A sea surface ship target SAR imaging method based on inverse conjugate-frequency modulation Z transform and maximum likelihood estimation

Abstract

This application discloses a SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation, belonging to the field of radar target imaging technology. The method includes: establishing a geometric motion model of the ship target based on its motion; calculating a range-time domain echo signal model based on the geometric motion model; adaptively extracting the echo signal from the echo signal model based on the inverted conjugate-frequency modulated Z-transform; establishing a linear observation equation for phase error using the echo signal to optimally estimate the two-dimensional spatially varied phase error parameters; constructing a compensation function using the optimally estimated two-dimensional spatially varied phase error parameters and performing adaptive iteration based on bandwidth contraction to transform the iterated target signal from the time domain to the image domain, obtaining the final imaging result. This application can effectively eliminate complex two-dimensional spatially varied defocus, improving image resolution and focusing quality.

Description

Technical Field

[0001] This application belongs to the field of radar target imaging technology, and in particular relates to a SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation. Background Technology

[0002] Under far-field imaging conditions, the complex motion of surface ships can typically be modeled as a superposition of three-dimensional steady motion and instantaneous higher-order vibrations (such as pitch, roll, and yaw). Range migration and phase errors caused by the overall translational motion of the target are spatially invariant, and can currently be well compensated for using range alignment and conventional autofocus algorithms. However, the unique three-dimensional oscillation of the ship target is coupled with the radar platform motion, introducing severe two-dimensional (2D) spatially varied phase errors into the echo, including phase errors that vary with range and phase errors that vary with azimuth. These errors result in varying degrees of defocus in different areas of the image, representing a core bottleneck restricting high-resolution imaging of moving targets on the surface.

[0003] Currently, motion compensation methods for two-dimensional spatially variable phase errors can be mainly divided into the following three categories: The first category is based on time-frequency analysis or signal decomposition methods (such as SPWVD, segmented clustering, etc.), which improve image quality by capturing the non-stationary characteristics of the signal. Although these methods can alleviate defocus to some extent, their azimuth resolution is often limited by the time-frequency clustering degree, and they are prone to causing discontinuities in the target structure when dealing with complex multi-scattering point targets, making it difficult to obtain high-precision focusing effects.

[0004] The second category is image focus quality optimization methods, which search for phase parameters that optimize image entropy, contrast, or sharpness. While these methods exhibit good robustness, the iterative search process is prone to getting trapped in local optima because the objective function is typically multi-peaked and non-convex. Furthermore, in large-scale observation scenarios and with massive amounts of data, these methods face enormous computational overhead, making them unsuitable for the needs of real-time monitoring in engineering applications.

[0005] The third category is based on maximum likelihood (ML) estimation methods (such as the traditional PGA algorithm and its variants). These methods utilize the statistical structure of the echo to estimate the phase error. However, existing improved PGA methods are mostly designed for stationary ground scenarios, mainly addressing range-based spatially varying errors. They are unable to effectively cope with the azimuth-based spatially varying and two-dimensional coupled phase errors unique to ship targets. Furthermore, they do not make sufficient use of the spatially varying characteristics of the signal in low signal-to-noise ratio environments, resulting in limited estimation accuracy.

[0006] In summary, achieving high-precision and robust estimation and compensation for two-dimensional spatially varying phase errors caused by complex motions while ensuring computational efficiency is a key technical challenge that urgently needs to be overcome in the field of high-resolution SAR imaging of moving targets on the sea surface. Summary of the Invention

[0007] The purpose of this application is to overcome the shortcomings of the prior art by providing a SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation. This method improves the problems in the prior art, such as two-dimensional spatially variable (2D-SV) phase defocusing of sea surface ship targets caused by complex three-dimensional oscillation, the huge computational load and easy trapping in local optima of existing optimization algorithms in large observation scenarios, and the inaccurate feature point extraction in low signal-to-noise ratio environments.

[0008] The objective of this application is achieved through the following technical solution: A SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation, the method comprising: A geometric motion model of the ship target is established based on the ship target's motion, and then a range time-domain echo signal model is calculated based on the geometric motion model. Based on the inverse conjugate-frequency modulated Z-transform, the echo signal is adaptively extracted from the echo signal model; A linear observation equation for the phase error is established based on the echo signal, and the optimal estimation of the two-dimensional spatially variable phase error parameters is performed. A compensation function is constructed using the optimally estimated two-dimensional spatially variable phase error parameters, and an adaptive iteration based on bandwidth contraction is performed to transform the iterated target signal from the time domain to the image domain, thus obtaining the final imaging result.

[0009] Furthermore, the calculation of the distance time-domain echo signal model based on the geometric motion model specifically includes: The range history from any scattering point to the radar is expanded in space under far-field conditions in the first order, and then the range history is expanded in slow time in the second order Taylor expansion to obtain the range history expansion formula, and the phase error parameter is extracted. The preprocessed distance-time domain echo signal model is constructed using the distance history expansion formula.

[0010] Furthermore, the specific steps of constructing the preprocessed range-time domain echo signal model using the range history expansion include: Translational compensation corrects for distance migration and phase errors caused by the spatially invariant distance history. After the first-order wedge transformation, the spatially variable distance migration is eliminated, and the echo signal model is obtained.

[0011] Furthermore, the adaptive extraction of the echo signal from the echo signal model based on the inverted conjugate-frequency modulated Z-transform specifically includes: The echo signal model is organized into an echo matrix. Based on the second-order phase error model, the echo matrix is ​​subjected to inversion conjugate and frequency-modulated Z-transform to obtain the RC-CZT spectrum. By searching the peak index of the RC-CZT spectrum, the azimuth Doppler centroid of the strongest scattering point is located, and the centroid is used as the center of the azimuth frequency domain window function. The instantaneous frequency curve is obtained by differentiating the phase error function of the window function, which includes range spatial variation, azimuth spatial variation and spatial invariance components. The maximum bandwidth of all scattering points is selected as the initial bandwidth to construct an iterative rectangular window filter; The rectangular window filter is used to perform a circular shift operation on each distance gate signal in the azimuth frequency domain, moving the centroid to a zero frequency position, and then windowing is performed using the rectangular window filter. The spectrum is restored by inverse circular shift transform, and the extracted echo signal is obtained by inverse fast Fourier transform in azimuth direction.

[0012] Furthermore, the step of establishing a linear observation equation for the phase error based on the echo signal and performing optimal estimation of the two-dimensional spatially variable phase error parameters specifically includes: Taking advantage of the small change in phase error between adjacent pulses, the phase of each range-gated signal is expanded to establish a linear observation model of the phase error, which is an observation matrix. Assuming the noise follows an independent and identically distributed complex Gaussian distribution, construct the probability density function of the observation matrix; Then, based on the observation matrix, a stationary point equation for the parameter vector is established. Using matrix differential theory and conjugate operations, the closed-form solution of the maximum likelihood estimate of the phase error parameter is derived.

[0013] Furthermore, the construction of the compensation function using the optimally estimated two-dimensional spatially variable phase error parameters specifically includes: The second-order coefficients of the range spatial variation, azimuth spatial variation, and spatial invariance phase error are calculated using the second-order coefficients obtained from the optimal estimation, and the corresponding compensation functions are constructed.

[0014] Furthermore, the step of performing adaptive iteration based on bandwidth contraction to transform the iterated target signal from the time domain to the image domain specifically includes: Each iteration reduces the window length of the rectangular window to half of the previous one, and then performs the adaptive extraction of the echo signal and the optimal estimation of the two-dimensional spatially variable phase error parameters. When the last window length meets the preset threshold, the iteration terminates. The two-dimensional echo data after the final iteration compensation is subjected to azimuth-to-Fourier transform to transform the target signal from the time domain to the image domain.

[0015] The beneficial effects of this application are as follows: The high-precision imaging method for ship targets on the sea surface proposed in this application, based on inverted conjugate-frequency modulated Z-transform (RC-CZT) and maximum likelihood estimation, can adaptively extract sub-band signals from centroids in different azimuths and achieve statistical optimal compensation by using the derived two-dimensional spatially variable phase error closed-form solution. While ensuring computational efficiency, it significantly improves the imaging clarity and noise resistance of ship targets under complex sea conditions. Attached Figure Description

[0016] Figure 1 This is a flowchart of a SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation; Figure 2 This is a schematic diagram of ship point clouds; Figure 3 This is a schematic diagram of echo defocus analysis; Figure 4 This is a schematic diagram of ship defocusing; Figure 5 This is a schematic diagram of the iterative process, where, Figure 5 (a) is a schematic diagram of the phase extremum iteration. Figure 5 (b) is a schematic diagram of the image entropy iteration process. Figure 5 (c) is a schematic diagram of the image sharpness iteration process. Figure 5 (d) is a schematic diagram of the image contrast iteration process; Figure 6 This is a schematic diagram comparing the imaging results, in which, Figure 6 (a) is a schematic diagram of the imaging results from the range-Doppler algorithm. Figure 6 (b) is a schematic diagram of the imaging results of the KT-PGA algorithm. Figure 6 (c) is a schematic diagram of the smoothed pseudo-WVD imaging results. Figure 6 (d) is a schematic diagram of the imaging results of the small entropy algorithm. Figure 6 (e) is a schematic diagram of the imaging results of the product-type GCPF algorithm. Figure 6 (f) is a schematic diagram of the imaging results of the method proposed in this embodiment. Detailed Implementation

[0017] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0018] Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] How to achieve high-precision and robust estimation and compensation of two-dimensional spatially varying phase errors caused by complex motion while ensuring computational efficiency is a key technical challenge that urgently needs to be overcome in the field of high-resolution SAR imaging of moving targets on the sea surface.

[0020] To address the aforementioned technical problems, the following embodiments of a SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation are proposed in this application.

[0021] This embodiment discloses a high-precision SAR imaging method for sea surface ship targets based on inverted conjugate-chirp Z-transform and maximum likelihood estimation. A reversal conjugate-chirp Z-transform (RC-CZT) is designed. By inverting and conjugating the echo signal and combining it with CZT, pure signals from strong scattering points with different azimuth centroids are adaptively and accurately extracted, laying the foundation for subsequent phase error estimation. Subsequently, based on the closed-form solution of the two-dimensional (2D) spatially varied phase error derived from maximum likelihood estimation, high-precision estimation of residual non-spatially varied phase error, range spatially varied phase error, and azimuth spatially varied phase error under noisy conditions is achieved, approaching statistical optimality. Finally, through matrix-based phase error compensation processing, focused imaging of the target is achieved.

[0022] Reference Figure 1 ,like Figure 1 The diagram shows a flowchart of a SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation. The method includes the following steps: Step 1: Establish the geometric motion model and echo model of the ship target.

[0023] The system parameters and motion target parameters used in this embodiment are shown in Table 1. Table 1 System Parameters and Motion Target Parameters First, establish an XYZ coordinate system, with the ship's center of mass as the origin, the bow direction as the X-axis, and the local normal direction as the Z-axis. Then, cross-multiply the Z-axis and X-axis and use a right-hand screw to obtain the Y-axis. (Refer to...) Figure 2 ,like Figure 2 The image shown is a point cloud diagram of a ship, illustrating its shape. The ship target exhibits translational and three-dimensional oscillating motions. The ship's own propulsion causes translational motion, with its velocity vector being... , where is the coordinate of a scattering point on the ship. Due to factors such as sea waves, wind, or ship turning, the ship may experience three-dimensional oscillations. These oscillations around the X, Y, and Z axes are called roll, pitch, and yaw motions, respectively. The total rotation axis ω is obtained by combining these three axes. The airborne radar platform flies at a certain altitude, with a velocity vector of . .

[0024] Considering the translational motion and axial three-dimensional oscillations (pitch, roll, and yaw) of the ship target, the distance history from the scattering point p to the radar can be expressed as: ; in, It is the difference in position vectors between the radar and the target's centroid at the reference time. It is the difference in velocity vectors between the radar and the target. It refers to location and time. It is the rotation matrix at time. These are the coordinates of the scattering point.

[0025] Next, under far-field conditions, a first-order expansion of this distance history is performed along space: ; in yes Direction of sight at any given moment: ; Next, we will analyze the location and time relative to history. The second-order Taylor expansion is used to extract the key phase error parameters that cause image defocusing. The expansion is expressed as:

[0026] The projection of the scattering point in the negative distance direction is: The projection in the negative azimuth direction is , It is the azimuth scaling factor. and These are the range spatial variation coefficient and the azimuth spatial variation coefficient, respectively. The distance to history is empty and unchanging.

[0027] Next, the obtained range history expansion is used to construct a preprocessed range-time domain echo signal model. Firstly, translational compensation can be used to correct... The resulting distance migration, and partial correction The resulting phase error is eliminated by a first-order wedge transform to remove the spatially variable range migration. Therefore, the preprocessed range-time domain echo can be expressed as: ; in, It is the amplitude of the scattering point. It is the Singer function. It is the range resolution. It's the wavelength. It is the imaginary unit. These are non-space variable coefficients.

[0028] Analyze the echo, referring to Figure 3 and Figure 4 ,like Figure 3 The diagram shown is a schematic of echo defocus analysis. Figure 4 The diagram shown is a schematic of the ship's defocusing. Its non-space-varying phase, range-space-varying phase, and azimuth-space-varying phase time-varying characteristics are as follows: Figure 3 As shown, the second row displays the corresponding defocused azimuth profile, with the directly imaged blurred image as follows. Figure 4 As shown above, the analysis indicates that it is necessary to... , as well as Only by estimating and compensating for the spatially varying phase error can target focusing be achieved.

[0029] Step 2: Adaptive extraction of space-varying signals based on RC-CZT.

[0030] For the echo signal of the i-th azimuth pulse with the k-th range gate after preprocessing in step one Considering the discretization phase error and noise effects, the echo signal is extracted using RC-CZT and bandwidth analysis. The specific process is as follows: First, based on the second-order phase error model, the echo matrix is ​​subjected to flip conjugation and CZT processing, i.e. ; in, Indicates the number of azimuth pulses. It is the complex amplitude of the scattering point. This refers to performing a Fast Fourier Transform along the azimuth direction. It is an intersection term.

[0031] Secondly, by searching for the peak value of the RC-CZT spectral plane, the azimuth Doppler centroid of the strongest scattering point is determined, and it is used as the center of the azimuth frequency domain window function.

[0032] Next, the window function length is determined. The phase error function, which includes range spatial variation, azimuth spatial variation, and spatial invariance components, is differentiated to obtain the instantaneous frequency curve. ; in , , It is in discrete form , as well as .

[0033] Based on the difference between the maximum and minimum frequency values, the frequency domain bandwidth is derived to satisfy the following relationship: ; Select the maximum bandwidth of all scattering points Using the initial bandwidth, construct the rectangular window filter for the iterth iteration: ; Where is the bandwidth of the iter-th iteration, when iter=1, In the iter-th iteration, After obtaining the filter, a circular shift operation is performed on each range gate signal in the azimuth frequency domain to move the Doppler centroid to the zero-frequency position, and the aforementioned rectangular window is uniformly applied for windowing. Subsequently, the spectrum is restored by inverse circular shift transform, and then subjected to inverse fast Fourier transform (IFFT) in the azimuth direction to obtain the extracted echo signal, ensuring the accuracy of subsequent phase error estimation.

[0034] Step 3: Derive the maximum likelihood (ML) estimation method for two-dimensional spatially variable phase error.

[0035] For the echo signal extracted in step two, a linear observation equation for the phase error is established, and the statistical optimal estimation of the two-dimensional spatially variable phase error parameter is achieved by combining the maximum likelihood estimation theory. The specific process is as follows: First, a linear observation model of the phase error is constructed. Taking advantage of the small change in phase error between adjacent pulses, the phase of each range-gated signal is expanded to establish the parameters to be solved. , , The linear observation equations formed are: ; in It is an ideal noise-free echo signal. It is a noise signal.

[0036] Next, the observation equations are rearranged into matrix form: ; in, , , This indicates column vectorization processing. , The observation matrix is ​​expressed as: ; Secondly, the closed-form solution for the maximum likelihood estimation of the phase error is derived. Assuming noise... The observation vector follows an independent and identically distributed complex Gaussian distribution. The likelihood function is expressed as follows: ; By observing the vector Taking the logarithm of the likelihood function, further... Find the first derivative and set it to zero to establish the stationary point equation. Using matrix differential theory and conjugate operations, derive the phase error parameters. The optimal estimated closed-form solution is expressed as: ; Step 4: Implement two-dimensional spatially variable phase compensation and adaptive shrinkage iterative focusing Using the second-order phase error coefficients estimated in step three, a progressively refined focusing of the target signal is achieved by constructing a compensation function and executing adaptive iteration based on bandwidth contraction. In the phase error estimation and compensation, only the optimal result obtained from the maximum likelihood estimation in step three needs to be used. This allows for the very accurate and rapid calculation of the second-order coefficients of the spatially variable range, spatially variable azimuth, and spatially invariant phase errors. Then, based on the phase error expansion model from step one, the corresponding compensation function is constructed. Since the phase error estimation formula is highly effective, the phase error spectrum bandwidth can be rapidly reduced through phase error estimation and compensation. This ensures that when the window length is halved in the next iteration, the remaining phase error spectrum can still be completely captured, making the algorithm exponentially efficient. The iteration terminates when the final window length is 4-6 units. (Refer to...) Figure 5 ,like Figure 5 The diagram shows the iterative process, where, Figure 5 (a) is a schematic diagram of the phase extremum iteration. Figure 5 (b) is a schematic diagram of the image entropy iteration process. Figure 5 (c) is a schematic diagram of the image sharpness iteration process. Figure 5 (d) is a schematic diagram illustrating the image contrast iteration process. (From...) Figure 5 The iterative changes of phase extrema, image entropy (IE), image sharpness (IS), and image contrast (IC) can be observed.

[0037] Finally, an azimuth-to-Fourier transform is performed on the two-dimensional echo data after final iterative compensation, transforming the signal from the time domain to the image domain to obtain the final imaging result. (Refer to...) Figure 6 ,like Figure 6 The image shown is a schematic diagram comparing the imaging results.

[0038] The results show that the method provided in this embodiment has robust focusing capabilities under complex scattering distributions. Compared with several commonly used methods (range Doppler algorithm, KT-PGA algorithm, smooth pseudo WVD algorithm, minimum entropy algorithm, and product-type GCPF algorithm), it can clearly recover detailed features such as ship masts. This method can improve upon existing technologies for two-dimensional spatial variation (2D-SV) phase defocusing of surface ship targets caused by complex three-dimensional oscillations, the huge computational cost and susceptibility to local optima in existing optimization algorithms under large observation scenarios, and the inaccurate feature point extraction in low signal-to-noise ratio environments.

[0039] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation, characterized in that, The method includes: A geometric motion model of the ship target is established based on the ship target's motion, and then a range time-domain echo signal model is calculated based on the geometric motion model. Based on the inverse conjugate-frequency modulated Z-transform, the echo signal is adaptively extracted from the echo signal model; A linear observation equation for the phase error is established based on the echo signal, and the optimal estimation of the two-dimensional spatially variable phase error parameters is performed. A compensation function is constructed using the optimally estimated two-dimensional spatially variable phase error parameters, and an adaptive iteration based on bandwidth contraction is performed to transform the iterated target signal from the time domain to the image domain, thus obtaining the final imaging result.

2. The SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation as described in claim 1, characterized in that, The calculation of the distance time-domain echo signal model based on the geometric motion model specifically includes: The range history from any scattering point to the radar is expanded in space under far-field conditions in the first order, and then the range history is expanded in slow time in the second order Taylor expansion to obtain the range history expansion formula, and the phase error parameter is extracted. The preprocessed distance-time domain echo signal model is constructed using the distance history expansion formula.

3. The SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation as described in claim 2, characterized in that, The specific steps of constructing the preprocessed range-time domain echo signal model using the range history expansion include: Translational compensation corrects for distance migration and phase errors caused by the spatially invariant distance history. After the first-order wedge transformation, the spatially variable distance migration is eliminated, and the echo signal model is obtained.

4. The SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation as described in claim 1, characterized in that, The adaptive extraction of the echo signal from the echo signal model based on the inverse conjugate-frequency modulated Z-transform specifically includes: The echo signal model is organized into an echo matrix. Based on the second-order phase error model, the echo matrix is ​​subjected to inversion conjugate and frequency-modulated Z-transform to obtain the RC-CZT spectrum. By searching the peak index of the RC-CZT spectrum, the azimuth Doppler centroid of the strongest scattering point is located, and the centroid is used as the center of the azimuth frequency domain window function. The instantaneous frequency curve is obtained by differentiating the phase error function of the window function, which includes range spatial variation, azimuth spatial variation and spatial invariance components. The maximum bandwidth of all scattering points is selected as the initial bandwidth to construct an iterative rectangular window filter; The rectangular window filter is used to perform a circular shift operation on each distance gate signal in the azimuth frequency domain, moving the centroid to a zero frequency position, and then windowing is performed using the rectangular window filter. The spectrum is restored by inverse circular shift transform, and the extracted echo signal is obtained by inverse fast Fourier transform in azimuth direction.

5. The SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation as described in claim 1, characterized in that, The process of establishing a linear observation equation for the phase error based on the echo signal and performing optimal estimation of the two-dimensional spatially variable phase error parameters specifically includes: Taking advantage of the small change in phase error between adjacent pulses, the phase of each range-gated signal is expanded to establish a linear observation model of the phase error, which is an observation matrix. Assuming the noise follows an independent and identically distributed complex Gaussian distribution, construct the probability density function of the observation matrix; Then, based on the observation matrix, a stationary point equation for the parameter vector is established. Using matrix differential theory and conjugate operations, the closed-form solution of the maximum likelihood estimate of the phase error parameter is derived.

6. The SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation as described in claim 1, characterized in that, The specific steps for constructing the compensation function using the optimally estimated two-dimensional spatially variable phase error parameters include: The second-order coefficients of the range spatial variation, azimuth spatial variation, and spatial invariance phase error are calculated using the second-order coefficients obtained from the optimal estimation, and the corresponding compensation functions are constructed.

7. The SAR imaging method for sea surface ship targets based on inverted conjugate-frequency modulated Z-transform and maximum likelihood estimation as described in claim 4, characterized in that, The execution of adaptive iteration based on bandwidth contraction, transforming the iterated target signal from the time domain to the image domain, specifically includes: Each iteration reduces the window length of the rectangular window to half of the previous one, and then performs the adaptive extraction of the echo signal and the optimal estimation of the two-dimensional spatially variable phase error parameters. When the last window length meets the preset threshold, the iteration terminates. The two-dimensional echo data after the final iteration compensation is subjected to azimuth-to-Fourier transform to transform the target signal from the time domain to the image domain.

Images