Multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient self-focusing

Abstract

The invention discloses a multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient self-focusing. Firstly, complete circumferential aperture echo data is divided into a plurality of sub-aperture data, in each sub-aperture, a back projection (BP) algorithm is applied to the echo data of each flight to obtain a plurality of two-dimensional CSAR images, and the images are registered. And secondly, an improved weighted phase gradient self-focusing method is adopted to realize chromatography phase error correction. And then, performing tomography focusing on each pixel group by using a conventional beam forming algorithm, and obtaining a sub-aperture three-dimensional image after coordinate conversion. And finally, performing incoherent superposition on all the sub-aperture three-dimensional images to obtain a final three-dimensional CSAR image, thereby solving the technical problems of tomographic direction offset, poor sub-aperture image correction result and the like in tomographic phase error correction in the prior art.

Description

Technical Field

[0001] The present invention relates to the technical field of radar, and more specifically, to a multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocusing. Background Art

[0002] Multi-baseline circular synthetic aperture radar (CSAR) is a microwave system with all-round three-dimensional imaging capabilities and can work all day and all weather. During the CSAR three-dimensional imaging process, the joint of tomographic phase error correction and tomographic focusing is beneficial to obtaining a more accurate CSAR three-dimensional image, so it is a research hotspot in this technical field.

[0003] The autofocusing method is the current mainstream tomographic phase error correction method. It processes multiple two-dimensional radar images generated from radar echo data and estimates the tomographic phase error vector from multiple two-dimensional radar images. The autofocusing method mainly includes the criterion optimization method and the direct estimation method. The criterion optimization method is to select an evaluation criterion for the image and search pixel by pixel for the phase error vector that makes the evaluation criterion optimal within the current pixel, mainly including minimum entropy autofocus (MEA), sharpness optimization autofocus (SOA), and phase derivative constrained optimization (PDCD). The advantage of the criterion optimization method is that it can correct pixel by pixel, so it is applicable to observation scenarios with strong phase error spatial variability. However, the computational cost of correcting pixel by pixel is large and time-consuming.

[0004] Another type of autofocus method is the direct estimation method, which regards the phase error as spatially invariant or slowly varying in space. Multiple prominent points are obtained from the scene according to a certain screening criterion, and these prominent points are used to iteratively estimate the phase error of the scene. This method has the advantage of high efficiency in phase error correction and can correct phase errors of any order. Due to the assumption of spatially invariant phase error, this method is mainly applicable to rapid phase error correction for relatively small observation scenes. The most commonly used method is the Phase Gradient Autofocus (PGA) algorithm. The PGA algorithm first selects prominent points with strong stability, then estimates the phase error gradient between two pass images using the maximum likelihood criterion, and then accumulates to obtain the phase error. However, the PGA algorithm has some deficiencies. First, according to the prominent point screening criterion in this method, more prominent points will be retained, which increases the computational complexity. Second, the set iterative convergence condition in this method converges slowly in some sub-aperture processing. On the one hand, it increases the time consumption. On the other hand, as the number of iterations increases, the phase error correction effect will not improve, but instead produces a position shift along the tomography direction, which causes the imaging position to shift. Since the position shift situations in different sub-aperture processing are different, the imaging resolution of some scatterers in the final 3D image will be affected. Summary of the Invention

[0005] The present invention provides a multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus, which solves the technical problems such as tomography direction shift and poor sub-aperture image correction results existing in the tomography phase error correction in the prior art.

[0006] To solve the above technical problems, the technical solution of the present invention is as follows:

[0007] The present invention provides a multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus, including the following steps:

[0008] Divide the complete circular aperture into multiple non-overlapping sub-apertures, and each sub-aperture includes radar echo data collected during multiple passes.

[0009] Within each sub-aperture, use the BP algorithm to image the radar echo data of multiple passes to obtain multiple two-dimensional sub-aperture ground range images, and organize them to obtain the two-dimensional image group of the current sub-aperture.

[0010] Register the two-dimensional image group of each sub-aperture by calculating the complex correlation of two two-dimensional sub-aperture ground range images in the two-dimensional image group of each sub-aperture.

[0011] Use the improved weighted phase gradient autofocus method to correct the tomography phase error of the registered two-dimensional image group.

[0012] Perform tomographic focusing on the two-dimensional image group after tomographic phase error correction to obtain the sub-aperture three-dimensional image of each sub-aperture;

[0013] Incoherently superimpose the sub-aperture three-dimensional images of all sub-apertures to obtain the final CSAR three-dimensional imaging result.

[0014] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0015] The present invention proposes a multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus. First, divide the complete circular aperture echo data into several sub-aperture data. In each sub-aperture, apply the Back Projection (BP) algorithm to the echo data of each pass to obtain multiple two-dimensional CSAR images, and register these images. Secondly, adopt the improved weighted phase gradient autofocus method to achieve tomographic phase error correction. Then, use the conventional beamforming algorithm to achieve tomographic focusing for each pixel group, and obtain the sub-aperture three-dimensional image after coordinate transformation. Finally, incoherently superimpose the sub-aperture three-dimensional images of all sub-apertures to obtain the final three-dimensional CSAR image. Description of the Drawings

[0016] Figure 1 It is a schematic flow chart of a multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus provided by an embodiment of the present invention;

[0017] Figure 2 It is a schematic diagram of the geometric configuration of multi-baseline CSAR three-dimensional imaging provided by an embodiment of the present invention;

[0018] Figure 3 It is a schematic diagram of the tomography direction of multi-baseline CSAR three-dimensional imaging provided by an embodiment of the present invention;

[0019] Figure 4 It is a schematic diagram of the framework of a multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus provided by an embodiment of the present invention;

[0020] Figure 5 It is a flow chart of the improved weighted phase gradient autofocus method within the sub-aperture provided by an embodiment of the present invention;

[0021] Figure 6 It is an optical image of the selected vehicle in the observation scene provided by an embodiment of the present invention;

[0022] Figure 7 It is a distribution diagram of the selected points A to D in the CSAR image of the Ford Taurus vehicle provided by an embodiment of the present invention;

[0023] Figure 8 Schematic diagram of tomographic focusing results obtained by using different phase error correction methods for points A - D selected for the Ford Taurus vehicle provided in the embodiments of the present invention;

[0024] Figure 9 Schematic diagram of two - dimensional projection results of three - dimensional imaging of the Ford Taurus vehicle provided in the embodiments of the present invention;

[0025] Figure 10 Schematic diagram of three - dimensional imaging results of the Ford Taurus vehicle provided in the embodiments of the present invention;

[0026] Figure 11 Distribution diagram of points E - H selected in the CSAR image of the Toyota Camry vehicle provided in the embodiments of the present invention;

[0027] Figure 12 Schematic diagram of tomographic focusing results obtained by using different phase error correction methods for points E - H of the Toyota Camry vehicle provided in the embodiments of the present invention;

[0028] Figure 13 Schematic diagram of two - dimensional projection results of three - dimensional imaging of the Toyota Camry vehicle provided in the embodiments of the present invention;

[0029] Figure 14 Schematic diagram of three - dimensional imaging results of the Toyota Camry vehicle provided in the embodiments of the present invention. Detailed implementation manners

[0030] The accompanying drawings are only for illustrative purposes and should not be construed as limitations on this patent;

[0031] To better illustrate this embodiment, some components in the accompanying drawings are omitted, enlarged or reduced, which do not represent the dimensions of the actual product;

[0032] For those skilled in the art, it is understandable that some well - known structures and their descriptions in the accompanying drawings may be omitted.

[0033] The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0034] Embodiment 1

[0035] The present invention provides a multi - baseline CSAR three - dimensional imaging method based on improved weighted phase gradient autofocus. As shown in Figure 1 and Figure 4 shown, it includes the following steps:

[0036] Divide the complete circular aperture into multiple non - overlapping sub - apertures, and each sub - aperture includes radar echo data collected during multiple passes;

[0037] Within each sub-aperture, the BP algorithm is used to image the radar echo data of multiple passes, obtaining multiple two-dimensional sub-aperture ground range images, and organizing them to obtain the two-dimensional image group of the current sub-aperture;

[0038] By calculating the complex correlation of two two-dimensional sub-aperture ground range images in the two-dimensional image group of each sub-aperture, the two-dimensional image group of each sub-aperture is registered;

[0039] The improved weighted phase gradient autofocus method is used to correct the tomographic phase error of the registered two-dimensional image group;

[0040] Tomographic focusing is performed on the two-dimensional image group after tomographic phase error correction to obtain the sub-aperture three-dimensional image of each sub-aperture;

[0041] The sub-aperture three-dimensional images of all sub-apertures are incoherently superimposed to obtain the final CSAR three-dimensional imaging result.

[0042] The present invention combines the autofocus method and tomographic focusing based on conventional beamforming to quickly obtain the CSAR three-dimensional image.

[0043] Embodiment 2

[0044] Based on Embodiment 1, the following technical content is further described in this embodiment:

[0045] The complete circular aperture is divided into multiple non-overlapping sub-apertures, and each sub-aperture includes radar echo data collected from multiple passes;

[0046] Within each sub-aperture, the BP algorithm is used to image the radar echo data of multiple passes, obtaining multiple two-dimensional sub-aperture ground range images, and organizing them to obtain the two-dimensional image group of the current sub-aperture;

[0047] By calculating the complex correlation of two two-dimensional sub-aperture ground range images in the two-dimensional image group of each sub-aperture, the two-dimensional image group of each sub-aperture is registered;

[0048] In a further embodiment, the multi-baseline CSAR three-dimensional imaging geometric configuration is as Figure 2 shown. The radar carrier aircraft flies along a 360° circular trajectory around the observation scene, and flies along the same circular trajectory at different flight altitudes, with a total of P circular passes. The azimuth angle of the radar relative to the scene center is θ, and the pitch angle of the p-th pass is

[0049] The complete circular aperture is divided into multiple non-overlapping sub-apertures, and each sub-aperture includes radar echo data collected from multiple passes, including:

[0050] The complete circular aperture is divided into M non-overlapping sub-apertures. The azimuth width of each sub-aperture corresponding to the motion trajectory is Δθ = 2π / M, and each sub-aperture contains P pieces of radar echo data collected during a flight pass.

[0051] In this embodiment, the full-aperture echo data is divided into sub-apertures, that is, the echo data is evenly divided into M non-overlapping parts along the azimuth direction. The echo data within each sub-aperture is processed separately.

[0052] In a further embodiment, within each sub-aperture, the BP algorithm is used to image the radar echo data of multiple flight passes, obtaining multiple two-dimensional sub-aperture ground range images, and organizing them to obtain a two-dimensional image group of the current sub-aperture. This step is to perform two-dimensional imaging processing on the echo data within each sub-aperture. Each sub-aperture contains P pieces of echo data collected during a flight pass. In the two-dimensional imaging processing, each flight pass is processed separately to generate a two-dimensional image, and a total of P two-dimensional images are generated. Specifically:

[0053] For the echo signal of the p-th flight pass, let the radar echo signal after quadrature demodulation and pulse compression be s p (η, τ). The slow time η corresponds to the echo signals in different azimuth directions, and the fast time τ corresponds to the echo signals in different range directions. In actual imaging, the flight trajectory of the radar carrier aircraft is generally a non-ideal circular trajectory, and the Back Projection (BP) algorithm has strong adaptability to different flight trajectories. Therefore, the BP algorithm is used for two-dimensional imaging processing. The specific implementation of the BP algorithm is as follows: First, an imaging grid needs to be divided. Assuming the imaging focusing height is 0m, the imaging plane is then the Figure 2 xOy plane in. Assume that the imaging ranges of the radar in the x and y directions in this plane are both [-R s , R s . At this time, the two-dimensional image to be generated is a square with a side length of 2R s . Within this square imaging range, according to the working parameters of the radar, the resolution in the x direction is dx and the resolution in the y direction is dy. Therefore, the number of grid pixels in the imaging grid is ceil(·) is rounding up. Then, each pixel in the imaging grid needs to be assigned a value according to the echo signal. The BP algorithm processes each azimuth echo signal separately. For a selected azimuth slow time η0, according to the "stop-and-go" motion assumption, the position of the radar system can be considered unchanged when collecting the current azimuth data, that is, located at (x r (η0), y r (η0), h p ), where h p is the flight height of the radar under the current flight pass, and the flight height remains unchanged during the same flight pass. xr (η0) and y r (η0) is the position of the radar in the x - direction and y - direction at the azimuth - slow time η0. At this time, the echo signal after quadrature demodulation and pulse compression is s p (η0,τ), and each fast time τ corresponds to a different slant range R = cτ / 2. For a certain point (x′,y′) in the imaging grid, its coordinates in the three - dimensional space are (x′,y′,0), and the distance from this point to the current azimuth - position of the radar (x r (η0),y r (η0),h p ) can be calculated A distance can be calculated for each pixel point Search the imaging grid for the pixel points equal to the slant range R, and assign the values corresponding to the slant range R in the echo signal to these pixel points. At the same azimuth, the echo signals at different range - directions τ will be assigned to all pixel points with equal distances in the grid. This process is called back - projection. To avoid not finding a matching echo signal, it is necessary to perform up - sampling processing on the echo signal. After completing the back - projection at the same azimuth, each pixel has obtained a value. Let the value obtained by the pixel point located at (x’,y’) from the echo signal at the azimuth - slow time η0 be At this time, it is also necessary to compensate the phase for each pixel to obtain the final value of this pixel point at the current azimuth

[0054]

[0055] where f c is the carrier frequency. After compensating the phase, the back - projection at this azimuth is completed. The above operations are performed on the echo signals at each azimuth within the current sub - aperture, that is, the imaging process of the BP algorithm is completed. The pixel value of each pixel point in the final sub - aperture two - dimensional image is the superposition of all azimuth - projections:

[0056]

[0057] In a further embodiment, by calculating the complex correlation of two two - dimensional sub - aperture ground - range images in the two - dimensional image group of each sub - aperture, the two - dimensional image group of each sub - aperture is registered, including:

[0058] Calculating the complex correlation between every two two - dimensional images, finding the maximum value of the complex correlation, and then obtaining the displacement value between the images;

[0059] In the registration step, any image in the image group is first selected as the main image, and the remaining images are registered with reference to this main image. The Fourier transform of the complex correlation function of two images is equal to the product of the Fourier transform of one image and the conjugate of the Fourier transform of the other image. Therefore, for two images g i (x′, y′) and g j (x′, y′), the complex correlation ρ c can be calculated in the following way:

[0060] ρ c = norm{|FFT -1 [FFT(g i (x′, y′)) FFT(g j (x′, y′)) * |} (3)

[0061] where i ≠ j, i, j = 1, 2, …, P, and norm(·) represents the normalization process.

[0062] Example 3

[0063] Based on Example 1 and Example 2, this example further explains the tomographic phase error correction step.

[0064] After completing the two-dimensional image registration, enter the three-dimensional imaging processing stage. First, analyze the signal model of three-dimensional imaging below.

[0065] In the two-dimensional sub-aperture image generated by using the echo signal of the p-th flight path, the pixel value of the pixel point at the position (x ′ , y ′ ) in the two-dimensional ground range plane is g p (x ′ , y ′ ). This pixel value is composed of the superposition of the echo data of multiple scatterers perpendicular to the radar main flight path line of sight (LOS) direction (i.e., the tomographic direction or LOS ⊥ direction, denoted as the s direction). Since the observation angles of the radar in each sub-aperture are different, and thus the line of sight directions are also different, the s direction of each sub-aperture is different. Figure 2 Figure 47 is a schematic diagram of the tomographic direction for multi-baseline CSAR three-dimensional imaging. The value of the pixel point g is contributed by the scatterers t1 and t2. This signal model is expressed as:

[0066]

[0067] where σ p represents the spatial frequency of the p-th flight path under the current sub-aperture, γ(x ′ , y ′, s) is the scattering coefficient at position s for upward tomography.

[0068] During the actual observation process, due to the influence of the deviation of the carrier aircraft's own flight trajectory from the ideal circular trajectory and factors such as atmospheric propagation delay, there is a phase error in the collected echo signal. Therefore, Equation (4) needs to be rewritten as:

[0069]

[0070] where φ o is the phase error of the p-th pass under the current sub-aperture. Based on the information provided by the obtained two-dimensional image group, estimate this phase error and then compensate it into each pixel group, that is, use the autofocus method to achieve tomographic phase error correction.

[0071] The improved weighted phase gradient autofocus is a direct estimation autofocus method. This type of method assumes that within a certain range of the observation scene, the phase error is space-invariant, that is, the phase error in the observation scene is different in different passes, but it does not change with the position of the pixel group. The phase errors in different passes form a phase error vector. Therefore, for the entire observation scene, only one phase error vector needs to be estimated, and all pixel groups in the entire observation scene are used to estimate the phase error vector. However, if all pixel groups are used to estimate the phase error vector, the computational amount will be too large. Therefore, it is necessary to select some pixel groups from the observation scene according to certain screening criteria for estimation, and these selected pixel groups are called prominent points.

[0072] Suppose a total of K prominent points are selected. For the k-th (k = 1, 2,..., K) prominent point, its phase error in the p-th pass is φ p,k , and the pixel value is g p,k . g p,k contains a scattering point with the strongest energy, and other weak scattering points and noise are classified as clutter c p,k . According to this model, the pixel value can be expressed as:

[0073]

[0074] where γ k represents the scattering coefficient of the scattering point with the strongest energy at the k-th prominent point, s k represents the position of the scattering point with the strongest energy in the s direction at the k-th prominent point. The linear phase term 2πσ p s k comes from the scattering point with the strongest energy.

[0075] According to the phase error estimation model established by equation (8), it is expected that the selected prominent points contain a scattering point that is different from the clutter component as much as possible. In a two-dimensional image, points with stronger energy are generally more likely to contain strong scattering points. Therefore, the prominent points are selected according to the following energy criteria:

[0076]

[0077] Where E th The energy threshold is set, and the points satisfying equation (9) are selected as the prominent points.

[0078] Since the expected formula (8) only contains the phase error φ p Therefore, the linear phase term needs to be removed before estimating the phase error. The key to removing the linear phase term is to estimate the position s of the strongest scattering point in the s direction. k The specific estimation method is: firstly, the conventional beamforming (CBF) method is used to obtain the preliminary image of the prominent point, then the maximum value point in the image is found, and this point is used as the estimated value of the position of the strongest scattering point, and finally s is obtained. k Therefore, it is necessary to process formula (8) as follows:

[0079]

[0080] in, After removing the linear phase term, the phase term of the strong scattering point contains only the phase error in addition to the phase of the scattering coefficient itself. Next, the phase error is estimated.

[0081] The specific idea of ​​phase error estimation is: first estimate the phase error gradient Then the phase error estimate is obtained by accumulating the phase error gradient The estimation of the phase error gradient requires the use of the pixel values ​​of two adjacent passes within all the highlighted points, and its weighted maximum likelihood (WML) estimate is:

[0082]

[0083] Among them, arg(·) represents the argument, (·) * represents conjugation, w k is the weight assigned to each prominent point, p = 1, 2, ..., P. In order to make the higher quality prominent points have a greater contribution to the estimation and reduce the influence of the poor quality prominent points, the weight is defined as the estimated value of the signal-to-noise ratio within the prominent point. Therefore, the weight is calculated as follows:

[0084]

[0085]

[0086] Among them, A k (p) represents the amplitude of the pixel value of the k-th prominent point in the p-th pass. After obtaining the phase error gradient by estimation, the phase error gradients are superimposed to obtain an estimated value of the phase error:

[0087]

[0088] Using the estimated value of the phase error Compensate the phase error term in formula (5) One autofocus is completed. However, accurate phase error correction requires multiple iterations until a certain convergence condition is met. Therefore, the change rate of contrast at the prominent point with the strongest energy is used as the control condition for iterative convergence, and the definition of contrast at this point is:

[0089]

[0090] Among them, f n = |γ(s n )| 2 . When the change rate of contrast along the s direction is less than the set threshold, the iteration converges and the iteration stops. Therefore, this control condition is:

[0091]

[0092] After the iteration converges, the autofocus processing within this sub-aperture is completed. Since the phase errors in each sub-aperture are different, it is necessary to perform autofocus processing independently in sequence.

[0093] According to the above analysis, the processing flow for tomographic phase error correction of the registered two-dimensional image group using the improved weighted phase gradient autofocus method is obtained, as Figure 5 shown, including:

[0094] 1.1) Select several prominent points from the registered two-dimensional image group according to the energy criterion; the energy criterion is to screen out the pixel points that may contain strong scattering points by setting a threshold and put them into the prominent point set;

[0095] 1.2) Within each prominent point, using the conventional beamforming method, only a single snapshot is used to estimate the position of the strongest scattering point within the current prominent point in the tomography upward direction, and the linear phase of the prominent point pixel value is removed using the estimated position, so that only the phase error term is included in the phase carried by the prominent point additionally;

[0096] 1.3) Estimate the phase gradient by jointly using all the prominent points with the weighted maximum likelihood criterion; in the weighted maximum likelihood criterion, it is necessary to calculate the weight of each prominent point. Specifically, by estimating the signal-to-clutter ratio within each prominent point, the signal-to-clutter ratio is used as the weight of the prominent point, so that the prominent points with good quality obtain larger weights and the influence of the prominent points with relatively poor quality is weakened. The phase error gradient of the p-th pass is estimated by using the pixel values of all prominent points in the (p - 1)-th and p-th passes;

[0097] 1.4) Accumulate the estimated values of the phase error gradient to obtain the estimated value of the phase error; the phase error of the first pass is set to 0, then the phase error of the p-th pass is the sum of the phase gradients of the previous p - 1 passes;

[0098] 1.5) Compensate the phase error term by using the estimated value of the phase error;

[0099] 1.6) Iterate steps 1.1) to 1.5) until the iteration convergence condition is satisfied to complete the tomographic phase error correction. When the contrast change rate within the prominent point with the strongest energy is lower than the set threshold, the iteration reaches convergence, and at this time, the tomographic phase error correction of this sub-aperture is completed.

[0100] In the step of tomographic phase error correction in the embodiment of the present invention, first, prominent points are screened based on a new energy criterion. Secondly, the signal-to-clutter ratio within the prominent points is used to define the weights, improving the phase gradient estimation, and the weighted maximum likelihood criterion is adopted based on the obtained weights, making it more effective in suppressing the prominent points with relatively poor quality and improving the processing efficiency by reducing the requirement for the number of prominent points. Finally, the contrast change rate is used to control the iteration convergence, improving the convergence speed and suppressing the tomographic position shift.

[0101] Embodiment 4

[0102] Based on Embodiments 1 to 3, this embodiment further describes the tomographic focusing method.

[0103] Perform tomographic focusing on the two-dimensional image group after tomographic phase error correction to obtain the sub-aperture three-dimensional image of each sub-aperture, including:

[0104] Tomographic focusing means that in the sub-aperture, according to the pixel values g of the pixel group at (x’, y’), p (x ′ , y ′ ) estimate the intensity distribution of the scattering coefficient γ along the s direction at this position. The same operation is performed on the pixel group at each position, and the intensity distribution of the scattering coefficient along the s direction at all positions can be obtained, that is, the sub-aperture three-dimensional image is obtained. This image is x ′ -y ′The sub-aperture three-dimensional image in the -s coordinate system, where the s direction varies with the sub-aperture. Therefore, before performing incoherent superposition on the sub-aperture three-dimensional image, coordinate transformation is required, that is, transforming the local coordinate system x ′ -y ′ -s of each sub-aperture to the unified coordinate system x-y-z, as shown in the coordinate system Figure 2 . The coordinate transformation is calculated as follows:

[0105]

[0106] After completing the coordinate transformation, the three-dimensional image of the m-th sub-aperture in the coordinate system x-y-z can be obtained, denoted as g m (x, y, z), m = 1, 2, …, M. At this time, it is necessary to superpose all the sub-aperture three-dimensional images. In the actual observation scenario, since most targets are anisotropic, the incoherent superposition method is used to obtain the final three-dimensional image g(x, y, z):

[0107]

[0108] In a specific embodiment, the following analysis mainly focuses on a certain pixel group, so the two-dimensional coordinates (x ′ , y ′ ) are ignored in the analysis. To facilitate the analysis of tomographic focusing, two vectors need to be defined first. The vector g composed of the pixel values corresponding to the pixel group is defined as g = [g1, g2,..., g P T . γ is continuously distributed along the s direction, but in actual calculations, discrete sampling points need to be selected in the s direction. Assuming that along the s direction, a total of N points s1, s2, …, s min , s max] are sampled within the range [s n , then the values of γ at the selected discrete points γ(s1), γ(s2), …, γ(s N ) need to be calculated as the result of tomographic focusing. Let s n (n = 1, 2, …, N) be the n-th sampling height, then the steering vector a(s n ) is defined as:

[0109]

[0110] The conventional beamforming method is used to calculate γ(s n ) as:

[0111]

[0112] Calculate γ(s n ​)The focusing result along the s direction at this position can be obtained. The focusing results at all positions constitute the three-dimensional image of the sub-aperture in the x ′ -y ′ -s coordinate system of the sub-aperture.

[0113] Example 5

[0114] In this example, experiments are carried out using the publicly available multi-baseline CSAR data to prove the effectiveness and practicability of a multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus proposed by the present invention.

[0115] In the publicly available multi-baseline CSAR dataset, the radar operates in the X-band with a bandwidth of 640 MHz, covering HH, HV, VH, and VV full-polarization data. It contains a total of 8 passes of data, and each pass observes the scene omnidirectionally from 360°. The pitch angle observation range of the 8 passes is 43.7° to 45°. In the experiments of the present invention, multi-baseline CSAR data under HH polarization is used. In the experiment, during the sub-aperture division stage, the sub-apertures are divided at intervals of 3°, and a total of 120 non-overlapping sub-apertures are divided. In the two-dimensional imaging stage of each sub-aperture, the back-projection algorithm is used to obtain the two-dimensional image group of the sub-aperture. The comparison methods use the Weighted Least Square (WLS) method and the PGA method.

[0116] The observation scene is a parking lot where multiple cars are parked. In the embodiment of the present invention, two cars in the observation scene are selected, namely Ford Taurus and Toyota Camry, and their optical images are as Figure 6 shown. The experimental results of the two cars are respectively compared: the tomographic focusing results obtained by different phase error correction methods for a single pixel group, the contrast and entropy of the tomographic focusing obtained by different phase error correction methods, the two-dimensional projection results of the full-aperture three-dimensional imaging, and the full-aperture three-dimensional imaging results.

[0117] In the experiment of realizing tomographic focusing for a single pixel group of the Ford Taurus vehicle using different phase error correction methods, a total of 4 points are selected from 4 different sub-apertures, and the positions of the selected points are as Figure 7 shown. The 4 points come from different sub-apertures respectively: point A comes from the sub-aperture 6° - 9°, point B comes from the sub-aperture 348° - 351°, point C comes from the sub-aperture 129° - 132°, and point D comes from the sub-aperture 192° - 195°. The tomographic focusing results obtained by a single pixel group using different phase error correction methods are as Figure 8 shown. From Figure 8It is found that, compared with the other two methods, the improved weighted phase gradient autofocus method can effectively increase the main lobe level and suppress the sidelobe level at all four points, maintain a good phase error correction effect, and there is no problem of tomographic position shift. Table 1 shows the contrast of the tomographic focusing results obtained by different phase error correction methods at the selected four points, and Table 2 shows the entropy of the tomographic focusing results obtained by different phase error correction methods at the selected four points. It is found from Table 1 and Table 2 that the improved weighted phase gradient autofocus method proposed in the present invention has the best performance at points B and D; the WLS method has the best performance at point C. However, combining Figure 8 (c), it can be found that there is an obvious position shift after correcting point C with the WLS method, and the main lobe level is lower than the other two methods; the PGA method has the best performance at point A, but there is also a phenomenon of position shift.

[0118] In the two-dimensional projection of the full-aperture 3D imaging and the full-aperture 3D imaging experiment, the final 3D imaging result is obtained by incoherent superposition of the imaging results of all sub-apertures. The two-dimensional projection results are as Figure 9 shown, and the 3D imaging is as Figure 10 shown. It can be found from Figure 9 that among the imaging results obtained by using different phase error correction methods, the improved weighted phase gradient autofocus method has the best false target suppression effect in the red box area, and at the same time, the imaging result contour obtained by this method is cleaner in the blue box area. It can be found from Figure 10 that among the imaging results obtained by using the improved weighted phase gradient autofocus method and the PGA method for phase error correction, the false target suppression effect is better in the red box area. In the purple box area, the improved weighted phase gradient autofocus method can better restore the contour of the vehicle. In the green box area, the imaging result obtained by the improved weighted phase gradient autofocus method is also cleaner.

[0119] In addition, the same experiment was also carried out on the Toyota Camry vehicle. In the experiment of realizing tomographic focusing of a single pixel group of the Toyota Camry vehicle by using different phase error correction methods, a total of four points were selected from four different sub-apertures. The positions of the selected points are as Figure 11 shown. The four points come from different sub-apertures: point E comes from sub-aperture 36° - 39°, point F comes from sub-aperture 183° - 186°, point G comes from sub-aperture 207° - 210°, and point H comes from sub-aperture 342° - 345°. The tomographic focusing results obtained by a single pixel group using different phase error correction methods are as Figure 12As shown in the figure. Table 3 gives the contrast of the tomographic focusing results obtained by using different phase error correction methods at the selected 4 points, and Table 4 gives the entropy of the tomographic focusing results obtained by using different phase error correction methods at the selected 4 points. It can be found from Table 3 and Table 4 that the improved weighted phase gradient autofocus method proposed in the present invention achieves the best phase error correction performance at points F, G, and H. In terms of the phase error correction performance at point E, the contrast of the PGA method is slightly higher than that of the method proposed in the present invention, and the entropy reduction situation is slightly better than that of the method proposed in the present invention, but the tomographic position shift is larger. In addition, the phase error correction performance of the WLS method at the 4 selected points is worse than that of the PGA method and the method proposed in the present invention.

[0120] The two-dimensional projection results of the full-aperture three-dimensional imaging of the Toyota Camry vehicle are as Figure 13 shown, and the full-aperture three-dimensional imaging results are as Figure 14 shown. It can be found from the full-aperture imaging results that the imaging method based on the improved weighted phase gradient autofocus in the present invention has achieved the best imaging results.

[0121] Table 1 Contrast of the tomographic focusing results obtained by using different phase error correction methods at points A - D of the Ford Taurus vehicle

[0122] Method Point A Point B Point C Point D No correction 2.7144 2.1876 1.6845 2.0516 WLS method 3.3208 2.6516 2.9569 2.1448 PGA method 3.5203 3.0063 2.8729 2.2360 Improved weighted phase gradient autofocus method 3.4971 3.1571 2.8692 2.2701

[0123] Table 2 Entropy of the tomographic focusing results obtained by using different phase error correction methods at points A - D of the Ford Taurus vehicle

[0124] Method Point A Point B Point C Point D No correction 3.1704 3.4985 3.8251 3.6227 WLS method 2.8297 3.2217 2.9044 3.5428 PGA method 2.7080 2.9720 2.9871 3.4989 Improved weighted phase gradient autofocus method 2.7239 2.8787 2.9936 3.4722

[0125] Table 3 Contrast of the tomographic focusing results obtained by using different phase error correction methods at points E - H of the Toyota Camry vehicle

[0126] Method Point E Point F Point G Point H No correction 2.2758 1.8996 2.1949 1.9020 WLS method 2.3622 1.7986 2.3105 2.5698 PGA method 3.1402 2.1437 2.3701 2.7867 Improved weighted phase gradient autofocus method 3.1327 2.1514 2.5369 2.7904

[0127] Table 4 Entropy of the tomographic focusing results obtained by using different phase error correction methods at points E - H of the Toyota Camry vehicle

[0128] Method Point E Point F Point G Point H No correction 3.3514 3.6316 3.4857 3.6294 WLS method 3.3563 3.7130 3.3290 3.1309 PGA method 2.9668 3.5241 3.2963 3.0583 Improved weighted phase gradient autofocus method 2.9771 3.5187 3.2250 3.0532

[0129] The terms describing the positional relationship in the drawings are for illustrative purposes only and should not be construed as a limitation of this patent;

[0130] Obviously, the above embodiments of the present invention are merely examples for clearly explaining the present invention, rather than limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation manners here. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the claims of the present invention. This patent application relies on the Shenzhen Science and Technology Plan Grant (Project No.: JCYJ20240813151238049), the Shenzhen Science and Technology Plan Grant (Project No.: 202206193000001, 20220815171723002), the Guangdong Basic and Applied Basic Research Foundation (Project No.: 2023A1515011588), and the project "Research on Airborne Staring SAR Moving Target Detection and Tracking Algorithm" of Beijing Institute of Radio Measurement (Contract No.: 20242467).

Claims

1. A multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus, characterized in that, It includes the following steps: Divide the complete circular aperture into multiple non - overlapping sub - apertures, and each sub - aperture contains radar echo data collected during multiple passes; Within each sub - aperture, use the BP algorithm to image the radar echo data collected during multiple passes, obtain multiple two - dimensional sub - aperture ground - range images, and organize them to obtain the two - dimensional image group of the current sub - aperture; Register the two - dimensional image group of each sub - aperture by calculating the complex correlation between two two - dimensional sub - aperture ground - range images in the two - dimensional image group of each sub - aperture; Use the improved weighted phase gradient autofocus method to correct the tomographic phase error of the registered two - dimensional image group; Perform tomographic focusing on the two - dimensional image group after tomographic phase error correction to obtain the sub - aperture three - dimensional image of each sub - aperture; Incoherently superimpose the sub - aperture three - dimensional images of all sub - apertures to obtain the final CSAR three - dimensional imaging result.

2. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 1, wherein Divide the complete circular aperture into multiple non - overlapping sub - apertures, and each sub - aperture contains radar echo data collected during multiple passes, including: The radar-carrying aircraft flies along a circular trajectory of 360° around the observation scene and flies along the same circular trajectory at different flight altitudes, with a total of P circular passes. The azimuth angle of the radar relative to the scene center is θ, and the pitch angle of the p-th pass is Divide the complete circular aperture into M non - overlapping sub - apertures. The azimuth angle width corresponding to each sub - aperture is Δθ = 2π / M, and each sub - aperture contains P radar echo data collected during multiple passes.

3. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 2, wherein Within each sub - aperture, use the BP algorithm to image the radar echo data collected during multiple passes, obtain multiple two - dimensional sub - aperture ground - range images, including: Let the radar echo data after the p-th pass through the quadrature demodulation and pulse compression be s p (η, τ), where η is the slow time and τ is the fast time; Set the imaging focusing height to 0m. At this time, the imaging plane is the xOy plane. Assume that the imaging ranges of the radar in the x-direction and y-direction in the xOy plane are both [-R s , R s . At this time, the two-dimensional image to be generated is a square with a side length of 2R s . Obtain the x-direction resolution dx and y-direction resolution dy according to the working parameters of the radar. Therefore, the number of pixels in the two-dimensional image to be generated is ceil(·) is rounding up. Use s p (η, τ) to assign a value to each pixel in the two-dimensional image to be generated: where g p (x′, y′) represents the value of the pixel at coordinates (x′, y′) in the two-dimensional image to be generated, represents the value of the pixel at coordinates (x′, y′) in the two-dimensional image to be generated corresponding to the slow time η, f c is the carrier frequency, represents the distance from the pixel at coordinates (x′, y′) in the two-dimensional image to be generated corresponding to the slow time η to the current azimuth position (x r (η), y r (η), h p ) of the radar, h p is the flight altitude of the radar during the current passage, c is the speed of light, represents the value obtained from the radar echo data at the slow time η for the pixel at coordinates (x′, y′) in the two-dimensional image to be generated: When the slow time is determined to be η0, the radar echo data after quadrature demodulation and pulse compression is s p (η0, τ), and for each fast time τ, there corresponds a different slant range R = cτ / 2. Calculate and assign the pixel points equal to the slant range R the value of s p (η0, τ).

4. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 3, characterized in that Register the two - dimensional image group of each sub - aperture by calculating the complex correlation between two two - dimensional sub - aperture ground - range images in the two - dimensional image group of each sub - aperture, including: Select any one of the two - dimensional sub - aperture ground - range images in the two - dimensional image group as the main image, and calculate the complex correlation between the remaining two - dimensional sub - aperture ground - range images and the main image: ρ c = norm{|FFT -1 [FFT(g i (x′,y′))FFT(g j (x′,y′)) * |} where ρ c represents complex correlation, norm(·) represents normalization processing, FFT represents Fourier transform, and g i (x′, y′), g j (x′, y′) represent two different two-dimensional sub-aperture ground distance images; Obtain the displacement values between the remaining two - dimensional sub - aperture ground - range images and the main image through the maximum value of the complex correlation between the remaining two - dimensional sub - aperture ground - range images and the main image; Complete the registration between the remaining two - dimensional sub - aperture ground - range images and the main image according to the displacement values.

5. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 4, wherein Use the improved weighted phase gradient autofocus method to correct the tomographic phase error of the registered two - dimensional image group, including: 1.1) Select several prominent points from the registered two - dimensional image group according to the energy criterion; 1.2) Within each prominent point, use the conventional beamforming method to only use a single snapshot to estimate the position of the strongest scatterer within the current prominent point in the tomographic direction, and use the estimated position to remove the linear phase of the pixel values of the prominent point; 1.3) Use the weighted maximum likelihood criterion to jointly estimate the phase gradient for all prominent points; 1.4) Accumulate the estimated values of the phase error gradient to obtain the estimated value of the phase error; 1.5) Use the estimated value of the phase error to compensate the phase error term; 1.6) Iterate steps 1.1) to 1.5) until the iteration convergence condition is met to complete the tomographic phase error correction.

6. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 5, characterized in that Select several prominent points from the registered two - dimensional image group according to the energy criterion, and the energy criterion includes: Where, E k represents energy, and g p,k represents the pixel value traversed in the p-th path for the k-th prominent point, and E th represents the energy threshold, and the points that satisfy the energy criterion are selected as prominent points.

7. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 6, wherein Use the weighted maximum likelihood criterion to jointly estimate the phase gradient for all prominent points, including: Wherein, is the phase error gradient, w k is the weight assigned to each highlighted point, arg(·) represents taking the argument, (·) * represents taking the conjugate, s k represents the position of the strongest scattering point in the s direction among the highlighted points at the k-th position, and the s direction is perpendicular to the line of sight of the radar's main navigation path, c p,k represents clutter, A k (p) represents the amplitude of the pixel value of the k-th highlighted point in the p-th navigation path.

8. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 7, characterized in that Accumulate the estimated values of the phase error gradient to obtain the estimated value of the phase error, including: In the formula, is the estimated value of the phase error.

9. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 8, characterized in that The iterative convergence condition: Where dC represents the contrast change rate of the most prominent feature point with the strongest energy, and C i represents the contrast of the most prominent feature point with the strongest energy in the i-th round of iteration, C i+1 represents the contrast of the most prominent feature point with the strongest energy in the (i + 1)-th round of iteration, C represents the contrast of the most prominent feature point with the strongest energy, and c th is the threshold of the contrast change rate of the most prominent feature point with the strongest energy, g = [g1, g2,..., g P T represents the vector composed of the pixel values corresponding to the pixel group, a(s n ) is the guiding vector, and s n is the n-th sampling height among a total of N points sampled along the s direction within the range [s min , s max] .​ 10. The multi-baseline CSAR three-dimensional imaging method based on improved weighted phase gradient autofocus according to claim 9, wherein, Performing tomographic focusing on the two-dimensional image group after tomographic phase error correction to obtain the sub-aperture three-dimensional image of each sub-aperture, including: In the sub-aperture, according to the pixel value g of the pixel group at (x’, y’) p (x′, y′), estimate the intensity distribution of the scattering coefficient γ in the s direction at this position, obtain the intensity distribution of the scattering coefficient in the s direction at all positions, that is, obtain the three-dimensional image of the sub-aperture; Performing coordinate transformation on all sub-aperture three-dimensional images so that all sub-aperture three-dimensional images are located in the same coordinate system.

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