Fast translation compensation two-dimensional imaging method based on ISAR (inverse synthetic aperture radar) dechirp echoes

Abstract

The invention discloses a fast translation compensation two-dimensional imaging method based on ISAR (inverse synthetic aperture radar) dechirp echoes, which comprises the following steps: performing coherence recovery on echo signals after dechirp processing to obtain preliminary recovery signals; carrying out azimuth difference on the preliminary recovery signal to obtain a two-dimensional differential phase observed quantity; based on the two-dimensional differential phase observed quantity, constructing a cost function taking coherent energy maximization as a target, and estimating a translation parameter of the target by adopting a gradient optimization algorithm to obtain an estimated translation parameter; constructing a compensation item based on the estimated translation parameter, and performing translation compensation on the preliminary recovery signal to obtain a signal after translation compensation; and azimuth random phase disturbance compensation is carried out on the signal after translation compensation, a signal after phase disturbance compensation is obtained, and an ISAR image of the target is obtained based on the signal after phase disturbance compensation. According to the method, stable estimation of the translation parameters can be kept under the condition of low signal-to-noise ratio, so that the accuracy of ISAR imaging is ensured.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a fast translational compensation two-dimensional imaging method based on ISAR deslant echo. Background Technology

[0002] Inverse Synthetic Aperture Radar (ISAR) imaging technology achieves high-resolution two-dimensional imaging of space targets by performing high-resolution range-direction and coherent azimuth-direction accumulation. In practical applications, the radial translation of the target relative to the radar introduces additional phase terms. If not accurately compensated, this will lead to azimuth coherence corruption, resulting in image defocusing and reduced resolution. Therefore, accurate estimation and effective compensation of translational parameters are key technical aspects of ISAR imaging. Currently, to reduce sampling rate and processing complexity, dechirp processing is often used for pulse compression. However, this process introduces reference range errors and slow-time random phase perturbations, resulting in impaired echo signal coherence, which in turn affects subsequent parameter estimation and imaging quality.

[0003] Existing translational compensation methods mainly fall into two categories: non-parametric methods and parametric methods. Non-parametric methods, such as envelope alignment and phase gradient autofocus (PGA), rely on the coherence between adjacent pulses and a high signal-to-noise ratio (SNR). Their performance degrades significantly under low SNR or with residual de-skew errors. Parametric methods, such as minimum entropy and contrast optimization, can utilize full aperture information, but they typically require multi-dimensional searches or repeated reconstructions, resulting in high computational complexity and difficulty in meeting real-time imaging requirements. Furthermore, traditional one-dimensional phase acceleration methods utilize only single-dimensional phase information and do not fully consider the influence of two-dimensional phase structure and residual de-skew perturbations. Their estimation accuracy is limited under large accumulation angles and strong noise conditions, and they often require phase de-blurring operations, which can easily introduce error propagation and numerical instability problems.

[0004] Therefore, improving the accuracy and robustness of ISAR imaging under conditions of incomplete deskewing error correction, low signal-to-noise ratio, and large accumulation angle remains a technical challenge that needs to be addressed. Summary of the Invention

[0005] To address the challenge of improving the accuracy and robustness of ISAR imaging under conditions of incomplete deslant error correction, low signal-to-noise ratio, and large accumulation angle, this invention provides a fast translational compensation two-dimensional imaging method based on ISAR deslant echoes. The technical problem solved by this invention is achieved through the following technical solution: This invention provides a fast translational compensation two-dimensional imaging method based on ISAR deslant echoes, comprising: The echo signal after deskewing is coherently recovered to obtain a preliminary recovered signal; The preliminary recovered signal is subjected to azimuth differential to obtain two-dimensional differential phase observations; Based on two-dimensional differential phase observations, a cost function with the objective of maximizing coherent energy is constructed, and a gradient optimization algorithm is used to estimate the translational parameters of the objective to obtain the estimated translational parameters. Based on the estimated translational parameters, a compensation term is constructed, and translational compensation is performed on the preliminary recovered signal to obtain the translationally compensated signal. The translationally compensated signal is subjected to azimuth random phase perturbation compensation to obtain the phase perturbation compensated signal, and the ISAR image of the target is obtained based on the phase perturbation compensated signal.

[0006] In one embodiment of the present invention, coherence recovery is performed on the echo signal after deskewing to obtain a preliminary recovered signal, including: Based on the reference distance sequence, construct a deskewing coherent recovery reference term; By using the deskewed coherent recovery reference term, the phase of each pulse in the deskewed echo signal is recovered, restoring the phase of all pulses to a uniform reference distance to obtain a preliminary recovered signal.

[0007] In one embodiment of the present invention, azimuth differential is performed on the preliminary recovered signal to obtain a two-dimensional differential phase observation, including: The adjacent pulses of the preliminary recovered signal are conjugately multiplied to obtain the azimuth differential signal, and the phase of the azimuth differential signal is determined as a two-dimensional differential phase observation.

[0008] In one embodiment of the present invention, the translational parameters include radial velocity and radial acceleration; The expression for the cost function is:

[0009] in, For phase residual function, Let the initial radial velocity of the target be to be estimated. The radial acceleration of the target to be estimated is... To observe the differential phase, For range-resolved cell index, For azimuth pulse index, The pulse repetition interval, This is the range-direction frequency value. It is the speed of light.

[0010] In one embodiment of the present invention, the gradient optimization algorithm is the Gauss-Newton-Lewinberg-Marquardt algorithm; The gradient optimization algorithm is used to estimate the translational parameters of the target, and the estimated translational parameters include: S3.1: Based on the reference ranging sequence of multiple targets acquired by radar, a coarse velocity measurement sequence is obtained; S3.2: Perform least-squares linear fitting on the coarse velocity measurement sequence to obtain the initial values ​​of the translation parameters, and use the initial values ​​of the translation parameters as the current translation parameters; S3.3: Based on the cost function, calculate the first cost function value, gradient vector, and Hessian matrix under the current translational parameters; S3.4: Calculate the update step size of the translational parameters based on the Levenberg–Marquardt algorithm, the current damping coefficient, the gradient vector, and the Hessian matrix; S3.5: Based on the update step size and the current translation parameters, obtain the updated translation parameters; S3.6: Determine if the termination condition is met. If the termination condition is met, use the updated translational parameter as the estimated translational parameter; otherwise, based on the cost function, the updated translational parameter, and the value of the first cost function, update the current damping coefficient, use the updated translational parameter as the new current translational parameter, and return to S3.3 to continue iterating. The termination conditions include the update step size being less than the step size threshold, or the maximum number of iterations being reached.

[0011] In one embodiment of the present invention, the update step size of the translational parameters is calculated based on the Levenberg-Marquardt algorithm, the current damping coefficient, the gradient vector, and the Hessian matrix, including: Based on the Levenberg–Marquardt algorithm, the Hessian matrix, and the current damping coefficient, the corrected Hessian matrix is ​​obtained. The update step size is calculated based on the corrected Hessian matrix and gradient vector.

[0012] In one embodiment of the present invention, updating the current damping coefficient based on the cost function, the updated translational parameters, and the first cost function value includes: Based on the cost function, calculate the value of the second cost function under the updated translational parameters; Compare the second cost function value with the first cost function value; When the value of the second cost function is less than the value of the first cost function, an updated damping coefficient is obtained based on the current damping coefficient and the preset damping coefficient increase factor. When the value of the second cost function is greater than the value of the first cost function, an updated damping coefficient is obtained based on the current damping coefficient and the preset damping coefficient reduction factor.

[0013] In one embodiment of the present invention, the expression for the compensation term is:

[0014] in, It is a complex exponential function. The center carrier frequency of the radar echo signal. For range-resolved cell index, For azimuth pulse index, This represents the frequency difference along the range. The pulse repetition interval, For the estimated initial radial velocity of the target, For the estimated target radial acceleration, The speed of light; The expression for the signal after translational compensation is:

[0015] in, The signal is after translational compensation. To multiply point by point, The signal has been initially restored.

[0016] In one embodiment of the present invention, azimuth random phase perturbation compensation is performed on the translationally compensated signal to obtain a phase-perturbation compensated signal, and an ISAR image of the target is obtained based on the phase-perturbation compensated signal, including: S5.1: Transform the translationally compensated signal to the image domain to obtain the current ISAR image, and calculate the first image entropy of the current ISAR image; S5.2: Based on the current ISAR image, construct an azimuth phase perturbation compensation term along the direction of image entropy gradient descent, and perform azimuth random phase perturbation compensation on the translationally compensated signal in the echo data domain based on the azimuth phase perturbation compensation term to obtain the phase perturbation compensated signal. S5.3: Transform the phase perturbation compensated signal to the image domain to obtain the updated ISAR image, and calculate the second image entropy of the updated ISAR image; S5.4: Calculate the entropy difference between the first image entropy and the second image entropy. If the entropy difference is less than the preset tolerance or the maximum number of iterations is reached, the updated ISAR image is output as the target's ISAR image. Otherwise, the signal after phase perturbation compensation is used as the new signal after translational compensation, and the process returns to S5.1 to continue iterating.

[0017] In one embodiment of the present invention, the expression for the azimuth phase perturbation compensation term is:

[0018]

[0019] in, For the first The azimuth random phase compensation term for each pulse. It is a complex exponential function. For the estimated random phase error, For azimuth pulse index, For range-resolved cell index, for The complex conjugate, For the first The complex weighted vector corresponding to each pulse. For azimuth frequency index, This is a two-dimensional ISAR image after perturbation compensation. for The complex conjugate, This is a one-dimensional high-resolution distance image after translational compensation; The expression for the signal after phase disturbance compensation is:

[0020] in, This is the signal after phase disturbance compensation. The signal is after translational compensation. This involves multiplying each point individually.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) Compared with the peak detection of traditional PDVM based on only one-dimensional phase difference, the method provided by this invention performs global optimization in the two-dimensional phase domain, enhances the signal characteristics by utilizing the phase coherence relationship, and significantly reduces the impact of noise interference and cross phase error. Therefore, it can still maintain stable estimation under low signal-to-noise ratio conditions, ensuring the accuracy of ISAR imaging.

[0022] (2) Traditional phase estimation accelerometers may produce deviations due to the failure of the phase approximation assumption under large-angle rotation conditions. The method provided by this invention effectively expands the applicability of the model under large-angle observation through two-dimensional phase perturbation compensation and energy consistency optimization, that is, it is compatible with larger rotation accumulation angles and improves the focusing clarity of the image.

[0023] (3) The gradient and Hessian matrix based on matrix operation of the present invention can be solved in parallel on the GPU. The computational complexity is significantly lower than that of traditional search-type optimization algorithms, which meets the dual requirements of speed and accuracy of real-time ISAR imaging system.

[0024] (4) Since the constructed cost function directly performs coherent energy summation in the complex exponential domain, it naturally possesses The periodicity eliminates the need for additional phase unrolling or fuzz correction steps, avoiding the accumulation of errors and numerical instability introduced during the unfuzzing process, thus making the model convergence more robust.

[0025] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0026] Figure 1 A flowchart of a fast translational compensation two-dimensional imaging method based on ISAR deslant echo provided in an embodiment of the present invention; Figure 2 A schematic diagram of a scattering point target observation model used in a simulation experiment provided in this embodiment of the invention; Figure 3 A schematic diagram showing the comparison between the simulated actual velocity of a target and the estimated velocity of a target, provided for an embodiment of the present invention; Figure 4 This invention provides an embodiment of a method for... Figure 2 The ISAR image obtained after compensating for the echo signal of the target.

[0027] Figure 5 This is a schematic diagram illustrating the verification results of a simulated compensation imaging method for randomly generated scattering center symmetrically distributed point targets provided in an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the verification results of a simulated compensation imaging method for a point target with an asymmetric distribution of randomly generated scattering centers, provided in an embodiment of the present invention. Detailed Implementation

[0028] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following describes in detail a fast translational compensation two-dimensional imaging method based on ISAR deslant echo proposed according to the present invention, in conjunction with the accompanying drawings and specific embodiments.

[0029] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0030] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element.

[0031] This invention addresses the challenge of improving the accuracy and robustness of ISAR imaging under conditions of incomplete deslant error correction, low signal-to-noise ratio, and large accumulation angle. It proposes a fast translational compensation two-dimensional imaging method based on ISAR deslant echoes. Please refer to [link to relevant documentation]. Figure 1 The method includes the following steps: Step 1: Perform coherence recovery on the echo signal after deskewing to obtain a preliminary recovered signal.

[0032] It should be noted that after receiving the target echo signal, the radar data processing system first reduces the signal sampling rate through dechirp processing to achieve pulse compression, then performs residual video phase (RVP) compensation, and finally outputs a discretized range image sequence echo signal, which serves as the initial echo signal input to this method, i.e., the echo signal after dechirp processing. Specifically, the expression for this echo signal is:

[0033] in, For range-resolved cell index, For azimuth pulse index, It is a complex exponential function. The center carrier frequency of the radar echo signal. This represents the frequency difference along the range. For the first The radial distance from the target spin center to the radar at each pulse moment. For the first The reference distance selected during Decirp processing at each pulse moment. For the first The scattering point at the th in the th ... The instantaneous slant range from the radar at each pulse moment. The total number of effective scattering points on the target. For scattering point index, For the first The scattering point at the th in the th ... The complex scattering intensity at each pulse moment, It is the speed of light.

[0034] Furthermore, the echo signal after deskewing processing... Coherence recovery is performed to obtain a preliminary recovered signal, including: constructing a de-skewed coherent recovery reference term based on the reference distance sequence, and using the de-skewed coherent recovery reference term to compensate the phase of each pulse in the de-skewed echo signal, restoring the phase of all pulses to a unified reference distance to obtain a preliminary recovered signal.

[0035] Specifically, the reference range sequence recorded by the radar system is as follows:

[0036] To eliminate the phase difference introduced by using different reference distances for each pulse, embodiments of the present invention restore the phase of all pulses to a uniform reference distance. This refers to the first reference distance in the reference distance sequence. Based on this, a de-skewed coherent recovery reference term is constructed. Phase compensation is then performed on each pulse echo signal to restore the phase of all pulses to a unified reference distance. This is to achieve preliminary coherence recovery and obtain preliminary recovery signals.

[0037] Specifically, the expression for recovering the reference term from the deskewed coherence is:

[0038] It should be noted that due to biases in the reference distance estimation and slow-time random perturbations during signal propagation, a small amount of phase error will remain. Therefore, the expression for the preliminary signal recovery is:

[0039] in, This is a random phase error sequence in the azimuth direction. , For the first pulse moment ~ the second pulse moment Random phase error at each pulse moment.

[0040] Step 2: Perform azimuth differential on the preliminary recovered signal to obtain two-dimensional differential phase observations.

[0041] Specifically, after receiving initial recovery signals After that, the initial recovery signal can be... The adjacent pulses are conjugately multiplied to obtain the azimuth differential signal, and then the phase of the azimuth differential signal is determined as a two-dimensional differential phase observation.

[0042] Specifically, the expression for the azimuth differential signal is:

[0043] in, To obtain the complex conjugate operation, The radial displacement of the target reference point (e.g., the centroid) within the time interval between adjacent pulses. For the first The scattering point and the th scattering point The difference in relative distance between the scattering points.

[0044] The expression for the two-dimensional differential phase observation is:

[0045] in, This is a phase-taking operation.

[0046] Step 3: Based on the two-dimensional differential phase observation, construct a cost function with the goal of maximizing coherent energy, and use a gradient optimization algorithm to estimate the translational parameters of the target to obtain the estimated translational parameters.

[0047] In this embodiment of the invention, the translational parameters include radial velocity and radial acceleration.

[0048] Specifically, based on two-dimensional differential phase observations, the expression for the cost function is as follows:

[0049]

[0050]

[0051] in, This is the phase residual function (the difference between the observed echo phase and the estimated fitted phase residual). Let the initial radial velocity of the target be to be estimated. The radial acceleration of the target to be estimated is... To observe the differential phase, The pulse repetition interval, This is the range-direction frequency value. For phase angle taking operation, This is a complex conjugate operation.

[0052] Optionally, while maintaining the principle of "maximizing coherent energy", the cost function can be extended to a weighted function. form:

[0053] It should be noted that the method provided by this invention is not only applicable to single-base ISAR systems, but can also be extended to multi-base, multi-channel, and distributed ISAR systems. For multiple receiver arrays, a channel coupling term can be added to the cost function:

[0054] in, For channel indexing.

[0055] Optionally, if the radar system has a higher modeling requirement for Decirp residual phase perturbations, the random perturbation term can be... Introduced into the expression of the phase residual function Furthermore, robust compensation is achieved through regularization terms or prior probability model constraints. This alternative form can further improve noise resistance and phase stability while ensuring the convergence of the algorithm. Optionally, the gradient optimization algorithm can be any one of the Gauss-Newton-Levenberg-Marquardt algorithm, trust region Newton algorithm, quasi-Newton algorithm, conjugate gradient algorithm, or Adam adaptive learning rate optimization algorithm, and the embodiments of the present invention are not limited thereto.

[0056] For example, taking the Gauss-Newton-Levonburg-Marquardt algorithm as a gradient optimization algorithm, the specific implementation process of obtaining the estimated translational parameters is described in detail in the following 6 steps.

[0057] S3.1: Based on the reference ranging sequence of multiple targets acquired by radar, a coarse velocity measurement sequence is obtained.

[0058] Specifically, the reference ranging sequence used by the radar system for each deslant processing step is as follows:

[0059] Furthermore, the coarse velocity sequence is obtained by subtracting two adjacent distance measurements as follows:

[0060]

[0061] in, The instantaneous radial velocities are estimated from the reference distances of two adjacent pulses, respectively. For the first The and the first The instantaneous radial velocity is estimated from the reference distance of each pulse.

[0062] S3.2: Perform least-squares linear fitting on the coarse velocity measurement sequence to obtain the initial values ​​of the translation parameters, and use the initial values ​​of the translation parameters as the current translation parameters.

[0063] It should be noted that, in order to suppress ranging jitter, the coarse velocity measurement sequence can be adjusted. A smoothing filter is performed to provide initial values ​​for subsequent fine motion parameter searches, i.e., initial values ​​for translational parameters. Using a second-order motion model Fit the velocity sequence, let:

[0064]

[0065] The least squares solution is

[0066] in, For the observation matrix, This is the observation vector.

[0067] Understandably, before executing S3.3, the parameters of the gradient optimization algorithm are initialized, including the initial damping coefficient ( Damping coefficient scaling factor (damping coefficient scaling factor) Damping coefficient reduction factor Step size threshold ( ), maximum number of iterations ( ), number of iterations .

[0068] S3.3: Calculate the current translational parameters based on the cost function. The first cost function value and gradient vector are given below. Hessian matrix .

[0069] Specifically, the current translational parameters are calculated based on the cost function. The first cost function value :

[0070] Next, we will introduce how to calculate the current translational parameters based on the cost function. The gradient vector below Hessian matrix The specific process; As can be seen from the above embodiments:

[0071]

[0072] In this embodiment of the invention, Treated as a constant, relative to constant.

[0073] Then, define the direction bit. The sum of the exponents at each pulse moment is:

[0074] Based on this exponent, the cost function can be simplified as follows:

[0075] Furthermore, regarding general parameters Differentiate: For cost function Regarding any parameter Find the partial derivative:

[0076] Depend on

[0077] We can obtain,

[0078] Define an intermediate variable:

[0079] Therefore, we can conclude that: Bring it back to the above-mentioned place. From the formula for partial derivatives, we can obtain

[0080] Furthermore, it can be obtained and bring it in Definition:

[0081] Furthermore, for the sake of simplicity in the following, it can be defined as follows:

[0082] Therefore, we can conclude that: Bring it in From the formula, we can obtain .

[0083] Then, using the identity

[0084] Obtain the cost function radial initial velocity First-order partial derivatives .

[0085] Similarly, calculation

[0086] Will Let it be denoted as azimuth basis function

[0087] We can obtain:

[0088] Similarly, there are

[0089] Further, definition ,then Bring it in From the formula, the cost function can be obtained. radial acceleration First-order partial derivatives .

[0090] That is, the current translational parameters The gradient vector below .

[0091] Furthermore, in an embodiment of the present invention, the current translational parameters The expression for the Hessian matrix is ​​as follows:

[0092] in, , , All are defined as the first The intermediate cumulants related to the Hessian matrix of each pulse. Specifically, .

[0093] S3.4: Calculate the update step size of the translational parameters based on the Levenberg–Marquardt algorithm, the current damping coefficient, the gradient vector, and the Hessian matrix.

[0094] Specifically, in embodiments of the present invention, the update step size of the translational parameters is calculated based on the Levenberg-Marquardt algorithm, the current damping coefficient, the gradient vector, and the Hessian matrix, including: Based on the Levenberg–Marquardt algorithm, the Hessian matrix, and the current damping coefficient, the corrected Hessian matrix is ​​obtained, and the update step size is calculated based on the corrected Hessian matrix and the gradient vector.

[0095] Specifically, the expression for calculating the corrected Hessian matrix is:

[0096] in, It is an identity matrix.

[0097] Furthermore, the expression for calculating the update step size is:

[0098] in, .

[0099] S3.5: Based on the update step size and the current translation parameters, obtain the updated translation parameters.

[0100] Specifically, let The updated translational parameters are: .

[0101] S3.6: Determine if the termination condition is met. If the termination condition is met, use the updated translational parameters as the estimated translational parameters. Otherwise, based on the cost function, the updated translational parameters, and the value of the first cost function, update the current damping coefficient, use the updated translational parameters as the new current translational parameters, and return to S3.3 to continue iterating.

[0102] The termination conditions include updating the step size. Less than step size threshold or reaching the maximum number of iterations. .

[0103] In an embodiment of the present invention, updating the current damping coefficient based on the cost function, the updated translational parameters, and the first cost function value includes: calculating a second cost function value under the updated translational parameters based on the cost function; comparing the second cost function value with the first cost function value; when the second cost function value is less than the first cost function value, obtaining an updated damping coefficient based on the current damping coefficient and a preset damping coefficient increase factor; when the second cost function value is greater than the first cost function value, obtaining an updated damping coefficient based on the current damping coefficient and a preset damping coefficient decrease factor.

[0104] It is understood that the method for calculating the second cost function value is the same as that for calculating the first cost function value, and will not be repeated here.

[0105] Specifically, when the value of the second cost function is less than the value of the first cost function, the damping coefficient decreases, and the updated damping coefficient is... When the value of the second cost function is greater than the value of the first cost function, the damping coefficient increases, and the updated damping coefficient is... .

[0106] Step 4: Construct a compensation term based on the estimated translational parameters, perform translational compensation on the preliminary recovered signal, and obtain the translationally compensated signal.

[0107] Specifically, the expression for the compensation term is:

[0108] in, It is a complex exponential function. The center carrier frequency of the radar echo signal. This represents the frequency difference along the range. For the estimated initial radial velocity of the target, This represents the estimated target radial acceleration.

[0109] The expression for the signal after translational compensation is:

[0110] in, The signal is after translational compensation. This involves multiplying each point individually.

[0111] Step 5: Perform azimuth random phase perturbation compensation on the translational compensated signal to obtain the phase perturbation compensated signal, and obtain the ISAR image of the target based on the phase perturbation compensated signal.

[0112] Specifically, S5.1: Transform the translationally compensated signal to the image domain to obtain the current ISAR image, and calculate the first image entropy of the current ISAR image.

[0113] In this embodiment of the invention, a one-dimensional high-resolution distance image after translational compensation is calculated based on the translationally compensated signal. .

[0114]

[0115] in, This is the transformed range-resolved cell index.

[0116] Furthermore, in one-dimensional high-resolution distance images Based on this, an inverse Fourier transform in the azimuth direction (slow time dimension) is performed to obtain a translationally compensated two-dimensional ISAR image. This refers to the current ISAR image.

[0117]

[0118] S5.2: Based on the current ISAR image, construct an azimuth phase perturbation compensation term along the direction of image entropy gradient descent, and perform azimuth random phase perturbation compensation on the translationally compensated signal in the echo data domain based on the azimuth phase perturbation compensation term to obtain the perturbation-compensated signal.

[0119] The expression for the azimuth phase disturbance compensation term is as follows:

[0120]

[0121] in, For the first The azimuth random phase compensation term for each pulse. For the estimated random phase error, for The complex conjugate, For the first The complex weighted vector corresponding to each pulse. For azimuth frequency index, for .

[0122] Finally, the expression for the disturbance-compensated signal is obtained as follows:

[0123] in, This is the signal after disturbance compensation.

[0124] S5.3: Transform the perturbation-compensated signal to the image domain to obtain the updated ISAR image, and calculate the second image entropy of the updated ISAR image.

[0125] S5.4: Calculate the entropy difference between the first image entropy and the second image entropy. If the entropy difference is less than the preset tolerance or the maximum number of iterations is reached, the updated ISAR image is output as the target's ISAR image. Otherwise, the perturbation-compensated signal is used as the new translation-compensated signal, and the process returns to S5.1 to continue iterating until the image entropy value converges or the maximum number of iterations is reached.

[0126] In summary, compared with the peak detection of traditional PDVM based only on one-dimensional phase difference, the method provided by this invention performs global optimization in the two-dimensional phase domain, enhances signal characteristics by utilizing phase coherence relationship, significantly reduces the impact of noise interference and cross-phase error, and can still maintain stable estimation under low signal-to-noise ratio conditions, thus ensuring the accuracy of ISAR imaging.

[0127] In addition, traditional phase estimation velocities can produce deviations under large-angle rotation conditions due to the failure of the phase approximation assumption. The method provided by this invention effectively expands the applicability of the model under large-angle observations through two-dimensional phase perturbation compensation and energy consistency optimization, that is, it is compatible with larger rotation accumulation angles and improves the focusing clarity of the image.

[0128] In addition, the gradient and Hessian matrix based on matrix operations in this invention can be solved in parallel on a GPU, with computational complexity significantly lower than traditional search-based optimization algorithms, thus meeting the dual requirements of speed and accuracy for real-time ISAR imaging systems.

[0129] Finally, since the constructed cost function directly performs coherent energy summation in the complex exponential domain, it naturally possesses... Periodicity eliminates the need for additional phase unrolling or fuzz correction steps, avoiding error accumulation and numerical instability introduced during the unambiguation process, resulting in more robust convergence.

[0130] To verify the effectiveness of the method provided in the embodiments of the present invention, a simulation experiment is conducted below.

[0131] Specifically, a simulation scenario for ground-based ISAR observation of space targets is set up, and the observed space targets are such as... Figure 2 As shown in Table 1, the simulation scene parameter settings are as follows: Table 1

[0132] This table sets the motion parameters of the observed targets and the signal parameters of the electromagnetic waves emitted by ISAR in the simulation scenario. ISAR echoes for all point targets are generated using these simulation parameters.

[0133] In general, the second-order translational parameters Sufficient to describe the radial motion of a space target, the target's radial motion along the radar line of sight can be set as uniformly accelerated linear motion with an initial velocity of 1000 m / s and an acceleration of 50 m / s², with an initial distance of 300 km from the radar. The simulation parameters of the radar signal are shown in the table above. Experiment 1 uses a MiG-25 scattering point model as the observation target, generates an electromagnetic simulation radar echo signal, and adds 0 dB of background noise and a random phase between [-pi, pi] in the azimuth direction.

[0134] The translational parameters are estimated using the method provided in this embodiment of the invention. The estimated motion parameters are as follows: , The root mean square error of the velocity sequence within the entire coherent accumulation interval is 0.25126 m / s. This meets the accuracy requirements for envelope alignment, and the computation time is 0.012548 s under a CPU 12400f and Matlab version 2022 environment, significantly reducing the time required for motion parameter search. Subsequently, the two-dimensional imaging results are applied to compensate for the azimuth random phase error of the phase gradient, achieving fast coherent high-resolution two-dimensional imaging.

[0135] The root mean square error of speed measurement is defined as follows:

[0136] in, It is a sequence of real translational velocities set up in the simulation experiment. This is a sequence of translational velocities estimated by the method provided in the embodiments of the present invention. It is the number of radar observations of the target within the coherent accumulation interval.

[0137] For example, such as Figure 3 As shown, Figure 3 This diagram illustrates a comparison between the simulated actual velocity and the estimated velocity of a target, provided as an embodiment of the present invention. The solid blue line represents the actual velocity of the target, and the dashed red line represents the estimated velocity. Figure 3As can be seen, the blue solid line and the red dashed line are very similar. Therefore, it can be concluded that the error between the translational parameters estimated by the method provided in this embodiment and the true translational parameters of the target is small. Thus, the higher the accuracy of translational compensation of the signal based on the estimated translational parameters, the higher the quality of the final ISAR image of the target. For example, see... Figure 4 , Figure 4 This invention provides an embodiment of a method for... Figure 2 The ISAR image obtained after compensating for the echo signal of the target.

[0138] To verify the robustness of the proposed method, repeated randomized experiments were conducted. The experiments randomly generated targets (both symmetrical and asymmetrical) with 30-40 scattering points within a width range of -30m to 30m and a height range of -30m to 30m. Target observation and echo translational compensation two-dimensional imaging were performed using the same signal simulation parameters as in Table 1. The results verifying the robustness of the proposed method are as follows: Figure 5 and Figure 6 As shown. Among them, Figure 5 This is a schematic diagram illustrating the verification results of a simulated compensation imaging method for randomly generated scattering center symmetrically distributed point targets, provided in an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the verification results of a simulated compensation imaging method for a point target with an asymmetric distribution of randomly generated scattering centers, provided in an embodiment of the present invention. Figure 5 and Figure 6 The first image in the series represents randomly generated symmetrical and asymmetrical scattering point targets, respectively. The middle image is a schematic diagram of the fitness surface of the cost function constructed in this invention in the corresponding translational parameter space. The last image is a two-dimensional ISAR image obtained using the compensation imaging method of this invention. Figure 5 It can be seen that, even under conditions of symmetrical target structure and significant interference from strong scattering points, the method of this invention can still accurately estimate motion parameters, the cost function surface exhibits obvious single-peak convexity, and the final imaging result shows good focusing with clearly identifiable scattering point positions; Figure 6 It can be seen that even in scenarios with asymmetrical target structures and uneven spatial distribution of scattering points, the method of this invention still exhibits stable parameter estimation capabilities and good imaging focusing effects. Figure 5 and Figure 6 It can be seen that the method of the present invention is not sensitive to whether the target scattering structure is symmetrical or whether the scattering point distribution is uniform. It can achieve high-precision motion parameter estimation and clear ISAR imaging under randomly generated target morphology, which demonstrates the strong adaptability and robustness of the method proposed in this invention.

[0139] Another embodiment of the present invention provides a storage medium storing a computer program for executing the steps of the fast translational compensation two-dimensional imaging method based on ISAR deslant echo described in the above embodiments.

[0140] Another aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the fast translational compensation two-dimensional imaging method based on ISAR deslant echo as described in the above embodiments.

[0141] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A fast translational motion compensation two-dimensional imaging method based on ISAR despread echo, characterized in that, The method comprises the following steps: coherence recovery is performed on the echo signal after desquaring to obtain a preliminary recovery signal; azimuth difference is performed on the preliminary recovery signal to obtain a two-dimensional differential phase observation; a cost function is constructed based on the two-dimensional differential phase observation, and a gradient optimization algorithm is used to estimate the translational parameters of the target to obtain estimated translational parameters; a compensation term is constructed based on the estimated translational parameters, and translational compensation is performed on the preliminary recovery signal to obtain a translational compensation signal; azimuth random phase perturbation compensation is performed on the translational compensation signal to obtain a phase perturbation compensation signal, and an ISAR image of the target is obtained based on the phase perturbation compensation signal.

2. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 1, characterized in that, The coherence recovery is performed on the echo signal after desquaring to obtain a preliminary recovery signal, which comprises the following steps: a desquaring coherence recovery reference term is constructed based on a reference distance sequence; the phases of each pulse in the echo signal after desquaring are recovered to a unified reference distance by using the desquaring coherence recovery reference term to obtain the preliminary recovery signal.

3. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 1, characterized in that, The azimuth difference is performed on the preliminary recovery signal to obtain a two-dimensional differential phase observation, which comprises the following steps: conjugate multiplication is performed on adjacent pulses of the preliminary recovery signal to obtain an azimuth difference signal, and the phase of the azimuth difference signal is determined as the two-dimensional differential phase observation.

4. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 1, characterized in that, The translational parameters comprise radial velocity and radial acceleration; The expression of the cost function is: wherein, is a phase residual function, is a target radial initial velocity to be estimated, is a target radial acceleration to be estimated, is an observed differential phase, is a range bin index, is an azimuth bin index, is a pulse repetition interval, is a range bin frequency value, is a speed of light.

5. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 4, characterized in that, The gradient optimization algorithm is a Gauss-Newton-Levenberg-Marquardt algorithm; The gradient optimization algorithm is used to estimate the translational parameters of the target to obtain estimated translational parameters, which comprises the following steps: S3.1: a reference distance sequence of the target is obtained based on a plurality of reference distance sequences obtained by a radar; S3.2: a least squares straight line fitting is performed on the coarse velocity sequence to obtain an initial value of the translational parameters, and the initial value of the translational parameters is taken as a current translational parameter; S3.3: a first cost function value, a gradient vector and a Hessian matrix under the current translational parameter are calculated based on the cost function; S3.4: an update step of the translational parameters is calculated based on the Levenberg-Marquardt algorithm, a current damping coefficient, the gradient vector and the Hessian matrix; S3.5: an updated translational parameter is obtained based on the update step and the current translational parameter; S3.6: a termination condition is judged, if the termination condition is met, the updated translational parameter is taken as the estimated translational parameter; otherwise, the current damping coefficient is updated based on the cost function, the updated translational parameter and the first cost function value, the updated translational parameter is taken as a new current translational parameter and the iteration is continued in S3.3, and the termination condition comprises that the update step is smaller than a step threshold value or a maximum iteration number is reached.

6. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 5, characterized in that, The update step of the translational parameters is calculated based on the Levenberg-Marquardt algorithm, the current damping coefficient, the gradient vector and the Hessian matrix, which comprises the following steps: obtaining a modified Hessian matrix based on the Levenberg-Marquardt algorithm and the Hessian matrix and the current damping coefficient; calculating the update step length based on the modified Hessian matrix and the gradient vector.

7. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 5, characterized in that, The updating the current damping coefficient based on the cost function, the updated translation parameters and the first cost function value comprises: calculating a second cost function value under the updated translation parameters based on the cost function; comparing the second cost function value and the first cost function value; when the second cost function value is less than the first cost function value, obtaining an updated damping coefficient based on the current damping coefficient and a preset damping coefficient increasing factor; when the second cost function value is greater than the first cost function value, obtaining an updated damping coefficient based on the current damping coefficient and a preset damping coefficient decreasing factor.

8. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 1, characterized in that, The expression of the compensation term is: wherein, is a complex exponential function, is a center carrier frequency of the radar return signal, is a range bin index, is an azimuth bin index, is a range bin frequency difference, is a pulse repetition interval, is an estimated target radial initial velocity, is an estimated target radial acceleration, is the speed of light; The expression of the translation compensated signal is: wherein is the panning compensated signal, is point-wise multiplied, is the preliminary recovered signal.

9. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 4, characterized in that, The azimuth random phase perturbation compensation based on the translation compensated signal to obtain a phase perturbation compensated signal and obtaining the ISAR image of the target based on the phase perturbation compensated signal comprises: S5.1: transforming the translation compensated signal to an image domain to obtain a current ISAR image and calculating a first image entropy of the current ISAR image; S5.2: constructing an azimuth dimension phase perturbation compensation term based on the current ISAR image along an image entropy gradient descent direction, and performing azimuth random phase perturbation compensation on the translation compensated signal in the echo data domain based on the azimuth dimension phase perturbation compensation term to obtain a phase perturbation compensated signal; S5.3: transforming the phase perturbation compensated signal to an image domain to obtain an updated ISAR image and calculating a second image entropy of the updated ISAR image; S5.4: calculating an entropy difference value between the first image entropy and the second image entropy, if the entropy difference value is less than a preset tolerance or reaches a maximum iteration number, outputting the updated ISAR image as the ISAR image of the target, otherwise taking the phase perturbation compensated signal as a new translation compensated signal and returning to S5.1 for iteration.

10. The ISAR despread echo based fast translational motion compensation two-dimensional imaging method according to claim 9, characterized in that, The expression of the azimuth dimension phase perturbation compensation term is: wherein, is the azimuth random phase compensation term of the th pulse, is the complex exponential function, is the estimated random phase error, is the azimuth pulse index, is the range resolution cell index, is the is the complex conjugate of is the complex weight vector corresponding to the th pulse, is the azimuth frequency index, is the translational motion compensated two-dimensional ISAR image, is the is the complex conjugate of is the translational motion compensated one-dimensional high resolution range profile; The expression of the phase perturbation compensated signal is: wherein is the signal after the phase perturbation compensation, is the signal after the translation compensation, is point-wise multiplication.

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