High-precision SAR imaging motion compensation and geometric correction method for large pre-astigmatism

Abstract

The application relates to the field of airborne synthetic aperture radar imaging, and discloses a high-precision large forward-looking SAR imaging motion compensation and geometric correction method, wherein Doppler center estimation is carried out on original echoes, the azimuth wavenumber spectrum is shifted to a baseband, distance direction Fourier transformation is carried out on the data, first-order motion compensation is carried out, then complete focusing of a scene center and consistent compression of a same LOS slant range target are completed according to a two-dimensional wavenumber domain reference function. Through Stolt interpolation of the two-dimensional wavenumber spectrum along the line-of-sight direction, distance-azimuth decoupling is realized, wavenumber spectrum utilization is improved, and defects such as needing azimuth zero padding to eliminate aliasing, having a black edge in the image, and side lobe tilting in the traditional wavenumber domain imaging algorithm are avoided; first-order consistent compensation and second-order space-variable motion compensation can also be realized, the image is focused to the wavenumber domain through azimuth de-bending, a large amount of zero padding in the space domain is avoided, a slant plane image with geometric distortion is converted to a ground plane image through geometric correction, and high-precision focusing is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of airborne synthetic aperture radar imaging, in particular to a high-precision large forward-looking SAR imaging motion compensation and geometric correction method. BACKGROUND

[0002] Synthetic aperture radar (SAR) is an active microwave remote sensing device, which has the ability of high-resolution imaging and moving target detection and positioning in all-weather and all-day. SAR image reflects the backscattering characteristics of the radiated scene, which can be an effective supplement to optical images. The significance of high-resolution airborne SAR imaging is self-evident. In the military field, it can conduct real-time reconnaissance on the battlefield and provide timely information for the command system by describing typical targets in detail. SAR has unique advantages in map surveying, geological exploration, disaster assessment, agricultural census and vegetation classification, etc. It has a wide application prospect and development potential.

[0003] Airborne large forward-looking SAR refers to the direction of radar beam sight deviates from the normal of flight path, and the forward-looking angle (the angle between the beam sight and the normal of flight path) can reach 60° or even 80°, as shown in the following figure. Figure 2 Traditional forward-looking SAR can only image the area on the side of the aircraft, and cannot obtain information in the forward-looking area of the aircraft. The main advantage of large forward-looking SAR is that it can detect targets in advance, and has a longer maneuvering time. The larger the forward-looking angle, the larger the imaging range, and the multi-angle scattering characteristics of the target can be obtained, which greatly improves the reconnaissance and identification ability of the radar. Therefore, large forward-looking SAR has important applications in military fields such as battlefield reconnaissance, target identification, accurate attack on the ground, and improving the survival ability of warplanes. In the 1980s, the United States began to study large forward-looking SAR, and Raython Company developed AN / APG-77 active phased array radar to verify the feasibility of forward-looking SAR on F / A-22 fighter aircraft.

[0004] The imaging algorithm research of large forward-looking SAR is the core problem of large forward-looking SAR. The main difficulty lies in that the distance migration of the target is large, which leads to serious two-dimensional coupling of the target and strong space variation. At the same time, due to the non-ideal characteristics of SAR platform motion and the measurement error of motion parameters, SAR motion compensation is also a problem that must be solved in large forward-looking high-resolution SAR imaging. In addition, due to the special imaging geometry of large forward-looking SAR, the slant range plane and the ground range plane not only have a rotation in the elevation direction, but also have a rotation in the azimuth direction. The geometric distortion of the ground range image is serious, which affects the high-precision positioning of the target. Therefore, the research on large forward-looking SAR imaging technology can further improve the battlefield reconnaissance, early perception and detection and identification ability of the radar, and provide support for military development.

[0005] After years of efforts by domestic and foreign scholars, the commonly used squint imaging algorithms include the back projection (BP) algorithm, the range-doppler (RD) algorithm, the omega-k (Omega-K) algorithm, the chirp scaling (CS) algorithm, the non-linear CS (NLCS) algorithm, and the polar format algorithm (PFA). The time-domain BP and the improved fast FFBP algorithm still have low computational efficiency in large-width and large-scene imaging, and are difficult to be combined with motion compensation, and require high precision of inertial navigation equipment. The RD imaging algorithm with the second range compression (SRC) processing step cannot be applied to large squint angle SAR imaging. The CS algorithm uses frequency modulation scaling to correct SAR range migration, which cannot be applied to large squint angles. The related extended algorithm such as NLCS considers the azimuth variable problem of the frequency modulation rate, and can adapt to a squint angle of about 60°. However, all of them make high-order approximation to the range migration, and the calculation is relatively complex and still has residual migration. In addition, the influence of motion error is not considered. The PFA algorithm can support large forward squint imaging of a small scene, but the plane wave assumption cannot meet the high resolution condition of a large scene, and the variable filtering compensation needs to calculate the real position of the target in blocks, which has a large amount of calculation, and the approximation error still exists in the compensation of the blocks. The Omega-K algorithm is a high-precision imaging algorithm under the condition of non-azimuth variable velocity. The extended Omega-K algorithm also supports second-order motion compensation, but the imaging plane is a slant plane, the imaging direction is consistent with the flight path, the effective scene is inclined under the condition of large squint, there are many black edges, the utilization efficiency is not high, and the sidelobes are inclined, which makes it difficult to combine with the self-focusing algorithm. In addition, the Omega-K algorithm focuses the image on a two-dimensional spatial domain. When the beam irradiation area is larger than the aperture length support domain (such as the strip mode), a large amount of zero padding is required to avoid image azimuth aliasing, which greatly increases the processing amount.

[0006] In summary, the existing large squint imaging technology has the following shortcomings:

[0007] 1) It is difficult to balance the computational efficiency and imaging accuracy. Except for the Omega-K algorithm, there is a certain degree of approximation. Even if the distance history is expanded to a high order, there is still a variable nature under the condition of large scene and high resolution, which makes it difficult to apply to squint angles above 75°.

[0008] 2) Most algorithms are difficult to combine with motion compensation and consider the variable nature of motion compensation.

[0009] 3) Omega-K, CS class algorithm imaging plane is slant range plane, image azimuth direction is consistent with heading, corrects target to the shortest slant range of vertical track, and a large number of azimuth zero points are filled in large oblique view, increase calculation amount, and image black edge is large, and zero needs to be filled to avoid azimuth aliasing.

[0010] 4) image in line of sight (LOS) direction establishes coordinate system, and most of images are slant plane images, which is not conducive to high-precision positioning of target. SUMMARY

[0011] Therefore, the application provides a high-precision large forward-looking SAR imaging motion compensation and geometric correction method, solves the difficulties caused by large forward-looking imaging geometry, such as large range migration, serious two-dimensional coupling, strong space variation, and difficult image focusing, and combines with measurement inertial navigation data to realize second-order range space variation motion compensation, and on this basis, corrects the slant plane image with two-dimensional rotation in pitch and azimuth to the ground plane to realize high-precision focusing and non-distortion imaging of the image.

[0012] A high-precision large forward-looking SAR imaging motion compensation and geometric correction method comprises the following steps:

[0013] Step one: Doppler center estimation is performed on the original echo to obtain a slant plane oblique angle, and a wave number spectrum center correction function is constructed; based on the wave number spectrum center correction function and the original echo, the azimuth wave number spectrum is shifted to the baseband to obtain an azimuth baseband echo;

[0014] Step two: distance Fourier transform is performed on the azimuth baseband echo, and first-order motion compensation is completed according to a first-order motion compensation function at the radar reference slant range;

[0015] Step three: the data after first-order motion compensation is transformed to a two-dimensional wave number domain, and scene center focusing and consistent compression are completed according to a scene center reference function of the two-dimensional wave number domain;

[0016] Step four: the two-dimensional wave number spectrum after consistent compression is expanded along the line of sight direction to obtain a two-dimensional wave number spectrum along the line of sight and the vertical line of sight direction, and distance-azimuth decoupling is realized;

[0017] Step five: the echo after the expansion Stolt interpolation is transformed to a two-dimensional space domain, and the motion error of the original echo is mapped to the line of sight direction, and second-order motion compensation in the line of sight direction is completed;

[0018] Step six: according to the data after the second-order motion compensation and the quadratic reference function in the azimuth direction, space domain declination is performed, and the azimuth wave number domain is transformed, target focusing is completed, and a slant plane focusing SAR image is obtained;

[0019] Step seven: according to the geometric mapping relationship between the target in the slant plane along the line of sight direction and the ground plane, a distortion-free ground plane forward-looking SAR image is obtained through two-dimensional interpolation geometric correction.

[0020] Further, in step one, the azimuth wavenumber spectrum is transformed to baseband by multiplying the constructed wavenumber spectrum center correction function and the two-dimensional spatial domain expression of the baseband original echo; wherein the wavenumber spectrum center correction function H azi_b (X,f dc )=exp{-jK xc X},K xc is the azimuth center wavenumber, K xc =2πf dc / v, f dc is the azimuth Doppler center frequency of the original echo, and v is the flight speed of the carrier.

[0021] Further, in step two, the range Fourier transform is performed on the azimuth baseband echo, and multiplied by a first-order motion compensation function at the reference imaging center to complete the first-order motion compensation; the first-order motion compensation function is H moco_1st (X,K r )=exp{j2K r ·R err_1st (X)},wherein K r =2π(f c +f r ) / c is the range wavenumber, c is the speed of light, f c is the center frequency, f r is the range frequency of the transmitted LFM signal, -f s / 2≤f r ≤f s / 2, f s is the range sampling rate.

[0022] Further, in step three, after the first-order motion compensation, the data is Fourier transformed along the azimuth direction to obtain the two-dimensional wavenumber spectrum of the scene center, and the two-dimensional wavenumber spectrum is multiplied by a two-dimensional wavenumber domain reference function to complete the scene center focusing and consistent compression; wherein the two-dimensional wavenumber domain reference function is:

[0023]

[0024] wherein P * (Kr) is the complex conjugate of P(Kr), is the wavenumber spectrum of the transmitted LFM signal, B r is the signal bandwidth, K rc is the range center wavenumber, X c , Y cK is a constant, X is the azimuth wavenumber.

[0025] Further, in step five, the Stolt interpolated echo data along the LOS direction is multiplied by the azimuth spatial domain expansion function, then a two-dimensional inverse Fourier transform is performed to the two-dimensional spatial domain, and the motion error in the original echo domain is mapped to the LOS direction, so that the second-order motion compensation in the LOS direction is completed; wherein the azimuth spatial domain expansion function H azi_ext (K a ; B c ) is,

[0026]

[0027] wherein K a is the wavenumber of the LOS ⊥ direction, and B is a constant, which is the distance from the center of the aircraft aperture to the reference imaging center.

[0028] Further, in step six, the data after the second-order motion compensation is multiplied by the quadratic phase reference function in the spatial domain, so that the dechirp in the LOS ⊥ direction is completed; wherein the quadratic dechirp reference function is

[0029]

[0030] wherein a is the target position in the LOS ⊥ direction, and b is the target position in the LOS direction.

[0031] Compared with the prior art, the present application has the following beneficial effects:

[0032] 1. The present application realizes the decoupling of range-azimuth by expanding the Stolt interpolation along the two-dimensional wavenumber spectrum in the line-of-sight direction, is easy to combine with motion compensation, improves the utilization rate of the wavenumber spectrum, avoids the defects such as needing to zero-pad for azimuth to remove aliasing, having black edges in the image, and tilt of sidelobes in the traditional wavenumber domain imaging algorithm; the transformation form of the original motion error in the LOS coordinate system is derived in detail, so that the first-order consistent compensation and the second-order spatially variable motion compensation are realized; the image is focused to the wavenumber domain through azimuth dechirp, a large amount of zero-padding in the spatial domain is avoided; the oblique plane image with geometric distortion is converted to the ground plane image through geometric correction, and high-precision focusing is realized.

[0033] 2. The present application can solve the problem of imaging center deviation caused by beam control error, antenna installation error and non-ideal motion error of the aircraft, and can be combined with the current real-time processing architecture based on the PFA algorithm to avoid the time lag problem in real-time processing, realize the real-time processing capability of estimating and compensating when a frame, and can be used in the fields of real-time imaging of airborne spotlight SAR and strip SAR. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only represent some of the embodiments of the present application, and all other drawings obtained by those of ordinary skill in the art without creative effort based on these drawings also belong to the scope of protection of the present application.

[0035] Figure 1 is a flow chart of the high-precision large forward-looking squint SAR imaging motion compensation and geometric correction method in embodiment 2;

[0036] Figure 2 is a large forward-looking squint SAR oblique plane imaging geometric schematic diagram in embodiment 2;

[0037] Figure 3 is a large forward-looking squint SAR ground plane imaging geometric schematic diagram in embodiment 2;

[0038] Figure 4 is a two-point target simulation result diagram in embodiment 2;

[0039] Figure 5 is a squint angle 72° measured data processing result diagram in embodiment 2;

[0040] Figure 6 is Figure 5 a local enlarged schematic diagram. DETAILED DESCRIPTION

[0041] The embodiments of the present application will be described in detail below with reference to the drawings.

[0042] The embodiments of the present application are described below through specific and detailed examples, and those skilled in the art can easily understand other advantages and effects of the present application from the disclosure. Obviously, the described embodiments are only some of the embodiments of the present application, not all. The present application can also be implemented or applied by other different specific embodiments, and each detail in the specification can be modified or changed based on different views and applications without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort also belong to the scope of protection of the present application.

[0043] Embodiment 1

[0044] A high-precision large forward-looking squint SAR imaging motion compensation and geometric correction method comprises the following steps:

[0045] Step one: Doppler center estimation is performed on the original echo to obtain the slant plane squint angle θs, and a wave number spectrum center correction function is constructed; based on the wave number spectrum center correction function and the original echo, the azimuth wave number spectrum is shifted to the baseband to obtain the azimuth baseband echo;

[0046] The main purpose is to solve the azimuth wave number spectrum aliasing phenomenon caused by large squint. Doppler center estimation is performed on the original echo, a wave number spectrum center correction function is constructed, and the two-dimensional wave number spectrum center is shifted to zero to solve the azimuth wave number spectrum aliasing problem.

[0047] Step two: distance Fourier transform is performed on the azimuth baseband echo, and first-order motion compensation is completed according to the first-order motion compensation function at the radar reference slant range;

[0048] Step three: the data after first-order motion compensation is transformed into two-dimensional wave number domain, and complete scene center focusing and consistent compression of the same LOS slant range target according to the scene center reference function of two-dimensional wave number domain;

[0049] Step four: along the line-of-sight direction, the two-dimensional wave number spectrum after consistent compression is expanded by Stolt interpolation to obtain the two-dimensional wave number spectrum along the line-of-sight and vertical line-of-sight directions, realize distance-azimuth decoupling, complete range migration correction, and at the same time, the azimuth phase history domain data is retained, which is convenient for carrying out distance space-varying second-order motion compensation;

[0050] Step five: the echo after extended Stolt interpolation is transformed into two-dimensional spatial domain, and the motion error of the original echo is mapped to the line-of-sight direction to complete the line-of-sight direction space-varying second-order motion compensation;

[0051] Step six: according to the data after second-order motion compensation and the quadratic reference function in the azimuth direction, spatial domain dechirp is performed, and the image is focused to the wave number domain to obtain a well-focused LOS slant plane image;

[0052] Step seven: according to the geometric mapping relationship between the slant plane along the line-of-sight direction and the ground plane of the target, two-dimensional interpolation geometric correction is performed to obtain a distortion-free ground plane forward-looking SAR image.

[0053] In this embodiment, to address the azimuth wavenumber spectrum aliasing caused by large squint, Doppler center estimation is performed on the original echo, and a wavenumber spectrum center correction function is constructed to shift the center of the two-dimensional wavenumber spectrum to zero, thus resolving the azimuth wavenumber spectrum aliasing problem. The echo data is transformed to the range frequency domain to complete first-order motion compensation at the reference slant range. Then, a two-dimensional wavenumber domain reference function is established based on the scene center position to achieve complete focusing of the scene center and consistent compression of targets with the same LOS slant range. By using two-dimensional wavenumber spectrum extended Stolt interpolation along the line of sight, range-azimuth decoupling is achieved, which is easily combined with motion compensation, improving the wavenumber spectrum utilization rate and avoiding the defects of traditional wavenumber domain imaging algorithms, such as azimuth zero-padding for aliasing, black borders in the image, and sidelobe tilt. It can also achieve first-order consistent compensation and second-order spatially variable motion compensation. By focusing the image to the wavenumber domain through azimuth deslant, a large amount of zero-padding in the spatial domain is avoided. The slant plane image with geometric distortion is converted to a ground plane image through geometric correction, achieving high-precision focusing.

[0054] Example 2

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the following description is provided in conjunction with specific embodiments and... Figures 1-3 The method and effects of the present invention will be further described in detail below.

[0056] In this embodiment, the geometric model of large forward-looking SAR imaging is as follows: Figure 2 , Figure 3 As shown, the aircraft's flight altitude is H, the radar's zero-time position is O, and the aircraft flies horizontally at a speed v along the X direction. The radar operates in strip mode, and the radar beam center at zero time intersects the ground at point C, which is also the reference scene center. The Y-axis is perpendicular to the X-axis, and OXY forms an imaging oblique plane with a range of R0 and θ. s Given an oblique plane and oblique viewpoint, the shortest distance from point C to the aircraft's flight path is Y. c The orientation is X c The angle between the beam and the Z-axis is Point P is any target point on the ground plane with coordinates (X...). p ,Y p ), O g X g Y g Forming the ground plane, θ g This is the oblique angle view from the ground plane. The b-axis is the line-of-sight (LOS) direction, and the a-axis is perpendicular to the line-of-sight (LOS). ⊥ The direction is Oab, which lies on the imaging oblique plane. The error of the aircraft deviating from the ideal trajectory at a certain moment is (Δx, Δy, Δz).

[0057] Step 1: Perform Doppler center estimation on the original echo to obtain the oblique angle θ in the oblique plane. s Construct the wavenumber spectrum center correction function H azi_b(X, f dc ) is multiplied by the original echo, and the azimuth wavenumber spectrum is transformed to the baseband to avoid spectrum aliasing.

[0058] The two-dimensional spatial domain expression of the demodulated baseband original echo is:

[0059]

[0060] where K is the frequency modulation slope of the linear frequency modulation (LFM) signal, λ is the wavelength, r is the distance sampling position, j is the imaginary part of the complex number, c is the speed of light, R p (X) is the instantaneous slant range of the radar to the target at X.

[0061] Doppler center estimation is performed on S(X, r) to obtain the slant plane squint angle θ s Doppler center estimation is to estimate the azimuth Doppler center frequency f dc of the echo. Since the squint angle is large, f dc usually spans multiple PRFs, and the PRF ambiguity number needs to be calculated given the squint angle instruction value. In this embodiment, the phase change between azimuth samples is measured to estimate the Doppler frequency of the signal.

[0062] According to f dc , the slant plane squint angle θ can be obtained. Since the azimuth wavenumber spectrum of the original echo is not in the baseband, directly performing azimuth FFT will cause spectrum folding, and the azimuth spectrum coordinates are discontinuous, which is not conducive to subsequent interpolation, so S(X, r) needs to be multiplied by a wavenumber spectrum center correction function H azi_b (X, f dc ) to move the azimuth wavenumber spectrum to the baseband, and the result is S1(X, r):

[0063] S1(X, r) = S(X, r) · H azi_b (X, f dc )

[0064] H azi_b (X, f dc ) = exp{-jK xc X}

[0065] The azimuth center wavenumber is K xc , and K xc = 2πf dc / v.

[0066] Step two: perform distance Fourier transform on the azimuth baseband echo S1(X, r), and multiply it by a first-order motion compensation function at the reference imaging center to complete the first-order motion compensation. The reference imaging center is the image center set during imaging, such as Figure 2C point in the center. The first order motion compensation function is calculated by the coordinates of the center and the carrier position. After imaging, the point is in the center of the image.

[0067] Because of the non-ideal linear motion of the carrier, motion errors are introduced, which make the ideal two-dimensional matched filtering mismatched and affect the focusing performance of the target. Here, only the range-dependent nature of motion errors is considered, that is, targets at the same range along the line-of-sight direction have the same motion error, and only the first order motion error needs to be calculated along the azimuth direction and compensated.

[0068] The true range cell migration (RCM) of the target (X c ,Y c ) at the scene center is

[0069]

[0070] where X = m · v / PRF, m ∈ [-N X / 2, N X / 2-1] is the ideal azimuth position of the carrier, m is the azimuth discrete sampling number, N X is the azimuth sampling point number, Δx(m), Δy(m), Δz(m) are the motion errors of the carrier at m time.

[0071] The first order motion compensation function is H moco_1st (X, K r ) = exp {j2K r ·R err_1st (X)}, where K r = 2π(f c +f r ) / c is the range wave number, c is the speed of light, f c is the center frequency, f r is the range frequency of the transmitted LFM signal, -f s / 2 ≤ f r ≤ f s / 2, f s is the range sampling rate. The first order motion compensation performs envelope compensation and phase compensation on the target at the reference slant range in the range wave number domain, so that the residual motion error which is range-dependent does not exceed one range cell, and only second order phase compensation is needed subsequently.

[0072] The data after first order motion compensation is where represents the Fourier transform along the range direction.

[0073] Step three: Fourier transform the data along the azimuth direction, transform to the two-dimensional wave number domain, and multiply with the two-dimensional wave number domain reference function, complete the scene center focusing and consistent compression. This step completes the matched filtering of the scene center target in the two-dimensional wave number domain, and the scene center is completely focused. The specific process is as follows:

[0074] After first-order motion compensation, the two-dimensional wave number spectrum of the scene center can be obtained by using the POSP (stationary phase principle) as follows:

[0075]

[0076] Where P(K r ) is the wave number spectrum of the transmitted LFM signal, B r is the signal bandwidth, is the distance center wave number, K X is the azimuth wave number.

[0077] Therefore, the two-dimensional wave number domain reference function is

[0078]

[0079] P * (K r ) is the complex conjugate of P(K r ).

[0080] The data after completing the scene center focusing

[0081] represents the Fourier transform along the azimuth direction X.

[0082] Step four: carry out the extension Stolt interpolation along the slant direction on the two-dimensional wave number spectrum after the scene center focusing, obtain the two-dimensional wave number spectrum along the slant and vertical slant directions, and realize the distance-azimuth decoupling.

[0083] For any point target P in the scene, the coordinates in the oblique plane OXY coordinate system are (X p ,Y p ), and the expression after the echo passes through the above steps is

[0084]

[0085] is the residual motion error.

[0086] Let The two-dimensional wave number spectrum of the target has a tilted fan-shaped support domain in K X -K Y , and the wave number center coordinates are (K xc ,K yc ), Kxc = 2K rc sin θ s ,

[0087] With the increase of squint angle, the slanting degree of wave number spectrum support region becomes larger. The traditional Stolt transform is to interpolate the uniform K r -K X spectrum into the uniform K X -K Y spectrum. Under this way, the effective spectrum in the rectangular support region will be reduced, the spectrum utilization will be reduced, or there will be a large number of blank areas, and the data operation efficiency will be reduced. The present application adopts the interpolation along the sight line, and interpolates the uniform K r -K X spectrum into the uniform K b -K a spectrum, wherein K b is the line of sight (LOS) direction, i.e. the squint angle direction, K a is the vertical line of sight (LOS ⊥ ) direction, forms a right-hand rule with K b , and K a -K b are all located in the oblique plane. This interpolation method is equivalent to being along the slanting direction of the wave number spectrum support region, which can maximize the preservation of the wave number spectrum support region and improve the spectrum utilization. In addition, for large squint SAR, due to the antenna pattern effect, its beam irradiation area in the OXY plane is an inclined strip, and using the traditional interpolation method, the spatial domain image only has targets in the line of sight direction, and the rest are black areas that cannot be covered by the beam, which is not conducive to interpretation and interpretation, and the scene support domain in the X direction is much larger than the synthetic aperture length, which needs to be additionally zero-padded to avoid aliasing, reducing the operation efficiency. The image black edge is less by using the interpolation method along the LOS direction, the wave number spectrum support region is approximately rectangular, and the two-dimensional sidelobe tilt directions are perpendicular to each other, which is conducive to subsequent self-focusing processing.

[0088] The wave number mapping relationship of the two-dimensional Stolt interpolation along the line of sight direction is:

[0089]

[0090] Similarly, the mapping relationship of K a , K b to K r , K X is

[0091]

[0092] The interpolation method realizes the functions of RCMC and azimuth matching filter, but the phase history domain data after RCMC cannot be combined with the conventional motion compensation algorithm to perform second-order distance-varying phase compensation, so an extended Stolt interpolation method along the LOS direction is needed to convert the uniform K r -K X spectrum into a uniform K b_ext -K a spectrum, and the mapping relationship is as follows:

[0093]

[0094] Since direct two-dimensional interpolation calculation is relatively complex, the present application decomposes it into two one-dimensional interpolations, that is, first, K r -K X spectrum is interpolated into K r -K a spectrum, and then K r -K a spectrum is interpolated into K a -K b_ext spectrum, which can avoid complex quadratic root calculation.

[0095] The method for interpolating K r -K x spectrum into K r -K a spectrum is as follows: a fixed K r (n) is selected each time, and the K a coordinates to be interpolated are calculated according to the K X_interp coordinates to be interpolated:

[0096]

[0097] wherein n=0, 1, …, N r -1 is the distance direction index, and N r is the number of distance direction sampling points.

[0098] The vector S3(K X ,K r (n)) is interpolated into S3(K X_interp ,K r (n)), and the interpolation kernel can be a sinc kernel function.

[0099] All n are traversed to obtain uniformly sampled S3(K a ,K r ).

[0100] The method for interpolating K r -K a spectrum into K a -K b_ext spectrum is as follows: a fixed Ka (m a ), according to the K b_ext coordinates to be interpolated, the K r_interp coordinates are calculated:

[0101] where m a = 0, 1, …, N a -1 is the LOS ⊥ direction order, N a is the LOS ⊥ direction number;

[0102]

[0103] The vector S3(K r ,K a (m a )) is interpolated into S3(K r_interp ,K a (m a )), and the interpolation kernel can be selected as a sinc kernel function. All m a are traversed to obtain uniformly sampled S4(K a ,K b_ext ), i.e.

[0104]

[0105] Step five: multiply the echo S4(K a ,K b_ext ) after Stolt interpolation along the LOS direction with the azimuth spatial domain expansion function H azi_ext (K a ; B c ), do two-dimensional inverse Fourier transform to the two-dimensional spatial domain, and map the motion error in the original echo domain to the LOS direction, to complete the second-order motion compensation in the LOS direction.

[0106] For any point P in the scene, the true instantaneous slant range is where (X p ,Y p ) is the coordinate of the target in the oblique plane OXY

[0107]

[0108] The ideal instantaneous slant range is After first-order motion compensation, the residual instantaneous slant range error is:

[0109]

[0110] The expression of the echo of the point target P after first-order motion compensation and distance matching filtering is

[0111]

[0112] After Fourier transform along azimuth direction

[0113] S MF (K r ,K X )

[0114] =∫S MF (K r ,X)exp(-jK X X)dX

[0115] =∫exp{-j[2K r (R p +ΔR err_res )]}exp(-jK X X)dX

[0116] According to POSP principle, take the partial derivative of integral phase with respect to X and take zero point

[0117]

[0118] Where Since ΔR err_res <<R p , it can be ignored when solving stationary phase point, and The stationary phase point X * is

[0119]

[0120] Substitute the phase integral formula, and get the two-dimensional wave number spectrum

[0121]

[0122] After multiplying the reference function, the echo becomes

[0123]

[0124] After Stolt interpolation along the LOS direction, the echo becomes

[0125]

[0126] After simplification

[0127]

[0128] Where

[0129] Y n =Y p -Y c , Xn = X p - X c

[0130] B n = Y n cos θ s + X n sin θ s , A n = -Y n sin θ s + X n cos θ s

[0131] (A n , B n ) is the coordinate of target P in the Cab coordinate system with C as the origin. The residual motion error phase is

[0132]

[0133] The interpolated is multiplied by the azimuth spatial domain spreading function H azi_ext (K a ; B c ) to obtain

[0134]

[0135] The interpolated is inverse Fourier transformed along the LOS ⊥ direction, and the stationary phase point is obtained by using the POSP principle as

[0136]

[0137] The spatial domain expression of data in the LOS ⊥ direction is

[0138]

[0139] In the above formula, the first phase term is the quadratic phase introduced by the spread Stolt interpolation, which is related to the LOS coordinate B n of the target and can be compensated in the subsequent azimuth matching filtering. The second phase term is the linear phase term about the LOS coordinate B n of the target, which compresses the target to the correct position after inverse Fourier transform, and the third term is the residual motion error, which is the focus of the second-order motion compensation.

[0140] The is expanded, and there are

[0141]

[0142] First item

[0143]

[0144] In the second item

[0145]

[0146] In second-order motion compensation, the motion error is generally considered to be along the LOS. ⊥ If it is empty and unchanging, then A can be used. p Substituting 0 into the above equation, we have

[0147]

[0148] denominator

[0149]

[0150] molecular

[0151]

[0152] therefore

[0153]

[0154] final

[0155]

[0156] Typically, the residual motion error ΔR err_res Much smaller than one resolving unit, in the above formula regarding K b_ext The distance migration caused by the linear phase is negligible; therefore, the spatial domain motion error at position a is related to the distance in the X direction. The motion error is the same. Since the orientation is discretely sampled, the motion error on the non-integer grid can be obtained through interpolation. A ΔR err_res (a) is approximately expressed as

[0157]

[0158] b represents the target position of the spatial variation in the LOS direction, Δb g (a) is the projection of the trajectory deviation error in the LOS direction on the ground, and Δz(a) is the projection of the trajectory deviation error in the elevation direction.

[0159] The data after second-order motion compensation is

[0160]

[0161] Step 6: Convert the second-order motion-compensated data to LOS ⊥The spatial domain is multiplied by a desquaring function, and transformed to the LOS ⊥ The wave number domain, and a slant plane focused SAR image is obtained.

[0162] Since all Omega-K type algorithms focus the image to the two-dimensional spatial domain, and in actual radar data acquisition, the radar beam illumination range is usually greater than the aperture length (spatial domain support area), which causes the image to alias in the support area. The commonly used method to avoid aliasing is to pad zeros in the spatial domain, and expand the spatial domain support area, but for some long-range imaging scenarios, the number of padding zeros will be much larger than the number of azimuth sampling points, causing the operation amount to increase sharply.

[0163] In view of this situation, in this paper, the second-order motion compensated data is multiplied by a quadratic phase reference function in the spatial domain, and the desquaring is completed in the LOS ⊥ direction, and then the Fourier transform is performed along the LOS ⊥ direction to complete the image focusing.

[0164] The quadratic desquaring reference function is where a is the target position in the LOS ⊥ direction, b is the target position in the LOS direction, and B c is the distance from the aircraft aperture center O to the reference imaging center C.

[0165] The second-order motion compensated data is

[0166]

[0167] The echo is an approximate linear frequency modulation signal along the LOS ⊥ direction, and the slope is -K rc / (B c +b). After desquaring, only the linear phase about the target position A n is left, and after the Fourier transform in the a direction, the result is

[0168]

[0169] where A kn is the focusing position of the target in the wave number domain, and has

[0170]

[0171] Therefore, the slant plane wave number domain coordinates A kn of the target are not only a function of the spatial domain coordinates A n , but also related to the LOS position B n , and there is a certain scaling that needs to be compensated in subsequent geometric correction.

[0172] Step 7: Based on the geometric mapping relationship between the target on the oblique plane along the LOS direction and the ground plane, geometric correction is completed through two-dimensional interpolation to obtain a distortion-free ground plane large forward-looking SAR image.

[0173] like Figure 2 and Figure 3 As shown, the target's coordinates in the inclined plane Cab are (A... n B n The coordinates of the inclined plane OXY are (X... p ,Y p ), ground level Ca g b g The coordinates are (A) gn B gn ), ground plane O g X g Y g The coordinates are (X gp ,Y gp ),

[0174] have

[0175] X p =A gn ·cosθ g +B gn ·sinθ g +X c

[0176]

[0177] in

[0178]

[0179] therefore

[0180] B n =(Y p -Y c )·cosθ s +(X p -X c )·sinθ s

[0181] A n =-(Y p -Y c )·sinθ s +(X p -X c )·cosθ s

[0182] Based on the coordinate transformation relationship, the oblique plane image (A) is transformed through two-dimensional interpolation. kn B n) to the ground plane image (A gn ,B gn ), complete geometric correction, and the final result is

[0183] S7(a g ,b g ) = interp{S6(K a ,b)}.

[0184] Table 1 shows the parameter settings involved in the simulation test of the present application. Nine point targets are arranged in a field-shaped pattern in the scene, with a distance interval of 1931.9m and an azimuth interval of 1488.9m. A sinusoidal motion error with a maximum amplitude of 5m is added along the line-of-sight direction, which has exceeded multiple range resolution cells. The scene azimuth width is greater than the aperture azimuth projection length. The present application focuses the image in the azimuth wavenumber domain, without zero padding to avoid image aliasing.

[0185] Table 1 Simulation parameter setting table

[0186] Center frequency 10 GHz Bandwidth 150 MHz Carrier speed 250 m / s Sampling rate 187.5 MHz Flight altitude 10 km PRF 750 Hz Range 80 km Azimuth resolution 1m Synthetic aperture time 23s Ground plane squint angle 75° Vertical aspect width 1 km Azimuth beam width 2.2°

[0187] Table 2 Point target simulation results

[0188]

[0189]

[0190] Figure 4 The two-dimensional simulation results of point target 1 and point target 5 are shown in the figure, and the simulation results are shown in Table 2. Point target 1 is located at the edge of the scene, and point target 5 is located at the center of the scene. After second-order motion compensation, each point target is well focused, the position is accurate, and the image has no geometric distortion. Since it is set to strip mode, the synthetic aperture angle of the scene edge target is small, and the resolution is reduced.

[0191] Figure 5 、 Figure 6 The measured data processing results are shown in the figure. The front angle is about 72°, and the resolution is 3m. Among them Figure 5 is the large-width full-scene image, Figure 6 is Figure 5 the local enlarged sub-image in the white box of the building area, and it can be seen that the image is well focused and the whole image has no geometric distortion.

[0192] The above is merely a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or replacements within the technical scope disclosed in the present application can be easily thought of by those skilled in the art, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A high-precision motion compensation and geometric correction method for large forward-looking SAR imaging, characterized in that, Includes the following steps: Step 1: Perform Doppler center estimation on the original echo to obtain the oblique angle plane, and construct the wavenumber spectrum center correction function; based on the wavenumber spectrum center correction function and the original echo, shift the azimuth wavenumber spectrum to the baseband to obtain the azimuth baseband echo; Step 2: Perform range-to-Fourier transform on the azimuth baseband echo and complete the first-order motion compensation based on the first-order motion compensation function at the radar reference slant range. Step 3: Transform the data after first-order motion compensation to the two-dimensional wavenumber domain, and complete scene center focusing and consistent compression according to the scene center reference function in the two-dimensional wavenumber domain; Step 4: Perform extended Stolt interpolation along the line of sight on the uniformly compressed two-dimensional wavenumber spectrum to obtain two-dimensional wavenumber spectra along the line of sight and perpendicular to the line of sight, thus achieving range-azimuth decoupling; Step 5: Transform the echo after extended Stolt interpolation to the two-dimensional spatial domain, and map the motion error of the original echo to the line of sight, thus completing the second-order motion compensation for the spatial variation of the line of sight. Step 6: Based on the data after second-order motion compensation and the quadratic reference function in the azimuth direction, perform spatial domain deslantification, transform to the azimuth wavenumber domain, complete target focusing, and obtain the oblique plane focused SAR image; Step 7: Based on the geometric mapping relationship between the target on the oblique plane along the line of sight and the ground plane, a distortion-free large forward-looking SAR image of the ground plane is obtained through two-dimensional interpolation geometric correction.

2. The high-precision large forward-looking SAR imaging motion compensation and geometric correction method according to claim 1, characterized in that, In step one, the azimuth wavenumber spectrum is transformed to baseband by multiplying the constructed wavenumber spectrum center correction function with the two-dimensional spatial domain expression of the original baseband echo, thus obtaining the azimuth baseband echo; where the wavenumber spectrum center correction function H azi_b (X,f dc )=exp{-jK xc X}, K xc K is the azimuth center wavenumber. xc =2πf dc / v,f dc denoted as azimuth Doppler center frequency of the original echo, and v is the aircraft's flight speed.

3. The high-precision large forward-looking SAR imaging motion compensation and geometric correction method according to claim 1, characterized in that, In step two, a range-to-Fourier transform is performed on the azimuth baseband echo, and then multiplied by the first-order motion compensation function at the reference imaging center to complete the first-order motion compensation; the first-order motion compensation function is H. moco_1st (X,K r )=exp{j2K r ·R err_1st (X)}, where K r =2π(f c +f r f / c is the range wavenumber, c is the speed of light, and f c f is the center frequency. r For the range-direction frequency of the transmitted LFM signal, -f s / 2≤f r ≤f s / 2,f s The sampling rate is the distance-oriented sampling rate.

4. The high-precision large forward-looking SAR imaging motion compensation and geometric correction method according to claim 3, characterized in that, In step three, after first-order motion compensation, the data is subjected to a Fourier transform along the azimuth direction to obtain the two-dimensional wavenumber spectrum of the scene center. The two-dimensional wavenumber spectrum is then multiplied by a two-dimensional wavenumber domain reference function to complete scene center focusing and uniform compression. The two-dimensional wavenumber domain reference function is: Wherein, P*(K r ) is P(K r The complex conjugate of ) It is the wavenumber spectrum of the transmitted LFM signal. B r K is the signal bandwidth. rc The wavenumber is the distance from the center. X c Y c K is a constant. X This represents the azimuth wave number.

5. The high-precision large forward-looking SAR imaging motion compensation and geometric correction method according to claim 4, characterized in that, In step five, the echo data after Stolt interpolation along the LOS direction is multiplied with the azimuth spatial domain spread function, then a two-dimensional inverse Fourier transform is performed to convert it to the two-dimensional spatial domain. The motion error of the original echo domain is mapped to the LOS direction, thus completing the second-order motion compensation for spatial variation along the LOS direction. The azimuth spatial domain spread function H... azi_ext (K a B c )for, Where K a For LOS ⊥ Wave number in direction, This is a constant value, representing the distance from the center of the aircraft's aperture to the center of the reference imaging.

6. The high-precision large forward-looking SAR imaging motion compensation and geometric correction method according to claim 5, characterized in that, In step six, the data after second-order motion compensation is multiplied with a quadratic phase reference function in the spatial domain to achieve LOS. ⊥ The direction has been adjusted to avoid the slant; The secondary descrambling reference function is: Where a is the LOS ⊥ The target position of the directional air change, b is the target position of the LOS directional air change.

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