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

Abstract

This invention provides a SA-ISAR autofocusing and calibration method based on sparse LVD, comprising: constructing an echo model of a sparse aperture maneuvering target; obtaining a sparse signal recovery model of the linear frequency modulated signal in the CFCR domain during the energy accumulation process by performing energy accumulation based on the CFCR domain under the echo model; solving the sparse signal recovery model based on the FSBL-LVD-CTF method to obtain an ISAR image; and performing lateral calibration processing on the ISAR image using the FSBL-LVD-CTF method to obtain the ISAR image calibration result. In this invention, the FSBL-LVD-CTF method combines the strong robustness of sparse Bayesian learning and the efficient processing capability of Lf distribution transformation for linear frequency modulated signals, while also suppressing cross terms through cross-term filtering of CTF to ensure reliable sparse recovery results, thereby improving the accuracy and robustness of ISAR imaging.

Description

Technical Field

[0001] This invention relates to the field of inverse synthetic aperture radar imaging technology, specifically to a method for autofocusing and calibration of SA-ISAR based on sparse LVD. Background Technology

[0002] Inverse Synthetic Aperture Radar (ISAR) imaging technology, with its unique advantages of all-weather, all-day operation and strong penetration, has become an important tool for space target detection. ISAR achieves high range resolution by transmitting wide-bandwidth signals and obtains high lateral range resolution by utilizing the relative rotation between the target and the radar, thus generating two-dimensional high-resolution images that effectively reflect target characteristics. These images provide necessary technical support for the identification and classification of non-cooperative targets. However, with the increasingly widespread application of ISAR, target types are becoming more complex. Especially when monitoring missiles and other non-cooperative high-speed targets, the complex maneuverability of the targets and their unknown trajectories pose serious challenges to imaging. Furthermore, in practical applications, the complexity of multi-functional radar missions, operational imperfections, and unknown environments can all lead to discontinuities in the available echoes, which will cause a significant degrade or even complete failure of traditional ISAR imaging algorithms, such as Range-Doppler (RD). Therefore, how to achieve high-precision ISAR imaging of maneuvering targets under sparse aperture conditions has become an urgent problem to be solved.

[0003] Currently, algorithms for acquiring high-resolution ISAR images of maneuvering targets are mainly divided into two categories: non-parametric methods and parametric methods. Non-parametric methods utilize time-frequency analysis to acquire instantaneous images at different time points. However, due to the maneuverability of non-cooperative targets, the instantaneous rotation speed corresponding to different snapshots is not constant, leading to scaling factor problems related to time variations. Parametric methods, on the other hand, model the echo phase as a polynomial function and construct an optimization problem based on a certain image quality assessment index (such as image contrast or image entropy) to estimate the phase error. By compensating for the estimated spatially varying phase error, a clear and 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. Furthermore, compressed sensing technology provides an effective and feasible solution for sparse aperture ISAR (SA-ISAR) imaging, but due to the strong maneuverability of non-cooperative targets, the echo no longer exhibits sparsity in the Doppler domain. Therefore, sparse reconstruction algorithms cannot be directly used for sparse aperture ISAR imaging of maneuvering targets.

[0004] While existing nonparametric methods have relatively low computational cost, the effective rotation velocity (ERV) varies significantly during the coherent processing interval (CPI) when the target exhibits strong maneuverability, posing a significant challenge to lateral calibration. Parametric algorithms can perform lateral calibration simultaneously with autofocus, but the focusing performance of the resulting ISAR image is directly limited by the estimation accuracy of the polynomial coefficients, resulting in unsatisfactory performance under low signal-to-noise ratio conditions. Furthermore, for SA-ISAR imaging of maneuvering targets, the strong maneuverability of non-cooperative targets diminishes the sparsity of the echoes in the Doppler domain, rendering sparse reconstruction algorithms unsuitable for sparse aperture ISAR imaging of maneuvering targets. Therefore, existing technologies still have significant limitations when handling ISAR imaging of complex maneuvering targets and under sparse aperture conditions. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a SA-ISAR autofocusing and calibration method based on sparse LVD.

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

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

[0008] Construct an echo model for a sparse aperture maneuvering target;

[0009] Under the echo model, a sparse signal recovery model of the linear frequency modulated signal in the CFCR domain is obtained by 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 transformation with cross-term suppression based on fast sparse Bayesian learning.

[0011] The ISAR image was laterally calibrated using the FSBL-LVD-CTF method to obtain the ISAR image calibration results.

[0012] Secondly, the present invention provides an SA-ISAR autofocusing and calibration device based on sparse LVD, which includes: a model building unit, a calculation unit and a lateral calibration unit.

[0013] The model building unit is used to: build echo models of sparse aperture maneuvering targets;

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

[0015] The computational 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 ISAR images using the FSBL-LVD-CTF method to obtain ISAR image calibration results.

[0017] Thirdly, the present invention provides a SA-ISAR autofocusing and calibration device based on sparse LVD, comprising: 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 autofocusing 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 autofocusing and calibration method based on sparse LVD as described in any of the first aspects above.

[0018] This invention provides a SA-ISAR autofocusing and calibration method based on sparse LVD, comprising: constructing an echo model of a sparse aperture maneuvering target; obtaining a sparse signal recovery model of the linear frequency modulated signal in the CFCR domain during the energy accumulation process by performing energy accumulation based on the CFCR domain under the echo model; solving the sparse signal recovery model based on the FSBL-LVD-CTF method to obtain an ISAR image; the FSBL-LVD-CTF method is a Lv distribution transform 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 the ISAR image calibration result. In this invention, an accurate echo model is constructed to address the characteristics of sparse apertures and maneuvering targets. Based on this, energy accumulation is performed in the center frequency-frequency modulation (CFCR) domain, effectively improving the signal-to-noise ratio and providing sufficient information for subsequent signal recovery and imaging. Furthermore, the FSBL-LVD-CTF method combines the strong robustness of SBL with the efficient processing capability of LVD transform for linear frequency modulated signals, while also filtering out CTF through cross-terms. ，This invention achieves suppression of cross terms, thereby ensuring reliable sparse recovery results. Therefore, by constructing an accurate sparse aperture maneuvering target echo model, combined with the energy accumulation strategy in the CFCR domain and the superior sparse signal recovery capability of the SBL method, this invention effectively solves the technical challenge of high-precision ISAR imaging of maneuvering targets under sparse aperture conditions, improving 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. Attached Figure Description

[0020] Figure 1 A flowchart illustrating a SA-ISAR autofocusing and calibration method based on sparse LVD provided in an embodiment of the present invention;

[0021] Figure 2 An exemplary schematic diagram of the ISAR imaging geometry scene is shown;

[0022] Figure 3 An exemplary schematic diagram of a sparse aperture signal structure is shown.

[0023] Figure 4 An exemplary schematic diagram of the complete process of ISAR imaging and lateral calibration algorithm based on FSBL-LVD-CTF is shown.

[0024] Figure 5 An exemplary diagram comparing the 2D and 1D reconstruction results of the FSBL-LVD-CTF and FSBL-LVD algorithms is shown.

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

[0026] Figure 7 An exemplary schematic diagram of the target scattering point model, range-Doppler imaging results, and ideal imaging results is shown.

[0027] Figure 8 Exemplary examples are shown of ISAR images corresponding to different algorithms applied under different data missing types for high-resolution range images;

[0028] Figure 9 The example shows ISAR images corresponding to different algorithms when using the same high-resolution range image under different data missing rates;

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

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

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

[0032] Figure 13 This is a schematic diagram of the structure of an SA-ISAR autofocusing and calibration device based on sparse LVD, provided in an embodiment of the present invention. Detailed Implementation

[0033] To address the problem that traditional imaging algorithms for high-speed maneuvering targets in complex environments suffer from poor focusing performance or even complete failure due to the influence of sidelobes, grating lobes, and time-varying Doppler frequencies, this invention proposes a novel 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 the Lv's Distribution (LVD) and utilizes the correlation between cross-terms and the signal to suppress cross-terms through adaptive filtering in the sparse recovery iteration, ensuring reliable sparse recovery performance. This method enables high-precision estimation of non-uniformly sampled multi-component linear frequency modulated signals. Furthermore, the SA-ISAR imaging and cross-range scaling of maneuvering targets is cleverly transformed into an energy accumulation problem in the centroid frequency-chirp rate (CFCR) domain, which is solved using the proposed FSBL-LVD-CTF algorithm, ultimately yielding well-focused and calibrated ISAR images.

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

[0035] To improve the accuracy and robustness of ISAR imaging, this invention provides a SA-ISAR autofocusing and calibration method based on sparse LVD. Figure 1 This is a flowchart illustrating a SA-ISAR autofocusing and calibration method based on sparse LVD, provided as an embodiment of the present invention. The sparse LVD can also be represented as FSBL-LVD-CTF. Figure 1 As shown, it includes:

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

[0037] To demonstrate the complete process of establishing the echo model, Figure 2 An exemplary schematic diagram of the ISAR imaging geometry scene is shown, such as... Figure 2 As shown, during the observation period, the target (maneuvering target) moves from point A to point D. Its motion can be decomposed into three parts: circumduction from point A to point B, rotation from point B to point C, and translation from point C to point D. Among these, the circumduction and translation components do not contribute to ISAR imaging, while the rotation component is the essential source of ISAR imaging azimuth resolution.

[0038] Instantaneous distance R between radar and scattering point p p (t m This can be represented 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 Let R0 be the initial distance between the target center and the radar, and r(t) be the slow time. m x represents the instantaneous change in distance introduced by translation. p With y p θ(t) represents the x and y coordinates of the scattering point p in the imaging projection plane, respectively. m () indicates the instantaneous change in angle.

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

[0042]

[0043] Where, v, ω, These represent the target's radial velocity, acceleration, effective rotational speed, and rotational acceleration, respectively.

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

[0045]

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

[0047]

[0048] Where rect(·) is the window function; Let and t represent fast time and total time, respectively. Their relationship with slow time can be described as follows: T p And γ represent the carrier frequency, pulse duration, and modulation frequency, respectively. c is the speed of light, σ p Let be the backscattering coefficient at scattering point p.

[0049] After deskewing the echo described in (4) and compensating for the remaining video phase terms, 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 For reference distance, In order to keep up with the fast time The corresponding frequency.

[0052] Clearly, (5) is the mathematical expression of the full-aperture signal. However, due to various factors, the effective echo usually exhibits discontinuity. Figure 3 A schematic diagram of the structure of a sparse aperture signal is shown as an example. For 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, causing some motion compensation algorithms to fail. Fortunately, research has shown that envelope alignment algorithms based on minimum entropy are still effective.

[0053] Taking sparse aperture factors into account, the signal of the nth distance cell after envelope alignment processing of the HRRPs represented in (5) can be further expressed as:

[0054]

[0055] in,

[0056]

[0057] Let m(t) be the amplitude of the k-th signal component, K be the number of scattering points contained in the n-th range cell, and m(t) be the amplitude of the k-th signal component. m ) represents the sampling sequence.

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

[0059]

[0060] As shown in (7), the signal of any range cell can be modeled as a multi-component LFM signal, and its key parameters are determined by the target motion state and the position of the scattering point:

[0061]

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

[0063] Therefore, the excellent focusing performance of LFM signals in the CFCR domain can be fully utilized to transform the autofocusing and lateral calibration of maneuvering targets in ISAR into the problem of LFM signal energy integration and parameter estimation in the CFCR domain.

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

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

[0066]

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

[0068] In practical applications, scaling and Fourier transform along the time dimension can be jointly implemented using the Chirp-Z transform to reduce computational costs. The implementation process can be simplified as follows:

[0069]

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

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

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

[0073]

[0074] Where f and γ represent the frequency variable and the frequency modulation variable, respectively, and B k This represents the magnitude of the k-th mapping component.

[0075] Performing an inverse Fourier transform along f-dimensional pair (11), we obtain:

[0076]

[0077] Then, by performing the inverse Chirp-Z transform along the γ dimension on (12), we obtain:

[0078]

[0079] Based on the definition of LVD, it can be found that (13) is s(t) m The PSIAF of ) is defined as follows:

[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[·] denotes vectorization operation, It is the inverse Fourier transform matrix. N is a block diagonal matrix defined by (16). t N τ N f and N γ These represent the number of samples along the time, delay, frequency, and frequency modulation dimensions, respectively. It is the identity matrix. This indicates 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 into account the sparse aperture factor and noise, the observed y(t) m The instantaneous autocorrelation function of can be expressed as:

[0088]

[0089] Wherein, n(t) m ),m(t m ), and CrossTerms(τ,t m ) represent noise, sampling sequence, and cross term, respectively.

[0090] Based on (15) and (18), y(t) m The vectorized instantaneous autocorrelation function of ) 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 The i-th component of r is represented by diag(·), where diag(·) denotes the diagonalization operation. m w, r c,ss and r c,sn Let r represent the vectorized PSIAF of the sampled sequence, the vectorized PSIAF of the noise, the vectorized cross term between different signal components, and the vectorized cross term between the signal component and the noise, respectively. For ease of representation, r will be used in the following text. y It will be represented as y'.

[0095] The SA-ISAR imaging and lateral calibration problem is transformed 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 both the frequency and the frequency modulation, and ω is implicit in the frequency. Therefore, the SA-ISAR autofocusing and lateral calibration problem of maneuvering targets can be described by (19), with the goal of recovering the unknown sparse signal x from the observation data y'. It can be seen that this is a typical SSR problem (sparse signal recovery problem), which can be solved by CS, where A can be regarded as the sensing matrix, w represents the noise vector, y' is the observation 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 the 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] By performing Lv. distribution transformation on the slow-time dimension signal in the echo model, the noise term, the signal to be recovered, and the observed signal are obtained.

[0101] Prior modeling is performed on the noise self-terms to obtain the prior probability model of the noise self-terms;

[0102] Prior modeling is performed on the signal to be recovered and the observed signal, resulting in the prior model of the signal to be recovered and the conditional likelihood function of the observed signal.

[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; where fast sparse Bayesian learning is an implementation method based on 2D-CGLS and 2D-EDEM.

[0104] ISAR images are obtained using the final sparse signal recovery results.

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

[0106] The noise self-term is modeled prior using the generalized double Pareto distribution, resulting in a prior probability model for the noise self-term.

[0107] Optionally, prior modeling is performed on the signal to be recovered and the observed signal to obtain the prior model of the signal to be recovered and the conditional likelihood function of the observed signal, including:

[0108] A Gaussian distribution is used to model the signal to be recovered, resulting in a prior model of the signal to be recovered.

[0109] The conditional likelihood function of the observed signal is obtained by using the prior model of the signal to be recovered to perform prior modeling of the observed signal.

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

[0111] The final sparse signal recovery result is sliced ​​to obtain one-dimensional sparse signal slice information.

[0112] ISAR images are obtained by stitching together one-dimensional sparse signal slices.

[0113] Optionally, 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, including:

[0114] S201. Obtain the current hyperparameters, and substitute the current hyperparameters, the prior probability model of the noise self-term, the prior model of the signal to be recovered, and the conditional likelihood function of the observed signal into the sparse signal recovery model. Calculate the posterior probability density of the signal to be recovered using Bayes' theorem. The current hyperparameters include: the accuracy of the signal to be recovered, the accuracy of the noise self-term, and the parameters of the gamma distribution to which the accuracy of the noise self-term follows.

[0115] S202. Take the mean of the posterior probability density of the signal to be recovered when the posterior probability density of the signal to be recovered is the maximum, and use it as the current sparse signal recovery result.

[0116] S203. Using the second type of maximum likelihood estimation criterion and the current sparse signal recovery result, update the current hyperparameters in S201 to obtain the updated hyperparameters, and use the updated hyperparameters as the current hyperparameters in S201.

[0117] S204. Re-execute S201-S203 until the iteration stop condition is met. Take 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 stopping conditions include: 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 reasoning process for implementing S103 is as follows:

[0120] As is well known, SBL can be used to handle the typical SSR problem described in (20), as follows:

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

[0122] Where A, y, x and n' represent the sensing 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 make the traditional SBL algorithm no longer applicable to solving 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 follows a Gaussian distribution in the traditional SBL. Second, in addition to the noise term, the observations in Equation (19) also contain cross terms between different signal components and cross terms between signal and noise, which will seriously weaken the performance of SBL sparse reconstruction.

[0124] To address the aforementioned issues, a generalized double Pareto (GDP) distribution is introduced to model the prior, and adaptive iterative filtering is used to suppress the cross terms.

[0125] a) Noise self-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, K0(·) represents the deviation (standard deviation) of a random variable, and K0(·) represents the zeroth-order Bessel function of the second kind.

[0129] However, the distribution function described in (21) is quite complex. If it is used directly to model the noise prior, it will cause great inconvenience to the derivation of SBL. Therefore, this invention uses the generalized double Pareto distribution to model the noise self-term prior. In order to simplify the inference process, this invention constructs the following three-level hierarchical prior so that the marginal probability density distribution of w conforms to the GDP prior.

[0130] First, assuming all elements of w follow the same complex Gaussian distribution, then:

[0131]

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

[0133] Secondly, 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 recovered, assume that all its elements follow a complex Gaussian distribution:

[0140]

[0141] in, Let α represent the variance of the i-th element of x. Further, assume α... i It follows a 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, and its expression is:

[0144]

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

[0146]

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

[0148] The hyperparameter update process is as follows:

[0149] For ease of inference, hyperparameter estimation is performed based on the second type of maximum likelihood estimation criterion. Given that the observation y' is known, and the source vector x and 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) Derive p(x|α,β,ε,y')

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

[0153]

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

[0155]

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

[0157] Obviously, (31) can be seen as the convolution of two complex Gaussian distributions, and according to the properties of the complex Gaussian distribution, it still follows a complex Gaussian distribution. Therefore, in order to accurately write the analytical expression of p(y'|α,β), it is essential to calculate its mean and variance. For ease 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] Therefore, 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] Based on (35), (31) can be rewritten as:

[0166]

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

[0168]

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

[0170]

[0171] Combining (25), (28), and (38), we know that p(x|α,β,ε,y') follows 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 Let w and Ax represent the covariance matrices, 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 as described in (19), in addition to w, the observation y' also contains cross terms r. c,ss and r c,sn Obviously, as the signal components increase, the energy of the cross term will be significantly enhanced, which poses a great threat to the performance of sparse recovery and may even cause the useful signal to be overwhelmed. 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 the signal x and the given signal, and its covariance matrix can be estimated during the iteration process. Furthermore, the estimation error decreases continuously with the increase in the number of iterations. Therefore, cross-term suppression can be achieved based on adaptive filtering. The following will focus on R... c,ss With R c,sn The estimates will be introduced separately.

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

[0182]

[0183] in

[0184]

[0185] and Represent and The estimated range.

[0186] Furthermore, in the field of radar signal processing, noise variance can be estimated based on reference cells, and signal variance can also be obtained in each iteration through... An estimate is made. Therefore, combining the cross term r c,sn By definition, its covariance matrix can be estimated as:

[0187]

[0188] Where I is the identity matrix, and These represent the variances of the signal and noise, respectively.

[0189] In summary, in order to filter out the cross terms, (40) should be modified 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 recovery 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 deduced using conditional independence and Bayes' theorem:

[0195]

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

[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 an exponential term, which will cause inconvenience in the derivation. Therefore, this invention simplifies it by taking the logarithm to obtain:

[0199]

[0200] Where C is a constant independent of hyperparameters.

[0201] (48) The hyperparameters corresponding to the maximum value of the likelihood function can well characterize the statistical features of the observations. Therefore, we can calculate (48) with respect to α. i By taking the partial derivatives of β and ε and setting them equal to zero, we can obtain the hyperparameter update criterion:

[0202]

[0203] Where, γ i =1-α i Σ ii , Σ ii Let be the i-th diagonal element of Σ.

[0204] Obviously, for the SSR model described in (19), the Kronecker process will introduce a large-scale sensing matrix, so the inversion of Q involved in (45) will lead to a huge computational burden. To solve the above problems, 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 problems of matrix inversion and matrix diagonal element calculation, respectively, which can significantly reduce the computational complexity.

[0205] For ease of expression, the following definition is provided:

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

[0207] in

[0208]

[0209] Where, r i,j Let i represent the cross term between the vectorized i-th signal component and the j-th signal component, where 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] As is well known, the conjugate gradient least squares method can be used to solve the normal equation expressed in (53). However, directly using the original CGLS algorithm to solve (53) also leads to a large computational burden, which is inherent to the large-scale SSR problem constructed by this invention. Fortunately, the matrix B constructed in this invention has a special structure. Based on its two-dimensional structure characteristics, a corresponding 2D-CGLS algorithm is proposed. This algorithm directly processes the two-dimensional data structure, avoiding flattening the data into a one-dimensional vector, thereby reducing the complexity of data transformation, significantly reducing storage requirements, and improving the efficiency and adaptability of the algorithm.

[0213] For Σ, only its diagonal elements are used to update hyperparameters, so calculating it via (39) would result in a serious waste of computational resources. Fortunately, EDEM can be used to estimate the diagonal elements of a matrix, achieving satisfactory parameter estimation accuracy even with a small number of iterations. To this end, this invention, taking into account the structural characteristics of matrix B, presents a two-dimensional implementation of EDEM for estimating the diagonal elements of a matrix.

[0214] S104. Use the FSBL-LVD-CTF method to perform lateral calibration processing on the ISAR image to obtain the ISAR image calibration result.

[0215] This invention provides a SA-ISAR autofocusing and calibration method based on sparse LVD, constructing an accurate echo model tailored to the characteristics of sparse apertures and maneuvering targets. Based on this, energy accumulation in the center frequency-frequency modulated (CFCR) domain effectively improves the signal-to-noise ratio, providing sufficient information for subsequent signal recovery and imaging. Furthermore, the FSBL-LVD-CTF method combines the strong robustness of SBL with the efficient processing capability of LVD for linear frequency modulated signals, while also suppressing cross-terms through CTF filtering to ensure reliable sparse recovery results. Therefore, by constructing an accurate sparse aperture maneuvering target echo model, combining the energy accumulation strategy in the CFCR domain with the sparse signal recovery capability of the SBL method, this invention effectively solves the technical challenge of high-precision ISAR imaging of maneuvering targets under sparse aperture conditions, improving the accuracy and robustness of ISAR image imaging.

[0216] Optionally, the ISAR image calibration results include: estimates of the range resolution and the lateral range resolution of the ISAR image; the ISAR image is laterally calibrated using the FSBL-LVD-CTF method to obtain the estimated lateral range resolution of the ISAR image in the ISAR image calibration results, including:

[0217] The effective rotational speed of the corresponding maneuvering target in the ISAR image is estimated using the FSBL-LVD-CTF method, and the estimated effective rotational speed of the maneuvering target is obtained.

[0218] The lateral range dimension resolution of the ISAR image is estimated by using the effective rotational speed estimate of the maneuvering target.

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

[0220]

[0221] Where, ρ r Let c represent the range dimension resolution of the ISAR image, and B represent the speed of light. w Indicates the bandwidth of the transmitted signal;

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

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

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

[0225] Clearly, 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. To obtain feature information such as target size and geometry, calibration of the ISAR image in both the range and lateral range dimensions is crucial.

[0226] ISAR achieves range resolution by transmitting wide-bandwidth signals and pulse compression processing; its image range dimension resolution is:

[0227]

[0228] Among them, B w This refers to the bandwidth of the transmitted signal.

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

[0230]

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

[0232] Obviously, range calibration is easy to achieve since the ISAR system parameters are known. However, ISAR targets are non-cooperative, and their trajectory information is unknown beforehand. Therefore, it is crucial to use echo information to accurately estimate the target rotation speed.

[0233] Suppose there exist two scattering points with the same x-coordinate but located in different distance cells, i.e., satisfying the following condition:

[0234]

[0235] x p =x q (58)

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

[0237] In practical applications, the position of the target's rotation center cannot be known, i.e., y p With y q Unmeasurable. However, the effect of reference center deviation is consistent across all scattering points, therefore y p -y q It is estimable. Therefore, by combining (56), (57), and (58), the estimated value of the target rotational speed is:

[0238]

[0239] Therefore, the estimated value of the lateral range dimension resolution of the ISAR image can be obtained as follows:

[0240]

[0241] In summary, Figure 4 An exemplary schematic diagram of the complete workflow for ISAR imaging and lateral calibration algorithms based on FSBL-LVD-CTF is shown. Figure 4As shown, firstly, the sparse aperture echo data is deskewed to obtain a high-resolution range envelope. Then, the high-resolution range envelope is aligned and its conjugate is taken to obtain N. r Each multi-component non-uniformly sampled LFM signal, i.e., each slow-time dimension signal (range cell signal), 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. This result is then sliced ​​and stitched to obtain an ISAR image. Simultaneously, the proposed FSBL-LVD-CTF algorithm is used to estimate the effective rotational speed of the target. After obtaining the estimated value, calibration processing is 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 cell signal as y, and perform necessary initialization processing to obtain the input of the algorithm, including: perception matrix A, observation signal y', and 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 The solution y' is obtained by solving for its two-dimensional analytical solution. 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 values ​​of the diagonal elements of Σ, and then update the current hyperparameters according to equations (49)-(51) to obtain the updated hyperparameters. 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 it does not, the updated hyperparameters are used as the current hyperparameters to continue the iteration.

[0243] In summary, this invention proposes a novel 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 utilizes the correlation between cross-terms and the signal to suppress cross-terms through adaptive filtering in the sparse recovery iteration, ensuring reliable sparse recovery performance. The proposed algorithm enables high-precision estimation of non-uniformly sampled multi-component linear frequency modulated signals. Furthermore, maneuvering target SA-ISAR imaging and lateral calibration are cleverly transformed into an energy accumulation problem in the CFCR domain and solved using the proposed FSBL-LVD-CTF algorithm. Its application in maneuvering target SA-ISAR imaging provides a new paradigm, freeing ISAR image autofocus performance from the limitations of error compensation accuracy. Moreover, it exhibits satisfactory accuracy and superior focusing performance even with low signal-to-noise ratios and large data missing rates, demonstrating significant advantages over existing algorithms.

[0244] To verify the effectiveness of the proposed SA-ISAR autofocusing and calibration method based on sparse LVD in complex environments, the following comparative experiments were conducted.

[0245] Experiment 1:

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

[0247] Figure 5 An exemplary diagram comparing the 2D and 1D reconstruction results of the FSBL-LVD-CTF and FSBL-LVD algorithms is shown. The 2D and 1D reconstruction results of FSBL-LVD are as follows: Figure 5 Figure (a) and Figure 5 Figure (b) shows the 2D and 1D reconstruction results of the FSBL-LVD-CTF algorithm, respectively. Figure 5 Figure (c) and Figure 5 As shown in Figure (d). Clearly, from... Figure 5 It can be seen that the SSR results of the FSBL-LVD algorithm are severely affected by the cross terms, while the FSBL-LVD-CTF algorithm proposed in this invention can effectively suppress the cross terms, and each signal component is clearly distinguishable. Therefore, the effectiveness of the method of this invention for 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 ManeuveringTarget 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, "ISARImaging 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 ISAR imaging and cross-range scaling of maneuvering targets based on sparse CICPF method," IEEE Sensors J., vol. 24, no. 11, pp. 18066-18081, 1 June 1, 2024, is denoted as SCICPF.

[0249] Experiment 2:

[0250] To further explore the sparse LFM signal reconstruction performance of the method of this invention, this experiment uses CPESBL, PC-MBSBL, SCICPF and the proposed FSBL-LVD-CTF algorithm to reconstruct three-component LFM signals with different missing rates and different signal-to-noise ratios, respectively. The superiority of the algorithm of this invention in terms of reconstruction accuracy and robustness is illustrated by comparison.

[0251] To facilitate the analysis of the reconstruction accuracy of each algorithm, the normalized root mean square error is defined as follows:

[0252]

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

[0254] Figure 6 The nRMSE curves of each algorithm 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 the variable. Figure 6 Figure (b) shows the nRMSE curves for each algorithm when the data missing rate is fixed at 30%, with the signal-to-noise ratio as the variable. Clearly, as... Figure 6 As shown, under the same conditions, the algorithm of this invention has superior reconstruction accuracy. Furthermore, the proposed algorithm exhibits satisfactory robustness; unlike the comparative algorithms, the reconstruction performance of the algorithm of this invention is minimally affected by the signal-to-noise ratio and the data missing rate.

[0255] Experiment 3:

[0256] In this simulation, it is assumed that the radar transmits a linear frequency modulated signal. Figure 7 An exemplary schematic diagram of the target scattering point model, range-Doppler imaging results, and ideal imaging results is shown. For example... Figure 7 Figure (a) shows that the target selected in the simulation consists of 84 scattering points. The main radar parameters, including carrier frequency, bandwidth, pulse width, and pulse repetition frequency, are set to 4 GHz, 1 GHz, 200 μs, and 200 Hz, respectively. Key target parameters include radial velocity, radial acceleration, ERV, and ERA, which are set to 200 m / s², 30 m / s², and 40 m / s², respectively. 2 0.08 rad / s and 0.008 rad / s 2 It should be noted that the signal-to-noise ratio mentioned in subsequent experiments is 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, respectively. (Comparison) Figure 7 Figure (b) and Figure 7 Figure (c) shows that the spatially varying phase error introduced by the target's maneuvering motion caused the ISAR image to defocus, which indicates that the spatially varying phase error is not negligible in high-resolution ISAR imaging.

[0257] In the following discussion, random missing data and gap missing data will be denoted as SA-Type 1 and SA-Type 2, respectively. Furthermore, image entropy and image contrast are introduced as evaluation metrics for 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 algorithm for 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, "Sparse Apertures ISAR Imaging and Scaling for Maneuvering Targets", IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., vol. 7, no. 7, pp. 2942-2956, July 2014, are respectively called PPEC and MDCFT algorithms. These two algorithms are used together as comparative algorithms for horizontal scaling.

[0258] Experiment 4:

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

[0260] Figure 8 Exemplary examples are shown of ISAR images corresponding to various algorithms applied under different data missing types for high-resolution range images. Among them, Figure 8 (a)- Figure 8 The missing data type for plot (c) is SA-Type1. Figure 8 Figure (a) shows the high-resolution distance envelopes (HRRPs) aligned under SA-Type 1; Figure 8 Figure (b) shows the ISAR image obtained by the CPESBL algorithm under SA-Type 1; Figure 8 (c) shows the ISAR image obtained by the algorithm of the present invention under SA-Type 1. Figure 8 (d)- Figure 8 The missing data type for plot (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 this invention under SA-Type2.

[0261] from Figure 8 It can be seen that the method proposed in this invention achieves optimal resolution and focusing performance in both SA-Type 1 and SA-Type 2 cases. In other words, the proposed algorithm is effective for both types of non-uniformly sampled echo data. Therefore, due to space limitations, subsequent experiments will not further distinguish between SA-Type 1 and SA-Type 2.

[0262] Experiment 5:

[0263] In this experiment, SA-ISAR imaging was performed using various algorithms at different missing rates to analyze the sensitivity of each algorithm to the missing data rate. Figure 9 The example shows ISAR images corresponding to the same high-resolution range image when using different algorithms under different data missing rates. Figure 9 (a)- Figure 9 (c): The data missing rate is 50%. Figure 9 Figure (a) shows the aligned HRRPs; Figure 9 Figure (b) shows the ISAR image obtained by the CPESBL algorithm; Figure 9 Figure (c) shows the ISAR image obtained by the proposed algorithm. Figure 9 (d) diagram - Figure 9 The missing data rate for plot (f) is 70%. Figure 9 The (d) diagram represents the aligned HRRPs; Figure 9 Figure (e) represents the ISAR image obtained by the CPESBL algorithm; Figure 9 Figure (f) shows the ISAR image obtained by the proposed algorithm. Clearly, even with a high data missing rate, the proposed method can obtain a clearer ISAR image than the comparative algorithm, and it exhibits lower sensitivity to data missing rates. Therefore, the effectiveness of the proposed method in sparse aperture conditions is verified.

[0264] Experiment Six:

[0265] In this experiment, the sensitivity of the proposed algorithm to the signal-to-noise ratio (SNR) is analyzed using the signal-to-noise ratio (SNR) as a variable. Figure 10 The example shows ISAR images obtained by various algorithms under different signal-to-noise ratio conditions for high-resolution range images. Figure 10 (a)- Figure 10(c) The signal-to-noise ratio is 0dB. Figure 10 Figure (a) shows the aligned HRRPs; Figure 10 Figure (b) shows the ISAR image obtained by the CPESBL algorithm; Figure 10 Figure (c) shows the ISAR image obtained by the proposed algorithm. Figure 10 (d)- Figure 10 The signal-to-noise ratio of the (f) image is 10 dB. Figure 10 The (d) diagram represents the aligned HRRPs; Figure 10 Figure (e) represents the ISAR image obtained by the CPESBL algorithm; Figure 10 Figure (f) shows the ISAR image obtained by the proposed algorithm. It can be observed that as the signal-to-noise ratio decreases, the entropy of the images 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] To further analyze the lateral scaling performance of PPEC, MDCFT, and the proposed method, this experiment uses the above algorithms to estimate the effective rotational speed (ERV) under different signal-to-noise ratios and different missing rates, and the comparison demonstrates the superior estimation accuracy and robustness of the proposed algorithm. Figure 11 The results of the comparative analysis of the effective rotational speed estimation performance of each algorithm under different missing rates and different signal-to-noise ratios are presented as an example. Figure 11 Figure (a) shows the comparison results of effective rotational speed estimation when the data missing rate is used as a variable. Figure 11 Figure (b) shows the comparison results of effective rotational speed estimation when the signal-to-noise ratio is used as a variable. Clearly, the algorithm proposed in this invention has higher parameter estimation accuracy compared to the comparison algorithms. Furthermore, as the data missing rate increases or the signal-to-noise ratio decreases, the estimation errors of each comparison algorithm gradually increase, while the proposed algorithm exhibits satisfactory robustness.

[0268] The method provided in this embodiment of the invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc., and this embodiment of the invention does not limit the application to such devices.

[0269] Based on the same inventive concept, embodiments of the present invention also provide a SA-ISAR autofocusing and calibration device based on sparse LVD. Figure 12 This is a schematic diagram of a SA-ISAR autofocusing and calibration device based on sparse LVD, provided as an embodiment of the present invention. Figure 12As shown, the SA-ISAR autofocusing and calibration device based on sparse LVD includes: a model building unit 601, a calculation unit 602, and a lateral calibration unit 603;

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

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

[0272] The computing 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 L-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 ISAR images using the FSBL-LVD-CTF method to obtain ISAR image calibration results.

[0274] Figure 13 This invention provides a schematic diagram of a SA-ISAR autofocusing and calibration device based on sparse LVD, comprising: a processor 710, a storage medium 720, and a bus 730. The storage medium 720 stores machine-readable instructions executable by the processor 710. When the SA-ISAR autofocusing and calibration device based on sparse LVD is running, the processor 710 and the storage medium 720 communicate via the bus 730. The processor 710 executes the machine-readable instructions to perform the steps of the above-described method embodiment. Specific implementations and technical effects are similar and will not be repeated here.

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

[0276] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0277] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the inventive concept, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for autofocusing and calibration of SA-ISAR based on sparse LVD, characterized in that, include: Construct an echo model for a sparse aperture maneuvering target; Under the aforementioned echo model, a sparse signal recovery model of the linear frequency modulated signal in the CFCR domain during the energy accumulation process is obtained based on energy accumulation in the CFCR domain. The sparse signal recovery model is solved using 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 solve the sparse signal recovery model to obtain the ISAR image, including: The Lü distribution transform is performed on the slow time dimension signal in the echo model to obtain the noise term, the signal to be recovered, and the observed signal. Prior modeling is performed on the noise self-terms to obtain the noise self-term prior probability model; Prior modeling is performed on the signal to be recovered and the observed signal to obtain the prior model of the signal to be recovered and the conditional likelihood function of the observed signal. 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; 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; The ISAR image is laterally calibrated using the FSBL-LVD-CTF method to obtain the ISAR image calibration result.

2. The SA-ISAR autofocusing and calibration method based on sparse LVD according to claim 1, characterized in that, The prior modeling of the noise term to obtain the prior probability model of the noise term includes: The noise self-term is modeled prior using a generalized double Pareto distribution to obtain the prior probability model of the noise self-term.

3. The SA-ISAR autofocusing and calibration method based on sparse LVD according to claim 1, characterized in that, The prior modeling of the signal to be recovered and the observed signal, corresponding to the prior model of the signal to be recovered and the conditional likelihood function of the observed signal, includes: A Gaussian distribution is used to model the signal to be recovered, resulting in a prior model of the signal to be recovered. The observed signal is modeled a priori using the prior model of the signal to be recovered, and the conditional likelihood function of the observed signal is obtained.

4. The SA-ISAR autofocusing and calibration method based on sparse LVD according to claim 1, characterized in that, The process of obtaining the ISAR image using the final sparse signal recovery result includes: The final sparse signal recovery result is sliced ​​to obtain one-dimensional sparse signal slice information. The one-dimensional sparse signal slice information is stitched together to obtain the ISAR image.

5. The SA-ISAR autofocusing and calibration method based on sparse LVD according to claim 1, characterized in that, The ISAR image calibration results include: estimated values ​​of the range dimension resolution and the lateral range dimension resolution of the ISAR image; the ISAR image is laterally calibrated using the FSBL-LVD-CTF method to obtain the estimated value of the lateral range dimension resolution of the ISAR image in the ISAR image calibration results, including: The effective rotational speed of the corresponding maneuvering target in the ISAR image is estimated using the FSBL-LVD-CTF method, and the effective rotational speed of the maneuvering target is estimated. The estimated value of the lateral range dimension resolution of the ISAR image is obtained by using the estimated effective rotational speed of the maneuvering target.

6. The SA-ISAR autofocusing and calibration method based on sparse LVD according to claim 5, characterized in that, The range dimension resolution of the ISAR image is expressed as: ； in, This represents the range dimension resolution of the ISAR image. Represents the speed of light. Indicates the bandwidth of the transmitted signal; The estimated value of the lateral range dimension resolution of the ISAR image is expressed as: ； in, This represents an estimate of the lateral range dimension resolution of the ISAR image. Indicates the radar carrier frequency. This represents the estimated effective rotational speed of the maneuvering target. This indicates the image accumulation time.

7. The SA-ISAR autofocusing and calibration method based on sparse LVD according to claim 1, characterized in that, The sparse signal recovery model corresponding to each slow time dimension signal is 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 then performed to obtain the final sparse signal recovery result, including: S201. Obtain the current hyperparameters, and substitute the current hyperparameters, the prior probability model of the noise self-term, the prior model of the signal to be recovered, and the conditional likelihood function of the observed signal into the sparse signal recovery model, and calculate the posterior probability density of the signal to be recovered using Bayes' theorem; the current hyperparameters include: the accuracy of the signal to be recovered, the accuracy of the noise self-term, and the parameters of the gamma distribution to which the accuracy of the noise self-term follows; S202. Take the mean of the posterior probability density of the signal to be recovered when the posterior probability density of the signal to be recovered is the maximum, and take it as the current sparse signal recovery result. S203. Using the second type of maximum likelihood estimation criterion and the current sparse signal recovery result, update the current hyperparameter in S201 to obtain the updated hyperparameter, and use the updated hyperparameter as the current hyperparameter in S201. S204. Re-execute S201-S203 until the iteration stop condition is met. Take the current sparse signal recovery result corresponding to the iteration stop condition as the final sparse signal recovery result. The iteration stopping conditions include: 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.

8. A SA-ISAR autofocusing and calibration device based on sparse LVD, characterized in that, The SA-ISAR autofocusing 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 to: obtain a sparse signal recovery model of the linear frequency modulated signal in the CFCR domain during the energy accumulation process based on energy accumulation in the CFCR domain under the echo model; The computing unit is used to: solve the sparse signal recovery model based on the FSBL-LVD-CTF method to obtain an ISAR image; the FSBL-LVD-CTF method is a Lv distribution transform with cross-term suppression based on fast sparse Bayesian learning; the process of solving the sparse signal recovery model based on the FSBL-LVD-CTF method to obtain an ISAR image includes: The Lü distribution transform is performed on the slow time dimension signal in the echo model to obtain the noise term, the signal to be recovered, and the observed signal. Prior modeling is performed on the noise self-terms to obtain the noise self-term prior probability model; Prior modeling is performed on the signal to be recovered and the observed signal to obtain the prior model of the signal to be recovered and the conditional likelihood function of the observed signal. 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; 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; 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.

9. A SA-ISAR autofocusing and calibration device based on sparse LVD, characterized in that, include: The device includes a processor, a storage medium, and a bus. The storage medium stores machine-readable instructions executable by the processor. When the SA-ISAR autofocusing and calibration device based on sparse LVD is running, the processor communicates with the storage medium via the bus. The processor executes the machine-readable instructions to perform the steps of the SA-ISAR autofocusing and calibration method based on sparse LVD as described in any one of claims 1-7.

Images