Time-frequency random sampling high-resolution ISAR imaging fast method based on AIWF

Abstract

The invention provides a time-frequency random sampling high-resolution ISAR imaging fast method based on AIWF, and the method employs a missing data estimation fast algorithm and an optimization algorithm to obtain complete distance frequency domain-slow time domain data and compensate motion errors. And an AIWF fast algorithm based on cyclic low shift rank decomposition and a method for reducing the dimension of a covariance matrix by using resampling are designed, so that the calculation complexity is greatly reduced, and the method is used for carrying out ISAR imaging with high efficiency and high precision. The method provided by the invention has relatively good noise suppression capability and relatively high calibration precision, and an ISAR image with good focusing can still be obtained even under the condition of relatively large data missing rate.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling. Background Art

[0002] Traditional imaging radars use wide-bandwidth modulated waveforms, uniformly stepped frequency, or stepped linear frequency modulation signals, along with a fixed pulse repetition interval (PRI) during the polycoherent processing interval. In this scenario, target echoes are uniformly sampled in both the range-frequency and slow-time domains. With the continuous advancement of digital radio frequency memory technology, radars have recently faced a serious threat from multiple repetitive interference patterns. If a radar transmits a traditional waveform, the target echo is almost completely suppressed by the interference, rendering the radar's detection, tracking, and imaging capabilities ineffective. Frequency jittering and PRI agility are two effective anti-interference measures. When the frequency of the radar's transmitted signal hops in a quasi-random pattern, a jammer cannot intercept and repeat the radar signal, making it difficult to effectively jam. Furthermore, PRI agility increases the difficulty for a jammer to intercept the radar signal, thereby reducing its jamming capability. When a radar employs both anti-interference techniques, the target echo is non-uniformly sampled in both the range-frequency and slow-time domains. Because the radar operates with a fixed reference clock frequency, the target echo in this scenario can be considered to be randomly missing from the uniformly sampled data. Under these conditions, traditional target imaging methods based on two-dimensional (2D) Fast Fourier Transform (FFT) are no longer applicable. Therefore, how to efficiently acquire well-focused 2D high-resolution Inverse Synthetic Aperture Radar (ISAR) images in the presence of random missing observation data has become a research hotspot in recent years.

[0003] In order to obtain well-focused high-resolution ISAR images of targets under range-pulse random sampling conditions, many methods have been proposed. These algorithms can be summarized into three categories: (1) Initial phase error compensation for randomly missing data and 2D joint sparse target imaging algorithm. This type of algorithm only considers the initial phase error that is independent of the range and performs self-focusing. (2) Hierarchical 2D reconstruction target imaging algorithm. This type of algorithm can overcome the problem of excessive dimensionality caused by image vectorization. However, the step-by-step implementation method reduces the sparsity, resulting in large imaging errors and inaccurate motion estimation. (3) Low-rank completion method. This type of algorithm is based on the property that the target data can be represented as the sum of several rank-1 matrices. Although this type of method effectively avoids matrix vectorization operations, the phase error compensation algorithm cannot be integrated.

[0004] In practical applications, initial phase error, migration through range cells (MTRC) caused by target translation and rotation, and range spatial-variant phase error (RSVPE) are also non-negligible and typically require correction to obtain a focused 2D high-resolution target image. Traditionally, MTRC caused by translation is corrected using envelope correlation methods, MTRC caused by target rotation is corrected using the Keystone transform, and RSVPE is estimated and compensated for within each range cell in the range-slow time domain. All of these methods require high-resolution range profiles (HRRPs) of the target. Therefore, both MTRC and RSVPE are difficult to handle when observations are incomplete in the range-frequency-slow time domain. However, currently proposed methods do not account for motion error or only consider initial phase error. Summary of the Invention

[0005] To solve the above problems in the prior art, the present invention provides a fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] A fast method for high-resolution ISAR imaging based on AIWF with random sampling of time and frequency includes:

[0007] S100, receiving echo data fed back by the target;

[0008] S200, recovering missing data on the echo data to obtain complete echo data;

[0009] S300, using an SQP algorithm to estimate motion parameters of the target, and using the motion parameters to perform motion compensation on the complete echo data to obtain motion-compensated echo data;

[0010] S400 uses the motion-compensated echo data and the AIWF-ME algorithm to obtain the target image with focus and azimuth positioning;

[0011] S500, repeating steps S200-S400 until the error of the target image is less than the convergence threshold or the maximum number of iterations is reached, and then outputting the final target image.

[0012] Beneficial effects:

[0013] For range-frequency pulse sampling echo signals, this invention parameterizes the motion error in target imaging and transforms the motion error compensation problem into a parameter estimation optimization problem. The proposed iterative missing data estimation algorithm, motion compensation algorithm, and adaptive iterative Wiener filtering fast algorithm enable more accurate and efficient missing data estimation, motion error compensation, and high-resolution ISAR imaging.

[0014] 2. To address the problem of increased computational complexity in the AIWF algorithm due to padding data, this paper uses resampling to construct a low-dimensional sampling covariance matrix with the same structure, resulting in higher computational efficiency when using the AIWF fast algorithm. The proposed AIWF-based motion compensation and 2D combined high-resolution ISAR imaging fast algorithm can effectively acquire clear target images in interference environments, providing strong support for subsequent target recognition and classification.

[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 Schematic diagram of a fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling provided by the present invention;

[0017] Figure 2 This is a schematic diagram of the 2D joint high-resolution rapid imaging process based on random sampling observation of AIWF provided by the present invention;

[0018] Figure 3 This is a schematic diagram of radar imaging geometry provided by the present invention;

[0019] Figure 4 is a schematic diagram of the geometric model of 2D random missing observations provided by the present invention;

[0020] Figure 5 This is a schematic diagram of imaging results under complete observation in the presence of motion errors provided by the present invention;

[0021] Figure 6 is a schematic diagram of randomly missing data and imaging results under different MR conditions provided by the present invention;

[0022] Figure 7 Schematic diagram of HRRPs and RD images of the Yak-42 aircraft provided by the present invention;

[0023] Figure 8 Schematic diagram of random missing observation and imaging results of a Yak-42 aircraft under different MR conditions provided by the present invention. DETAILED DESCRIPTION

[0024] 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.

[0025] This paper proposes a fast algorithm for high-resolution target imaging with 2D randomly missing observations based on an adaptive iterative Wiener filter (AIWF). Given that radar coherence is intact and the position of the range window can be determined during imaging, the induced MTRC and phase errors can be parameterized based on velocity and acceleration and modeled in the range-frequency and slow-time domains, which is sufficient for modern radars. MTRC due to rotation is ignored, assuming that the MTRC due to rotation is less than one range resolution unit. This assumption holds true when the target extends over a small number of range units and the rotation angle within the imaging interval is small. A missing data recovery algorithm is used to obtain the HRRP, ensuring that the translation error and RSVPE can be estimated and compensated independently in each range unit. To reduce the computational complexity and memory usage of the AIWF algorithm, this paper also proposes an efficient AIWF algorithm and resampling method. The proposed algorithm exhibits high parameter estimation accuracy and computational efficiency, as well as excellent signal reconstruction capabilities.

[0026] Combine Figure 1 and Figure 2 The present invention provides a fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling, including:

[0027] S100, receiving echo data fed back by the target;

[0028] refer to Figure 3 As shown, Figure 3 The figure is a schematic diagram of radar imaging geometry. Since the coherent integration angle of radar imaging is usually small (3-5°), the target can be approximated to rotate at a constant speed during the imaging coherent integration time. Assume that the target's rotation speed is ω, there are I scattering points on the target, and t m The target's rotation angle at the moment is Δθ(t m ), the coordinates of the i-th scattering point on the target are (x i ,y i ).according to Figure 2 , the instantaneous distance R between the scattering point and the radar can be obtained i (t m )for

[0029]

[0030] Among them, R T (t m ) and R Ci (t m ) represent the instantaneous translation distance and rotation distance of the target, Ro is the distance from the target equivalent center to the radar. The target translation can be modeled as a finite order polynomial, namely v represents the target translational velocity, and a represents the acceleration.

[0031] Assuming that the radar transmits a broadband linear frequency modulation (LFM) signal, after pulse compression or de-skewing, the baseband echo signal can be expressed in the range-frequency domain-slow time domain as:

[0032]

[0033] Wherein, the distance frequency f∈[-B / 2,B / 2]. c are the center frequencies of the transmitted signal, c is the speed of light, and B is the bandwidth of the transmitted signal.

[0034] In the case of small-volume targets and small imaging rotation angles, the MTRC caused by target rotation is less than one range unit and can therefore be ignored. After eliminating the phase constant term and ignoring the MTRC, the echo with translation error and RSVPE can be expressed as:

[0035]

[0036] in, represents the 2D ideal echo, which is in the form of:

[0037]

[0038] The noisy discretization model of the echo shown in formula (3) is:

[0039]

[0040] in, and They represent the 2D echo observation matrix, target image matrix, complex Gaussian white noise matrix and complete Fourier dictionary matrix respectively. and Represent the overcomplete Fourier dictionary matrices of the distance dimension and the orientation dimension respectively. Represents RSVPE, E R The inner element is In this chapter represents the translation error, E T The inner element is of the form where f n =-B / 2+nB / N.

[0041] The 2D joint high-resolution imaging model under complete observation obtained by vectorizing (5) is:

[0042]

[0043] in,

[0044] S200, recovering missing data on the echo data to obtain complete echo data;

[0045] This step uses a fast missing data recovery method based on conditional mean estimation to recover missing data from the target echo and obtain complete echo data. This fast missing data recovery method based on conditional mean estimation improves the matrix inversion operation in the missing data recovery method based on conditional mean estimation by using the circular convolution theorem and least squares approximation.

[0046] refer to Figure 4 , Figure 4 is the geometric model of 2D random missing observations. Assuming that the number of valid data is L, the missing rate of 2D random missing observations is Valid data a and missing datas m They are:

[0047] s a =Z a s c (7)

[0048] s m =Z m s c (8)

[0049] in, is a row selection matrix, that is, if s a The lth element comes from s c The mth element of Z a The element in row l and column m is 1, and the remaining elements are 0. m Same thing.

[0050] The principle of the missing data recovery algorithm based on conditional mean estimation is as follows:

[0051] Given that the observation noise follows a zero-mean complex Gaussian distribution, without motion error, the mean vectors of valid data and missing data are:

[0052] u a =Z a Hx (9)

[0053] u m =Z m Hx (10)

[0054] Let the complete observation data y without motion error, the valid observation data and the missing observation data be ya =Z a y and y m =Z m y. Since the complete data is a complex Gaussian distribution, the effective data y a and missing data y m Then it obeys the joint complex Gaussian distribution, and y m Is y a The complex Gaussian distribution is conditioned on y. According to the characteristics of the conditional complex Gaussian distribution, a Condition y m The mean vector of is:

[0055]

[0056] in, Here you will m|a Treated as recovered values for missing data.

[0057] make and Then the missing data estimation formula shown in (11) can be written as:

[0058] u m|a =E(y m |y a ,x)=u m +Q ma (b2-b1) (12)

[0059] And the estimation of sparse signals using valid data can be expressed as:

[0060]

[0061] Assume that the estimated value of missing data is The complete data obtained after filling the data with the estimated values of missing data is Using the recovered complete data, the estimation formula of the sparse signal can be expressed as:

[0062]

[0063] If the estimated value of missing data is very close to the true value, then and Approximately equal. Use the least squares criterion to measure and The similarity between them can be obtained by solving the following WLS fitting problem:

[0064]

[0065] And the WLS estimate of b2 is:

[0066]

[0067] The present invention proposes a fast implementation method for the missing data recovery algorithm. From (16), it can be seen that the WLS estimate of b2 contains a matrix inversion operation. Due to the sparse nature of the signal, the condition number of the weight matrix Λ is large, and a small change will have a significant impact on the WLS result. Therefore, it cannot be directly eliminated by multiplying its inverse matrix in the WLS problem given by (15). This also leads to the direct calculation based on (16) Next, we will introduce a fast implementation method that can avoid matrix inversion operations.

[0068] Since the signal is continuous and has a small dynamic range in the measurement domain, a 2D Fourier transform at points K1 and K2 can be performed on both sides of (13) and (14) to convert the equation to the measurement domain. According to the circular convolution theory of DFT, (13) and (14) can be expressed in the measurement domain as:

[0069]

[0070] in, is a 2D complete Fourier dictionary matrix of dimension K1K2×K1K2, and are complete Fourier dictionary matrices of dimensions K2×K2 and K1×K1, respectively.

[0071] make because It can be regarded as a signal in the measurement domain, so it can be converted into Replace the data at the same position in the Right now:

[0072]

[0073] make Then the estimated value of b2 can be obtained by solving the following WLS problem:

[0074]

[0075] And the WLS estimate of b2 is:

[0076]

[0077] Similarly, the WLS estimate of b1 is:

[0078]

[0079] Substituting (21) and (22) into (12), we can get the estimation formula for missing data:

[0080]

[0081] Because HH H =(K1K2)I NM×NM and So in (21) and (22) and The solution does not involve matrix inversion. Therefore, v1 and v2 can be quickly calculated using 2D-FFT / IFFT. It can be seen that the missing data estimation shown in (23) can be quickly implemented using 2D-FFT / IFFT. The specific implementation steps are as follows: the elements in x and Q can be calculated using the fast algorithm introduced in step 3; the product of H and x can be quickly calculated using 2D-FFT / IFFT; and 2D-FFT / IFFT can be used for fast calculation.

[0082] Using the above method, we can obtain Afterwards, Filling in the missing positions of the observed data will give an estimate of the complete data. That is, complete echo data.

[0083] S300, using an SQP algorithm to estimate motion parameters of the target, and using the motion parameters to perform motion compensation on the complete echo data to obtain motion-compensated echo data;

[0084] This step explains how to estimate the target's translational velocity, translational acceleration, and rotational speed by solving an optimization problem, thereby compensating for translational error and RSVPE and achieving azimuth calibration.

[0085] As an optional implementation manner of the present invention, S300 includes:

[0086] S310, setting an optimization function that minimizes the Tsallis entropy of the target image, wherein the optimization function includes motion parameters to be estimated;

[0087] Based on the minimum Tsallis entropy criterion, the target motion parameters are estimated as follows:

[0088]

[0089] Among them, T(X) represents the Tsallis entropy of the target image, which is in the form of

[0090] The first-order partial derivatives of T(X) with respect to the target motion parameters to be estimated are:

[0091]

[0092] S320, using the SQP algorithm to perform multiple iterations on the optimization function to obtain motion parameters that minimize the Tsallis entropy of the target image;

[0093] The image reconstructed using the IWF algorithm can be obtained:

[0094]

[0095]

[0096] in,

[0097]

[0098] According to the solution method of x in the fast AIWF algorithm, and It can also be calculated quickly. The SQP optimization algorithm is used to solve the non-convex problem shown in Equation (24) to estimate the target motion parameters and thus compensate for the motion error. For the solution of non-convex problems, the results are highly sensitive to the initial values. In practical applications, the radar tracker can obtain parameters such as the radial distance, velocity, acceleration, angle, and angle change rate of the target. Therefore, the information provided by the radar tracker can be used as the initial value and constraint conditions of the SQP algorithm to obtain a more robust and accurate estimation result. The parameter estimation algorithm that combines the minimum entropy criterion and the SQP algorithm is called the ME algorithm.

[0099] S330 , performing motion compensation on the complete echo data using the motion parameters to obtain motion-compensated echo data.

[0100] This step uses the motion parameters to perform translation compensation and range-dependent space-variation error compensation on the complete echo data to obtain motion-compensated echo data.

[0101] In summary, the missing data recovery and efficient AIWF algorithm proposed in this paper is referred to as AIWF-ME. The complete process of using the AIWF-ME algorithm to realize 2D joint high-resolution ISAR imaging with random missing observations is as follows: Figure 2 shown.

[0102] Represents the complete data obtained after filling missing data with zeros. As can be seen from the figure, the proposed algorithm fully utilizes the TBT structure of the observation covariance matrix, maximizes the use of FFT operations, and eliminates the need to construct a 2D dictionary matrix. This significantly improves computational efficiency and reduces memory requirements. Therefore, the proposed 2D high-resolution target imaging algorithm can effectively acquire high-quality target images.

[0103] S400 uses the motion-compensated echo data and the AIWF-ME algorithm to obtain the target image with focus and azimuth positioning;

[0104] As an optional implementation manner of the present invention, S400 includes:

[0105] S410, estimating a noise variance value using an AIWF algorithm and auxiliary data; the auxiliary data is echo data that does not contain the target in the target echo;

[0106] Based on the fact that auxiliary data can be used to estimate noise variance in radar imaging and that the amplitude of the target scattering point can be regarded as an unknown deterministic signal, an IWF algorithm is proposed in Reference 1 [Y. Wang, F. Dai, Q. Liu, et al. Fast Iterative Wiener Filter-Based ISAR Imaging and Cross-Range Scaling With Periodically Gapped CPI[J]. IEEE Transactions on Geoscience and Remote Sensing, 2024, 62: 1-18]. The steps of the IWF algorithm are as follows:

[0107]

[0108] In radar signal processing, the traditional IWF algorithm can use auxiliary data to estimate the noise variance value. But even for unbiased consistent estimators, the noise variance estimate is poorly estimated when the auxiliary data are limited.

[0109] Therefore, the present invention proposes an adaptive IWF algorithm, referred to as AIWF, which estimates the noise variance during iteration. The design concept is described below.

[0110] In order to make full use of the noise information contained in the sample, we let represents the noise data, where Represents the estimated value of the original signal. It is known that the noise data n obeys the complex Gaussian distribution. Then the auxiliary data n' and the main data All elements in obey the same complex Gaussian distribution:

[0111]

[0112] Among them, β n represents the accuracy of the noise, i.e. Furthermore, we assume that β n Gamma distribution with parameters c and d:

[0113]

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

[0115] The hyperparameters, β, are estimated based on the second-kind maximum likelihood function. n The posterior probability distribution of is:

[0116]

[0117] Since the edge function p(n) of the original noise is only related to the model, p(β n |n)∝p(n|β n )p(β n ).

[0118] Taking the logarithm further and ignoring the constant we get

[0119] ln(p(n|β n )p(β n ))=(M+c-1)lnβ n -β n nn H -dβ n (37)

[0120] Let equation (37) be n The partial derivative is 0, so β n The update formula is:

[0121]

[0122] S420, determining an observation covariance matrix in an AIWF algorithm according to the noise variance value;

[0123] It has been proved in reference 2 [F.Dai, Y.Wang, and L.Hong.Gohberg-semencul factorization-based fast implementation of sparse Bayesian learning with a Fourierdictionary[J].IEEE Transactions on Geoscience and Remote Sensing, 2022, 60:1-15] that under the condition of complete and uniformly sampled observation data, the observation covariance matrix Q in the AIWF algorithm has a TBT structure. Based on the TBT structure of Q, this paper designs a new cyclic shift decomposition method to calculate Q -1 , further utilizing Q -1The cyclic decomposition factor of is used to estimate sparse signals. Compared with the GS decomposition and LC decomposition proposed in references 2 and 1, the cyclic shift decomposition method proposed in the present invention has lower computational complexity when calculating sparse signals.

[0124] Assume that the noise variance estimated in the iteration is Then the calculation formula and structure of the observation covariance matrix Q in the AIWF algorithm are:

[0125]

[0126] Among them, the sub-matrix Q within Q m is a Toeplitz matrix, Q m The form is:

[0127]

[0128] Reference [2] has proved that Q has a TBT structure and the elements in Q can be quickly calculated using 2D-FFT, which will not be introduced in the present invention.

[0129] S430, resampling the observation covariance matrix using a sampling matrix to obtain a sampling covariance matrix; wherein the sampling covariance matrix has the same structure as the observation covariance matrix, but has a lower dimension than the observation covariance matrix;

[0130] To address the significant increase in computational complexity in the AIWF algorithm caused by padding, this paper proposes a resampling method. This method uses a sampling matrix to transform the covariance matrix into a lower-dimensional matrix with the same structure. This matrix after sampling is called the sampling covariance matrix. Furthermore, this paper uses a cyclic shift decomposition method to solve the inverse of the sampling covariance matrix, which reduces computational complexity.

[0131] After the signal is fully filled, its covariance matrix has a TBT structure, indicating that the fully filled signal is a two-dimensional wide-sense stationary random process. According to the properties of a wide-sense stationary random process, after passing through a two-dimensional finite impulse response (FIR) system, it remains a two-dimensional wide-sense stationary random process, and its covariance matrix also has a TBT structure. Therefore, a linear convolution matrix constructed using a two-dimensional FIR filter is used as the resampling matrix. To avoid the loss of effective signal bandwidth and time width caused by resampling, an FIR filter with coefficients following a Gaussian distribution is used to construct the resampling matrix.

[0132] According to the construction method of the linear convolution matrix, the time domain length of the filled complete signal is M, the time domain length of the resampled signal is J, and the length of the random FIR filter should be (M-J+1). Similarly, the frequency domain length of the filled complete signal is N, the frequency domain length of the resampled signal is K, and the length of the random FIR filter should be (N-K+1). After obtaining the resampling matrices of the time domain and frequency domain respectively, their Kronecker product constitutes a two-dimensional resampling matrix Right now

[0133]

[0134] Among them, Z1 and Z2 are the resampling matrices in the frequency domain and time domain respectively. Assuming that their coefficient vectors are [a(0)a(1)…a(NK)] and [b(0)b(1)…b(JK)] respectively, the forms of Z1 and Z2 are

[0135]

[0136] Using the sampling matrix Z, a low-dimensional sampling covariance matrix Q with the same TBT structure can be constructed R ,Right now

[0137] Q R =ZQZ H (44)

[0138] At this time, the signal reconstruction formula is

[0139]

[0140] S440, using a low cyclic shift rank decomposition method to solve the inverse matrix of the sampling covariance matrix, and using the inverse matrix and the target echo after motion compensation to reconstruct the target image that has achieved focus and azimuth positioning.

[0141] Based on Q RThe TBT structure is obtained by using the GS decomposition and LC decomposition introduced in reference 2 [F.Dai,Y.Wang,and L.Hong.Gohberg-semencul factorization-based fast implementation of sparse Bayesian learningwith a Fourier dictionary[J].IEEE Transactions on Geoscience and Remote Sensing,2022,60:1-15.] and [Y.Wang,F.Dai,Q.Liu,et al.Fast Iterative WienerFilter-Based ISAR Imaging and Cross-Range Scaling With Periodically GappedCPI[J].IEEE Transactions on Geoscience and Remote Sensing,2024,62:1-18]. The GS decomposition formula and LC decomposition formula are:

[0142]

[0143] where Q -1 The decomposition factors T, P and The form is:

[0144]

[0145]

[0146] A (J-1 ) K,K 、W K 、 and The form of A is shown in reference [2], and the 2D-LD algorithm can be used to calculate A (J-1)K,K and W K .

[0147] Define an inverse cyclic shift matrix and a Skew-cyclic-block (CB) shift matrix:

[0148]

[0149] make

[0150]

[0151] The following relationship can be obtained:

[0152]

[0153] in, is a CB matrix, The form is:

[0154]

[0155] Substituting (54)-(56) into (47), Q -1 It can be written as:

[0156]

[0157] The right side of Equation (58) is the product of some circulant and anti-circulant matrices, so (58) is called The cyclic shift decomposition formula, T, and called The cyclic shift decomposition factor of . According to (58), The displacement rank is 2K.

[0158] use The cyclic shift decomposition of has a lower computational complexity than the GS decomposition and LC decomposition. According to reference [2], the solution of x is divided into three steps: and Substituting Equation (58) into φ, the right side of φ is now the product of some circulant matrices and vectors, so it can be converted into a circular convolution, which can be further quickly calculated using FFT. Based on φ, the steps for calculating x are the same as the method introduced in Reference [2]. As shown above, the number of FFT points required for fast calculation of circular convolution is only half of that for linear convolution. It can be seen that the cyclic decomposition method used in this invention has higher computational efficiency when calculating sparse signals x. Table 1 summarizes the number of FFT points and computational complexity required for fast solution of φ using GS decomposition, LC decomposition, and cyclic shift decomposition.

[0159] Table 1. The number of FFT points and computational complexity of solving φ using GS decomposition, LC decomposition, and cyclic shift decomposition.

[0160]

[0161] The following Algorithm 2 summarizes the fast algorithm for 2D joint high-resolution imaging based on AIWF.

[0162]

[0163]

[0164] S500, repeating steps S200-S400 until the error of the target image is less than the convergence threshold or the maximum number of iterations is reached, and then outputting the final target image.

[0165] As an optional implementation manner of the present invention, S500 includes:

[0166] S510, determining whether the error of the target image in S400 is less than a convergence threshold; if not, using the target image and the estimated motion parameters as a basis for the next update of the motion parameters and the target image; and repeating steps S200-S400 based on the basis in the next iterative cycle;

[0167] S520: If the error of the target image in S400 is less than the convergence threshold, output the target image when the error is less than the convergence threshold.

[0168] S530, determining whether the error of the target image is still not less than the convergence threshold when the iterative loop reaches the maximum number of iterations, and then outputting the target image of the last iteration.

[0169] To verify the effectiveness of the proposed AIWF-based random sampling high-resolution ISAR imaging fast algorithm, the following simulation and field-measurement comparison experiments were conducted. The missing data estimation and sparse signal reconstruction algorithm based on SLIM, proposed in Reference 4 [Vu D, Xu L, Xue M, et al. Nonparametric missing sample spectral analysis and its applications to interrupted SAR [J]. IEEE Journal of Selected Topics in Signal Processing, 2011, 6(1): 1-14], was used as a comparison algorithm. This algorithm is called GS-SLIM. The super-resolution factor of each algorithm in the experiment was set to 4. Under the same conditions, the dynamic display range of the target image obtained by each algorithm was the same.

[0170] Example 1

[0171] The effectiveness of the proposed high-resolution imaging fast algorithm based on AIWF is verified by simulating the imaging results of randomly missing observation data with translation error and RSVPE. The parameter settings of the radar system and target motion are shown in Table 1.

[0172] Table 1 Radar and target motion parameters

[0173] parameter value parameter value <![CDATA[Center frequency f c > 9GHz Full aperture number M 256 Bandwidth B 500MHz Target translational velocity v 180m / s PRF 300Hz Target translational acceleration a <![CDATA[2m / s 2 ]]> Distance frequency point number N 128 Target rotation speed ω 0.068rad / s

[0174] Figure 5 The scattering point model of the simulated aircraft and the imaging results using the RD algorithm when there is motion error are shown. They are used as a comparison benchmark for subsequent imaging results with missing data. The SNR is 5dB. Figure 5 As can be seen in Figures (c)-(d), for small targets, the MTRC caused by target rotation is less than one range resolution unit and can therefore be ignored. When the range-varying phase error is not compensated, the RD algorithm fails, and RSVPE causes severe defocusing of the high-resolution target image. As can be seen in Figures (e)-(f), translational errors cause range offset, rendering the RD algorithm ineffective.

[0175] Example 2:

[0176] This experiment shows the target image of the algorithm proposed in this invention under different missing rate conditions. Assume that the initial value of the target motion parameters is [v, a, ω] = [185m / s, 2.5m / s 2 ,0.078rad / s].

[0177] Figure 6 The GS-SLIM algorithm and the proposed algorithm are presented with randomly missing observation data and imaging results under different MR conditions to compare the impact of MR on the algorithms. The first, second, and third rows show 2D randomly missing observation data with MR values of 50%, 75%, and 85%, respectively, along with the imaging results using the GS-SLIM and AIWF-ME algorithms. The SNR is 5dB. The computation time, image entropy, and estimated object motion parameters are annotated in the figure. Figure 6 The imaging results of each algorithm intuitively reflect the performance of the algorithm. Although the GS-SLIM algorithm can obtain target images, its imaging quality is poor and the estimation accuracy of target motion parameters is low. As the amount of missing data increases, the target image defocus becomes more obvious. The algorithm proposed in this paper can obtain clear target images and achieve good focusing effects even when only 15% of the data is available. The image entropy of the target image obtained using the AIWF-ME algorithm is lower than that of the GS-SLIM algorithm, indicating that the proposed algorithm has better imaging effects. In terms of target motion parameter estimation, the estimated values of the AIWF-ME algorithm are very close to the actual values. In this experiment, the maximum number of iterations of the AIWF-ME algorithm was set to 25, so the calculation time of the algorithm at different MR levels was similar. Because the imaging quality of the GS-SLIM algorithm is poor when the number of iterations is small, the number of iterations of the GS-SLIM-ME algorithm was set to 35 in this experiment, resulting in a longer calculation time than the AIWF-ME algorithm.

[0178] Example 3:

[0179] This example uses the measured data of the Yak-42 aircraft to conduct experiments to demonstrate the effectiveness of the algorithm proposed in the present invention.

[0180] The radar used to collect ISAR data operates in the C-band, with a bandwidth of 400 MHz and a pulse repetition frequency of 400 Hz. The range window contains 256 sampling points, and the imaging time contains 256 pulses. The HRRPs and RD imaging results of the complete data after motion compensation are shown in Figure 2. Figure 7 shown.

[0181] To demonstrate the advantages of 2D high-resolution imaging, this experiment intercepted 128 consecutive frequency points (corresponding to a 200-MHz bandwidth) from the original data and extracted 128 pulses at equal intervals (corresponding to a 200-Hz PRF). Figure 8 The first and second rows in the figure show the 2D observation data when MR is 50% and 75%, respectively, as well as the imaging and calibration results of RD, GS-SLIM and the proposed algorithm. The imaging time of each algorithm is marked in the figure. Figure 8 As shown, the RD algorithm has failed. The target image obtained by the GS-SLIM algorithm is poorly focused and blurred, especially when there is less available data. However, the algorithm proposed in the present invention can obtain a clearer and better focused target image, and the calculation time is also shorter. The target rotation speeds estimated by the proposed algorithm are 0.0265rad / s and 0.0263rad / s respectively. Based on the estimated target rotation speed, the calibration result of the target is close to the actual size of the Yak-42 aircraft. Since the target rotation speed estimated by other algorithms deviates greatly from the true value, the target rotation speed estimated by the algorithm proposed in this chapter is used for calibration.

[0182] To address the problem that target ISAR imaging algorithms in interference environments are susceptible to the effects of sidelobes, grating lobes, and time-varying Doppler frequencies, resulting in poor focusing performance or even complete failure, this application proposes a fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling. This method utilizes a fast missing data estimation algorithm and an optimization algorithm to obtain complete range-frequency-slow-time domain data and compensate for motion errors. A fast AIWF algorithm based on cyclic low-shift rank decomposition and a method for reducing the dimension of the covariance matrix using resampling are designed to greatly reduce computational complexity, allowing for high-efficiency and high-precision ISAR imaging. The method proposed in this application has good noise suppression capabilities and high calibration accuracy, and can obtain well-focused ISAR images even in the presence of a large data missing rate.

[0183] It is worth noting that the terms "first" and "second" in this disclosure are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of this disclosure, "plurality" means two or more, unless otherwise specifically defined.

[0184] Although the present application is described herein with reference to various embodiments, those skilled in the art will be able to understand and implement other variations of the disclosed embodiments in practicing the claimed application by reviewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0185] 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 fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling, characterized by: include: S100, receiving echo data fed back by the target; S200, recovering missing data on the echo data to obtain complete echo data; S300, using an SQP algorithm to estimate motion parameters of the target, and using the motion parameters to perform motion compensation on the complete echo data to obtain motion-compensated echo data; S400 uses the motion-compensated echo data and the AIWF-ME algorithm to obtain the target image with focus and azimuth positioning; S500, repeating steps S200-S400 until the error of the target image is less than the convergence threshold or the maximum number of iterations is reached, and then outputting the final target image.

2. The AIWF-based time-frequency random sampling high-resolution ISAR imaging fast method according to claim 1, characterized in that: S200 includes: A fast missing data recovery method based on conditional mean estimation is used to recover missing data of the target echo to obtain complete echo data.

3. The AIWF-based time-frequency random sampling high-resolution ISAR imaging fast method according to claim 2, characterized in that: The fast missing data recovery method based on conditional mean estimation is obtained by improving the matrix inversion operation in the missing data recovery method based on conditional mean estimation by utilizing the circular convolution theorem and least squares approximation.

4. The fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling according to claim 1 is characterized in that: S300 includes: S310, setting an optimization function that minimizes the Tsallis entropy of the target image, wherein the optimization function includes motion parameters to be estimated; S320, using the SQP algorithm to perform multiple iterations on the optimization function to obtain motion parameters that minimize the Tsallis entropy of the target image; S330 , performing motion compensation on the complete echo data using the motion parameters to obtain motion-compensated echo data.

5. The AIWF-based time-frequency random sampling high-resolution ISAR imaging fast method according to claim 4, characterized in that: The motion parameters include: translational velocity, translational acceleration and rotational speed.

6. The AIWF-based time-frequency random sampling high-resolution ISAR imaging fast method according to claim 4, characterized in that: The S330 includes: The motion parameters are used to perform translation compensation and range-dependent space-variation error compensation on the complete echo data to obtain motion-compensated echo data.

7. The fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling according to claim 1, characterized in that: S400 includes: S410, estimating a noise variance value using an AIWF algorithm and auxiliary data; the auxiliary data is echo data that does not contain the target in the target echo; S420, determining an observation covariance matrix in an AIWF algorithm according to the noise variance value; S430, resampling the observation covariance matrix using a sampling matrix to obtain a sampling covariance matrix; wherein the sampling covariance matrix has the same structure as the observation covariance matrix, but has a lower dimension than the observation covariance matrix; S440, using a low cyclic shift rank decomposition method to solve the inverse matrix of the sampling covariance matrix, and using the inverse matrix and the target echo after motion compensation to reconstruct the target image that has achieved focus and azimuth positioning.

8. The AIWF-based time-frequency random sampling high-resolution ISAR imaging fast method according to claim 1, characterized in that: S500 includes: S510, determining whether the error of the target image in S400 is less than a convergence threshold; if not, using the target image and the estimated motion parameters as a basis for the next update of the motion parameters and the target image; and repeating steps S200-S400 based on the basis in the next iterative cycle; S520: If the error of the target image in S400 is less than the convergence threshold, output the target image when the error is less than the convergence threshold. S530, determining whether the error of the target image is still not less than the convergence threshold when the iterative loop reaches the maximum number of iterations, and then outputting the target image of the last iteration.

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