Distributed spaceborne synthetic aperture radar coherent imaging method and equipment

Abstract

This application proposes a heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method and device. By combining the spectrum extrapolation method and compressed sensing theory, it can effectively compensate for the imaging degradation caused by range spectrum mismatch and azimuth aperture loss in heterogeneous frequency distributed observation scenarios constructed from real SAR observation data. It significantly improves image clarity, target focus and detail preservation, thus demonstrating superior imaging performance compared to traditional methods.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and device for coherent imaging of a distributed spaceborne synthetic aperture radar with different frequencies. Background Technology

[0002] With the rapid development of distributed synthetic aperture radar (SAR) systems, the contradictions between performance indicators such as resolution, coverage swath, and revisit period of single-satellite platforms are becoming increasingly prominent. To overcome the physical constraints of traditional single-platform systems, multi-frequency distributed spaceborne SAR has gradually become an important development direction for high-resolution SAR Earth imaging. Compared to single-satellite systems, multi-frequency distributed spaceborne SAR can reuse and optimize resource allocation in the time, space, and frequency dimensions, achieving higher resolution, wider coverage, and stronger anti-interference capabilities through multi-platform information fusion.

[0003] However, in practical engineering applications, distributed radar systems often struggle to obtain continuous and complete observation data in both the range and azimuth directions due to limitations in the number of platforms, orbital layout, hardware performance, and data acquisition conditions. In the range direction, because the center carrier frequencies of signals transmitted by different sub-satellites differ, direct echo fusion leads to range-spectrum mismatch, resulting in significant phase distortion and sidelobe enhancement in the range direction. In the azimuth direction, limited by observation time and multi-platform coordination, only discontinuous, slow-time echo data is often obtained, resulting in incomplete azimuth equivalent aperture, leading to main lobe broadening, sidelobe elevation, and even grating lobe structures.

[0004] Existing traditional SAR imaging algorithms based on the assumption of complete data are difficult to apply directly to the above-mentioned multi-frequency distributed spaceborne SAR scenarios, especially when there are both range-spectral misalignments and missing azimuth apertures. Conventional direct stitching and conventional focusing processing will severely limit the realization of the system's potential resolution advantages. Summary of the Invention

[0005] This application proposes a heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method and device, which can solve one of the problems existing in the background technology.

[0006] To achieve the above objectives, this application adopts the following technical solution:

[0007] Firstly, a method for coherent imaging using a distributed, multi-frequency spaceborne synthetic aperture radar is provided, including:

[0008] Obtain synthetic aperture radar (SAR) echo data of the same observation area collected by several sub-satellites;

[0009] Based on the established unified coordinate system, the SAR echo data collected by each sub-satellite is preprocessed to obtain the heterogeneous distributed SAR signal to be processed.

[0010] Perform a range-to-Fourier transform on the distributed SAR signal to be processed to obtain a range spectrum sequence;

[0011] Based on the forward linear prediction model and the backward linear prediction model constructed for the range spectrum sequence for each range gate, a recursive algorithm is adopted. Under the framework of the autoregressive model, the prediction coefficients of the autoregressive model are recursively updated by minimizing the joint prediction error objective function. Then, the estimated prediction coefficients are used to extrapolate the unknown frequency bands at the boundary of the range spectrum sequence point by point to obtain the extrapolated range spectrum signal, so as to realize the range spectrum alignment and bandwidth expansion of different sub-satellites. The joint prediction error is jointly determined by the forward prediction error of the forward linear prediction model and the backward prediction error of the backward linear prediction model.

[0012] Based on the constructed multi-task compressed sensing joint recovery model, the missing azimuth aperture data in the range spectrum extrapolated signal is jointly reconstructed to obtain the recovered two-dimensional frequency domain signal. The multi-task compressed sensing joint recovery model is constructed based on the sparsity of the range spectrum extrapolated signal in the two-dimensional frequency domain and the fact that its real and imaginary parts share a common support set characteristic.

[0013] Furthermore, coherent imaging processing is performed based on the recovered two-dimensional frequency domain signal.

[0014] In one possible design of the first aspect, the heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method further includes:

[0015] From all the sub-satellites, a reference sub-satellite is determined;

[0016] Furthermore, based on the determined reference sub-satellite, a unified coordinate system is established, which includes a unified range-frequency coordinate system and a unified azimuth-time coordinate system.

[0017] In one possible design of the first aspect, the preprocessing specifically includes:

[0018] The SAR echo data of each sub-satellite are rearranged in terms of range spectrum according to the center carrier frequency difference of each sub-satellite relative to the reference sub-satellite;

[0019] Furthermore, based on the slow time center offset of each sub-satellite relative to the reference sub-satellite, the SAR echo data of each sub-satellite after the range spectrum rearrangement is rearranged in the azimuth time domain to obtain the unprocessed heterogeneous distributed SAR signal.

[0020] In one possible design approach of the first aspect, distance spectrum rearrangement specifically involves:

[0021] Based on the first reference satellite For reference, construct the range-frequency shift function H1(i) for the i-th sub-satellite:

[0022] in, Indicates distance in terms of time. For any integer, Indicates the first Subsatellite relative to reference subsatellite The center carrier frequency difference, For the first The center carrier frequency of the satellite As a reference subsatellite The center carrier frequency;

[0023] SAR echo data after range spectrum rearrangement for:

[0024] in, For location, slow time, This is the SAR echo data before rearrangement;

[0025] At this time, the distance frequency variable satisfy:

[0026] in, This refers to the bandwidth of a single signal.

[0027] In one possible design approach of the first aspect, orientation temporal rearrangement specifically involves:

[0028] With the second reference satellite SAR echo data after range spectrum rearrangement For reference, the first SAR echo data after range spectrum rearrangement of sub-satellites Represented as:

[0029] Among them, the Subsatellite relative to reference subsatellite The slow time center offset is ;

[0030] No. Effective observation range of the satellite satisfy:

[0031] in, This indicates the effective observation duration of a single sub-satellite in the azimuth time slow.

[0032] Construct the azimuth time shift function H2(i):

[0033] in, The distributed SAR signal to be processed is obtained by rearranging the azimuth frequency in the time domain. for:

[0034] in, Indicates the first The two-dimensional time-domain SAR echo signal obtained from the satellite after range spectrum rearrangement and azimuth time-domain rearrangement. Indicates the first Corresponding to the sub-satellite The azimuth frequency domain signal obtained by performing a Fourier transform along the azimuth slow time;

[0035] In one possible design approach for the first aspect, for the third Distance spectrum sequence of distance gates ,in, Given the number of sampling points in the distance frequency domain, the forward linear prediction model is as follows:

[0036] The backward linear prediction model is as follows:

[0037] in, Indicates the sub-satellite number, Indicates the index of prediction coefficients. Indicates the order of the autoregressive model. Indicates the first The forward linear prediction value obtained in the next iteration Indicates the first The backward linear prediction value obtained in the next iteration and They represent the first The prediction coefficients of the forward linear prediction model and the backward linear prediction model during the first iteration. and They represent the first After the range spectrum is rearranged and the azimuth time domain is rearranged, the satellite is in the 1st... At the distance from the door, the first The and the first The distance spectrum value corresponding to each distance frequency domain sampling point;

[0038] The objective function for the joint prediction error is:

[0039] in, Forward prediction error, This is the backward prediction error. The number of sub-satellites participating in the synthesis;

[0040] Distance spectrum extrapolated signal for:

[0041] in, Indicates the first The frequency domain signal obtained by extrapolating the range spectrum of the satellite. Indicates by The SAR echo signal obtained by performing an inverse range-frequency domain transform back to the two-dimensional time domain This indicates that the autoregressive prediction model is used to predict the first... The spectrum estimate obtained by extrapolating and predicting the unknown frequency bands at the distance of the satellite from the spectrum boundary. This indicates the newly added interval relative to the original frequency band range after extrapolation.

[0042] In one possible design of the first aspect, the heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method further includes: using a reference function Multiplying the signal obtained by the extrapolation of the range spectrum with the complete SAR signal yields the coarsely focused signal. Specifically:

[0043] Where A is the measurement matrix, For a complete SAR signal, The closest slope distance. For radar speed, For the operating wavelength, The frequency is a linear modulation along the distance, and c is the speed of light;

[0044] Due to the sparsity of the signal in the two-dimensional frequency domain after the distance spectrum extrapolation, the following equation holds:

[0045] in, Indicates the signal after coarse focusing The two-dimensional frequency domain signal obtained after two-dimensional Fourier transform It is a sparse representation base;

[0046] The corresponding complex signal compressed sensing observation model is:

[0047] in, It is a two-dimensional frequency domain sparse coefficient matrix. For undersampled observation data, This is the equivalent sensing matrix.

[0048] The real signal model corresponding to the complex signal compressed sensing observation model is:

[0049] Where Re represents the real part and Im represents the imaginary part. Represents the observations of complex numbers The real-valued observation vector obtained after real-valued expansion and They represent the observations of complex numbers respectively. and The real-valued observation vector obtained after real-valued expansion;

[0050] Therefore, the real-valued azimuth-spaced aperture signal observation model is obtained as follows:

[0051] The multi-task compressed sensing joint recovery model is as follows:

[0052] in, For azimuth frequency The joint sparse matrix constructed below, For distance frequency The sparse representation to be estimated below, Indicates For the variables to be optimized, minimize the mixture of the joint sparse matrix. Using norms to solve for the joint sparse recovery of missing azimuth aperture data Indicates mixing Norm, Indicates the slow time in the direction. Next The real-valued undersampled observation vector corresponding to each distance-directed sampling location. Indicates the number of distance-oriented pulse sampling points. This indicates the number of azimuth pulse sampling points for the interval aperture signal. This represents the sparse representation of the real signal to be estimated. For the equivalent sensing matrix of the real signal, This is the error tolerance.

[0053] In one possible design approach of the first aspect, based on the constructed multi-task compressed sensing joint recovery model, the missing azimuth aperture data in the range spectrum extrapolated signal is jointly reconstructed, specifically including:

[0054] We introduce a hierarchical Bayesian model, assuming that all tasks share the same set of sparse hyperparameters. By introducing the hyperparameter γ, the sparse components are... To perform adaptive adjustment, the prior model is established as follows:

[0055] in, Represented by vector The elements in the matrix form a diagonal matrix consisting of the main diagonal elements.

[0056] Under the prior model, the joint likelihood function of the multi-task data is:

[0057] in, ; Indicates the slow time in the direction. The following is a set of observation data consisting of observation vectors corresponding to multiple reconstruction tasks. Indicates a normal distribution. For noise variance;

[0058] By maximizing the posterior probability, the two-dimensional frequency domain sparse coefficient matrix to be estimated is obtained. sparse hyperparameters and noise variance The joint estimation is then used to obtain the recovered two-dimensional frequency domain signal. .

[0059] In one possible design approach of the first aspect, coherent imaging processing is performed based on the recovered two-dimensional frequency domain signal, specifically including:

[0060] The recovered two-dimensional frequency domain signal Perform a two-dimensional inverse Fourier transform to obtain the coarse-focused time-domain signal. ;

[0061] coarse-focused time-domain signal With reference function The conjugate multiplication yields the reconstructed aperture SAR signal. This is to complete the coherent imaging process.

[0062] In a second aspect, an electronic device is provided, comprising: a processor and a memory coupled to the processor, the memory for storing a computer program; the processor for executing the computer program stored in the memory such that the electronic device performs the heterogeneous distributed spaceborne synthetic aperture radar coherent imaging method as described in any possible implementation of the first aspect.

[0063] Beneficial effects:

[0064] Based on the above technical solution, firstly, SAR echo data collected by multiple sub-satellites from the same observation area are acquired, and the center carrier frequency, signal bandwidth, and slow-time observation interval of each sub-satellite are determined. Then, a unified range-frequency coordinate system and a unified azimuth-time coordinate system are established, and the range spectrum and azimuth-time domain of each sub-satellite echo are rearranged to construct a heterogeneous distributed spaceborne SAR signal model. Next, a range-direction Fourier transform is performed on the rearranged sub-satellite echoes, and an iterative autoregressive model is used to extrapolate the unknown frequency bands at the range spectrum boundaries to achieve range spectrum alignment and bandwidth expansion for different sub-satellites. Finally, for the azimuth aperture spacing that still exists after extrapolation, a reference function is constructed to adjust the signal. Coarse focusing is used to establish an azimuth-interval aperture undersampling measurement model. Then, a multi-task compressed sensing method is used to jointly reconstruct the missing azimuth aperture data to obtain the recovered two-dimensional frequency domain signal. Finally, the recovered two-dimensional frequency domain signal is transformed back to the two-dimensional time domain and coherent imaging processing is completed to obtain the reconstructed aperture SAR image. In this way, by combining the spectrum extrapolation method and compressed sensing theory, it is possible to effectively compensate for the imaging degradation caused by range-spectrum mismatch and missing azimuth aperture in a heterogeneous distributed observation scenario constructed from real SAR observation data. This significantly improves image clarity, target focus, and detail preservation, thus demonstrating superior imaging performance compared to traditional methods. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0066] Figure 1 This is a schematic diagram of the overall process of the heterogeneous frequency distributed spaceborne SAR coherent imaging method provided in the embodiments of this application;

[0067] Figure 2 This is a schematic diagram of the geometric configuration of a heterogeneous distributed spaceborne SAR provided in an embodiment of this application;

[0068] Figure 3 This is a two-dimensional time-domain and spectrum diagram of the signals of each sub-satellite provided in the embodiments of this application, wherein, Figure 3 (a) is a two-dimensional time-domain schematic diagram and a corresponding two-dimensional spectrum diagram of the range pulse of the first sub-satellite after compression. Figure 3 (b) is a two-dimensional time-domain schematic diagram and a corresponding two-dimensional spectrum diagram of the range pulse of the second sub-satellite after compression. Figure 3 (c) is a two-dimensional time-domain schematic diagram and a corresponding two-dimensional spectrum diagram of the range pulse of the third sub-satellite after compression;

[0069] Figure 4 This is a schematic diagram of the complete imaging results of the measured data provided in the embodiments of this application;

[0070] Figure 5 This is a schematic diagram showing the local area imaging comparison of measured data provided in an embodiment of this application, wherein, Figure 5 (a) shows the imaging results of three typical local regions after processing using traditional methods. Figure 5 (b) is the imaging result of the corresponding local area after processing using the method of this embodiment. Detailed Implementation

[0071] 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.

[0072] It should be noted that although functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification and the above-mentioned figures are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0073] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0074] The following description, in conjunction with the accompanying drawings and embodiments, further illustrates the heterogeneous frequency distributed spaceborne SAR coherent imaging method provided in this embodiment. However, the scope of protection of this embodiment is not limited to the following embodiments.

[0075] like Figures 1 to 5 As shown, the heterogeneous frequency distributed spaceborne SAR coherent imaging method provided in this embodiment includes the following steps:

[0076] S1. Acquire SAR echo data collected by multiple sub-satellites from the same observation area, and determine the center carrier frequency, signal bandwidth, and slow-time observation interval of each sub-satellite;

[0077] S2. Based on the SAR echo data obtained in step S1, the center carrier frequency, signal bandwidth, and slow-time observation interval of each sub-satellite, establish a unified range-frequency coordinate system and a unified azimuth-time coordinate system. Rearrange the range spectrum of each sub-satellite echo according to the center carrier frequency difference of each sub-satellite relative to the reference sub-satellite, and rearrange the azimuth-time domain of each sub-satellite echo according to the slow-time center offset of each sub-satellite relative to the reference sub-satellite to obtain the heterogeneous distributed SAR signal to be processed.

[0078] S3. Based on the distributed SAR signal to be processed obtained in step S2, perform range-to-Fourier transform on the rearranged distributed SAR signal to be processed, and establish a forward linear prediction model and a backward linear prediction model for the range spectrum sequence of each range gate. A Burg recursive algorithm is adopted. Under the autoregressive model (AR) framework, the AR prediction coefficients are recursively updated by minimizing the objective function of the joint mean square prediction error of the forward prediction error and the backward prediction error. Then, the estimated AR prediction coefficients are used to extrapolate the unknown frequency bands of the range spectrum boundary point by point to achieve range spectrum alignment and bandwidth expansion of different sub-satellites.

[0079] S4. Based on the signal after extrapolation of the range spectrum in step S3, construct a reference function for the still existing azimuth aperture interval and multiply it with the signal to perform coarse focusing. Based on the coarsely focused signal, establish an azimuth interval aperture undersampling measurement model.

[0080] S5. Based on the azimuth interval aperture undersampling measurement model established in step S4, decompose the complex signal corresponding to the undersampling measurement model into real and imaginary parts, construct a multi-task compressed sensing joint recovery model with a common support set, and jointly reconstruct the missing azimuth aperture data to obtain the recovered two-dimensional frequency domain signal.

[0081] S6. Based on the recovered two-dimensional frequency domain signal obtained in step S5, transform the recovered two-dimensional frequency domain signal back to the two-dimensional time domain, and multiply it with the conjugate of the reference function to obtain the reconstructed aperture SAR signal. Then, perform coherent imaging processing based on the reconstructed aperture SAR signal to obtain the reconstructed aperture SAR image.

[0082] Step S1, distributed spaceborne SAR echo acquisition, specifically includes the following steps:

[0083] Assume there is a total Sub-satellite, the first The linear frequency modulated signal transmitted by the satellite is represented as:

[0084] in For the transmit pulse width, For distance-directed linear frequency modulation, For the first The center carrier frequency of the satellite Indicates distance in terms of time. Represents a rectangular window function. Indicates by the first Carrier frequency of the satellite center The resulting carrier frequency phase term, This represents the range-direction second-order phase modulation term corresponding to the linear frequency modulated signal, used to describe the frequency modulation characteristics of the transmitted signal as a function of fast time within the pulse width. For any two different sub-satellites, the following condition must be met:

[0085] in and Yes The value of , for the The SAR echo signal received by the satellite is represented as follows:

[0086] in, For location, slow time, For the first The slant range from the satellite to the target. It is the speed of light. Because... Because of the differences between the sub-satellites, the echoes from each sub-satellite exhibit a spectral misalignment distribution under a unified distance-frequency axis. At the same time, since the start and end times of each sub-satellite's observation of the same observation area are different, each sub-satellite corresponds to a different continuous sub-aperture in the azimuth direction, resulting in an overall intermittent sampling structure.

[0087] Step S2, the two-dimensional rearrangement and the construction of the heterogeneous frequency distributed SAR signal model, specifically includes the following steps:

[0088] To achieve a unified rearrangement of the range spectra of different sub-satellites, a sub-satellite must first be designated as a reference sub-satellite, and a range-frequency shift function is constructed using this reference sub-satellite as a reference. The reference sub-satellite is used to establish a unified range-frequency coordinate system and a unified azimuth-time coordinate system. Its selection does not change the processing flow of this method, but only affects the frequency and time shifts of each sub-satellite relative to the reference sub-satellite. In actual processing, a sub-satellite whose center carrier frequency is located in the middle of the carrier frequency sequence of all sub-satellites and whose slow-time observation center is closest to the center of the overall synthetic aperture can be selected as the reference sub-satellite to reduce the maximum frequency and maximum slow-time shifts of other sub-satellites relative to the reference sub-satellite; the reference sub-satellite... Construct a distance-frequency shift function for reference:

[0089] in Let be any integer, and , For the first Subsatellite relative to reference subsatellite The center carrier frequency difference; and:

[0090] The signal after the distance spectrum rearrangement can be written as:

[0091] At this time, the distance frequency variable satisfy:

[0092] in The bandwidth of a single signal; therefore, the first... The satellite echoes are shifted to the corresponding center frequency position in a unified range-frequency coordinate system, thereby eliminating the overall range spectrum shift caused by the difference in the center carrier frequency.

[0093] There is a discontinuity in the azimuth and time domains among multiple stars, defined as follows: Let be any integer, and In actual handling, The reference subsatellite can be determined based on the slow-time observation center of each subsatellite. Typically, the subsatellite whose slow-time observation center is closest to the overall synthetic aperture center is selected as the baseline subsatellite. Based on the signal, the first The radar signal of a satellite can be represented as:

[0094] Among them, the first The slow time center offset of the sub-satellite relative to the reference sub-satellite is , No. The effective observation range of the satellite satisfy:

[0095] in, This represents the effective observation duration of a single sub-satellite in the azimuth time domain; to achieve unified rearrangement of the azimuth time domains of different sub-satellites, an azimuth time shift function is constructed:

[0096] in, Since the azimuth frequency is used, the azimuth time-domain rearrangement process can be represented as:

[0097] Therefore, the consecutive sub-apertures corresponding to different sub-satellites are rearranged to their respective positions on a unified slow time axis.

[0098] The echoes of each sub-satellite, after range spectrum rearrangement and azimuth time-domain rearrangement, are synthesized to obtain the heterogeneous distributed SAR signal to be processed:

[0099] The signal exhibits a multi-subband structure described by a unified coordinate system in the range frequency domain and an interval aperture structure in the azimuth time domain. It serves as the input signal for subsequent range spectrum extrapolation and azimuth aperture recovery.

[0100] Step S3, distance spectrum extrapolation based on the iterative AR model, specifically includes the following steps:

[0101] rearranged signals Transforming to the range frequency domain yields:

[0102] in, Indicates to The range-frequency domain signal obtained by performing a fast-time Fourier transform along the range axis can then be used to... Discretization ,in This represents the number of sampling points in the distance frequency domain. This represents the number of sampling points in the azimuth time domain.

[0103] For the A distance gate will signal Treating it as a one-dimensional complex sequence, we choose the model order as... In the In this iteration, its forward linear prediction model and backward linear prediction model are respectively expressed as:

[0104] in, Indicates the sub-satellite number, Indicates the index of prediction coefficients. Indicates the order of the autoregressive model. Indicates the first The forward linear prediction value obtained in the next iteration Indicates the first The backward linear prediction value obtained in the next iteration and Indicates the first AR prediction coefficients at the first iteration, and They represent the first After the range spectrum is rearranged and the azimuth time domain is rearranged, the satellite is in the 1st... At the distance from the door, the first The and the first The distance spectrum value corresponding to the nth distance frequency domain sampling point; in the nth In the first iteration, the corresponding forward prediction error is defined as:

[0105] The corresponding backward prediction error is:

[0106] The Burg method is used to recursively update the AR model parameters by minimizing the joint mean square prediction error objective function.

[0107] in, The number of subsatellites participating in the synthesis.

[0108] During the iteration process, the order of the AR model is gradually increased, and the prediction coefficients are updated accordingly. The iteration stops when the set order or error convergence condition is reached. Then, the final AR prediction model is used to extrapolate the distance to the spectral boundary point by point to obtain the extrapolated signal.

[0109] in, Indicates the first The frequency domain signal obtained by extrapolating the range spectrum of the satellite. This represents the newly added interval relative to the original frequency band range after extrapolation; the formula will... The range spectrum data actually observed by the satellite within its original effective subband is not subject to prediction correction; the original rearranged spectrum values ​​are directly retained. Only the data from the satellite itself is not subject to prediction correction. The spectrum of the newly added interval that cannot be directly observed is extrapolated point by point for prediction, and then the extrapolated spectrum is calculated based on the distance. The signals from the satellites were directly synthesized to obtain:

[0110] The Burg recursion mechanism shown in this method can continuously correct the statistical model of the spectral sequence during the extrapolation process, reduce the accumulation of errors caused by model mismatch in the extrapolation results of the spectral boundary, and achieve effective alignment and equivalent bandwidth expansion of the range spectrum of different sub-satellites, thereby improving the range resolution.

[0111] Step S4, establishing the reference function coarse focusing and undersampling measurement model, specifically includes the following steps:

[0112] After extrapolating the range spectrum, aperture discontinuities still exist in the azimuth direction. The complete signal is defined as the partially recovered interval aperture signal, and let the complete signal be... Then there exists a measurement matrix. Make:

[0113] To ensure strong sparsity of the aperture interval signal in the transform domain, a reference function is constructed:

[0114] in The closest slope distance. For radar speed, For the operating wavelength, As a range-direction linear frequency modulation, multiplying the reference function with the complete SAR signal is equivalent to coarsely focusing the two-dimensional time-domain signal, making the target scattered energy more concentrated in the two-dimensional frequency domain.

[0115] The signal after coarse focusing is represented as:

[0116] Since SAR signals are sparse in the two-dimensional frequency domain, a transform basis can be constructed. Let be a two-dimensional inverse Fourier transform matrix, such that:

[0117] in , Indicates the signal after coarse focusing The two-dimensional frequency domain signal obtained after two-dimensional Fourier transform;

[0118] Therefore, the following equation holds:

[0119] Therefore, sparse representation bases can be constructed based on the two-dimensional inverse Fourier transform. and measurement matrix Establish a compressed sensing observation model:

[0120] in, It is a two-dimensional frequency domain sparse coefficient matrix. For undersampled observation data, The equivalent sensing matrix is ​​used; this method can transform the azimuth spacing aperture recovery problem into a sparse reconstruction problem in the two-dimensional frequency domain.

[0121] Since SAR signals are complex signals, and their real and imaginary parts share a common support set property, the complex observation model is extended to a real-valued model to establish a joint real-signal reconstruction model. The common support set property means that, under the same sparse representation basis, the sets of non-zero positions of the sparse coefficients corresponding to the real and imaginary parts of the complex signal are consistent or highly consistent. This is because the real and imaginary parts of the SAR complex signal originate from the amplitude and phase responses of the same scattering center in the same observation scene; they simply correspond to different components in the complex representation and do not change the positional distribution of the target scattering unit in the two-dimensional frequency domain sparse representation. Based on this property, a joint real-signal reconstruction model is established:

[0122] in, To extract the real part of the signal, To extract the imaginary part of the signal, Represents the observations of complex numbers The real-valued observation vector obtained after real-valued expansion and They represent the observations of complex numbers respectively. and The real-valued observation vector is obtained after real-valued expansion; thus, the real-valued azimuth-spaced aperture signal observation model is obtained as follows:

[0123] This method can transform the complex complex number recovery problem into a real number joint sparse recovery problem, thereby enhancing the sparse representation capability and improving the numerical stability and robustness of the subsequent recovery process.

[0124] Step S5, multi-task compressed sensing joint reconstruction, specifically includes the following steps:

[0125] Multiple observation vectors obtained by azimuth sampling Treating these as multiple related reconstruction tasks, the observation model is represented as follows:

[0126] Since multiple azimuth observation vectors originate from different sampling locations within the same scene, their two-dimensional frequency domain sparse representation typically exhibits consistency at non-zero support locations. Based on this characteristic, a joint sparse matrix is ​​introduced to characterize this joint sparse constraint property, and the corresponding joint sparse matrix is ​​expressed as:

[0127] A multi-task joint reconstruction model is constructed using row sparse constraints:

[0128] in, Indicates the number of distance-oriented pulse sampling points. This indicates the number of azimuth pulse sampling points for the interval aperture signal. Indicates the signal to be recovered at the azimuth frequency. The joint sparse representation matrix in the domain, This represents the sparse representation of the real signal to be estimated. For the equivalent sensing matrix of the real signal, As an error tolerance, this method demonstrates that by introducing a shared non-zero support structure among multiple reconstruction tasks, the correlation between different observation vectors can be used to jointly recover missing azimuth aperture data.

[0129] To further enhance the adaptive expressive power of the joint sparse structure, a hierarchical Bayesian model is introduced into the multi-task compressed sensing framework, assuming that each task shares the same set of sparse hyperparameters. By introducing shared hyperparameters to adaptively adjust each sparse component, the prior model is established as follows:

[0130] in, Represented by vector The elements in the matrix are diagonal matrices formed by the elements on the main diagonal.

[0131] Under this model, the joint likelihood function for multi-task data is:

[0132] in ; Indicates the slow time in the direction. The following is a set of observation data consisting of observation vectors corresponding to multiple reconstruction tasks. Indicates a normal distribution. This represents the noise variance.

[0133] By maximizing the posterior probability, the two-dimensional frequency domain sparse coefficient matrix to be estimated is obtained. sparse hyperparameters and noise variance The joint estimation of these structural parameters, using the method described above, allows for the reconstruction of each azimuth vector data, yielding the signal after azimuth spacing aperture recovery in the two-dimensional frequency domain. ;in yes The estimated value. Compared with the single-task independent recovery method, the hierarchical Bayesian modeling shown in this method can establish a closer statistical association between multiple reconstruction tasks, thereby further improving the accuracy of missing azimuth aperture recovery.

[0134] The specific steps of step S6, reconstructing the aperture signal and final coherent imaging, are as follows:

[0135] The signal obtained after recovering the lower directional spacing aperture in the two-dimensional frequency domain Perform a two-dimensional inverse Fourier transform to obtain the coarse-focused time-domain signal. Then, multiplying it by the conjugate of the reference function, we obtain the reconstructed aperture SAR signal:

[0136] in, This is the conjugate of the reference function. The 2D time-domain SAR signal with azimuth aperture completion can be recovered using this formula, and the final coherent imaging processing can be completed accordingly. After the above steps, the final imaging result simultaneously achieves range spectrum alignment and azimuth aperture recovery, thereby improving range resolution, azimuth resolution, and image focusing quality.

[0137] The method of this embodiment will be further described below with reference to the embodiments:

[0138] like Figure 1As shown, the method in this embodiment first acquires SAR echo data collected by multiple sub-satellites from the same observation area, and determines the center carrier frequency, signal bandwidth, and slow-time observation interval of each sub-satellite. Then, a unified range-frequency coordinate system and a unified azimuth-time coordinate system are established, and the range spectrum and azimuth-time domain of each sub-satellite echo are rearranged to construct a heterogeneous distributed spaceborne SAR signal model. Next, a range-direction Fourier transform is performed on the rearranged sub-satellite echoes, and an iterative AR model is used to extrapolate the unknown frequency bands at the range spectrum boundaries to achieve range spectrum alignment and bandwidth expansion for different sub-satellites. Then, for the azimuth aperture intervals that still exist after extrapolation, a reference function is constructed to coarsely focus the signal, establishing an azimuth-direction interval aperture undersampling measurement model. Next, a multi-task compressed sensing method is used to jointly reconstruct the missing azimuth aperture data to obtain the recovered two-dimensional frequency domain signal. Finally, the recovered two-dimensional frequency domain signal is transformed back to the two-dimensional time domain, and coherent imaging processing is completed to obtain a reconstructed aperture SAR image.

[0139] Figure 2 The geometric configuration of heterogeneous distributed spaceborne SAR is shown, such as Figure 2 As shown, Satellite 1, Satellite 2, and Satellite 3 represent three sub-satellites participating in the multi-frequency distributed observation, and the three sub-satellites move sequentially along the radar trajectory; V1, V2, and V3 represent the velocity directions of Satellite 1, Satellite 2, and Satellite 3 along the azimuth direction, respectively. , , These represent the center carrier frequencies of the signals transmitted by Satellite 1, Satellite 2, and Satellite 3, respectively. Because the center carrier frequencies of the signals transmitted by each subsatellite are different, their range echoes exhibit a spectral misalignment distribution in a unified range-frequency coordinate system. Figure 2 The blue, green, and red waveforms in the image represent carrier frequencies of 1000, ... , , The transmitted signal is represented by the dashed line; the dotted line represents the illumination path of each sub-satellite radar beam onto the ground observation area; the beam coverage area represents the common illumination range of multiple sub-satellites on the same target area; the scene center represents the center position of the area to be imaged; the radar trajectory direction corresponds to the azimuth direction, and the ground direction corresponds to the range direction. It can be seen that the heterogeneous distributed spaceborne SAR system exhibits spectral misalignment in the range direction caused by different central carrier frequencies, and a discontinuous sub-aperture structure in the azimuth direction caused by differences in the observation time and orbital position of different sub-satellites.

[0140] To more intuitively illustrate the aforementioned spectral misalignment distribution and different continuous sub-aperture structures, a rectangular imaging scene simulation platform was constructed, in which nine symmetrically distributed point targets were arranged at intervals. Each satellite transmits a linear frequency modulated signal with a consistent signal bandwidth, but the center carrier frequency is set to different values, thus forming a heterogeneous frequency structure for each satellite signal. Due to the difference in the center frequencies of each satellite, the acquired range echoes exhibit a misaligned distribution in the frequency domain. In the azimuth dimension, due to the orbital intervals between satellites, there is a certain time delay between when one satellite finishes observing the target area and before the next satellite begins observation. Therefore, directly synthesizing the signals results in discontinuous azimuth sampling intervals in the equivalent synthesized aperture. The two-dimensional time domain diagram and two-dimensional spectrum of the range pulses received by the three satellites after compression are shown below. Figure 3 As shown.

[0141] Figure 4 A schematic diagram of the complete imaging results of the measured data is shown.

[0142] To intuitively evaluate the improvement effect of the method in this embodiment on the imaging quality of the measured data, three representative local areas were selected from the processed scene for comparative analysis. Figure 5 (a) shows the imaging results of three typical local regions after processing using traditional methods. Figure 5 (b) shows the imaging result of the corresponding local region after processing using the method of this embodiment. Figure 5 As can be seen, the images processed by traditional methods are affected by both distance-spectrum mismatch and azimuth aperture discontinuity. As a result, the edges of some ground features in the images appear blurred, stretched, or broken, the details of the target structure are not clear enough, and there is a certain degree of defocus and fringe interference in local areas. After processing with the method of this embodiment, the scattering center of the target area is more concentrated, the outlines of building edges, road structures, and strong scattering areas are more complete and clear, the image detail preservation effect is significantly improved, and the overall focusing quality is improved.

[0143] Compared with existing technologies, this embodiment has the following advantages: First, by establishing a unified range-frequency coordinate system and a unified azimuth-time coordinate system, unified rearrangement of multi-satellite echo data of different frequencies is achieved, providing a unified signal basis for subsequent coherent synthesis; Second, by using an iterative AR model based on the Burg method to extrapolate the unknown frequency bands at the range spectrum boundary, alignment of the range spectrum of different sub-satellites and equivalent bandwidth expansion are achieved, thereby improving range resolution; Third, by constructing an azimuth-interval aperture undersampling measurement model and using a multi-task compressed sensing method to jointly recover missing azimuth aperture data, azimuth equivalent continuous aperture reconstruction is achieved, thereby improving azimuth resolution and focusing performance; Fourth, by jointly compensating for range spectrum mismatch and azimuth aperture loss, the overall imaging quality of multi-frequency distributed spaceborne SAR images is improved, the target energy concentration is enhanced, sidelobes and artifacts are suppressed, and image clarity and stability are improved.

[0144] Therefore, the method of this embodiment can effectively compensate for the imaging degradation caused by range-spectrum mismatch and azimuth aperture loss in the heterogeneous distributed observation scenario constructed from real SAR observation data, and significantly improve image clarity, target focus and detail preservation ability, thus proving that the method of this embodiment has better imaging performance than traditional methods.

[0145] This application also provides an electronic device, including: a processor, and a memory coupled to the processor, the memory being used to store a computer program; the processor being used to execute the computer program stored in the memory, so that the electronic device performs the method as described in any of the above embodiments.

[0146] Electronic devices can be computing devices such as desktop computers, laptops, handheld computers, and cloud servers. These electronic devices may include, but are not limited to, processors and memory.

[0147] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the electronic device, connecting various parts of the device via various interfaces and lines.

[0148] The memory can be used to store the computer program, and the processor implements various functions of the electronic device by running or executing the computer program stored in the memory and calling the data stored in the memory.

[0149] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function, etc.; the data storage area may store data created based on the use of the mobile phone, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0150] This application also provides a storage medium, which is a computer-readable storage medium. The computer program is stored in the computer-readable storage medium, and when executed by a processor, the computer program can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0151] This application also provides a computer program product, including: a computer program or instructions that, when the computer program or instructions are run on a computer, cause the computer to perform any of the above possible implementation methods.

[0152] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A method for interferometric imaging of a synthetic aperture radar on board a satellite in a distributed manner at different frequencies, characterized in that, include: Obtain synthetic aperture radar (SAR) echo data of the same observation area collected by several sub-satellites; Based on the established unified coordinate system, the SAR echo data collected by each sub-satellite is preprocessed to obtain the heterogeneous distributed SAR signal to be processed. Perform a range-to-Fourier transform on the distributed SAR signal to be processed to obtain a range spectrum sequence; Based on the forward linear prediction model and the backward linear prediction model constructed for the range spectrum sequence for each range gate, a recursive algorithm is adopted. Under the framework of the autoregressive model, the prediction coefficients of the autoregressive model are recursively updated by minimizing the joint prediction error objective function. Then, the estimated prediction coefficients are used to extrapolate the unknown frequency bands at the boundary of the range spectrum sequence point by point to obtain the extrapolated range spectrum signal, so as to realize the range spectrum alignment and bandwidth expansion of different sub-satellites. The joint prediction error is jointly determined by the forward prediction error of the forward linear prediction model and the backward prediction error of the backward linear prediction model. Based on the constructed multi-task compressed sensing joint recovery model, the missing azimuth aperture data in the range spectrum extrapolated signal is jointly reconstructed to obtain the recovered two-dimensional frequency domain signal. The multi-task compressed sensing joint recovery model is constructed based on the sparsity of the range spectrum extrapolated signal in the two-dimensional frequency domain and the fact that its real and imaginary parts share a common support set characteristic. Furthermore, coherent imaging processing is performed based on the recovered two-dimensional frequency domain signal; The heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method also includes: From all the sub-satellites, a reference sub-satellite is determined; Furthermore, based on the determined reference sub-satellite, a unified coordinate system is established, which includes: a unified range-frequency coordinate system and a unified azimuth-time coordinate system; The preprocessing specifically includes: The SAR echo data of each sub-satellite are rearranged in range and spectrum according to the center carrier frequency difference of each sub-satellite relative to the reference sub-satellite; and, Based on the slow time center offset of each sub-satellite relative to the reference sub-satellite, the SAR echo data of each sub-satellite after the range spectrum rearrangement is rearranged in the azimuth time domain to obtain the unprocessed heterogeneous distributed SAR signal.

2. The method of claim 1, wherein the step of generating the complex image comprises the steps of: generating a complex image of the first frequency band; generating a complex image of the second frequency band; and combining the complex images of the first and second frequency bands to generate the complex image of the combined frequency band. Distance spectrum rearrangement specifically involves: Based on the first reference satellite For reference, construct the range-frequency shift function H1(i) for the i-th sub-satellite: in, Indicates distance in advance time. For any integer, Indicates the first Subsatellite relative to reference subsatellite The center carrier frequency difference, For the first The center carrier frequency of the satellite As a reference sub-satellite The center carrier frequency, SAR echo data after range spectrum rearrangement for: in, For location, slow time, This is the SAR echo data before rearrangement. At this time, the distance frequency variable satisfy: in, This refers to the bandwidth of a single signal.

3. The heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method as described in claim 2, characterized in that, Orientation time-domain rearrangement specifically involves: With the second reference satellite SAR echo data after range spectrum rearrangement For reference, the first SAR echo data after range spectrum rearrangement of sub-satellites Represented as: Among them, the Subsatellite relative to reference subsatellite The slow time center offset is , No. Effective observation range of the satellite satisfy: ， in, This indicates the effective observation time of a single sub-satellite in the azimuth timescale. Construct the azimuth time shift function H2(i): in, The distributed SAR signal to be processed is obtained by rearranging the azimuth frequency in the time domain. for: in, Indicates the first The two-dimensional time-domain SAR echo signal obtained from the satellite after range spectrum rearrangement and azimuth time-domain rearrangement. Indicates the first Corresponding to the sub-satellite The azimuth frequency domain signal obtained by performing a Fourier transform along the azimuth slow time. The number of subsatellites participating in the synthesis.

4. The heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method as described in claim 3, characterized in that, Regarding the first Distance spectrum sequence of distance gates ,in, Given the number of sampling points in the distance frequency domain, the forward linear prediction model is as follows: The backward linear prediction model is as follows: in, Indicates the sub-satellite number, Indicates the index of prediction coefficients. Indicates the order of the autoregressive model. Indicates the first The forward linear prediction value obtained in the next iteration Indicates the first The backward linear prediction value obtained in the next iteration and They represent the first The prediction coefficients of the forward linear prediction model and the backward linear prediction model during the first iteration. and They represent the first After the range spectrum is rearranged and the azimuth time domain is rearranged, the satellite is in the 1st... At the distance from the door, the first The and the first The distance spectrum value corresponding to each distance frequency domain sampling point. The objective function for the joint prediction error is: in, Forward prediction error, This is the backward prediction error. Distance spectrum extrapolated signal for: in, Indicates the first The frequency domain signal obtained by extrapolating the range spectrum of the satellite. Indicates by The SAR echo signal obtained by performing an inverse range-frequency domain transform back to the two-dimensional time domain This indicates that the autoregressive prediction model is used to predict the first... The spectrum estimate obtained by extrapolating and predicting the unknown frequency bands at the distance of the satellite from the spectrum boundary. This indicates the newly added interval relative to the original frequency band range after extrapolation.

5. The heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method as described in claim 4, characterized in that, The heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method further includes: using a reference function Multiplying the signal obtained by the extrapolation of the range spectrum with the complete SAR signal yields the coarsely focused signal. Specifically: Where A is the measurement matrix, For a complete SAR signal, The closest slope distance, For radar speed, For the operating wavelength, The frequency is linearly tuned along the distance, and c is the speed of light. Due to the sparsity of the signal in the two-dimensional frequency domain after the distance spectrum extrapolation, the following equation holds: in, Indicates the signal after coarse focusing The two-dimensional frequency domain signal obtained after two-dimensional Fourier transform For sparse representation base, The corresponding complex signal compressed sensing observation model is: in, It is a two-dimensional frequency domain sparse coefficient matrix. For undersampled observation data, For the equivalent sensing matrix, The real signal model corresponding to the complex signal compressed sensing observation model is: Where Re represents the real part and Im represents the imaginary part. Represents the complex observations The real-valued observation vector obtained after real-valued expansion and They represent the observations of complex numbers respectively. and The real-valued observation vector obtained after real-valued expansion Therefore, the real-valued azimuth-spaced aperture signal observation model is obtained as follows: The multi-task compressed sensing joint recovery model is as follows: in, For azimuth frequency The joint sparse matrix constructed below, For distance frequency The sparse representation to be estimated below, Indicated by For the variables to be optimized, minimize the mixture of the joint sparse matrix. Using norms to solve for the joint sparse recovery of missing azimuth aperture data Indicates mixing Norm, Indicates the slow time in the direction. Next The real-valued undersampled observation vector corresponding to each distance-directed sampling location. Indicates the number of distance-oriented pulse sampling points. This indicates the number of azimuth pulse sampling points for the interval aperture signal. This represents the sparse representation of the real signal to be estimated. For the equivalent sensing matrix of the real signal, This is the error tolerance.

6. The heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method as described in claim 5, characterized in that, Based on the constructed multi-task compressed sensing joint recovery model, the missing azimuth aperture data in the range spectrum extrapolated signal is jointly reconstructed, specifically including: We introduce a hierarchical Bayesian model, assuming that all tasks share the same set of sparse hyperparameters. By introducing the hyperparameter γ, the sparse components are... To perform adaptive adjustment, the prior model is established as follows: in, Represented by vector The elements in the matrix form a diagonal matrix consisting of the main diagonal elements. Under the prior model, the joint likelihood function of the multi-task data is: in, ; Indicates the slow time in the direction. The following is a set of observation data consisting of observation vectors corresponding to multiple reconstruction tasks. Indicates a normal distribution. For noise variance, By maximizing the posterior probability, the two-dimensional frequency domain sparse coefficient matrix to be estimated is obtained. sparse hyperparameters and noise variance The joint estimation is then used to obtain the recovered two-dimensional frequency domain signal. .

7. The heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method as described in claim 6, characterized in that, Based on the recovered two-dimensional frequency domain signal, coherent imaging processing is performed, specifically including: The recovered two-dimensional frequency domain signal Perform a two-dimensional inverse Fourier transform to obtain the coarse-focused time-domain signal. ; coarse-focused time-domain signal With reference function The conjugate multiplication yields the reconstructed aperture SAR signal. This is to complete the coherent imaging process.

8. An electronic device, characterized in that, The electronic device includes: a processor, and a memory coupled to the processor. The memory is used to store computer programs; The processor is configured to execute the computer program stored in the memory, so that the electronic device performs the heterogeneous frequency distributed spaceborne synthetic aperture radar coherent imaging method as described in any one of claims 1-7.

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