Sparse Aperture Bi-ISAR Imaging and Calibration Method Based on FAIWF-CICPF-CTF

Abstract

This paper utilizes ground-based and space-based radars to construct a novel Bi-ISAR architecture with significant advantages, including wide coverage and high flexibility. Furthermore, a sparse-aperture Bi-ISAR imaging and calibration method based on the FAIWF-CICPF-CTF algorithm is proposed for this Bi-ISAR system. This imaging and calibration method breaks with traditional thinking by innovatively transforming the sparse-aperture Bi-ISAR imaging and calibration problem into a sparse signal recovery problem in the CFCR domain, providing a new paradigm for sparse-aperture Bi-ISAR imaging and calibration. Benefiting from the excellent energy accumulation and noise suppression performance of the CICPF algorithm and the superior reconstruction performance of the proposed adaptive iterative Wiener filter, this method demonstrates superior performance compared to existing algorithms under conditions of low signal-to-noise ratios and high data loss rates.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar imaging and calibration, and in particular relates to a sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF. Background Art

[0002] In recent years, bistatic configurations have been widely used in inverse synthetic aperture radar (ISAR) imaging due to their unique potential for anti-interference and counter-stealth capabilities. However, conventional bistatic inverse synthetic aperture radar (Bi-ISAR) systems are limited in their radar deployment locations, which inevitably results in their being affected by factors such as the Earth's curvature, thus degrading their detection performance. To overcome the bottleneck of conventional Bi-ISAR detection performance being limited by the deployment location of ground-based radars, space-based combined configurations have emerged. These configurations utilize a transmitting system aboard a satellite or spacecraft platform, while the receiving system is deployed on the ground. By combining the advantages of space-based radars, which enable continuous global surveillance, with the advantages of ground-based radar configurations, such as unconstrained size, mass, power consumption, and ease of maintenance, the application of space-based combined configurations in ISAR imaging can effectively expand the system's detection range and greatly facilitate the acquisition of diverse target perspectives.

[0003] In recent years, scholars have conducted relevant research on bistatic ISAR imaging. Ding Jiabao et al. gave an accurate expression for the spatially varying phase error in Bi-ISAR imaging of maneuvering targets and proposed an optimization function based on minimum entropy to estimate and compensate for the spatially varying phase error to obtain well-focused Bi-ISAR images. Wang Yong, Jiang Yicheng et al. proposed a parameter estimation-based Bi-ISAR imaging and azimuth calibration algorithm for maneuvering targets in passive bistatic ISAR systems. They first select two range cells containing ideal prominent points. Then, they use the CIGCPF and CICPF algorithms to estimate the equivalent frequency, frequency modulation, and frequency modulation rate of each component of the two slow-time signal. Finally, based on these estimated parameters, they calculate the target's rotation center, effective rotation speed, and other information to achieve bistatic distortion correction and azimuth calibration.

[0004] Furthermore, in practical applications, when Bi-ISAR systems are used to observe high-speed maneuvering targets, factors such as uncertainty in the trajectory of non-cooperative targets, interference, and non-ideal operation can all lead to discontinuous effective echoes. However, if the sparse aperture echoes of maneuvering targets are directly Fourier transformed, in addition to the space-varying phase error caused by maneuvering, the image quality will also be affected by sidelobes and grating lobes. Fortunately, space targets can be viewed as consisting of a number of isolated scattering points, so Bi-ISAR images have significant sparsity, which perfectly matches the prerequisite for the application of compressed sensing algorithms. To address these issues, Min-Seok Kang et al. proposed a sparse aperture Bi-ISAR imaging algorithm for maneuvering targets based on compressed sensing. This algorithm utilizes sensing matrix estimation technology to reconstruct the Bi-ISAR echo signal. It then performs translation compensation, rotation compensation, distortion correction, and range-to-lateral range calibration to obtain a well-focused, calibrated Bi-ISAR image. Shi Lin et al. proposed a joint processing algorithm for Bi-ISAR image reconstruction and cross-range unit motion correction based on Bayesian inference, which can simultaneously achieve cross-range unit motion correction and autofocusing.

[0005] The focusing performance of the image acquired by the algorithm proposed by Wang Yong et al. is constrained by the accuracy of parameter estimation. Furthermore, in practical applications, distinct point units may not exist, severely limiting its application scenarios. Furthermore, its performance under conditions of non-uniform sampling of target echoes is unsatisfactory. The algorithm proposed by Min-Seok Kang et al. reconstructs the echo signals of each range unit separately, which consumes significant computational resources. Furthermore, the OMP algorithm used is only suitable for noise-free or high signal-to-noise ratio data recovery, which results in unsatisfactory performance under low signal-to-noise ratio conditions. The algorithm proposed by Shi Lin et al. assumes that the target rotational speed and time-varying dual base angles can be obtained from prior information. However, in practical applications, the motion trajectory of non-cooperative maneuvering targets is difficult to obtain. Furthermore, the sparse reconstruction algorithm used limits its application in low signal-to-noise ratio environments.

[0006] Furthermore, current Bi-ISAR imaging is mostly based on ground-based radars, which are inevitably affected by factors such as the Earth's curvature, thus reducing its detection performance. Therefore, the core issue addressed by this paper is how to perform high-precision sparse-aperture Bi-ISAR imaging in low signal-to-noise ratio environments. Summary of the Invention

[0007] To address the above-mentioned problems in the prior art, the present invention provides a sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0008] A sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF includes:

[0009] S100, using a Bi-ISAR imaging system consisting of space-based radar and ground-based radar, receives echo data from non-cooperative targets;

[0010] S200, preprocessing the echo data to obtain a preprocessed echo signal, and extracting the preprocessed echo signal along the slow time dimension to obtain a slow time dimension signal;

[0011] S300, using the proposed FAIWF-CICPF-CTF algorithm to process the slow time dimension signals obtained after the preprocessing until an iteration termination condition is met, thereby obtaining a Bi-ISAR image and an ERV estimation value;

[0012] S400, performing distortion correction on the Bi-ISAR image using a distortion correction function, estimating the lateral range resolution using an ERV estimation value, and calibrating the Bi-ISAR image after the distortion correction in combination with the range resolution to obtain a Bi-ISAR image after the distortion correction and calibration.

[0013] Beneficial effects:

[0014] This paper utilizes ground-based and space-based radars to construct a novel Bi-ISAR architecture with significant advantages, such as wide coverage and high flexibility. A sparse-aperture Bi-ISAR imaging and calibration method based on the FAIWF-CICPF-CTF framework is proposed for this Bi-ISAR system. This imaging and calibration method breaks with traditional thinking by innovatively transforming the sparse-aperture Bi-ISAR imaging and calibration problem into a sparse signal recovery problem in the CFCR domain, providing a new paradigm for sparse-aperture Bi-ISAR imaging and calibration. Benefiting from the excellent energy accumulation and noise suppression performance of the CICPF algorithm and the superior reconstruction performance of the proposed adaptive iterative Wiener filter algorithm, the present invention demonstrates superior performance compared to existing algorithms under conditions of low signal-to-noise ratio and high data loss rate.

[0015] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of a sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF provided by the present invention;

[0017] Figure 2 It is a schematic diagram of Bi-ISAR imaging geometry;

[0018] Figure 3is a schematic diagram of sparse aperture echo;

[0019] Figure 4 This is a schematic diagram of the GDP distribution and the product distribution of two independent and identically normal noises;

[0020] Figure 5 It is a schematic diagram of bistatic distortion;

[0021] Figure 6 It is a schematic diagram of simulation data;

[0022] Figure 7 HRRP under different data missing types and Bi-ISAR images obtained by each algorithm;

[0023] Figure 8 These are HRRP and Bi-ISAR images at different data missing rates;

[0024] Figure 9 These are the HRRP and Bi-ISAR imaging results at different signal-to-noise ratios;

[0025] Figure 10 This is a schematic diagram of ERV estimation performance analysis under different signal-to-noise ratios and different data missing rates. DETAILED DESCRIPTION

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

[0027] This paper constructs a novel bistatic inverse synthetic aperture radar (Bi-ISAR) imaging system using space-based and ground-based radars to effectively extend the system's detection range. A non-parametric sparse aperture Bi-ISAR imaging and calibration algorithm is proposed. This algorithm approximates the slow-time signal after traditional translational compensation as a multi-component linear frequency modulation (LFM) signal. Furthermore, the significant sparsity of the multi-component LFM signal in the center frequency-chirp rate (CFCR) domain is exploited to transform the Bi-ISAR autofocusing and calibration problem into a typical sparse signal recovery (SSR) problem. To achieve reliable sparse recovery performance, this paper proposes an adaptive iterative Wiener filter-based coherently integrated cubic phase function with cross-terms filtering (AIWF-CICPF-CTF) algorithm to solve the SSR problem. It also incorporates iterative cancellation techniques to effectively suppress cross-terms. Furthermore, a fast implementation algorithm is provided to ensure its feasibility in practical applications. The proposed algorithm demonstrates superior energy accumulation and noise suppression performance compared to existing algorithms.

[0028] like Figure 1 As shown, the present invention provides a sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF, including:

[0029] S100, using a Bi-ISAR imaging system consisting of space-based radar and ground-based radar, receives echo data from non-cooperative targets;

[0030] As a specific embodiment of the present invention, S100 includes:

[0031] S110, constructing a geometric model of Bi-ISAR imaging consisting of a space-based radar as a transmitting radar and a ground-based radar as a receiving radar;

[0032] The Bi-ISAR imaging system to be discussed in this invention is constructed by a space-based radar and a ground-based radar. The former is only used to transmit signals due to its limited processing capability, while the latter serves as a receiver. Figure 2Figure (a) shows the geometric diagram of Bi-ISAR imaging of the maneuvering target to be discussed. The global coordinate system O-UVW and the target coordinate system O'-XYZ are constructed in the figure. The global coordinate system O-UVW is an absolute reference system with the location of the stationary ground-based radar as the origin; while the target coordinate system O'-XYZ has the center of the target as the origin, and its X, Y, and Z axes correspond to the angular velocity directions of the target roll, pitch, and yaw, respectively. β(t m ) is t m Double base angle at time r T (t m ) and r R (t m ) represent the instantaneous distance between the target and the transmitting radar and the receiving radar respectively. In order to analyze the complex motion characteristics of the maneuvering target, Figure 2 Figure (b) describes the target motion state in the target coordinate system. and η E (t m ) represent the instantaneous azimuth and elevation angles of the target, respectively.

[0033] The sum of the instantaneous distances between the scattering point p and the transmitting radar and the receiving radar can be decomposed into the translational component r trans (t m ) and the rotational component r rot (t m )Two parts:

[0034] r p (t m )=r trans (t m )+r rot (t m ) (1)

[0035] r trans (t m )=r T (t m )+r R (t m ) (2)

[0036]

[0037] in

[0038]

[0039] M rot (t m )=M yaw (t m )·M roll (t m )·M pitch (tm ) (6)

[0040]

[0041]

[0042] is the initial position of the scattering point p; i T (t m ) and i R (t m ) represent the unit vectors of the LOS directions of the transmitting radar and the receiving radar respectively; r T (t m ) and r R (t m ) represent the instantaneous distance between the target and the transmitting radar and the receiving radar respectively; M yaw (t m ), M roll (t m ) and M pitch (t m ) represent t m The rotation matrix corresponding to yaw, roll and pitch at each moment; θ yaw (t m ),θ roll (t m ) and θ pitch (t m ) represent t m The instantaneous yaw, roll and pitch angle changes at the moment.

[0043] S120, constructing a mathematical model of non-cooperative target echoes using the Bi-ISAR imaging geometric model;

[0044] S130: Utilize the space-based radar to transmit a signal, utilize the ground-based radar to receive a target echo signal, and obtain an expression form of the target echo data according to the mathematical model.

[0045] Assuming that Bi-ISAR transmits a linear frequency modulation signal, it can be expressed as:

[0046]

[0047] Where rect(·) represents the window function; T p is the pulse width; f c is the carrier frequency of the LFM signal; γ is the modulation frequency; For quick time, represents full time, t m For slow time.

[0048] Assuming that the target consists of P scattering points and the “walk-stop-walk” model still holds, the high-resolution range profile (HRRP) after de-skewing and compensating the residual video phase (RVP) can be expressed as:

[0049]

[0050] in, For fast time The corresponding frequency; c is the speed of light; r Δ,p (t m )=r p (t m )-r ref , r ref is the total reference distance.

[0051] S200, preprocessing the high-resolution range image to obtain a preprocessed echo signal;

[0052] As a specific embodiment of the present invention, S200 includes:

[0053] S210, performing range pulse compression on the echo data to obtain a high-resolution range image;

[0054] S220, performing translation compensation on the high-resolution range image to obtain an aligned range envelope;

[0055] S230: Taking a conjugate of the aligned range envelope to obtain a preprocessed echo signal.

[0056] Combining equations (1)-(9), it is clear that the signal form described by (11) is very complex. Fortunately, it can be simplified when only considering two-dimensional ISAR imaging. The imaging plane of two-dimensional ISAR is the XOY plane, and the target angular velocity is in the YOZ plane, which can be decomposed into the effective component parallel to the Z axis that contributes to the lateral resolution of ISAR imaging: e , and the invalid rotation component ω perpendicular to the Z axis n At this point, the instantaneous rotation matrix can be described by the following formula:

[0057]

[0058] Furthermore, the instantaneous distance introduced by the rotation component can be further simplified as:

[0059]

[0060] Since the observation time required for Bi-ISAR imaging is short and the target is inert and its motion state will not change drastically during this period, the following polynomials are used to approximate the rotation angle θ(t m ) and the time-varying double base angle β(tm ) is sufficiently precise:

[0061]

[0062] However, in practical applications, the available echo signals may be obtained by non-uniform sampling, that is, their observation aperture is sparse, such as Figure 3 shown.

[0063] Fortunately, studies have shown that the envelope alignment algorithm based on global minimum entropy and the initial phase correction algorithm based on eigenvectors are still effective in Bi-ISAR imaging processing under sparse aperture conditions. Therefore, the present invention performs subsequent processing based on the assumption that translation compensation has been completed.

[0064] Substituting (4)(13)(14) into (11), we can get the conjugate of the lateral distance dimension signal after translation compensation as:

[0065]

[0066] The Taylor series expansion of trigonometric functions is used.

[0067] m(t m ) is a sequence composed of 0 and 1, and its specific value needs to be determined according to the echo energy intensity; (1) In complex environments, some data segments in the echo signal after preprocessing contain interference signals in addition to target information. In order to achieve reliable target detection and recognition, it is necessary to select the echo data. (2) Affected by non-ideal operations and the complexity of the multi-function radar system tasks, discontinuous sampling of target echoes often occurs, that is, only some data segments contain target echoes. In order to extract useful echo data from the echo data segment, it is necessary to design a sampling sequence m(t m ): By setting the energy threshold, the part of the echo signal with energy higher than the energy threshold will be discarded.

[0068] S300, extracting signals along the slow time dimension from the preprocessed echo signals to obtain slow time dimension signals, processing the slow time dimension signals using the proposed FAIWF-CICPF-CTF algorithm until an iteration termination condition is satisfied, thereby obtaining a Bi-ISAR image and an ERV estimation value;

[0069] As a specific implementation of the present invention, S300 includes:

[0070] S310, extracting a slow time dimension signal from the preprocessed echo signal along the slow time dimension, and approximating the slow time dimension signal to a multi-component linear frequency modulation signal;

[0071] S320, utilizing the significant sparsity of the multi-component linear frequency modulation signal in the center frequency-frequency modulation domain, converting the Bi-ISAR autofocusing and calibration problem into an SSR problem;

[0072] S330 , using FAIWF-CICPF-CTF to iteratively solve the SSR problem until an iteration termination condition is met, thereby obtaining a Bi-ISAR image and an ERV estimation value.

[0073] As a specific implementation of the present invention, S320 includes:

[0074] S321, analyzing an ideal mapping value of the multi-component linear frequency modulation signal in the center frequency-frequency modulation rate domain, and confirming a sparse characteristic of the multi-component linear frequency modulation signal in the center frequency-frequency modulation rate domain according to the ideal mapping value;

[0075] For the QFM signal described in (15), its key parameter estimation methods can be roughly divided into parameter search algorithms and energy accumulation algorithms. The parameter search algorithm is very sensitive to the environmental signal-to-noise ratio, and its performance is not satisfactory under low signal-to-noise ratio conditions; while the existing energy accumulation algorithm does not have the ability to simultaneously obtain the frequency, modulation rate, and second-order modulation rate parameters of multi-component QFM signals. Fortunately, for short-time Bi-ISAR, the impact of third-order phase error on imaging focusing performance can be ignored. For this reason, the present invention conducts research on short-time Bi-ISAR imaging and further simplifies it into:

[0076]

[0077] Obviously, the signal It can be approximated as a sparse aperture multi-component LFM signal, whose frequencies and frequency modulation components are determined by the target motion parameters and the scattering point positions, respectively expressed as:

[0078]

[0079] The first phase term in equation (16) indicates that scattering points at different lateral distance units will produce different Doppler frequencies, which is the source of the azimuth resolution of Bi-ISAR imaging. The second term is the root cause of bistatic distortion. The remaining phase terms are space-varying phase errors, which will cause image defocus. Existing algorithms all try to compensate for the above phase errors to obtain well-focused Bi-ISAR images. However, it should be noted that the present invention does not follow this idea. Instead, it converts Bi-ISAR imaging and calibration into the energy accumulation problem of multi-component LFM signals for processing. This is the key to the focusing performance of the algorithm proposed in the present invention, which is not limited by the parameter estimation accuracy.

[0080] S322, integrating noise and data missing factors, and combining the multi-component linear frequency modulation signal to construct an autocorrelation function of the noisy non-uniformly sampled observation data; the autocorrelation function characterizes the Bi-ISAR autofocusing and calibration problem;

[0081] Assume that the ideal mapping value of the multi-component LFM signal in the CFCR domain can be expressed as:

[0082]

[0083] Among them, B i , f i ' and γ i ' are the amplitude, frequency and modulation rate parameters of the i-th component of the multi-component LFM signal respectively.

[0084] Then, the instantaneous autocorrelation function of the noisy non-uniformly sampled observation data y can be expressed as:

[0085]

[0086] Among them, R m 、R y and R n are the instantaneous autocorrelation functions of the sampling sequence, observation signal and noise respectively; R c,ss is the cross term between different signal components; R c,sn is the cross term between signal and noise; is the non-uniform inverse Fourier transform matrix; is the inverse Fourier transform matrix; represents the frequency modulation matrix; N t , N τ , N f and N g Represent the number of sampling points of time dimension, delay dimension, frequency dimension and modulation frequency dimension respectively.

[0087] R m (t m ,τ)=m(t m +τ)m(t m -τ)

[0088] Among them, R m (t m ,τ) is the instantaneous autocorrelation function of the sampling sequence, t m is the slow time, τ is the delay variable, m(t m +τ) and m(t m -τ) are the sampling sequences m(t m ) is a shifted signal obtained by shifting it left and right by τ.

[0089]

[0090] in, For The corresponding frequency.

[0091] According to the definition of X, the mapping position of each signal component in the CFCR domain is determined by the target motion state and the scattering point position parameters, and its effective rotation speed can be reflected in the CF dimension.

[0092] S323, convert the Bi-ISAR autofocusing and calibration problem into an SSR problem.

[0093] Combining steps 3 and 4, we can see that the sparse aperture Bi-ISAR imaging problem can be represented by equation (19), which can be vectorized as:

[0094] r y =Ax+r c,ss +r c,sn +r n (twenty two)

[0095] in

[0096]

[0097] r m =vec[m(t m +τ)m(t m -τ)]

[0098] r y =vec[y(t m +τ)y(t m -τ)]

[0099] r n =r m ⊙vec[n(t m +τ)n(t m -τ)]

[0100]

[0101]

[0102] Here, vec[·] represents vectorized processing.

[0103] Obviously, the problem described by formula (22) is a typical SSR problem, and the purpose of this invention is to obtain the y Therefore, in order to obtain high-precision Bi-ISAR images under low signal-to-noise ratio and high data missing rate conditions, the present invention proposes a fast adaptive iterative Wiener filtering algorithm suitable for processing large-scale SSR problems to solve the problem represented by equation (22).

[0104] As a specific implementation of the present invention, S330 includes:

[0105] S331, at each iteration, using the designed FAIWF-CICPF-CTF algorithm to solve the SSR problem, obtaining a sparse recovery result of the mapping value of each slow-time dimension signal in the center frequency-to-frequency modulation domain at each iteration; determining whether the iteration termination condition is met, and if so, using the current sparse recovery result as the output sparse recovery result;

[0106] As a specific embodiment of the present invention, the process of solving the SSR problem using the designed FAIWF-CICPF-CTF algorithm includes:

[0107] The SSR problem is solved by the FAIWF-CICPF-CTF algorithm, and the 2D-CGLS algorithm is introduced in the solution process to avoid the inversion process and improve the algorithm operation efficiency, and the sparse recovery result of the center frequency-modulation frequency domain mapping value of each slow time dimension signal is obtained in each iteration.

[0108] In order to make full use of the noise information contained in the auxiliary data, the present invention assumes that the auxiliary data n and All elements in obey the same complex Gaussian distribution:

[0109]

[0110] To facilitate reasoning, the present invention defines a new variable: We can get:

[0111]

[0112] in, represents the estimated value of the original signal; β n is the precision of n'. Further, the present invention assumes that n' obeys the gamma distribution with parameters a and b:

[0113]

[0114] where a and b represent the shape parameter and inverse scale factor, respectively; Γ(·) is the gamma function.

[0115] The distribution function of the product of two independent and normally distributed random numbers can be characterized by the following formula:

[0116]

[0117] where σ represents the divergence of w and K0(·) is the zero-order Bessel function of the second kind.

[0118] However, the distribution function described by Equation (26) is very complex, which will bring great inconvenience to Bayesian inference. Fortunately, as Figure 4 As described, n The distribution of can be well fitted by the GDP distribution, which can be obtained by constructing a three-level prior.

[0119] Therefore, in order to facilitate inference, the present invention constructs the following three layers of priors to obtain GDP distribution and then realize r n First, the present invention assumes that IAF[n] is All elements of have the same complex Gaussian distribution:

[0120]

[0121] Among them, IAF[·] represents the instantaneous autocorrelation operation; β w IAF[n] and IAF precision.

[0122] Similarly, according to the definition of n', (27) can be rewritten as:

[0123]

[0124] For ease of presentation, IAF[n'] will be expressed as

[0125] Secondly, the hyperparameter β w It is assumed to be gamma distributed with parameters ε and k:

[0126]

[0127] Finally, the hyperparameter ε is modeled as following a gamma distribution with parameter h:

[0128]

[0129] Here, h is a small positive number.

[0130] In the problem (22) constructed by the present invention, the present invention hopes to estimate the expected signal x from the observation mixed with interference terms, and the error between the estimated value and the true value is defined as:

[0131]

[0132] Among them, w opt is the optimal weight of the filter. Obviously, in order to obtain the expression of x, the present invention needs to further determine the optimal weight w opt . For this purpose, the minimum mean square error is defined as follows:

[0133]

[0134] According to (31), (32) can be rewritten as:

[0135]

[0136] Among them, Q xx =E[xx H ];

[0137] Let E[e(n) 2 ] opt The partial derivative is zero, and the analytical solution of the optimal weight is:

[0138]

[0139] in,

[0140] Q xy =AΛ (35)

[0141] Q yy =AΛA H +Q c,ss +Q c,sn +Q n (36)

[0142] Λ is a diagonal matrix whose diagonal elements are: Λ(k,k)=|x(k)| 2 .

[0143] According to (34), (35) and (36), the MMSE estimate of x can be expressed as:

[0144]

[0145] From (37), we can see that the observation r y The covariance matrix of is composed of four parts, among which AΛA H , Q c,ss , Q c,sn and Q n Represent Ax, r respectively c,ss , r c,sn and r n Obviously, the covariance matrix Q of the signal cross term is c,ss It can be estimated in iterations. Assume that the signal x estimated in the lth iteration is l The frequency and modulation rate of the i-th component are and They can all be based on x l The peak position in the CFCR domain is read out. c,ss It can be estimated as:

[0146]

[0147] in

[0148]

[0149] and They represent the amplitude estimates of the i-th and j-th signal components in the multi-component LFM signal respectively.

[0150] In addition, based on previous prior modeling work, the covariance matrix Q can be obtained using Bayesian inference c,sn With Q n This is the core of the adaptive iterative Wiener filtering proposed in this invention. First, the present invention first gives Q c,sn Specific derivation of the estimate:

[0151] According to r c,sn From the definition of c,sn can be estimated as: This is due to the statistical independence between signal and noise. The accuracy of the signal can be obtained by reconstructing the signal It is estimated that, in addition represents the accuracy of the original noise, which can be obtained through Bayesian inference.

[0152] To facilitate inference, the present invention estimates hyperparameters based on the second-class maximum likelihood function. n The posterior probability distribution of can be expressed as:

[0153]

[0154] Among them, p(n') is the marginal probability density of the original noise n', which is only related to the model, so

[0155] p(β n |n')∝p(n'|β n )p(β n ) (43)

[0156] However, p(β n |n') contains exponential terms, so for the convenience of analysis, the present invention takes the logarithm of (43) and ignores the constant term to obtain:

[0157] ln f(β n )=(M+a-1)lnβ n -β n n'n' H -bβ n (44)

[0158] Among them, f(β n )=p(n'|β n )p(β n ).

[0159] Let lnf(β n ) for β n The partial derivative of is zero, and the parameter update rule can be described as:

[0160]

[0161] For the covariance matrix Q n , which can also be estimated based on the second-type maximum likelihood function. According to the Bayesian criterion, the hyperparameter β w The joint posterior probability density of ε and ε can be expressed as:

[0162]

[0163] Likewise, the present invention Taking the logarithm to simplify this gives:

[0164]

[0165] Among them, C is related to the hyperparameter β w A constant that is independent of ε.

[0166] Furthermore, define f(β w ,ε)=ln[p(r n |β w )p(β w |ε)p(ε)], and let it be w The partial derivatives of ε are zero respectively, and the update formulas can be expressed as:

[0167]

[0168] At this point, (37) can be rewritten as:

[0169]

[0170] Benefiting from the fact that n' is continuously updated as the algorithm iterates, the error between its variance estimate and the true value will also continue to shrink during the iteration. It is worth noting that in the method proposed in the present invention, the noise information contained in the test data and the auxiliary data is fully utilized, which overcomes the problem of large noise variance estimation error caused by the coupling of signal estimation and noise estimation in the SBL algorithm and the problem of unsatisfactory estimation performance caused by a small number of samples in the traditional Wiener filtering algorithm. For ease of understanding, the proposed AIWF-CICPF-CTF algorithm process can be summarized as Table 1. That is, the process of solving the SSR problem using the AIWF-CICPF-CTF algorithm includes:

[0171] a. Input the perception matrix, observation signal, accuracy threshold, maximum number of iterations, and multiple hyperparameters, initialize the sparse recovery result, and initialize the current iteration number to 1;

[0172] b. Estimate the frequency and modulation rate of each original signal component based on the peak position of the sparse restored signal in the CFCR domain obtained in the previous iteration, and construct the covariance matrix of the signal cross term based on the expression of the LFM signal and the definition of the signal cross term;

[0173] c. Update the accuracy of the original noise dataset and the signal, and update the hyperparameters based on the second-type maximum likelihood estimation;

[0174] d. Using the updated hyperparameters, calculate the covariance matrix of the observed signal;

[0175] e. Update the sparse recovery signal of the current iteration according to the minimum mean square error criterion and update the diagonal matrix;

[0176] f, increment the current iteration by 1;

[0177] g. Determine whether the maximum number of iterations has been reached or whether the change between the sparse recovery signals of two adjacent iterations has met the accuracy requirements. If any requirement is met, output the sparse recovery result that meets the requirements.

[0178] Table I Proposed AIWF-CICPF-CTF algorithm

[0179]

[0180]

[0181] Obviously, in the SSR model constructed by Equation (22), the Kronecker product will introduce a large perception matrix, which will undoubtedly bring a huge computational burden. To ensure the feasibility of the proposed AIWF-CICPF-CTF algorithm in practical applications, this paper further proposes a corresponding fast implementation method, called FAIWF-CICPF-CTF, which will be described in detail below.

[0182] For the convenience of derivation, define:

[0183] u=Q -1 r y =(B H B) -1 B H z (51)

[0184] in

[0185]

[0186] ηI and Represents r c,sn With r n The covariance matrix of r i,j represents the vectorized cross term between the i-th and j-th signal components, i,j=1,2,…,K and i≠j

[0187] Then, formula (51) can be further rewritten as:

[0188] B H Bu=B H z (55)

[0189] Therefore, by solving the linear equation expressed in equation (55), we can obtain the estimated value of u and avoid the large matrix inversion operation involved in the original problem (51). To overcome the above problems, the present invention proposes a 2D-CGLS algorithm based on the structural characteristics of the matrix B to solve the least squares problem ||Bu-z|| 2 , which can significantly improve the computational efficiency of the algorithm.

[0190] To facilitate derivation, the present invention summarizes the key steps of the CGLS algorithm as follows:

[0191]

[0192] u l+1 =u l +δ l p l (57)

[0193] h l+1 =h l +δ l Bpl (58)

[0194] r l+1 =B H h l+1 (59)

[0195] θ l =((r l+1 ) H (r l+1 )) / ((r l ) H (r l )) (60)

[0196] p l+1 =r l+1 +θ l p l (61)

[0197] Among them, the parameters are initialized as: l=0,u0=0,h0=z-Bu0,r0=B H h0,p0=r0.

[0198] Obviously, when the CGLS algorithm is directly used to solve the above problem, the computational complexity of the algorithm mainly depends on Bp l With B H h l+1 To solve the above problem, the present invention uses the structural characteristics of matrix B and proposes a 2D-CGLS algorithm to solve Q -1 r y To avoid large matrix multiplication and improve algorithm efficiency, it can be summarized as Table 2.

[0199] Table II 2D-CGLS solution Q -1 r y

[0200]

[0201] Where Π=mat[diag(Λ)]; mat[·] represents rearranging the vector into a matrix; R y For r y Two-dimensional form; R m For r m The two-dimensional form of ; L is the maximum number of iterations; δ is the iteration termination accuracy of 2D-CGLS; represent The cross term between the i-th signal component and the j-th signal component in ; represents the t obtained in the l+1th iteration 2,l+1 in The corresponding coefficient.

[0202] After obtaining the estimated value of U using the 2D-CGLS algorithm, the 2D form of x can be rewritten as:

[0203]

[0204] S332, slicing and splicing the sparse recovery results corresponding to the slow-time dimension signals to obtain a Bi-ISAR image;

[0205] S333 : Calculate an ERV estimation value using the sparse recovery results of the two selected slow-time dimension signals, wherein the two selected slow-time dimension signals contain information of scattering points with the same abscissa.

[0206] The iteration termination condition is that the maximum number of iterations is reached or the variation between the sparse restored signals obtained by two adjacent iterations meets the accuracy requirement.

[0207] S400, performing distortion correction on the Bi-ISAR image using a distortion correction function to obtain a distortion-corrected Bi-ISAR image, estimating the lateral range resolution using an ERV estimation value, and calibrating the distortion-corrected Bi-ISAR image in combination with the range resolution to obtain a distortion-corrected and calibrated Bi-ISAR image.

[0208] As a specific implementation of the present invention, S400 includes:

[0209] S410, constructing a distortion correction function;

[0210] S420, using the distortion correction function to perform distortion correction on the Bi-ISAR image to obtain a Bi-ISAR image after distortion correction;

[0211] S430 , calculating the lateral range resolution using the obtained ERV estimation value, and calibrating the distortion-corrected Bi-ISAR image in combination with the range resolution to obtain a distortion-corrected and calibrated Bi-ISAR image.

[0212] Observing (16), it should be noted that Bi-ISAR images have two significant features compared to monostatic ISAR images. One of them is that the K0 introduced by the bistatic geometry will lead to image resolution scaling. The other is that the time-varying bistatic angle will introduce linear geometric distortion, that is, scatterers of different distance units will have different amounts of offset along the Doppler direction, and from formula (16), it can be seen that the larger the ordinate of the scattering point, the greater the Doppler offset it produces. The schematic diagram of bistatic distortion is as follows Figure 5 Obviously, in order to reliably identify the target, distortion correction must be performed to obtain the correct target shape.

[0213] According to formula (16), the offset between the focus position and the true position of the scattering point p caused by bistatic distortion can be expressed as:

[0214]

[0215] in, represents the focal position of the scattering point p, x p represents the true position of the scattering point p.

[0216] Fortunately, in practical applications, K0 and K1 can be estimated from the target motion trajectory obtained by the radar tracking system. Therefore, the present invention can construct the following geometric correction function to eliminate the distortion of Bi-ISAR images.

[0217]

[0218] in, is the ordinate of the estimated scattering point p.

[0219] Assuming that there are two scattering points with the same abscissa located in different distance units, after bistatic distortion correction, the following relationship holds:

[0220]

[0221] x p =x q (67)

[0222] Among them, y p with y q Represents the vertical coordinates of scattering points p and q respectively; x p with x q Represent the horizontal coordinates of the scattering points p and q respectively; γ' p With γ' q They represent the modulation frequencies corresponding to the scattering points p and q respectively.

[0223] However, in practical applications, p is unknown, that is, the ordinate of the scattering point calculated by the present invention Its true value y p There are some deviations between them: Then a new error term exp[-j4f c K1Δyt m / c], but fortunately Δy is constant for all scattering points and does not cause additional image distortion. Therefore, ERV can be estimated by the following formula:

[0224]

[0225] According to the Bi-ISAR imaging model constructed by the present invention in equation (22), the range resolution and lateral range resolution of the Bi-ISAR image can be estimated as follows:

[0226]

[0227] Where B is the transmission signal bandwidth; λ is the LFM signal wavelength; T obs is the Bi-ISAR imaging observation time.

[0228] At this point, Bi-ISAR imaging, bistatic distortion correction, and range and lateral range dimension calibration processing have been completed. The results obtained can provide strong support for target recognition, classification, and size estimation.

[0229] The present invention uses a space-based radar as a transmitting radar and equips a ground-based radar as a receiver to construct a new type of space-ground dual-base configuration and apply it to ISAR imaging. The significant sparsity of the echo in the CFCR domain is utilized to cleverly transform the sparse aperture Bi-ISAR imaging and calibration problem into a sparse signal recovery problem in the CFCR domain for processing. In order to obtain reliable sparse signal recovery results, the present invention proposes an adaptive iterative Wiener filtering algorithm to solve the sparse signal recovery problem. It fully utilizes the noise information contained in the auxiliary data and the test data, introduces Gaussian distribution and generalized bi-Pareto distribution respectively to approximate the original noise and the prior of the instantaneous autocorrelation function of the noise, and then obtains an accurate covariance matrix estimate through Bayesian inference. The signal cross terms introduced in the algorithm are suppressed by iterative cancellation to obtain a reliable sparse recovery effect. In addition, the present invention also provides a fast implementation method of the proposed algorithm to ensure the feasibility of the proposed algorithm in practical applications.

[0230] In order to effectively illustrate the effectiveness of the algorithm proposed in this invention and its superiority in the cases of high data loss rate and low signal-to-noise ratio, the following simulation experiments are set up, and the algorithms in the literature M.-S.Kang, S.-H.Lee, K.-T.Kim and J.-H.Bae,"Bistatic ISAR imaging and scaling of highly maneuvering target with complex motion via compressive sensing,"IEEE Trans.Aerosp.Electron.Syst.,vol.54,no.6,pp.2809-2826,Dec.2018. and L.Shi,X.-X.Zhu,C.-X.Shang,B.-F.Guo,J.-T.Ma and N.Han,"High-resolution bistatic ISAR imaging of a space target withsparse aperture,"Electronics,2019,8,874. are used as comparison algorithms. For the convenience of description, they are respectively referred to as Algorithm I and Algorithm II.

[0231] Example 1

[0232] In the simulation: Assume that the space-based radar transmits LFM signals and the target model used is as follows: Figure 6 As shown in Figure (a), a fighter jet consists of 95 scatterers. In addition, the main parameters of the radar system and non-cooperative targets are shown in Table III.

[0233] Table III Radar system and target parameter settings

[0234]

[0235]

[0236] Figure 6 For simulation data. Figure 6 (b), (c), and (d) respectively show the range image after traditional translation compensation under ideal noise-free and full-aperture conditions, the Bi-ISAR image before distortion correction, and the ideal Bi-ISAR image. (b) shows the high-resolution range image after alignment, with the horizontal axis Pulse Index being the pulse index and the vertical axis Range Cell being the range unit; (c) shows the Bi-ISAR image before bistatic distortion correction; (d) shows the ideal Bi-ISAR image, with the horizontal axis Cross-Range Cell being the cross-range unit. Comparison Figure 6(c) and (d) show that Bi-ISAR imaging will produce shear deformation, which is consistent with theoretical analysis. Therefore, in order to obtain reliable target recognition results, bistatic distortion correction is extremely important.

[0237] To demonstrate the universality of the proposed algorithm for processing data of different sparse aperture types, we sampled complete echoes based on the characteristics of SA-Type 1 and SA-Type 2 to obtain the two types of echoes. In this experiment, the data loss rate and signal-to-noise ratio of the echoes were set to 50% and 10dB, respectively.

[0238] Figure 7 HRRP under different data missing types and ISAR images obtained by each algorithm. Figure 7 As revealed in Figure 7 Figures (a)-(d) correspond to SA-Type 1; (a) shows HRRP; (b) shows the Bi-ISAR image obtained by Algorithm I; (c) shows the Bi-ISAR image obtained by Algorithm II; (d) shows the Bi-ISAR imaging result of the proposed algorithm; (e)-(h) correspond to SA-Type 2; (e) shows HRRP; (f) shows the Bi-ISAR image obtained by Algorithm I; (g) shows the Bi-ISAR image obtained by Algorithm II; (h) shows the Bi-ISAR imaging result of the proposed algorithm. The proposed algorithm is effective in processing data of both sparse aperture types. Therefore, due to space limitations, the sensitivity analysis of the proposed algorithm with respect to other key parameters will not specifically distinguish between the non-uniform sampling type (sparse aperture type) and the non-uniform sampling type (sparse aperture type).

[0239] Example 2

[0240] To verify the effectiveness of the proposed algorithm under sparse aperture conditions, we randomly sampled 210, 150, and 90 pulses from the full-aperture pulses to simulate sparse aperture signals with data missing rates of 30%, 50%, and 70%.

[0241] Figure 8 The processing results of the proposed algorithm and two comparison algorithms for signals with different data missing rates are given respectively. Figure 8 As can be seen from the figure, the two compared algorithms are highly sensitive to the data missing rate, and their performance decreases significantly with the increase of the data missing rate. However, the proposed algorithm can still obtain clear target Bi-ISAR images even under the condition of large data missing rate. In other words, the effectiveness and superiority of the proposed algorithm under the condition of large data missing rate are verified.

[0242] Figure 8 HRRP and ISAR images under different data missing rates. Figure 8In (a)-(d), MR = 30%; (a) is HRRP; (b) is the Bi-ISAR image obtained by algorithm I; (c) is the Bi-ISAR image obtained by algorithm II; (d) is the Bi-ISAR imaging result of the proposed algorithm; in (e)-(h), MR = 50%; (e) is HRRP; (f) is the Bi-ISAR image obtained by algorithm I; (g) is the Bi-ISAR image obtained by algorithm II; (h) is the Bi-ISAR imaging result of the proposed algorithm; in (i)-(l), MR = 70%; (i) is HRRP; (j) is the Bi-ISAR image obtained by algorithm I; (k) is the Bi-ISAR image obtained by algorithm II; (l) is the Bi-ISAR imaging result of the proposed algorithm.

[0243] Example 3

[0244] To further explore the performance of the proposed algorithm in practical applications, this experiment will perform imaging and calibration processing under different signal-to-noise ratio conditions to analyze its sensitivity to noise. To simulate different noise environments, we artificially add complex Gaussian white noise according to different signal-to-noise ratios. It should be noted that the signal-to-noise ratios mentioned in the experimental section are all defined in the HRRP domain:

[0245]

[0246] in, is the average power of noise-free HRRP, E(Noise 2 ) is the average power of Gaussian white noise.

[0247] Figure 9 HRRP and imaging results under different signal-to-noise ratios; Figure 9 The results of the three algorithms for processing data with different signal-to-noise ratios are presented in Figure 2. Clearly, as the signal-to-noise ratio decreases, the focusing performance of the Bi-ISAR images obtained by the two compared algorithms significantly degrades. However, the proposed algorithm maintains satisfactory focusing performance even under low signal-to-noise ratio conditions, thanks to the coherent accumulation process in the constructed model and the full utilization of prior statistical information by the proposed adaptive iterative Wiener filter. The experiments confirm that the proposed algorithm has superior energy accumulation performance and noise suppression capabilities, which is consistent with the theoretical analysis.

[0248] Figure 9In (a)-(d), SNR=10dB; (a) is HRRP; (b) is the Bi-ISAR image obtained by algorithm I; (c) is the Bi-ISAR image obtained by algorithm II; (d) is the Bi-ISAR imaging result of the proposed algorithm; (e)-(h) are SNR=5dB; (e) is HRRP; (f) is the Bi-ISAR image obtained by algorithm I; (g) is the Bi-ISAR image obtained by algorithm II; (h) is the Bi-ISAR imaging result of the proposed algorithm; (i)-(l) are SNR=0dB; (i) is HRRP; (j) is the Bi-ISAR image obtained by algorithm I (k) is the Bi-ISAR image obtained by algorithm II; (l) is the Bi-ISAR imaging result of the proposed algorithm.

[0249] Example 4

[0250] To further verify the robustness of the proposed algorithm, we conducted Monte Carlo experiments under different MR and SNR, and confirmed the superior robustness of the proposed method by comparing the mean square error of ERV estimation of each algorithm.

[0251] Figure 10 The ERV estimation performance analysis diagram is shown in Figure (a), where the data missing rate is the variable, the horizontal axis MR is the data missing rate, and the vertical axis MSE is the mean square error. The signal-to-noise ratio is the variable, and the horizontal axis SNR is the signal-to-noise ratio. Figure 10 As revealed, under the same conditions, the algorithm proposed in this patent has higher parameter estimation accuracy than other algorithms. In addition, it can be seen that the parameter estimation accuracy of the comparison algorithm decreases significantly with the decrease of signal-to-noise ratio or the increase of data missing rate, while the algorithm proposed in this patent shows stronger robustness.

[0252] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF, characterized in that: include: S100, using a Bi-ISAR imaging system consisting of space-based radar and ground-based radar, receives echo data from non-cooperative targets; S200, preprocessing the echo data to obtain a slow time dimension signal that can be approximated to an LFM form; S300, using the proposed FAIWF-CICPF-CTF algorithm to process the slow time dimension signal obtained after the preprocessing until an iteration termination condition is met, thereby obtaining a Bi-ISAR image and an ERV estimation value; S400, performing distortion correction on the Bi-ISAR image using a distortion correction function to obtain a distortion-corrected Bi-ISAR image, estimating the lateral range resolution using an ERV estimation value, and calibrating the distortion-corrected Bi-ISAR image based on the range resolution to obtain a distortion-corrected and calibrated Bi-ISAR image; S300 includes: S310, extracting a slow time dimension signal from the preprocessed echo signal along the slow time dimension, and approximating the slow time dimension signal to a multi-component linear frequency modulation signal; S320, utilizing the significant sparsity of the multi-component linear frequency modulation signal in the center frequency-frequency modulation domain, converting the Bi-ISAR autofocusing and calibration problem into an SSR problem; S330, using FAIWF-CICPF-CTF to iteratively solve the SSR problem until an iteration termination condition is satisfied, thereby obtaining a Bi-ISAR image and an ERV estimation value; The S320 includes: S321, analyzing an ideal mapping value of the multi-component linear frequency modulation signal in the center frequency-frequency modulation rate domain, and confirming a sparse characteristic of the multi-component linear frequency modulation signal in the center frequency-frequency modulation rate domain according to the ideal mapping value; S322, integrating noise and data missing factors, and combining the multi-component linear frequency modulation signal to construct an autocorrelation function of the noisy non-uniformly sampled observation data; the autocorrelation function characterizes the Bi-ISAR autofocusing and calibration problem; S323, convert the Bi-ISAR autofocusing and calibration problem into an SSR problem.

2. The sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF according to claim 1, characterized in that: S100 includes: S110, constructing a geometric model of Bi-ISAR imaging consisting of a space-based radar as a transmitting radar and a ground-based radar as a receiving radar; S120, constructing a mathematical model of non-cooperative target echoes using the Bi-ISAR imaging geometric model; S130: Utilize the space-based radar to transmit a signal, obtain a target echo signal received by the ground-based radar, and obtain an expression form of the target echo signal according to the mathematical model.

3. The sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF according to claim 1, characterized in that: S200 includes: S210, performing range pulse compression on the echo data to obtain a high-resolution range image; S220, performing translation compensation on the high-resolution range image to obtain an aligned range envelope; S230: Taking a conjugate of the aligned range envelope to obtain a preprocessed echo signal.

4. The sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF according to claim 1, characterized in that: The S330 includes: S331, at each iteration, using the designed FAIWF-CICPF-CTF algorithm to solve the SSR problem, obtaining a sparse recovery result of the mapping value of each slow-time dimension signal in the center frequency-to-frequency modulation domain at each iteration; determining whether the iteration termination condition is met, and if so, using the current sparse recovery result as the output sparse recovery result; S332, slicing and splicing the sparse recovery results corresponding to the slow-time dimension signals to obtain a Bi-ISAR image; S333 : Calculate an ERV estimation value using the sparse recovery results of the two selected slow-time dimension signals, wherein the two selected slow-time dimension signals contain information of scattering points with the same abscissa.

5. The sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF according to claim 4, characterized in that: The iteration termination condition is that the maximum number of iterations is reached or the change in the sparse recovery results between two adjacent iterations meets the accuracy requirement.

6. The sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF according to claim 4, characterized in that: The process of solving the SSR problem using the designed FAIWF-CICPF-CTF algorithm includes: The SSR problem is solved by the FAIWF-CICPF-CTF algorithm, and the 2D-CGLS algorithm is introduced in the solution process to avoid the inversion process and thus improve the algorithm solution speed, and the sparse recovery result of the mapping value of each slow time dimension signal in the center frequency-modulation frequency domain is obtained in each iteration.

7. The sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF according to claim 6, characterized in that: The process of solving the SSR problem using the FAIWF-CICPF-CTF algorithm includes: a. Input the sensing matrix, observation signal, accuracy threshold, maximum number of iterations, and multiple hyperparameters, initialize the sparse signal recovery result, and initialize the current iteration number to 1; b. Estimate the frequency and modulation rate of each original signal component at the peak position of the CFCR domain based on the sparse recovery result obtained in the previous iteration, and construct the covariance matrix of the signal cross term based on the expression of the LFM signal and the definition of the signal cross term; c. Update the accuracy of the original noise dataset and the signal, and update the hyperparameters based on the second-type maximum likelihood estimation; d. Using the updated hyperparameters, calculate the covariance matrix of the observed signal; e. Update the sparse recovery result of the current iteration according to the minimum mean square error criterion and update the diagonal matrix; f, increment the current iteration by 1; g. Determine whether the maximum number of iterations has been reached or whether the change between the sparse recovery results obtained by the current two adjacent iterations meets the accuracy requirements. If any requirement is met, output the sparse recovery result that meets the requirements.

8. The sparse aperture Bi-ISAR imaging and calibration method based on FAIWF-CICPF-CTF according to claim 1, characterized in that: S400 includes: S410, constructing a distortion correction function; S420, using the distortion correction function to perform distortion correction on the Bi-ISAR image to obtain a Bi-ISAR image after distortion correction; S430 , calculating the lateral range resolution using the obtained ERV estimation value, and calibrating the distortion-corrected Bi-ISAR image in combination with the range resolution to obtain a distortion-corrected and calibrated Bi-ISAR image.

Images