Maneuvering target ISAR imaging method and system based on EM algorithm

Abstract

The invention discloses a maneuvering target ISAR (Inverse Synthetic Aperture Radar) imaging method and system based on an EM (Expectation Mode) algorithm, and the method comprises the steps: constructing a dynamic Bayesian model which takes a time-varying amplitude envelope as an observation basis, and introducing a target motion state parameter into an imaging process as a hidden variable; and respectively realizing posterior inference of hidden variables and maximum likelihood estimation of scattering coefficients in E-Step and M-Step by adopting an EM algorithm, and completing joint optimization of trajectory estimation and imaging results. Aiming at the problems that a traditional method depends on accurate phase information and a target motion model needs to be preset, the method effectively overcomes the problem of phase misalignment caused by Doppler frequency shift, realizes parameter adaptive adjustment, still shows high robustness in a low signal-to-noise ratio and a nonlinear motion scene, does not need to preset the motion model, and is high in robustness. The imaging quality is ensured, the flexibility of non-cooperative target imaging is enhanced, and a new solution is provided for ISAR imaging in a complex dynamic scene.

Description

Technical Field

[0001] The present invention relates to the field of radar imaging technology, and in particular to an ISAR imaging method and system for maneuvering targets based on an EM algorithm. Background Art

[0002] Accurately measuring amplitude and phase is crucial for obtaining high-quality ISAR images. For slow and relatively stable targets, the classic Range Doppler (RD) algorithm, by constructing a "stop-go" fast-time-slow-time joint processing model, effectively achieves two-dimensional focusing of scattering points, thereby obtaining ISAR images that meet resolution requirements.

[0003] As a classic ISAR imaging method, the RD algorithm mainly includes three key steps: first, the received radar echo is pulse compressed to form a high-resolution one-dimensional range image; then, the range image sequence is motion compensated for the range offset and phase error caused by target motion; on this basis, the azimuth signal in each range unit is processed by FFT to extract the Doppler information, and finally the two-dimensional ISAR image is reconstructed.

[0004] In practical applications, ISAR targets often have complex motion characteristics such as high-speed maneuvers, rotations, or nonlinear trajectories. This causes the energy of the target scattering points to spread across different distance units, causing the echo envelope to fluctuate dramatically. At the same time, the Doppler frequency corresponding to each scattering point is time-varying, making it difficult to accurately estimate the phase information, which in turn leads to imaging blur and defocus problems in traditional RD algorithms. In this case, the limitations of phase information in traditional methods make high-resolution imaging more complex and difficult. Therefore, for complex moving targets, this patent proposes an algorithm for ISAR imaging that does not rely on precise phase information but only uses envelope information.

[0005] ISAR imaging is widely used in non-cooperative target monitoring, remote sensing, and battlefield situational awareness. However, when imaging complex moving targets, phase information is difficult to accurately obtain, resulting in limitations in traditional Fourier transform-based range-Doppler algorithms when dealing with rotating, translational, and nonlinear targets. Existing methods often assume a known target trajectory or use simplified linear motion models, but such assumptions are difficult to meet in practical applications. In particular, the motion state of non-cooperative targets often exhibits significant uncertainty, posing a greater challenge to traditional ISAR imaging methods.

[0006] Therefore, a method that can achieve high-quality ISAR imaging is needed. Summary of the Invention

[0007] In view of this, an object of the present invention is to provide a maneuvering target ISAR imaging method and system based on an EM algorithm. The method is a phase-free ISAR imaging algorithm based on expectation-maximization (EM).

[0008] Inverse synthetic aperture radar imaging in radar imaging technology

[0009] In order to achieve the above object, the present invention provides the following technical solutions:

[0010] The present invention provides an ISAR imaging method for maneuvering targets based on an EM algorithm, comprising the following steps:

[0011] S1. Perform range compression processing on the maneuvering target echo signal received by the radar to obtain a time-varying amplitude envelope matrix;

[0012] S2. Constructing a dynamic Bayesian observation model, the model includes an observation matrix, a latent variable matrix and a scattering coefficient matrix, wherein the latent variable matrix represents the target motion parameters;

[0013] S3. Iterate and optimize using the EM algorithm, alternating the following operations until convergence:

[0014] E-Step: Estimate the posterior probability distribution of latent variables based on the current scattering coefficient matrix;

[0015] M-Step: Maximize the expected log-likelihood function and update the scattering coefficient matrix.

[0016] S4. Output the target ISAR image according to the converged scattering coefficient matrix.

[0017] Furthermore, the latent variable matrix in step S2 obeys a first-order Markov chain model, and its transition probability satisfies:

[0018]

[0019] Among them, p(Θ|Φ) represents the transition probability; p(Θ1|Φ) represents the prior distribution of the latent variable at the initial moment; p(Θ m |Θ m―1 ,Φ) represents the state Θ at the known last moment m―1 and the current scattering coefficient matrix Φ Θ m The transition probability.

[0020] Furthermore, the expected log-likelihood function in the E-Step of step S3 is defined as follows:

[0021]

[0022] Among them, Φ( n)is the current parameter estimate; Q(Φ,Φ( n) ) indicates that the current parameter estimate Φ( n) The expected value of the joint likelihood function p(Y,Θ|Φ) for the observed data Y.

[0023] Furthermore, in the M-Step of step S3, the expected log-likelihood function is maximized and the scattering coefficient matrix is ​​updated, specifically in the following manner:

[0024] The optimization objective of the Q function is converted to minimizing the following objective function:

[0025]

[0026] Take the derivative of the objective function and set it equal to zero:

[0027]

[0028] Finally, the optimal scattering coefficient matrix is ​​obtained:

[0029]

[0030] Among them, Φ( n+1) Represents the optimal scattering coefficient matrix obtained by the n+1th iterative update.

[0031] Furthermore, the distance compression process in step S1 is implemented by a matched filter, and the matching reference signal is the complex conjugate of the linear frequency modulation signal.

[0032] Furthermore, the time-varying amplitude envelope matrix in step S1 is obtained in the following manner:

[0033] Through matched filtering, the echo signal is compressed into the range resolution unit:

[0034]

[0035] in, Represents the convolution operation. The main lobe amplitude of the compressed signal corresponds to the scattering intensity of the target, and the noise is suppressed to the side lobe; h(t m ) represents the impulse response of the matched filter, which is the time-reversed and complex-conjugate version of the transmitted signal; s rc (t m ) represents the echo signal after range compression. The compression result is concentrated in the main lobe, reflecting the scattering intensity;

[0036] The analytical expression of the compressed signal is obtained by convolution calculation according to the following formula:

[0037]

[0038] Taking the absolute value of the compressed signal amplitude, we can get the time-varying amplitude envelope matrix, which is expressed as:

[0039]

[0040] Among them, T p represents the duration of the radar transmit pulse; B represents the radar signal bandwidth.

[0041] Furthermore, in the E-Step of step S3, a particle filter algorithm is used to approximately calculate the posterior probability distribution of the latent variable.

[0042] The present invention provides an EM algorithm-based maneuvering target ISAR imaging system, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor implements the above method when executing the program.

[0043] The beneficial effects of the present invention are:

[0044] The present invention provides a method and system for ISAR imaging of maneuvering targets based on the EM algorithm. This method constructs a dynamic observation model through a Bayesian framework to obtain a dynamic Bayesian observation model, embeds the target's time-varying motion parameters into the signal reconstruction process, and uses the time-varying amplitude envelope matrix information of the radar echo to replace the traditional phase measurement, effectively overcoming the phase misalignment problem caused by Doppler frequency shift. Through iterative optimization of the EM algorithm (alternating updates of E-step and M-step), a joint estimation of the target motion trajectory and the scattering coefficient distribution is achieved. In the E-step, the posterior probability distribution of the target position is calculated based on the current parameter estimate; in the M-step, the motion parameters and scattering point intensity are updated by maximizing the expected likelihood function. The algorithm achieves parameter adaptive adjustment by introducing latent variable modeling and loss function convergence analysis, and still exhibits high robustness in low signal-to-noise ratio and nonlinear motion scenarios. Compared with the gradient descent (GD) algorithm that relies on known trajectories, this method does not require a preset motion model, while ensuring imaging quality and enhancing the flexibility of non-cooperative target imaging, providing a new solution for ISAR imaging in complex dynamic scenes.

[0045] To address the problem that traditional methods rely on precise phase information and require a preset target motion model, this method constructs a dynamic Bayesian model based on the time-varying amplitude envelope observation, introduces the target motion state parameters as latent variables into the imaging process, and uses the EM algorithm to realize the posterior inference of latent variables and the maximum likelihood estimation of the scattering coefficient in the E-Step and M-Step respectively, completing the joint optimization of trajectory estimation and imaging results.

[0046] Different from the traditional imaging method based on phase information, this method uses the time-varying amplitude envelope information of the radar echo for motion compensation, avoiding the error caused by phase misalignment and improving the adaptability of the algorithm in non-cooperative target imaging tasks.

[0047] Compared with the traditional Fourier transform-based algorithms, the proposed method does not rely on precise phase information, but uses envelope information for motion compensation, thus achieving high-quality ISAR imaging and target trajectory.

[0048] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration.

[0050] Figure 1 Schematic diagram of the ISAR imaging algorithm based on the EM algorithm.

[0051] Figure 2 For aircraft models.

[0052] Figure 3 The aircraft trajectory.

[0053] Figure 4 is the radar amplitude envelope data.

[0054] Figure 5 This is the reconstructed ISAR image of the aircraft.

[0055] Figure 6 is the reconstructed trajectory of the aircraft. DETAILED DESCRIPTION

[0056] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0057] like Figure 1 As shown, Figure 1 FIG. 1 is a schematic diagram of an ISAR imaging algorithm based on the EM algorithm. The ISAR imaging method for a maneuvering target based on the EM algorithm provided in this embodiment includes the following steps:

[0058] S1. Perform range compression processing on the maneuvering target echo signal received by the radar to obtain a time-varying amplitude envelope matrix;

[0059] S2. Constructing a dynamic Bayesian observation model, the model includes an observation matrix, a latent variable matrix and a scattering coefficient matrix, wherein the latent variable matrix represents the target motion parameters;

[0060] S3. Iterate and optimize using the EM algorithm until convergence:

[0061] E-Step: Estimate the posterior probability distribution of latent variables based on the current scattering coefficient matrix;

[0062] M-Step: Maximize the expected log-likelihood function and update the scattering coefficient matrix;

[0063] S4. Output the target ISAR image according to the converged scattering coefficient matrix.

[0064] The ISAR imaging method for maneuvering targets based on the EM algorithm provided in this embodiment has the following specific implementation process:

[0065] The complex motion of the target can be decomposed into the synthesis of rigid body translation and rotation around the center of mass. Assume that the position of the target center of mass in the radar coordinate system is T(t m )=[t x (t m ),t y (t m ),0] T , the rotation posture of the target around the origin of its own coordinate system is described by the rotation matrix R(tm). Any scattering point P k =[x k ,y k ,z k ] T The instantaneous position in the radar coordinate system is:

[0066] P k (t m )=R(t m )p k +T(t m ) (1)

[0067] Among them, t m represents the mth moment; t x (t m ) indicates that the target is at time t m The x-direction translation position; t y (t m ) indicates that the target is at time t m The y-direction translation position of x k 、y k 、z k represents the spatial coordinates of the kth scattering point in the target body coordinate system; P k (tm ) indicates that at time t m The position of the kth scattering point in the radar coordinate system; R(t m ) indicates that the target is at time t m The rotational posture matrix (describing the posture change around the origin of the target body coordinate system) p k represents the position vector of the kth scattering point in the target body coordinate system; T(t m ) represents the translation vector of the target center of mass in the radar coordinate system.

[0068] Assuming that the target rotates around the z-axis and the instantaneous angle is θ(tm), its rotation matrix is:

[0069]

[0070] Among them, R(t m ) represents the rotation matrix; θ(tm) represents the instantaneous rotation angle of the target.

[0071] During the target motion, the scattering point P is modulated by the rotation and translation of the target. k Instantaneous distance to the radar R k (t m ) can be expressed as:

[0072]

[0073] Among them, x k 、y k 、z k represents the spatial coordinates of the kth scattering point in the target body coordinate system;

[0074] In general, the inverse synthetic aperture radar transmits a linear frequency modulation signal s tx (t), assuming that the target is composed of K isotropic scattering points, the received echo signal can be expressed as the superposition of the echo signals of each scattering point:

[0075]

[0076] Among them, A k is the amplitude of the kth scattering point; It represents the round-trip time of electromagnetic waves from the radar to the target and back; ε(t m )~N(0,σ 2 ) is Gaussian noise; K represents the total number of scattering points on the target; f c Indicates the carrier frequency of the radar signal; R k represents the distance from the kth scattering point to the radar;

[0077] Range compression is achieved through a matched filter, where the matching reference signal is the complex conjugate of the transmitted LFM signal:

[0078]

[0079] Through matched filtering, the echo signal can be compressed to the range resolution unit:

[0080]

[0081] in, Represents the convolution operation. The main lobe amplitude of the compressed signal corresponds to the scattering intensity of the target, and the noise is suppressed to the side lobe; h(t m ) represents the impulse response of the matched filter, which is the time-reversed and complex-conjugate version of the transmitted signal; s rc (t m ) represents the echo signal after range compression. The compression result is concentrated in the main lobe, reflecting the scattering intensity;

[0082] Substituting Equations (4) and (5) into the convolution calculation of Equation (6), we can obtain the analytical expression of the compressed signal:

[0083]

[0084] After range compression, the echo signal behaves as a sinc function in the range direction, with a main lobe width of 1 / B. The peak position of the sinc function corresponds to the instantaneous distance R of the scattering point. k (t m ).

[0085] Taking the absolute value of the compressed signal amplitude, we can get the time-varying amplitude envelope matrix, which is expressed as:

[0086]

[0087] Among them, T p Indicates the duration of the radar transmit pulse; B indicates the radar signal bandwidth;

[0088] The time-varying amplitude envelope matrix obtained in this embodiment has a strong anti-noise capability, and the phase noise mainly affects the phase term exp(-j4πf c R k (t m ) / c), while the amplitude envelope only depends on the superposition of sinc functions and is insensitive to phase disturbances. At the same time, the amplitude envelope has a strong ability to represent motion. When the target is moving, R k (t m ) changes with time, resulting in a time shift and amplitude fluctuation of the sinc peak. By tracking the time-varying characteristics of the envelope, the target trajectory can be indirectly inverted.

[0089] Based on the theoretical framework of Bayesian learning, the radar imaging problem is transformed into a linear equation solving problem. The time-varying motion parameters of the target are embedded in the signal reconstruction process through latent variable modeling, thereby establishing a dynamic Bayesian observation model. This model uses the time-varying amplitude envelope matrix information of the radar echo to replace the traditional phase measurement, effectively overcoming the phase misalignment problem caused by Doppler frequency shift.

[0090] Assume that the radar obtains observation data at M pulse times, each pulse contains N range units, and the ISAR observation matrix is It can be expressed as:

[0091] Y=ΦΘ+ε (9)

[0092] Where Φ is the target scattering coefficient matrix with a dimension of N×K. Each column corresponds to the scattering intensity of a distance unit, reflecting the static geometric structure of the target. Θ is the latent variable matrix with a dimension of K×M, where K represents the number of discretized scattering points of the target. Each column corresponds to the motion parameters of the target at M moments, including rotation and translation components, which can invert the motion trajectory of the target. ε is the additive noise matrix with a dimension of N×M, which is assumed to be independent and identically distributed complex Gaussian noise.

[0093] In ISAR imaging, the observed data is a variable amplitude envelope matrix after range compression. The latent variable matrix is ​​the motion parameter matrix The parameter to be estimated is the target scattering coefficient matrix

[0094] According to Bayesian theory, the joint probability density can be decomposed into:

[0095] p(Y,Θ|φ)=p(Y|Θ,φ)p(Θ|Φ) (10)

[0096] Where p(Y, Θ|Φ) is the observation likelihood function, p(Θ|Φ) is the prior distribution of the latent variable; p(Y|Θ,Φ) represents the conditional probability density function of the observation data Y under the known motion state Θ and scattering coefficient Φ, that is, the observation likelihood function;

[0097] Since the target motion parameters are time-continuous, it can be assumed that they obey the first-order Markov chain model, that is:

[0098]

[0099] Among them, p(Θ1|Φ) represents the prior distribution of latent variables at the initial moment; p(Θ m |Θ m―1 ,Φ) describes the state Θ at the known last moment m―1 and the current scattering coefficient matrix Φ, Θ mThe transition probability. p(Θ|Φ) represents the prior distribution of the latent variable (motion parameter) under a given Φ, which is usually modeled as a first-order Markov process; p(Θ1|Φ) represents the prior distribution of the latent variable at the initial moment; p(Θ m |Θ m―1 ,Φ) represents the state Θ at the known last moment m―1 and the current scattering coefficient matrix Φ Θ m The transition probability of p(Θ1) represents the unconditional prior distribution of the initial state when ignoring the influence of Φ or simplifying the model; p(Θ m |Θ m―1 ) represents the transition probability of the motion state at the mth moment given the state Θm-1 at the previous moment and the current parameter Φ, which is used to model the state evolution in the time series. m represents the time index, which represents the current pulse moment number; M represents the total number of pulses; Θ m Represents the motion state vector of the target at the mth moment;

[0100] In actual modeling, the target's motion state Θ m Mainly depends on the previous moment Θ m―1 , and has nothing to do with Φ, that is, the Markov chain satisfies the first-order Markov assumption, thereby simplifying the computational complexity.

[0101] According to the Maximum Likelihood Estimation (MLE) theory, the objective function of the ISAR imaging problem is:

[0102]

[0103] The goal of MLE is to estimate the parameter Φ by maximizing the marginal likelihood p(Y|Φ) of the observed data. However, due to the existence of latent variables Θ, directly solving the above equation requires marginalizing the latent variables. By integrating the latent variables, we can obtain:

[0104] p(Y|Φ)=∫ Θ p(Y,Θ|Φ)dΘ=∫ Θ p(Y|Θ,Φ)p(Θ|Φ)dΘ (13)

[0105] Where p(Y, Θ|Φ) is the observation likelihood function, p(Θ|Φ) is the prior distribution of the latent variable; p(Y|Θ,Φ) represents the conditional probability density function of the observation data Y under the known motion state Θ and scattering coefficient Φ, that is, the observation likelihood function;

[0106] When the dimension of the latent variable Θ is high, the complexity of the integral calculation increases exponentially.

[0107] The EM algorithm iteratively optimizes the expected log-joint likelihood Q function to avoid direct integration and thus approximate the MLE solution.

[0108] In the E-Step, the expected Q function is calculated, that is, the current parameter estimate Φ( n) Under the condition of , the expected value of the joint likelihood function p(Y, Θ|Φ) of the observed data Y; the Q function is defined as follows:

[0109]

[0110] Among them, Φ( n) is the current parameter estimate; where Φ( n) is the current parameter estimate; Q(φ,Φ( n) ) represents the expected log-joint likelihood function.

[0111] The MLE solution is iteratively approximated by alternating execution of the E-Step (calculating the expectation) and the M-Step (maximizing the Q function).

[0112] Split the log joint probability into the observation likelihood term and the latent variable prior term:

[0113] logp(Y,Θ∣Φ)=log p(Y∣Θ,Φ)+log p(Θ∣Φ) (15)

[0114] Substituting formula (15) into formula (14) and performing integral calculation, we can obtain:

[0115] Q(Φ,Φ (n) )=∫ Θ p(Θ|Y,Φ (n) )logp(Y∣Θ,Φ)dΘ+∫ Θ p(Θ|Y,Φ (n) )logp(Θ|Φ)dΘ (16)

[0116] Since the latent variable Θ consists of L independent components, each component Θ l belongs to the discrete set Ω, then the Q function can be decomposed into a summation form:

[0117]

[0118] Among them, p(Θ l ∣Y,Φ (n) ) is given the observed data Y and the current parameter estimate Φ (n) Next, the lth latent variable component Θ l The posterior probability of log p(Y|Θ l ,Φ) is given the hidden variable state Θ l The log-likelihood of the observed data Y under the parameter Φ; log p(Θ l |Φ) is the hidden variable component Θ under given parameter Φ l The logarithmic prior probability of ;

[0119] In the M-Step, maximize the expected function Q(φ,φ (n) ), update the scattering coefficient matrix φ:

[0120]

[0121] Since the form of the Q function contains the observation likelihood term and the prior term of the latent variable, it can be decomposed and solved as follows:

[0122]

[0123] Among them, the first term involves the update of the ISAR scattering coefficient matrix φ, which determines the quality of image reconstruction; the second term involves the prior distribution of the latent variable, which is used to constrain the update of the motion parameters; Ω represents the set of latent variable state spaces, that is, the set of all possible motion parameter states; L represents the number of samples used for discrete approximate integration or summation, that is, the total number of latent variable state samples; l is an index variable, which represents the position of the lth sample (hidden variable state) in Ω;

[0124] Since the prior p(Θ l |Φ) is independent of Φ, then the prior terms of the latent variables do not affect the maximization process, so the optimization objective is simplified to:

[0125]

[0126] In ISAR imaging, it is assumed that the additive noise has a mean of zero and a variance of σ 2 The independent and identically distributed complex Gaussian noise, then the likelihood function of the observed data can be expressed as:

[0127]

[0128] Taking the logarithm of formula (21), we can get:

[0129]

[0130] Therefore, after removing the constant term from Equation (22) and inserting it into Equation (20), the optimization objective of the Q function can be converted to minimizing the following objective function:

[0131]

[0132] Take the derivative of the objective function and set it equal to zero:

[0133]

[0134] Finally, the optimal scattering coefficient matrix is ​​obtained:

[0135]

[0136] Among them, Φ( n+1) represents the optimal scattering coefficient matrix obtained by the n+1th iteration update, which represents the estimation result of the target scattering structure by the EM algorithm in the current round;

[0137] At this point, the EM algorithm completes one round of iteration, continuously and alternately executing the E step and the M step, and finally converges to obtain the ISAR image of the target.

[0138] In order to verify the ISAR imaging performance of the EM algorithm, the radar system in the simulation experiment uses the millimeter-wave radar AWR2243 produced by Texas Instruments in our laboratory. The main simulation parameters of the radar system are shown in Table 1.

[0139] Table 1 Main parameters of radar system simulation

[0140]

[0141] The simulation target is the Yak-42 aircraft model, as shown in the schematic diagram. Figure 2 As shown in Figure 2, the model consists of 330 scattering points, and the target size is about 10m×10m. The target's motion includes rotation and translation around its own center of mass, and its motion trajectory is shown in Figure 2. Figure 3 shown.

[0142] During the experiment, the echo signal is composed of linear frequency modulation signal, and the amplitude envelope information is extracted by range compression processing, such as Figure 4 As shown in Figure 3, the amplitude envelope reflects the time-varying scattering characteristics of the target and is the input data for the EM algorithm.

[0143] Figure 4 This figure shows the echo signal after range compression processing. The horizontal axis represents the pulse sequence, that is, the pulse signal emitted by the radar at different times, and the vertical axis represents the range unit, that is, the distribution of different scattering points of the target in the direction of the radar's line of sight. In this figure, the envelope information depicts the target's motion trajectory at different times, and the amplitude information reflects the target's scattering characteristics. Specifically, as the target moves, the envelope drifts, indicating that the target's range position is constantly changing, while the amplitude fluctuations of the echo signal reflect the changes in the target's scattering intensity.

[0144] This patent combines envelope information and amplitude information to invert the shape and motion trajectory of the aircraft through the EM algorithm. The final imaging results and trajectory reconstruction are as follows Figure 5 、 Figure 6 shown.

[0145] Figure 5The ISAR image of the aircraft reconstructed by the EM algorithm is displayed. Through EM iterative optimization and combined with the envelope information of the echo data, the defocusing effect caused by the target motion is effectively compensated, so that the target structure can be clearly presented and the scattering characteristics of the aircraft can be better reflected. Figure 6 The figure shows the reconstructed aircraft trajectory. The black dots represent the true trajectory, the color gradient dots represent the trajectory estimated by the EM algorithm, and the light red and dark blue dots correspond to the initial and final positions of the target, respectively. The color of the dots changes over time, showing the target's motion path. As can be seen from the figure, the EM algorithm can accurately estimate the target trajectory. Although there are small deviations at certain moments, the overall trend is consistent with the true trajectory.

[0146] The EM-based ISAR imaging algorithm for maneuvering targets proposed in this embodiment addresses the issues that traditional methods rely on precise phase information and require a pre-defined target motion model. By constructing a dynamic Bayesian model based on the time-varying amplitude envelope matrix, the target motion state parameters are introduced as latent variables into the imaging process. The EM algorithm is used to implement posterior inference of the latent variables and maximum likelihood estimation of the scattering coefficient in the E-Step and M-Step, respectively, achieving joint optimization of trajectory estimation and imaging results. Compared to traditional Fourier transform-based algorithms, the EM-based ISAR imaging algorithm for maneuvering targets proposed in this method does not rely on precise phase information, but instead uses envelope information for motion compensation, thereby achieving high-quality ISAR imaging and target trajectory.

[0147] The above embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention. The scope of protection of the present invention shall be subject to the claims.

Claims

1. A maneuvering target ISAR imaging method based on the EM algorithm, characterized by: The following steps are involved: S1. Perform range compression processing on the maneuvering target echo signal received by the radar to obtain a time-varying amplitude envelope matrix; S2. Constructing a dynamic Bayesian observation model, the model includes an observation matrix, a latent variable matrix and a scattering coefficient matrix, wherein the latent variable matrix represents the target motion parameters; S3. Iterate and optimize using the EM algorithm, alternating the following operations until convergence: E-Step: Estimate the posterior probability distribution of latent variables based on the current scattering coefficient matrix; M-Step: Maximize the expected log-likelihood function and update the scattering coefficient matrix; S4. Output the target ISAR image according to the converged scattering coefficient matrix.

2. The method for ISAR imaging of maneuvering targets based on the EM algorithm according to claim 1, wherein: In step S2, the latent variable matrix obeys the first-order Markov chain model, and its transition probability satisfies: Among them, p(Θ|Φ) represents the transition probability; p(Θ1|Φ) represents the prior distribution of the latent variable at the initial moment; p(Θ m |Θ m―1 ,Φ) represents the state Θ at the known last moment m―1 and the current scattering coefficient matrix Φ Θ m The transition probability.

3. The method for ISAR imaging of maneuvering targets based on the EM algorithm according to claim 1, wherein: The expected log-likelihood function in the E-Step of step S3 is defined as follows: Q(Φ,Φ (n) )=E Θ|Y,Φ(n) [logp(Y,Θ|Φ)]=∫ Θ p(Θ∣Y,Φ (n) )log[p(Y∣Θ,Φ)·(Θ∣Φ)]dΘ; Among them, Φ( n) is the current parameter estimate; Q(Φ,Φ( n) ) indicates that the current parameter estimate Φ( n) The expected value of the joint likelihood function p(Y,Θ|Φ) for the observed data Y.

4. The method for ISAR imaging of maneuvering targets based on the EM algorithm according to claim 1, wherein: In the M-Step of step S3, the expected log-likelihood function is maximized and the scattering coefficient matrix is ​​updated, specifically in the following manner: The optimization objective of the Q function is converted to minimizing the following objective function: Take the derivative of the objective function and set it equal to zero: Finally, the optimal scattering coefficient matrix is ​​obtained: Among them, Φ( n+1) Represents the optimal scattering coefficient matrix obtained by the n+1th iterative update.

5. The method for ISAR imaging of maneuvering targets based on the EM algorithm according to claim 1, wherein: The distance compression process in step S1 is implemented by a matched filter, and the matching reference signal is the complex conjugate of the linear frequency modulation signal.

6. The method for ISAR imaging of maneuvering targets based on the EM algorithm according to claim 1, wherein: The time-varying amplitude envelope matrix in step S1 is obtained in the following manner: Through matched filtering, the echo signal is compressed into the range resolution unit: in, represents the convolution operation. The main lobe amplitude of the compressed signal corresponds to the scattering intensity of the target, and the noise is suppressed to the side lobe. m ) represents the impulse response of the matched filter, which is the time-reversed and complex-conjugate version of the transmitted signal; s rc (t m ) represents the echo signal after range compression. The compression result is concentrated in the main lobe, reflecting the scattering intensity; The analytical expression of the compressed signal is obtained by convolution calculation according to the following formula: Take the absolute value of the compressed signal amplitude to obtain the time-varying amplitude envelope matrix, which is expressed as: Among them, T p represents the duration of the radar transmit pulse; B represents the radar signal bandwidth.

7. The method for ISAR imaging of maneuvering targets based on the EM algorithm according to claim 1, wherein: In the E-Step of step S3, a particle filtering algorithm is used to calculate the posterior probability distribution of the latent variable.

8. A maneuvering target ISAR imaging system based on an EM algorithm, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

Images