A Bistatic ISAR Sparse Aperture Cross-Range Migration Correction Algorithm

Abstract

The present invention relates to a bistatic ISAR sparse aperture cross-range unit migration correction algorithm, comprising: constructing a sparse basis for each range unit based on a full-aperture radar echo signal; acquiring an initial sparse signal based on a linear frequency modulation signal emitted by a transmitting station to a target area at a receiving station; obtaining a sparse azimuth range signal based on the initial sparse signal and each sparse basis; performing likelihood estimation and iterative optimization on the sparse azimuth range signal to obtain an azimuth range signal; and performing an inverse Fourier transform on the azimuth range signal to obtain an inverse synthetic aperture radar image. The present invention has improved noise immunity and robustness, and can still complete compensation and high-quality imaging under low SNR conditions.

Description

Technical Field

[0001] The present invention relates to the field of radar echo technology, in particular to a bistatic ISAR sparse aperture cross-range unit migration correction algorithm. Background Art

[0002] Bistatic Inverse Synthetic Aperture Radar (Bi-ISAR) has unique advantages and potential in electronic warfare due to its separate transmit and receive mode. It enhances system flexibility and improves imaging probability, giving Bi-ISAR a natural advantage in countering the "four major threats" and becoming an important research direction in modern radar imaging technology.

[0003] After translation compensation, the target echo is converted into a turntable target. However, traditional envelope alignment methods can only correct for the linear range shift caused by the translation component, but are unable to correct for the range migration caused by the rotation component. If the target is large, or if higher resolution is required and a larger rotation angle is used, the range migration caused by rotation cannot be ignored. In 1999, Perry et al. proposed the Keystone transform, which eliminates the coupling between frequency and slow time through slow-time coordinate transformation, thus compensating for migration through resolution cells (MTRC).

[0004] However, in modern warfare, the presence of unpredictable non-cooperative target poses, the bi-directional transmit / receiver separation of Bi-ISAR (Inter-SAR SAR), the alternating transmission of wideband and narrowband signals, and frequency agility can lead to echo loss during observations, resulting in sparse apertures. Traditional MTRC correction methods, including Keystone, fail under sparse apertures and are unable to compensate for motion. In recent years, with the development of compressed sensing (CS) technology, many researchers have applied CS theory to ISAR imaging. This theory can achieve high-quality imaging under undersampling, paving the way for MTRC compensation in Bi-ISAR sparse apertures.

[0005] To achieve high-quality signal reconstruction and imaging, the reconstruction algorithm selected was based on a Bayesian framework. The MTRC process of sparse aperture ISAR imaging was modeled using a Laplace prior. Signal reconstruction was then performed using the Expectation Maximization-based Variational Bayesian (EM-VB) algorithm. However, this algorithm assumes that all elements in the target image follow the same Laplace distribution and does not distinguish between the amplitudes of individual pixels. Greedy iterative algorithms, such as Compressive Sampling Matching Pursuit (CoSaMP), were used for signal reconstruction. While these algorithms are simple in principle and easy to implement, they suffer from low reconstruction accuracy, and their performance is easily affected by low signal-to-noise ratio (SNR) conditions. Summary of the Invention

[0006] In view of this, the present invention provides a bistatic ISAR sparse aperture cross-range unit migration correction algorithm, which establishes a sparse basis for each range unit that contains Keystone transformation parameters and conforms to the bistatic angle time-varying property, fully utilizes the energy concentration and structural characteristics of the target during imaging, has better anti-noise interference ability and robustness, and can still complete compensation and high-quality imaging under low SNR conditions.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A bistatic ISAR sparse aperture cross-range unit migration correction algorithm, including:

[0009] Construct a sparse basis for each range unit based on the full-aperture radar echo signal;

[0010] The receiving station collects the echo signal of the linear frequency modulation signal transmitted by the transmitting station to the target area, and obtains the initial sparse signal;

[0011] Obtaining a sparse azimuth and distance signal based on the initial sparse signal and each of the sparse bases;

[0012] Performing likelihood estimation on the sparse azimuth and distance signals and performing iterative optimization to obtain azimuth and distance signals;

[0013] Performing inverse Fourier transform on the azimuth range signal to obtain an inverse synthetic aperture radar image.

[0014] Preferably, constructing a sparse basis for each distance unit based on the full-aperture radar echo signal includes:

[0015] Transmitting a linear frequency modulation signal to a target area based on a transmitting station, collecting all echo signals, and obtaining the full-aperture radar echo signal;

[0016] performing frequency down-conversion and range compression on the full-aperture radar echo signal to obtain a full-aperture compressed signal;

[0017] Approximating the full-aperture compression signal to obtain a full-aperture approximation signal;

[0018] performing translation compensation on the full-aperture approximate signal to obtain a full-aperture compensated signal;

[0019] Converting the full-aperture compensation signal from the fast time domain to the range frequency domain-azimuth time domain to obtain a test full-aperture azimuth range signal;

[0020] Performing a Keystone transform on the test full-aperture azimuth range signal to obtain a test correction signal;

[0021] A sparse basis of each of the distance cells is obtained based on the test correction signal.

[0022] Preferably, the step of collecting, by the receiving station, an echo signal of a linear frequency modulation signal transmitted by the transmitting station to the target area to obtain an initial sparse signal includes:

[0023] Based on the linear frequency modulation signal transmitted by the transmitting station to the target area, the echo signal is collected by the receiving station to obtain the received sparse signal;

[0024] down-converting and range-compressing the received sparse signal to obtain a sparse aperture compressed signal;

[0025] Down-converting and range-compressing a reference signal to obtain a reference compressed signal; the reference signal is a complex conjugate of the transmitted linear frequency modulation signal;

[0026] The sparse aperture compressed signal and the reference compressed signal are multiplied to obtain the initial sparse signal.

[0027] Preferably, obtaining a sparse azimuth and distance signal based on the initial sparse signal and each of the sparse bases includes:

[0028] Decomposing the initial sparse signal to obtain a sparse signal of each distance unit;

[0029] The sparse signal of each distance unit is divided by the corresponding sparse basis to obtain the signal to be solved of each distance unit; the sparse azimuth distance signal includes the signal to be solved of each distance unit.

[0030] Preferably, performing likelihood estimation on the sparse azimuth range signal and performing iterative optimization to obtain the azimuth range signal includes:

[0031] The following process is performed on the signal to be solved of each distance unit to obtain the azimuth distance signal, where the azimuth distance signal includes the solution signal of each distance unit:

[0032] Performing likelihood estimation on the signal to be solved to obtain an estimated signal;

[0033] Constructing solution parameters based on the estimated signal;

[0034] The estimated signal is solved by using a conjugate gradient method in combination with the solution parameters, and iterative optimization is performed based on the Cauchy-Newton method to obtain the solution signal.

[0035] The present invention also provides a bistatic ISAR sparse aperture cross-range unit migration correction system, comprising:

[0036] Sparse basis module, used to construct a sparse basis of each range unit based on the full-aperture radar echo signal;

[0037] A signal module is used to collect, based on the receiving station, an echo signal of the linear frequency modulation signal transmitted by the transmitting station to the target area to obtain an initial sparse signal;

[0038] A sparse module, configured to obtain a sparse azimuth and distance signal based on the initial sparse signal and each of the sparse bases;

[0039] A solution module, configured to perform likelihood estimation on the sparse azimuth and distance signals and perform iterative optimization to obtain azimuth and distance signals;

[0040] The imaging module is used to perform inverse Fourier transform on the azimuth range signal to obtain an inverse synthetic aperture radar image.

[0041] Preferably, the sparse basis module includes:

[0042] A full-aperture signal acquisition unit, configured to transmit a linear frequency modulation signal to a target area based on a transmitting station, collect all echo signals, and obtain the full-aperture radar echo signal;

[0043] a full-aperture preprocessing unit, configured to perform frequency down-conversion and range compression on the full-aperture radar echo signal to obtain a full-aperture compressed signal;

[0044] an approximation unit, configured to approximate the full-aperture compression signal to obtain a full-aperture approximation signal;

[0045] a compensation unit, configured to perform translation compensation on the full-aperture approximation signal to obtain a full-aperture compensated signal;

[0046] a transform unit, configured to transform the full-aperture compensation signal from a fast time domain to a range-frequency-azimuth time domain to obtain a test full-aperture azimuth range signal;

[0047] a correction unit, configured to perform a Keystone transform on the test full-aperture azimuth range signal to obtain a test correction signal;

[0048] A sparse basis unit is used to obtain a sparse basis of each of the distance units based on the test correction signal.

[0049] Preferably, the signal module includes:

[0050] A sparse signal acquisition unit is used to acquire an echo signal based on a linear frequency modulation signal transmitted by a transmitting station to a target area and based on a receiving station to obtain a received sparse signal;

[0051] a sparse preprocessing unit, configured to perform down-conversion and range compression on the received sparse signal to obtain a sparse aperture compressed signal;

[0052] A reference signal preprocessing unit, configured to perform down-conversion and range compression on a reference signal to obtain a reference compressed signal; the reference signal being the complex conjugate of the transmitted linear frequency modulation signal;

[0053] A product unit is configured to multiply the sparse aperture compressed signal and the reference compressed signal to obtain the initial sparse signal.

[0054] Preferably, the sparse module includes:

[0055] a decomposition unit, configured to decompose the initial sparse signal to obtain a sparse signal of each distance unit;

[0056] A division unit is used to divide the sparse signal of each distance unit by the corresponding sparse basis to obtain the signal to be solved of each distance unit; the sparse azimuth distance signal includes the signal to be solved of each distance unit.

[0057] Preferably, the solution module includes: a repeated execution unit, an estimation unit, a parameter unit and a solution optimization unit;

[0058] The repeatedly executing unit is configured to execute the estimation unit, the parameter unit, and the solution optimization unit on the signal to be solved of each distance unit to obtain the azimuth distance signal, wherein the azimuth distance signal includes the solution signal of each distance unit;

[0059] The estimation unit is used to perform likelihood estimation on the signal to be solved to obtain an estimated signal;

[0060] The parameter unit is used to construct a solution parameter based on the estimated signal;

[0061] The solution optimization unit is used to adopt the conjugate gradient method in combination with the solution parameters to solve the estimated signal, and perform iterative optimization based on the Cauchy-Newton method to obtain the solution signal.

[0062] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0063] The present invention relates to a bistatic ISAR sparse aperture cross-range unit migration correction algorithm, comprising: constructing a sparse basis for each range unit based on a full-aperture radar echo signal; acquiring an initial sparse signal based on a linear frequency modulation signal emitted by a transmitting station to a target area at a receiving station; obtaining a sparse azimuth range signal based on the initial sparse signal and each sparse basis; performing likelihood estimation and iterative optimization on the sparse azimuth range signal to obtain an azimuth range signal; and performing an inverse Fourier transform on the azimuth range signal to obtain an inverse synthetic aperture radar image. The present invention has improved noise immunity and robustness, and can still complete compensation and high-quality imaging under low SNR conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0065] Figure 1 This is a flow chart of the bistatic ISAR sparse aperture cross-range unit migration correction algorithm of the present invention;

[0066] Figure 2 This is a structural diagram of the bistatic ISAR sparse aperture cross-range unit migration correction system of the present invention;

[0067] Figure 3 It is the geometric model of bistatic inverse synthetic aperture radar imaging;

[0068] Figure 4 This is a simulation scene diagram for Bi-ISAR sparse aperture maneuvering target imaging;

[0069] Figure 5 is a scattering point model;

[0070] Figure 6 This is the full-aperture imaging result diagram;

[0071] Figure 7The figure is a comparison of imaging results under different SNRs between the present invention and the prior art.

[0072] Explanation of symbols: 1. Sparse basis module; 2. Signal module; 3. Sparse module; 4. Solution module; 5. Imaging module. DETAILED DESCRIPTION

[0073] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0074] The purpose of the present invention is to provide a bistatic ISAR sparse aperture cross-range unit migration correction algorithm, which establishes a sparse basis containing Keystone transformation parameters and conforming to the bistatic angle time-varying property for each range unit, fully utilizes the energy concentration and structural characteristics of the target during imaging, has better noise interference resistance and robustness, and can still complete compensation and high-quality imaging under low SNR conditions.

[0075] The principle of bistatic inverse synthetic aperture radar imaging is as follows Figure 3 As shown in the figure, Tr is the transmitting station, Re is the receiving station, L is the radar baseline length, and E is the equivalent monostatic radar position. Assume that the target moves uniformly in space with a velocity of v and an acceleration of a0. At the imaging start time t0, the target mass center is O, the bistatic angle at time t0 is β0, and with the target mass center as the origin and the bistatic angle bisector as the y-axis, a right-handed coordinate system xOy is established. The coordinates of the scattering point P in this coordinate system are (x p ,y p ), OP length is d, and the angle with x-axis is α0. m At this moment, the target center of mass moves to O m Point, coordinate system x'Oy' is obtained by translating coordinate system xOy, with O m is the origin, t m The bistatic angle β at time m The bisector is the v axis, and the right-hand coordinate system uO is established. m v, the coordinates of the scattering point P in this coordinate system are O m The angle between P and u axis is α m , the equivalent turning angle of the equivalent monostatic radar is θ m .

[0076] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0077] Figure 1 This is a flow chart of the bistatic ISAR sparse aperture cross-range unit migration correction algorithm of the present invention. Figure 1 As shown, the present invention provides a bistatic ISAR sparse aperture cross-range unit migration correction algorithm, comprising:

[0078] Step S1: construct a sparse basis for each range unit based on the full-aperture radar echo signal.

[0079] Specifically, step S1 includes:

[0080] In step S11, a linear frequency modulation (LFM) signal is transmitted to the target area based on the transmitting station, and all echo signals are collected to obtain the full-aperture radar echo signal. The linear frequency modulation signal is shown in formula (1).

[0081]

[0082] Where: A represents the backscatter amplitude, rect(·) represents the rectangular window function and t represents full time, t m =mPRT represents slow time, PRT is the pulse repetition period, represents fast time, M represents the total number of pulses, m is an integer from 1 to M, T p is the pulse width, f c is the carrier frequency, μ is the modulation frequency, j is the imaginary unit, 2 =-1.

[0083] Assume that the target contains K scattering points, R k (t m ) represents the kth scattering point at slow time t m The sum of the distances from the transmitting station and the receiving station at any moment (the echo signal analysis adopts the "stop-go" assumption).

[0084]

[0085] Among them, R T (t m ) indicates that the target equivalent rotation center is at t m The instantaneous distance to the transmitting station and the receiving station at the moment, β m Corresponding to t m The bistatic angle at time θ m represents the rotation angle of the target, Indicates the distance change due to target rotation.

[0086] Step S12: down-convert and range-compress the full-aperture radar echo signal to obtain a full-aperture compressed signal. The full-aperture compressed signal is shown in formula (3).

[0087]

[0088] Among them, σ k is the backscattering coefficient corresponding to the kth scattering point, c is the propagation speed of electromagnetic waves, and B represents the bandwidth.

[0089] Step S13: Approximate the full-aperture compression signal to obtain a full-aperture approximation signal.

[0090] Considering that the distance change of the scattering point on the observed target in the direction of the radar line of sight is greater than one range resolution unit due to rotation, the target's migration across range units cannot be ignored. The following approximation can be made: ω is the equivalent angular velocity of rotation, ω a is the equivalent rotational angular acceleration. Therefore, equation (3) is approximately as follows:

[0091]

[0092] In formula (4), due to the sinc envelope The correlation term is usually smaller than a distance unit, so only the influence of the slow time first order term on the envelope is considered, while the phase part needs to be considered. It can be seen from Equation (4) that the echo envelope will change with slow time due to rotation, which is why MTRC is generated.

[0093] Step S14: performing translation compensation on the full-aperture approximation signal to obtain a full-aperture compensation signal. The full-aperture compensation signal is shown in formula (5).

[0094]

[0095] Where: σ' k is σ k The combination of some constant terms, which are terms that are irrelevant to imaging, such as y in formula (4) k .

[0096] Step S15: transform the full-aperture compensation signal from the fast time domain to the range frequency domain-azimuth time domain to obtain a test full-aperture azimuth range signal. The test full-aperture azimuth range signal is shown in formula (6).

[0097]

[0098] Where: σ” k Also represents σ k Combined with some constant terms.

[0099] Step S16: performing a Keystone transform on the test full-aperture azimuth range signal to obtain a test correction signal.

[0100] From formula (6), we can see that the fundamental reason for the occurrence of MTRC is the distance dimension frequency f r and azimuth time t m The cross coupling is generated in the second exponential term, the distance dimension frequency f r The larger the change, the greater the phase change with azimuth time t m The faster the change. Since the existence of high-order phase will not affect the MTRC correction, in the theoretical derivation, it is assumed that the high-order phase has been eliminated. Using Keystone transform This coupling relationship can be eliminated to correct the MTRC. The test correction signal is as follows:

[0101]

[0102] Step S17: obtaining a sparse basis of each of the distance units based on the test correction signal.

[0103] Step S2: The receiving station collects the echo signal of the linear frequency modulation signal transmitted by the transmitting station to the target area to obtain an initial sparse signal.

[0104] Furthermore, the step S2 includes:

[0105] Step S21 : Based on the linear frequency modulation signal transmitted by the transmitting station to the target area, the echo signal is collected by the receiving station to obtain a received sparse signal.

[0106] Step S22: down-convert and range-compress the received sparse signal to obtain a sparse aperture compressed signal.

[0107] Step S23 , down-converting and range-compressing the reference signal to obtain a reference compressed signal; the reference signal is the complex conjugate of the transmitted linear frequency modulation signal.

[0108] Step S24: multiply the sparse aperture compressed signal and the reference compressed signal to obtain the initial sparse signal.

[0109] When radar signals have a wide bandwidth, large imaging angles, and long observation times, target rotation during the imaging time can cause first-order motion and second-order curvature of the one-dimensional range profile. Generally, the envelope curvature caused by the rotational component is small and negligible, necessitating correction for the first-order motion. For echo signals in slow-time sparse apertures, discontinuities cause the signal to lose coherence. The Keystone transform cannot be directly applied under sparse aperture conditions. Instead, the data must be converted to the range-frequency-azimuth-time domain. Then, corresponding basis matrices are constructed for different range units. This approach not only corrects for inter-pulse range motion in sparse sampling but also restores and reconstructs the one-dimensional range profile at the locations where samples are missing.

[0110] In order to better illustrate the sparse aperture model, the scattering area of the target scene is divided into grids of equal size. The size of each grid is Δx×Δy, where Δx is the azimuth resolution of the full aperture, x=uΔx, λ c is the wavelength, T m is the total imaging time. Δy is the distance resolution of the full aperture, y = vΔy, For the slow time t m and fast time The following replacements can be made: m =hT r , in, Q represents the number of range cells of full aperture data, and H represents the number of Doppler cells of full aperture data. r =T m / H, PRT represents the pulse repetition period, T s =T p / Q, h represents slow time t m The number of blocks divided, T r The length of slow time is divided, and q represents fast time The number of blocks divided, T s is the length of the fast time division. Therefore, the radar signal can be written as:

[0111]

[0112] Where Y(h,q)=s(hT r ,qT s ) represents the radar echo after translation compensation as shown in (5), and X(u,v)=σ(uΔx,vΔy) represents the ISAR image to be focused. s represents the sampling frequency, are the parameters based on the Keystone transformation.

[0113] Therefore, for each distance unit in the frequency domain, the following model can be constructed:

[0114] Y q =A q Xb q =A q a (9)

[0115] Y q represents the echo signal within the qth range unit, X represents the ISAR image, b q =exp(-j2πqv / Q) represents the Fourier basis corresponding to the qth distance unit during distance compression, Indicates containing α q The azimuthally compressed variable-scale Fourier transform basis of the parameters and the time-varying bistatic angle is the sparse basis of the qth distance unit, where the bistatic angle can be obtained according to the geometric relationship, a∈C H Indicates the range frequency domain-azimuth time domain signal that needs to be solved. In the case of sparse aperture, an underdetermined sampling data selection matrix Ψ can be defined by removing the rows of the identity matrix according to the sparse data sparsity pattern. Therefore, the sparse aperture radar echo can be expressed as ΨY q Therefore, formula (9) can be written as

[0116] y=Φa+r (10)

[0117] Where y = ΨY q ∈C Z×1 Represents the effective aperture echo signal, Φ=ΨA q ∈C Z×Q Represents the sparse basis matrix formed after removing the rows corresponding to the missing aperture, r∈C Z×1 represents the complex noise matrix, Z represents the effective aperture number, and C represents the complex domain.

[0118] Step S3: obtaining a sparse azimuth and distance signal based on the initial sparse signal and each of the sparse bases.

[0119] Preferably, step S3 includes:

[0120] Step S31: Decompose the initial sparse signal to obtain a sparse signal of each distance unit.

[0121] Step S32: Divide the sparse signal of each distance unit by the corresponding sparse basis to obtain the signal to be solved of each distance unit; the sparse azimuth distance signal includes the signal to be solved of each distance unit.

[0122] Step S4: performing likelihood estimation on the sparse azimuth and distance signals and performing iterative optimization to obtain azimuth and distance signals.

[0123] Specifically, step S4 includes:

[0124] Step S41 , executing steps S42 - S44 on the signal to be solved of each distance unit to obtain the azimuth distance signal, wherein the azimuth distance signal includes the solved signal of each distance unit.

[0125] Step S42: performing likelihood estimation on the signal to be solved to obtain an estimated signal.

[0126] Assume r is complex Gaussain white noise, whose elements are random and independent and identically distributed, obeying the complex Gaussain distribution, with mean 0 and variance δ 2 , then the probability density function of r is:

[0127]

[0128] At a given a, δ 2 Under these conditions, the likelihood function corresponding to the echo data can be expressed as

[0129]

[0130] In order to make better use of the sparse information of the image, the Laplace probability distribution is used to characterize the sparsity of the target. Assume that each pixel a of the target mn Obey different Laplace prior distributions, then,

[0131]

[0132] Where, γ hq is the Laplace scaling factor, || ||2 represents the 2-norm operation, || ||1 represents the 1-norm operation, and F represents the missing A. q .

[0133] The MTRC concurrent imaging problem of Bi-ISAR sparse aperture maneuvering targets can be viewed as the reconstruction problem of estimating the target range frequency domain-azimuth time domain signal a from the effective echo data y. Combined with the Bayesian criterion, the maximum a posteriori probability estimation function of signal a can be established:

[0134]

[0135] Where, represents the estimated value of the range frequency domain-azimuth time domain signal a. Taking the logarithm of equation (14), we have

[0136]

[0137] Substituting equations (12) and (13) into (15), we can obtain

[0138]

[0139] Where T represents transpose, w represents weight matrix,

[0140] It can be seen from formula (14) that by introducing the non-identical distribution sparse prior model, that is, using the Laplace prior scale coefficient γ hq If the amplitude of the scattering point is large, the γ value is set to a smaller value to increase the possibility of its large value. If the amplitude of the scattering point is small or it is a noise space, the γ value is set to a larger value to achieve a suppression effect. This weight matrix that distinguishes the amplitude of each pixel can improve the ability to extract scattering points and suppress noise.

[0141] Step S43: constructing solution parameters based on the estimated signal.

[0142] Step S44: using the conjugate gradient method in combination with the solution parameters to solve the estimated signal, and performing iterative optimization based on the Cauchy-Newton method to obtain the solution signal.

[0143] According to equation (16), we can solve a to get the range frequency domain-azimuth time domain signal. First, we need to solve the Laplace prior scale coefficient γ hq , and then solve the l1 norm optimization problem.

[0144] Solve γ hq and noise variance δ 2 The estimated value is first estimated by the maximum likelihood method, and the likelihood function is taken in the logarithmic domain and the scale coefficient γ is obtained by derivation. hq Estimates.

[0145]

[0146] After the echo is compensated for translation, the Doppler shift is basically eliminated. It is believed that the target is concentrated around zero Doppler and the noise is mainly distributed in the high-frequency area of Doppler. The noise variance δ is obtained by using the high-frequency area as the noise sample. 2 The maximum likelihood estimate of Then, a constant false alarm rate (CFAR) detector is established using the noise sample. The part with an amplitude greater than the CFAR threshold is identified as the target, and the other part is regarded as noise and reset to zero. The strong scattering center is detected and denoised on the range Doppler (RD) image of SA-ISAR. The scale coefficients γ are calculated from the denoised image and formula (17). hq Estimated value of The scale coefficient matrix w is obtained. The estimation of noise variance will affect the final image quality. In order to obtain a higher quality image, manual adjustment can also be performed based on the estimated noise variance.

[0147] It can be seen from formula (17) that the size of the scale factor is related to the amplitude of each pixel in the image, that is, the weighted l1 norm constrained optimization algorithm determines the weight size by the size of the non-zero element in the target image. Therefore, the difference in the amplitude of the non-zero element is utilized in the imaging process, which is more conducive to improving the imaging accuracy and noise resistance.

[0148] The l1-weighted norm optimization algorithm mainly solves the optimization problem expressed in Equation (16). It can be solved using the Cauchy-Newton iteration method and the conjugate gradient method is used to accelerate the convergence speed. The specific process is as follows:

[0149] Since the l1 norm in Equation (16) is not differentiable at zero, we can first introduce a smooth approximation:

[0150]

[0151] Where, is a small non-negative constant, then the optimization problem in formula (16) can be approximately expressed as:

[0152]

[0153] make Then its conjugate gradient function can be written as:

[0154]

[0155] Where,

[0156] Construct diagonal matrices H(a) and U(a), which are the parameters required by the algorithm. The superscript H is the conjugate transpose.

[0157] According to Newton's method, the g+1th iteration expression of the range frequency domain-azimuth time domain signal a is:

[0158]

[0159] Where β is the iteration step size. Substituting equation (20) into equation (22) and setting β = 1, we can obtain the estimated value of the range frequency domain-azimuth time domain signal:

[0160] a (g+1) =2H(a (g) ) -1 F H y (23)

[0161] In order to avoid the large amount of computation caused by matrix inversion, the conjugate gradient method can be used to solve equation (23), and the obtained a (g+1) That is the reconstructed range frequency domain-azimuth frequency domain signal.

[0162] Step S5: performing inverse Fourier transform on the azimuth range signal to obtain an inverse synthetic aperture radar image.

[0163] Figure 2 This is a structural diagram of the bistatic ISAR sparse aperture cross-range unit migration correction system of the present invention. Figure 2 As shown, the present invention provides a bistatic ISAR sparse aperture cross-range unit migration correction system, comprising: a sparse basis module 1, a signal module 2, a sparse module 3, a solution module 4 and an imaging module 5.

[0164] The sparse basis module 1 is used to construct a sparse basis of each range unit based on the full-aperture radar echo signal.

[0165] The signal module 2 is used to collect the echo signal of the linear frequency modulation signal transmitted by the transmitting station to the target area based on the receiving station to obtain an initial sparse signal.

[0166] The sparse module 3 is used to obtain a sparse azimuth distance signal based on the initial sparse signal and each sparse basis.

[0167] The solving module 4 is used to perform likelihood estimation on the sparse azimuth and distance signals and perform iterative optimization to obtain azimuth and distance signals.

[0168] The imaging module 5 is used to perform inverse Fourier transform on the azimuth range signal to obtain an inverse synthetic aperture radar image.

[0169] Specifically, the sparse basis module 1 includes: a full-aperture signal acquisition unit, a full-aperture preprocessing unit, an approximation unit, a compensation unit, a transformation unit, a correction unit and a sparse basis unit.

[0170] The full-aperture signal acquisition unit is used to transmit a linear frequency modulation signal to a target area based on a transmitting station, collect all echo signals, and obtain the full-aperture radar echo signal.

[0171] The full-aperture preprocessing unit is used to perform down-conversion and range compression on the full-aperture radar echo signal to obtain a full-aperture compressed signal.

[0172] The approximation unit is used to approximate the full-aperture compression signal to obtain a full-aperture approximation signal.

[0173] The compensation unit is used to perform translation compensation on the full-aperture approximation signal to obtain a full-aperture compensated signal.

[0174] The transformation unit is used to transform the full-aperture compensation signal from the fast time domain to the range frequency domain-azimuth time domain to obtain a test full-aperture azimuth range signal.

[0175] The correction unit is used to perform Keystone transformation on the test full-aperture azimuth range signal to obtain a test correction signal.

[0176] The sparse basis unit is used to obtain a sparse basis of each of the distance units based on the test correction signal.

[0177] Furthermore, the signal module 2 includes: a sparse signal acquisition unit, a sparse preprocessing unit, a reference signal preprocessing unit and a product unit.

[0178] The sparse signal acquisition unit is used to acquire the received sparse signal based on the linear frequency modulation signal transmitted by the transmitting station to the target area and the echo signal collected by the receiving station.

[0179] The sparse preprocessing unit is used to perform down-conversion and range compression on the received sparse signal to obtain a sparse aperture compressed signal.

[0180] The reference signal preprocessing unit is used to perform down-conversion and range compression on the reference signal to obtain a reference compressed signal; the reference signal is the complex conjugate of the transmitted linear frequency modulation signal.

[0181] The multiplication unit is used to multiply the sparse aperture compressed signal and the reference compressed signal to obtain the initial sparse signal.

[0182] Preferably, the sparse module 3 includes: a decomposition unit and a division unit.

[0183] The decomposition unit is used to decompose the initial sparse signal to obtain a sparse signal of each distance unit.

[0184] The division unit is used to divide the sparse signal of each distance unit by the corresponding sparse basis to obtain the signal to be solved of each distance unit; the sparse azimuth distance signal includes the signal to be solved of each distance unit.

[0185] Furthermore, the solution module includes: a repeated execution unit, an estimation unit, a parameter unit and a solution optimization unit.

[0186] The repeated execution unit is used to execute the estimation unit, the parameter unit and the solution optimization unit on the signal to be solved of each distance unit to obtain the azimuth distance signal, which includes the solution signal of each distance unit.

[0187] The estimation unit is used to perform likelihood estimation on the signal to be solved to obtain an estimated signal.

[0188] The parameter unit is used to construct a solution parameter based on the estimated signal.

[0189] The solution optimization unit is used to adopt the conjugate gradient method in combination with the solution parameters to solve the estimated signal, and perform iterative optimization based on the Cauchy-Newton method to obtain the solution signal.

[0190] The method provided by the present invention is simulated in an experimental environment using a Windows 10 64-bit operating system and a Matlab R2018b software platform. The main parameters of the computer used for the simulation are: an Intel Core i7-6700HQ processor with a main frequency of 2.60GHz and a memory of 16.0GB. This section verifies the performance of the method provided by the present invention from the perspective of echo SNR through experimental simulation. In order to conveniently and intuitively illustrate the superiority of the algorithm, the target to background ratio (TBR) and image entropy E are used. n As a benchmark, here's a brief description of both:

[0191]

[0192] In formula (24), T and B represent the signal inside the target area and the signal outside the target area respectively, A represents the target image, TBR is the ratio of the signal intensity within the target area to the signal intensity outside the target area. It can effectively characterize the SNR of the imaging and evaluate the estimation accuracy and noise suppression performance of the imaging. The larger the value, the better. Image entropy value E n It is used to reflect the average amount of information in the image and can evaluate the overall quality of the target image. The smaller the value, the better the effect.

[0193] Bi-ISAR sparse aperture maneuvering target imaging simulation scenario Figure 4 As shown, the target scattering point model is as follows Figure 5 As shown, the full aperture range-Doppler imaging results are as follows Figure 6 As shown in the figure, it can be seen that the scattering points have different degrees of cross-range unit migration. Assume that the length of the double base baseline is 40km, and the target is at an altitude of 20km with v = 400m / s and a = 10m / s. 2 The speed moves uniformly to the right from the median of the transmitting and receiving radar distance. The median of the transmitting and receiving radar distance is used as the imaging starting point, and 500 pulses are intercepted as imaging data. The cumulative rotation angle during the observation time is 3.857°, and the bistatic angle variation range is (85.90°, 88.21°). The simulation parameter settings are shown in Table 1.

[0194] Table 1 Imaging parameters

[0195]

[0196] To further illustrate the robustness of the present invention, the present invention is compared with the EM-VB algorithm and the CoSaMP algorithm under different SNR conditions, considering the case where the sparse aperture is 50% random missing data. Figure 7 (a) is the imaging result of EM-VB algorithm when SNR is 20dB. Figure 7 (b) is the imaging result of CoSaMP algorithm when SNR is 20dB. Figure 7 (c) is the imaging result of the present invention when the SNR is 20dB; Figure 7 (d) is the imaging result of EM-VB algorithm when SNR is 10dB. Figure 7 (e) is the imaging result of CoSaMP algorithm when SNR is 10dB. Figure 7 (f) is the imaging result of the present invention when the SNR is 10dB; Figure 7 (g) is the imaging result of EM-VB algorithm when SNR is 5dB. Figure 7 (h) is the imaging result of CoSaMP algorithm when SNR is 5dB. Figure 7 (i) is the imaging result of the present invention when the SNR is 2dB; Figure 7 (j) is the imaging result of the EM-VB algorithm when the SNR is 0dB. Figure 7 (k) is the imaging result of CoSaMP algorithm when SNR is 0dB. Figure 7 (1) is the imaging result of the present invention when the SNR is 0 dB; the imaging indicators are shown in Table 2.

[0197] Depend on Figure 7 It can be seen that when the SNR is high, the three algorithms can all achieve compensation and imaging well, the compensation is good, and the scattering points are clearer. As the SNR decreases, the EM-VB algorithm and the CoSaMP algorithm are gradually affected by noise. The EM-VB algorithm gradually cannot clearly distinguish between scattering points and noise scattering points. The CoSaMP scattering points gradually become defocused, and false scattering points appear at the same time. The quality of the imaging results of the method of the present invention is less affected by the SNR. When the SNR is 0dB, the CoSaMP algorithm has more false scattering points. In the imaging results of the EM-VB algorithm, the scattering points have been submerged by noise, and it is impossible to distinguish between real scattering points and false scattering points. It can be seen from the data in Table 2 that as the SNR decreases, the entropy values of the imaging results of the EM-VB algorithm and the CoSaMP algorithm gradually increase, and the entropy value of the present invention is at a lower level and changes slowly. The TBR values of the EM-VB algorithm and the CoSaMP algorithm decrease more significantly, and the TBR value of the present invention always remains at a higher level.

[0198] Therefore, it can be seen from the experimental results that the method of the present invention can complete the MTRC of maneuvering targets under the sparse aperture of Bi-ISAR, and the Laplace prior scale coefficient γ hqA weight matrix w was established, and the weight size was determined by the amplitude of each pixel, reflecting the size difference of the non-zero element amplitude. Not only was the imaging accuracy higher, but the noise resistance was also better. The entropy value and TBR reflected the above conclusions, with stronger scattering point extraction capabilities and better noise resistance.

[0199] Table 2 Comparison of imaging indicators under different SNR conditions

[0200]

[0201] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0202] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A method for correcting the cross-range unit migration of a sparse aperture bistatic ISAR, characterized by: include: Constructing a sparse basis for each distance unit based on a full-aperture radar echo signal, the method comprises: transmitting a linear frequency modulation signal to a target area based on a transmitting station, collecting all echo signals to obtain the full-aperture radar echo signal; down-converting and range-compressing the full-aperture radar echo signal to obtain a full-aperture compressed signal; approximating the full-aperture compressed signal to obtain a full-aperture approximation signal; performing translation compensation on the full-aperture approximation signal to obtain a full-aperture compensated signal; transforming the full-aperture compensated signal from a fast time domain to a range frequency domain-azimuth time domain to obtain a test full-aperture azimuth range signal; performing Keystone transformation on the test full-aperture azimuth range signal to obtain a test correction signal; and obtaining a sparse basis for each distance unit based on the test correction signal; The receiving station collects the echo signal of the linear frequency modulation signal transmitted by the transmitting station to the target area, and obtains the initial sparse signal; Obtaining a sparse azimuth and distance signal based on the initial sparse signal and each of the sparse bases; Performing likelihood estimation on the sparse azimuth and distance signals and performing iterative optimization to obtain azimuth and distance signals; Performing inverse Fourier transform on the azimuth range signal to obtain an inverse synthetic aperture radar image.

2. The bistatic ISAR sparse aperture cross-range unit migration correction method according to claim 1, characterized in that: The step of collecting the echo signal of the linear frequency modulation signal transmitted by the transmitting station to the target area based on the receiving station to obtain the initial sparse signal includes: Based on the linear frequency modulation signal transmitted by the transmitting station to the target area, the echo signal is collected by the receiving station to obtain the received sparse signal; down-converting and range-compressing the received sparse signal to obtain a sparse aperture compressed signal; Down-converting and range-compressing a reference signal to obtain a reference compressed signal; the reference signal is a complex conjugate of the transmitted linear frequency modulation signal; The sparse aperture compressed signal and the reference compressed signal are multiplied to obtain the initial sparse signal.

3. The bistatic ISAR sparse aperture cross-range unit migration correction method according to claim 1, characterized in that: The obtaining of a sparse azimuth and distance signal based on the initial sparse signal and each of the sparse bases includes: Decomposing the initial sparse signal to obtain a sparse signal of each distance unit; The sparse signal of each distance unit is divided by the corresponding sparse basis to obtain the signal to be solved of each distance unit; the sparse azimuth distance signal includes the signal to be solved of each distance unit.

4. The bistatic ISAR sparse aperture cross-range unit migration correction method according to claim 3, characterized in that: The performing likelihood estimation on the sparse azimuth and distance signals and performing iterative optimization to obtain the azimuth and distance signals includes: The following process is performed on the signal to be solved of each distance unit to obtain the azimuth distance signal, wherein the azimuth distance signal includes the solution signal of each distance unit: performing likelihood estimation on the signal to be solved to obtain an estimated signal; Constructing solution parameters based on the estimated signal; The estimated signal is solved by using a conjugate gradient method in combination with the solution parameters, and iterative optimization is performed based on the Cauchy-Newton method to obtain the solution signal.

5. A bistatic ISAR sparse aperture cross-range unit migration correction system, characterized by: include: Sparse basis module, used to construct a sparse basis of each range unit based on the full-aperture radar echo signal; A signal module is used to collect, based on the receiving station, an echo signal of the linear frequency modulation signal transmitted by the transmitting station to the target area to obtain an initial sparse signal; A sparse module, configured to obtain a sparse azimuth and distance signal based on the initial sparse signal and each of the sparse bases; A solution module, configured to perform likelihood estimation on the sparse azimuth and distance signals and perform iterative optimization to obtain azimuth and distance signals; The imaging module is used to perform inverse Fourier transform on the azimuth range signal to obtain an inverse synthetic aperture radar image.

6. The bistatic ISAR sparse aperture cross-range unit migration correction system according to claim 5, characterized in that: The sparse basis module includes: A full-aperture signal acquisition unit, configured to transmit a linear frequency modulation signal to a target area based on a transmitting station, collect all echo signals, and obtain the full-aperture radar echo signal; a full-aperture preprocessing unit, configured to perform frequency down-conversion and range compression on the full-aperture radar echo signal to obtain a full-aperture compressed signal; an approximation unit, configured to approximate the full-aperture compression signal to obtain a full-aperture approximation signal; a compensation unit, configured to perform translation compensation on the full-aperture approximation signal to obtain a full-aperture compensated signal; A transformation unit is used to transform the full aperture compensation signal from the fast time domain to the range frequency domain-azimuth time domain to obtain Test full aperture azimuth range signal; a correction unit, configured to perform a Keystone transform on the test full-aperture azimuth range signal to obtain a test correction signal; A sparse basis unit is used to obtain a sparse basis of each of the distance units based on the test correction signal.

7. The bistatic ISAR sparse aperture cross-range unit migration correction system according to claim 5, characterized in that: The signal module includes: A sparse signal acquisition unit is used to acquire an echo signal based on a linear frequency modulation signal transmitted by a transmitting station to a target area and based on a receiving station to obtain a received sparse signal; a sparse preprocessing unit, configured to perform down-conversion and range compression on the received sparse signal to obtain a sparse aperture compressed signal; A reference signal preprocessing unit, configured to perform down-conversion and range compression on a reference signal to obtain a reference compressed signal; the reference signal being the complex conjugate of the transmitted linear frequency modulation signal; A product unit is configured to multiply the sparse aperture compressed signal and the reference compressed signal to obtain the initial sparse signal.

8. The bistatic ISAR sparse aperture cross-range unit migration correction system according to claim 5, characterized in that: The sparse module includes: a decomposition unit, configured to decompose the initial sparse signal to obtain a sparse signal of each distance unit; A division unit is used to divide the sparse signal of each distance unit by the corresponding sparse basis to obtain the signal to be solved of each distance unit; the sparse azimuth distance signal includes the signal to be solved of each distance unit.

9. The bistatic ISAR sparse aperture cross-range unit migration correction system according to claim 5, characterized in that: The solution module includes: a repeated execution unit, an estimation unit, a parameter unit and a solution optimization unit; The repeatedly executing unit is configured to execute the estimation unit, the parameter unit, and the solution optimization unit on the signal to be solved of each distance unit to obtain the azimuth distance signal, wherein the azimuth distance signal includes the solution signal of each distance unit; The estimation unit is used to perform likelihood estimation on the signal to be solved to obtain an estimated signal; The parameter unit is used to construct a solution parameter based on the estimated signal; The solution optimization unit is used to adopt the conjugate gradient method in combination with the solution parameters to solve the estimated signal, and perform iterative optimization based on the Cauchy-Newton method to obtain the solution signal.

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