An AIWF-based time-frequency random sampling high-resolution ISAR imaging fast method

Abstract

The application provides an AIWF-based time-frequency random sampling high-resolution ISAR imaging fast method, which utilizes 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 designs an AIWF fast algorithm based on cyclic low displacement rank decomposition and a resampling method for reducing the dimension of a covariance matrix to greatly reduce the calculation complexity, so as to efficiently and accurately perform ISAR imaging. The method provided by the application has good noise suppression capability and high calibration precision, and even in the case of a large data missing rate, an ISAR image with good focusing can still be obtained.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of signal processing, and particularly relates to a time-frequency random sampling high-resolution ISAR imaging fast method based on AIWF. BACKGROUND

[0002] Traditional imaging radars use large bandwidth modulated waveforms, uniformly stepped frequency or stepped linear frequency modulation signals, and use a fixed pulse repetition interval (PRI) during multiple coherent processing intervals. In this case, target echoes are uniformly sampled in the range-frequency domain and slow time domain. With the continuous progress of digital radio frequency memory technology, radars have faced serious threats from various repeated pattern jamming in recent years. If the radar transmits a traditional waveform, the target echo will be completely suppressed by the jammer, and the radar's detection, tracking and imaging functions will fail. Frequency dithering and PRI agility are two effective anti-jamming means. When the frequency of the radar signal jumps in a quasi-random manner, the jammer will not be able to intercept and repeat the radar signal, making it difficult to form effective jamming. In addition, PRI agility increases the difficulty of the jammer to intercept the radar signal, thereby reducing its jamming capability. When the radar uses both of these anti-jamming techniques, the target echo is non-uniformly sampled in the range-frequency domain and the slow time domain. Since the radar works at a fixed reference clock frequency, the target echo in this case can be regarded as randomly missing from the uniformly sampled data. Under this condition, the traditional target imaging method based on two-dimensional (2D) fast Fourier transform (FFT) will no longer be applicable. Therefore, under the condition of randomly missing observation data, how to efficiently obtain a well-focused 2D high-resolution inverse synthetic aperture radar (ISAR) image has become a research hotspot in recent years.

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

[0004] In practical applications, initial phase error, target translation and rotation induced migration through range cells (MTRC) and range spatial-variant phase error (RSVPE) cannot be ignored, and usually need to be corrected to obtain focused 2D high resolution target image. Traditionally, MTRC induced by translation is corrected by envelope correlation method, MTRC induced by target rotation is corrected by Keystone transform, and RSVPE is estimated and compensated in each range cell in range-slow time domain. All these methods require high resolution range profiles (HRRPs) of the target, so MTRC and RSVPE are difficult to handle when the observation is incomplete in range frequency-slow time domain. However, the methods proposed so far do not consider motion error or only consider initial phase error. SUMMARY

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

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

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

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

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

[0010] S400, obtaining a focused and azimuth positioned target image by using the motion compensated echo data and through an AIWF-ME algorithm;

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

[0012] Advantages:

[0013] 1. For the range frequency-pulse sampling echo signal, the present application parameterizes the motion error of target imaging, and converts the motion error compensation problem into a parameter estimation optimization problem. The iterative missing data estimation algorithm, motion compensation algorithm and adaptive iterative Wiener filter fast algorithm proposed by the present application can more accurately and efficiently estimate the missing data, compensate the motion error and realize high resolution ISAR imaging.

[0014] 2. For the problem that filling data increases the calculation amount of AIWF algorithm, the present application uses resampling to construct a low-dimensional sampling covariance matrix with the same structure, and has higher calculation efficiency when using the AIWF fast algorithm. The motion compensation based on AIWF and 2D joint high resolution ISAR imaging fast algorithm proposed by the present application can effectively obtain clear target image in the interference environment, and provides strong support for subsequent target recognition and classification.

[0015] The present application will be further described in detail below in combination with the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a schematic diagram of a time-frequency random sampling high resolution ISAR imaging fast method based on AIWF provided by the present application;

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

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

[0019] Figure 4 is a schematic diagram of a 2D random missing observation geometry model provided by the present application;

[0020] Figure 5 is a schematic diagram of an imaging result under complete observation when there is motion error provided by the present application;

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

[0022] Figure 7 is a schematic diagram of HRRPs and RD images of Yak 42 aircraft provided by the present application;

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

[0024] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0025] This invention proposes a fast algorithm for high-resolution target imaging using 2D random missing observations based on Adaptive Iterative Wiener Filter (AIWF). Since the radar coherence remains intact and the position of the range window can be determined during imaging, the resulting MTRC and phase errors can be parameterized based on velocity and acceleration, and modeled in the range frequency and slow time domains, which is satisfied in modern radars. The MTRC caused by rotation is ignored, assuming it is less than one range resolution cell. This assumption holds true when the number of range cells extended by the target is small and the rotation angle within the imaging interval is small. A missing data recovery algorithm is used to obtain HRRP, ensuring that translational errors and RSVPE can be estimated and compensated independently in each range cell. To reduce the computational complexity and memory usage of the AIWF algorithm, this invention also proposes an efficient AIWF algorithm and a resampling method. The proposed algorithm has high parameter estimation accuracy and computational efficiency, as well as good signal reconstruction capabilities.

[0026] Combination Figure 1 and Figure 2 This invention provides a fast method for high-resolution ISAR imaging based on AIWF time-frequency random sampling, comprising:

[0027] S100 receives echo data from the target.

[0028] refer to Figure 3 As shown, Figure 3 This is a schematic diagram of radar imaging geometry. Since the coherence accumulation angle of radar imaging is typically small (3-5°), the target can be approximated as rotating at a uniform speed during the imaging coherence accumulation time. Assume the target's rotational speed is ω, and there are I scattering points on the target, t... m The target's rotation angle at time t is Δθ(t) m At this time, 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 R represents the instantaneous translational distance and the instantaneous rotational distance of the target, respectively.o is the distance from the target equivalent center to the radar. The target translation can be modeled as a finite order polynomial, i.e. v represents the target translation velocity, and a represents the acceleration.

[0031] Assume that the radar transmits a wideband LFM signal. After pulse compression or dechirp processing, the baseband of the echo signal in the range-frequency-slow-time domain can be expressed as

[0032]

[0033] where the range frequency f ∈ [-B / 2, B / 2]. f c and f0are the center frequencies of the transmitted signal, respectively. c is the speed of light. 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 cell, and thus can be ignored. After removing the constant phase term and ignoring the MTRC, the echo with translation error and RSVPE can be expressed as:

[0035]

[0036] where represents the 2D ideal echo, which has the form:

[0037]

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

[0039]

[0040] where and represent the 2D echo observation matrix, the target image matrix, the complex Gaussian white noise matrix, and the complete Fourier dictionary matrix, respectively. and represent the over-complete Fourier dictionary matrix in the range dimension and the azimuth dimension, respectively. represents the RSVPE, E R The inner elements of E In this chapter, represents the translation error, E T The form of the inner elements of E where f n = -B / 2 + nB / N.

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

[0042]

[0043] wherein,

[0044] S200, missing data recovery is performed on the echo data to obtain complete echo data;

[0045] In this step, a fast missing data recovery method based on conditional mean estimation is used to perform missing data recovery on the target echo to obtain complete echo data. The 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 cyclic convolution theorem and least square approximation.

[0046] Reference Figure 4 , Figure 4 is a geometric model of 2D random missing observation. Assuming that the number of valid data is L, the missing rate of 2D random missing observation is Valid data s a and missing data s m are respectively:

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

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

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

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

[0051] In view of the fact that the observation noise obeys zero-mean complex Gaussian distribution and does not contain motion error, the mean vectors of valid data and missing data are respectively:

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

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

[0054] Let the complete observation data without motion error be y, the valid observation and missing observation data be ya = Z a y and y m = Z m y. Since the complete data is complex Gaussian distributed, the effective data y a and the missing data y m are jointly complex Gaussian distributed, and y m is complex Gaussian distributed given y a . According to the property of conditional complex Gaussian distribution, the mean vector of y a given y m is:

[0055]

[0056] where, Here u m|a is treated as the recovered value of the missing data.

[0057] Let and Then the missing data estimator shown in (11) can be written as:

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

[0059] And the sparse signal estimation using the effective data can be expressed as:

[0060]

[0061] Assuming the missing data estimator is , then the complete data obtained by filling the data with the missing data estimator is Using the recovered complete data, the sparse signal estimator can be expressed as:

[0062]

[0063] If the missing data estimator is very close to the true value, then and are approximately equal. Using the least square criterion to measure the similarity between and , the estimator of b2 can be obtained by solving the following WLS fitting problem:

[0064]

[0065] And the WLS estimator of b2 is:

[0066]

[0067] The present application proposes a fast implementation method of the missing data recovery algorithm. As known from (16), there is a matrix inversion operation in the WLS estimation value of b2. Since the signal is sparse, the condition number of the weight matrix Λ is large, and a slight change will have a great impact on the result of WLS, so it cannot be directly eliminated by multiplying its inverse matrix in the WLS problem given in (15), which also leads to the fact that the matrix inversion operation cannot be avoided when calculating b2 according to (16) directly. Next, a fast implementation method that can avoid the matrix inversion operation will be introduced.

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

[0069]

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

[0071] Let Since can be regarded as a signal in the measurement domain, the same position data in can be replaced by the effective data to further obtain that is:

[0072]

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

[0074]

[0075] And the WLS estimation value of b2 is:

[0076]

[0077] Similarly, the WLS estimation value of b1 is:

[0078]

[0079] Substituting (21) and (22) into (12), the estimation formula of the missing data can be obtained as:

[0080]

[0081] Because HH H =(K1K2)I NM×NM and Therefore, in (21) and (22) and The solution does not involve matrix inversion. Furthermore, because... Therefore, v1 and v2 can be quickly calculated using 2D-FFT / IFFT. Thus, 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] The above method was used to obtain Afterwards, By filling in the missing positions in the observed data, we can obtain an estimate of the complete data. That is, complete echo data.

[0083] S300: The motion parameters of the target are estimated using the SQP algorithm, and the motion parameters are used 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 errors and RSVPE, and achieving azimuth calibration.

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

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

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

[0088]

[0089] Where T(X) represents the Tsallis entropy of the target image, which has the form:

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

[0091]

[0092] S320, the motion parameters that minimize the Tsallis entropy of the target image are obtained by using the SQP algorithm to solve the optimization function multiple times;

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

[0094]

[0095]

[0096] wherein,

[0097]

[0098] According to the solution method of x in the fast AIWF algorithm, and can also be calculated quickly. The non-convex problem shown in equation (24) is solved using the SQP optimization algorithm to estimate the target motion parameters, thereby compensating for the motion error. For the solution of the non-convex problem, the result has high sensitivity to the initial value. In practical applications, the radar tracker can obtain the parameters of the target such as radial distance, speed, acceleration, angle and angle change rate. Therefore, the information provided by the radar tracker can be used as the initial value and constraint condition of the SQP algorithm, so as to obtain more robust and more accurate estimation results. The parameter estimation algorithm combining the minimum entropy criterion and the SQP algorithm is called the ME algorithm.

[0099] S330, using the motion parameters, the complete echo data is motion compensated to obtain the motion compensated echo data.

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

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

[0102] represents the complete data obtained by filling the missing data with zeros. As can be seen from the figure, the proposed algorithm fully utilizes the TBT structure of the observation covariance matrix, maximally utilizes the FFT operation, and does not need to construct a 2D dictionary matrix. This greatly improves the calculation efficiency and reduces the memory requirement. Therefore, the proposed 2D high-resolution target imaging algorithm can effectively obtain high-quality target images.

[0103] S400, obtaining a focused and azimuthally positioned target image using the motion-compensated echo data and through an AIWF-ME algorithm;

[0104] As an optional embodiment of the present application, S400 comprises:

[0105] S410, estimating a noise variance value using an AIWF algorithm and with the aid of auxiliary data; the auxiliary data being echo data not containing a target in the target echo;

[0106] Based on the fact that noise variance can be estimated using auxiliary data in radar imaging and the amplitude of a target scattering point can be regarded as an unknown deterministic signal, 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] proposes an IWF algorithm, the steps of which are as follows:

[0107]

[0108] In radar signal processing, the traditional IWF algorithm can estimate the noise variance value using auxiliary data However, even for an unbiased consistent estimator, the accuracy of noise variance estimation is poor when the auxiliary data is limited.

[0109] Therefore, the present application proposes an adaptive IWF algorithm, referred to as AIWF, which estimates the noise variance in iteration. The design idea is described as follows.

[0110] In order to make full use of the noise information contained in the sample, we let denote the noise data, where represents the estimated value of the original signal, and the known noise data n follows a complex Gaussian distribution. The auxiliary data n' and the main data each element of which follows the same complex Gaussian distribution:

[0111]

[0112] where, β n represents the accuracy of the noise, i.e. Further, we assume that β n follows a gamma distribution with parameters c and d:

[0113]

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

[0115] Estimate hyperparameters, β n , based on the second type of maximum likelihood function.

[0116]

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

[0118] Further taking the logarithm and ignoring the constant, we can get

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

[0120] Let the partial derivative of equation (37) with respect to β n be 0, and we can get the update formula of β n :

[0121]

[0122] S420, determining the observation covariance matrix in the 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 Fourier dictionary[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60: 1-15] that the observation covariance matrix Q in the AIWF algorithm has a TBT structure under the condition of complete uniform sampling of observation data. Based on the TBT structure of Q, a new cyclic shift decomposition method is designed to solve Q -1 , and further Q -1The cyclic shift decomposition factor estimates the sparse signal.

[0124] Assuming the estimated noise variance in iteration is The calculation formula and structure of the observation covariance matrix Q in the AIWF algorithm are as follows:

[0125]

[0126] The inner sub-matrix Q of Q is a Toeplitz matrix, and the form of Q is as follows: m m

[0127]

[0128] It has been proved in reference [2] that Q has the TBT structure and the elements in Q can be calculated quickly by using 2D-FFT, and the present application will not be introduced.

[0129] S430, resampling the observation covariance matrix by using a sampling matrix to obtain a sampling covariance matrix; wherein the sampling covariance matrix and the observation covariance matrix have the same structure, but the dimension is lower than that of the observation covariance matrix.

[0130] In view of the problem that the filling causes the calculation amount of the AIWF algorithm to increase significantly, the present application proposes a resampling method, which uses a sampling matrix to change the covariance matrix into a matrix with a lower dimension and the same structure, and the matrix after sampling is called a sampling covariance matrix. In addition, the present application uses the cyclic shift decomposition method to solve the inverse matrix of the sampling covariance matrix, which has a lower calculation complexity.

[0131] After the signal is filled completely, the covariance matrix has the TBT structure, indicating that the signal filled completely is a two-dimensional generalized stationary random process. According to the properties of the generalized stationary random process, it is still a two-dimensional generalized stationary random process after passing through a two-dimensional finite impulse response (FIR) system, and the covariance matrix also still has the TBT structure. Therefore, the linear convolution matrix constructed by using the two-dimensional FIR filter is used as the resampling matrix. In order to avoid the loss of the effective bandwidth and time width of the signal caused by resampling, the FIR filter with the coefficients obeying the 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 in the time domain and the frequency domain respectively, the Kronecker product of the resampling matrices constitutes a two-dimensional resampling matrix That is

[0133]

[0134] wherein Z1 and Z2 are the resampling matrices in the frequency domain and the time domain respectively, and the coefficient vectors of Z1 and Z2 are [a(0)a(1)…a(N-K)] and [b(0)b(1)…b(J-K)] respectively. The forms of Z1 and Z2 are

[0135]

[0136] By using the sampling matrix Z, a low-dimensional sampling covariance matrix Q with the same TBT structure can be constructed R That is

[0137] Q R = ZQZ H (44)

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

[0139]

[0140] S440, the inverse matrix of the sampling covariance matrix is solved by using the low cyclic shift rank decomposition method, and the target image with focused and azimuth positioning is reconstructed by using the inverse matrix and the motion compensated target echo.

[0141] Based on Q RThe TBT structure, using the GS decomposition and LC decomposition described in references 2 [F.Dai, Y.Wang, and L.Hong. Gohberg-semencul factorization-based fast implementation of sparse Bayesian learning with 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 Gapped CPI[J].IEEE Transactions on Geoscience and Remote Sensing, 2024, 62:1-18], yields the following results. The GS decomposition and LC decomposition are as follows:

[0142]

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

[0144]

[0145]

[0146] A (J-1 ) K,K W K , and As shown in reference [2], A can be calculated using the 2D-LD algorithm. (J-1)K,K and W K .

[0147] Define an inverse circular shift matrix And a skew-cyclic-block (CB) shift matrix:

[0148]

[0149] make

[0150]

[0151] The following relationship can be obtained:

[0152]

[0153] wherein, is a CB matrix, is in the form of:

[0154]

[0155] Substituting (54)-(56) into (47), Q -1 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 circulant displacement decomposition of , T, and are called the circulant displacement decomposition factors of . According to (58), the displacement rank of is 2K.

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

[0159] Table 1 FFT points and calculation complexity for solving φ using GS decomposition, LC decomposition and circulant displacement decomposition

[0160]

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

[0162]

[0163]

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

[0165] As an optional embodiment of the present application, S500 comprises:

[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 updating the motion parameters and the target image in the next iteration, and repeating the steps of S200-S400 according to the basis in the next iteration cycle;

[0167] S520, if the error of the target image in S400 is less than a convergence threshold, outputting the target image when the error is less than the convergence threshold.

[0168] S530, determining whether the iteration cycle has reached a maximum number of iterations, and if the error of the target image is still not less than the convergence threshold, outputting the target image at the last cycle iteration.

[0169] To verify the effectiveness of the random sampling high-resolution ISAR imaging fast algorithm based on the AIWF algorithm proposed in the present application, the following simulation and actual measurement comparison experiments are set. 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] is used as a comparison algorithm, which is called GS-SLIM. The super-resolution factor of the algorithm in the experiment is set to 4. Under the same conditions, the dynamic display range of the target image obtained by each algorithm is the same.

[0170] Example 1

[0171] The effectiveness of the high-resolution imaging fast algorithm based on AIWF proposed in the present application is verified by the imaging results of simulated random missing observation data containing translational error and RSVPE. The parameters 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 Center frequency f c ]] 9 GHz Full aperture number M 256 Bandwidth B 500 MHz Target translational velocity v 180 m / s PRF 300 Hz Target translational acceleration a 2 m / s 2 ]]> Distance frequency number N 128 Target rotational velocity ω 0.068 rad / s

[0174] Figure 5 The scatter point model of the simulated aircraft is shown, and the imaging results using the RD algorithm in the presence of motion errors are shown for comparison with the subsequent missing data imaging results. The SNR is 5 dB. From Figure 5 As can be seen from Figs. (c)-(d), for small-sized targets, the MTRC caused by target rotation is less than one range resolution cell, and thus can be ignored. When the range-dependent phase error is not compensated, the RD algorithm fails, and the RSVPE causes the high-resolution target image to be severely defocused. As can be seen from Figs. (e)-(f), the translational error causes a range offset, and the RD algorithm has failed.

[0175] Example 2:

[0176] This experiment demonstrates the target images obtained by the algorithm proposed in the present application under different missing data rates. It is assumed that the initial value of the target motion parameters is [v, a, ω] = [185 m / s, 2.5 m / s 2 , 0.078 rad / s].

[0177] Figure 6 The random missing observation data and imaging results of the GS-SLIM algorithm and the algorithm proposed in the present application under different MR conditions are shown for comparison of the influence of MR on the algorithms. The first row, the second row and the third row respectively show the 2D random missing observation data with MRs of 50%, 75% and 85%, and the imaging results obtained using the GS-SLIM, AIWF-ME algorithms. The SNR = 5 dB. The calculation time, image entropy and estimated value of the target motion parameters are marked in the figures. Figure 6 The imaging results of the algorithms in Figs. (a)-(c) intuitively reflect the performance of the algorithms. Although the GS-SLIM algorithm can obtain a target image, the imaging quality is poor, and the estimation accuracy of the target motion parameters is low. As the amount of missing data increases, the target image defocuses more obviously. The algorithm proposed in the present application can obtain a clear target image, and good focusing effect can be achieved even with only 15% available data. The image entropy of the target image obtained using the AIWF-ME algorithm is lower than that of the GS-SLIM algorithm, which indicates that the imaging effect of the algorithm proposed in the present application is better. In terms of target motion parameter estimation, the estimated value of the AIWF-ME algorithm is very close to the actual value. In this experiment, the maximum number of iterations of the AIWF-ME algorithm is set to 25, so the calculation time of the algorithm under different MR levels is similar. Since 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 is set to 35 in the experiment, so the calculation time is longer than that of the AIWF-ME algorithm.

[0178] Example 3:

[0179] This example proves the effectiveness of the algorithm proposed in the present application by using the measured data of a Yak 42 aircraft for experiments.

[0180] The radar collecting ISAR data works in C-band with a bandwidth of 400MHz and a pulse repetition frequency of 400Hz. The range window contains 256 sampling points and the imaging time contains 256 pulses. The HRRPs of the complete data after motion compensation and the RD imaging results are shown in Figs. 4(a) and 4(b). Figure 7

[0181] In order to show the advantage of 2D high-resolution imaging, 128 consecutive frequency points (corresponding to a 200-MHz bandwidth) are extracted from the original data and 128 pulses (corresponding to a 200-Hz PRF) are extracted at equal intervals in this experiment. Figure 8 The first and second rows in Fig. 5 show the 2D observation data when the MR is 50% and 75%, respectively, as well as the imaging and scaling results of the RD, GS-SLIM and proposed algorithms. The imaging time of each algorithm is labeled in the figure. As shown in Fig. 5, the RD algorithm has failed. The target image obtained by the GS-SLIM algorithm is not well focused and is blurred, especially when the available data is less. However, the proposed algorithm can obtain a clearer and better focused target image, and the calculation time is also shorter. The estimated target rotation speeds of the proposed algorithm are 0.0265 rad / s and 0.0263 rad / s, respectively. Based on the estimated target rotation speeds, the scaling results of the target are close to the actual size of the Yak-42 aircraft. Since the target rotation speeds estimated by other algorithms deviate greatly from the true value, the target rotation speed estimated by the proposed algorithm in this chapter is used for scaling. Figure 8

[0182] In view of the problem that target ISAR imaging algorithms in an interference environment are easily affected by sidelobes and time-varying Doppler frequencies, and thus have poor focusing performance or even completely fail, the present application provides a time-frequency random sampling high-resolution ISAR imaging fast method based on AIWF. The method uses a missing data estimation fast algorithm and an optimization algorithm to obtain complete range frequency domain-slow time domain data and compensate motion errors, and designs an AIWF fast algorithm based on cyclic low displacement rank decomposition and a re-sampling method for reducing the dimension of a covariance matrix, so as to greatly reduce the calculation complexity and efficiently and accurately perform ISAR imaging. The method provided by the present application has good noise suppression capability and high scaling accuracy, and can obtain an ISAR image with good focusing even in the case of a large data missing rate.

[0183] It should be noted that the terms "first", "second" in the present application are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first", "second" can explicitly or implicitly include one or more of the features. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise specifically limited.​​

[0184] Although the application has been described in connection with specific embodiments thereof, it will be understood that it is capable of further modifications and this application is intended to cover any variations using the principles of the application. For example, "comprising" as used throughout the specification and in each claim is not meant to exclude other components or steps. The terms "a" or "an" as used herein mean "one or more."

[0185] The above description is further to specific preferred embodiments of the present application and cannot be deemed to limit the specific implementation of the present application to these descriptions. For those skilled in the art of the present application, a number of simple deductions or replacements can be made without departing from the concept of the present application, and all of these should be deemed to fall within the protection scope of the present application.

Claims

1. An AIWF-based fast time-frequency random sampling high-resolution ISAR imaging method, characterized in that, Comprise: S100, receive echo data of target feedback; S200, missing data recovery is carried out to the echo data to obtain complete echo data; S300, the motion parameters of the target are estimated by using the SQP algorithm, and the complete echo data is motion compensated by using the motion parameters to obtain the echo data after motion compensation; S400, the echo data after motion compensation is used, and the target image of focusing and azimuth positioning is obtained by the AIWF-ME algorithm; S500, the steps S200-S400 are repeated until the error of the target image is less than the convergence threshold or the maximum iteration number is reached, and then the final target image is output; S400 comprises: S410, the noise variance value is estimated by using the AIWF algorithm and with the aid of auxiliary data; the auxiliary data is echo data without target in the target echo; the design process of the AIWF algorithm is as follows: Let denote the noisy data, where represents the estimate of the original signal, and the noisy data n is known to follow a complex Gaussian distribution, then the auxiliary data and the primary data each element of which follows the same complex Gaussian distribution: （34） where denotes the precision of the noise, ; assuming obeys the parameter c and d gamma distribution: （35） wherein, c with d denote shape parameters and inverse scale factors, respectively; is the gamma function; estimating the hyperparameters based on a second type of maximum likelihood function, the posterior probability distribution of the hyperparameters is （36） Given the edge function of the original noise Only in relation to the model, so Taking the logarithm further and ignoring constants gives: （37） Taking the partial derivative of equation (37) with respect to and setting it to zero, we obtain the update equation for ​ （38）； The time domain length of the filled complete signal is M ; S420, the observation covariance matrix in the AIWF algorithm is determined according to the noise variance value; S430, the observation covariance matrix is resampled to obtain a sampling covariance matrix by using a sampling matrix; wherein, the sampling covariance matrix and the observation covariance matrix have the same structure, but the dimension is lower than that of the observation covariance matrix; S440, the inverse matrix of the sampling covariance matrix is solved by using a low cyclic displacement rank decomposition method, and the target image of focusing and azimuth positioning is reconstructed by using the inverse matrix and the target echo after motion compensation.

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

3. The AIWF-based fast time-frequency random sampling high-resolution ISAR imaging method according to claim 2, characterized in that, The missing data recovery method based on conditional mean estimation is improved by using the cyclic convolution theorem and the least square approximation to solve the matrix inversion operation in the missing data recovery method based on conditional mean estimation.

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

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

6. The AIWF-based fast time-frequency random sampling high-resolution ISAR imaging method according to claim 4, characterized in that, S330 comprises: The complete echo data is compensated by using the motion parameters to obtain the echo data after motion compensation.

7. The AIWF-based fast time-frequency random sampling high-resolution ISAR imaging method according to claim 1, characterized in that, S500 comprises: S510, it is judged whether the error of the target image in S400 is less than the convergence threshold, if not, the target image and the estimated motion parameters are used as the basis for updating the motion parameters and the target image next time; and in the next iteration cycle, the steps S200-S400 are repeated according to the basis; S520, if the error of the target image in S400 is less than the convergence threshold, the target image when the error is less than the convergence threshold is output. S530, when the iteration loop reaches the maximum iteration number, and the error of the target image is still not less than the convergence threshold, output the target image in the last loop iteration.

Images