Wave number spectrum reconstruction and fast fusion imaging method and system for arbitrary dual base SAR

Abstract

This invention proposes a wavenumber spectrum reconstruction and rapid fusion imaging method and system for arbitrary bistatic SAR. It proposes a method to consistently center the wavenumber spectrum of the spatial domain signal of the imaging scene, introduces a two-dimensional wavenumber spectrum position correction filter to compress the wavenumber spectrum width of the imaging scene, reduces the Nyquist sampling requirement in the spatial domain, and achieves accurate SAR imaging of the imaging scene with less computation, thus improving the imaging efficiency of the imaging method. Furthermore, while achieving accurate and consistent centering of the wavenumber spectrum of the imaging scene, this invention proposes a new method for calculating the minimum Nyquist sampling requirement of the spatial domain signal of the imaging scene. Based on the framework of the time-domain FFBP imaging method, this invention enables the imaging method to have good parallelism, utilizing parallel processing mechanisms on hardware platforms such as GPUs and FPGAs, which will further significantly improve the imaging efficiency of the time-domain FFBP imaging method in bistatic SAR systems in practical applications.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to a wavenumber spectrum reconstruction and rapid fusion imaging method and system for arbitrary bistatic SAR. Background Technology

[0002] The main imaging methods of bistatic SAR imaging systems include time-domain imaging algorithms and frequency-domain imaging algorithms. Frequency-domain imaging methods have been well-appointed in practical bistatic SAR systems; however, the diverse configurations of bistatic SAR systems increase the difficulty of developing frequency-domain algorithms. Furthermore, frequency-domain imaging methods have significant limitations in bistatic SAR imaging applications with arbitrary curved trajectories. Time-domain imaging methods, on the other hand, can effectively avoid these limitations.

[0003] Temporal imaging methods mainly include Back Projection (BP) and Fast Factorized Back Projection (FFBP). In monostatic SAR systems, the application of temporal imaging methods is mature; however, in bistatic SAR systems, their application needs further development and improvement. BP imaging can reconstruct images on any imaging grid, unconstrained by the configuration of the bistatic SAR system, and can achieve accurate imaging of nonlinear trajectories. However, its high computational cost limits its application. FFBP imaging can achieve the same imaging accuracy as BP imaging with significantly reduced computational cost, exhibiting excellent imaging efficiency.

[0004] In both single-static and bistatic SAR imaging systems, the FFBP imaging method shares the same imaging framework. Existing FFBP imaging methods applied to bistatic SAR systems establish imaging grids based on elliptical polar coordinates or orthogonal elliptical polar coordinates. Target points on the same polar radius cell in such polar coordinate systems have approximately the same bistatic slant range history, enabling current sub-aperture image fusion, similar to that achieved in single-static SAR systems. However, the FFBP imaging method suffers from the following drawbacks:

[0005] 1. The imaging grid is established based on an elliptical polar coordinate system or an orthogonal elliptical polar coordinate system. The mapping process between polar coordinates and spatial rectangular coordinates is approximate, lacking an accurate mathematical representation of the mapping relationship. Furthermore, the mapping calculation process is complex and constrained by the configuration of the bistatic SAR system. 2. The wavenumber spectrum position correction solution is computationally complex and computationally intensive, with low accuracy, making it impossible to consistently center the wavenumber spectrum of each target point in a wide-swath imaging scene. 3. The sampling interval of the imaging grid depends on the wavenumber spectrum width of the entire imaging scene, i.e., it is related to the swath width of the imaging scene. This results in high Nyquist sampling requirements in the spatial domain, leading to high computational load and low imaging efficiency in the imaging method. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides a method and system for wavenumber spectrum reconstruction and rapid fusion imaging of arbitrary bistatic SAR. The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] In a first aspect, the present invention provides a wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR, comprising:

[0008] S100, the echo signal from the imaging area is acquired through a bistatic SAR system, and the echo signal is subjected to range pulse compression focusing to obtain a two-dimensional time domain signal; the bistatic SAR system includes a receiving platform and a transmitting platform, both in a spatial rectangular coordinate system;

[0009] S200, based on the positions of the receiving platform and the transmitting platform at the center time of the synthetic aperture, and based on the orthogonal elliptical mapping polar coordinates, establishes a unified imaging polar coordinate system;

[0010] S300, the synthetic aperture is divided into multiple current sub-apertures to establish a sub-aperture imaging grid in the imaging polar coordinate system;

[0011] S400 uses the two-dimensional time domain signal of S100 to project the sub-aperture imaging grid to obtain multiple current sub-aperture images, and performs wavenumber spectrum position correction on each current sub-aperture image to center the beam spectrum position.

[0012] The S500 fuses the corrected current sub-aperture images to obtain the full-aperture SAR image with the best resolution.

[0013] In a second aspect, the present invention provides a wavenumber spectrum reconstruction and rapid fusion imaging system for arbitrary bistatic SAR, the imaging system comprising a transmitting platform, a receiving platform, and an imaging device, the imaging device being used to implement the wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR as described in any one of claims 1 to 9.

[0014] Beneficial effects:

[0015] 1. This invention provides a wavenumber spectrum reconstruction and rapid fusion imaging method and system for arbitrary bistatic SAR. It proposes establishing a new imaging polar coordinate system based on orthogonal elliptical mapping polar coordinates, simplifying the conversion process between polar coordinates and spatial rectangular coordinates. Compared with traditional methods for establishing imaging polar coordinate systems, this invention is not constrained by the configuration of the bistatic SAR system, and the coordinate conversion method is simple and approximate.

[0016] 2. This invention proposes a wavenumber spectrum position correction and centering method for arbitrary sub-apertures in a synthetic aperture. This method can accurately and quickly achieve consistent centering of the wavenumber spectrum of a spatial domain signal, that is, consistently centering the wavenumber spectrum of any target point in an imaging scene. This helps to reduce the amount of wavenumber variable variation in the entire imaging scene, i.e., the scene wavenumber spectrum width, thereby reducing the Nyquist sampling requirement of the spatial domain signal and improving the imaging efficiency of the method. Compared with traditional wavenumber spectrum position correction methods, the method proposed in this invention is not constrained by the configuration of the bistatic SAR system, the method of establishing the imaging coordinate system, or the width of the imaging scene, and its implementation and calculation methods are simple.

[0017] 3. Under the premise that the wavenumber spectrum position can be consistently corrected and centered, this invention proposes a method for calculating the Nyquist sampling requirements of the spatial domain signal in the proposed imaging polar coordinate system. This calculation method is simple, efficient, and easy to implement on a computer. Compared with traditional methods, the analysis process of this method is simplified, and the influence of the wavenumber spectrum shape is considered during the analysis process, enabling accurate calculation of the Nyquist sampling requirements for the entire imaging scene.

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR provided by the present invention.

[0020] Figure 2 This is a spatial geometric configuration diagram of the transceiver platform and imaging scene provided by the present invention;

[0021] Figure 3 This is a schematic diagram of the establishment of the imaging polar coordinate system provided by the present invention;

[0022] Figure 4 This is a schematic diagram of the wavenumber spectrum shape of any target P in the imaging scene provided by the present invention;

[0023] Figure 5 This is a schematic diagram of the polar coordinate system grid of the imaging scene provided by the present invention;

[0024] Figure 6 This is a diagram showing the wavenumber spectrum position correction results provided by the present invention;

[0025] Figure 7 This is a wavenumber spectrum shape diagram of a single-point target before and after sub-aperture image fusion in the scenario provided by the present invention. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0027] Combination Figures 1 to 5 This invention provides a wavenumber spectrum reconstruction and fast fusion imaging method for arbitrary bistatic SAR, comprising:

[0028] S100, the echo signal from the imaging area is acquired through a bistatic SAR system, and the echo signal is subjected to range pulse compression focusing to obtain a two-dimensional time domain signal; the bistatic SAR system includes a receiving platform and a transmitting platform, both in a spatial rectangular coordinate system;

[0029] Figure 2 The image illustrates the spatial geometry of a Bi-SAR (Bistatic Synthetic Aperture Radar) system. In practical applications, the receiving platform R can perform forward-looking or large-angle forward-looking imaging of the target imaging area. At the center of the synthetic aperture, the nadir point of the receiving platform R is taken as the origin O of the coordinate system. The velocity vector of the receiving platform R is projected onto the ground plane, and the direction of the projected vector is defined as the Y-axis direction of the spatial rectangular coordinate system O-XYZ. The vertical upward direction of the origin O is taken as the Z-axis direction. The X-axis direction of the spatial rectangular coordinate system O-XYZ is determined according to the right-hand rule. The reference point in the imaging scene is defined as C(x). c ,y c In this coordinate system, the velocity vectors of the receiving platform R and the transmitting platform T are respectively expressed as: and Let θ be the angle between the velocity vectors of the transmitting and receiving platforms projected onto the XOY plane. Let t m For a slow-time variable, the value is t. m At time t, the position coordinates of the transmitting and receiving motion platform can be expressed as R(x) r ,y r ,z r ) and T(x t ,y t ,z t ), where x r y r z r x t y t and z t Both can be considered as slow time tm It is a function with the independent variable.

[0030] Specifically, S100 of the present invention includes:

[0031] S110, acquires echo signals from the imaging scene through a bistatic SAR system, considering an arbitrary, illuminated scattering target point P0(x) in the imaging scene. p ,y p Given a radar signal with a constant reflection coefficient α, and considering that the radar transmitted signal is a linear frequency modulated signal, in slow time t... m =t, the echo from P0 can be represented as:

[0032]

[0033] Among them, t r w is a distance-time variable. r () and w a () represent the range window function and azimuth window function of the transmitted signal, respectively; c is the speed of light; γ is the frequency modulation rate of the transmitted signal; λ is the wavelength of the transmitted signal; (x p ,y p R(t) represents the spatial rectangular coordinates of the scattering target point P0 in the imaging scene, α is the constant reflection coefficient, and R(t) is the slow time t. m =The sum of the slant distances from the transceiver platform to the target point P0 at time t, expressed as:

[0034] R(t)=R R (t)+R T (t) (2);

[0035] in,

[0036] S120, Perform a range-to-Fourier transform on the echo signal to obtain the echo signal S(f r ,t m );

[0037]

[0038] Among them, W r () is the window function of the signal in the range frequency domain, f r For the range-directed frequency variable, f c Let be the carrier frequency of the transmitted signal, and λ = c / f c The first exponential term is the modulation term of the echo signal, which is independent of the imaging scene;

[0039] S130, construct the range-direction pulse compression matched filter, represented as:

[0040]

[0041] S140, using the range-directed pulse compression matched filter to process the echo signal S(f) r ,t m Range-directed pulse compression focusing is performed to obtain the echo signal S1(f) r ,t m );

[0042] S1(f r ,t m )=S(f r ,t m )·H rc (f r (5);

[0043] S150 will send the echo signal S1(f) r ,t m Performing an inverse distance-to-Fourier transform yields the two-dimensional time-domain echo signal s1(t). r ,t m );

[0044]

[0045] Among them, B r This refers to the bandwidth of the linear frequency modulated signal transmitted by the radar.

[0046] S200 establishes a unified imaging polar coordinate system based on the positions of the receiving platform and the transmitting platform at the center time of the synthetic aperture.

[0047] Specifically, S200 of the present invention includes:

[0048] S210, at the center time t of the synthetic aperture m =t0, project the spatial coordinates of the receiving platform and the transmitting platform onto the XOY plane to obtain the position R of the receiving platform. xy and launch platform location T xy ;

[0049] In plane XOY, S220, along the baseline direction And its orthogonal direction is the axis direction, with T xy R xy With the midpoint O′ as the origin, establish an elliptical reference rectangular coordinate system mO′n;

[0050] S230, with R xy and T xy The ellipse is formed by finding the foci of the ellipse and a point in the imaging scene that is also a point on the ellipse.

[0051] S240, with the midpoint O′ of the baseline as the pole, the semi-major axis length a of the ellipse as the polar radius, and the parameter angle θ corresponding to a point on the ellipse as the polar angle, the orthogonal elliptical mapping polar coordinate representation of the point is obtained as (a,θ), and a unified imaging polar coordinate system is established with (a,θ).

[0052] In the spatial rectangular coordinate system O-XYZ, at the time of the synthesis aperture center, i.e., t m At time t0, the spatial coordinates of the receiving platform and the transmitting platform are projected onto the XOY plane to obtain R. xy and T xy That is, ignoring the height along the Z-axis. In the XOY plane, with the baseline direction... And its orthogonal direction is the axis direction, with T xy R xy With the midpoint O′ as the origin, establish an elliptical reference rectangular coordinate system mO′n, as follows: Figure 3 As shown. At this time, the receiving platform R xy Launch platform T xy And the relative position of the imaging scene reference point C in the elliptical reference rectangular coordinate system, such as Figure 3 As shown. Using R xy and T xy Let C be a focus of the ellipse and C be a point on the ellipse. We can obtain the ellipse. According to the relevant definition of an ellipse, the length of its semi-major axis can be expressed as: The semi-focal length of an ellipse can be expressed as: The semi-minor axis of an ellipse can be expressed as: Parameter angle θ C The representation in plane geometry is as follows: Figure 3 As shown in the figure, points A and C have the same ordinate in the elliptical reference rectangular coordinate system, and points B and C have the same abscissa in the same elliptical reference rectangular coordinate system. The arc containing point A is centered at O′ with a semi-minor axis length b. C An arc with radius a, where point B is an arc centered at O′ with semi-major axis length a. C An arc of radius θ, with parameter angle θ C for and The included angle.

[0053] This invention proposes using the midpoint O′ of the baseline as the pole, and... direction or The direction is the polar axis direction, with the semi-major axis length 'a' of the ellipse as the polar radius and the parametric angle θ of the ellipse as the polar angle, to establish a unified imaging polar coordinate system. The orthogonal elliptical mapping polar coordinates of any point P′(m,n) in the elliptical reference rectangular coordinate system mO′n can be represented as (a,θ) or (b,θ) in the imaging polar coordinate system.

[0054] The mapping relationship between the polar coordinate representation (a,θ) in the imaging polar coordinate system and the coordinate representation P′(m,n) in the coordinate system mO′n is as follows:

[0055] (m,n)=(acosθ,bsinθ)(7);

[0056]

[0057] Where β is direction and The angle between directions. The coordinate representations (m,n) of coordinate system mO′n and coordinate representations (x,y) of coordinate system XOY can be converted to each other by rotating and offsetting the coordinate axes.

[0058] This invention proposes to establish a polar coordinate system based on the parameter angle θ and the polar radius variable a of an ellipse. The axes of the polar radius and polar angle in this polar coordinate system are orthogonal. This polar coordinate system is called the orthogonal elliptic mapping polar coordinate system. When the polar coordinates of this coordinate system are mapped to the coordinates of the spatial rectangular coordinate system, the calculation is simple, there are no approximations, and no reference point is required.

[0059] S300, the synthetic aperture is divided into multiple current sub-apertures to divide the sub-aperture imaging grid in the imaging polar coordinate system;

[0060] The entire synthetic aperture is divided into N=2 j In a given sub-aperture, this invention determines the minimum Nyquist sampling condition for the current sub-aperture image in the spatial domain by determining the range of wavenumber variation of the signal, and obtains the sub-aperture imaging grid in the imaging polar coordinate system according to the minimum Nyquist sampling condition. This process mainly consists of:

[0061] The entire synthetic aperture is divided into N=2 j Individual aperture;

[0062] Within a current sub-aperture, calculate the wavenumber variable k at the scene reference point C. a and k θ And the corresponding range of change Δk a Δk θ ;

[0063] Based on the lowest Nyquist principle, determine the signal in the spatial domain. direction and The minimum Nyquist sampling conditions for the sampling interval sizes Δa and Δθ in the direction;

[0064] The sub-aperture imaging grid in the imaging polar coordinate system is obtained according to the minimum Nyquist sampling condition.

[0065] In slow time t mAt time t, at scene reference point C in the imaging scene, in a bistatic SAR system, the signal combination vector is defined as:

[0066]

[0067] Among them, R l (t) and T l (t) represents the slow time t. m = The position coordinates of the receiving platform and the transmitting platform at time t. Define the wavenumber variable k corresponding to the polar coordinate system coordinate variables a and θ. a k θ Slow time t m =At time t, the wavenumber variable k at the scene reference point C in the imaging scene a k θ The formula for calculating the value is:

[0068]

[0069]

[0070] in, For the center of the synthetic aperture t m =The direction of change of the polar coordinate variable a at the scene reference point C at time t0 (i.e. The unit vector (direction). For the center of the synthetic aperture t m = The direction of change of the polar coordinate variable θ at the scene reference point C at time t0 (i.e. A unit vector (orthogonal direction). Similar to the Nyquist sampling requirement in the frequency domain for time-domain signals, the sampling rate of a signal in the spatial domain depends on the range of values ​​of the wavenumber variable corresponding to the coordinate system variable. The wavenumber variable k at the scene reference point C in the imaging scene. a k θ The range of variation depends on both the propagation process of the radar signal and the motion of the transceiver platform during the synthetic aperture time.

[0071] For any given aperture time interval, a simple method for calculating the range of wavenumber variation at the scene reference point C is as follows:

[0072] A. Wavenumber variable k θ The range of variation is related to the change in the position of the transmitting and receiving platform during the aperture time, considering that this aperture time starts from the slow time t. m =From time t1 to t m =At time t2, in slow time t m =At time t1, the wavenumber variable k at the scene reference point C θ The value of k is θ (t1,C); at slow time t m=At time t2, the wavenumber variable k at the scene reference point C θ The value of k is θ (t2,C). During this aperture time, the wavenumber variable k... θ The change is:

[0073] Δk θ =|k θ (t1,C)-k θ (t2,C)| (12);

[0074] B. Wavenumber variable k a The range of variation is related to the propagation process of the radar signal; the bandwidth of the radar's transmitted signal is B. r In the propagation of radar signals, the longest and shortest wavelengths of the transmitted signal can be expressed as follows: Hz

[0075]

[0076]

[0077] At any time t within any aperture time interval m =t, wavenumber variable k a The boundary values ​​are as follows:

[0078]

[0079]

[0080] wavenumber variable k a The change is:

[0081] Δk a1 =|k a_max (t,C)-k a_min (t,C)| (17);

[0082] C, such as Figure 4 As shown, k a_C_cent and k θ_C_cent Let k be the position of the wavenumber spectrum center at scene reference point C in the imaging scene within the wavenumber domain, i.e., the wavenumber variable k. a and k θ Modulation amount on; Δk θ Let k be the wavenumber variable at scene reference point C in an aperture time period. θ The change in the value of Δk a1 Let k be the wavenumber variable at the scene reference point C at any slow time point in an aperture time period. a The change in the value; considering the Doppler gradient at scene reference point C at the center of an aperture time. orthogonal direction and The direction is deflected by an angle σ, which causes the wavenumber spectrum at the scene reference point C to be parallelogram-shaped. To ensure the integrity of the wavenumber spectrum at the target point P within one aperture time, the actual wavenumber variable k is considered. a The range of variation is:

[0083] Δk a =Δk a1 +Δk a2 (18);

[0084] in:

[0085] Δk a2 =Δk θ tanσ (19);

[0086]

[0087] acos() is the inverse cosine function; · is the dot product of vectors; Vectors satisfy: and A slow time t in an aperture time m = Doppler gradient at scene reference point C at time t The calculation expression is:

[0088]

[0089] Based on the above processes A, B, and C, the wavenumber variable k at the scene reference point C can be obtained. a and k θ Range of variation Δk a and Δk θ According to the Nyquist sampling criterion, the corresponding signal in the spatial domain is... direction and The sampling intervals Δa and Δθ in the direction need to meet the following requirements to ensure the integrity of the wavenumber spectrum of the spatial domain signal in the wavenumber domain:

[0090]

[0091]

[0092] Where, η os The oversampling coefficient is typically set to 0.8–1. Thus, steps S300 and S400 yield a sampling point grid of the aperture-time spatial domain signal on the ground imaging scene. A schematic diagram of the sampling point grid is shown below. Figure 5As shown, each point in the imaging scene has a unique orthogonal elliptical polar coordinate representation. Compared with the existing elliptical polar coordinate system or orthogonal elliptical polar coordinate system used in dual-base SAR imaging applications, the proposed orthogonal elliptical polar coordinate system does not involve approximations in its establishment process and has an accurate mapping relationship between polar coordinates and spatial rectangular coordinates. For a given aperture time, the proposed method for solving the wavenumber variable variation is simple and easy to implement on a computer, and can accurately solve for the minimum sampling rate of polar coordinate variables that ensures no aliasing of the wavenumber spectrum of the spatial domain signal.

[0093] S400 uses the two-dimensional time domain signal of S100 to project the sub-aperture imaging grid to obtain multiple current sub-aperture images, and performs wavenumber spectrum position correction on each current sub-aperture image to center the beam spectrum position.

[0094] Specifically, S400 of the present invention includes:

[0095] S410 uses the two-dimensional time domain signal of S100 to perform back projection imaging on the sub-aperture imaging grid to obtain multiple current sub-aperture images;

[0096] S420 introduces a two-dimensional filter with wavenumber spectrum position correction;

[0097] S430, the wavenumber spectrum position correction two-dimensional filter is used to correct the wavenumber spectrum position of each current sub-aperture image, so that the wavenumber spectrum of each target point in each current sub-aperture image is consistently aligned and centered.

[0098] In a single bistatic SAR imaging process, considering a synthetic aperture length of T a That is, the slow time t in a synthesis aperture time. m The actual signal sample values ​​are discrete sample values, and it is assumed that the number of sampling points in the slow time of a synthetic aperture time is N. a In the first stage of the FFBP imaging algorithm, the synthesis aperture time is first uniformly divided into N=2... j There are n sub-apertures, where j is a positive integer. For the i-th sub-aperture, i = 1 to N, the corresponding initial slow-time sampling number is n. s_i The corresponding number of slow-time sampling points at termination is n. e_i Relationship exists:

[0099]

[0100] First, obtain the grid of sub-aperture image spatial domain signal sampling points for the i-th sub-aperture (img). i Δθ of the signal sampling point grid in this spatial domain i Related to the sub-aperture time length, the smaller the sub-aperture length, the lower the Δθ. iThe larger the value, the fewer the number of sampling points in the sampling point grid, which is beneficial to improving the imaging efficiency of the imaging algorithm; the Δa of the sampling point grid of the spatial domain signal is independent of the sub-aperture time length, and Δa remains unchanged for each sub-aperture and the entire synthetic aperture.

[0101] Next, the sub-aperture image of the i-th sub-aperture is obtained using the back projection method. The process is represented as follows:

[0102]

[0103] Where, (θ grid ,a grid ) represents a sub-aperture image grid point, t k R(θ) represents the slow time corresponding to the k-th slow time sampling point. grid ,a grid ;t k ) represents the slow time as t k At time, the receiver and transmitter reach the sub-aperture image imaging grid points (θ). grid ,a grid The slant distance history and ). For signal s1(t) r ,t) in slow time t m =Time t, distance from fast time t r The signal from the most recent two-dimensional time-domain sampling point. The spatial domain variables a and θ, and the wavenumber domain variable k of the signal. a k θ The fourfold transform pairs are respectively used to obtain the wavenumber spectrum of the spatial domain signal by performing a two-dimensional Fourier transform on the sub-aperture image.

[0104] After completing imaging of all sub-apertures in a unified imaging coordinate system, the remaining stage of the FFBP imaging algorithm is sub-aperture image fusion. This is achieved by coherently adding the sub-aperture images in the polar direction, which requires sinc interpolation of the sub-aperture images in the polar direction. Within a single aperture, the wavenumber spectra of different point targets in the imaging scene have different modulation terms, resulting in blurring of the wavenumber spectra of different point targets. Before performing sinc interpolation on the sub-aperture images, the wavenumber spectra of each point target need to be centered.

[0105] The traditional wavenumber spectrum centering method compensates for the phase in the spatial domain of the signal by exp(-j2πx·k). x0 Realize the wavenumber spectrum of a spatial domain signal in k x Move k in direction x0 Where x is the spatial domain variable of the signal, k x For the wavenumber domain variables of the signal. This method can only uniformly shift the wavenumber spectrum of point targets within the same polar radius cell. Multiple point targets within the same polar radius cell will have different wavenumber spectra due to k...x The modulation terms are different and fail to be located at the center of the wavenumber spectrum, thus affecting the actual k-value of the entire imaging scene. x The change is much greater than k for a single target point. x The variation in wavenumber makes the sampling requirements for the signal in the spatial domain more stringent. Traditional non-baseband sinc interpolation can avoid the requirement of centering the wavenumber spectrum, but this method has poor accuracy and low computational efficiency.

[0106] This invention proposes an accurate and efficient method for centering the wavenumber spectra of each target point in a sub-aperture image. For the sub-aperture image of the i-th sub-aperture, a two-dimensional wavenumber spectrum position correction filter is introduced in the signal spatial domain:

[0107]

[0108] Where R(θ) grid ,a grid ;t c_i ) represents the center time of the i-th sub-aperture, i.e., the slow time is t. m =t c_i At time, the receiver and transmitter reach the sub-aperture image imaging grid points (θ). grid ,a grid The slant distance history and ).

[0109] The process of obtaining the i-th sub-aperture image after introducing a two-dimensional filter with wavenumber spectrum position correction is represented as follows:

[0110]

[0111] Thus, imaging N sub-apertures will yield N sub-aperture images. Figure 6 Figure (a) shows the spatial domain signal of a single target point located at an arbitrary position in the imaging scene. Figure (b) shows the wavenumber domain signal of the single target point before wavenumber spectrum position correction. Figure (c) shows the wavenumber domain signal of the single target point after wavenumber spectrum position correction. Figure (d) shows the spatial domain signals of three target points, where A' and B' are target points in the same variable 'a' unit, and A' and C' are target points in the same variable 'θ' unit. Figure (e) shows the wavenumber domain signals of the three target points before wavenumber spectrum position correction. Figure (f) shows the wavenumber domain signals of the three target points after wavenumber spectrum position correction. Comparing Figures (c) and (f), it can be seen that after wavenumber spectrum position correction, the wavenumber spectrum width of the spatial domain signals of multiple target points is consistent with the wavenumber spectrum width of a single target point.

[0112] This invention proposes a two-dimensional wavenumber spectrum position correction filter. Using this filter, the wavenumber spectrum of the spatial domain signal in any sub-aperture can be accurately, quickly, and efficiently centered within the scene. Accurate and consistent centering of the wavenumber spectrum helps compress the variation in wavenumber variables across the entire imaging scene, i.e., the wavenumber spectrum width of the imaging scene, reducing the Nyquist sampling requirement for the spatial domain signal and improving algorithm efficiency. Furthermore, the method for solving the Nyquist sampling conditions in the proposed polar coordinate system is computationally simple, efficient, and easily implemented on a computer.

[0113] The S500 fuses the corrected current sub-aperture images to obtain the full-aperture SAR image with the best resolution.

[0114] S510, for any current stage l from 1 to j, merge the adjacent sub-apertures in the previous stage l-1 in slow time to obtain the sub-aperture of this stage l; the value of j is determined according to the number of sub-apertures.

[0115] S520, repeat S300 in the current stage to obtain the sub-aperture imaging grid;

[0116] S530, in the current stage l, the sub-aperture images that are adjacent in slow time in the previous stage l-1 are fused pairwise to obtain the sub-aperture image of this stage l.

[0117] S540, determine if l equals j;

[0118] S550, if not, proceed to the next stage, let l = l + 1, and repeat S510-S540;

[0119] S540, if so, then the last sub-aperture image is determined as the optimal full-aperture SAR image.

[0120] Consistent with the framework of traditional time-domain FFBP imaging methods, N=2 j Each sub-aperture requires j stages of sub-aperture image fusion. In the l-th stage (l = 1 to j), the 2... j-l-1 Two sub-aperture images are fused together to obtain 2 j-l Sub-aperture images. First, the new sub-aperture obtained by combining two sub-apertures needs to be divided into imaging grids according to the S300 method. Since the aperture time length of one fusion is doubled, the sampling requirements of the new imaging grid in the θ direction are more stringent. The sub-aperture image fusion process proposed in this invention differs from the traditional FFBP imaging method in that the process of fusing sub-aperture images of two adjacent sub-apertures is expressed as follows:

[0121]

[0122] After the fusion process described above, a new sub-aperture image img′ is obtained.w (θ grid ,a grid ). Among them, img′ u and img′ v These are the u-th and v-th sub-aperture images adjacent to each other before fusion in this stage, respectively, img′ w For the w-th sub-aperture image after fusion in this stage, the relationships u = 2w-1 and v = 2w are satisfied. and H, respectively, of the filter u (θ grid ,a grid ) and H v (θ grid ,a grid The conjugate expression of ). For the extreme radius variable a = a grid At that time, in img′ u In the θ direction, through sinc interpolation, we obtain the polar angle variable θ = θ. grid The sampled value at that location; For the extreme radius variable a = a grid At that time, in img′ v In the θ direction, through sinc interpolation, we obtain the polar angle variable θ = θ. grid The sampled values ​​at the location. Since the imaging coordinate system of each sub-aperture image is uniform, and the only difference between the imaging grids of each sub-aperture image is the sampling rate of the θ variable, only the sinc interpolation in the θ direction needs to be considered during the sub-aperture image fusion process, which helps to reduce the computational burden of the imaging algorithm.

[0123] exist Figure 7 In this context, considering an arbitrary point target in the imaging scene, during a certain stage of sub-aperture image fusion, Figure 7 Figures (a) and (b) show the wavenumber spectra of the two sub-aperture images before sub-aperture image fusion, respectively; figure (c) shows the wavenumber spectrum of the sub-aperture image obtained after fusion of the two sub-aperture images. The results in the figures show that after fusion of the two old sub-aperture images, a new sub-aperture image is obtained. The wavenumber spectrum of the new sub-aperture image is the result of correctly stitching together the wavenumber spectra of the two old sub-aperture images. The wavenumber spectrum of the new sub-aperture image is at k... θ The width of the direction is the sum of the widths of the two sub-aperture images.

[0124] During sub-aperture image fusion, the aperture time length corresponding to the newly obtained sub-aperture image is doubled. In the new sub-aperture image, the wavenumber spectrum of a target point is k θ As the directional width increases, the resolution of the target point in the θ direction is improved. After j stages of sub-aperture image fusion, a high-resolution SAR image corresponding to the synthetic aperture is finally obtained.

[0125] This invention provides a wavenumber spectrum reconstruction and rapid fusion imaging system for arbitrary bistatic SAR, comprising a transmitting platform, a receiving platform, and an imaging device. The imaging device is used to realize the wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR.

[0126] This invention improves upon existing time-domain FFBP imaging methods for bistatic SAR systems by proposing a novel method for establishing the imaging polar coordinate system and a method for consistently centering the wavenumber spectrum of the spatial domain signal of the imaging scene. By introducing a two-dimensional filter for wavenumber spectrum position correction, the wavenumber spectrum width of the imaging scene is compressed, reducing the Nyquist sampling requirement in the spatial domain and improving the imaging efficiency. While ensuring accurate and consistent centering of the wavenumber spectrum of the imaging scene, this invention proposes a new method for calculating the minimum Nyquist sampling requirement of the spatial domain signal of the imaging scene. The improved time-domain FFBP imaging method of this invention can achieve accurate SAR imaging of the imaging scene with less computation. The framework of the time-domain FFBP imaging method determines its excellent parallelizability, allowing the use of parallel processing mechanisms on hardware platforms such as GPUs and FPGAs, which will further significantly improve the imaging efficiency of the time-domain FFBP imaging method for bistatic SAR systems in practical applications.

[0127] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0128] Although this application has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0129] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR, characterized in that, include: S100, the echo signal from the imaging area is acquired through a bistatic SAR system, and the echo signal is subjected to range pulse compression focusing to obtain a two-dimensional time domain signal; the bistatic SAR system includes a receiving platform and a transmitting platform, both in a spatial rectangular coordinate system; S200, based on the positions of the receiving platform and the transmitting platform at the center time of the synthetic aperture, and based on the orthogonal elliptical mapping polar coordinates, establishes a unified imaging polar coordinate system; S300, the synthetic aperture is divided into multiple current sub-apertures to establish a sub-aperture imaging grid in the imaging polar coordinate system; S400 utilizes the two-dimensional time-domain signal from S100 to project and image the sub-aperture imaging grid, obtaining multiple current sub-aperture images. Wavenumber spectral position correction is then applied to each current sub-aperture image to center its position. S400 includes: S410 uses the two-dimensional time domain signal of S100 to perform back projection imaging on the sub-aperture imaging grid to obtain multiple current sub-aperture images; S420 introduces a two-dimensional filter with wavenumber spectrum position correction; S430, the wavenumber spectrum position correction two-dimensional filter is used to correct the wavenumber spectrum position of each current sub-aperture image, so that the wavenumber spectrum of each target point in each current sub-aperture image is consistently aligned and centered. The S500 fuses the corrected current sub-aperture images to obtain the full-aperture SAR image with the best resolution.

2. The wavenumber spectrum reconstruction and fast fusion imaging method for arbitrary bistatic SAR according to claim 1, characterized in that, The spatial rectangular coordinate system is constructed by the following steps: At the center of the synthetic aperture, the receiving platform will The point below the machine is taken as the origin of the coordinate system. ; receiving platform The velocity vector is projected onto the ground plane, and the direction of the resulting vector is defined in a spatial rectangular coordinate system. of Axial direction; set the origin of the coordinate system The vertical upward direction is used as Axial direction; determine the spatial rectangular coordinate system using the right-hand rule. of Axial direction.

3. The wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR according to claim 2, characterized in that, The bistatic SAR system in the spatial rectangular coordinate system includes: Reference points in the imaging scene In a spatial rectangular coordinate system, the receiving platform Launch platform The velocity vectors are respectively expressed as: and , For the speed vector of the transceiver platform in The included angle after the plane projection; For slow time variables, in slow time... At each moment, the position coordinates of the transceiver motion platform are represented as follows: and ,in, , , , , and All are considered to be in slow time A function with variables.

4. The wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR according to claim 3, characterized in that, S100 includes: S110 acquires echo signals from the imaging scene through a bistatic SAR system; S120, Perform a range-to-Fourier transform on the echo signal to obtain the echo signal. ; S130, construct a range-oriented pulse compression matched filter; S140, using the range-directed pulse compression matched filter to process the echo signal Echo signals were obtained by range-directed pulse compression focusing. ; S150 will transmit the echo signal Two-dimensional time-domain echo signal is obtained by performing inverse distance-to-Fourier transform. .

5. The wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR according to claim 3, characterized in that, S200 includes: S210, at the center of the synthetic aperture The spatial coordinates of the receiving platform and the transmitting platform are mapped to the plane. The positions of the receiving platform are obtained by projection. and launch platform location ; S220, Plane In the middle, with the baseline direction And its orthogonal direction is the axis direction, with midpoint Establish an elliptical reference rectangular coordinate system with the origin as the coordinate origin. ; S230, with and The focal point of the ellipse, the reference point for the imaging scene. Given a point on the ellipse, we obtain the ellipse; S240, with the midpoint of the baseline With the pole as the point, and the length of the semi-major axis of the ellipse... The polar radius is the parametric angle of a point on the ellipse. The polar angle is used to obtain the orthogonal elliptic mapping polar coordinates. and with Establish a unified imaging polar coordinate system.

6. The wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR according to claim 5, characterized in that, The S300 includes: The entire synthetic aperture is divided into In a given sub-aperture, the minimum Nyquist sampling condition of the current sub-aperture image in the spatial domain is determined by the range of wavenumber variation of the signal in the spatial domain, and the sub-aperture imaging grid in the imaging polar coordinate system is obtained according to the minimum Nyquist sampling condition.

7. The wavenumber spectrum reconstruction and rapid fusion imaging method for arbitrary bistatic SAR according to claim 6, characterized in that, The entire synthetic aperture is divided into Each sub-aperture, within a current sub-aperture, determines the minimum Nyquist sampling condition of the current sub-aperture image in the spatial domain by measuring the range of wavenumber variation of the signal in the spatial domain, and obtains the sub-aperture imaging grid in the imaging polar coordinate system according to the minimum Nyquist sampling condition, including: The entire synthetic aperture is divided into Individual aperture; Calculate scene reference points in the imaging scene within a current sub-aperture. wavenumber variable at the location and and the corresponding range of change , ; Based on the lowest Nyquist principle, determine the signal in the spatial domain. direction and Sampling interval size in direction and The minimum Nyquist sampling condition; The sub-aperture imaging grid in the imaging polar coordinate system is obtained according to the minimum Nyquist sampling condition.

8. The wavenumber spectrum reconstruction and fast fusion imaging method for arbitrary bistatic SAR according to claim 1, characterized in that, The S500 includes: S510, targeting any current stage The previous stage In the slow time phase, adjacent sub-apertures are merged pairwise to obtain this stage. Sub-aperture; The value of is determined based on the number of sub-apertures. S520, at the current stage Repeat step S300 to obtain the sub-aperture imaging grid; S530, at the current stage The previous stage In the slow time phase, adjacent sub-aperture images are fused pairwise to obtain this stage. Sub-aperture image; S540, judgment Is it equal to ; S550, if not, proceed to the next stage, let And repeat S510-S540; S560, if so, then the last sub-aperture image is determined as the optimal full-aperture SAR image.

9. A wavenumber spectrum reconstruction and rapid fusion imaging system for arbitrary bistatic SAR, characterized in that, The imaging system includes a transmitting platform, a receiving platform, and an imaging device, wherein the imaging device is used to implement the wavenumber spectrum reconstruction and rapid fusion imaging method of any bistatic SAR as described in any one of claims 1 to 8.

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