Terahertz ISAR imaging method and device for non-uniform rotating target

Abstract

The application relates to a terahertz ISAR imaging method and device for a non-uniform rotating target. The method comprises the following steps: obtaining radar echo signals of the non-uniform rotating target, pre-processing the radar echo signals, performing phase compensation and azimuth Fourier transform on the obtained one-dimensional range image, constructing an image entropy function, performing coarse search on the rotating parameters of the target according to an image entropy minimum algorithm, iteratively solving the image entropy function by using a modified Newton algorithm, obtaining fine estimation results of the rotating speed and the rotating center, and performing secondary range space-varying phase error compensation, performing one-dimensional search on the rotating acceleration according to the coarse estimation results of the rotating acceleration, obtaining fine estimation results of the rotating acceleration, and performing secondary azimuth space-varying phase error compensation and azimuth Fourier transform, so that a focused ISAR image is obtained. By using the method, high-precision parameter estimation and motion compensation can be performed on the non-uniform rotating target, and a focused imaging result is obtained.

Description

Technical Field

[0001] This application relates to the fields of radar imaging and radar signal processing technology, and in particular to a terahertz ISAR imaging method and apparatus for non-uniformly rotating targets. Background Technology

[0002] Unaffected by the atmosphere, space-based terahertz inverse synthetic aperture radar (ISAR) can acquire high-resolution images of space satellites at long distances, thus holding significant application potential. However, due to the complex relative motion between the space-based platform and the space satellite, and the non-uniform change in the imaging angle relative to the space-based terahertz radar for some uncontrolled tumbling or orbital maneuvers, spatially varied phase errors result in image defocusing.

[0003] Currently, terahertz ISAR imaging algorithms for non-uniformly rotating targets are mainly divided into parameterized methods based on rotation parameter estimation and range-instantaneous Doppler (RID) algorithms. Parameterized methods based on rotation parameter estimation primarily estimate the target's rotational velocity and acceleration using parameter estimation algorithms, compensating for the secondary spatially varying phase to obtain better imaging results. The most classic algorithm is the Adaptive Joint Time-Frequency Technique (AJTF), which estimates the target's rotational velocity and acceleration using multiple key points and employs line-frequency modulation de-modulation techniques, then uses the Polar Format Algorithm (PFA) to achieve image focusing. However, such methods rely on multiple key points to estimate rotational parameters, resulting in low parameter estimation accuracy and poor robustness.

[0004] The RID algorithm primarily treats non-uniform rotation as a maneuvering target, utilizing time-frequency analysis to obtain instantaneous Doppler information and thus acquire a two-dimensional image of the target. Commonly used time-frequency analysis methods include Short Time Fourier Transform (STFT) and Smoothed Pseudo Wigner-Ville Distribution (SPWVD). While these methods do not require estimation of rotation parameters, the imaging resolution is significantly reduced after processing with a short time window. Furthermore, these methods only reduce the influence of the secondary phase on the imaging but do not compensate for the secondary phase error. Summary of the Invention

[0005] Therefore, it is necessary to provide a terahertz ISAR imaging method and apparatus for non-uniformly rotating targets that can improve the accuracy and robustness of parameter estimation in terahertz ISAR imaging and achieve high-quality focused imaging, in order to address the above-mentioned technical problems.

[0006] A terahertz ISAR imaging method for non-uniformly rotating targets, the method comprising:

[0007] The radar echo signal of a non-uniformly rotating target is acquired by space-based terahertz inverse synthetic aperture radar and preprocessed to obtain a one-dimensional range profile of the radar echo signal. Phase compensation and azimuth Fourier transform are performed on the one-dimensional range profile to obtain an ISAR image after range-space-variable phase error compensation.

[0008] The image entropy function of the ISAR image after range-varying phase error compensation is constructed. Based on the image entropy minimization algorithm, the rotation speed, rotation center and rotation acceleration of the target are coarsely searched sequentially within the preset coarse search interval to obtain the coarse estimation results of rotation speed, rotation center and rotation acceleration.

[0009] The modified Newton algorithm is adopted, and the image entropy function is iteratively solved by the coarse estimation results of rotation speed and rotation center. When the image entropy function converges, the fine estimation results of rotation speed and rotation center are obtained, and the one-dimensional range image is compensated for by secondary range spatial variation phase error based on the fine estimation results of rotation speed and rotation center, so as to obtain the one-dimensional range image after secondary range spatial variation phase error compensation.

[0010] Based on the coarse estimation of rotational acceleration, the fine search interval of rotational acceleration is determined. Within the fine search interval, a one-dimensional search of rotational acceleration is performed according to the preset fine search step size to obtain the fine estimation result of rotational acceleration. Based on the fine estimation result of rotational acceleration, a second azimuth-spatial-phase error compensation and azimuth Fourier transform are performed on the one-dimensional range image after second-order range spatial-phase error compensation to obtain the focused ISAR image.

[0011] In one embodiment, radar echo signals from a non-uniformly rotating target are acquired based on space-based terahertz inverse synthetic aperture radar and preprocessed to obtain a one-dimensional range profile of the radar echo signals, including:

[0012] The radar echo signal of a non-uniformly rotating target is obtained by acquiring the radar echo signal of the space-based terahertz inverse synthetic aperture radar. The radar echo signal is then subjected to de-interpolation frequency modulation, pulse compression, translational compensation and first-order range migration correction in sequence to obtain a one-dimensional range profile of the radar echo signal.

[0013] In one embodiment, phase compensation and azimuth Fourier transform are performed on the one-dimensional range image to obtain an ISAR image after range-space-variable phase error compensation, including:

[0014] Phase compensation and azimuth Fourier transform are performed on the one-dimensional range image to obtain the ISAR image after range-space-variable phase error compensation, as shown below:

[0015]

[0016] Where g(n; m; x) is the ISAR image after range-space-variable phase error compensation, M is the number of points in the azimuth dimension, n and m represent the coordinates of pixels in the image, S(n, h) is the discretization result of the one-dimensional range image, and h is the slow time t. m Discretized variables, j is the imaginary unit, x = [K r [y0] represents the secondary distance spatial variation phase error parameter. Here, PRF is the pulse repetition frequency, α is the target's rotational speed, and f is the related quantity. c y0 is the radar carrier frequency, c is the speed of light, y0 is the target's rotation center, and B is the bandwidth.

[0017] In one embodiment, the image entropy function E of the ISAR image after range-space-variable phase error compensation is constructed. g (x), represented as:

[0018]

[0019] Among them, E g denoted as the total energy of the image, N as the number of points in the range dimension, and g(n;m;x) as the ISAR image after range-space-variable phase error compensation.

[0020] In one embodiment, the rotational speed, rotation center, and rotational acceleration of the target are coarsely searched sequentially within a preset coarse search interval according to the image entropy minimization algorithm to obtain coarse estimates of the rotational speed, rotation center, and rotational acceleration, including:

[0021] Set the rotation center and rotation acceleration of the target to 0, search for the rotation speed of the target within the preset coarse search interval according to the preset coarse search step size, and select the search result with the smallest image entropy function value as the coarse estimate of the rotation speed.

[0022] Substitute the coarse estimate of the rotation speed into the equation and set the rotation acceleration to 0. Search for the rotation center of the target within the preset coarse search interval according to the preset coarse search step size. Select the search result with the smallest image entropy function value as the coarse estimate of the rotation center.

[0023] Substitute the coarse estimate of the rotation center into the search results, and search for the rotational acceleration of the target within the preset coarse search interval according to the preset coarse search step size. Select the search result with the smallest image entropy function value as the coarse estimate of the rotational acceleration.

[0024] In one embodiment, a modified Newton algorithm is employed, and the image entropy function is iteratively solved using coarse estimates of the rotation speed and rotation center. Once the image entropy function converges, fine estimates of the rotation speed and rotation center are obtained, including:

[0025] Calculate the image entropy function E g The gradient and Hessian matrix of (x) with respect to the quadratic range-varying phase error parameter x are expressed as follows:

[0026]

[0027]

[0028] in, For E g (x) Related quantity K of rotational speed r The partial derivatives, For E g (x) is the partial derivative with respect to the rotation center y0. For E g (x) Related quantity K of rotational speed r The second-order partial derivative, For E g (x) is the second partial derivative with respect to the rotation center y0. For E g The second-order mixed partial derivative of (x), where the superscript T denotes matrix transpose;

[0029] The coarse estimates of the rotation speed and rotation center are substituted into the image entropy gradient ▽E and the Hessian matrix H as initial values ​​for the iterative solution, and the modified Newton algorithm is used to refine the image entropy function E. g (x) is solved iteratively until E is obtained. g (x) converges to meet the preset accuracy requirement, and the result obtained at this point is used as the precise estimate of the rotational speed and rotation center; wherein, the iterative process using the modified Newton algorithm is expressed as:

[0030]

[0031] H′=H+μI;

[0032] Where, x k+1 Let x be the value obtained in the (k+1)th iteration. k Let x be the result of the k-th iteration, and H′ be the corrected Hessian matrix. k This is the corrected Hessian matrix obtained in the k-th iteration. Let μ be the image entropy gradient obtained in the k-th iteration, λ be the step size factor, I be the identity matrix, and the parameter μ satisfy μ + λ.i >0,i=1,2,…,A and μ>max{-λ i}, λ i Let be the i-th eigenvalue of the Hessian matrix, and A be the number of eigenvalues.

[0033] In one embodiment, a second-order spatially variable phase error compensation is performed on the one-dimensional range image based on the precise estimation results of the rotation speed and rotation center, resulting in a one-dimensional range image S′(f) after the second-order spatially variable phase error compensation. r ,t m ), represented as:

[0034]

[0035] Among them, f r For distance frequency, t m σ represents the slow time, Q represents the number of scattering points that make up the radar echo signal, and σ represents the slow time. i Let T be the reflection coefficient at the i-th scattering point. p Pulse width, γ is the signal modulation frequency, c is the speed of light, f c Where is the radar carrier frequency, j is the imaginary unit, α is the target's rotational velocity, β is the target's rotational acceleration, and x... i and y i Let x and y be the x and y coordinates of the i-th scattering point.

[0036] In one embodiment, a fine search interval for rotational acceleration is determined based on the coarse estimation result of the rotational acceleration. Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to a preset fine search step size to obtain a fine estimation result of the rotational acceleration, including:

[0037] Based on the coarse estimate of rotational acceleration, the fine search interval for rotational acceleration is determined as follows: in, This is a coarse estimate of the rotational acceleration, where L is the coarse search step size;

[0038] Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to a preset fine search step size to obtain a fine estimate of the rotational acceleration; wherein, the one-dimensional search process for the rotational acceleration is expressed as:

[0039]

[0040] Among them, E g (β) represents the image entropy after compensating for the quadratic spatial phase error. This is a precise estimate of the rotational acceleration.

[0041] In one embodiment, based on the precise estimation of rotational acceleration, a second azimuth-based spatially varying phase error is compensated and an azimuth Fourier transform is performed on the one-dimensional range image after second-order range spatially varying phase error compensation to obtain a focused ISAR image, represented as:

[0042]

[0043] Where g′(n; m; x) is the focused ISAR image, M is the number of points in the azimuth dimension, n and m represent the coordinates of pixels in the image, and S′(n, h) is the one-dimensional range image S′(f) after secondary range spatial variation phase error compensation. r ,t m The discretization result of ), where h is the slow time t. m The discretized variable, where j is the imaginary unit. For the rotational acceleration related quantity of the target, f c Where is the radar carrier frequency, c is the speed of light, PRF is the pulse repetition frequency, and β is the rotational acceleration. Here, α represents the azimuth resolution, T represents the imaging coherence processing time, α represents the target rotation speed, and λ represents the step size factor.

[0044] A terahertz ISAR imaging device for non-uniformly rotating targets, the device comprising:

[0045] The echo signal preprocessing module is used to acquire radar echo signals of non-uniformly rotating targets based on space-based terahertz inverse synthetic aperture radar and perform preprocessing to obtain a one-dimensional range profile of the radar echo signal.

[0046] The coarse search module is used to construct the image entropy function of the ISAR image after range-varying phase error compensation. According to the image entropy minimization algorithm, it sequentially performs a coarse search on the target's rotation speed, rotation center, and rotation acceleration within a preset coarse search interval to obtain coarse estimates of the rotation speed, rotation center, and rotation acceleration.

[0047] The secondary range spatially variable phase error compensation module is used to employ the modified Newton algorithm and iteratively solve the image entropy function using the coarse estimation results of rotation speed and rotation center. After the image entropy function converges, the fine estimation results of rotation speed and rotation center are obtained, and secondary range spatially variable phase error compensation is performed on the one-dimensional range image based on the fine estimation results of rotation speed and rotation center to obtain the one-dimensional range image after secondary range spatially variable phase error compensation.

[0048] The secondary azimuth spatially varying phase error compensation module is used to determine the fine search interval of rotational acceleration based on the coarse estimation result of rotational acceleration. Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to the preset fine search step size to obtain the fine estimation result of rotational acceleration. Based on the fine estimation result of rotational acceleration, the secondary azimuth spatially varying phase error compensation and azimuth Fourier transform are performed on the one-dimensional range image after secondary range spatially varying phase error compensation to obtain the focused ISAR image.

[0049] Compared with the prior art, the beneficial effects of this application include:

[0050] 1. This application uses a combination of coarse search and fine search to estimate the target's rotational speed, rotational center, and rotational acceleration. This reduces the amount of search while improving the accuracy of the rotational parameter estimation and exhibits strong robustness.

[0051] 2. Based on the image entropy minimization algorithm, this application performs a coarse search on the target's rotation speed, rotation center, and rotation acceleration sequentially within a preset coarse search interval, which makes the algorithm converge faster and reduces the coupling effect of the range spatially variable second phase and the azimuth spatially variable second phase.

[0052] 3. This application modifies the Newton method by using a modified Newton algorithm and iteratively solving the image entropy function using coarse estimates of rotation speed and rotation center to obtain fine estimates of rotation speed and rotation center. This ensures the convergence of the Newton method while preventing iteration from getting trapped in local optima, thus improving the accuracy of rotation parameter estimation. Finally, based on the fine estimation results, secondary range-varying phase error compensation and secondary azimuth-varying phase error compensation are performed to achieve high-resolution imaging of non-uniformly rotating space targets by space-based terahertz inverse synthetic aperture radar.

[0053] 4. This application does not rely on prominent points in the radar echo signal for rotation parameter estimation, and has good adaptability. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating a terahertz ISAR imaging method for a non-uniformly rotating target in one embodiment.

[0055] Figure 2 This is a schematic diagram of the geometric model of terahertz ISAR imaging in one embodiment;

[0056] Figure 3 This is a schematic diagram of the point target imaging results in a simulation experiment of one embodiment; wherein, Figure 3 (a) is a schematic diagram of the imaging results based on the RD (range Doppler) algorithm in the simulation experiment; Figure 3 (b) is a schematic diagram of the imaging results based on the PFA algorithm in the simulation experiment; Figure 3(c) is a schematic diagram of the imaging results based on the minimum entropy algorithm in the simulation experiment; Figure 3 (d) is a schematic diagram of the imaging results based on the algorithm proposed in this application in the simulation experiment;

[0057] Figure 4 This is a schematic diagram of the imaging results of a point target in a measured experiment in one embodiment; wherein, Figure 4 (a) is a schematic diagram of the imaging results based on the RD (range Doppler) algorithm in the actual experiment; Figure 4 (b) is a schematic diagram of the imaging results based on the PFA algorithm in the actual experiment; Figure 4 (c) is a schematic diagram of the imaging results based on the minimum entropy algorithm in the actual experiment; Figure 4 (d) is a schematic diagram of the imaging results based on the algorithm proposed in this application in the actual test. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0059] In one embodiment, such as Figure 1 As shown, a terahertz ISAR imaging method for non-uniformly rotating targets is provided, including the following steps:

[0060] Step S1: Based on space-based terahertz inverse synthetic aperture radar, the radar echo signal of the non-uniformly rotating target is acquired and preprocessed to obtain a one-dimensional range image of the radar echo signal. Phase compensation and azimuth Fourier transform are performed on the one-dimensional range image to obtain the ISAR image after range-space-variable phase error compensation.

[0061] Step S2: Construct the image entropy function of the ISAR image after range-varying phase error compensation. Based on the image entropy minimization algorithm, perform a coarse search on the target's rotation speed, rotation center, and rotation acceleration in a preset coarse search interval to obtain coarse estimation results of rotation speed, rotation center, and rotation acceleration.

[0062] Step S3: The modified Newton algorithm is adopted, and the image entropy function is solved iteratively by using the coarse estimation results of rotation speed and rotation center. When the image entropy function converges, the fine estimation results of rotation speed and rotation center are obtained, and the one-dimensional range image is compensated for secondary range spatial variation phase error based on the fine estimation results of rotation speed and rotation center to obtain the one-dimensional range image after secondary range spatial variation phase error compensation.

[0063] Step S4: Determine the fine search interval of rotational acceleration based on the coarse estimation result of rotational acceleration. Within the fine search interval, perform a one-dimensional search on rotational acceleration according to the preset fine search step size to obtain the fine estimation result of rotational acceleration. Based on the fine estimation result of rotational acceleration, perform secondary azimuth spatial phase error compensation and azimuth Fourier transform on the one-dimensional range image after secondary range spatial phase error compensation to obtain the focused ISAR image.

[0064] In such Figure 2 In the geometric model of terahertz ISAR imaging shown, the target's motion can be decomposed into three parts according to the far-field assumption. First, the target translates from point A to point C along the radar line of sight. During this process, all scattering points move in the same way and produce the same Doppler effect, hence the term translation. Second, the target rotates around the rotation center at point C. Due to the rotation, the distances from different scattering points to the radar change inconsistently, and the resulting Doppler effect can be used to distinguish different scattering points and provide azimuth resolution. Finally, the target moves in a circle from point C to point B around the radar. During this process, the distances from all scattering points to the radar remain constant, thus not affecting the imaging results. Therefore, the target's motion relative to the radar can be independently decomposed into translation and rotation components. Considering the initial slant range and the change in instantaneous slant range caused by the translational motion, the instantaneous slant range of the i-th scattering point can be expressed as:

[0065] R i (t m )=r0+r(t m )+x i sinθ(t m )+y i cosθ(t m (1)

[0066] Where r0 represents the initial slope distance, t m Representing slow time, r(t) m x represents the change in slant distance caused by translation. i and y i Let θ(t) be the x and y coordinates of the i-th scattering point. m x represents the target's rotation angle relative to the radar. i sinθ(t m )+y i cosθ(t m ) represents the change in slant distance caused by the rotation of the target.

[0067] This application assumes that a space-based terahertz inverse synthetic aperture radar transmits a linear frequency modulated signal, expressed as:

[0068]

[0069] In the formula, T indicates a fast time. p This represents the pulse width, where j is the imaginary unit, and f c Let γ be the radar carrier frequency and γ be the signal modulation frequency. The time delay for the signal to travel from the transmitting antenna, be reflected from the target, and return to the receiving antenna is:

[0070] The radar echo signal of the i-th scattering point is finally obtained as follows:

[0071]

[0072] In the formula, c is the speed of light.

[0073] In one embodiment, the method proposed in this application further includes: acquiring radar echo signals of a non-uniformly rotating target based on a space-based terahertz inverse synthetic aperture radar, and sequentially performing de-linearization frequency modulation, pulse compression, translational compensation, and first-order skip range migration correction on the radar echo signals to obtain a one-dimensional range profile of the radar echo signals. Specific preprocessing steps include:

[0074] First, due to the large bandwidth of space-based terahertz inverse synthetic aperture radar (ISAR), using direct sampling would result in an excessively high sampling rate and a surge in data volume. In practical engineering, dechirp (de-firing frequency modulation) mode is used to reduce the sampling rate requirement. Assuming the target's radar echo signal consists of Q scattering points, after dechirp processing and pulse compression, a high-resolution preliminary one-dimensional range profile is obtained, represented as:

[0075]

[0076] Among them, f r Represents the distance frequency, σ i Let be the reflection coefficient of the i-th scattering point. The one-dimensional range image result after dechirp processing is represented in the range frequency. In the above equation (4), the phase of the first exponential term is the phase error caused by translation, and the phase of the second exponential term is the phase caused by rotation. The azimuth information of the scattering point is included in this term. It can be seen from the above equation (4) that for any scattering point, the distance travel and phase error caused by translation only change with slow time. Therefore, they can be uniformly compensated. The one-dimensional range image after translation compensation is expressed as:

[0077]

[0078] For three-axis stable spatial targets undergoing attitude adjustment or targets experiencing attitude loss during slow tumbling, the rotation angle is non-uniform. Typically, only the second-order rotation component is considered, approximating it as uniformly accelerated rotation. The target's rotation angle relative to the radar can be approximately expanded into a second-order polynomial:

[0079]

[0080] Therefore, the target's rotational speed ω relative to the radar can be expressed as:

[0081] ω=α+βt m (7)

[0082] Turning angle θ(t) m Substituting the trigonometric functions and performing a third-order Taylor expansion, it can be expressed as:

[0083]

[0084] Where α is the target's rotational velocity and β is the target's rotational acceleration.

[0085] The phase error generated by the cubic term is usually negligible. Substituting formula (8) into the radar echo signal, we obtain the radar echo signal of all scattering points, which is expressed as:

[0086]

[0087] The radar echo signals from all scattering points are subjected to Keystone transform to correct the first-order range migration (MTRC), while ignoring the range migration caused by the quadratic term. After pulse compression, the final one-dimensional range image is obtained, represented as:

[0088]

[0089] In one embodiment, the method proposed in this application further includes: by adjusting the one-dimensional distance image S(f) in equation (10) r ,t m Multiplied by phase compensation term Phase compensation is performed, and the result after phase compensation is subjected to azimuth Fourier transform to obtain the ISAR image after range-space-varying phase error compensation, as shown below:

[0090]

[0091] Where g(n; m; x) is the ISAR image after range-space-variable phase error compensation, M is the number of azimuth dimension points, n and m represent the coordinates of pixels on the image, and S(n, h) is the one-dimensional range image S(f) in equation (10). r ,t m The discretization result of ), where h is the slow time t. m Discretized variables, j is the imaginary unit, x = [K r [y0] represents the secondary distance spatial variation phase error parameter. Here, PRF is the pulse repetition frequency, α is the target's rotational speed, and f is the related quantity. c y0 is the radar carrier frequency, c is the speed of light, y0 is the target's rotation center, and B is the bandwidth.

[0092] In one embodiment, the method proposed in this application further includes: constructing the image entropy function E of the ISAR image after range-varying phase error compensation. g (x), represented as:

[0093]

[0094] Where N is the number of range dimension points, g(n; m; x) is the ISAR image after range-space-variable phase error compensation, and E g The total energy of the image is calculated using the following formula:

[0095]

[0096] In one embodiment, the method proposed in this application further includes:

[0097] Set the rotation center and rotation acceleration of the target to 0, search for the rotation speed of the target within the preset coarse search interval according to the preset coarse search step size, and select the search result with the smallest image entropy function value as the coarse estimate of the rotation speed.

[0098] Substitute the coarse estimate of the rotation speed into the equation and set the rotation acceleration to 0. Search for the rotation center of the target within the preset coarse search interval according to the preset coarse search step size. Select the search result with the smallest image entropy function value as the coarse estimate of the rotation center.

[0099] Substitute the coarse estimate of the rotation center into the search results, and search for the rotational acceleration of the target within the preset coarse search interval according to the preset coarse search step size. Select the search result with the smallest image entropy function value as the coarse estimate of the rotational acceleration.

[0100] In one embodiment, the method proposed in this application further includes:

[0101] Since the target's rotation center is usually not the same as its geometric center, this application performs precise estimation of both the target's rotation center and rotation velocity simultaneously. The precise estimation results of the rotation velocity and rotation center are based on the image entropy function E. g (x) is obtained, represented as:

[0102]

[0103] in, This provides a precise estimate of the spatially varying phase error parameter x for the second distance. Since Newton's method is applicable to unconstrained optimization problems and exhibits fast convergence, this application employs Newton's method to solve the aforementioned problem. Furthermore, to prevent getting trapped in local optima while ensuring the convergence of Newton's method, this application also modifies Newton's method, using an iterative solution through a modified Newton algorithm. The specific steps include:

[0104] Calculate the image entropy function E g (x) The gradient and Hessian matrix of the quadratic range-varying phase error parameter x are expressed as follows:

[0105]

[0106]

[0107]

[0108]

[0109] in, For E g (x) Related quantity K of rotational speed r The partial derivatives, For E g (x) is the partial derivative with respect to the rotation center y0. For E g (x) Related quantity K of rotational speed r The second-order partial derivative, For E g (x) is the second partial derivative with respect to the rotation center y0. For E g The second-order mixed partial derivative of (x), where the superscript T denotes matrix transpose, Re denotes taking the real part, and g * (n; m; x) denotes the conjugate of g(n; m; x);

[0110] The coarse estimates of the rotation speed and rotation center are substituted into the image entropy gradient ▽E and the Hessian matrix H as initial values ​​for the iterative solution, and the modified Newton algorithm is used to refine the image entropy function E. g (x) is solved iteratively until E is obtained. g (x) converges to meet the preset accuracy requirement, and the result obtained at this point is used as the precise estimate of the rotation velocity and rotation center; where, after obtaining the image entropy gradient ▽E and the Hessian matrix H, the Newton iteration process can be expressed as:

[0111]

[0112] To prevent getting trapped in local optima while ensuring the convergence of Newton's method, the above equation is modified, resulting in the iterative process of the modified Newton's algorithm, expressed as:

[0113]

[0114] H′=H+μI; (21)

[0115] Where, x k+1 Let x be the value obtained in the (k+1)th iteration. k Let x be the result of the k-th iteration, and H′ be the corrected Hessian matrix. k This is the corrected Hessian matrix obtained in the k-th iteration. Let λ be the image entropy gradient obtained in the k-th iteration, and λ be the step size factor. The step size factor is used to prevent Ek from being calculated. g (x) gets trapped in a local optimum, which is usually determined by a one-dimensional line search (e.g., the golden section method), where I is the identity matrix, and the parameter μ satisfies:

[0116] μ+λ i >0, i=1,2…A; (22)

[0117] μ>max{-λ i}; (twenty three)

[0118] In the formula, λ i Let be the i-th eigenvalue of the Hessian matrix, and A be the number of eigenvalues.

[0119] In one embodiment, the method proposed in this application further includes: performing secondary range-space-variable phase error compensation on the one-dimensional range image based on the precise estimation results of the rotation speed and rotation center, to obtain the one-dimensional range image S′(f) after secondary range-space-variable phase error compensation. r ,t m ), represented as:

[0120]

[0121] Among them, f r For distance frequency, t m Indicates slow time. Q σ represents the number of scattering points that make up the radar echo signal. i Let T be the reflection coefficient at the i-th scattering point. p Pulse width, γ is the signal modulation frequency, c is the speed of light, f c Where is the radar carrier frequency, j is the imaginary unit, α is the target's rotational velocity, β is the target's rotational acceleration, and x... i and y i Let x and y be the x and y coordinates of the i-th scattering point.

[0122] In one embodiment, the method proposed in this application further includes: since the compensation process of azimuth spatial phase variation is implied in the process of azimuth Fourier transform, and after obtaining the precise estimation results of rotational speed and rotation center, the only unknown parameter is rotational acceleration β, so the precise estimation result of rotational acceleration can be estimated through a one-dimensional search process.

[0123] Specifically, the fine search interval for rotational acceleration is determined based on the coarse estimate of rotational acceleration. in, This is a coarse estimate of the rotational acceleration, where L is the coarse search step size;

[0124] Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to a preset fine search step size to obtain a precise estimate of the rotational acceleration; wherein, the one-dimensional search process for the rotational acceleration is expressed as follows:

[0125]

[0126] Among them, E g (β) represents the image entropy after compensating for the quadratic spatial phase error. This is a precise estimate of the rotational acceleration.

[0127] In one embodiment, the method proposed in this application further includes: performing secondary azimuth spatially varied phase error compensation and azimuth Fourier transform on the one-dimensional range image after secondary range spatially varied phase error compensation based on the precise estimation result of rotational acceleration, to obtain a focused ISAR image, represented as:

[0128]

[0129] Where g′(n; m; x) is the focused ISAR image, M is the number of points in the azimuth dimension, n and m represent the coordinates of pixels in the image, and S(n, h) is the one-dimensional range image S′(f) after secondary range spatial variation phase error compensation. r ,t m The discretization result of ), where j is the imaginary unit. For the rotational acceleration related quantity of the target, f c Where is the radar carrier frequency, c is the speed of light, PRF is the pulse repetition frequency, and β is the rotational acceleration. Here, α represents the azimuth resolution, T represents the imaging coherence processing time, α represents the target rotation speed, and λ represents the step size factor.

[0130] Furthermore, to verify the effectiveness of the proposed terahertz ISAR imaging method for non-uniformly rotating targets, simulation and experimental experiments were conducted on point targets. The imaging results obtained based on the proposed algorithm were compared and analyzed with those obtained based on traditional RD, PFA, and minimum entropy algorithms. The simulation parameter settings are shown in Table 1.

[0131] Table 1 Simulation Parameters

[0132] Center frequency 216GHz bandwidth 20GHz Sampling frequency 1200Hz Target rotation speed 0.1 rad / s Target rotational acceleration <![CDATA[0.01rad / s 2 ]]> Number of sampling points in the distance dimension 1200

[0133] The point target imaging results in the simulation experiment are as follows: Figure 3 As shown, where, Figure 3 (a) is a schematic diagram of the imaging results based on the RD (range Doppler) algorithm in the simulation experiment; Figure 3 (b) is a schematic diagram of the imaging results based on the PFA algorithm in the simulation experiment; Figure 3 (c) is a schematic diagram of the imaging results based on the minimum entropy algorithm in the simulation experiment; Figure 3 (d) is a schematic diagram of the imaging results based on the algorithm proposed in this application in the simulation experiment.

[0134] The point target imaging results in the actual experiment are as follows: Figure 4 As shown, where, Figure 4 (a) is a schematic diagram of the imaging results based on the RD (range Doppler) algorithm in the actual experiment; Figure 4 (b) is a schematic diagram of the imaging results based on the PFA algorithm in the actual experiment; Figure 4 (c) is a schematic diagram of the imaging results based on the minimum entropy algorithm in the actual experiment; Figure 4 (d) is a schematic diagram of the imaging results based on the algorithm proposed in this application in the actual test.

[0135] Depend on Figure 3 and Figure 4 It is evident that traditional algorithms suffer from severe defocusing in both simulation and field experiments. However, after imaging using the method proposed in this application, the target azimuth defocusing is significantly suppressed, and the quality of the obtained ISAR image is significantly improved, verifying the effectiveness of the method proposed in this application.

[0136] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0137] In one embodiment, a terahertz ISAR imaging device for non-uniformly rotating targets is provided, comprising:

[0138] The echo signal preprocessing module is used to acquire radar echo signals of non-uniformly rotating targets based on space-based terahertz inverse synthetic aperture radar and perform preprocessing to obtain a one-dimensional range profile of the radar echo signal.

[0139] The coarse search module is used to construct the image entropy function of the ISAR image after range-varying phase error compensation. According to the image entropy minimization algorithm, it sequentially performs a coarse search on the target's rotation speed, rotation center, and rotation acceleration within a preset coarse search interval to obtain coarse estimates of the rotation speed, rotation center, and rotation acceleration.

[0140] The secondary range spatially variable phase error compensation module is used to employ the modified Newton algorithm and iteratively solve the image entropy function using the coarse estimation results of rotation speed and rotation center. After the image entropy function converges, the fine estimation results of rotation speed and rotation center are obtained, and secondary range spatially variable phase error compensation is performed on the one-dimensional range image based on the fine estimation results of rotation speed and rotation center to obtain the one-dimensional range image after secondary range spatially variable phase error compensation.

[0141] The secondary azimuth spatially varying phase error compensation module is used to determine the fine search interval of rotational acceleration based on the coarse estimation result of rotational acceleration. Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to the preset fine search step size to obtain the fine estimation result of rotational acceleration. Based on the fine estimation result of rotational acceleration, the secondary azimuth spatially varying phase error compensation and azimuth Fourier transform are performed on the one-dimensional range image after secondary range spatially varying phase error compensation to obtain the focused ISAR image.

[0142] Specific limitations regarding terahertz ISAR imaging devices for non-uniformly rotating targets can be found in the above section on limitations of terahertz ISAR imaging methods for non-uniformly rotating targets, and will not be repeated here. The modules in the aforementioned terahertz ISAR imaging device for non-uniformly rotating targets can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independent of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0143] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0144] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A terahertz ISAR imaging method for non-uniformly rotating targets, characterized in that, The method includes: The radar echo signal of a non-uniformly rotating target is acquired by space-based terahertz inverse synthetic aperture radar and preprocessed to obtain a one-dimensional range image of the radar echo signal. Phase compensation and azimuth Fourier transform are performed on the one-dimensional range image to obtain an ISAR image after range-space-variable phase error compensation. The image entropy function of the ISAR image after range-varying phase error compensation is constructed. According to the image entropy minimization algorithm, the rotation speed, rotation center and rotation acceleration of the target are coarsely searched sequentially within the preset coarse search interval to obtain the coarse estimation results of rotation speed, rotation center and rotation acceleration. The modified Newton algorithm is adopted, and the image entropy function is iteratively solved using the coarse estimation results of rotation speed and rotation center. When the image entropy function converges, the fine estimation results of rotation speed and rotation center are obtained, and the one-dimensional range image is compensated for secondary range spatial variation phase error based on the fine estimation results of rotation speed and rotation center to obtain the one-dimensional range image after secondary range spatial variation phase error compensation. Based on the coarse estimation result of the rotational acceleration, a fine search interval for the rotational acceleration is determined. Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to a preset fine search step size to obtain a fine estimation result of the rotational acceleration. Based on the fine estimation result of the rotational acceleration, a second azimuth-spatial-phase error compensation and azimuth Fourier transform are performed on the one-dimensional range image after the second range spatial-phase error compensation to obtain a focused ISAR image. Based on space-based terahertz inverse synthetic aperture radar, radar echo signals from non-uniformly rotating targets are acquired and preprocessed to obtain a one-dimensional range profile of the radar echo signals, including: The radar echo signal of a non-uniformly rotating target is obtained by space-based terahertz inverse synthetic aperture radar. The radar echo signal is then subjected to de-firing frequency modulation, pulse compression, translational compensation and first-order range migration correction in sequence to obtain a one-dimensional range profile of the radar echo signal. Phase compensation and azimuth Fourier transform are performed on the one-dimensional range image to obtain an ISAR image with range-space-varying phase error compensation, including: Phase compensation and azimuth Fourier transform are performed on the one-dimensional range image to obtain the ISAR image after range-space-variable phase error compensation, as shown below: ； in, This is an ISAR image after range-space-varying phase error compensation. Let n be the number of points in the orientation dimension, and m be the coordinates of pixels on the image. This is the discretization result of a one-dimensional distance image. The imaginary unit, For slow time Discretized variables, This represents the secondary distance spatial variation phase error parameter. The rotational speed of the target is a related quantity, and PRF is the pulse repetition frequency. The rotational speed of the target For radar carrier frequency, At the speed of light, Center of rotation for the target For bandwidth; Based on the precise estimation results of the rotation speed and rotation center, a second-order spatially variable phase error compensation is performed on the one-dimensional range image to obtain the one-dimensional range image after second-order spatially variable phase error compensation. , is represented as: ； in, For distance frequency, This indicates the number of scattering points that make up the radar echo signal. For the first The reflection coefficient at each scattering point The pulse width. To adjust the frequency of the signal, For the rotational acceleration of the target, and For the first The horizontal and vertical coordinates of the scattering points; Based on the coarse estimation result of the rotational acceleration, a fine search interval for the rotational acceleration is determined. Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to a preset fine search step size to obtain a fine estimation result of the rotational acceleration, including: Based on the coarse estimate of the rotational acceleration, the fine search interval for the rotational acceleration is determined as follows: ,in, This is a coarse estimate of the rotational acceleration. This is the coarse search step size; Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to a preset fine search step size to obtain a fine estimate of the rotational acceleration; wherein, the one-dimensional search process for the rotational acceleration is expressed as follows: ； in, To compensate for the image entropy after the quadratic spatial phase error, This is a precise estimate of the rotational acceleration; Based on the precise estimation result of the rotational acceleration, a second azimuth-based spatially varying phase error is compensated and an azimuth Fourier transform is performed on the one-dimensional range image after the second range spatially varying phase error compensation to obtain a focused ISAR image, represented as: ； in, A focused ISAR image. One-dimensional range image after secondary range spatial variation phase error compensation The discretization result, The rotational acceleration related to the target, For azimuth resolution, For imaging coherence processing time, This is the step size factor.

2. The method according to claim 1, characterized in that, Construct the image entropy function of the ISAR image after range-space-varying phase error compensation. , is represented as: ； in, The total energy of the image. N denoted as the number of points in the distance dimension.

3. The method according to claim 2, characterized in that, Based on the image entropy minimization algorithm, a coarse search is performed sequentially on the target's rotational velocity, rotation center, and rotational acceleration within a preset coarse search interval to obtain coarse estimates of the rotational velocity, rotation center, and rotational acceleration, including: Set the rotation center and rotation acceleration of the target to 0, search for the rotation speed of the target within the preset coarse search interval according to the preset coarse search step size, and select the search result with the smallest image entropy function value as the coarse estimate of the rotation speed. Substitute the coarse estimate of the rotation speed into the equation and set the rotation acceleration to 0. Search for the rotation center of the target within the preset coarse search interval according to the preset coarse search step size. Select the search result with the smallest image entropy function value as the coarse estimate of the rotation center. Substitute the coarse estimate of the rotation center into the search results, and search for the rotational acceleration of the target within the preset coarse search interval according to the preset coarse search step size. Select the search result with the smallest image entropy function value as the coarse estimate of the rotational acceleration.

4. The method according to claim 3, characterized in that, A modified Newton algorithm is employed, and the image entropy function is iteratively solved using coarse estimates of rotation speed and rotation center. Once the image entropy function converges, fine estimates of rotation speed and rotation center are obtained, including: Calculate the image entropy function Regarding the secondary distance spatial variation phase error parameters The gradient and Hessian matrix are expressed as follows: ； ； in, for Quantities related to rotational speed The partial derivatives, for Regarding the center of rotation The partial derivatives, for Related quantities of rotational speed The second-order partial derivative, for Regarding the center of rotation The second-order partial derivative, for The second-order mixed partial derivatives, where the superscript T denotes matrix transpose; The coarse estimates of the rotation speed and rotation center are used as initial values ​​for the iterative solution and substituted into the image entropy gradient. and the Hesse matrix In the process, a modified Newton algorithm is used to refine the image entropy function. Perform iterative solutions until... The iteration converges to meet the preset accuracy requirements, and the result obtained at this point is used as the precise estimate of the rotational speed and rotation center; the iterative process using the modified Newton algorithm is expressed as follows: ； ； in, Indicates the first Solving in the next iteration , Indicates the first Solving in the next iteration , This is the corrected Hessian matrix. For the first The corrected Hessian matrix obtained in the next iteration. For the first The image entropy gradient is solved in the next iteration. Step size factor For the identity matrix, the parameters satisfy and , The first of the Hessian matrices 1 eigenvalue, The number of eigenvalues.

5. A terahertz ISAR imaging device for non-uniformly rotating targets, characterized in that, The device includes: The echo signal preprocessing module is used to acquire radar echo signals of non-uniformly rotating targets based on space-based terahertz inverse synthetic aperture radar and preprocess them to obtain a one-dimensional range profile of the radar echo signal. The one-dimensional range profile is then subjected to phase compensation and azimuth Fourier transform to obtain an ISAR image after range-space-variable phase error compensation. The coarse search module is used to construct the image entropy function of the ISAR image after range-space-variable phase error compensation. According to the image entropy minimum algorithm, it sequentially performs a coarse search on the target's rotation speed, rotation center, and rotation acceleration within a preset coarse search interval to obtain coarse estimation results of rotation speed, rotation center, and rotation acceleration. The secondary distance spatially variable phase error compensation module is used to employ a modified Newton algorithm and iteratively solve the image entropy function using coarse estimation results of rotation speed and rotation center. When the image entropy function converges, it obtains fine estimation results of rotation speed and rotation center, and performs secondary distance spatially variable phase error compensation on the one-dimensional distance image based on the fine estimation results of rotation speed and rotation center to obtain the one-dimensional distance image after secondary distance spatially variable phase error compensation. The secondary azimuth spatially varying phase error compensation module is used to determine the fine search interval of the rotational acceleration based on the coarse estimation result of the rotational acceleration, perform a one-dimensional search on the rotational acceleration within the fine search interval according to a preset fine search step size to obtain the fine estimation result of the rotational acceleration, and perform secondary azimuth spatially varying phase error compensation and azimuth Fourier transform on the one-dimensional range image after secondary range spatially varying phase error compensation based on the fine estimation result of the rotational acceleration to obtain a focused ISAR image; Based on space-based terahertz inverse synthetic aperture radar, radar echo signals from non-uniformly rotating targets are acquired and preprocessed to obtain a one-dimensional range profile of the radar echo signals, including: The radar echo signal of a non-uniformly rotating target is obtained by space-based terahertz inverse synthetic aperture radar. The radar echo signal is then subjected to de-firing frequency modulation, pulse compression, translational compensation and first-order range migration correction in sequence to obtain a one-dimensional range profile of the radar echo signal. Phase compensation and azimuth Fourier transform are performed on the one-dimensional range image to obtain an ISAR image with range-space-varying phase error compensation, including: Phase compensation and azimuth Fourier transform are performed on the one-dimensional range image to obtain the ISAR image after range-space-variable phase error compensation, as shown below: ； in, This is an ISAR image after range-space-varying phase error compensation. Let n be the number of points in the orientation dimension, and m be the coordinates of pixels on the image. This is the discretization result of a one-dimensional distance image. The imaginary unit, For slow time Discretized variables, This represents the secondary distance spatial variation phase error parameter. The rotational speed of the target is a related quantity, and PRF is the pulse repetition frequency. The rotational speed of the target For radar carrier frequency, At the speed of light, Center of rotation for the target For bandwidth; Based on the precise estimation results of the rotation speed and rotation center, a second-order spatially variable phase error compensation is performed on the one-dimensional range image to obtain the one-dimensional range image after second-order spatially variable phase error compensation. , is represented as: ； in, For distance frequency, This indicates the number of scattering points that make up the radar echo signal. For the first The reflection coefficient at each scattering point The pulse width. To adjust the frequency of the signal, For the rotational acceleration of the target, and For the first The horizontal and vertical coordinates of the scattering points; Based on the coarse estimation result of the rotational acceleration, a fine search interval for the rotational acceleration is determined. Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to a preset fine search step size to obtain a fine estimation result of the rotational acceleration, including: Based on the coarse estimate of the rotational acceleration, the fine search interval for the rotational acceleration is determined as follows: ,in, This is a coarse estimate of the rotational acceleration. This is the coarse search step size; Within the fine search interval, a one-dimensional search is performed on the rotational acceleration according to a preset fine search step size to obtain a fine estimate of the rotational acceleration; wherein, the one-dimensional search process for the rotational acceleration is expressed as follows: ； in, To compensate for the image entropy after the quadratic spatial phase error, This is a precise estimate of the rotational acceleration; Based on the precise estimation result of the rotational acceleration, a second azimuth-based spatially varying phase error is compensated and an azimuth Fourier transform is performed on the one-dimensional range image after the second range spatially varying phase error compensation to obtain a focused ISAR image, represented as: ； in, A focused ISAR image. One-dimensional range image after secondary range spatial variation phase error compensation The discretization result, The rotational acceleration related to the target, For azimuth resolution, For imaging coherence processing time, This is the step size factor.

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