SA-ISAR self-focusing and calibration method based on sparse LVD

Abstract

The invention provides an SA-ISAR self-focusing and calibration method based on sparse LVD. The method comprises the following steps: constructing an echo model of a sparse aperture maneuvering target; under the echo model, performing energy accumulation based on the CFCR domain to obtain a sparse signal recovery model of the linear frequency modulation signal of the CFCR domain in the energy accumulation process; the sparse signal recovery model is solved based on an FSBL-LVDCTF method, and an ISAR image is obtained; and carrying out transverse calibration processing on the ISAR image by using an FSBL-LVDCTF method to obtain an ISAR image calibration result. According to the ISAR imaging method, the FSBL-LVDCTF method combines the strong robustness of sparse Bayesian learning and the efficient processing capacity of Lv distribution transformation on linear frequency modulation signals, meanwhile, cross term suppression is achieved through cross term filtering CTF, a reliable sparse recovery result is further guaranteed, and the precision and robustness of ISAR imaging are improved.

Description

Technical Field

[0001] The invention relates to the technical field of inverse synthetic aperture radar imaging, and in particular to a SA-ISAR self-focusing and calibration method based on sparse LVD. Background Art

[0002] Inverse Synthetic Aperture Radar (ISAR) imaging technology has become an important tool for space target detection due to its unique advantages such as all-day, all-weather, and strong penetration. ISAR achieves high range resolution by transmitting large-bandwidth signals and obtains high lateral range resolution by using the relative rotation between the target and the radar, thereby generating two-dimensional high-resolution images that effectively reflect the characteristics of the target. These images provide the necessary technical support for the identification and classification of non-cooperative targets. However, with the increasing application of ISAR, the types of targets have become more complex. Especially when monitoring missiles and other non-cooperative high-speed targets, the complex maneuverability of the target and the unknown motion trajectory pose severe challenges to imaging. In addition, in practical applications, the complexity of multi-function radar tasks, the unsatisfactory operation, and the unknown environment may all lead to discontinuity in the available echoes, which will cause the performance of traditional ISAR imaging algorithms represented by Range-Doppler (RD) to seriously degrade or even completely fail. Therefore, how to perform high-precision ISAR imaging of maneuvering targets under sparse aperture conditions has become an urgent problem to be solved.

[0003] At present, the algorithms that can be used to obtain high-resolution ISAR images of maneuvering targets are mainly divided into two categories: non-parametric methods and parametric methods. Non-parametric methods use time-frequency analysis to obtain instantaneous images at different time points, but due to the mobility of non-cooperative targets, the instantaneous rotation speed corresponding to different snapshots is not constant, resulting in the problem of time-varying scaling factors. Parametric methods model the phase of the echo as a polynomial function, and construct an optimization problem based on a certain image quality evaluation index (such as image contrast or image entropy) to estimate the phase error. By compensating for the estimated spatially varying phase error, a clearly focused ISAR image is obtained. However, the focusing performance of these methods is limited by the accuracy of phase error estimation, and their performance in complex environments is not ideal. In addition, compressed sensing technology provides an effective and feasible solution for sparse aperture ISAR (SA-ISAR) imaging, but due to the strong mobility of non-cooperative targets, the echo no longer exhibits sparseness in the Doppler domain, so the sparse reconstruction algorithm cannot be directly used in sparse aperture ISAR imaging of maneuvering targets.

[0004] Although the existing non-parametric methods have a small amount of computation, when the target is highly maneuverable, the effective rotation velocity (ERV) will change significantly during the coherent processing interval (CPI), which poses a severe challenge to lateral calibration. Parametric algorithms can complete lateral calibration processing while achieving self-focusing, but the focusing performance of the resulting ISAR image is directly limited by the estimation accuracy of the polynomial coefficients, so its performance under low signal-to-noise ratio conditions is often unsatisfactory. In addition, for SA-ISAR imaging of maneuvering targets, due to the strong maneuverability of non-cooperative targets, the echo no longer exhibits sparsity in the Doppler domain, so the sparse reconstruction algorithm cannot be directly used in sparse aperture ISAR imaging of maneuvering targets. Therefore, the existing technology still has significant limitations when dealing with ISAR imaging under complex maneuvering targets and sparse aperture conditions. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a SA-ISAR self-focusing and calibration method based on sparse LVD.

[0006] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0007] In a first aspect, the present invention provides a SA-ISAR self-focusing and calibration method based on sparse LVD, comprising:

[0008] Construct echo models for maneuvering targets with sparse apertures;

[0009] Under the echo model, the sparse signal recovery model of the linear frequency modulation signal in the CFCR domain during the energy accumulation process is obtained based on the energy accumulation in the CFCR domain.

[0010] The sparse signal recovery model is solved based on the FSBL-LVD-CTF method to obtain the ISAR image; the FSBL-LVD-CTF method is a LV distribution transform with cross-term suppression based on fast sparse Bayesian learning;

[0011] The FSBL-LVD-CTF method is used to perform lateral calibration on the ISAR image and obtain the ISAR image calibration result.

[0012] In a second aspect, the present invention provides a SA-ISAR self-focusing and calibration device based on sparse LVD, and the SA-ISAR self-focusing and calibration device based on sparse LVD includes: a model building unit, a calculation unit and a lateral calibration unit;

[0013] The model building unit is used to: build an echo model of a sparse aperture maneuvering target;

[0014] The model building unit is also used for: under the echo model, performing energy accumulation based on the CFCR domain to obtain a sparse signal recovery model of the linear frequency modulation signal in the CFCR domain during the energy accumulation process;

[0015] The computing unit is used to solve the sparse signal recovery model based on the FSBL-LVD-CTF method to obtain the ISAR image; the FSBL-LVD-CTF method is a LV distribution transformation with cross-term suppression based on fast sparse Bayesian learning;

[0016] The lateral calibration unit is used to perform lateral calibration processing on the ISAR image using the FSBL-LVD-CTF method to obtain the ISAR image calibration result.

[0017] In a third aspect, the present invention provides a SA-ISAR self-focusing and calibration device based on sparse LVD, comprising: a processor, a storage medium and a bus, the storage medium storing machine-readable instructions executable by the processor, when the SA-ISAR self-focusing and calibration device based on sparse LVD is running, the processor and the storage medium communicate through the bus, and the processor executes the machine-readable instructions to perform the steps of the SA-ISAR self-focusing and calibration method based on sparse LVD as described in any one of the above-mentioned first aspects.

[0018] The invention provides a SA-ISAR self-focusing and calibration method based on sparse LVD, comprising: constructing an echo model of a sparse aperture maneuvering target; under the echo model, performing energy accumulation based on a CFCR domain to obtain a sparse signal recovery model of a linear frequency modulation signal in the CFCR domain during an energy accumulation process; solving the sparse signal recovery model based on a FSBL-LVD-CTF method to obtain an ISAR image; the FSBL-LVD-CTF method is a LV distribution transformation with cross-term suppression based on fast sparse Bayesian learning; and performing lateral calibration processing on the ISAR image using the FSBL-LVD-CTF method to obtain an ISAR image calibration result. In the present invention, an accurate echo model is constructed according to the characteristics of sparse aperture and maneuvering target; on this basis, energy accumulation is performed in the center frequency-frequency modulation CFCR domain, which can effectively improve the signal-to-noise ratio of the signal and provide sufficient information for subsequent signal recovery and imaging; secondly, the FSBL-LVD-CTF method combines the strong robustness of SBL and the efficient processing ability of LVD transform for linear frequency modulation signals, and also removes CTF through cross-term filtering. ，The suppression of cross terms is achieved to ensure reliable sparse recovery results. Therefore, the present invention effectively solves the technical problem of high-precision ISAR imaging of maneuvering targets under sparse aperture conditions by constructing an accurate sparse aperture maneuvering target echo model, combining the energy accumulation strategy in the CFCR domain and the superior sparse signal recovery ability of the SBL method, and improves the accuracy and robustness of ISAR imaging.

[0019] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic flow chart of a SA-ISAR self-focusing and calibration method based on sparse LVD provided in an embodiment of the present invention;

[0021] Figure 2 A schematic diagram of an ISAR imaging geometric scene is shown as an example;

[0022] Figure 3 The schematic diagram of the structure of the sparse aperture signal is shown exemplarily;

[0023] Figure 4 The complete process diagram of the ISAR imaging and lateral calibration algorithm based on FSBL-LVD-CTF is shown as an example;

[0024] Figure 5 The schematic diagram of the comparison of 2D and 1D reconstruction results of FSBL-LVD-CTF and FSBL-LVD algorithms is shown as an example;

[0025] Figure 6 The nRMSE curves of various algorithms under different data missing rates and different signal-to-noise ratios are shown as examples;

[0026] Figure 7 A result schematic diagram showing a target scattering point model and a range-Doppler imaging result and an ideal imaging result is exemplarily shown;

[0027] Figure 8 The corresponding ISAR images of high-resolution range images when each algorithm is used under different data missing types are shown by way of example;

[0028] Fig. 9 The corresponding ISAR images of the same high-resolution range image when each algorithm is used under different data missing rate conditions are shown by way of example;

[0029] Fig.10 The ISAR images obtained by various algorithms under different signal-to-noise ratio conditions are shown as examples of high-resolution range images;

[0030] Fig.11The comparative analysis results of the effective speed estimation performance of each algorithm under different missing rates and different signal-to-noise ratios are shown as an example;

[0031] Fig.12 A schematic structural diagram of a SA-ISAR self-focusing and calibration device based on FSBL-LVD-CTF provided in an embodiment of the present invention;

[0032] Fig.13 A schematic structural diagram of a SA-ISAR self-focusing and calibration device based on sparse LVD provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] Aiming at the problem that the ISAR imaging results of high-speed maneuvering targets obtained by traditional imaging algorithms in complex environments will be affected by side lobes, grating lobes and time-varying Doppler frequencies, resulting in poor algorithm focusing performance or even complete failure, the present invention proposes a new SA-ISAR imaging and cross-range scaling (CRS) method based on FSBL-LVD-CTF. The proposed FSBL-LVD-CTF algorithm linearizes the signal self-terms in Lv's Distribution (LVD), and uses the correlation between cross terms and signals to suppress cross terms by adaptive filtering in sparse recovery iterations to ensure reliable sparse recovery performance. The proposed method makes it possible to estimate non-uniformly sampled multi-component linear frequency modulation signals with high precision. Furthermore, SA-ISAR imaging and cross-range scaling of maneuvering targets are cleverly converted into energy accumulation problems in the center frequency-chirp rate (CFCR) domain and solved by the proposed FSBL-LVD-CTF algorithm, and finally a well-focused and calibrated ISAR image can be obtained.

[0034] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0035] In order to improve the accuracy and robustness of ISAR imaging, an embodiment of the present invention provides a SA-ISAR self-focusing and calibration method based on sparse LVD. Figure 1 The present invention provides a flow chart of a SA-ISAR self-focusing and calibration method based on sparse LVD, wherein the sparse LVD can also be expressed as FSBL-LVD-CTF. Figure 1 As shown, including:

[0036] S101. Construct an echo model of a sparse aperture maneuvering target.

[0037] In order to show the complete process of echo model establishment, Figure 2 The schematic diagram of ISAR imaging geometric scene is shown as an example. Figure 2 As shown in the figure, during the observation time, the target (maneuvering target) moves from point A to point D, and its motion can be decomposed into three parts: orbit from point A to point B, rotation from point B to point C, and translation from point C to point D. Among them, the orbit component and translation component have no contribution to ISAR imaging, while the rotation component is the essential source of ISAR imaging azimuth resolution.

[0038] The instantaneous distance R between the radar and the scattering point p p (t m ) can be expressed as:

[0039] R p (t m )≈R0+r(t m )+x p sinθ(t m )+y p cosθ(t m )(1)

[0040] Among them, t m is the slow time, R0 is the distance between the target center and the radar at the initial moment, r(t m ) represents the instantaneous distance change introduced by translation, x p With y p Respectively represent the horizontal and vertical coordinates of the scattering point p in the imaging projection plane, θ(t m ) represents the instantaneous change in the rotation angle.

[0041] Considering the short observation time of the target and its inertia, the following polynomials are accurate enough to describe the radial and rotational motion of the target:

[0042]

[0043] Among them, v, ω, They represent the radial velocity, acceleration, effective speed and speed acceleration of the target respectively.

[0044] Substituting (2) into (1) and using the first-order Taylor expansion of trigonometric functions, R p (t m ) can be rewritten as:

[0045]

[0046] Assume that the radar transmits a linear frequency modulation (LFM) signal and the target consists of P scattering points. Then, the echo signal It can be expressed as:

[0047]

[0048] Among them, rect(·) is the window function; and t represent fast time and full time respectively, and their relationship with slow time can be described as: T p and γ represent the carrier frequency, pulse duration, and modulation rate, respectively. c is the speed of light, σ p is the backscattering coefficient of the scattering point p.

[0049] After de-skewing the echo described in (4) and compensating the residual video phase term, a high-resolution range image can be obtained:

[0050]

[0051] Among them, R Δ,p (t m )=R p (t m )-R ref , R ref is the reference distance, For fast time The corresponding frequency.

[0052] Obviously, (5) is the mathematical expression of the full aperture signal. However, due to various factors, the effective echo usually presents discontinuity. Figure 3 The schematic diagram of the structure of the sparse aperture signal is shown as an example. Figure 3 As shown, s 1,n -s 5,n Both represent sub-apertures. Under sparse aperture conditions, the correlation between echoes is significantly reduced, which causes some motion compensation algorithms to fail. Fortunately, studies have shown that envelope alignment algorithms based on minimum entropy are still effective.

[0053] Taking the sparse aperture factor into account, the signal of the nth range unit after envelope alignment of the HRRPs represented by (5) can be further expressed as:

[0054]

[0055] in,

[0056]

[0057] is the amplitude of the kth signal component, K is the number of scattering points contained in the nth distance unit, m(t m ) is the sampling sequence.

[0058] Substituting (3) into (6), taking the conjugate and ignoring the constant phase, the signal of the nth range unit, i.e. the echo model, can be expressed as:

[0059]

[0060] From (7), we can see that the signal of any distance unit can be modeled as a multi-component LFM signal, and its key parameters are determined by the target motion state and the scattering point position:

[0061]

[0062] Among them, f' k With γ' k are the center frequency and modulation rate of the kth signal component respectively.

[0063] Therefore, the good focusing performance of LFM signal in CFCR domain can be fully utilized to transform the ISAR self-focusing and lateral calibration of maneuvering targets into LFM signal energy integration and parameter estimation problems in CFCR domain for processing.

[0064] S102 . Under the echo model, energy accumulation is performed based on the CFCR domain to obtain a sparse signal recovery model of the linear frequency modulation signal in the CFCR domain during the energy accumulation process.

[0065] LVD is a time-frequency analysis method proposed by X.Lv et al., which is suitable for detecting multi-component LFM signal parameters. LVD maps LFM signals to the CFCR domain to achieve energy accumulation. Its implementation process can be summarized as follows:

[0066]

[0067] Among them, t' m =(τ+q)h't m ,h' and τ represent the scale factor and delay variable respectively; q represents the delay constant associated with the scale transformation; and denote the Fourier transform along the delay dimension and the time dimension respectively; Γ s [·] indicates scale transformation; PSIAF s (τ,t m ) is the signal s(t m ) is the parameterized symmetric instantaneous autocorrelation function PSIAF.

[0068] In practical applications, the Chirp-Z transform can be used to jointly implement the scale transform and the Fourier transform along the time dimension to reduce the computational cost. The implementation process can be simplified as follows:

[0069]

[0070] in, Represents the Chirp-Z transform along the time dimension.

[0071] However, as mentioned above, when the multi-component LFM signal is non-uniformly sampled, the energy integration performance of LVD is not ideal or even completely ineffective. To solve this problem, the present invention linearizes the self-term introduced by LVD and provides its sparse signal recovery model, which is described in detail below.

[0072] Assume that s(t m ) in the f-γ plane is:

[0073]

[0074] Among them, f and γ represent the frequency variable and the modulation frequency variable respectively, B k represents the magnitude of the kth mapped component.

[0075] Performing an inverse Fourier transform on (11) along dimension f yields:

[0076]

[0077] Then, perform an inverse Chirp-Z transform on (12) along the γ dimension, and we get:

[0078]

[0079] Combined with the definition of LVD, it can be found that (13) is s(t m ) is defined as:

[0080]

[0081] The above operation can be vectorized as follows:

[0082]

[0083] Where x = vec[LVD s ],r s =vec[PSIAF s (τ,t m )], vec[·] represents vectorized operation, is the inverse Fourier transform matrix, is a block diagonal matrix defined by (16), N t ,N τ ,N f and N γ denote the number of samples along the time, delay, frequency and modulation rate dimensions respectively, is the identity matrix, Represents the Kronecker product operation.

[0084]

[0085] in

[0086]

[0087] κ i =(2m' i T s +q)h',m' i ∈(-N τ / 2,N τ / 2-1),T s represents the sampling period. Taking the sparse aperture factor and noise into account, the observation y(t m ) can be expressed as:

[0088]

[0089] Among them, n(t m ),m(t m ), and CrossTerms(τ,t m ) represent noise, sampling sequence and cross terms respectively.

[0090] According to (15) and (18), y(t m ) can be rewritten as:

[0091] r y =Ax+r c,ss +r c,sn +w (19)

[0092] in

[0093]

[0094] s i (t m ) represents s(t m ), diag(·) represents the diagonalization operation. m ,w,r c,ss and r c,sn They represent the vectorized PSIAF of the sampling sequence, the vectorized PSIAF of the noise, the vectorized cross terms between different signal components, and the vectorized cross terms between the signal components and the noise, respectively. y will be denoted as y'.

[0095] The SA-ISAR imaging and lateral calibration problem is converted into a sparse signal recovery (compressed sensing) problem in the CFCR domain. The specific expansion process is as follows:

[0096] According to (8) and (19), the mapping position of the LFM signal in the CFCR domain is determined by the frequency and the modulation rate, and ω is implicit in the frequency. Therefore, the SA-ISAR self-focusing and lateral calibration problem of maneuvering targets can be described by (19), and its goal is to recover the unknown sparse signal x from the observed data y'. It can be seen that this is a typical SSR problem (sparse signal recovery problem) and can be solved by CS, where A can be regarded as a perception matrix, w represents the noise vector, y' is the observed signal, and x is the sparse signal to be recovered in the CFCR domain.

[0097] S103. Solve the sparse signal recovery model based on the FSBL-LVD-CTF method to obtain an ISAR image.

[0098] Among them, the FSBL-LVD-CTF method is a LV distribution transformation with cross-term suppression based on fast sparse Bayesian learning.

[0099] Optionally, S103 may specifically include:

[0100] Perform Lu distribution transformation on the slow time dimension signal in the echo model to obtain the noise term, the signal to be recovered and the observed signal;

[0101] Conduct a priori modeling of the noise self-term to obtain a priori probability model of the noise self-term;

[0102] A priori modeling is performed on the signal to be restored and the observed signal, and the priori model of the signal to be restored and the conditional likelihood function of the observed signal are obtained accordingly;

[0103] For the sparse signal recovery model corresponding to each slow-time dimension signal, fast sparse Bayesian learning is performed based on the noise self-term prior probability model, the prior model of the signal to be recovered and the conditional likelihood function of the observed signal to obtain the final sparse signal recovery result; among them, fast sparse Bayesian learning is an implementation method based on 2D-CGLS and 2D-EDEM;

[0104] The ISAR image is obtained using the final sparse signal recovery result.

[0105] Optionally, a priori modeling of the noise self-term is performed to obtain a priori probability model of the noise self-term, including:

[0106] The generalized double Pareto distribution is used to model the noise term a priori and the prior probability model of the noise term is obtained.

[0107] Optionally, a priori modeling is performed on the signal to be restored and the observed signal, and a priori model of the signal to be restored and a conditional likelihood function of the observed signal are obtained accordingly, including:

[0108] The signal to be recovered is modeled using Gaussian distribution to obtain a priori model of the signal to be recovered;

[0109] The observed signal is modeled a priori using the prior model of the signal to be restored to obtain the conditional likelihood function of the observed signal.

[0110] Optionally, the ISAR image is obtained using the final sparse signal recovery result, including:

[0111] Slice the final sparse signal recovery result to obtain one-dimensional sparse signal slice information;

[0112] The one-dimensional sparse signal slice information is spliced ​​to obtain the ISAR image.

[0113] Optionally, a sparse signal recovery model corresponding to each slow time dimension signal is subjected to fast sparse Bayesian learning based on a noise self-term prior probability model, a signal prior model to be recovered, and a conditional likelihood function of the observed signal to obtain a final sparse signal recovery result, including:

[0114] S201, obtaining current hyperparameters, and substituting the current hyperparameters, the noise self-term prior probability model, the to-be-recovered signal prior model and the observed signal conditional likelihood function into the sparse signal recovery model, and calculating the posterior probability density of the to-be-recovered signal using the Bayesian theorem; the current hyperparameters include: the accuracy of the to-be-recovered signal, the accuracy of the noise self-term and the parameters of the gamma distribution to which the accuracy of the noise self-term obeys;

[0115] S202, taking the mean of the posterior probability density of the signal to be restored corresponding to the maximum posterior probability density of the signal to be restored as the current sparse signal restoration result;

[0116] S203, using the second type maximum likelihood estimation criterion and the current sparse signal recovery result, updating the current hyperparameter in S201 to obtain an updated hyperparameter, and using the updated hyperparameter as the current hyperparameter in S201;

[0117] S204, re-execute S201-S203 until the iteration stop condition is met, and use the current sparse signal recovery result corresponding to the time when the iteration stop condition is met as the final sparse signal recovery result;

[0118] The iteration stop condition includes: the number of iterations meets the iteration number threshold, or the difference between the current sparse signal recovery result and the sparse signal recovery result corresponding to the previous iteration is less than the accuracy threshold.

[0119] Specifically, the specific implementation reasoning process of S103 is as follows:

[0120] It is well known that SBL can be used to deal with the typical SSR problem expressed by (20) as follows:

[0121] y=Ax+n' (20)

[0122] Where A, y, x and n' represent the perception matrix, measurement vector, sparse signal and noise vector respectively.

[0123] However, there are two significant differences between the SSR model described by equation (19) and the typical SSR model represented by equation (20), which will cause the traditional SBL algorithm to no longer be applicable to solve the SSR problem represented by (19). First, the noise term w in (19) is composed of the product of two independent and identically distributed normal noises, which will invalidate the assumption that the noise in traditional SBL obeys the Gaussian distribution. Second, in addition to the noise term, the observation of equation (19) is also mixed with cross terms between different signal components and cross terms between signal and noise, which will seriously weaken the performance of SBL sparse reconstruction.

[0124] In order to solve the above problems, the generalized double Pareto (GDP) distribution is introduced to model the prior, and the cross terms are suppressed through adaptive iterative filtering.

[0125] a) Noise self-term prior modeling

[0126] The distribution function of the product of two independent and identically distributed normal random variables can be expressed as:

[0127]

[0128] in, represents the dispersion (standard deviation) of the random variable, and K0(·) represents the zero-order second-kind Bessel function.

[0129] However, the distribution function described in (21) is relatively complex. If it is used directly to model the noise prior, it will bring great inconvenience to the SBL derivation. Therefore, the present invention adopts the generalized double Pareto distribution to model the noise prior. In order to simplify the inference process, the present invention constructs the following three-layer hierarchical prior to make the marginal probability density distribution of w conform to the GDP prior.

[0130] First, assuming that all elements of w obey the same complex Gaussian distribution, we have:

[0131]

[0132] Where β = η -1, η is the variance of w.

[0133] Second, assume that the hyperparameter β follows a gamma distribution with parameters ε and k:

[0134]

[0135] Finally, the hyperparameter ε is modeled as following a gamma distribution with parameter h:

[0136]

[0137] Here, h is a small positive constant.

[0138] b) Prior modeling of the signal to be recovered and the observed signal

[0139] For the signal x to be restored, assume that all its elements obey the complex Gaussian distribution:

[0140]

[0141] in, represents the variance of the ith element of x. Further, assuming that α i Gamma distribution with parameters a and b:

[0142]

[0143] Where a>0 and b>0 represent the shape parameter and inverse scale parameter respectively. Γ(·) is the gamma function, which is expressed as:

[0144]

[0145] Based on the above distribution assumptions, the conditional likelihood function of y' can be expressed as:

[0146]

[0147] Finally, a hierarchical prior framework of SBL was formed based on the above assumptions.

[0148] The hyperparameter update process is as follows:

[0149] In order to facilitate inference, hyperparameter estimation is performed based on the second-class maximum likelihood estimation criterion. When the observation y' is known, the source vector x and the hyperparameters α, β and ε are unknown, the joint posterior probability can be expressed as:

[0150] p(x,α,β,ε|y')=p(x|α,β,ε,y')p(α,β,ε|y') (29)

[0151] a) Derivation of p(x|α,β,ε,y')

[0152] First, let’s analyze the first term p(x|α,β,ε,y') in (29). According to conditional independence and Bayes’ theorem, it can be derived as:

[0153]

[0154] The analytical expressions of p(x|α) and p(y'|x,β) are (25) and (28) respectively. p(y'|α,β) can be solved by the total probability formula as follows:

[0155]

[0156] Among them, Λ=diag(1 / α1,1 / α2,…,1 / α N ).

[0157] Obviously, (31) can be regarded as the convolution of two complex Gaussian distributions. According to the properties of complex Gaussian distribution, it still obeys complex Gaussian distribution. Therefore, in order to accurately write the analytical expression of p(y'|α,β), it is necessary to calculate its mean and variance. For the convenience of derivation, the auxiliary variable E(x) is defined as follows:

[0158]

[0159] And define

[0160] Σ=(Λ -1 +βA H A) -1 (33)

[0161] μ=βΣA H y' (34)

[0162] Then, E(x) can be rewritten as:

[0163] E(x)=E(y')+(x-μ) H Σ -1 (x-μ) (35)

[0164] Where, E(y') = βy' H y'-μ H Σ -1 μ.

[0165] According to (35), (31) can be rewritten as:

[0166]

[0167] The probability density function of a multidimensional Gaussian variable can be expressed as:

[0168]

[0169] Therefore, using the property that the integral of the probability density function in its definition interval is always 1, p(y'|α,β) can be further simplified to:

[0170]

[0171] Combining (25), (28) and (38), we can see that p(x|α,β,ε,y') obeys a complex Gaussian distribution with parameters μ and Σ, which can be expressed as:

[0172] According to the matrix inversion lemma, formula (33) can be simplified to:

[0173] Σ=Λ-ΛA H Q -1 AΛ (39)

[0174] in

[0175] Q=ηI+AΛA H (40)

[0176] ηI and AΛA H Represent the covariance matrices of w and Ax respectively.

[0177] Substituting (39) into (34), the mean of the posterior distribution of x can be simplified to:

[0178] μ=ΛA H Q -1 y' (41)

[0179] However, in the sparse signal recovery model (SSR model) constructed by the present invention described in (19), in addition to w, the observation y' is also mixed with the cross term r c,ss and r c,sn Obviously, as the signal components increase, the energy of the cross terms will increase significantly, which poses a great threat to the performance of sparse recovery and may even cause the useful signal to be submerged. In other words, directly using (41) to recover the sparse signal x in (19) cannot guarantee reliable and satisfactory reconstruction performance.

[0180] Fortunately, the cross term r c,ss and r c,sn There is a specific correlation between it and the signal x, and its covariance matrix can be estimated in the iterative process. As the number of iterations increases, the estimation error will continue to decrease. For this reason, the cross-term suppression can be achieved based on adaptive filtering. c,ss With R c,sn The estimates are introduced separately.

[0181] First, assume that the center frequency and modulation rate corresponding to the i-th signal component read out from the peak position of the sparsely restored signal in the CFCR plane are and Then the cross term r c,ss The covariance matrix of can be estimated by the following formula:

[0182]

[0183] in

[0184]

[0185] and Respectively represent and The estimated range of .

[0186] In addition, in the field of radar signal processing, the noise variance can be estimated based on the reference unit, and the signal variance can also be estimated in each iteration by Therefore, combined with the cross term r c,sn The covariance matrix can be estimated as:

[0187]

[0188] Where I is the unit matrix, and represent the variance of signal and noise respectively.

[0189] In summary, in order to filter the cross terms, (40) should be corrected to (44), which is the key to the proposed algorithm being able to effectively recover x from y' and ensure its reliable reconstruction performance.

[0190]

[0191] Finally, substituting (44) into (41), the mean of the posterior distribution of x (the recovered result of the sparse signal x) can be expressed as:

[0192]

[0193] (b) Derivation of p(α,β,ε|y')

[0194] Next, we analyze the second term p(α,β,ε|y') in (29). Similarly, it can be inferred using conditional independence and Bayes' theorem:

[0195]

[0196] Among them, p(y') is the marginal probability density of the observed data y', which is only related to the model, so:

[0197] p(α,β,ε|y')∝p(y'|α,β)p(α)p(β|ε)p(ε) (47)

[0198] However, as shown in (38), p(y'|α,β) contains exponential terms, which will bring inconvenience to the derivation. Therefore, the present invention simplifies it by taking the logarithm to obtain:

[0199]

[0200] Where C is a constant that has nothing to do with the hyperparameters.

[0201] When the likelihood function represented by (48) reaches its maximum value, the corresponding hyperparameter can well characterize the statistical characteristics of the observation. Therefore, we calculate the effect of (48) on α i ,β, and the partial derivative of ε, and set them equal to zero, we can get the update criterion of the hyperparameters:

[0202]

[0203] Among them, γ i =1-α i Σ ii ,Σ ii is the i-th diagonal element of Σ.

[0204] Obviously, for the SSR model described in (19), the Kronecker process will introduce a large-scale perception matrix, so the inversion of Q involved in (45) will lead to a huge computational burden. To solve the above problem, the method of the present invention makes full use of the structural characteristics of the constructed matrix B, and proposes a two-dimensional conjugate gradient least squares method and a two-dimensional matrix diagonal element estimation method, which are used to solve the matrix inversion and matrix diagonal element calculation problems, respectively, which can significantly reduce the computational complexity.

[0205] For ease of presentation, define:

[0206] u=Q -1 y'=(B H B) -1 B H z (52)

[0207] in

[0208]

[0209] Among them, r i,j represents the cross term between the vectorized i-th signal component and the j-th signal component, i,j=1,2,…,K and i≠j.

[0210] Furthermore, formula (52) can be restated as:

[0211] B H Bu=B H z (53)

[0212] It is well known that the conjugate gradient least squares method can be used to solve the normal equations expressed in (53). However, directly using the original CGLS algorithm to solve (53) will also lead to a large computational burden, which is destined by the large-scale SSR problem constructed by the present invention. Fortunately, the matrix B constructed in the present invention has a special structure. Based on its two-dimensional structural characteristics, a corresponding 2D-CGLS algorithm is proposed. The algorithm directly processes the two-dimensional data structure, avoids flattening the data into a one-dimensional vector, thereby reducing the complexity of data conversion, significantly reducing storage requirements, and improving the efficiency and adaptability of the algorithm.

[0213] For Σ, only its diagonal elements are used to update the hyperparameters, so calculating it by (39) will lead to a serious waste of computing resources. Fortunately, EDEM can be used to estimate the diagonal elements of the matrix, and even a small number of iterations can have satisfactory parameter estimation accuracy. To this end, the present invention combines the structural characteristics of the matrix B and gives a two-dimensional implementation of the matrix diagonal element estimation EDEM.

[0214] S104, performing lateral calibration processing on the ISAR image using the FSBL-LVD-CTF method to obtain an ISAR image calibration result.

[0215] The embodiment of the present invention provides a SA-ISAR self-focusing and calibration method based on sparse LVD, and constructs an accurate echo model according to the characteristics of sparse aperture and maneuvering targets; on this basis, energy accumulation is performed in the center frequency-frequency modulation CFCR domain, which can effectively improve the signal-to-noise ratio of the signal and provide sufficient information for subsequent signal recovery and imaging; secondly, the FSBL-LVD-CTF method combines the strong robustness of SBL and the efficient processing capability of LVD for linear frequency modulation signals, and also suppresses cross terms by filtering CTF through cross terms, thereby ensuring reliable sparse recovery results. Therefore, the present invention effectively solves the technical problem of high-precision ISAR imaging of maneuvering targets under sparse aperture conditions by constructing an accurate sparse aperture maneuvering target echo model, combining the energy accumulation strategy of the CFCR domain and the sparse signal recovery capability of the SBL method, and improves the accuracy and robustness of ISAR image imaging.

[0216] Optionally, the ISAR image calibration result includes: an estimated value of the range dimension resolution of the ISAR image and a lateral range dimension resolution of the ISAR image; performing lateral calibration processing on the ISAR image by using the FSBL-LVD-CTF method to obtain an estimated value of the lateral range dimension resolution of the ISAR image in the ISAR image calibration result includes:

[0217] The FSBL-LVD-CTF method is used to estimate the effective rotation speed of the maneuvering target in the ISAR image, and the estimated value of the effective rotation speed of the maneuvering target is obtained;

[0218] The estimated value of the lateral range resolution of the ISAR image is estimated using the estimated value of the effective rotation speed of the maneuvering target.

[0219] Optionally, the range dimension resolution of the ISAR image is expressed as:

[0220]

[0221] Among them, ρ r represents the distance resolution of the ISAR image, c represents the speed of light, and B w Indicates the bandwidth of the transmitted signal;

[0222] The estimated value of the lateral range resolution of the ISAR image is expressed as:

[0223] in, represents the estimated value of the lateral range resolution of the ISAR image, f c represents the radar carrier frequency, represents the estimated effective rotation speed of the maneuvering target, T a Indicates the imaging accumulation time.

[0224] The process of realizing effective speed estimation based on FSBL-LVD-CTF is as follows:

[0225] Obviously, the imaging results obtained by the proposed FSBL-LVD-CTF algorithm are located in the range-Doppler plane, which cannot meet the needs of practical applications. In order to obtain characteristic information such as target size and geometric shape, it is crucial to calibrate the ISAR image in the range dimension and the lateral range dimension.

[0226] ISAR achieves distance resolution by transmitting large bandwidth signals and pulse compression processing. The distance resolution of its image is:

[0227]

[0228] Among them, B w is the transmit signal bandwidth.

[0229] ISAR uses the relative rotation between the target and the radar to achieve lateral range resolution. According to (8), the lateral range resolution of the ISAR image obtained by the proposed FSBL-LVD-CTF algorithm can be expressed as:

[0230]

[0231] Among them, T a Accumulation time for ISAR imaging.

[0232] Obviously, since the ISAR system parameters are known, distance calibration is easy to achieve. However, the ISAR observed target is non-cooperative and its motion trajectory information is unknown, so it is crucial to use the echo information to accurately estimate the target rotation speed.

[0233] Assume that there are two scattering points with the same horizontal coordinate but located in different distance units, that is, satisfying the following conditions:

[0234]

[0235] x p =x q (58)

[0236] Among them, y p ,y q ,γ' p With γ' q They represent the coordinates of the scattering points p and q and the corresponding modulation frequencies respectively.

[0237] In practical applications, the position of the target rotation center cannot be known, that is, y p With y q However, the effect of the reference center deviation on all scatter points is the same, so y p -y q is estimable. Therefore, combining (56), (57) and (58), the estimated value of the target speed is:

[0238]

[0239] Then, the estimated value of the lateral distance resolution of the ISAR image can be obtained as follows:

[0240]

[0241] In summary, Figure 4 The complete flow chart of ISAR imaging and lateral calibration algorithm based on FSBL-LVD-CTF is shown as an example. Figure 4As shown, the sparse aperture echo data is first de-skewed to obtain a high-resolution range envelope, and the high-resolution range envelope is aligned and conjugated to obtain N r The multi-component non-uniformly sampled LFM signals, that is, each slow time dimension signal (range unit signal) at this time can be approximated as a multi-component non-uniformly sampled LFM signal. The FSBL-LVD-CTF algorithm proposed in this patent is used to process each multi-component non-uniformly sampled LFM signal to obtain the corresponding sparse signal recovery (SSR) result, and the ISAR image can be obtained by slicing and splicing it. At the same time, the proposed FSBL-LVD-CTF algorithm is used to estimate the effective speed of the target, and after obtaining the estimated value, calibration processing can be performed to obtain a calibrated ISAR image.

[0242] The implementation framework of FSBL-LVD-CTF can be briefly described as follows: take a certain distance unit signal as y, and perform necessary initialization processing to obtain the input of the algorithm, including: perception matrix A, observation signal y', hyperparameters α, β, ε. Then perform the following iterative processing until the iteration termination condition is met. The iterative processing includes: first, update the covariance matrix Q of the observation y' according to (44), and then use 2D-CGLS to update Q -1 y' is solved to obtain its two-dimensional analytical solution, and then the mean of the posterior distribution of the sparse signal to be recovered is updated, and the updated mean of the posterior distribution of the sparse signal to be recovered is used as the current sparse signal recovery (SSR) result. The next step is to update the estimated value of the diagonal element of Σ, and then update the current hyperparameter according to equations (49)-(51) to obtain the updated hyperparameter. Finally, it is determined whether the current iteration step meets the iteration termination condition. If it does, the current sparse signal recovery result is used as the final sparse signal recovery result output; if not, the updated hyperparameter is used as the current hyperparameter to continue iterating.

[0243] In summary, the present invention proposes a new SA-ISAR imaging and CRS algorithm based on FSBL-LVD-CTF. The proposed FSBL-LVD-CTF algorithm linearizes the signal self-terms in LVD, and uses the correlation between cross-terms and signals to suppress cross-terms by adaptive filtering in sparse recovery iterations to ensure reliable sparse recovery performance. The proposed algorithm makes it possible to estimate non-uniformly sampled multi-component linear frequency modulation signals with high precision. Furthermore, the SA-ISAR imaging and lateral calibration of maneuvering targets are cleverly converted into energy accumulation problems in the CFCR domain and solved using the proposed FSBL-LVD-CTF algorithm. Its application in SA-ISAR imaging of maneuvering targets provides a new paradigm for SA-ISAR imaging of maneuvering targets, which makes the self-focusing performance of ISAR images no longer limited by the error compensation accuracy, and it shows satisfactory accuracy and superior focusing performance under low signal-to-noise ratio and large data missing rate, which has significant advantages over existing algorithms.

[0244] In order to verify the effectiveness of the SA-ISAR self-focusing and calibration method based on sparse LVD proposed in the present invention in complex environments, the following comparative experiments were set up.

[0245] Experiment 1:

[0246] In this experiment, the length of the LFM signal is fixed to 200, and the signal-to-noise ratio and data loss rate are set to 10dB and 50% respectively. In order to illustrate the impact of cross-terms on the reconstruction performance and verify the effectiveness of the proposed algorithm in suppressing cross-terms, the signal is reconstructed using the FSBL-LVD-CTF and FSBL-LVD algorithms respectively.

[0247] Figure 5 The 2D and 1D reconstruction results of FSBL-LVD-CTF and FSBL-LVD are compared. Figure 5 Figure (a) and Figure 5 (b) The 2D and 1D reconstruction results of the FSBL-LVD-CTF algorithm are shown in Figure 2. Figure 5 Figure (c) and Figure 5 As shown in Figure (d). Obviously, from Figure 5 It can be seen that the SSR result of the FSBL-LVD algorithm is seriously affected by the cross terms, while the FSBL-LVD-CTF algorithm proposed in the present invention can effectively suppress the cross terms, and each signal component is clearly distinguishable. Therefore, the effectiveness of the method of the present invention in processing non-uniformly sampled multi-component LFM signals is verified.

[0248] In the following discussion, the algorithm in the literature S.-C. Xiong, K.-M. Li, H.-B. Wang, S.-Y. Zhao, Y. Luo, Q. Zhang, "Sparse Aperture High-Resolution RID ISAR Imaging of Maneuvering Target Based on Parametric Efficient Sparse Bayesian Learning," IEEE Geosci. Remote Sens. Lett., vol. 21, pp. 1-5, 2024, Art no. 4005905. is denoted as CPESBL; the algorithm in the literature T. Yang, H.-Y. Shi, J.-W. Guo, X. Wang, S.-L. Yao, and W.-J. Jiang, "ISARI imaging for maneuvering target based on suitable CPI extraction and PC-MBSBL," IEEE The algorithm in Trans.Aerosp.Electron.Syst.,vol.60,no.6,pp.8118-8135,Dec.2024. is denoted as PC-MBSBL; the algorithm in the literature Q.Liu,Y.-Y.Wang,and F.-Z.Dai,"Sparse aperture ISARimaging and cross-range scaling of maneuvering targets based on sparse CICPFmethod,"IEEE Sensors J.,vol.24,no.11,pp.18066-18081,1June1,2024. is denoted as SCICPF.

[0249] Experiment 2:

[0250] In order to further explore the sparse LFM signal reconstruction performance of the method of the present invention, CPESBL, PC-MBSBL, SCICPF and the proposed FSBL-LVD-CTF algorithm were used in this experiment to reconstruct three-component LFM signals with different missing rates and different signal-to-noise ratios, and the superiority of the algorithm of the present invention in reconstruction accuracy and robustness was explained through comparison.

[0251] In order to analyze the reconstruction accuracy of each algorithm, the normalized root mean square error is defined as follows:

[0252]

[0253] in, and s represent the reconstructed signal and the true signal respectively.

[0254] Figure 6 The nRMSE curves of various algorithms under different data missing rates and different signal-to-noise ratios are shown as examples. Figure 6 Figure (a) shows the nRMSE curves of each algorithm when the signal-to-noise ratio is fixed at 10 dB and the data missing rate is a variable. Figure 6 Figure (b) shows the nRMSE curves of each algorithm when the data missing rate is fixed at 30% and the signal-to-noise ratio is used as a variable. Figure 6 As shown in the figure, under the same conditions, the proposed algorithm has a better reconstruction accuracy. In addition, the proposed algorithm also shows satisfactory robustness. Unlike the comparison algorithm, the reconstruction performance of the proposed algorithm is slightly affected by the signal-to-noise ratio and data missing rate.

[0255] Experiment 3:

[0256] In this simulation, it is assumed that the radar transmits a linear frequency modulation signal. Figure 7 The target scattering point model and the range-Doppler imaging results and the ideal imaging results are shown as an example. Figure 7 As shown in Figure (a), the target selected in the simulation consists of 84 scattering points. The main parameters of the radar include carrier frequency, bandwidth, pulse width and pulse repetition frequency, which are set to 4GHz, 1GHz, 200μs and 200Hz respectively. The key parameters of the target include radial velocity, radial acceleration, ERV and ERA, which are set to 200m / s, 30m / s respectively. 2 , 0.08rad / s and 0.008rad / s 2 It should be pointed out that the signal-to-noise ratios mentioned in subsequent experiments are all defined in the HRRP domain. Figure 7 Figure (b) and Figure 7 Figure (c) shows the range-Doppler (RD) imaging results and the ideal imaging results. Figure 7 Figure (b) and Figure 7 From Figure (c), we can see that the space-varying phase error introduced by the target maneuvering motion causes the ISAR image to defocus, which means that the space-varying phase error cannot be ignored in high-resolution ISAR imaging.

[0257] In the following discussion, random missing and gap missing will be denoted as SA-Type 1 and SA-Type 2, respectively. In addition, image entropy and image contrast are introduced as evaluation indicators of image focusing performance. In addition, the algorithms in the literature S.Shao, L.Zhang, H.-W.Liu, Y.-J.Zhou. "Spatial-variant contrast maximization autofocus algorithmfor ISAR imaging of maneuvering targets".Sci.China Inf.Sci., vol.62, no.4, Apr.2019. and G.Xu, M.-D.Xing, L.Zhang, J.Duan, Q.-Q.Chen and Z.Bao, "SparseApertures ISAR Imaging and Scaling for Maneuvering Targets," IEEE J.Sel.TopicsAppl.Earth Observ.Remote Sens., vol.7, no.7, pp.2942-2956, July 2014. are respectively called PPEC and MDCFT algorithms. The above two algorithms are used together as comparison algorithms for lateral calibration.

[0258] Experiment 4:

[0259] In order to analyze the ISAR autofocusing performance of the proposed algorithm and the comparative algorithms under different data missing types, the complete echoes are sampled according to the SA-Type1 and SA-Type2 structural characteristics to simulate two types of non-uniform sampling data. To avoid the influence of other factors, in this experiment, the sampling rate and signal-to-noise ratio are set to 50% and 10dB respectively.

[0260] Figure 8 The ISAR images corresponding to the high-resolution range image when each algorithm is used under different data missing types are shown as examples. Figure 8 (a)- Figure 8 The missing data type in (c) is SA-Type1. Figure 8 (a) shows the high-resolution range envelope HRRPs after alignment under SA-Type1; Figure 8 (b) shows the ISAR image obtained by the CPESBL algorithm under SA-Type1; Figure 8 (c) shows the ISAR image obtained by the algorithm of the present invention under SA-Type1. Figure 8 (d)- Figure 8 The missing data type in (f) is SA-Type2. Figure 8 Figure (d) shows the HRRPs after alignment under SA-Type2; Figure 8 Figure (e) shows the ISAR image obtained by the CPESBL algorithm under SA-Type2; Figure 8 Figure (f) shows the ISAR image obtained by the algorithm proposed in the present invention under SA-Type2.

[0261] from Figure 8 It can be seen that the resolution and focusing performance of the method proposed in the present invention are optimal in both SA-Type1 and SA-Type2. In other words, the proposed algorithm is effective for both types of non-uniformly sampled echo data. Therefore, due to space limitations, SA-Type1 and SA-Type2 will no longer be specifically distinguished in subsequent experiments.

[0262] Experiment 5:

[0263] In this experiment, each algorithm is used to realize SA-ISAR imaging under different missing rates to analyze the sensitivity of each algorithm to the data missing rate. Fig. 9 The ISAR images corresponding to the same high-resolution range image when each algorithm is used under different data missing rate conditions are shown as an example. Fig. 9 (a)- Fig. 9 (c): The data missing rate is 50%. Fig. 9 (a) shows the aligned HRRPs; Fig. 9 Figure (b) shows the ISAR image obtained by the CPESBL algorithm; Fig. 9 Figure (c) shows the ISAR image obtained by the proposed algorithm. Fig. 9 Figure (d) - Fig. 9 The data missing rate in Figure (f) is 70%. Fig. 9 Figure (d) shows the aligned HRRPs; Fig. 9 Figure (e) shows the ISAR image obtained by the CPESBL algorithm; Fig. 9 Figure (f) shows the ISAR image obtained by the proposed algorithm. Obviously, even in the case of a higher data missing rate, the proposed method can obtain clearer ISAR images than the comparison algorithm, and it shows a lower sensitivity to the data missing rate. Therefore, the effectiveness of the proposed method in the case of sparse aperture is verified.

[0264] Experiment 6:

[0265] In this experiment, the signal-to-noise ratio (SNR) is used as a variable to analyze the sensitivity of the proposed algorithm to the signal-to-noise ratio (SNR). Fig.10 The ISAR images obtained by various algorithms under different signal-to-noise ratio conditions for high-resolution range images are shown as examples. Fig.10 (a)- Fig.10(c) The signal-to-noise ratio is 0dB. Fig.10 (a) shows the aligned HRRPs; Fig.10 Figure (b) shows the ISAR image obtained by the CPESBL algorithm; Fig.10 Figure (c) shows the ISAR image obtained by the proposed algorithm. Fig.10 (d)- Fig.10 The signal-to-noise ratio of Figure (f) is 10dB. Fig.10 Figure (d) shows the aligned HRRPs; Fig.10 Figure (e) shows the ISAR image obtained by the CPESBL algorithm; Fig.10 Figure (f) shows the ISAR image obtained by the proposed algorithm. It can be observed that with the decrease of the signal-to-noise ratio, the entropy of the image obtained by the comparison algorithm increases significantly and the contrast decreases significantly, while the proposed method can obtain clear ISAR images for echoes with different signal-to-noise ratios, which proves the superior noise suppression performance of the proposed algorithm.

[0266] Experiment 7:

[0267] In order to further analyze the lateral calibration performance of PPEC, MDCFT and the proposed method, this experiment uses the above algorithms to estimate the effective rotation speed (ERV) under different signal-to-noise ratios and different missing rates, and illustrates the superior estimation accuracy and robustness of the proposed algorithm through comparison. Fig.11 The comparative analysis results of the effective speed estimation performance of each algorithm under different missing rates and different signal-to-noise ratios are shown by way of example. Fig.11 Figure (a) shows the comparison results of effective speed estimation when the data missing rate is a variable. Fig.11 Figure (b) shows the comparison results of effective speed estimation when the signal-to-noise ratio is used as a variable. Obviously, the algorithm proposed in the present invention has higher parameter estimation accuracy than the comparison algorithm. And with the increase of data missing rate or the decrease of signal-to-noise ratio, the estimation error of each comparison algorithm gradually increases, while the proposed algorithm shows satisfactory robustness.

[0268] The method provided in the embodiment of the present invention can be applied to an electronic device. Specifically, the electronic device can be: a desktop computer, a portable computer, an intelligent mobile terminal, a server, etc., which is not limited in the embodiment of the present invention.

[0269] Based on the same inventive concept, an embodiment of the present invention further provides a SA-ISAR self-focusing and calibration device based on sparse LVD. Fig.12 The present invention provides a schematic diagram of the structure of a SA-ISAR self-focusing and calibration device based on sparse LVD. Fig.12As shown, the SA-ISAR self-focusing and calibration device based on sparse LVD includes: a model building unit 601, a calculation unit 602 and a lateral calibration unit 603;

[0270] The model building unit 601 is used to: build an echo model of a sparse aperture maneuvering target;

[0271] The model building unit 601 is further used to: under the echo model, perform energy accumulation based on the CFCR domain to obtain a sparse signal recovery model of the linear frequency modulation signal in the CFCR domain during the energy accumulation process;

[0272] The calculation unit 602 is used to solve the sparse signal recovery model based on the FSBL-LVD-CTF method to obtain the ISAR image; the FSBL-LVD-CTF method is a LV distribution transformation with cross-term suppression based on fast sparse Bayesian learning;

[0273] The lateral calibration unit 603 is used to perform lateral calibration processing on the ISAR image using the FSBL-LVD-CTF method to obtain the ISAR image calibration result.

[0274] Fig.13 A schematic structural diagram of a SA-ISAR self-focusing and calibration device based on sparse LVD provided by an embodiment of the present invention includes: a processor 710, a storage medium 720 and a bus 730, wherein the storage medium 720 stores machine-readable instructions executable by the processor 710, and when the SA-ISAR self-focusing and calibration device based on sparse LVD is running, the processor 710 communicates with the storage medium 720 through the bus 730, and the processor 710 executes the machine-readable instructions to execute the steps of the above method embodiment. The specific implementation method and technical effect are similar and will not be repeated here.

[0275] The storage medium may include a random access memory (RAM) or a non-volatile memory (NVM), such as at least one disk storage. Optionally, the storage medium may also be at least one storage device located away from the aforementioned processor.

[0276] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0277] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the scope of protection of the present invention.

Claims

1. A SA-ISAR self-focusing and calibration method based on sparse LVD, characterized in that: include: Construct echo models for maneuvering targets with sparse apertures; Under the echo model, energy accumulation is performed based on the CFCR domain to obtain a sparse signal recovery model of the linear frequency modulation signal in the CFCR domain during the energy accumulation process; The sparse signal recovery model is solved based on the FSBL-LVD-CTF method to obtain the ISAR image; the FSBL-LVD-CTF method is a LV distribution transformation with cross-term suppression based on fast sparse Bayesian learning; The FSBL-LVD-CTF method is used to perform lateral calibration processing on the ISAR image to obtain an ISAR image calibration result.

2. The SA-ISAR self-focusing and calibration method based on sparse LVD according to claim 1, characterized in that: The sparse signal recovery model is solved based on the FSBL-LVD-CTF method to obtain the ISAR image, including: Performing Lu distribution transformation on the slow-time dimension signal in the echo model to obtain the noise term, the signal to be restored and the observation signal; Performing a priori modeling on the noise term to obtain a noise term prior probability model; Performing a priori modeling on the signal to be restored and the observed signal, and obtaining a priori model of the signal to be restored and a conditional likelihood function of the observed signal accordingly; For the sparse signal recovery model corresponding to each slow time dimension signal, based on the noise self-term prior probability model, the prior model of the signal to be recovered and the conditional likelihood function of the observed signal, fast sparse Bayesian learning is performed to obtain the final sparse signal recovery result; wherein, the fast sparse Bayesian learning is an implementation method based on 2D-CGLS and 2D-EDEM; The ISAR image is obtained using the final sparse signal recovery result.

3. The SA-ISAR self-focusing and calibration method based on sparse LVD according to claim 2, characterized in that: The prior modeling of the noise self-term to obtain a noise self-term prior probability model includes: The noise term is modeled a priori by using a generalized dual Pareto distribution to obtain a priori probability model of the noise term.

4. The SA-ISAR self-focusing and calibration method based on sparse LVD according to claim 2, characterized in that: The a priori modeling of the signal to be restored and the observed signal to obtain a corresponding a priori model of the signal to be restored and a conditional likelihood function of the observed signal includes: Modeling the signal to be restored by using Gaussian distribution to obtain a priori model of the signal to be restored; The observed signal is modeled a priori by using the prior model of the signal to be restored to obtain a conditional likelihood function of the observed signal.

5. The SA-ISAR self-focusing and calibration method based on sparse LVD according to claim 2, characterized in that: The method of obtaining the ISAR image by using the final sparse signal recovery result includes: Slicing the final sparse signal recovery result to obtain one-dimensional sparse signal slice information; The one-dimensional sparse signal slice information is spliced ​​to obtain the ISAR image.

6. The SA-ISAR self-focusing and calibration method based on sparse LVD according to claim 1, characterized in that: The ISAR image calibration result includes: an estimated value of the range dimension resolution of the ISAR image and a lateral range dimension resolution of the ISAR image; performing lateral calibration processing on the ISAR image using the FSBL-LVD-CTF method to obtain an estimated value of the lateral range dimension resolution of the ISAR image in the ISAR image calibration result, including: Using the FSBL-LVD-CTF method, the effective rotation speed of the maneuvering target corresponding to the ISAR image is estimated to obtain an estimated value of the effective rotation speed of the maneuvering target; The estimated value of the lateral range resolution of the ISAR image is estimated by using the estimated value of the effective rotation speed of the maneuvering target.

7. The SA-ISAR self-focusing and calibration method based on sparse LVD according to claim 6, characterized in that: The distance dimension resolution of the ISAR image is expressed as: Among them, ρ r represents the distance resolution of the ISAR image, c represents the speed of light, and B w Indicates the bandwidth of the transmitted signal; The estimated value of the lateral range resolution of the ISAR image is expressed as: in, represents the estimated value of the lateral range resolution of the ISAR image, f c represents the radar carrier frequency, represents the estimated effective rotation speed of the maneuvering target, T a Indicates the imaging accumulation time.

8. The SA-ISAR self-focusing and calibration method based on sparse LVD according to claim 2, characterized in that: The sparse signal recovery model corresponding to each slow time dimension signal performs fast sparse Bayesian learning based on the noise self-term prior probability model, the prior model of the signal to be recovered and the conditional likelihood function of the observed signal to obtain the final sparse signal recovery result, including: S201, obtaining current hyperparameters, and substituting the current hyperparameters, the noise self-term prior probability model, the to-be-recovered signal prior model and the observed signal conditional likelihood function into the sparse signal recovery model, and calculating the posterior probability density of the to-be-recovered signal using Bayes' theorem; the current hyperparameters include: the accuracy of the to-be-recovered signal, the accuracy of the noise self-term and the parameters of the gamma distribution to which the accuracy of the noise self-term obeys; S202, taking the mean of the posterior probability density of the signal to be restored corresponding to the maximum posterior probability density of the signal to be restored as the current sparse signal restoration result; S203, using the second type maximum likelihood estimation criterion and the current sparse signal recovery result, updating the current hyperparameter in S201 to obtain an updated hyperparameter, and using the updated hyperparameter as the current hyperparameter in S201; S204, re-execute S201-S203 until the iteration stop condition is met, and use the current sparse signal recovery result corresponding to the time when the iteration stop condition is met as the final sparse signal recovery result; The iteration stopping condition includes: the number of iterations meets the iteration number threshold, or the difference between the current sparse signal recovery result and the sparse signal recovery result corresponding to the previous iteration is less than the accuracy threshold.

9. A SA-ISAR self-focusing and calibration device based on sparse LVD, characterized in that: The SA-ISAR self-focusing and calibration device based on sparse LVD includes: a model building unit, a calculation unit and a lateral calibration unit; The model building unit is used to: build an echo model of a sparse aperture maneuvering target; The model building unit is also used for: under the echo model, performing energy accumulation based on the CFCR domain to obtain a sparse signal recovery model of the linear frequency modulation signal in the CFCR domain during the energy accumulation process; The computing unit is used to solve the sparse signal recovery model based on the FSBL-LVD-CTF method to obtain the ISAR image; the FSBL-LVD-CTF method is a LV distribution transformation with cross-term suppression based on fast sparse Bayesian learning; The lateral calibration unit is used to perform lateral calibration processing on the ISAR image using the FSBL-LVD-CTF method to obtain an ISAR image calibration result.

10. A SA-ISAR self-focusing and calibration device based on sparse LVD, characterized in that: include: A processor, a storage medium and a bus, wherein the storage medium stores machine-readable instructions executable by the processor, and when the SA-ISAR self-focusing and calibration device based on sparse LVD is running, the processor and the storage medium communicate via the bus, and the processor executes the machine-readable instructions to perform the steps of the SA-ISAR self-focusing and calibration method based on sparse LVD as described in any one of claims 1 to 8.

Images