Inverse synthetic aperture radar imaging and motion compensation method

Abstract

The invention discloses an inverse synthetic aperture radar imaging and motion compensation method based on OFDM signals. Interference between distance units is effectively suppressed in a distance compression process by utilizing OFDM signals with enough long cyclic prefixes, and estimation errors are reduced. In order to solve the problem of over-resolution unit migration occurring under high-resolution or long-coherent processing, a vectorization observation model containing low-order and high-order phase error terms of target motion is constructed, and a target image and rotation parameters are jointly estimated through two layers of prior models under a sparse Bayesian framework. In order to enhance the calculation robustness of matrix inversion, joint optimization is carried out by adopting an alternating direction multiplier method, and target rotation parameters are accurately estimated by utilizing a maximum image contrast criterion, so that joint imaging and motion compensation are realized. A simulation result shows that the method has remarkable advantages in the aspects of reducing sidelobe interference, improving resolution and realizing real-time imaging, and is suitable for high-resolution inverse synthetic aperture radar imaging of a non-cooperative target.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and particularly relates to a method for inverse synthetic aperture radar (ISAR) imaging and motion compensation of OFDM signals under sparse aperture. Background Art

[0002] In recent years, radar systems have played an important role in fields such as national defense, civil aviation, marine monitoring, and geological exploration. Synthetic aperture radar (SAR) uses the virtual large aperture generated by platform motion to achieve high-resolution imaging of targets, while inverse synthetic aperture radar is for non-cooperative targets and obtains high azimuth resolution images through the Doppler frequency shift generated by the target's own rotation. Traditional ISAR imaging systems mostly use linear frequency modulation (LFM) waveforms. Due to the matching filter design and pulse compression mechanism of LFM signals, they often face problems such as sidelobe interference in practical applications, resulting in a decline in image quality. In addition, when the imaging resolution requirement increases or under a long coherent processing time, the migration through resolution cells (MTRC) effect caused by target motion will become more obvious, making motion compensation more complex and crucial.

[0003] In recent years, due to its inherent multi-carrier structure, frequency domain equalization advantage, and good integration with communication systems, OFDM signals have received extensive attention in the field of SAR imaging. By adding a sufficiently long cyclic prefix to the OFDM signal, the inter-range-cell interference (IRCI) problem caused by signal interference can be effectively eliminated, thereby achieving interference-free range compression. However, when applying the CP-OFDM waveform to ISAR imaging, due to the non-cooperativeness of the target and the complexity of the motion state, the existing algorithms for motion compensation and autofocus often have deficiencies such as insufficient robustness, high computational complexity, and insensitivity to high-order phase errors in the prior art, resulting in poor image focusing or defocusing phenomena. At the same time, under the sparse aperture (SA) condition, due to the loss of some pulse signals affected by factors such as noise, interference, or signal occlusion, the traditional autofocus algorithm based on high echo coherence fails, and more robust joint sparse imaging and motion compensation technologies need to be developed.

[0004] In the prior art, there are many published literatures on the application of OFDM signals in SAR, but there are few studies on ISAR imaging; at the same time, how to jointly consider the high-order terms of motion errors, enhance the robustness of matrix inversion and achieve autofocus and motion compensation under the sparse Bayesian learning framework, and how to accurately reconstruct the target image under sparse data conditions are still technical problems to be solved urgently. Summary of the Invention

[0005] Object of the Invention: The present invention solves the problems of defocusing caused by inaccurate modeling and compensation and instability in matrix inversion under sparse aperture conditions in OFDM-ISAR imaging.

[0006] Technical Solution: To achieve the above object of the invention, the first technical solution adopted by the present invention is an inverse synthetic aperture radar imaging and motion compensation method based on OFDM waveform, comprising the following steps:

[0007] Step 1: Use an OFDM waveform with a sufficiently long cyclic prefix as the transmitted signal. The radar receiver performs down-conversion, resampling on the received signal, and preprocesses the data to remove the cyclic prefix.

[0008] Step 2: By designing a target geometric model and a range cell division method different from traditional SAR, realize the IRCI-free reconstruction of the target range image. Specifically, during range compression processing, perform FFT on the OFDM received signal, convert it to the frequency domain for processing, and use the cyclic prefix to eliminate the interference caused by the echo signal delay of different scatterers on the target, meeting the requirement of reducing sidelobes.

[0009] Step 3: For the phase defocusing problem caused by target rotation during the imaging process, establish a vectorized observation model including high-order phase error terms caused by rotation, so as to accurately describe the non-linear phase mismatch generated by target motion.

[0010] Step 4: Under the sparse Bayesian learning framework, calculate the approximate posterior distribution of the target image vector x based on variational expectation maximization.

[0011] Step 5: To solve the singular value problem occurring in matrix inversion operations, the present invention uses the alternating direction method of multipliers (ADMM) to decompose the joint optimization problem, decomposes the coupled problem into multiple sub-problems for separate solution, so that the algorithm has high robustness.

[0012] Step 6: During the motion compensation process, to compensate for the high-order phase mismatch caused by target rotation, use the maximum image contrast criterion to estimate the target rotation parameters Then substitute the target rotation parameters Back into the initial value of the sparse Bayesian solution; repeat the above steps 4, 5, and 6, and perform alternating iteration to finally achieve joint imaging and autofocus.

[0013] Furthermore, the following steps are included in Step 1:

[0014] Step 1-1: The transmitted signal uses OFDM modulation, and the expression of its continuous time s(t) is:

[0015]

[0016] Where: M is the number of OFDM symbols; m is the m-th OFDM symbol; N is the number of subcarriers; W n is the modulation symbol on the n-th subcarrier; Δf is the subcarrier spacing; T sym = T CP + T is the OFDM symbol period, T CP is the cyclic prefix length, T is the effective symbol duration; p(·) is the pulse shaping function; t is the fast time;

[0017] Step 1-2, after upconversion, the transmitted RF signal is:

[0018]

[0019] Where f c is the carrier frequency, is to take the real part of the signal;

[0020] Step 1-3, the baseband echo signal is obtained after downconversion at the receiving end, and its model considers the phase changes caused by target scattering, range delay, and motion. Assume that the target rotation center is located at a distance R from the radar o . {(x p , y p )|p = 1, 2,..., P} are the coordinates of the p-th scattering point on the target in the target local coordinate system. The distance R from the radar to the p-th scattering point for the m-th echo generated by target rotation m,p is expressed as:

[0021]

[0022] w, w a are the rotation speed and rotation acceleration respectively. Using the Taylor series to approximate the sin and cos functions: sin x ≈ x, cos x ≈ 1 - x 2 / 2, the approximate expression of the instantaneous distance R m,p can be obtained:

[0023]

[0024] Therefore, the received time-domain discrete signal g m,p (i) is:

[0025]

[0026] i = 0, 1,..., N + R - 2

[0027] Where R represents the number of range cells, r represents the range cell index, P rrepresents the total number of scatterers contained in the r-th range cell, r r,p represents the integer part difference of the actual position of the p-th scatterer in the r-th range cell relative to the sampling point position i; R m,r,p = R m,p ; R s is the sampling interval, and n(i) is the additive white Gaussian noise after sampling;

[0028] is the m-th echo and the range cell coefficient for different range cells r.

[0029] Furthermore, the step 2 includes the following steps:

[0030] Step 2-1, the received signal g m,p (i) is further written in matrix form as follows:

[0031]

[0032] g is the column vector form of the m-th received echo, H is a circulant matrix, and the elements in the circulant matrix H are the range cell coefficients u m,r values of the m-th echo at different range cells r, s is the vector form of the transmitted signal, and the elements in s are the values of the transmitted signal s at different sampling times, and c is the vector form of the noise, and the elements in c are the additive white Gaussian noise values at different sampling times;

[0033] Step 2-2, due to the circulant property of the circulant matrix H, perform FFT operation on the echo signal g and perform correlation operation with the transmitted signal s to obtain independent frequency domain channel estimation coefficients Use the cyclic prefix to achieve range profile reconstruction without IRCI:

[0034]

[0035] where G(n)=FFT(g), and G(n) is the FFT operation on the m-th received echo g;

[0036] Step 2-3, further, perform IFFT back to the time domain to obtain the range cell estimation value :

[0037]

[0038] c r is the noise term, and finally, obtain the range compressed signal g rc (t):

[0039]

[0040] δ(·) is the impulse function, crc (t) is the noise signal after range compression processing.

[0041] Furthermore, the step 3 includes the following steps:

[0042] Step 3-1, to fully describe the non-linear influence of the target motion on the phase, the present invention introduces quadratic and higher-order phase error terms on the basis of the traditional low-order model. Specifically, the target echo phase error model φ is expressed as:

[0043]

[0044] where x q , y q are the coordinates of the target on the two-dimensional coordinate axes with the rotation center as the coordinate origin, w0 and w a are the rotational speed and rotational acceleration respectively;

[0045] Step 3-2, in practical applications, due to factors such as noise, interference or system failures, some pulse data may be missing, forming a sparse aperture phenomenon. To address this issue, the present invention uses Bayesian prior information and sparse reconstruction methods to compensate for the missing data. By performing sparse coding on the observation matrix Θ and combining with a global optimization algorithm, the complete target image data is restored, thus ensuring that the imaging quality is not degraded due to data loss;

[0046] Specifically, the obtained all range compression signals g rc (t) in the M echoes are rewritten in matrix form S:

[0047] S = E[(AX)⊙B]

[0048] where E is the initial phase error matrix, X is the target image matrix to be reconstructed, A is a matrix composed of the rotation Doppler information and azimuth error required for imaging, and B is the range error matrix:

[0049]

[0050]

[0051] where μ is the column subscript of A, μ = 1, 2,..., Q, Q is the total number of azimuth dimensions of the target image matrix X, is the initial phase, and diag(·) is the diagonalization operation;

[0052] Step 3-3, further, the received data S is written in vectorized form:

[0053] h = Φx + c

[0054] where,

[0055]

[0056] h = vec(S) is the observation vector; Φ is the observation matrix, which includes factors such as range compression and phase error model; c is the noise vector.

[0057] Furthermore, the step 4 includes the following steps:

[0058] Step 4-1, to promote the sparsity of the target image vector x, first assume that the pixel value x of each target image vector i obeys a complex Gaussian distribution, and the reciprocal of its covariance is used as the sparse prior parameter; furthermore, on this basis, a Gamma distribution is introduced for the prior parameter to achieve a two-layer Bayesian modeling. The specific implementation is as follows:

[0059] Establish a complex Gaussian prior model for the target image vector x, and the probability density p(x|γ) is:

[0060]

[0061] J = QN, representing the total dimension number of the vector;

[0062] Introduce a Gamma distribution prior for the prior parameter γ, and the probability density p(γ) is:

[0063]

[0064] Introduce a Gamma distribution prior for the noise inverse variance β, and the probability density p(β; a, b) is:

[0065] p(β; a, b) = G(β; a, b)

[0066] where a, b, c, and d are all hyperparameters, making the reconstructed image have better sparsity;

[0067] Step 4-2, jointly estimate x, γ, and β through the Expectation-Maximization (EM) algorithm and variational inference, and obtain the posterior estimate q(x) of the target image vector x, thereby effectively solving the image reconstruction problem under the conditions of missing data and sparse aperture:

[0068]

[0069] where:

[0070]

[0071] Furthermore, the step 5 includes the following steps:

[0072] Since the above Bayesian sparse reconstruction problem is usually a high-dimensional joint optimization problem, in the matrix inversion operation, a singular value problem will occur, and the computational robustness is very low. Therefore, the present invention uses the alternating direction multiplier method (ADMM) to decompose the joint optimization problem, and the specific form is as follows:

[0073] Step 5-1: Construct an augmented Lagrangian function, and alternately iterate to solve the target image vector x, the auxiliary variable z, and the Lagrange multiplier y, so that each sub-problem can be solved in a closed form, thereby greatly reducing the computational burden of large-scale matrix inversion. While ensuring the accuracy, this method improves the real-time performance and robustness of the algorithm;

[0074] Construct the Lagrangian augmented function L ρ (x, z, u):

[0075]

[0076] where β is the inverse noise variance, Γ is the prior matrix, ρ is the penalty factor, and y is the Lagrange multiplier;

[0077] Step 5-2: Then, the update formula for the target image vector x is obtained as follows:

[0078] x (k+1) =(βΦ H Φ + ρI) -1 (βΦ H y + ρz (k) -y (k) )

[0079] The update formula for the auxiliary variable z is as follows:

[0080] z (k+1) =(Γ + ρI) -1 (ρx (k+1) +y (k) )

[0081] The update formula for the Lagrange multiplier y is as follows:

[0082] y (k+1) =y (k) +ρ(x (k+1) -z (k+1) )

[0083] Finally, the posterior estimates q(x) and q(z) of x and z are obtained:

[0084]

[0085] where,

[0086] μ x =∑(βΦ H h + ρz - y)

[0087] ∑ = (βΦ H Φ + ρI) -1

[0088] μ z = ∑ z (y + ρx)

[0089] ∑ z = (Γ + ρI) -1

[0090] μ x 、∑、μ z 、∑ z are the mean and variance of x and z respectively.

[0091] Further, the step 6 includes the following steps:

[0092] Step 6-1, define the image contrast function C(θ) as:

[0093] C(θ) = ‖|μ(θ)| 2 ‖2

[0094] θ = {w, w a} is the vector composed of the target rotation parameters, and μ(θ) is the maximum a posteriori expectation related to the target rotation parameter θ;

[0095] Step 6-2, optimize C(θ) by maximizing the image contrast to obtain the estimated value of the target rotation parameter :

[0096]

[0097] Step 6-3, use the obtained parameter value to replace the initial value given by the sparse Bayesian solution algorithm, iterate and update, and finally obtain the optimal image.

[0098] The second technical solution adopted by the present invention is an ISAR imaging process of the inverse synthetic aperture radar imaging and motion compensation method as described above, including:

[0099] Transmission process: used to generate an OFDM signal with sufficient cyclic prefix and form a radio frequency signal through upconversion;

[0100] Receiving process: used to receive the target echo signal and perform downconversion and resampling;

[0101] Data processing process: including a range compression module, a sparse Bayesian reconstruction, an ADMM optimization module and a motion compensation autofocus module, and the modules jointly process the received data to reconstruct the ISAR image;

[0102] Display and storage process: used to display the reconstructed ISAR image and store relevant processing data.

[0103] Advantages: The CP-OFDM waveform is adopted to achieve range compression, making full use of the advantages of the cyclic prefix to eliminate IRCI, thereby significantly reducing the sidelobe level and obtaining a range image with higher resolution; a high-order phase error model is introduced in the sparse Bayesian learning framework, which can more accurately describe the uncertainty of target motion and the image defocusing effect caused by it, making the motion compensation algorithm more robust and adaptive; the ADMM technology is used to split the coupled problem to improve the computational robustness; the maximum image contrast criterion is adopted for rotation parameter estimation, ensuring the automatic focusing effect of the target and enabling clear imaging even in the case of sparse data or high noise; the technical solution of the present invention is applicable to ISAR imaging of non-cooperative targets and has broad practical application prospects and engineering value in applications such as target detection, tracking, and recognition. Description of the Drawings

[0104] Figure 1 It is a geometric schematic diagram of the ISAR imaging model of the present invention, showing the relationship between the radar transceiver and the object to be imaged.

[0105] Figure 2 It is a transmission schematic diagram of the OFDM signal in the ISAR system, continuously transmitting M OFDM symbols.

[0106] Figure 3 It is the complete algorithm flow chart proposed by the present invention.

[0107] Figure 4 It is the ISAR simulation parameter design index.

[0108] Figure 5 It is the two-dimensional image of the point target in the simulation settings.

[0109] Figure 6 It is the normalized range image of the point spread function of the LFM signal and the CP-OFDM signal proposed by the present invention.

[0110] Figure 7(a)-7(f) It is a schematic diagram of the simulation experiment results. Among them, 7(a), 7(c), 7(e) and 7(b), 7(d), 7(f) respectively show the image results of the full aperture and sparse aperture based on the OFDM waveform. The results processed by the range-Doppler algorithm are shown in Fig. 7(a) and Fig. 7(b); the results processed by the phase gradient autofocus (PGA) algorithm are as Figure 7(c) , 7(d) ; 7(e), 7(f) are the results diagrams of the algorithm proposed by the present invention. Detailed Implementation Manner

[0111] The present invention will be further illustrated below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0112] The present invention proposes a joint ISAR imaging and motion compensation scheme based on OFDM signals under sparse aperture in existing imaging methods. The imaging and motion compensation method includes: the transmitting end generates a multi-subcarrier signal using OFDM modulation and inserts a cyclic prefix with a sufficient length before each OFDM symbol to meet the requirement of eliminating IRCI; the data processing steps at the receiving end include operations of removing the carrier frequency and resampling the received echo, then performing range compression on the signal after removing the first CP data, then performing vector quantization on the range-compressed signal, further using sparse Bayesian learning and an ADMM optimization module to solve for the target image vector x, and performing rotation parameter estimation and motion compensation, and alternately optimizing to finally achieve the reconstruction of the target image vector x; finally, the reconstructed ISAR image is displayed, and the processing results are stored for subsequent analysis.

[0113] The application scenario of the present invention is as Figure 1 shown: A turntable imaging model based on CP-OFDM signals is considered, where the transmitter and receiver of the radar are set at the same / very close positions. O is the rotation center of the target. Let the distance between the radar and the rotation center of the target be R O = 200 meters, and r p = (x p , y p ) are the coordinate values of the scattering points on the target in the coordinate system with the origin at O. We assume that there are P resolvable scattering points on the target. During the rotation of the target, the relative positions of the scattering points with respect to the coordinate system X-O-Y remain unchanged.

[0114] As Figure 2 shown, M OFDM symbols are continuously transmitted, and the relevant specific parameters are included in Figure 4 . The carrier frequency f c = 9.6e9 Hz, corresponding to a wavelength λ = 0.03125 meters, the number of subcarriers N = 1024, the cyclic prefix length T CP meets the range cell requirement, the bandwidth BW = 368.64 MHz, and a total of 512 OFDM symbols are transmitted.

[0115] As Figure 5 shown, the target consists of 61 scattering points, and its lateral and longitudinal offsets are respectively in the range of [-20, 20] meters, and the target rotation angular velocity is 10 rad / s.

[0116] The specific complete process is as follows Figure 3 as shown below:

[0117] Step 1: The expression of the transmitted OFDM signal s(t) is:

[0118]

[0119] where: M is the number of OFDM symbols; m is the m-th OFDM symbol; N is the number of subcarriers; W n is the modulation symbol on the n-th subcarrier; Δf is the subcarrier spacing; T sym = T CP + T is the OFDM symbol period, T CP is the cyclic prefix length, and T is the effective symbol duration; p(·) is the pulse shaping function; t is the fast time; after up-conversion, a radio frequency signal is formed

[0120]

[0121] where f c is the carrier frequency, taking the real part of the signal, this step ensures the stability and high energy transmission of the signal during long-distance transmission;

[0122] At the receiving end, the received signal is demodulated to the baseband. The received baseband signal g m (t) is the superposition of the echoes of the transmitted signal at different OFDM symbol periods m and a total of P scattering points, and its expression is as follows:

[0123]

[0124] where a(p) is the radar cross-section coefficient of the p-th scattering point, ε(p) is the path loss experienced by the p-th scattering point, R m,p represents the distance from the radar to the p-th scattering point for the m-th echo, τ m,p = 2R m,p / c, c is the speed of light, λ is the wavelength, and n(t) represents additive white Gaussian noise;

[0125] The instantaneous distance R m,p generated by each scatterer is:

[0126]

[0127] Step 2: After using the cyclic property to eliminate the interference between range cells, the obtained range-compressed signal g rc (t):

[0128]

[0129] is the obtained range cell estimate value, δ(·) is the impulse function, and c rc (t) is the noise signal after range compression processing.

[0130] Range cell estimate value

[0131]

[0132] Step 3: To simulate the defocus phenomenon caused by insufficient rotational compensation, consider the high-order phase error φ in the echo phase:

[0133]

[0134] Step 4: Vectorize the received signal, and then jointly estimate x, γ, and β through the Expectation-Maximization algorithm and variational inference to obtain the posterior estimate of the target image vector x, where the objective function ln q i (Θ i ) is:

[0135] ln q i (Θ i ) = <ln p(h,Θ)> k≠i + const, Θ = {x, β, γ}

[0136] q i (Θ i ) represents the posterior distribution of the i-th element in Θ, const represents a constant, p(h,Θ) represents the likelihood function of the observed signal, and <·> represents the expectation;

[0137] Furthermore, the approximate posterior distribution q(x) of x is derived:

[0138]

[0139] μ, ∑ are the posterior mean and variance of x, respectively, represents being subject to a Gaussian distribution.

[0140] Step 5: Solve the joint optimization problem through the ADMM algorithm to obtain the posterior estimates q(x) and q(z) of x and z:

[0141]

[0142] where,

[0143] μ x = ∑(βΦ H h + ρz - y)

[0144] ∑ = (βΦ H Φ + ρI) -1

[0145] μ z = ∑ z (y + ρx)

[0146] ∑ z = (Γ + ρI) -1

[0147] μ x 、∑、μ z 、∑ z are the mean and variance of x and z, respectively.

[0148] Step 6: Optimize C(θ) by maximizing the image contrast to obtain the estimated value of the target rotation parameter :

[0149]

[0150] Use the estimated value of the target rotation parameter to replace the initial value given by the sparse Bayesian solution algorithm, and iteratively update to finally obtain the optimal image.

[0151] Figure 6 The results of the proposed CP-based OFDM waveform range compression algorithm are compared with those of the traditional de-chirping method using the LFM waveform. It is worth noting that the range image of the point spread function obtained by the OFDM method shows a sidelobe level lower than -300 dB, significantly lower than the -60 dB result generated by the LFM waveform. This result clearly demonstrates the ability of the proposed method to reconstruct the range without IRCI.

[0152] Figure 7(a)-7(f) is a schematic diagram of the simulation experiment results, where Figure 7(a) 、 7(c) 、7(e) and 7(b), 7(d), 7(f) respectively show the image results of the full aperture and sparse aperture based on the CP-OFDM waveform. The results after processing by the range-Doppler algorithm are shown in Fig. 7(a) and Fig. 7(b); the processed results are as Figure 7(c) 、 7(d); Figures 7(e) and 7(f) are the results of the algorithm proposed in the present invention. It can be seen that, under the same sparsity, the motion compensation and autofocus methods proposed in this patent are significantly superior to the traditional range-Doppler algorithm and the phase gradient autofocus algorithm. The ISAR images reconstructed by the method proposed in this patent are significantly superior to the traditional methods in terms of range resolution, azimuth resolution, and target details. The sidelobe level is reduced, and the target focusing effect is significantly improved. Considering the situation of missing some pulse data in the actual scenario, by randomly removing some pulse data during the sampling process, the robustness of the present invention under the condition of missing data is verified. The results show that using the Bayesian prior and sparse reconstruction method can ensure that the image focusing effect and target detection accuracy are not affected.

[0153] Due to the adoption of the ADMM optimization technology, the matrix inversion problem is decomposed. The original joint optimization problem is decomposed into multiple sub-problems, and each sub-problem can be solved in a closed form. During the iterative update process, the penalty factor ρ is dynamically adjusted to ensure the convergence speed and global optimality. The simulation experiment shows that this method can reduce the solution time by about 40% or more while ensuring the reconstruction accuracy, providing the possibility for real-time processing.

[0154] The present invention provides an idea and method for joint imaging, parameter estimation, and motion compensation of sparse-aperture inverse synthetic aperture radar (ISAR) using orthogonal frequency division multiplexing (OFDM) signals with a sufficiently long cyclic prefix (CP). There are many methods and ways to specifically implement this technical solution. The above description is only the preferred implementation manner of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by the prior art.

Claims

1. An inverse synthetic aperture radar imaging and motion compensation method based on OFDM waveform, characterized in that, It includes the following steps: Step 1: Transmit an OFDM signal with a sufficiently long cyclic prefix; The radar receiver receives the echo signal scattered by the target, which is down-converted and resampled, and the data with the length of the head cyclic prefix is removed so as to only leave the useful data part; Step 2: Perform a fast Fourier transform on the data block after removing the cyclic prefix, convert the time-domain signal to the frequency domain, then analyze the frequency response of the channel in the frequency domain, and further obtain the range image; Step 3: Vectorize the data after range compression processing, and establish an observation model including low-order and high-order phase error terms of target motion; Step 4: Under the sparse Bayesian learning framework, establish a prior model for the target image vector x, and obtain an approximate posterior distribution of the target image vector x based on Bayesian inference of variational expectation maximization; Step 5: To solve the singular value problem that occurs in the inversion of large-scale matrices in solving the joint optimization problem, the alternating direction multiplier method is adopted. By introducing auxiliary variables z and Lagrange multipliers y, the coupled problem is split into two sub-problems, and x, z, and y are iteratively updated until convergence, so as to obtain an estimate of the target image vector x; Step 6: Parameter estimation and motion compensation step: To compensate for the high-order phase mismatch caused by the rotation of the target, the maximum image contrast criterion is used to estimate the target rotation parameters Then the target rotation parameters are re-substituted into the initial values solved by sparse Bayesian, and steps 4, 5, and 6 are repeated until the threshold is reached to achieve motion compensation.

2. The method for inverse synthetic aperture radar imaging and motion compensation according to claim 1, wherein In the said Step 1, the expression of the OFDM signal s(t) is: Where: M is the number of OFDM symbols; m is the m-th OFDM symbol; N is the number of subcarriers; W n is the modulation symbol on the n-th subcarrier; Δf is the subcarrier spacing; T sym = T CP + T is the OFDM symbol period, T CP is the cyclic prefix length, T is the effective symbol duration; p(·) is the pulse shaping function; t is the fast time; after up-conversion, a radio frequency signal is formed where f c is the carrier frequency, takes the real part of the signal, and this step ensures the stability and high energy transmission of the signal during long-distance transmission; At the receiving end, the received signal is demodulated to the baseband, and the received baseband signal g m (t) is the superposition of the echoes of the transmitted signal at different OFDM symbol periods m and a total of P scattering points, and its expression is as follows: where \(a(p)\) is the radar cross-section coefficient of the \(p\)th scattering point, \(\varepsilon(p)\) is the path loss experienced by the \(p\)th scattering point, and \(R\) m,p represents the distance from the radar to the \(p\)th scattering point for the \(m\)th echo, and \(\tau\) m,p = 2R m,p / c is the time delay, \(c\) is the speed of light, \(\lambda\) is the wavelength, and \(n(t)\) represents additive white Gaussian noise; Assume that the target rotation center is located at a distance R from the radar o . Let {(x p , y p )|p = 1, 2, …, P} be the coordinates of the p-th scatterer on the target in the target local coordinate system. The distance R m,p from the radar to the p-th scatterer for the m-th echo generated by the target rotation is expressed as: where w, w a are the rotational speed and rotational acceleration respectively. By using the Taylor series approximation to expand the sin and cos functions: sinx≈x, cosx≈1 - x 2 / 2, the instantaneous distance R m,p approximate expression can be obtained: The received signal is sampled to obtain a discrete digital signal g m,p (i) is expressed as: Among them, R represents the total number of range cells, r represents the range cell index, and P r represents the total number of scatterers contained in the r-th range cell, and r r,p represents the integer part difference of the actual position of the p-th scatterer relative to the sampling point position i; R m,r,p = R m,p , T s is the sampling interval, and n(i) is the additive Gaussian white noise after sampling; is the m-th echo and the range cell coefficient for different range cells r.

3. The method for inverse synthetic aperture radar imaging and motion compensation according to claim 1, characterized in that The signal obtained in step 2 is the received signal g m,p (i) It is further written in the following matrix form: g is the column vector form of the m-th received echo, H is a circulant matrix, and the elements in the circulant matrix H are the range cell coefficients u at different range cells r in the m-th echo m,r values, s is the vector form of the transmitted signal, the elements in s are the values of the transmitted signal s at different sampling instants, c is the vector form of the noise, and the elements in c are the additive white Gaussian noise values at different sampling instants. Due to the circulant property of the circulant matrix H, the echo signal g is subjected to an FFT operation and correlated with the transmitted signal s to obtain mutually independent frequency-domain channel estimation coefficients Use the cyclic prefix to achieve range profile reconstruction without IRCI: where G(n)=FFT(g), and G(n) is the FFT operation on the mth received echo g; Furthermore, the IFFT returns to the time domain to obtain the range cell estimation value c r is the noise term. Finally, after using the cyclic property to eliminate the interference between range cells, the obtained range-compressed signal g rc (t): is the obtained distance unit coefficient estimation value, δ(·) is the impulse function, and c rc (t) is the noise signal after range compression processing.

4. The method for inverse synthetic aperture radar imaging and motion compensation according to claim 1, wherein The observed signal h obtained in step 3 is to rewrite all the range-compressed signals g rc (t) obtained in step 2 in matrix form S: S = E[(AX)⊙B] where E is the initial phase error matrix, X is the target image matrix to be reconstructed, A is a matrix composed of rotation Doppler information and azimuth error required for imaging, B is the range-direction error matrix, and ⊙ is the element-wise multiplication operation: where μ is the column index of A, μ = 1, 2, …, Q, and Q is the total number of azimuth dimensions of the target image matrix X. is the initial phase, and diag(·) is the diagonalization operation; further, the received data S is written in the vectorized form h, and the expression is as follows: h = Φx + c where Φ is the observation matrix, c is the observation noise, and when it is constructed, the range compression and the phase mismatch caused by target motion are fully considered. The phase mismatch term φ includes the azimuth change term and the range change term, and these two terms are also considered as rotation phase errors: where x q and y q are the coordinates of the target on the two-dimensional coordinate axes with the rotation center as the origin of coordinates, and w0 and w a are the rotational speed and rotational acceleration respectively.

5. The method for inverse synthetic aperture radar imaging and motion compensation according to claim 1, wherein The posterior distribution of the target image vector x obtained in the said Step 4 is derived as follows: Step 4-1, establish a complex Gaussian prior model for the target image vector x, and the probability density p(x|γ) is: J = QN, representing the total dimension number of the vector, Q is the total number of azimuth dimensions; γ is the hyperparameter that controls the sparsity of x; Step 4-2, introduce a Gamma distribution prior for the hyperparameter γ, and the probability density p(γ) is: Step 4-3, introduce a Gamma distribution prior for the noise inverse variance β, and the probability density p(β; a, b) is: p(β; a, b) = G(β; a, b) where a, b, c, and d are all hyperparameters, so that the reconstructed image has better sparsity; Step 4-4, jointly estimate x, γ, and β through the Expectation-Maximization algorithm and variational inference to obtain the posterior estimate of the target image vector x, where the objective function lnq i (Θ i ) is as follows: lnq i (Θ i ) = <lnp(h, Θ)> k≠i + const, Θ = {x, β, γ} q i (Θ i ) represents the posterior distribution of the i-th element in Θ, const represents a constant, p(h, Θ) represents the likelihood function of the observed signal, and <·> represents the expectation; Furthermore, the approximate posterior distribution q(x) of the target image vector x is derived: μ and ∑ are the posterior mean and variance of x respectively. It means following a Gaussian distribution.

6. The method for inverse synthetic aperture radar imaging and motion compensation according to claim 1, characterized in that, The alternating direction multiplier method adopted in the said Step 5 further includes: Step 5-1, construct the Lagrangian augmented function L ρ (x, z, y): where Γ = diag(vec(γ)), z is the auxiliary variable, ρ is the penalty factor, and y is the Lagrange multiplier; Step 5-2, the update formula for the target image vector x is: x (k+1) = (βΦ h Φ + ρI) -1 (βΦ H y + ρz (k) -y (k) ) The update formula for the auxiliary variable z is: z (k+1) =(Γ + ρI) -1 (ρx (k+1) + y (k) ) The update formula for the Lagrange multiplier y is: y (k+1) = y (k) + ρ(x (k+1) - z (k+1) ) where i represents the identity matrix, and k is the kth iteration; Finally, the posterior estimates q(x) and q(z) of x and z are obtained: where μ x = ∑(βΦ H h + ρz - y) ∑ = (βΦ H Φ + ρI) -1 μ z = ∑ z (y + x) ∑ z =(Γ + ρI) -1 μ x 、∑、μ z 、∑ z are the mean and variance of x and z respectively.

7. The method for inverse synthetic aperture radar imaging and motion compensation according to claim 1, characterized in that The maximum image contrast criterion adopted in Step 6 is further specified as follows: Step 6-1: Define the image contrast function C(θ) as: C(θ) = ‖|μ(θ)| 2 ‖2 θ = {w, w a} is the vector composed of the target rotation parameters, and μ(θ) is the maximum a posteriori expectation related to the target rotation parameter θ; Step 6-2, optimize the image contrast function C(θ) using the nonlinear least squares method to obtain the estimated value of the target rotation parameter The estimated value of the target rotation parameter is used to replace the initial value given by the sparse Bayesian solution algorithm, and is iteratively updated to finally obtain the optimal image.

8. An inverse synthetic aperture radar imaging process based on the inverse synthetic aperture radar imaging and motion compensation method according to any one of claims 1 to 7, comprising: Transmission process: used to generate an OFDM signal with a sufficient cyclic prefix and form a radio frequency signal through up-conversion; Receiving process: used to receive the target echo signal and perform down-conversion and resampling; Data processing process: includes a range compression module, a sparse Bayesian reconstruction, an alternating direction multiplier method optimization module, and a parameter estimation motion compensation module. The modules jointly process the received data to reconstruct the inverse synthetic aperture radar image; Display and storage process: used to display the reconstructed inverse synthetic aperture radar image and store the relevant processing data.

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