Satellite-borne synthetic aperture radar resolution calculation method, device, equipment and storage medium

Abstract

The application discloses a kind of space-borne synthetic aperture radar resolution calculation method, device, equipment and storage medium, method includes: based on first time-frequency echo signal value and second time-frequency echo signal value, the correlation coefficient between first ground point target and second ground point target is determined, and based on correlation coefficient, the correlation function between first ground point target and second ground point target is determined;High orbit synthetic aperture radar resolution calculation model is constructed;Taylor expansion is carried out to the correlation function of the approximate processing of singularity function of high orbit synthetic aperture radar resolution calculation model, and the first singularity function model coefficient and the second singularity function model coefficient are solved;Based on the corresponding relationship of peak point and half-power point in high orbit synthetic aperture radar resolution calculation model and the second singularity function model coefficient solved, the image geometric resolution of high orbit space-borne synthetic aperture radar in any direction is determined.

Description

Technical Field

[0001] This application relates to the field of synthetic aperture radar technology, and in particular to a method, apparatus, device and storage medium for calculating the resolution of a spaceborne synthetic aperture radar. Background Technology

[0002] Currently, Synthetic Aperture Radar (SAR) is a device that uses radar technology to process surface images. Its main function is to emit pulsed electromagnetic waves and receive the reflected signals to acquire relevant data about the target system. Combined with a moving platform and signal processing technology, it generates high-resolution remote sensing images. Compared to the limitations of optical imaging, which relies on natural light sources, SAR can generate high-resolution remote sensing images around the clock and in all weather conditions. Therefore, it has been widely used in remote sensing, military reconnaissance, and geological exploration. As an important branch of this technology, spaceborne SAR uses satellites as carriers to achieve wide-area coverage observation. In recent years, the rapidly developing medium- and high-orbit spaceborne SAR (with an orbital altitude between low Earth orbit and geostationary orbit) has further improved observation efficiency and sustainability due to its long synthetic aperture time and wide coverage swath.

[0003] However, the operational trajectories of medium- and high-orbit spaceborne SAR exhibit complex three-dimensional curved shapes, resulting in significant range-azimuth coupling effects during imaging (i.e., the mutual influence between the radar beam direction and the platform's motion direction). Traditional geometric resolution assessment methods, designed based on the assumption of straight-line trajectories, suffer from model mismatch due to trajectory curvature and coupling effects when directly applied to medium- and high-orbit SAR, leading to substantial errors. Therefore, establishing an accurate geometric resolution assessment model adapted to three-dimensional curved trajectories to precisely and efficiently evaluate image geometric resolution has become a crucial issue in medium- and high-orbit spaceborne SAR data processing research.

[0004] To address this problem, field experiments and theoretical calculations are commonly used, but both have significant limitations.

[0005] (1) Field experiment method:

[0006] By deploying artificial point targets (such as corner reflectors or active calibrators), the system resolution is inferred from the broadening of the point target response at the 3dB half-power point in the radar image (i.e., 3dB resolution). Here, "3dB" is a unit of power attenuation, defined as the amount of attenuation when the signal power drops to 50% of its peak value (corresponding to a voltage amplitude drop to approximately 70.7%), and its physical meaning is the minimum distance at which two adjacent targets can be distinguished.

[0007] However, medium- and high-orbit SAR imaging has a large swath width, reaching hundreds of kilometers, requiring the coordinated deployment of multiple high-precision point targets across a vast area. Furthermore, manual adjustment of equipment parameters is necessary during satellite transits, resulting in long field testing cycles and high costs. In addition, the subsequent reliance on manual processing of massive amounts of echo data is inefficient and fails to meet the demands for rapid resolution assessment.

[0008] (2) Theoretical calculation method (numerical analytical method):

[0009] This method constructs a mathematical model based on radar system parameters and directly calculates the resolution through analytical or numerical approximation (such as polynomial fitting). Its advantage lies in eliminating the need for field experiments. However, considering the long synthetic aperture time and strong range-azimuth coupling characteristics of medium- and high-orbit SAR, the traditional polynomial model suffers a significant decrease in resolution estimation accuracy due to the accumulation of approximation errors. If high-precision numerical methods (such as full-waveform simulation) are used, the computational complexity increases exponentially, making it difficult to balance efficiency and accuracy.

[0010] In summary, existing methods cannot meet the engineering requirements of medium- and high-orbit spaceborne SAR in terms of accuracy, efficiency, and applicability, and there is an urgent need for a new resolution evaluation method with high efficiency and high accuracy. Summary of the Invention

[0011] In view of this, embodiments of this application provide a method, apparatus, device, and storage medium for calculating the resolution of spaceborne synthetic aperture radar, aiming to solve the technical problems of low calculation efficiency and accuracy of medium- and high-orbit spaceborne SAR resolution.

[0012] The technical solution of this application embodiment is implemented as follows:

[0013] In a first aspect, embodiments of this application provide a method for calculating the resolution of a spaceborne synthetic aperture radar, the method comprising:

[0014] The first time-frequency echo signal value of the first ground point target corresponding to the medium-high orbit synthetic aperture radar and the second time-frequency echo signal value of the second ground point target adjacent to the first ground point target are obtained. The first time-frequency echo signal value and the second time-frequency echo signal value are obtained based on range pulse compression processing and do not contain amplitude information.

[0015] Based on the first time-frequency echo signal value and the second time-frequency echo signal value, the correlation coefficient between the first ground point target and the second ground point target is determined, and based on the correlation coefficient, the correlation function between the first ground point target and the second ground point target is determined;

[0016] The relevant function is simplified, and the simplified relevant function is approximated based on the distance between the first ground point target and the second ground point target and the Singer function to construct a medium-high orbit synthetic aperture radar resolution calculation model. The medium-high orbit synthetic aperture radar resolution calculation model includes the first Singer function model coefficient and the second Singer function model coefficient.

[0017] The resolution calculation model for the medium-to-high orbit synthetic aperture radar is as follows:

[0018] Δ(R MN )=l1sinc(l2·R MN )

[0019] Where l1 is the coefficient of the first singer function model, l2 is the coefficient of the second singer function model, and Δ(R) MN ) represents the simplified correlation function, R MN Let M be the distance between the first ground target M and the second ground target N, and sinc be the singer function.

[0020] Taylor expansion is performed on the correlation function after the Singer function approximation of the medium-high orbit synthetic aperture radar resolution calculation model. Based on the coefficients of the zeroth, second, and fourth terms after the matched Taylor expansion, the coefficients of the first and second Singer function models are solved.

[0021] Based on the solved second singer function model coefficients and the correspondence between peak points and half-power points in the medium-high orbit synthetic aperture radar resolution calculation model, the geometric resolution of the medium-high orbit spaceborne synthetic aperture radar image in any direction is determined.

[0022] In some embodiments, the method further includes:

[0023] Obtain the first initial time-frequency echo signal value of the first ground point target;

[0024] Based on the first initial time-frequency echo signal value and the first distance pulse processing formula, the second initial time-frequency echo signal value is generated;

[0025] The amplitude information of the second initial time-frequency echo signal value is filtered to generate the first time-frequency echo signal value;

[0026] The first distance pulse processing formula is as follows:

[0027]

[0028] Among them, s M (f r ,t af is the second initial time-frequency echo signal value of the first ground point target M, where M is the first ground point target. r For the range frequency, t a Let ar(·) be the azimuth-time domain, aa(·) be the envelope function of the transmitted signal in the range-frequency domain, and sat be the envelope function of the transmitted signal in the azimuth-time domain. M Let v be the satellite position where the beam center passes through target M, v be the satellite's velocity, and f be the position of the satellite. c For carrier frequency, R M R is the instantaneous slant range from the satellite to the first ground target M when the satellite transmits the signal. M' This is the instantaneous slant distance from the satellite to the first ground target when the satellite receives the signal.

[0029] In some embodiments, the method further includes:

[0030] Obtain the third initial time-frequency echo signal value of the second ground point target;

[0031] Based on the third initial time-frequency echo signal value and the second distance pulse processing formula, a fourth initial time-frequency echo signal value is generated.

[0032] The amplitude information of the fourth initial time-frequency echo signal value is filtered to generate the second time-frequency echo signal value;

[0033] The second distance pulse processing formula is:

[0034]

[0035] Among them, s N (f r ,t a f is the fourth initial time-frequency echo signal value of the second ground point target N, where N is the second ground point target. r For the range frequency, t a Let ar(·) be the azimuth-time domain, aa(·) be the envelope function of the transmitted signal in the range-frequency domain, and sat be the envelope function of the transmitted signal in the azimuth-time domain. M Let v be the satellite position where the beam center passes through target N, v be the satellite's velocity, and f be the position of the satellite. c For carrier frequency, R N R is the instantaneous slant range from the satellite to the second ground target M when the satellite transmits the signal. N' This is the instantaneous slant distance from the satellite to the first ground target when the satellite receives the signal.

[0036] In some embodiments, the correlation coefficient is:

[0037]

[0038] Where Δ(M,N) is the correlation coefficient between the first ground target M and the second ground target N, f r For the range frequency, t a For the direction of time, St M (fr,ta) represents the first time-frequency echo signal value, St N (fr,ta) represents the value of the second time-frequency echo signal, St N * (f r ,t a ) is the second time-frequency echo signal value St N (f r ,t a The complex conjugate of ).

[0039] In some embodiments, the method further includes:

[0040] Based on the unified configuration rule of single- and double-base synthetic aperture, the correlation function is simplified to generate a simplified correlation function.

[0041] The simplified related function is:

[0042]

[0043] Wherein, Δ(R) MN ) represents the simplified correlation function, R MN Let f be the distance between the first ground point target M and the second ground point target N, and f be the radar frequency. Defined as R M' With R MN The angle between them, R M' denoted as , where is the instantaneous slant distance from the satellite to the first ground target when the satellite receives the signal, and c is the speed of light.

[0044] In some embodiments, the correspondence between peak points and half-power points in the medium-to-high orbit synthetic aperture radar resolution calculation model is as follows:

[0045]

[0046] Wherein, Δ(R) MN ) represents the simplified correlation function, ρ represents the resolution in any direction, and Δ(R) represents the resolution in any direction. MN =0) indicates that the first ground point target and the second ground point target coincide (R MN The correlation function value (=0) coincides with the first and second ground point targets, and the correlation function value reaches its peak point. Δ is the absolute value of the change in the correlation function at the half-power point when the resolution is halved; Δ(ρ=0) is the absolute value of the change in the correlation function at the peak point when the resolution approaches 0.

[0047] In some embodiments, the method further includes:

[0048] Based on the image geometric resolution and first image resolution calculation formula of the medium-high orbit spaceborne synthetic aperture radar in any direction, the image geometric resolution of the spaceborne synthetic aperture radar in the range direction is determined.

[0049] Based on the image geometric resolution and second image resolution calculation formula of the medium-high orbit spaceborne synthetic aperture radar in any direction, the image geometric resolution of the spaceborne synthetic aperture radar in the azimuth direction is determined.

[0050] The formula for calculating the first image resolution is as follows:

[0051]

[0052] Where, ρ r The image geometric resolution is given by f, where f is the radar frequency; t a λ represents the azimuth time, which is set to 0 here. l2 represents the coefficients of the second singer function model, and arcsin represents the arcsine function.

[0053] The formula for calculating the resolution of the second image is:

[0054]

[0055] Where, ρ a The image geometric resolution is given by f, where f is the radar frequency; t a λ represents the azimuth time, which is set to 0 here. l2 represents the coefficients of the second singer function model, and arcsin represents the arcsine function.

[0056] Secondly, embodiments of this application also provide a spaceborne synthetic aperture radar resolution calculation device, the device comprising:

[0057] The acquisition module is used to acquire the first time-frequency echo signal value of the first ground point target corresponding to the medium-high orbit synthetic aperture radar and the second time-frequency echo signal value of the second ground point target adjacent to the first ground point target. The first time-frequency echo signal value and the second time-frequency echo signal value are obtained based on range pulse compression processing and do not contain amplitude information.

[0058] The first determining module is used to determine the correlation coefficient between the first ground point target and the second ground point target based on the first time-frequency echo signal value and the second time-frequency echo signal value, and to determine the correlation function between the first ground point target and the second ground point target based on the correlation coefficient;

[0059] The construction module is used to simplify the relevant function and approximate the simplified relevant function based on the distance between the first ground point target and the second ground point target and the Singer function to construct a medium- and high-orbit synthetic aperture radar resolution calculation model. The medium- and high-orbit synthetic aperture radar resolution calculation model includes the first Singer function model coefficients and the second Singer function model coefficients.

[0060] The resolution calculation model for the medium-to-high orbit synthetic aperture radar is as follows:

[0061] Δ(R MN )=l1sinc(l2·R MN )

[0062] Where l1 is the coefficient of the first singer function model, l2 is the coefficient of the second singer function model, and Δ(R) MN ) represents the simplified correlation function, R MN Let M be the distance between the first ground target M and the second ground target N, and sinc be the singer function.

[0063] The calculation module is used to perform Taylor expansion on the correlation function after the Singer function approximation of the medium-high orbit synthetic aperture radar resolution calculation model, and to solve for the first Singer function model coefficients and the second Singer function model coefficients based on the coefficients of the zeroth, second, and fourth terms after the matched Taylor expansion.

[0064] The second determining module is used to determine the image geometric resolution of the medium-high orbit spaceborne synthetic aperture radar in any direction based on the solved second singer function model coefficients and the correspondence between the peak point and the half-power point in the medium-high orbit synthetic aperture radar resolution calculation model.

[0065] Thirdly, embodiments of this application provide an electronic device, including: a processor and a memory for storing a computer program capable of running on the processor, wherein, when the processor is used to run the computer program, it performs the steps of the method described in the first aspect above.

[0066] Fourthly, embodiments of this application provide a computer storage medium storing a computer program, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0067] The technical solution provided in this application embodiment is a method for calculating the resolution of a spaceborne synthetic aperture radar (SAR). The method includes: acquiring the first time-frequency echo signal value of a first ground point target corresponding to a medium-to-high orbit SAR and the second time-frequency echo signal value of a second ground point target adjacent to the first ground point target, wherein the first and second time-frequency echo signal values ​​are obtained based on range pulse compression processing and neither contains amplitude information; determining the correlation coefficient between the first and second ground point targets based on the first and second time-frequency echo signal values, and determining the correlation function between the first and second ground point targets based on the correlation coefficient; simplifying the correlation function, and approximating the simplified correlation function based on the distance between the first and second ground point targets and the Singer function, thereby constructing a medium-to-high orbit SAR resolution calculation model, wherein the medium-to-high orbit SAR resolution calculation model includes the coefficients of the first and second Singer function models; wherein the medium-to-high orbit SAR resolution calculation model is:

[0068] Δ(R MN )=l1sinc(l2·R MN )

[0069] Where l1 is the coefficient of the first singer function model, l2 is the coefficient of the second singer function model, and Δ(R) MN ) represents the simplified correlation function, R MN Let M be the distance between the first ground target and N, and sinc be the Singer function.

[0070] Taylor expansion is performed on the correlation function after the singer function approximation of the resolution calculation model of medium- and high-orbit synthetic aperture radar. Based on the coefficients of the zeroth, second, and fourth terms after the matched Taylor expansion, the coefficients of the first and second singer function models are solved. Based on the solved second singer function model coefficients and the correspondence between the peak point and the half-power point in the resolution calculation model of medium- and high-orbit synthetic aperture radar, the geometric resolution of the image of medium- and high-orbit spaceborne synthetic aperture radar in any direction is determined.

[0071] Thus, in embodiment (1) of this application, the resolution in any direction is calculated by using the Singer function to approximate the correlation function. Compared with the traditional resolution calculation method based on complex integrals or numerical simulation, this method simplifies the calculation process, reduces the demand for computing resources, and can fully meet the required resolution accuracy. It also provides new theoretical progress in the calculation of resolution indicators. (2) The proposed resolution calculation method is not highly correlated with the platform trajectory and is applicable to SAR resolution calculation for various non-straight trajectory platforms and bistatic SAR platforms, with a wide range of applications. (3) It takes into account both accuracy and efficiency issues and has strong engineering application significance for data from different spaceborne SAR platforms. It is especially important for practical application scenarios that require real-time processing of large amounts of SAR data. Attached Figure Description

[0072] Figure 1 This is a schematic diagram illustrating the working principle of a medium-to-high orbit synthetic aperture radar (SAR) provided in an embodiment of this application.

[0073] Figure 2 A flowchart illustrating the method for calculating the resolution of a medium-to-high orbit synthetic aperture radar provided in this application embodiment;

[0074] Figure 3 A flowchart illustrating the method for calculating the resolution of a medium-to-high orbit synthetic aperture radar provided as an application example of this application;

[0075] Figure 4 A schematic diagram of the structure of the medium-to-high orbit synthetic aperture radar resolution calculation device provided in the embodiments of this application;

[0076] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0077] The present application will now be described in further detail with reference to the accompanying drawings and embodiments.

[0078] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0079] Here, we will first introduce the working principle of medium- and high-orbit synthetic aperture radar (SAR), such as... Figure 1 As shown, Figure 1 This is a schematic diagram illustrating the working principle of Synthetic Aperture Radar (SAR). The diagram mainly includes a coordinate system, SAR satellites, and ground point targets (A and B).

[0080] (1) Coordinate system: The origin O is located at the center of the Earth. X, Y, and Z represent the directions of motion of the three-dimensional coordinate axes. X-axis: The direction of motion of the SAR satellite (azimuth). Y-axis: The horizontal direction perpendicular to the direction of motion (range). Z-axis: The vertical direction of altitude (elevation). R represents the radius of the Earth.

[0081] (2) Medium and high orbit SAR satellites: SAR is a satellite system that uses radar technology to observe the Earth and can generate high-resolution images of the Earth's surface. The figure shows the positions of the same SAR satellite at two different locations.

[0082] The core principle of SAR satellites is to transmit electromagnetic waves and receive signals reflected from the ground, combining these signals with the satellite's trajectory to create a "virtual large-aperture antenna," thereby achieving high-resolution imaging. Specifically, the operation of a SAR satellite can be divided into a transmission phase and a reception phase.

[0083] 1. Launch Phase. The SAR satellite's radar antenna transmits microwave pulse signals (such as linear frequency modulated signals) towards the ground.

[0084] 2. Reception Phase. During the reception phase, SAR satellites receive electromagnetic wave signals reflected from ground targets. These reflected signals contain information such as the target's location, shape, and material. By recording the signal's time delay, phase, and amplitude, SAR satellites can reconstruct images of the target.

[0085] 3. Synthetic Aperture Principle. A key technology of SAR satellites lies in the synthetic aperture principle. During flight, the satellite's radar antenna continuously transmits and receives signals. By processing these signals, the antenna effects at different locations can be "synthesized" into a virtual large-aperture antenna. This synthetic aperture effect is equivalent to a giant antenna, significantly improving imaging resolution. Synthetic aperture technology enables SAR satellites to operate over long synthetic aperture lengths, achieving high-resolution imaging. This high resolution is reflected not only in the range direction (along the radar beam direction) but also in the azimuth direction (the satellite's flight direction).

[0086] 4. There are two point targets, A and B, on the ground. Figure 1 The points A and B are marked with a red asterisk. The distance between point targets A and B is r. Furthermore, R... A and R B R represents the slant range from the SAR satellite to targets A and B, respectively. A1 and R B1 This indicates the slant distance from the SAR satellite to ground point targets A and B at different times or locations.

[0087] This application provides a method for calculating the resolution of a spaceborne synthetic aperture radar, such as... Figure 2 As shown, the method includes the following steps:

[0088] Step 210: Obtain the first time-frequency echo signal value of the first ground point target corresponding to the medium-high orbit synthetic aperture radar and the second time-frequency echo signal value of the second ground point target adjacent to the first ground point target. The first time-frequency echo signal value and the second time-frequency echo signal value are obtained based on range pulse compression processing and do not contain amplitude information.

[0089] In this embodiment, the time-frequency echo signal values ​​of two adjacent ground point targets captured by a medium-to-high orbit synthetic aperture radar (SAR) system are acquired. Specifically, the first ground point target generates a first time-frequency echo signal value, while the adjacent second ground point target generates a second time-frequency echo signal value. Both signal values ​​are obtained through range compression processing, and amplitude information is removed from the processed signals.

[0090] Here, the first and second ground point targets are adjacent ground point targets, meaning they are targets that are close to each other within the radar imaging field of view and need to be distinguished by the radar system. In SAR imaging, the ability to clearly distinguish these adjacent targets is crucial for achieving high-resolution imaging. High resolution means that the radar system can identify and distinguish adjacent ground targets more precisely, which has significant advantages for various applications such as topographic mapping, environmental monitoring, and target identification.

[0091] Here, range pulse compression is a key signal processing technique aimed at improving the range resolution of radar systems. This technique enhances the accuracy of radar range measurements by compressing the pulse width of the radar's transmitted signal. In SAR systems, range pulse compression is crucial for extracting accurate target range information from radar data. This embodiment avoids the possibility that amplitude information, which can vary due to various factors (such as environmental noise and system gain), might affect the accurate calculation of resolution by removing the amplitude information of the time-frequency echo signal.

[0092] For example, assuming the first ground point target is M and the second ground point target is N, the echo signals of two adjacent ground point targets M and N are obtained: the time-frequency echo signal St of point target M without amplitude information is obtained respectively. M (f r ,t a The time-frequency echo signal St of point target N does not contain amplitude information. N (fr,ta). Where f r For the range frequency, t a This refers to the direction of time.

[0093] Step 220: Based on the first time-frequency echo signal value and the second time-frequency echo signal value, determine the correlation coefficient between the first ground point target and the second ground point target, and based on the correlation coefficient, determine the correlation function between the first ground point target and the second ground point target.

[0094] Understandably, in order to quantify the similarity between the time-frequency echo signals reflected back from two adjacent ground point targets, the correlation coefficient between the first ground point target and the second ground point target is determined based on the first time-frequency echo signal value and the second time-frequency echo signal value, and the correlation function between the first ground point target and the second ground point target is determined based on the correlation coefficient.

[0095] Here, the correlation function characterizes the similarity between two signals in the time-frequency domain; the closer the correlation coefficient is to 1, the more difficult it is to distinguish the target point. In this embodiment, based on the calculated correlation coefficient, the present invention further determines the correlation function between the first ground point target and the second ground point target. The correlation function is a mathematical expression describing the similarity between two signals, and it can be defined according to the specific value of the correlation coefficient. In some embodiments, the expression for the correlation coefficient can be directly used as the expression for the correlation function, thereby simplifying the calculation process.

[0096] For example, the time-frequency echo signal St obtained above, which does not contain amplitude information, can be used as a basis. M (f r ,t a The time-frequency echo signal St of the second ground point target N does not contain amplitude information. N (f r ,t a Calculate the correlation coefficient Δ(M,N) between the two point targets, and determine the correlation function based on the correlation coefficient Δ(M,N).

[0097] Understandably, in practical applications, the correlation function decreases as the distance between two points increases. If the two points are very close, they will become very similar and difficult to distinguish. Therefore, in order to distinguish point targets, there must be a specific minimum distance (the theoretical resolution size in the satellite design) between two ground point targets.

[0098] Step 230: Simplify the relevant functions, and approximate the simplified relevant functions based on the distances between the first and second ground point targets and the Singer function to construct a medium-to-high orbit synthetic aperture radar (SAR) resolution calculation model. The SAR resolution calculation model includes the coefficients of the first and second Singer functions; the SAR resolution calculation model for medium-to-high orbit is as follows:

[0099] Δ(R MN )=l1sinc(l2·RMN )

[0100] Where l1 is the coefficient of the first singer function model, l2 is the coefficient of the second singer function model, and Δ(R) MN ) represents the simplified correlation function, R MN Let M be the distance between the first ground target and N, and sinc be the Singer function.

[0101] In this embodiment, the relevant function obtained in step 220 first needs to be simplified. This is to facilitate subsequent analysis and calculation, especially to improve efficiency and maintain sufficient accuracy when dealing with complex scenarios. In this embodiment, the relevant function Δ(R) obtained by the above simplification is... MN The profile of the function in any direction is close to the shape of the Singer function between 0dB and -3dB.

[0102] In the correlation function, the 0dB point corresponds to the case where two signals are perfectly aligned, at which point the signal similarity is highest and the correlation function reaches its maximum value. The -3dB point refers to the point where the signal strength or power drops to half of its maximum value (i.e., a decrease of 3 dB). In the correlation function, this is often referred to as the half-power point or half-energy point.

[0103] Next, using the simplified correlation function Δ(R) MN A resolution calculation model is constructed by approximating the simplified correlation function using the distance between the first ground target M and the second ground target N and the Singer function model.

[0104] Here, the resolution calculation model for medium- and high-orbit synthetic aperture radar is:

[0105] Δ(R MN )=l1sinc(l2·R MN )

[0106] Where l1 is the coefficient of the first singer function model, l2 is the coefficient of the second singer function model, and Δ(R) MN ) represents the simplified correlation function, R MN Let M be the distance between the first ground target and N, and sinc be the Singer function.

[0107] Here, the Sinc function is a commonly used function form with important applications in signal processing. It can effectively describe the distribution characteristics of a signal in the frequency domain. Furthermore, by using the Sinc function to approximate the correlation function, the method of calculating the resolution in any direction can significantly improve efficiency compared to traditional resolution calculation methods while still fully meeting the required resolution accuracy. Details are shown in the table below:

[0108] Table 1. Efficiency Comparison of Three Resolution Evaluation Methods

[0109]

[0110] As shown in Table 1 above, the Singer function approximation method uses the Singer function (sinc function) to approximate the relevant functions. This approximation method utilizes the favorable properties of the Singer function, making the calculation process more efficient. Only two double integrals need to be calculated, which means relatively less computational resources and time, simplifying the originally complex integral calculation. Due to the reduced computational load, this method can significantly improve computational efficiency while maintaining high accuracy.

[0111] The quartic polynomial approximation method, compared to the Singer function approximation method, requires calculating four double integrals, resulting in higher computational complexity. Although the quartic polynomial approximation method may offer higher accuracy, its computational efficiency is lower than that of the Singer function approximation method because it requires more computational resources.

[0112] The computational complexity of numerical methods depends on the required resolution. This demonstrates the relationship between resolution ρ and the required computation, where l is the target length, Δx is the pixel pitch, and σ is the pixel spacing. r Here, 'n' represents the system parameter, and 'n' represents the required computational load, which can usually be understood as the number of data points to be processed or the number of computational steps to be performed. Therefore, as the resolution increases, the number of double integrals required for numerical computation also increases, which typically means that computation time and resource consumption will also rise accordingly.

[0113] To achieve a specific resolution ρ, the required computational cost n is at least l divided by 2·σ. r •ρ. This means that as the resolution increases (i.e., ρ decreases), the required computational cost n increases. This is because higher resolution requires finer grids or more data points to capture the details of the target, leading to increased computational cost and resource consumption. Therefore, numerical methods can provide very high accuracy, especially when high resolution is required. However, its main drawback is its very high computational cost, especially when dealing with large amounts of data.

[0114] Thus, the comparison shows that the Singer function approximation method significantly improves computational efficiency while maintaining a certain level of accuracy, making it suitable for applications with high demands on computational resources and time. The fourth-order polynomial approximation method and the numerical method offer varying degrees of accuracy improvement, but at the cost of computational efficiency. Therefore, when choosing a suitable resolution evaluation method, it is necessary to comprehensively consider factors such as accuracy requirements, computational resources, and time constraints.

[0115] Step 240: Perform Taylor expansion on the correlation function after the singer function approximation of the medium- and high-orbit synthetic aperture radar resolution calculation model, and solve for the coefficients of the first singer function model and the second singer function model based on the coefficients of the zeroth, second, and fourth terms after the matched Taylor expansion.

[0116] Understandably, Taylor expansion is a mathematical tool that allows a complex function to be approximated by a series of simple polynomials around a certain point.

[0117] Understandably, the expanded expression will contain multiple terms, including zero-degree terms, first-degree terms, and quadratic terms. Since the sinc function is an even function, odd-degree terms (such as first-degree terms) will disappear. Therefore, this application's embodiments mainly focus on zero-degree terms, quadratic terms, and quartic terms. A zero-degree term represents when R... MN =0. This is the correlation function value when the two point targets completely overlap, which should theoretically be the maximum value (usually 1). The quadratic and quartic terms provide information about the distance R. MN The information on the second and fourth order rates of change is obtained. Based on the coefficients of the zeroth, second, and fourth orders after the matched Taylor expansion, the coefficients of the first and second singer function models are solved.

[0118] For example, for the Singer function model l1 sinc(l2·R) MN First, a Taylor expansion is needed. MN Let l1 be the distance between the first ground target M and the second ground target N, and l2 be the coefficients of the first and second singer function models to be solved, respectively.

[0119] For example, the correlation function Δ(R) obtained by approximating the Singer function obtained in step 240 is... MN Performing a Taylor expansion yields the Taylor expanded correlation function Ty(M,N), which is:

[0120]

[0121] The zero-order, quadratic, and quartic coefficients of the distance between the first ground target M and the second ground target N are calculated based on the correlation function Ty(M,N) after Taylor expansion. The values ​​of the Singer function model coefficients l1 and l2 are then calculated based on the zero-order, quadratic, and quartic coefficients.

[0122] Step 250: Based on the solved second singer function model coefficients and the correspondence between peak points and half-power points in the medium-to-high orbit synthetic aperture radar resolution calculation model, determine the image geometric resolution of the medium-to-high orbit spaceborne synthetic aperture radar in any direction.

[0123] In this embodiment, the peak point typically refers to the location where the signal strength reaches its maximum value, while the half-power point (also known as the half-energy point or -3dB point) refers to the location where the signal strength drops to half of the peak value. Resolution is generally defined as twice the width between the peak point and the half-power point. This is because in radar imaging, it is desirable to measure the minimum distance at which two adjacent target points can be clearly distinguished. The distance from the peak point to the half-power point represents the range from complete signal alignment to when significant distinction begins; therefore, twice this distance gives the smallest target size that the radar system can resolve in that direction.

[0124] Here, the geometric resolution of the spaceborne SAR image in any direction is calculated by using the correspondence between the peak point and the half-power point and the coefficients of the solved second singer function model.

[0125] Thus, in embodiment (1) of this application, the resolution in any direction is calculated by using the Singer function to approximate the correlation function. Compared with the traditional resolution calculation method based on complex integrals or numerical simulation, this method simplifies the calculation process, reduces the demand for computing resources, and can fully meet the required resolution accuracy. It also provides new theoretical progress in the calculation of resolution indicators. (2) The proposed resolution calculation method is not highly correlated with the platform trajectory and is applicable to SAR resolution calculation for various non-straight trajectory platforms and bistatic SAR platforms, with a wide range of applications. (3) It takes into account both accuracy and efficiency issues and has strong engineering application significance for data from different spaceborne SAR platforms. It is especially important for practical application scenarios that require real-time processing of large amounts of SAR data.

[0126] In some embodiments, the method further includes:

[0127] Obtain the first initial time-frequency echo signal value of the first ground point target;

[0128] Based on the first initial time-frequency echo signal value and the first distance pulse processing formula, a second initial time-frequency echo signal value is generated;

[0129] The amplitude information of the second initial time-frequency echo signal value is filtered to generate the first time-frequency echo signal value;

[0130] The formula for processing the first distance pulse is as follows:

[0131]

[0132] Among them, s M (f r ,t a f is the second initial time-frequency echo signal value of the first ground point target M, where M is the first ground point target. r For the range frequency, t aLet ar(·) be the azimuth-time domain, aa(·) be the envelope function of the transmitted signal in the range-frequency domain, and sat be the envelope function of the transmitted signal in the azimuth-time domain. M Let v be the satellite position where the beam center passes through target M, v be the satellite's velocity, and f be the position of the satellite. c For carrier frequency, R M R is the instantaneous slant range from the satellite to the first ground target M when the satellite transmits the signal. M' This is the instantaneous slant distance from the satellite to the first ground target when the satellite receives the signal.

[0133] In some embodiments, the method further includes:

[0134] Obtain the third initial time-frequency echo signal value of the second ground point target;

[0135] Based on the third initial time-frequency echo signal value and the second distance pulse processing formula, a fourth initial time-frequency echo signal value is generated.

[0136] The amplitude information of the fourth initial time-frequency echo signal value is filtered to generate the second time-frequency echo signal value;

[0137] The formula for processing the second distance pulse is:

[0138]

[0139] Among them, s N (f r ,t a f is the fourth initial time-frequency echo signal value of the second ground point target N, where N is the second ground point target. r For the range frequency, t a Let ar(·) be the azimuth-time domain, aa(·) be the envelope function of the transmitted signal in the range-frequency domain, and sat be the envelope function of the transmitted signal in the azimuth-time domain. M Let v be the satellite position where the beam center passes through target N, v be the satellite's velocity, and f be the position of the satellite. c For carrier frequency, R N R is the instantaneous slant range from the satellite to the second ground target M when the satellite transmits the signal. N' This is the instantaneous slant distance from the satellite to the first ground target when the satellite receives the signal.

[0140] The process of determining the first time-frequency echo signal value and the second time-frequency echo signal value will be described by way of example.

[0141] For example, the echo signal of ground point target M (i.e., the first initial time-frequency echo signal value) and the echo signal of point target N (the third initial time-frequency echo signal value) are acquired respectively, and then subjected to range pulse compression to obtain the time-frequency echo signal s of point target M. M (f r ,t a(Second initial time-frequency echo signal value) and the time-frequency echo signal s of point target N N (f r ,t a (Fourth initial time-frequency echo signal value), after ignoring the amplitude information of the time-frequency echo signals of the two points obtained above, the time-frequency echo signal St of point target M without amplitude information is obtained. M (f r ,t a (First time-frequency echo signal value) and the time-frequency echo signal St of point target N without amplitude information N (f r ,t a (Second time-frequency echo signal value).

[0142] Specifically, the echo signals of two adjacent ground targets M and N are acquired: the echo signal of ground target M is compressed by range pulse to obtain the time-frequency echo signal s of point target M. M (f r ,t a )for:

[0143]

[0144] The echo signal of ground point target N is compressed by range pulse to obtain the time-frequency echo signal s of point target N. N (f r ,t a )for:

[0145]

[0146] Ignoring amplitude information, the time-frequency echo signal St of point target M without amplitude information is obtained. M (f r ,t a )for:

[0147]

[0148] Ignoring amplitude information, the time-frequency echo signal St of point target N without amplitude information is obtained. N (f r ,t a )for:

[0149]

[0150] Among them, f r For the range frequency, t a Let ar(·) be the azimuth-time domain, aa(·) be the envelope function of the transmitted signal in the range-frequency domain, and sat be the envelope function of the transmitted signal in the azimuth-time domain. M and sat Nf represents the satellite position where the beam center passes through targets M and N. c For carrier frequency, R M and R N R represents the instantaneous slant range from the satellite to two ground targets M and N when the satellite transmits the signal. M' and R N' These are the instantaneous slant distances from the satellite to two ground targets, M and N, respectively, when the satellite receives the signal.

[0151] In some embodiments, the correlation coefficient is:

[0152]

[0153] Where Δ(M,N) is the correlation coefficient between the first ground target M and the second ground target N, f r For the range frequency, t a For the direction of time, St M (fr,ta) represents the first time-frequency echo signal value, St N (fr,ta) represents the value of the second time-frequency echo signal, St N * (f r ,t a ) is the second time-frequency echo signal value St N (f r ,t a The complex conjugate of ).

[0154] In some embodiments, the expression for the correlation coefficient can be directly used as the expression for the correlation function, thereby simplifying the calculation process.

[0155] For example, based on the time-frequency echo signal St of the point target M obtained above, which does not contain amplitude information... M (f r ,t a The time-frequency echo signal St of point target N does not contain amplitude information. N (f r ,t a The correlation coefficient Δ(M,N) between the two point targets is calculated as follows:

[0156]

[0157] Where Δ(M,N) is the correlation coefficient between the first ground target M and the second ground target N, f r For the range frequency, t a For the direction of time, St M (fr,ta) represents the first time-frequency echo signal value, St N (fr,ta) represents the value of the second time-frequency echo signal, St N *(f r ,t a ) is the second time-frequency echo signal value St N (f r ,t a The complex conjugate of ).

[0158] Here, the above expression can be used as the expression for the relevant function.

[0159] From the above formula, we can see that the correlation function decreases as the distance between two points increases. If the two points are very close, they will become very similar and difficult to distinguish. Therefore, in order to distinguish point targets, they must be separated by a specific minimum distance (the theoretical resolution size in satellite design).

[0160] In some embodiments, the method further includes:

[0161] Based on the unified configuration rule of single- and double-base synthetic aperture, the correlation function is simplified to generate the simplified correlation function.

[0162] The simplified related functions are:

[0163]

[0164] Wherein, Δ(R) MN ) represents the simplified correlation function, R MN Let f be the distance between the first ground point target M and the second ground point target N, and f be the radar frequency. Defined as R M' With R MN The angle between them, R M' denoted as , where is the instantaneous slant distance from the satellite to the first ground target when the satellite receives the signal, and c is the speed of light.

[0165] In this embodiment, the correlation function is the expression for the correlation coefficient (step 220) mentioned above:

[0166]

[0167] Ignoring amplitude information, the time-frequency echo signal St of point target M without amplitude information is obtained. M (f r ,t a )for:

[0168]

[0169] Ignoring amplitude information, the time-frequency echo signal St of point target N without amplitude information is obtained. N (f r ,t a )for:

[0170]

[0171] Thus, the time-frequency echo signal St of the point target M obtained in step 210, which does not contain amplitude information, is transformed. M (f r ,t a The specific expression for ) and the time-frequency echo signal St of point target N without amplitude information N (f r ,t a Substituting the relevant function in step 220, we can obtain:

[0172]

[0173] Where, r M and r N These are the two-way slant distance trajectories for point targets M and N, respectively.

[0174] Here, the distance between ground point target M and point target N is defined as R. MN Substituting into the relevant functions above, we get:

[0175]

[0176] Where c is the speed of light, and Δ(M,N)β is the speed of R. M With R MN The angle between them Defined as R M' With R MN The angle between them. f is the radar frequency, R M ·R MN and R M' R MN Let R represent the vector dot product, R MN R is the distance between the first ground target M and the second ground target N. M R is the vector from the satellite when it transmits the signal to the first ground target M. M' This is the vector from the satellite to the first ground target M when the satellite receives the signal.

[0177] Here, we can use R M R MN And the angle relationship between the two, R M' R MN And the angle between the two, for Perform the conversion to obtain

[0178]

[0179] The above formula Simplifying to a unified single- and dual-statistic SAR configuration, i.e., a unified single- and dual-statistic synthetic aperture configuration rule, the correlation function is simplified to generate a simplified correlation function, which is:

[0180]

[0181] Where, when ψ=β, the SAR system is approximately a single SAR system, when At that time, the SAR system was a binary configuration.

[0182] The correlation function Δ(R) obtained by the above approximate simplification MN As can be seen, the profile of its function in any direction is close to the shape of the Singer function between 0dB and -3dB. Therefore, a Singer function model can be established to approximate the correlation function Δ(R). MN ),Right now:

[0183] Δ(R MN )=l1sinc(l2·R MN )

[0184] Where l1 and l2 are the coefficients of the Singer function model.

[0185] Based on the correlation function Ty(M,N) after Taylor expansion, it can be seen that only the values ​​of coefficients l1 and l2 are needed to obtain an approximate model of the Singer function. According to the local approximation criterion, the correlation function Δ(R) MN The correlation function Ty(M,N) after Taylor expansion following the approximation of the Singer function and R is related to R. MN The zeroth, second, and fourth partial derivatives should be kept consistent, thus yielding:

[0186]

[0187]

[0188] Solving for:

[0189]

[0190] In some embodiments, the correspondence between peak points and half-power points in the resolution calculation model of medium- and high-orbit synthetic aperture radar is as follows:

[0191]

[0192] Wherein, Δ(R) MN ) represents the simplified correlation function, ρ represents the resolution in any direction, and Δ(R) represents the resolution in any direction. MN =0) indicates that the first ground point target and the second ground point target coincide (R MN The correlation function value (=0) coincides with the first and second ground point targets, and the correlation function value reaches its peak point. This represents the absolute value of the change in the correlation function at the half-power point when the resolution is halved.

[0193] In practical applications, the definition of resolution (twice the width from the peak point to the half-power point) is determined based on the solved second singer function model coefficients and the correspondence between the peak point and the half-power point in the resolution calculation model of medium- and high-orbit synthetic aperture radar, thus determining the geometric resolution of the image of medium- and high-orbit spaceborne synthetic aperture radar in any direction.

[0194]

[0195] In some embodiments, the method further includes:

[0196] Based on the calculation formulas for the geometric resolution of images in any direction and the first image resolution of medium- and high-orbit spaceborne synthetic aperture radar, the geometric resolution of images in the range direction of spaceborne synthetic aperture radar is determined.

[0197] Based on the calculation formulas for the geometric resolution and second image resolution of the medium- and high-orbit spaceborne synthetic aperture radar in any direction, the geometric resolution of the spaceborne synthetic aperture radar in the azimuth direction is determined.

[0198] The formula for calculating the resolution of the first image is as follows:

[0199]

[0200] Where, ρ r The image geometric resolution is given by f, where f is the radar frequency; t a λ represents the azimuth time, which is set to 0 here. l2 represents the coefficients of the second singer function model, and arcsin represents the arcsine function.

[0201] The formula for calculating the second image resolution is:

[0202]

[0203] Where, ρ a The image geometric resolution is given by f, where f is the radar frequency; t a λ represents the azimuth time, which is set to 0 here. l2 represents the coefficients of the second singer function model, and arcsin represents the arcsine function.

[0204] For example, the definition of resolution (twice the width from the peak point to the half-power point) yields the resolution ρ in any direction as follows:

[0205]

[0206] Furthermore, according to the image quality evaluation system, calculating the resolution performance index of the SAR system can accurately evaluate and analyze the imaging results. Therefore, the commonly used range resolution ρ can be obtained from the above formula. r The first image resolution calculation formula and azimuth resolution ρ a The second image resolutions are as follows:

[0207]

[0208] Where, ρ r The image geometric resolution is given by f, where f is the radar frequency; t a λ represents the azimuth time, which is set to 0 here. l2 represents the coefficients of the second singer function model, and arcsin represents the arcsine function.

[0209]

[0210] Where, ρ a The image geometric resolution is given by f, where f is the radar frequency; t a λ represents the azimuth time, which is set to 0 here. l2 represents the coefficients of the second singer function model, and arcsin represents the arcsine function.

[0211] The technical solution of this application will be described in detail below with reference to an application example.

[0212] This application example provides a highly efficient and accurate method for calculating the resolution of medium- and high-orbit spaceborne SAR, such as... Figure 3 As shown, the steps are as follows:

[0213] Step 301: Obtain the echo signals of targets at two adjacent points on the ground.

[0214] Here, the echo signals of ground point target M and point target N are acquired respectively, and then subjected to range pulse compression to obtain the time-frequency echo signal s of point target M. M (f r ,t a The time-frequency echo signal s of point target N and point target N N (f r ,t a After ignoring the amplitude information of the time-frequency echo signals from the two points obtained above, the time-frequency echo signal St of point target M without amplitude information is obtained. M (f r ,t a The time-frequency echo signal St of point target N does not contain amplitude information. N (f r ,t a ).

[0215] Specifically, the echo signal of the ground point target M is compressed by range pulse to obtain the time-frequency echo signal s of the point target M. M (f r ,t a )for:

[0216]

[0217] The echo signal of ground point target N is compressed by range pulse to obtain the time-frequency echo signal s of point target N. N (f r ,t a )for:

[0218]

[0219] Ignoring amplitude information, the time-frequency echo signal St of point target M without amplitude information is obtained. M (f r ,t a )for:

[0220]

[0221] Ignoring amplitude information, the time-frequency echo signal St of point target N without amplitude information is obtained. N (f r ,t a )for:

[0222]

[0223] Among them, f r For the range frequency, t a Let ar(·) be the azimuth-time domain, aa(·) be the envelope function of the transmitted signal in the range-frequency domain, and sat be the envelope function of the transmitted signal in the azimuth-time domain. M and sat N f represents the satellite position where the beam center passes through targets M and N. c For carrier frequency, R M and R N R represents the instantaneous slant range from the satellite to two ground targets M and N when the satellite transmits the signal. M' and R N' These are the instantaneous slant distances from the satellite to two ground targets, M and N, respectively, when the satellite receives the signal.

[0224] Step 302: Determine the correlation function between two adjacent ground targets.

[0225] Here, based on the time-frequency echo signal St obtained above, which does not contain amplitude information for the point target M,... M (f r ,t aThe time-frequency echo signal St of point target N does not contain amplitude information. N (f r ,t a Calculate the correlation coefficient Δ(M,N) between the two point targets.

[0226] For example, the time-frequency echo signal St obtained above, which does not contain amplitude information, can be used as a basis. M (f r ,t a The time-frequency echo signal St of point target N does not contain amplitude information. N (f r ,t a The correlation coefficient Δ(M,N) between the two point targets is calculated as follows:

[0227]

[0228] Here, the above formula can be defined as the correlation function. As can be seen from the formula, the correlation function will decrease as the distance between two points increases. If the distance between two points is very close, they will become very similar and difficult to distinguish. Therefore, in order to distinguish point targets, the two must be separated by a specific minimum distance (the theoretical resolution size when the satellite was designed).

[0229] Step 303: Construct a calculation model for medium- and high-orbit SAR resolution.

[0230] In practical applications, the time-frequency echo signal St of the point target M obtained in step 301, which does not contain amplitude information, is used. M (f r ,t a The time-frequency echo signal St of point target N does not contain amplitude information. N (f r ,t a Substituting the relevant function in step 302, we get:

[0231]

[0232] Where, r M and r N These are the two-way slant distance trajectories for point targets M and N, respectively.

[0233] In this step, the distance between ground point target M and point target N is defined as R. MN Substituting into the relevant functions above, we get:

[0234]

[0235] Where β is R M With R MN The angle between them Defined as R M' With R MN The angle between them.

[0236] The above formula simplifies to a unified single- and dual-base SAR configuration, namely:

[0237]

[0238] Where, when ψ=β, the SAR system is approximately a single SAR system, when At that time, the SAR system was a binary configuration.

[0239] The correlation function Δ(R) obtained by the above approximate simplification MN As can be seen, the profile of its function in any direction is close to the shape of the Singer function between 0dB and -3dB. Therefore, a Singer function model can be established to approximate the correlation function Δ(R). MN ),Right now:

[0240] Δ(R MN )=l1sinc(l2·R MN )

[0241] Where l1 and l2 are the coefficients of the Singer function model.

[0242] Step 304: Solve for the coefficients of the Singer function model.

[0243] Based on the correlation function Ty(M,N) after Taylor expansion, it can be seen that only the values ​​of coefficients l1 and l2 are needed to obtain an approximate model of the Singer function. According to the local approximation criterion, the correlation function Δ(R) MN The correlation function Ty(M,N) after Taylor expansion following the approximation of the Singer function and R is related to R. MN The zeroth, second, and fourth partial derivatives should be kept consistent, thus yielding:

[0244]

[0245]

[0246] Solving for:

[0247]

[0248] Step 305: Calculate the resolution.

[0249] According to the definition of resolution (twice the width from the peak point to the half-power point), the resolution ρ in any direction can be obtained as:

[0250]

[0251] According to the image quality evaluation system, calculating the resolution performance index of the SAR system can accurately evaluate and analyze the imaging results. Therefore, the commonly used range resolution ρ can be obtained from the above formula. r and azimuth resolution ρ a They are respectively:

[0252]

[0253] The advantages of this application example compared to existing technologies are:

[0254] (1) The method of using the Singer function to approximate the correlation function to calculate the resolution in any direction can be greatly improved in terms of efficiency compared with the traditional resolution calculation method and can fully meet the required resolution accuracy requirements. This provides a new theoretical advancement in the calculation of resolution indicators.

[0255] (2) The proposed resolution calculation method is not highly correlated with the platform trajectory and is applicable to SAR resolution calculation of various non-straight trajectory platforms and bistatic SAR platforms, with a wide range of applications.

[0256] (3) The proposed resolution calculation method takes into account both accuracy and efficiency issues, and has strong engineering application significance for data from different spaceborne SAR platforms.

[0257] To implement the method of the embodiments of this application, the embodiments of this application also provide a spaceborne synthetic aperture radar resolution calculation device, which corresponds to the above-mentioned spaceborne synthetic aperture radar resolution calculation method. The steps in the above-mentioned spaceborne synthetic aperture radar resolution calculation method embodiments are also fully applicable to the embodiments of this spaceborne synthetic aperture radar resolution calculation device.

[0258] like Figure 4As shown, the spaceborne synthetic aperture radar resolution calculation device 400 includes an acquisition module 401, a first determination module 402, a construction module 403, a calculation module 404, and a second determination module 405. The acquisition module 301 is used to acquire the first time-frequency echo signal value of the first ground point target corresponding to the medium-high orbit synthetic aperture radar and the second time-frequency echo signal value of the second ground point target adjacent to the first ground point target. The first time-frequency echo signal value and the second time-frequency echo signal value are obtained based on range pulse compression processing and do not contain amplitude information. The first determination module 402 is used to determine the correlation coefficient between the first ground point target and the second ground point target based on the first time-frequency echo signal value and the second time-frequency echo signal value, and to determine the correlation function between the first ground point target and the second ground point target based on the correlation coefficient. The construction module 403 is used to simplify the correlation function and to approximate the simplified correlation function based on the distance between the first ground point target and the second ground point target and the Singer function to construct a medium-high orbit synthetic aperture radar resolution calculation model. The medium-high orbit synthetic aperture radar resolution calculation model includes the first Singer function model coefficient and the second Singer function model coefficient.

[0259] The resolution calculation model for medium- and high-orbit synthetic aperture radar is as follows:

[0260] Δ(R MN )=l1sinc(l2·R MN )

[0261] Where l1 is the coefficient of the first singer function model, l2 is the coefficient of the second singer function model, and Δ(R) MN ) represents the simplified correlation function, R MN Let M be the distance between the first ground target and N, and sinc be the Singer function.

[0262] The calculation module 404 is used to perform Taylor expansion on the correlation function after the singer function approximation of the medium- and high-orbit synthetic aperture radar resolution calculation model, and to solve for the first and second singer function model coefficients based on the coefficients of the zeroth, second, and fourth terms after the matched Taylor expansion; the second determination module 405 is used to determine the image geometric resolution of the medium- and high-orbit spaceborne synthetic aperture radar in any direction based on the solved second singer function model coefficients and the correspondence between the peak point and the half-power point in the medium- and high-orbit synthetic aperture radar resolution calculation model.

[0263] In some embodiments, the acquisition module 401 is further configured to acquire a first initial time-frequency echo signal value of a first ground point target; and generate a second initial time-frequency echo signal value based on the first initial time-frequency echo signal value and a first range pulse processing formula; the spaceborne synthetic aperture radar resolution calculation device further includes a generation module 406, configured to filter the amplitude information of the second initial time-frequency echo signal value to generate the first time-frequency echo signal value.

[0264] In some embodiments, the acquisition module 401 is further configured to acquire the third initial time-frequency echo signal value of the second ground point target; the generation module 406 is further configured to generate the fourth initial time-frequency echo signal value based on the third initial time-frequency echo signal value and the second distance pulse processing formula; and to filter the amplitude information of the fourth initial time-frequency echo signal value to generate the second time-frequency echo signal value.

[0265] In some embodiments, the synthetic aperture radar resolution calculation device further includes a simplification module 407, which is used to simplify the correlation function based on the single- and double-base synthetic aperture unified configuration rules to generate the simplified correlation function.

[0266] In some embodiments, the second determining module 405 is further configured to determine the image geometric resolution of the spaceborne synthetic aperture radar in the range direction based on the image geometric resolution of the medium-high orbit spaceborne synthetic aperture radar in any direction and the first image resolution calculation formula; and to determine the image geometric resolution of the spaceborne synthetic aperture radar in the azimuth direction based on the image geometric resolution of the medium-high orbit spaceborne synthetic aperture radar in any direction and the second image resolution calculation formula.

[0267] In practical applications, the acquisition module 401, the first determination module 402, the construction module 403, the calculation module 404, the second determination module 405, the generation module 406, and the simplification module 407 can be implemented by the processor in the spaceborne synthetic aperture radar resolution calculation device. Of course, the processor needs to run the computer program in the memory to implement its functions.

[0268] It should be noted that the spaceborne synthetic aperture radar (SAR) resolution calculation device provided in the above embodiments is only illustrated by the division of the above-described program modules when performing SAR resolution calculations. In practical applications, the above processing can be assigned to different program modules as needed, that is, the internal structure of the device can be divided into different program modules to complete all or part of the processing described above. Furthermore, the spaceborne SAR resolution calculation device and the spaceborne SAR resolution calculation method embodiments provided in the above embodiments belong to the same concept, and their specific implementation process is detailed in the method embodiments, which will not be repeated here.

[0269] Based on the hardware implementation of the above program modules, and in order to implement the method of the embodiments of this application, the embodiments of this application also provide an electronic device. Figure 5 The diagram shows only an exemplary structure of the electronic device, not the entire structure; implementation is possible as needed. Figure 5 The diagram shows part or all of the structure. For example... Figure 5 As shown, the electronic device 500 provided in this application embodiment includes: at least one processor 501, a memory 502, a user interface 503, and at least one network interface 504. The various components in the electronic device 500 are coupled together via a bus system 505. It can be understood that the bus system 505 is used to implement communication between these components. In addition to a data bus, the bus system 505 also includes a power bus, a control bus, and a status signal bus. However, for clarity, in... Figure 5 The general designated all buses as Bus System 505.

[0270] The user interface 503 may include a monitor, keyboard, mouse, trackball, click wheel, buttons, touchpad, or touch screen.

[0271] The memory 502 in this embodiment is used to store various types of data to support the operation of the electronic device. Examples of such data include any computer program used to operate on the electronic device.

[0272] The method for calculating the resolution of a spaceborne synthetic aperture radar (SAR) in an electronic device disclosed in this application can be applied to, or implemented by, a processor 501. The processor 501 may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the method for calculating the resolution of a spaceborne SAR in an electronic device can be completed by integrated logic circuits in the hardware of the processor 501 or by instructions in software form. The processor 501 can be a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor 501 can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in the embodiments of this application can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium, which is located in memory 502. The processor 501 reads the information in memory 502 and, in conjunction with its hardware, completes the steps of the satellite synthetic aperture radar resolution calculation method for the electronic device provided in this application embodiment.

[0273] In an exemplary embodiment, the electronic device may be implemented by one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers (MCUs), microprocessors, or other electronic components to perform the aforementioned method.

[0274] It is understood that memory 502 can be volatile memory or non-volatile memory, or both. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), ferromagnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc, or compact disc read-only memory (CD-ROM); magnetic surface memory can be disk storage or... Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Synchronous Static Random Access Memory (SSRAM), Dynamic Random Access Memory (DRAM), Synchronous Dynamic Random Access Memory (SDRAM), Double Data Rate Synchronous Dynamic Random Access Memory (DDRSDRAM), Enhanced Synchronous Dynamic Random Access Memory (ESDRAM), SyncLink Dynamic Random Access Memory (SLDRAM), and Direct Rambus Random Access Memory (DRRAM). The memories described in the embodiments of this application are intended to include, but are not limited to, these and any other suitable types of memory.

[0275] In an exemplary embodiment, this application also provides a computer storage medium, specifically a computer-readable storage medium storing a computer program thereon. This computer program can be executed by a processor to complete the steps of the method described in this application. The computer-readable storage medium can be a ROM, PROM, EPROM, EEPROM, Flash Memory, magnetic surface memory, optical disc, or CD-ROM, etc. Furthermore, the technical solutions described in this application can be arbitrarily combined without conflict.

[0276] It should be noted that terms such as "first" and "second" are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0277] Furthermore, the technical solutions described in the embodiments of this application can be combined arbitrarily without conflict.

[0278] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for calculating the resolution of a spaceborne synthetic aperture radar, characterized in that the method... include: The first time-frequency echo signal value of the first ground point target corresponding to the medium-high orbit synthetic aperture radar and the second time-frequency echo signal value of the second ground point target adjacent to the first ground point target are obtained. The first time-frequency echo signal value and the second time-frequency echo signal value are obtained based on range pulse compression processing and do not contain amplitude information. Based on the first time-frequency echo signal value and the second time-frequency echo signal value, the correlation coefficient between the first ground point target and the second ground point target is determined, and based on the correlation coefficient, the correlation function between the first ground point target and the second ground point target is determined; The relevant function is simplified, and the simplified relevant function is approximated based on the distance between the first ground point target and the second ground point target and the Singer function to construct a medium-to-high orbit synthetic aperture radar (SAR) resolution calculation model. The SAR resolution calculation model includes the coefficients of the first and second Singer functions. The SAR resolution calculation model is as follows: ； in, These are the coefficients of the first singer function model. These are the coefficients of the second Singer function model. The simplified related functions, Let M be the distance between the first ground target M and the second ground target N, and sinc be the singer function. Taylor expansion is performed on the correlation function after the Singer function approximation of the medium-high orbit synthetic aperture radar resolution calculation model. Based on the coefficients of the zeroth, second, and fourth terms after the matched Taylor expansion, the coefficients of the first and second Singer function models are solved. Based on the solved second singer function model coefficients and the correspondence between peak points and half-power points in the medium-high orbit synthetic aperture radar resolution calculation model, the geometric resolution of the medium-high orbit spaceborne synthetic aperture radar image in any direction is determined.

2. The method according to claim 1, characterized in that, The method further includes: Obtain the first initial time-frequency echo signal value of the first ground point target; Based on the first initial time-frequency echo signal value and the first distance pulse processing formula, a second initial time-frequency echo signal value is generated; The amplitude information of the second initial time-frequency echo signal value is filtered to generate the first time-frequency echo signal value; The first distance pulse processing formula is as follows: ； in, For the first ground point target The second initial time-frequency echo signal value, the first ground point target is , For range frequency, For direction and time, Let be the envelope function of the transmitted signal in the range frequency domain. Let be the envelope function of the transmitted signal in the azimuth-time domain. For the beam center to pass through the target The satellite's position is v, and the satellite's velocity is v. For carrier frequency, For the first ground point target when the satellite transmits signals The instantaneous slant distance, This is the instantaneous slant distance from the satellite to the first ground target when the satellite receives the signal.

3. The method according to claim 1, characterized in that, The method further includes: Obtain the third initial time-frequency echo signal value of the second ground point target; Based on the third initial time-frequency echo signal value and the second distance pulse processing formula, a fourth initial time-frequency echo signal value is generated. The amplitude information of the fourth initial time-frequency echo signal value is filtered to generate the second time-frequency echo signal value; The second distance pulse processing formula is: ； in, For the second ground point target The fourth initial time-frequency echo signal value, the second ground point target is , For range frequency, For direction and time, Let be the envelope function of the transmitted signal in the range frequency domain. Let be the envelope function of the transmitted signal in the azimuth-time domain. For the beam center to pass through the target The satellite's position is v, and the satellite's velocity is v. For carrier frequency, For the second ground point target when the satellite transmits signals The instantaneous slant distance, This is the instantaneous slant distance from the satellite to the first ground target when the satellite receives the signal.

4. The method according to claim 1, characterized in that, The correlation coefficient is: ； in, Let M be the correlation coefficient between the first ground target M and the second ground target N. For range frequency, For direction and time, The first time-frequency echo signal value, The second time-frequency echo signal value, It is the second time-frequency echo signal value .

5. The method according to claim 1, characterized in that, The method further includes: Based on the unified configuration rule of single- and double-base synthetic aperture, the correlation function is simplified to generate a simplified correlation function. The simplified related function is: ； in, The simplified related functions, The distance between the first ground target M and the second ground target N. For radar frequency, Defined as and The angle between them Let be the instantaneous slant distance from the satellite to the first ground target when it receives the signal, and c be the speed of light. This refers to the direction of time.

6. The method according to claim 1, characterized in that, The correspondence between the peak point and the half-power point in the resolution calculation model of the medium-high orbit synthetic aperture radar is as follows: ； in, The simplified related functions, For resolution in any direction, The first ground point target and the second ground point target coincide ( The correlation function value (=0) coincides with the first and second ground point targets, and the correlation function value reaches the peak point. This represents the absolute value of the change in the correlation function at the half-power point when the resolution is halved. It represents the absolute value of the change in the correlation function corresponding to the peak point when the resolution approaches 0.

7. The method according to claim 1, characterized in that, The method further includes: Based on the image geometric resolution and first image resolution calculation formula of the medium-high orbit spaceborne synthetic aperture radar in any direction, the image geometric resolution of the spaceborne synthetic aperture radar in the range direction is determined. Based on the image geometric resolution and second image resolution calculation formula of the medium-high orbit spaceborne synthetic aperture radar in any direction, the image geometric resolution of the spaceborne synthetic aperture radar in the azimuth direction is determined. The formula for calculating the first image resolution is as follows: ； in, The geometric resolution of the image in the distance direction. For radar frequency; For azimuth time, the value here is 0. These are the coefficients of the second Singer function model. It is the arcsine function; The formula for calculating the resolution of the second image is: ； in, The geometric resolution of the image in the distance direction. For radar frequency; For azimuth time, the value here is 0. These are the coefficients of the second Singer function model. It is an arcsine function.

8. A spaceborne synthetic aperture radar resolution calculation device, characterized in that, The device includes: The acquisition module is used to acquire the first time-frequency echo signal value of the first ground point target corresponding to the medium-high orbit synthetic aperture radar and the second time-frequency echo signal value of the second ground point target adjacent to the first ground point target. The first time-frequency echo signal value and the second time-frequency echo signal value are obtained based on range pulse compression processing and do not contain amplitude information. The first determining module is used to determine the correlation coefficient between the first ground point target and the second ground point target based on the first time-frequency echo signal value and the second time-frequency echo signal value, and to determine the correlation function between the first ground point target and the second ground point target based on the correlation coefficient; The construction module is used to simplify the relevant functions and approximate the simplified relevant functions based on the distances between the first and second ground point targets and the Singer function to construct a medium-to-high orbit synthetic aperture radar (SAR) resolution calculation model. The SAR resolution calculation model includes first and second Singer function model coefficients. The SAR resolution calculation model is as follows: ； in, These are the coefficients of the first singer function model. These are the coefficients of the second Singer function model. The simplified related functions, Let M be the distance between the first ground target M and the second ground target N, and sinc be the singer function. The calculation module is used to perform Taylor expansion on the correlation function after the Singer function approximation of the medium-high orbit synthetic aperture radar resolution calculation model, and to solve for the first Singer function model coefficients and the second Singer function model coefficients based on the coefficients of the zeroth, second, and fourth terms after the matched Taylor expansion. The second determining module is used to determine the image geometric resolution of the medium- and high-orbit spaceborne synthetic aperture radar in any direction based on the solved second singer function model coefficients and the correspondence between the peak point and the half-power point in the medium- and high-orbit synthetic aperture radar resolution calculation model.

9. An electronic device, characterized in that, include: A processor and a memory for storing a computer program capable of running on the processor, wherein, when the processor is used to run the computer program, it performs the steps of the spaceborne synthetic aperture radar resolution calculation method according to any one of claims 1 to 7.

10. A computer storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the spaceborne synthetic aperture radar resolution calculation method as described in any one of claims 1 to 7.

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