Three-dimensional polar coordinate format algorithm and rapid implementation method thereof

Abstract

The invention discloses a three-dimensional polar coordinate format algorithm and a rapid implementation method thereof, which reduce the required three interpolation operations into two interpolation operations, reduce the calculation complexity of the algorithm and improve the overall execution efficiency of the algorithm. The azimuth dechirp operation in the three-dimensional space is converted into the two-dimensional space processing, so that the phase error caused by the azimuth dechirp is effectively reduced, and the precision of the imaging result is further improved; according to the method, time-consuming distance direction interpolation operation, azimuth direction interpolation operation and introduced interpolation errors in a traditional method are avoided, the processing efficiency is remarkably improved while the imaging quality is guaranteed, and the problems that sinc interpolation is low in speed and prone to being influenced by the interpolation errors are effectively solved; the invention provides an efficient and high-precision solution for a three-dimensional imaging scene meeting the union in a wavenumber domain, and solves the problem that the precision is reduced due to the fact that a numerical value in a root number of Stolt interpolation in a traditional three-dimensional Omega-K imaging algorithm is smaller than 0.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of time domain algorithm, more particularly, to a three-dimensional polar coordinate format algorithm and an implementation method thereof. BACKGROUND

[0002] Anti-terrorism work is a key task to maintain national security and social stability, and has great significance to guarantee the national economy and people's livelihood. In the field of security inspection, traditional metal detectors have problems such as short detection distance and low detection efficiency, which are difficult to meet the actual combat needs of modern security inspection; the infrared imaging technology is not clear and lacks detail resolution when the target is covered by fabric. Under this background, millimeter wave imaging technology shows its significant advantages in concealed target detection, which can effectively identify metal objects, guns and other dangerous objects hidden in clothes, and obtain more complete three-dimensional scattering characteristic information of the target, so it has become a research hotspot in the field of domestic and foreign security inspection of concealed weapons imaging and identification. At present, the millimeter wave radar system applied to the security inspection scene mainly uses two-dimensional planar antenna array, and realizes high-resolution three-dimensional imaging of the target by constructing synthetic aperture through multiple elements.

[0003] As the core of the system, the imaging algorithm must achieve a good balance between calculation accuracy and calculation efficiency. In actual security inspection applications, the algorithm needs to have near real-time processing capability and high imaging accuracy. However, in traditional three-dimensional reconstruction algorithms, although the time-domain three-dimensional imaging algorithm has intuitive principle and high imaging accuracy, when realizing high-resolution imaging, due to the small imaging grid spacing and large number, the calculation burden is significantly increased, which is difficult to meet the real-time requirements of passenger security inspection. On the other hand, common frequency domain algorithms, such as range-doppler algorithm, frequency scaling algorithm, polar format algorithm (PFA) and three-dimensional Omega-K imaging algorithm, are usually based on the ideal trajectory assumption of platform uniform linear motion and the stationary phase principle, and introduce approximation about distance model and space variation in the processing process, which limits the imaging accuracy to a certain extent. For the interpolation operation involved in PFA and Omega-K algorithms, researchers often use fast calculation methods such as non-uniform fast Fourier transform (NUFFT) and its improved form FGG-NUFFT to improve the calculation efficiency. Therefore, for two-dimensional planar antenna array, it has important theoretical value and clear practical significance to carry out research on efficient and high-precision millimeter wave three-dimensional reconstruction algorithm.

[0004] For the three-dimensional imaging task based on two-dimensional uniform planar array, the back-projection (BP) algorithm has the advantages of flexible imaging grid setting, no restriction on radar operating frequency band, support for parallel processing, and can be applied to complex imaging modes such as squint and curved trajectory. However, its high computational complexity makes it difficult to meet the real-time imaging requirements. In addition, the interpolation operation in the algorithm will introduce additional errors, which will adversely affect the final imaging accuracy. To improve efficiency, improved methods such as fast back-projection (FBP) algorithm and fast factorized back-projection (FFBP) algorithm have been proposed, which have improved the processing speed to some extent, but still cannot realize real-time imaging processing.

[0005] After the traditional three-dimensional polar coordinate format algorithm performs the azimuth Dechirp operation, the residual phase error is distributed in three dimensions, and three times of interpolation is required to complete the data rearrangement. Due to the heavy calculation burden of the interpolation process, not only the imaging efficiency is limited, but also interpolation errors are easily introduced, which seriously affects the imaging quality and accuracy. The three-dimensional Omega-K imaging algorithm is a high-precision frequency domain method in theory, and its implementation depends on the three-dimensional Stolt interpolation operation with large amount of calculation. However, when the three-dimensional imaging scene satisfies and , and , the present application provides an efficient and high-precision solution, which overcomes the problem of accuracy decline caused by the Stolt interpolation root number value less than 0 in the traditional three-dimensional Omega-K imaging algorithm.

[0006] In addition, the present application is supported by the Guangdong Provincial Basic and Applied Basic Research Fund Regional Joint Fund-Young Fund Project "Three-dimensional Imaging Algorithm Research of Millimeter Wave Near-field Radar Based on FMCW" (Project Number: 2022A1515110864), and the present application expresses its gratitude. The following is the relevant literature.

[0007] [1] Peng X M, Hong W, Wang Y P, Tan W X, Wu Y R. Polar Format Algorithm for Airborne DLSLA Three-dimensional Synthetic Aperture Radar with Wavefront Curvature Phase Error Compensation[J]. IEEE Geoscience and Remote Sensing Letters, 2014, 11(6): 1036-1040. [2] Zeng X, Ma Y X, Li Z Y, Wu J J, Yang J Y. Near-field Fast Time-frequency Joint Three-dimensional Imaging Algorithm Based on Aperture Linearization[C]. 2021 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Brussels, Belgium, 2021, IEEE: 5163-5166. [3] Mao X, Zhu DY, Zhu ZD. Wavefront curvature compensation for polar format algorithm under arbitrary radar flight path[J]. IEEE Geoscience and Remote Sensing Letters, 2012, 9(3): 526-530. [4] KANATZIDIS M, GOLDBERG E, MAYEWSKI R. Spotlight synthetic aperture radar: signal processing algorithms[M]. Boston, MA, USA: Artech House, 1995. [5] DOGARIU T. Polar format algorithm for 3D imaging in forward looking synthetic aperture radar[R]. Technical report, September 2020. [6] Dai CY, Zhang XL. Bistatic polar format algorithm based on non-uniform fast Fourier transform[J]. Journal of Electromagnetic Waves and Applications, 2011, 25(17-18): 2328-2340. SUMMARY

[0008] The technical problem to be solved by the present application is to provide a three-dimensional polar format algorithm. The algorithm can solve the following technical problems: 1. Compared with the traditional three-dimensional PFA, the present algorithm reduces the required cubic interpolation operation to twice, significantly reduces the computational complexity of the algorithm, and improves the overall execution efficiency of the algorithm; 2. By converting the azimuth Dechirp operation in three-dimensional space into two-dimensional space processing, the present algorithm effectively reduces the phase error caused by azimuth Dechirp, thereby further improving the accuracy of the imaging result; 3. The present algorithm avoids the time-consuming distance interpolation operation, azimuth interpolation operation and interpolation error introduced in the traditional method, significantly improves the processing efficiency while ensuring the imaging quality, and effectively solves the problem that the sinc interpolation is slow and easily affected by interpolation error; 4. For the three-dimensional imaging scene satisfying and , and , the present application provides an efficient and high-precision solution, which overcomes the problem of accuracy decline caused by the Stolt interpolation root number less than 0 in the traditional three-dimensional Omega-K imaging algorithm.

[0009] In order to solve the above technical problems, the technical scheme of the present application is: 1) A two-dimensional uniform planar antenna array is used to obtain antenna element echo data; 2) Height direction fast Fourier transform is performed; 3) The along Each two-dimensional echo signal slice in the axial direction is subjected to range-azimuth focusing processing: azimuth dechirp operation, range interpolation and azimuth interpolation, range inverse Fourier transform and azimuth Fourier transform; 4) inverse Fourier transform in the height direction to obtain the final three-dimensional SAR imaging result.

[0010] By adopting the technical scheme, the following beneficial effects are achieved: 1. Compared with the traditional three-dimensional PFA, the present algorithm reduces the required three times of interpolation operation to twice, significantly reduces the calculation complexity of the algorithm, and improves the overall execution efficiency of the algorithm; 2. By converting the azimuth dechirp operation in the three-dimensional space into a two-dimensional space processing, the present algorithm effectively reduces the phase error caused by the azimuth dechirp, thereby further improving the accuracy of the imaging result; 3. The present algorithm avoids the time-consuming range interpolation operation, azimuth interpolation operation and interpolation error introduced in the traditional method, significantly improves the processing efficiency while ensuring the imaging quality, and effectively solves the problem that the sinc interpolation is slow and is easily affected by the interpolation error; 4. For the three-dimensional imaging scene satisfying and , and , the present application provides an efficient and high-precision solution, which overcomes the problem of accuracy decline caused by the fact that the root number in the Stolt interpolation in the traditional three-dimensional Omega-K imaging algorithm is less than 0. BRIEF DESCRIPTION OF DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced below. Obviously, the drawings in the following description are only exemplary, and for those skilled in the art, other implementation drawings can also be obtained from the provided drawings without creative labor.

[0012] The structures, proportions, sizes, etc. shown in the specification are only used to cooperate with the content disclosed in the specification, to be understood and read by those skilled in the art, and do not define the limiting conditions for the implementation of the present application, so they do not have technical significance. Any modification of the structure, change of the proportion relationship or adjustment of the size, without affecting the effect and purpose that the present application can produce, should still fall within the scope of the technical content disclosed by the present application.

[0013] Figure 1 The three-dimensional PFA and the fast implementation method thereof are provided. Figure 2 This is the echo signal model. Detailed Implementation

[0014] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. It should be noted that these descriptions are for the purpose of aiding understanding the present invention, but do not constitute a limitation thereof. Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0015] See Figures 1-2 As shown, this invention discloses a three-dimensional polar coordinate format algorithm and its fast implementation method, as detailed below: A two-dimensional uniform planar antenna array is used to acquire antenna element echo data and perform three-dimensional imaging. The three-dimensional geometric model of the echo data acquisition is as follows: Figure 2 As shown, the transmitting antenna elements and the receiving antenna elements are located in approximately the same position. This is centered on the uniformly distributed linear array. Establish a three-dimensional rectangular coordinate system with the origin as the coordinate origin. The linear array is located in In the plane, and in shaft and The lengths of the antenna arrays along the axial direction are respectively and , The positive direction of the axis points to the object being measured or the imaging scene.

[0016] For the convenience of describing the imaging algorithm later, let's call it... , and The positive directions of the axes represent the azimuth, altitude, and range directions, respectively.

[0017] During the process of acquiring echo data from the object under test, the transmit and receive antenna edges The antenna transmits a millimeter-wave band frequency modulated continuous wave (FMCW) signal at the bottom of the antenna array along the axis and receives the echo, obtaining an echo data slice stored in a two-dimensional matrix.

[0018] Subsequently, the transmit and receive antenna edges Translate one sampling unit along the positive axis and repeat the above process. The axial sampling process yields another slice of echo data stored in a two-dimensional matrix, until the transmit and receive antennas are moved to... The last element in the positive axis direction, and completes the process along the axis. The sampling process along the axial direction involves obtaining complete three-dimensional echo data of the object being measured or the imaging scene. This three-dimensional echo data includes... The first echo data slice was obtained during the acquisition of the first echo data slice. In the process of storing echo data slices in a two-dimensional matrix, the coordinates of the transmitting and receiving antennas are: Scene center point to the plane where the antenna array is located The reference distance is Then any point target in the scene The coordinates are Ignoring the attenuation of the transmitted signal amplitude with propagation distance and the influence of the interaction between the antenna array elements and the target, the target at any point in the scene... The Each echo signal slice is represented as (1) (2) in, Represents the range wavenumber. Indicates that it is located at The first axis Each transceiver antenna and point Instantaneous slant distance between targets Indicates the speed of electromagnetic wave propagation. Indicates the center frequency of the carrier. Indicates the distance-directed frequency modulation. Indicates distance in advance time. The imaginary unit and Therefore, the target coordinates at any point in the scene The three-dimensional echo signal is represented as (3) in, Represents a two-dimensional echo signal slice along The arrangement along the positive axis, i.e., the three-dimensional echo signal of the measured object, can be obtained from along... The proposed algorithm combines two-dimensional echo signal slices along the axial direction. It first performs a height-to-direction Fast Fourier Transform (FFT) on the three-dimensional echo signal, and then performs a height-to-direction Fast Fourier Transform (FFT) on the echo signal along the axial direction. Each two-dimensional echo signal slice along the axial direction is subjected to range-azimuth focusing, and finally, height focusing is performed by inverse FFT (IFFT). A height-direction Fourier transform is performed on (3), i.e. (4) (5) in, This indicates the three-dimensional echo signal after height-to-Fourier transform processing. The first in the axial direction A two-dimensional echo signal slice, for the first phase term in equation (5) in Performing a Taylor series expansion at this point, we get (6).

[0019] Among them, containing and The first term will cause the focus position of the measured object to shift, containing Items and containing The phase error introduced by the phase error will cause the orientation impulse response function of the measured object to broaden or defocus, which is due to the inherent model approximation error of the PFA algorithm. However, under the condition of a small imaging range, the impact of the above-mentioned spatial variability and phase error on the image quality can be limited to an acceptable range.

[0020] Perform the orientation Decirp operation, i.e., multiply by (7) have to (8).

[0021] Performing range interpolation and azimuth interpolation on equation (8) respectively, we have: (9) (10) get (11) along The positive axis is used to process each two-dimensional echo slice signal according to formulas (7) to (11), resulting in... (12).

[0022] Finally, range IFFT, azimuth FFT, and height IFFT are performed on equation (12) respectively to obtain the final three-dimensional SAR imaging results. The processing flowchart of the proposed algorithm is shown below. Figure 1 As shown in (a). To effectively improve the computational efficiency of the algorithm, a fast implementation method based on the FiNUFFT guru interface is adopted to replace the time-consuming range and azimuth interpolation and corresponding IFFT operations in the traditional processing flow. While avoiding the time overhead and potential errors caused by interpolation processing, this method can ensure image quality and significantly improve the overall computational efficiency of the algorithm. The specific implementation process is as follows: Figure 1 As shown in (b).

[0023] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A three-dimensional polar coordinate format algorithm, characterized in that... Includes the following steps: 1) Two-dimensional uniform planar antenna arrays are used to acquire antenna element echo data; 2) Perform height-to-fast Fourier transform; 3) Along Each two-dimensional echo signal slice along the axis is subjected to range-azimuth focusing processing: azimuth delinear frequency modulation, range interpolation and azimuth interpolation, range inverse Fourier transform and azimuth Fourier transform; 4) Perform an inverse Fourier transform to obtain the final three-dimensional SAR imaging result.

2. The three-dimensional polar coordinate format algorithm according to claim 1, characterized in that: In S1, in the three-dimensional geometric model for echo data acquisition, the transmitting antenna elements and the receiving antenna elements are located at the same position, with a uniformly distributed linear array center. Establish a three-dimensional rectangular coordinate system with the origin as the coordinate origin. The linear array is located in In the plane, and in shaft and The lengths of the antenna arrays along the axial direction are respectively and , The positive direction of the axis points towards the object being measured or the imaging scene, and is denoted as... , and The positive directions of the axes represent the azimuth, altitude, and range directions, respectively; during the acquisition of echo data from the measured object, the transmitting and receiving antennas move along... The transceiver antenna transmits a millimeter-wave band frequency-modulated continuous wave signal at the bottom of the antenna array along the axial direction and receives the echo, obtaining an echo data slice stored in a two-dimensional matrix. Subsequently, the transceiver antennas... Translate one sampling unit along the positive axis and repeat the above process. The axial sampling process yields another slice of echo data stored in a two-dimensional matrix, until the transmitting and receiving antennas are moved to... The last element in the positive axis direction, and completes the process along the axis. The sampling process along the axial direction involves obtaining complete three-dimensional echo data of the object being measured or the imaging scene. This three-dimensional echo data includes... The first echo data slice was obtained during the acquisition of the first echo data slice. In the process of storing echo data slices in a two-dimensional matrix, the coordinates of the transmitting and receiving antennas are: Scene center point to the plane where the antenna array is located The reference distance is Then any target point in the scene The coordinates are Ignoring the attenuation of the transmitted signal amplitude with propagation distance and the influence of the interaction between the antenna array elements and the target, the target at any point in the scene... The Each echo signal slice is represented as （1） （2） in, Represents the range wavenumber. Indicates that it is located at The first axis Each transceiver antenna and point Instantaneous slant distance between targets Indicates the speed of electromagnetic wave propagation. Indicates the center frequency of the carrier. Indicates the distance-directed frequency modulation. Indicates distance in advance time. The imaginary unit and Therefore, the target coordinates at any point in the scene The three-dimensional echo signal is represented as （3） in, Represents a two-dimensional echo signal slice along The arrangement along the positive axis, i.e., the three-dimensional echo signal of the measured object, can be obtained from along... It is composed of two-dimensional echo signal slices along the axial direction.

3. The three-dimensional polar coordinate format algorithm according to claim 2, characterized in that: In S2, perform a height-to-Fourier transform on (3), i.e. （4） （5） in, This indicates the three-dimensional echo signal after height-to-Fourier transform processing. The first in the axial direction A two-dimensional echo signal slice, for the first phase term in equation (5) in Performing a Taylor series expansion at this point, we get （6）。 4. According to the three-dimensional polar coordinate format algorithm described in claim 3, in S3, the azimuth delinear frequency modulation operation is performed on equation (6), that is, multiplied by （7） have to （8）。 5. The three-dimensional polar coordinate format algorithm according to claim 4, characterized in that: In S3, range interpolation and azimuth interpolation are performed on equation (8) respectively, i.e. （9） （10） get （11） along The positive axis is used to process each two-dimensional echo slice signal according to formulas (7) to (11), resulting in... （12）。 6. The three-dimensional polar coordinate format algorithm according to claim 5, characterized in that: The final three-dimensional SAR imaging results are obtained by performing range-direction inverse Fourier transform, azimuth-direction inverse Fourier transform, and altitude-direction inverse Fourier transform on equation (12).

7. A fast implementation method for a three-dimensional polar coordinate format algorithm, characterized in that: The algorithm adopts a fast implementation method based on the FiNUFFTguru interface, replacing the time-consuming range interpolation, azimuth interpolation and corresponding inverse Fourier transform operations in the traditional processing flow.

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