Fast ISAR imaging method based on fractional Fourier transform
By using a fast ISAR imaging method based on fractional Fourier transform, the problems of large computational load and propagation error in traditional methods are solved, achieving efficient target frequency modulation estimation and image focusing, thus improving the ISAR imaging quality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-31
- Publication Date
- 2026-03-10
AI Technical Summary
Traditional ISAR imaging methods for maneuvering targets suffer from high computational complexity and significant propagation errors when estimating the target's frequency modulation, leading to a decline in imaging quality.
A fast ISAR imaging method based on fractional Fourier transform is adopted. By establishing the relationship between the target frequency modulation frequency and the time-frequency transformation angle, the time-frequency transformation angle is calculated using geometric relationships, the frequency modulation frequency of the target signal is quickly estimated, and phase compensation is performed to obtain ISAR images with good focusing effect.
It significantly reduces the computational complexity of the algorithm, avoids the impact of propagation errors, improves image accuracy and resolution, and achieves fast and accurate parameter estimation.
Smart Images
Figure CN121634097A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of ISAR imaging technology, and specifically to a fast ISAR imaging method based on fractional Fourier transform. Background Technology
[0002] Inverse Synthetic Aperture Radar (ISAR) can achieve high-resolution imaging observation of non-cooperative maneuvering targets using a fixed radar antenna, attracting widespread attention from research institutions both domestically and internationally in recent years. In ISAR imaging, accurately estimating the frequency modulation of the target echo signal is crucial for obtaining well-focused ISAR images. Based on this, a series of range-instantaneous Doppler (RID) algorithms, such as the Coherent Accumulation Generalized Cubic Function (CIGCPF) algorithm and the Integral Generalized Cubic Function (PGCPF) algorithm, have been proposed and applied to ISAR imaging of maneuvering targets, achieving high-resolution radar imaging observation of maneuvering targets to a certain extent. However, traditional RID algorithms like CIGCPF often introduce significant propagation errors, reducing the accuracy of target motion parameter estimation and leading to deterioration of the final ISAR image quality. Furthermore, traditional algorithms often require a search method to determine the optimal matching values of motion parameters, significantly increasing algorithm complexity and hindering engineering implementation and real-time signal processing applications.
[0003] Time-frequency distribution functions (TF-DCFs) are a powerful and widely used analytical tool in parameter estimation. By rotating the signal at a certain angle, they can establish an equivalent relationship between motion parameters and the transformed angle, transforming the parameter estimation problem into a transformed angle estimation problem. This weakens the estimation dependencies between parameters, thereby suppressing the impact of propagation errors on the accuracy of parameter estimation. Therefore, TF-DCFs have a unique advantage in estimating target motion parameters in ISAR imaging. However, traditional TF-DCFs still require searching for the optimal matching angle when estimating the transformed angle. To ensure search accuracy, a small iterative search step size is often needed, thus the huge computational load still limits its application in engineering implementation.
[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention
[0005] Traditional ISAR imaging methods for maneuvering targets often suffer from high computational complexity and significant propagation errors when estimating the target chirp frequency, leading to a decline in image quality. This invention provides a fast ISAR imaging method based on fractional Fourier transform, which can overcome the shortcomings of existing technologies to some extent.
[0006] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.
[0007] According to a first aspect of the present invention, a fast ISAR imaging method based on fractional Fourier transform is provided, the method comprising: Receive the echo signal, and perform down-conversion and distance compression on the echo signal; The echo signal, after down-conversion and range compression, undergoes envelope alignment and initial phase correction to ensure all target scattering points are within the correct range cell, thus obtaining the [missing information]. Within the nth distance unit Expressions for each scattering point with respect to azimuth and time; The phase term of the obtained scattering point expression is subjected to Wiener distribution transformation and then substituted into the echo signal expression for rewriting. Based on the rewritten formula, ignoring the linear phase term in the echo signal expression after Wiener distribution transformation, and according to the characteristics of Wiener distribution transformation, combined with the system pulse repetition frequency, a relationship between the target modulation frequency and the time-frequency transformation angle is established. Calculating the tangent of the time-frequency conversion angle using geometric relationships: The angles are obtained through two sets of FRFT transformations. and The transformation result is used to obtain the normalized projection length of the FRFT result at the corresponding angle. and Furthermore, the angular relationship equation is satisfied. By dividing the two sets of normalized projection length equations and rewriting them, the time-frequency conversion angle is obtained. The formula for calculating the tangent value; According to the time-frequency conversion angle The tangent value, combined with the established relationship between the modulation frequency and the transformation angle, is used to calculate the modulation frequency of the target signal; By constructing a corresponding compensation phase using the estimated target signal modulation frequency, phase compensation is performed on the echo signal to obtain a well-focused ISAR image of the maneuvering target.
[0008] In some exemplary embodiments, the echo signal is expressed as:
[0009] in, Indicates the signal amplitude term. Represents distance in terms of fast time. At the speed of light, and These represent the signal bandwidth and the accumulation time of the scattering point, respectively.
[0010] In some exemplary embodiments, the obtaining of the first Within the nth distance unit The expression for the scattering point with respect to azimuth and time is:
[0011] in, , and These represent the initial phase, center frequency, and modulation frequency, respectively. This represents the signal amplitude term at the nth scattering point. The wavelength of the radar transmitted signal. Indicates direction and time. This represents the instantaneous distance from the scattering point to the radar at the initial moment.
[0012] In some exemplary embodiments, the substitution of the echo signal expression is rewritten.
[0013] in, The frequency is the Doppler frequency.
[0014] In some exemplary embodiments, the angles of the two sets of FRFT transformations are respectively and The transformation result is used to obtain the normalized projection length of the FRFT result at the corresponding angle. and Specifically:
[0015]
[0016] in, and They represent angles respectively. With angle The normalized projection length of the FRFT result. The length of the normalized projection, This is the time-frequency transformation angle.
[0017] In some exemplary embodiments, the relationship between the two sets of normalized projection lengths is divided and rewritten to obtain the time-frequency conversion angle. The formula for calculating the tangent is as follows: .
[0018] In some exemplary embodiments, the step of adjusting the time-frequency conversion angle... The tangent value, combined with the established relationship between the modulation frequency and the transformation angle, is used to calculate the modulation frequency of the target signal, specifically:
[0019] in, To adjust the frequency of the target signal, is the pulse repetition frequency.
[0020] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the fast ISAR imaging method based on fractional Fourier transform described in the first aspect above.
[0021] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, it implements the fast ISAR imaging method based on fractional Fourier transform described in the first aspect above.
[0022] According to a fourth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the fast ISAR imaging method based on fractional Fourier transform described in the first aspect above by executing the executable instructions.
[0023] The fast ISAR imaging method based on fractional Fourier transform provided by the embodiments of the present invention, through the aid of geometric information, significantly reduces the computational complexity of the algorithm while effectively avoiding the influence of propagation errors, achieving a trade-off between image accuracy and computational load, and ensuring the accuracy of the final parameter estimation and the resolution of the obtained ISAR image.
[0024] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description
[0025] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.
[0026] Figure 1 The geometry for ISAR imaging observation of moving targets to which this invention applies; Figure 2 The frequency modulation (FRFT) result of the maneuvering target to which this invention applies; Figure 3This relates to the relationship between the projection length and the time-frequency transformation angle to which this invention applies; Figure 4 This is a flowchart of the method of the present invention. Detailed Implementation
[0027] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
[0028] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.
[0029] To address the shortcomings and deficiencies of existing technologies, this example embodiment provides a fast ISAR imaging method based on fractional Fourier transform. By analyzing and extracting the geometric relationship between the target frequency modulation and two sets of FRFT transform angles, a corresponding motion parameter estimation algorithm is designed. This method can quickly, independently, and accurately estimate the target frequency modulation, thereby effectively avoiding the impact of propagation errors on the accuracy of parameter estimation and thus improving imaging quality.
[0030] like Figure 4 The fast ISAR imaging method based on fractional Fourier transform provided in this embodiment of the invention may include the following steps: Step S1: Establish an ISAR imaging echo signal model; Step S11: Establish a geometric model for ISAR imaging observation of moving targets; Step S12: Calculate the equivalent position vector of the target scattering point; Step S13: Give the expression for the scattering point after envelope alignment and initial phase correction.
[0031] Step S2: Fast estimation and imaging of motion parameters based on FRFT; Step S21: Perform Wiener distribution transformation on the echo signal; Step S22: Establish the relationship between frequency modulation and angle transformation; Step S23: Calculate the tangent of the time-frequency conversion angle using geometric relationships; Step S24: Calculate the signal modulation frequency based on the time-frequency conversion angle.
[0032] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and embodiments.
[0033] In step S1, an ISAR imaging echo signal model is established.
[0034] Figure 1 The geometric configuration for ISAR imaging of moving targets is given. The origin of the coordinate system is taken as the center of rotation of the target. ,Establish Three-dimensional Cartesian coordinate system and These represent the unit vector along the radar line of sight and the three-dimensional angular velocity vector of the moving target, respectively. (Three-dimensional angular velocity vector) It can also be decomposed into two components that are parallel and perpendicular to the radar line of sight, namely the horizontal component. With vertical component Considering the horizontal component It does not produce rotational motion, meaning it does not contribute to the Doppler effect of the signal echo; therefore, this invention primarily considers the vertical component. The role and impact.
[0035] Assume there is a scattering point on the target. Its coordinates are represented as At this point, its Doppler frequency can be expressed as (1) in, and These represent the inner product and the outer product, respectively. This indicates the distance from the origin of the coordinate system to the scattering point. Vectors between This represents the translational velocity of the scattering point. The wavelength of the radar transmitted signal is given. The scattering point can be obtained by integrating the Doppler signal along the time dimension. The instantaneous distance to the radar is expressed as follows: (2) in, and These represent the initial radial velocity and the initial acceleration, respectively. and These represent the constant coefficients and first-order coefficients of the components projected onto the three coordinate axes, respectively. Indicates direction and time. The instantaneous distance from the scattering point to the radar at the initial moment is denoted as . Let be the equivalent position vector of the scattering point, and have (3) in, and Representing vectors respectively and along , , The component along the axial direction. The radar transmitted signal waveform is a linear frequency modulated (LFM) signal. After down-conversion and range compression, the final received echo signal expression is: (4) in, Indicates the signal amplitude term. Represents distance in terms of fast time. At the speed of light, and These represent the signal bandwidth and the accumulation time of the scattered point illumination, respectively. After envelope alignment and initial phase correction, all scattered points on the target are within the correct range cell. At this point, the [missing information]... Within the nth distance unit The expression for the scattering point with respect to azimuth and time can be rewritten as follows: (5) in, , and These represent the initial phase, center frequency, and frequency modulation (FM), respectively. Since the center frequency only determines the location of the scattering point, accurate estimation and compensation of the signal FM are necessary to obtain a well-focused ISAR image.
[0036] In step S2, motion parameters are rapidly estimated and imaged based on FRFT.
[0037] Based on the previously introduced ISAR echo signal model for maneuvering targets, the analysis and derivation are carried out. First, the phase term in equation (5) is rewritten as follows: (6) After performing the Wiener distribution (WVD) transformation on the above equation, we can obtain... (7) in, , and Let represent the impulse response function, the time delay variable, and the Doppler frequency, respectively. Substituting equation (7) into the echo signal expression, equation (5) is rewritten as follows: (8) Define the time-frequency transformation angle of the maneuvering target in the time-frequency domain as: From the above equation, it is easy to see that after the WVD transformation, the linear phase term only determines the position of the WVD projection and does not contribute to the estimation of the frequency modulation. Therefore, the linear term will be ignored in the following discussion, and the estimation of the frequency modulation will be the main focus. Based on the characteristics of the WVD transformation, the relationship between the frequency modulation and the transformation angle can be established as follows: (9) in, This represents the pulse repetition frequency of the system. From the above equation, it is easy to see that the target frequency modulation estimation has now been transformed into a time-frequency transformation angle. The problem of estimating the frequency modulation frequency (FM) is addressed. Traditional estimation methods involve setting a search range and iteration step size, searching for all angles within that range to obtain the transformed angle value, which significantly increases the computational complexity of the algorithm. To reduce the computational load, this invention proposes a fast FM estimation method based on FRFT. The corresponding principles and algorithm steps will be explained later. Figure 2 and Figure 3 A detailed derivation explanation is provided.
[0038] Figure 2 and Figure 3 The geometric information used in the proposed fast FRFT estimation algorithm is presented. Since FRFT can be viewed as a projection of the target trajectory transformed along a specific angle, Figure 3 In Representing the normalized projected length within the distance compression domain, it is easy to see from the figure that the projected length... With time-frequency transformation angle There are specific geometric relationships that can be measured. Derivation of time-frequency transformation angle from length value This allows for the estimation of the modulation frequency. However, within the two-dimensional distance compression domain, the length of the normalized projection... It is often difficult to obtain through measurement, and therefore the angle cannot be calculated. To estimate the frequency modulation, the estimation approach is changed. The elimination of the time-frequency transformation angle is achieved by using the transformation results of two sets of FRFT transformations with angles of and , respectively. This directly yields the relationship between the time-frequency transformation angle and the two sets of FRFT transformation angles. Therefore, from Figure 3 The following geometric relationship can be obtained. (10) (11) in, and They represent angles respectively. With angle The normalized projection length of the FRFT result. To ensure that equations (10) and (11) hold, the relevant angles need to satisfy the following relationship: (12) The above equation holds true when the time-frequency transformation angle is finite. Considering that the corresponding observation angle is often a small value when observing maneuvering targets with ISAR, the above equation usually holds true in ISAR imaging of maneuvering targets. After dividing equation (10) and equation (11) and rewriting, the tangent of the time-frequency angle can be obtained by the following equation. (13) Therefore, the time-frequency conversion angle can be estimated using the above formula. Then, by combining with equation (9), the estimated frequency modulation (FM) can be quickly calculated. The algorithm only uses two sets of FRFT transform angles and results to quickly and accurately estimate the target FM, greatly reducing the computational complexity of the algorithm. Finally, by constructing the corresponding compensation phase using the estimated FM and performing phase compensation on the echo, a well-focused ISAR image of the maneuvering target can be obtained.
[0039] It should be noted that, as another aspect, this application also provides a storage medium, which may be included in an electronic device or may exist independently without being assembled into the electronic device. The storage medium carries one or more programs, which, when executed by an electronic device, cause the electronic device to perform the methods described in the following embodiments.
[0040] In one embodiment, this application provides a computer program product including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.
[0041] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.
[0042] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.
[0043] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.
Claims
1. A fast ISAR imaging method based on fractional Fourier transform, characterized in that, The method comprises: receiving echo signals, performing down-conversion processing and range compression on the echo signals; The echo signal which is processed by frequency down conversion and range compression is subjected to envelope alignment and initial phase correction, so that all scattering points of the target are in correct range cells, and an expression of the first scattering point in the first range cell with respect to azimuth time is obtained. performing Wiener distribution transformation on a phase term of a scattering point expression obtained, and substituting the scattering point expression into an echo signal expression to rewrite the echo signal expression; based on the rewritten expression, ignoring a linear phase term in the echo signal expression after the Wiener distribution transformation, establishing a relationship between a target frequency modulation and a time-frequency transformation angle according to characteristics of the Wiener distribution transformation and in combination with a system pulse repetition frequency; The tangent value of the time-frequency conversion angle is calculated by using geometric relations: the normalized projection lengths of the FRFT results corresponding to the angles and are obtained by using the transformation results of the two groups of FRFT transformation angles and , and the tangent value calculation formula of the time-frequency conversion angle is obtained by dividing the relation formula of the two groups of normalized projection lengths and rewriting. According to the time-frequency conversion angle The tangent value, combined with the established relationship between the modulation frequency and the transformation angle, is used to calculate the modulation frequency of the target signal; constructing a corresponding compensation phase by using an estimated target signal frequency modulation, performing phase compensation on the echo signals, and obtaining a mobile target ISAR image with good focusing effect.
2. The method of claim 1, wherein, The expression of the echo signals is: where, denotes the signal amplitude term, denotes the distance-to-time conversion, is the speed of light, and denotes the signal bandwidth and the illumination accumulation time of the scattering point, respectively.
3. The method of claim 2, wherein, The expression of the first scattering point in the first distance unit about the azimuth time is: The expression of the first scattering point in the first distance unit about the azimuth time is: wherein, , and represent the initial phase, the center frequency and the frequency modulation rate, respectively, denotes the signal amplitude term of the n-th scatterer, is the wavelength of the radar transmitted signal, denotes the azimuth time, is the instantaneous distance of the scatterer to the radar at the initial time.
4. The method of claim 1, wherein, the rewritten echo signal expression wherein, is the Doppler frequency.
5. The method of claim 1, wherein, The two sets of FRFT transformation angles are respectively And The normalized projection length of the FRFT result under the corresponding angle is obtained And Specifically: wherein with denote the angle with the angle is the normalized projection length of the FRFT result, is the length of the normalized projection, is the time-frequency transform angle.
6. The method of claim 5, wherein, The relationship of the two sets of normalized projection lengths is divided and rewritten to obtain a tangent value calculation formula of the time-frequency conversion angle , specifically: 。 7. The method of claim 6, wherein, The tangent value according to the time-frequency conversion angle The target signal frequency is calculated according to the tangent value of the time-frequency conversion angle and the established relationship between the frequency modulation rate and the conversion angle. wherein is the frequency of the target signal, is the pulse repetition frequency.
8. A storage medium having stored thereon a computer program, characterized in that The computer program, when executed by a processor, implements the fast ISAR imaging method based on the fractional Fourier transform according to any one of claims 1 to 7.
9. A computer program product comprising a computer program, characterized in that, The computer program, when executed by a processor, implements the fast ISAR imaging method based on the fractional Fourier transform according to any one of claims 1 to 7.
10. An electronic device, comprising: comprise: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to implement the fast ISAR imaging method based on the fractional Fourier transform according to any one of claims 1 to 7 by executing the executable instructions.