Synthetic aperture radar jammer parameter inversion method based on image domain fractional fourier transform

Abstract

The application discloses a synthetic aperture radar jammer parameter inversion method based on image domain fractional Fourier transform, which firstly utilizes the two-dimensional separable and low rank characteristics of the linear frequency modulation jamming in the SAR image domain, performs singular value decomposition on the jammed image data matrix and retains the rank-1 component, realizes separation and coherent accumulation of the jamming principal component and ground object clutter, then transforms the separated distance waveform to the frequency domain and performs narrowband interception, performs fractional Fourier transform on the intercepted data and searches for an optimal rotation angle to estimate the image domain distance frequency, and finally inversely obtains the jammer linear frequency modulation frequency according to a preset mapping relationship. The application can accurately invert the jammer parameter under a low jamming-to-signal ratio condition, greatly reduces the calculation complexity through frequency domain narrowband interception, and provides an efficient and feasible technical means for SAR electronic reconnaissance and electromagnetic situation awareness.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing and electronic countermeasures technology, specifically relating to a method for inverting synthetic aperture radar interference source parameters based on image domain fractional Fourier transform. Background Technology

[0002] Synthetic Aperture Radar (SAR) is an all-weather, all-day, high-resolution microwave imaging system that plays a crucial role in military reconnaissance and battlefield surveillance. However, SAR systems are inevitably subject to electromagnetic interference from ground-based radars, communication equipment, and other sources. While these interference signals degrade SAR image quality, they themselves contain key technical parameters of the interference sources (such as center frequency, frequency modulation, and pulse width), making them highly valuable for electronic intelligence.

[0003] In existing technologies, the treatment of SAR interference mainly focuses on two aspects: interference suppression and interference source localization. Regarding interference suppression, parameterized estimation methods construct mathematical models of the interference signal and estimate its parameters, thereby reconstructing and canceling the interference. For interference source localization, the geographical location of the interference source is calculated by extracting the Doppler parameters of the interference signal and combining them with localization algorithms.

[0004] However, the aforementioned existing technologies all aim to eliminate interference or locate the interference source, and research on estimating the signal parameters of the interference source itself from SAR images remains relatively scarce. Especially in covert reconnaissance scenarios, the radiated power of non-cooperative interference sources is often far below the level that degrades SAR imaging performance, and the interference signal is usually intercepted in the form of low interference-to-signal ratio (LFM). Under this low LFM background, existing methods struggle to effectively purify the interference signal and accurately invert its parameters such as linear frequency modulation (LFM), and also suffer from high computational complexity and difficulty in real-time processing. Therefore, there is an urgent need for a technical solution that can efficiently and accurately invert the parameters of non-cooperative linear frequency modulation (LFM) interference sources from SAR images under low LFM conditions. Summary of the Invention

[0005] The present invention aims to provide a synthetic aperture radar interference source parameter inversion method based on image domain fractional Fourier transform, in order to solve the technical problem in the prior art that it is difficult to efficiently and accurately invert non-cooperative linear frequency modulated interference source signal parameters from SAR images under low interference-to-signal ratio environment.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for inverting synthetic aperture radar interference source parameters based on image domain fractional Fourier transform, comprising the following steps:

[0007] Step 1: Obtain the target sub-image from the interfered SAR image and construct a data matrix; perform singular value decomposition on the data matrix, retain the rank-1 component to extract the interference principal component, and obtain the range waveform vector;

[0008] Step 2: Transform the distance-oriented waveform vector to the frequency domain and extract narrowband frequency domain data within its effective frequency range;

[0009] Step 3: Perform fractional Fourier transform on the narrowband frequency domain data, perform peak detection in the fractional domain, search for the optimal rotation angle, and estimate the image domain range axial modulation frequency based on the optimal rotation angle.

[0010] Step 4: Based on the preset mapping relationship, obtain the linear frequency modulation parameters of the interference source by inverting the frequency modulation of the distance direction in the image domain.

[0011] Furthermore, the interference mentioned in step 1 is linear frequency modulation (LFM) interference.

[0012] Furthermore, the narrowband frequency domain data to be extracted within its effective spectral range in step 2 is specifically determined by: determining the extraction range based on the 3dB bandwidth of the distance waveform spectrum.

[0013] Furthermore, the peak detection in the fractional order domain described in step 3 specifically involves: traversing the transformation order [0,2] with a set step size, and performing ordered statistical constant false alarm rate (OS-CFAR) peak detection on the transformation results to determine the optimal rotation angle.

[0014] Furthermore, the mapping relationship determined in step 4 is as follows:

[0015]

[0016] in, For the image domain range modulated frequency, To adjust the frequency of the SAR transmission signal, The frequency modulation of the interference source is given by this formula; during inversion, the linear frequency modulation of the interference source is obtained by solving this formula.

[0017] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described above.

[0018] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the above-described method.

[0019] A computer program product includes a computer program that, when executed by a processor, implements the steps of the above-described method.

[0020] Compared with the prior art, the present invention has the following advantages:

[0021] (1) Superior performance in low interference-to-signal ratio: This invention utilizes the low-rank characteristics of LFM interference in the SAR image domain and effectively gathers interference energy through SVD coherent accumulation. It can accurately extract the main interference components under low interference-to-signal ratio conditions, and the inversion accuracy is significantly better than the row-by-row non-coherent accumulation method.

[0022] (2) The computational complexity is significantly reduced: This invention reduces the number of FRFT processing points from N points in the full time domain / full frequency domain to M points (M is less than N) through the frequency domain narrowband interception strategy, which reduces the computational load by about two orders of magnitude and facilitates real-time or near-real-time processing.

[0023] (3) The estimation accuracy is further improved: the frequency domain truncation operation itself filters out the out-of-band ground clutter components, making the energy focus of the FRFT domain more concentrated, which further improves the estimation accuracy compared with the full bandwidth processing method.

[0024] (4) High practicality: Verified by actual spaceborne SAR data, the frequency modulation estimation error for various unknown interference sources is within 6%, which proves the effectiveness and universality of the invention. Attached Figure Description

[0025] Figure 1 This is an overall flowchart of the method of the present invention.

[0026] Figure 2 This is a comparison diagram of the time-domain and frequency-domain characteristics of the LFM interference range signal in this invention; where (a) is the time-domain waveform and (b) is the frequency-domain spectrum.

[0027] Figure 3 This is a comparison chart of the frequency modulation estimation error between the method of the present invention and existing methods.

[0028] Figure 4 This is a comparison chart of the frequency modulation estimation errors of three different FRFT processing strategies in the method of this invention.

[0029] Figure 5 The figure shows the verification results of the measured data of the present invention; where (a) is a local area of ​​the interfered SAR image, (b) is the range-direction frequency domain after SVD processing, (c) is the FRFT search result of interference band one, and (d) is the FRFT search result of interference band two. Detailed Implementation

[0030] Combination Figure 1This invention proposes a method for inverting synthetic aperture radar interference source parameters based on image domain fractional Fourier transform, comprising the following steps:

[0031] Step 1: Interference Principal Component Separation and Coherent Accumulation. Acquire the interfered SAR image and extract the target sub-image containing the interference stripes; arrange the target sub-image row by row according to the azimuth direction to construct a data matrix; utilize the two-dimensional separability and low-rank characteristics of LFM interference in the SAR image domain to perform Singular Value Decomposition (SVD) on the data matrix; retain the rank-1 component corresponding to the largest singular value for matrix reconstruction to obtain the separated interference principal component signal, and output its range waveform vector; the SVD processing achieves effective separation of interference and ground clutter, and coherent accumulation of multi-azimuth observations.

[0032] Step 2: Range-Frequency Domain Transformation and Narrowband Truncation. The range-oriented waveform vector obtained in Step 1 is subjected to a Fourier transform to transform it into the range-frequency domain. Based on the amplitude distribution of the transformed spectrum, the effective frequency range of the interference signal is determined, and the data within this narrowband range is truncated to obtain narrowband frequency domain data. This narrowband truncation utilizes the time-frequency duality of the LFM signal, where energy is concentrated in a finite frequency band, to reduce the number of processing points in the subsequent fractional Fourier transform.

[0033] Step 3: Frequency modulation estimation based on fractional Fourier transform. A fractional Fourier transform (FRFT) is performed on the narrowband frequency domain data extracted in Step 2, and peak detection is performed in the fractional domain to determine the optimal rotation angle. Based on the properties of FRFT, the range-direction frequency modulation of the interference in the SAR image domain is calculated.

[0034] Step 4: Interference source parameter inversion. Using the pre-established mapping relationship between the range modulation frequency in the SAR image domain and the linear modulation frequency of the interference source, the range modulation frequency of the interference in the SAR image domain estimated in Step 3 is substituted to calculate the linear modulation frequency parameters of the non-cooperative interference source.

[0035] The present invention will now be described in further detail with reference to the accompanying drawings. These specific embodiments are for illustrative purposes only and do not constitute a limitation on the scope of protection of the present invention.

[0036] This invention provides a method for inverting synthetic aperture radar interference source parameters based on image domain fractional Fourier transform, comprising the following steps:

[0037] Step 1: Interference Principal Component Separation and Coherent Accumulation. Acquire the interfered SAR image and extract the target sub-image containing interference fringes. Arrange the target sub-images row by row along the azimuth direction to construct a data matrix Y, the size of which is the number of points in the azimuth direction. × Distance to points LFM interference, after being imaged by SAR, can be represented in the image domain as a two-dimensional separable linear frequency modulation form in range-azimuth:

[0038]

[0039] In the formula, and These represent distance time and direction time, respectively. Represents the complex amplitude of the interference, and rect(·) is a rectangular window function. Doppler frequency modulation for SAR processing and These are widening in the range direction and widening in the azimuth direction, respectively. For constant phase term, where This indicates the slant distance corresponding to each distance gate. Indicates the carrier frequency of the SAR transmitted signal. Let be the speed of light, and C be the constant phase term after merging. For LFM interference, the range-modulated frequency in the image domain satisfies the following mapping:

[0040]

[0041] in, Frequency modulation for SAR signals, Frequency modulation for LFM interference signals.

[0042] Singular value decomposition is performed on the data matrix Y, taking advantage of the two-dimensional separability and low-rank characteristics of LFM interference in the SAR image domain:

[0043]

[0044] in It is a singular value diagonal matrix. It is a left singular vector matrix. It is a right singular vector matrix. This represents the conjugate transpose, with diagonal elements being singular values. Because the interference components have a rank-1 structure, their energy is concentrated in the maximum singular value. The energy of ground clutter is distributed across multiple singular values. Therefore, only the rank-1 component corresponding to the largest singular value is retained for reconstruction, resulting in the reconstructed interference matrix. :

[0045]

[0046] in the formula is the first left singular vector, is the first right singular vector, that is, the range-wise waveform vector of the jamming signal. This processing realizes the separation of jamming and clutter, and azimuth-wise observation coherences are accumulated into a single vector , which effectively improves the purity of the jamming signal under low jamming-to-signal ratio.

[0047] Step 2: Range frequency domain transformation and narrowband interception. Fast Fourier Transform (FFT) is performed on the range-wise waveform vector obtained in Step 1 to transform it into the range frequency domain, so as to obtain the frequency domain vector . As shown in Figure 2 (a), the LFM jamming almost fills the entire observation window in the time domain, and the width of the entire observation window is N points; while according to the time-frequency duality characteristic of the LFM signal, its frequency domain energy is concentrated in a limited bandwidth, as shown in Figure 2 (b). According to the amplitude spectrum of , the effective frequency spectrum interval of the jamming signal is determined, and the interval is denoted as , with a width of M points (M<<N). The data in this narrowband interval is intercepted to obtain a frequency domain vector with a length of M . This narrowband interception greatly reduces the number of processing points for subsequent FRFT.

[0048] Step 3: Modulation rate estimation based on fractional Fourier transform. Fractional Fourier Transform (FRFT) is performed on the narrowband frequency domain data obtained in Step 2 . The definition of FRFT is:

[0049]

[0050] where is the -order fractional Fourier spectrum, is the fractional frequency, represents the fractional Fourier transform with a rotation angle of . Within the search range of the rotation angle , the FRFT amplitude spectrum at each order is traversed and calculated at a set step size. In the plane, the optimal rotation angle is searched by OS-CFAR peak detection , according to the property of fractional Fourier transform, the corresponding modulation rate is , and according to the time-frequency duality characteristic of the LFM signal, the range-wise modulation rate of the jamming in the image domain is .

[0051] Step 4: Interference source parameter inversion. Using a pre-established mapping relationship between the SAR image domain range modulation frequency and the interference source linear modulation frequency:

[0052]

[0053] in, The frequency modulation frequency of the SAR signal is a known constant. The frequency modulation of the LFM interference source (parameters to be inverted). The values ​​estimated in step 3... Substituting into the above equation, the linear modulation frequency of the interference source can be calculated:

[0054]

[0055] This completes the entire process of retrieving the frequency modulation parameters of the non-cooperative LFM interference source from the jammed SAR image.

[0056] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0057] Example 1

[0058] This embodiment uses Sentinel-1 satellite parameters for simulation. SAR system parameter settings are as follows: carrier frequency... Distance sampling rate Azimuth sampling rate Transmission bandwidth pulse width Frequency modulation Platform speed Reference slope distance Interference source parameter settings: Frequency modulation pulse width The pulse count is 3, and the repetition interval is 2.5 ms. The SAR image size is... The Omega-K imaging algorithm was used. 600 rows of azimuth data were extracted, and the data was processed to a size of [size missing]. The data matrix is ​​processed using SVD. The FRFT search order is... Step length A total of 2251 searches were performed. Frequency domain truncation length. The comparison method is azimuth-wise FRFT noncoherent accumulation: 16 azimuth directions are selected at equal intervals, and each row undergoes the same FRFT search independently followed by noncoherent accumulation. OS-CFAR detection is performed on the two-dimensional FRFT search matrix, with a false alarm probability set to 10. -6 The frequency modulation estimation error is defined as the relative root mean square error.

[0059] Under the above settings, 100 Monte Carlo experiments were conducted within the dry-to-signal ratio range of -25 dB to -15 dB. Figure 3 As shown, the normalized root mean square error (NRMSE) of the method of the present invention is always lower than that of the directional noncoherent accumulation method, and the error increases slowly with the decrease of the interference-to-signal ratio, demonstrating excellent low signal-to-noise ratio robustness.

[0060] To verify the effectiveness of the frequency domain truncation strategy, three strategies were compared under the same conditions: Strategy 1 (frequency domain truncation FRFT of this invention), Strategy 2 (full bandwidth frequency domain FRFT, i.e., not truncating all frequency points), and Strategy 3 (full time domain sampling FRFT). Figure 4 As shown, the estimation error of strategy 1 is lower than that of strategy 2 and strategy 3 under all interference-to-signal ratio conditions, indicating that frequency domain truncation not only reduces the amount of computation, but also further improves the estimation accuracy by filtering out out-of-band clutter.

[0061] Example 2

[0062] This embodiment uses a Gaofen-3 (GF-3) single-view complex (SLC) image with known interference source parameters for verification. Figure 5 (a) shows a local area of ​​the interfered SAR image, where obvious interference stripe artifacts are visible. The interfered area is truncated and SVD rank-1 reconstruction is performed to obtain the range waveform of the interference component, the spectrum of which is shown below. Figure 5 As shown in (b), two distinct interference frequency bands are visible. Data from each interference frequency band is extracted from the spectrum, and FRFT scans are performed on each band to search for the optimal rotation angle. The search results are shown below. Figure 5 As shown in (c) and (d), the image domain modulation frequency is estimated using the optimal rotation angle, and the linear modulation frequency of the interference source is obtained by inversion. The estimation results are listed in the table below:

[0063] Table 1 Estimation results of measured data

[0064]

[0065] The estimation errors of the frequency modulation of both interference sources were within 6%, which confirms the effectiveness and accuracy of the present invention for actual spaceborne SAR data.

[0066] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for inverting synthetic aperture radar interference source parameters based on image domain fractional Fourier transform, characterized in that, Includes the following steps: Step 1: Obtain the target sub-image from the interfered SAR image and construct a data matrix; perform singular value decomposition on the data matrix, retain the rank-1 component to extract the interference principal component, and obtain the range waveform vector; Step 2: Transform the distance-oriented waveform vector to the frequency domain and extract narrowband frequency domain data within its effective frequency range; Step 3: Perform fractional Fourier transform on the narrowband frequency domain data, perform peak detection in the fractional domain, search for the optimal rotation angle, and estimate the image domain range axial modulation frequency based on the optimal rotation angle. Step 4: Based on the preset mapping relationship, obtain the linear frequency modulation parameters of the interference source by inverting the frequency modulation of the distance direction in the image domain.

2. The method according to claim 1, characterized in that, The interference is a linear frequency modulation (LFM) interference.

3. The method according to claim 1, characterized in that, Step 2, which involves extracting narrowband frequency domain data within its effective spectral range, specifically involves determining the extraction range based on the 3dB bandwidth of the distance waveform spectrum.

4. The method according to claim 1, characterized in that, The peak detection in the fractional order domain described in step 3 is specifically as follows: traversing the transformation order [0,2] with a set step size, performing OS-CFAR peak detection on the transformation result, thereby determining the optimal rotation angle.

5. The method according to claim 1, characterized in that, The preset mapping relationship in step 4 is as follows: ； in, For the image domain range modulated frequency, To adjust the frequency of the SAR transmission signal, The frequency modulation of the interference source is given by this formula; during inversion, the linear frequency modulation of the interference source is obtained by solving this formula.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of any of the methods described in claims 1-5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method described in any one of claims 1-5.

8. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method described in any one of claims 1-5.

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