS signal, whose signal form is as follows:

[0140]

[0141] in,

[0142]

[0143] (5.d) Perform IFFT on the azimuth frequency domain NCS signal to obtain the azimuth time domain NCS signal, the signal form of which is:

[0144]

[0145] in,

[0146]

[0147] Obtain the uniform orientation compression function H AC (X):

[0148] H AC (X)=exp[-jK rc A(X)] (38)

[0149] in, It is the azimuth compression coefficient. The azimuth compression factor in x n =0. Phase compensation is performed on the azimuth time-domain NCS signal using the unified azimuth compression function, and then a two-dimensional SAR image is obtained using azimuth FFT. The signal that achieves final focusing can be expressed as:

[0150] ss(R,K x )=A·sinc[B r·(R-η)]·sinc[B a ·(K x -K n )], (39)

[0151] Among them, B a It is the azimuth bandwidth, K n =K rc k 2e x n / 2δη r The final focal position is Q(η,K). n ).

[0152] The effectiveness of this invention can be further demonstrated by the following experiments.

[0153] (I) SAR Simulation Parameters and Results

[0154] Key parameters of the simulation experiment are listed in Table 1. No windowing was used throughout the processing. A 5×5 target array with a scene size of 1.5km × 1.5km (X-axis and Y-axis) was uniformly set on the ground. The imaging results of the proposed algorithm are shown below. Figure 3 As shown. The azimuth resolution is approximately 1.5m × 3.0m.

[0155] Table 1 Experimental parameters of vehicle-mounted SAR

[0156]

[0157] MFNCSA [K. Deng et al., “A modified frequency nonlinear chirp scaling algorithm for high-speed high-squint synthetic aperture radar with curved trajectory,” Remote Sens., vol. 16, no. 9, 2024.] and EOKA [T. Zhang, Y. Li, J. Wang, M. Xing, L. Guo, and P. Zhang, “A modified range model and extended omega-K algorithm for high-speed-highsquint SAR with curved trajectory,” IEEE Trans. Geosci. Remote Sens., vol. 61, pp. 1–15, 2023.] were selected as comparison algorithms, and... Figure 3 The effectiveness of the algorithm is demonstrated by comparing the simulation results of point targets T1-T3 in the model.

[0158] The MFNCSA algorithm uses a two-step NCS to achieve imaging. Its approximate substitution equation and neglect of the effects of range spatial variation mean that range-azimuth coupling cannot be completely eliminated during NCS processing. Figure 4 Images (a) to (c) are contour plots for the MFNCSA algorithm. Figure 5 (a) to (c) are the azimuth profiles of the MFNCSA algorithm. The center point T2 has a good focusing effect, but in the large oblique view scene, the edge points T2 and T3 are severely out of focus in the azimuth dimension.

[0159] The EOKA algorithm neglects some higher-order azimuth spatial phase terms in NCS processing; therefore, its azimuth focusing performance is not optimal, exhibiting slight defocusing at T1 and T3. Figure 4 (d)~(f) and Figure 5 As shown in (d) to (f).

[0160] This embodiment utilizes a novel differentiation process to obtain fifth-order NCS parameters, thereby eliminating azimuth spatial variation and improving azimuth imaging quality. Therefore, point targets T1-T3 processed by this algorithm are well focused in both the range and azimuth dimensions, as shown below. Figure 4 (g)~(i) and Figure 5 As shown in (g)~(i).

[0161] To further analyze the focusing quality of the algorithms, azimuth profiles of point targets from three algorithms were selected, such as... Figure 5 Each row, from top to bottom, represents the azimuth profile processed by MFNCSA, EOKA, and the proposed algorithm, respectively. Furthermore, to further quantitatively analyze the performance of these algorithms, Table 2 presents the performance parameters of these three methods, including peak sidelobe ratio (PSLR) and integral sidelobe ratio (ISLR).

[0162] Table 2. Azimuth performance analysis of selected targets

[0163]

[0164] It can be seen that the performance parameters of all targets processed by the algorithm in this embodiment are basically close to the theoretical value of the sinc function. Target T2, after EOKA processing, matches the theoretical value, while edge targets T1 and T3 are suboptimal. MFNCSA achieves good focusing on center point targets, but completely fails to focus on edge point targets. In conclusion, in this multi-target large-scene simulation scenario, the algorithm in this embodiment has significant advantages over the two reference algorithms.

[0165] (II) Processing of Measured Data

[0166] The SAR system operates in the Ku-band in spotlight mode. The equivalent angle of view is approximately 72°. The velocity vector of the SAR system is approximately v = (71.44, -0.41, -3.50) m / s, and the acceleration vector is approximately a = (1.85, -0.18, 2.03) m / s. 2 The entire imaging scene has a range of approximately 5.5 km in the range direction and approximately 6.4 km in the azimuth direction. The range resolution and azimuth resolution are both approximately 3.0 m.

[0167] MFNCSA and EOKA were selected as comparison algorithms, based on Figure 6 Our proposed method is generally the best, while MFNCSA's method is generally the worst. (Comparison) Figure 6 The proposed algorithm achieves the best image quality within the yellow rectangular area. Table 3 presents the image quality metrics for the final images processed by different methods; higher contrast and lower entropy indicate optimal image quality. As shown in Table 3, the proposed algorithm delivers the best image quality.

[0168] Table 3 Image quality indicators of the final images

[0169]

[0170] This invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of a high-speed large-slant-look curve trajectory SAR imaging method based on the aforementioned method combining Omega-K and FNCS.

[0171] The program code used to implement the method of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the steps of the method of the present invention to be performed. The program code can be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a standalone software package, or entirely on a remote machine or server. All aspects not detailed in this invention are well-known to those skilled in the art.

[0172] Formula Appendix:

[0173] A 42 =8δρ1 2 (4δ-1)-κ 2e ρ3v e 2 (2δ-1)(4δ-3),

[0174]

[0175] A40 =-2k 2e v e 6 sinth e (3k 3e -4s 2e sinth e );

[0176] A 53 =2δ1[8δ1 2 (4d-1)+k 2e p3v e 2 (16d 2 -10s+1)],

[0177]

[0178] A 50 =k 2e v e 9 sinth e [4sq 2e 2 sin 2 i e (6d+1)-48s 2e k 3e sinth e +36s 3e 2 +3k 4e k 2e (1-2d)]; (40)

[0180] B 32 =-ρ1(4δ-1),

[0181] B 31 =-v e 3 [k 2e sinth e (1+2d)-3k 3e ];

[0182] B 43 =ρ1 2 (-40d 2 +22d-3)+2k 2e p3δv e 2 (2d-1),

[0183]

[0184] B 41 =-ve 6 [12k 2e k 3e sinth e (d 2 +d-1)+k 2e 2 sin 2 i e (3-2d)+(3k 4e k 2e -27k 3e 2 (2d-1)];

[0185] B 54 =-ρ1(4δ-1)[ρ1 2 (172d 2 -100d+15)-14k 2e p3δv e 2 (2d-1)],

[0186]

Claims

1. A high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS, characterized in that, Includes the following steps: Step 1: Based on the SAR imaging geometric model of the high-speed large-slant-sight-zone curve trajectory, the instantaneous slant range history is extended to the fifth order using Taylor series to obtain a polynomial slant range model. Step 2: The SAR system transmits a linear frequency modulated signal and receives the corresponding echo signal. In the range wavenumber domain of the echo signal, linear range travel correction, range pulse compression and acceleration deskewing preprocessing are performed. After obtaining the echo signal after linear range travel correction, range compression filtering and acceleration deskewing, azimuth Fourier transform is performed to obtain the echo signal with a two-dimensional spectrum. Step 3: Divide the signal after linear distance migration correction, distance pulse compression and acceleration deskewing into two-dimensional time-domain distance blocks, perform distance Fourier transform to obtain the echo signal in the two-dimensional wavenumber domain, introduce a reference function in the two-dimensional wavenumber domain of the sub-block data, and use the improved Stolt mapping to implement the improved Omega-K algorithm for distance cell migration correction. Step 4: An alignment function is introduced into the signal after range cell migration correction. Two-dimensional IFFT is used to realize range-focused sub-block data. The sub-block data is stitched together one by one to obtain the azimuth signal to be processed. Step 5: For the azimuth signal to be processed, introduce a fifth-order perturbation function in the azimuth time domain, introduce a fifth-order NCS function in the azimuth frequency domain, perform uniform azimuth compression in the azimuth time domain, and finally use azimuth FFT to obtain a two-dimensional SAR image.

2. The high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS according to claim 1, characterized in that, In step 1, a fifth-order Taylor expansion is performed on the instantaneous slant range history of the extended slant range model: ； in, Indicates the reference slope distance. and For the three-dimensional velocity and three-dimensional acceleration of the SAR platform, Indicates location or orientation. Indicates the location of the target signal. For location, slow time, To achieve the zero Doppler moment, For equivalent speed, It is the slope distance between the model and the reference slope. The relevant Taylor expansion coefficients, Is and The Taylor expansion coefficients related to velocity and acceleration in the model below.

3. The high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS according to claim 2, characterized in that, The distance pulse compression function used in step 2 Linear distance travel correction function Acceleration deslope function They are respectively: ； in, To reference slope distance Furthermore, the second-order Taylor expansion coefficients related to velocity and acceleration in the model at the zero Doppler time... For distance full wave number, Here, c is the distance reference wavenumber, and c is the speed of light. To adjust the frequency of the signal, This is the equivalent oblique angle.

4. The high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS according to claim 3, characterized in that, The sub-block data reference function used in step 3 for: ； in, For azimuth wave number, For Doppler frequency, This represents the reference distance corresponding to the center of different sub-blocks in the scene. These are the expansion coefficients of the signal's remaining range-azimuth coupling. Is the signal in The remaining range-azimuth coupling expansion coefficients are calculated; each sub-block data is uniformly compensated according to the sub-block data reference function; the improved Stolt mapping interpolation kernel is obtained. ； in, This represents the new distance full wave number. Let the distance to each sub-block of data be a spatially invariant value. Indicates the range of the focus position. The expansion coefficient represents the remaining range-azimuth coupling of the signal at different focusing positions. express exist Time about Taylor expansion coefficients; using the improved Stolt mapping interpolation kernel, Stolt interpolation is performed on the signal after unified compensation of the reference function to realize range cell migration correction.

5. The high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS according to claim 4, characterized in that, The alignment function used in step 4 for: ； Phase compensation is performed on the distance cell migration-corrected signal using an alignment function to obtain range-focused sub-block data.

6. The high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS according to claim 5, characterized in that, The orientation signal to be processed in step 5 is: Where A represents the signal amplitude. This represents the time-domain envelope of the signal's orientation. This represents the sinc function. This represents the distance bandwidth, where R is the distance cell index. This is the slant range information after focusing, which is used to replace the reference slant range. , Indicates distance after focusing The Taylor expansion coefficients are given.

7. A high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS according to claim 6, characterized in that, The fifth-order perturbation function introduced in the azimuth time domain in step 5 for: ； in, The coefficients of the 3rd to 5th order azimuth time-domain perturbation functions related to the slant range information η of range focusing are given. The time-domain perturbation functions are introduced into the azimuth signal to be processed to obtain the azimuth time-domain perturbation signal, whose signal form is as follows: ； in, 。 8. The high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS according to claim 7, characterized in that, The fifth-order NCS function introduced in the azimuth frequency domain in step 5 for: ； in, The coefficients of the 2nd to 5th order frequency domain NCS functions related to the slant range information η of range focusing are given; the signal before NCS processing is obtained by performing an azimuth FFT on the azimuth time-domain perturbation signal, and its signal form is as follows: ； in, The signal's azimuth frequency domain envelope. ； Introducing a fifth-order NCS function into the signal before NCS processing yields an azimuth frequency domain NCS signal, the signal form of which is: ； in, 。 9. A high-speed, large-slant-look curve trajectory SAR imaging method combining Omega-K and FNCS according to claim 8, characterized in that, The uniform orientation compression function used in step 5 for: ； in, It is the azimuth compression coefficient. Is the azimuth compression coefficient in The value; 。 10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of a high-speed large-slant-look curve trajectory SAR imaging method according to any one of claims 1-9.

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