Satellite-borne SAR coverage performance analysis and simulation method

Abstract

This invention discloses a method for analyzing and simulating spaceborne SAR coverage performance, used for accurate and efficient analysis of spaceborne SAR coverage indicators and visualization. The method comprises two parts: First, by combining antenna pointing and real-time satellite position, a nadir trajectory map is generated. The intersection of the beam and the Earth ellipsoid is solved using a vector triangle coverage model to visualize the beam coverage area. Second, after coordinate transformation of the target position, the relative radius vector between the satellite and the target is calculated. Target visibility is determined through multi-dimensional coordinate system transformation, and then the single illumination time and revisit time are calculated. This invention uses an accurate Earth ellipsoid model as a benchmark, integrating satellite orbital dynamics, precise coordinate transformation under multi-factor perturbations, and TLE parameter analysis to ensure high-precision analysis. Its process is clear, core steps can be efficiently implemented using mature algorithms, and it features both visualization output and high customizability. It can adapt to different SAR system parameters and scenarios, achieving targeted performance evaluation and optimization, demonstrating outstanding efficiency and practicality.

Description

Technical Field

[0001] This invention belongs to the field of satellite remote sensing technology, specifically relating to an analysis and simulation method for the coverage performance of a spaceborne synthetic aperture radar (SAR), and particularly to a system and method that can accurately calculate the satellite nadir trajectory, beam coverage area, and target revisit time, which can be used to assist in the system design, mission planning, and performance evaluation of spaceborne SAR. Background Technology

[0002] Spaceborne synthetic aperture radar (SAR), as an active microwave remote sensing technology, boasts advantages such as all-weather, all-time, high-resolution imaging and a certain degree of ground penetration capability, playing a crucial role in military reconnaissance, topographic mapping, resource exploration, environmental monitoring, and disaster assessment. With the rapid development of spaceborne SAR technology and the increasing demands for its applications, a comprehensive and accurate analysis and evaluation of its coverage performance is of paramount importance.

[0003] Coverage performance analysis is a core component of spaceborne SAR system design and mission planning. Accurate coverage performance analysis enables:

[0004] 1. Optimize satellite orbit design to ensure that the SAR system can provide the best observation services in the predetermined area and meet specific application requirements.

[0005] 2. Auxiliary antenna parameter design and deployment: By analyzing the coverage performance under different antenna configurations, the optimal solution is determined.

[0006] 3. Guide the selection of working modes and select the appropriate imaging mode according to task requirements (such as high resolution or wide coverage).

[0007] 4. Supports mission planning and forecasting, predicts satellite observation capabilities and revisit characteristics for specific areas, and improves mission execution efficiency.

[0008] 5. Optimize the utilization of satellite resources by rationally planning coverage areas and observation timing to maximize data acquisition efficiency.

[0009] Currently, while some commercial software such as STK (Satellite Tool Kit) can perform satellite coverage performance simulation analysis, such software is usually expensive and lacks openness and customization for specific applications such as military applications. Furthermore, existing coverage analysis methods, such as the traditional grid point method or strip method, have limitations in accuracy and computational efficiency, especially when dealing with complex sensor models and Earth models. For spaceborne SAR systems, their unique imaging mechanisms and beam characteristics require more targeted coverage analysis models and computational methods.

[0010] Therefore, there is an urgent need to develop a method and system that can accurately and efficiently analyze the coverage performance of spaceborne SAR and provide intuitive visualization results to meet the growing application demands and the trend of independent and controllable technological development. Summary of the Invention

[0011] To overcome the problems of insufficient accuracy of calculation models, complex processes, low visualization, and strong dependence on commercial software in existing spaceborne SAR coverage performance analysis methods, this invention proposes an accurate and efficient method and system for spaceborne SAR coverage performance analysis and simulation. This method comprehensively considers Earth models, satellite orbital dynamics, coordinate system transformation, TLE parameter analysis, and the unique geometric relationships of the SAR system, achieving accurate calculation of nadir point trajectories, beam coverage areas, and target revisit times.

[0012] The method for analyzing and simulating the coverage performance of spaceborne SAR in this invention comprises the following steps:

[0013] Step 1: Construct a spaceborne SAR geogeometric model by inputting preset TLE parameters or resolved standard TLE parameters.

[0014] Step 2: Analysis and simulation of the coverage area of ​​spaceborne SAR beams.

[0015] 1) Calculate the real-time position of the satellite based on the given simulation time series.

[0016] First, at a given moment Calculate the mean anterior point Subsequently, the Kepler equations were solved using Newton's iterative method to obtain... The angle of proximity at time The initial value is taken as It quickly converges to the correct value after multiple iterations.

[0017] Then, calculate the true anterior angle. and vector diameter Then, the position coordinates of the satellite in the orbital plane coordinate system can be calculated. The origin of the coordinate system is the Earth's center, the X-axis points towards the perigee of the orbit, and the Y-axis lies in the orbital plane and is perpendicular to the X-axis, pointing in the direction of the satellite's motion.

[0018] Furthermore, by designing a transformation matrix, the satellite's coordinates in a stationary geocentric coordinate system can be obtained. coordinates in ;

[0019] 2) Calculate the latitude and longitude of the point on the ground that the antenna is pointing to based on the antenna's orientation.

[0020] 3) Calculation of the ground point and beam coverage area of ​​the spaceborne SAR.

[0021] By setting different perspectives to calculate the latitude and longitude of the point on the ground where the beam points, and further calculating the real-time position of the satellite based on the simulation time series given in 1), the points are continuously drawn to form the final coverage image.

[0022] Step 3: Perform latitude revisit time analysis for spaceborne SAR.

[0023] 1) Set the target geographical location to be analyzed, and convert the latitude and longitude coordinates of the target location into coordinates in the geocentric coordinate system.

[0024] 2) Calculate arbitrary simulation time Real-time position of the satellite in a non-rotating geocentric coordinate system And transform the satellite's coordinates to the geocentric coordinate system. Then subtract the coordinates of the satellite and the target point to obtain the relative radius vector between them. .

[0025]

[0026] 3) Perform coordinate system transformation, successively transforming the relative radius vector to the non-rotating geocentric coordinate system, the orbital plane coordinate system, the satellite platform coordinate system, the satellite body coordinate system, and finally to the antenna coordinate system.

[0027] 4) Perform visibility assessment to determine whether the target is within the antenna beam.

[0028] 5) Calculate the single irradiation time and the revisit time.

[0029] Set a simulation period and select a time step Δt; starting from the simulation start time... By the end time Repeat steps 2) to 4), and record all time points that meet the judgment conditions. The continuous visible time points are combined into a visible time window, and then the duration of a single irradiation is calculated. Revisit time: ; and These are the start and end times for each window.

[0030] The advantages of this invention are:

[0031] (1) The method of this invention uses the Earth ellipsoid model as a reference and comprehensively considers satellite orbital dynamics, precise transformation of the spatial coordinate system including various perturbations such as precession, nutation, and polar motion, as well as accurate analysis of the TLE (two-line orbital elements) parameter. Based on this high-precision technology, this method can comprehensively analyze and simulate the key coverage performance indicators of spaceborne SAR, including accurately drawing the nadir point trajectory, dynamically simulating the coverage area of ​​the beam on the Earth's surface, and accurately calculating the revisit time for any specific geographical location.

[0032] (2) The method of this invention combines high efficiency, practicality, and flexibility. Its calculation process is clearly designed, and core steps (such as solving the near-point angle and performing coordinate transformation) can be efficiently implemented using mature numerical algorithms or standardized program libraries in the industry. Combined with intuitive visualization output, complex coverage analysis results can be clearly presented, greatly enhancing the practical value of the method. In addition, the method also has a high degree of customizability, allowing users to flexibly configure simulation parameters according to different spaceborne SAR system parameters (such as orbit type, antenna size, working mode, etc. and diverse application scenario requirements), thereby conducting highly targeted coverage performance evaluation and optimization. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the overall process of the spaceborne SAR coverage performance analysis and simulation method of the present invention;

[0034] Figure 2 This is a schematic diagram of an Earth ellipsoid model;

[0035] Figure 3 It is the azimuth geometric model for spaceborne SAR data acquisition;

[0036] Figure 4 It is a range-oriented geometric model for spaceborne SAR data acquisition;

[0037] Figure 5 This is a diagram illustrating the TLE ephemeris input data;

[0038] Figure 6 This is a schematic diagram illustrating the calculation of the latitude and longitude of the point on the ground pointed by the antenna.

[0039] Figure 7 This is a schematic diagram of the beam coverage area;

[0040] Figure 8 This is a schematic diagram of the result of drawing the trajectory of the sub-satellite point;

[0041] Figure 9 This is a schematic diagram of the beam coverage area. Detailed Implementation

[0042] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] The present invention provides a method for analyzing and simulating the coverage performance of spaceborne SAR, such as... Figure 1 As shown, the specific steps are as follows:

[0044] Step 1: Construct a spaceborne SAR geogeometric model and analyze the standard TLE parameters.

[0045] 1) Select a rotating ellipsoid as the model to describe the Earth, and read in the relevant parameters used to accurately describe the Earth's true shape, size, and rotation characteristics, including: the semi-major axis of the reference ellipsoid. reference ellipsoid flattening Earth's rotational angular velocity The gravitational constant (GM) and the coordinate system were used for subsequent coordinate calculations and geometric analysis. The WGS84 ellipsoid model was chosen as the Earth model, as shown in Figure 2. The semi-major axis of the ellipsoid in this model is a = 6378137.0 meters, and the flattening of the ellipsoid is f = 1 / 298.257223563.

[0046] Satellite orbits are described using the Kepler six-root system, including: the semi-major axis of the orbit. Orbital eccentricity e, orbital plane inclination i, right ascension of the ascending node Perigeal argument and the satellite mean apogee at epoch times (or the closest time to Earth) 2) Construct a spaceborne SAR ground geometry model.

[0047] like Figure 3 , Figure 4 As shown, where, The azimuth and homing angle is given, where H is the satellite altitude. For the Earth's radius, These are the downward viewing angles from the beam center, near end, and far end, respectively. These are the slant ranges at the beam center, near end, and far end, respectively. These are the ground incidence angles at the beam center, near end, and far end, respectively. These are the geocentric angles corresponding to the beam center, near end, and far end, respectively. This represents the width of the range observation band.

[0048] 3) Obtain the satellite orbit parameters from sub-step 2).

[0049] Parameter acquisition methods include:

[0050] Method A: Directly input the preset number of six tracks.

[0051] Method B: Parse the standard TLE (Two-Line Element) ephemeris data file to extract the six orbital elements. The specific method is as follows:

[0052] Enter a standard TLE file, such as Figure 5 As shown. Data is read row by row and field by field according to the TLE format definition:

[0053] The first line extracts: satellite number, international code, epoch year, date within the year and its decimal part, first derivative of mean motion, second derivative, BSTAR resistance term, etc.

[0054] The second line extracts: orbital inclination i, right ascension of the ascending node Ω, eccentricity e, argument of perigee ω, angle of average anomaly M0, and average number of orbits around the Earth. .

[0055] Then, the angle units were uniformly converted to radians, and Kepler's third law was used to calculate the semi-major axis of the orbit from the average motion. The calculation method is as follows:

[0056]

[0057] in, is the Earth's gravitational constant.

[0058] Step 2: Analysis and simulation of the coverage area of ​​spaceborne SAR beams.

[0059] 1) Calculate the real-time position of the satellite based on the given simulation time series.

[0060] First, at a given moment Calculate the mean anterior point The formula is as follows:

[0061]

[0062] in, The average angular velocity of the satellite's motion can be calculated using the following formula:

[0063]

[0064] In the formula, is the gravitational constant.

[0065] Subsequently, the Kepler equations were solved using Newton's iterative method. ,get The angle of proximity at time Initial value is taken as Using the iterative formula:

[0066]

[0067] After multiple iterations, the correct value can be quickly converged. In actual calculations, to improve efficiency, a series expansion can also be used to approximate the angle of approach at each time step, as shown in the following formula:

[0068]

[0069] Where M is the mean aperimeter at the current time; E is the deviated aperimeter angle at the current time, and its subscript indicates the order of the series expansion, E4

[0070] This is the final approximation value used.

[0071] Then calculate the true anterior angle using the following formula. and vector diameter :

[0072]

[0073]

[0074] The satellite's position coordinates in the orbital plane coordinate system (Perifocal Frame) can then be calculated. In this coordinate system, the origin is the Earth's center, the X-axis points towards the perigee of the orbit, and the Y-axis lies in the orbital plane and is perpendicular to the X-axis, pointing in the direction of the satellite's motion. The calculation formula is as follows:

[0075]

[0076] Furthermore, through The satellite can be obtained in a stationary geocentric coordinate system using only two transformation matrices. coordinates in The formula is as follows:

[0077]

[0078]

[0079] .

[0080] In the formula, I represents the orbital inclination.

[0081] 2) Calculate the latitude and longitude of the point on the ground that the antenna is pointing to based on the antenna's orientation.

[0082] Let the Earth's semi-major axis be The minor semi-axis is In a stationary geocentric coordinate system, the antenna points as follows: The antenna phase center is The coordinates of the point on the ground pointed to by the antenna are: Since the initial pointing in the antenna coordinate system is defined as Furthermore, the coordinate transformation process does not change the vector magnitude, therefore As unit vectors, the relationship between the three is shown in the following equation:

[0083]

[0084] In the formula, R is the distance from the satellite to the ground.

[0085] Substitute the coordinates of the point where the antenna points to the ground into the equation of the Earth's surface. In the middle, we get:

[0086]

[0087] Based on the requirement that the antenna pointing vector must be parallel to the direction vector from the phase center of the satellite antenna to the point where the antenna points to the ground, we can obtain:

[0088]

[0089] Combining the above three equations, we can obtain the quadratic equation as follows:

[0090]

[0091] The coefficients of each term in the equation are as follows:

[0092]

[0093] Calculate the distance from the satellite to the ground using the quadratic equation formula. Since the line of sight intersects the Earth's surface at two points, the smaller positive root is taken as the visible near-Earth intersection point:

[0094]

[0095] Thus, the distance can be solved. .

[0096] Then, based on the antenna pointing vector The coordinates of the ground observation point pointed to by the antenna in a stationary geocentric coordinate system can then be calculated. .

[0097] according to Figure 6 As shown, The normal length of the satellite beam pointing point. For satellite altitude, Here are the coordinates of the aforementioned ground observation points. Latitude Given the longitude, first calculate the square of the first eccentricity of the Earth's ellipsoid.

[0098]

[0099] Therefore, it can be calculated that and latitude and longitude:

[0100]

[0101]

[0102] 3) Calculation of nadir point and beam coverage area of ​​spaceborne SAR:

[0103] Based on the coordinates of the ground target point in 2), Inverse geodetic latitude and longitude solution The conversion algorithm calculates the latitude and longitude of the point on the ground pointed to by the beam by setting different viewing angles. Among these, the near-end downward viewing angle can be determined based on the SAR system's observation zone design specifications. and far-end downward perspective and the downward angle from the beam center At the same time, take The direction is the sub-satellite point; in this embodiment, to verify the effectiveness of the method, typical parameters are selected for simulation: [Setting parameters would be here]. The sub-star point, For near-end downward perspective , For the far-end downward perspective , View from the beam center .

[0104] Finally, five points representing the beam coverage area at the current moment are obtained (sub-step 2 and sub-step 3, calculated from each viewpoint). Further, based on the simulated time series given in 1), the real-time position of the satellite is calculated, and five such points are continuously plotted to form the final coverage image, as shown below. Figure 7 As shown.

[0105] Step 3: Perform latitude revisit time analysis for spaceborne SAR.

[0106] 1) Define the target geographical location to be analyzed, and convert the latitude and longitude coordinates of the target location to coordinates in the geocentric coordinate system; the conversion formula is as follows:

[0107]

[0108] 2) Based on the calculation method in step 2, calculate the time at any simulation time. Real-time position of the satellite in a non-rotating geocentric coordinate system And transform the satellite's coordinates to the geocentric coordinate system. Then subtract the coordinates of the satellite and the target point to obtain their relative radius vector. ,Right now

[0109]

[0110] 3) Perform coordinate system transformation, successively transforming the relative radius vector to the non-rotating geocentric coordinate system, the orbital plane coordinate system, the satellite platform coordinate system, the satellite body coordinate system, and finally to the antenna coordinate system.

[0111] 4) Perform visibility assessment, i.e., determine whether the target is within the antenna beam.

[0112] The final relative radius vector in the antenna coordinate system is Based on the definition of the antenna coordinate system (with the Y-axis pointing in the direction of the aiming line), visibility is determined by calculating the included angle, where the front and side view included angles are... Distance deviation angle .

[0113] The specific judgment method is as follows:

[0114] A: According to radar wavelength and antenna length The antenna azimuth main lobe width is obtained as follows: Then the angle between the front and side views must satisfy:

[0115]

[0116] B: Based on the maximum angle of incidence in the distance direction and minimum angle of incidence The distance deviation angle must satisfy:

[0117]

[0118] When conditions A and B are met, the target is located within the beam antenna.

[0119] 5) Calculate the single irradiation time and the revisit time.

[0120] Set a simulation period (e.g., 24 hours) and select a suitable time step Δt (e.g., 1 second). Start from the simulation start time... By the end time Repeat steps 2) through 4).

[0121] Record all time points that satisfy conditions A and B. .

[0122] Consecutive visible time points are combined into a "visible time window". The start time of each window is... The end time is The duration of a single irradiation session can then be calculated. Revisit time: , which is the time interval between the start of two consecutive over-the-top tasks.

[0123] To demonstrate the effectiveness of this method, the following simulation experiment was conducted, with the orbital TLE parameter data as follows: Figure 7 As shown in Table 1, based on the satellite orbit parameters obtained in Step 1 and the set simulation parameters, the latitude of the ground target is shown in Table 2. The coordinates of the satellite in the non-rotating geocentric coordinate system at different times, obtained in Step 2, are shown in Table 2. The nadir point and coverage area calculated based on the nadir point and coverage area in Step 2 are shown in Table 3. Figure 8 and Figure 9 As shown in Tables 3 and 4, the single irradiation times for the first and second sessions were 20.7 seconds and 26.6 seconds, respectively, and the calculated revisit time was 11 hours, 47 minutes, and 31.4 seconds.

[0124] Table 1 Simulation Parameters

[0125] Simulation parameters Selected parameter value Earth's semi-major axis (m) 6378140.0 Earth's minor axis (m) 6356755.0 Earth's average radius (m) 6371140.0 Semi-major axis (m) 7000639.3664 Argument of perigee (degrees) 83.227849321 Track inclination (degrees) 61.787768627 Right ascension (degrees) of the ascending node 150.99729733 Eccentricity 0.0001534 Simulation Center Time and Date November 25, 2023, 20:22:50 Antenna length (m) 5 Antenna width (m) 2.08 Range beamwidth (degrees) 35 Operating wavelength (m) 0.03125 Longitude (degrees) of ground target 39.906217 Latitude (degrees) of ground target 116.3912757

[0126] Table 2 Output satellite coordinates

[0127] Time: 20:00 on November 25, 2023 X / km Y / km Z / km 22 minutes and 50 seconds -3463.32 3657.001 4860.966 23 minutes and 50 seconds -3166.49 3498.019 5170.479 24 minutes and 50 seconds -2857.95 3321.824 5458.366 25 minutes and 50 seconds -2539.11 3129.054 5723.423 26 minutes and 50 seconds -2211.47 2920.427 5964.54 27 minutes and 50 seconds -1876.51 2696.742 6180.71 28 minutes and 50 seconds -1535.75 2458.872 6371.027 29 minutes and 50 seconds -1190.74 2207.763 6534.605 30 minutes and 50 seconds -843.021 1944.431 6671.03 31 minutes and 50 seconds -494.145 1669.956 6779.461

[0128] Table 3 Results of the first irradiation

[0129] Irradiation time: 21:00 on November 25, 2023 Angle between frontal and lateral views (degrees) Range-direction deviation from antenna normal angle (degrees) 58 minutes and 24.4 seconds 4.960111 -2.44482 58 minutes and 24.5 seconds 4.912392 -2.445113 58 minutes and 24.6 seconds 4.864665 -2.445403 58 minutes and 24.7 seconds 4.81693 -2.445691 58 minutes and 24.8 seconds 4.769187 -2.445976 58 minutes and 24.9 seconds 4.721436 -2.446257 58 minutes and 25.0 seconds 4.673678 -2.446536 58 minutes and 25.1 seconds 4.625912 -2.446813 58 minutes and 25.2 seconds 4.578138 -2.447086 58 minutes and 25.3 seconds 4.530357 -2.447356

[0130] Table 4 Results of the second irradiation

[0131] Irradiation time: 9:00 AM, November 26, 2023 Angle between frontal and lateral views (degrees) Range-direction deviation from antenna normal angle (degrees) 45 minutes and 55.8 seconds 4.981115 -15.535103 45 minutes and 55.9 seconds 4.943961 -15.535481 45 minutes 56.0 seconds 4.906801 -15.535856 45 minutes and 56.1 seconds 4.869637 -15.536228 45 minutes and 56.2 seconds 4.832467 -15.536598 45 minutes and 56.3 seconds 4.795293 -15.536964 45 minutes and 56.4 seconds 4.758113 -15.537328 45 minutes and 56.5 seconds 4.720928 -15.537689 45 minutes and 56.6 seconds 4.683739 -15.538047 45 minutes and 56.7 seconds 4.646544 -15.538403

Claims

1. A method and system for analyzing and simulating the coverage performance of spaceborne SAR, characterized in that: The specific steps are as follows: Step 1: Construct a spaceborne SAR ground geometry model, and input the preset TLE parameters or the resolved standard TLE parameters; Step 2: Analysis and simulation of spaceborne SAR beam coverage area; 1) Calculate the real-time position of the satellite based on the given simulation time series; First, at a given moment Calculate the mean anterior point Subsequently, the Kepler equations were solved using Newton's iterative method to obtain... The angle of proximity at time The initial value is taken as It quickly converges to the correct value after multiple iterations; Then, calculate the true anterior angle. and vector diameter Then, the position coordinates of the satellite in the orbital plane coordinate system can be calculated. The origin of the coordinate system is the Earth's center, the X-axis points towards the perigee of the orbit, and the Y-axis lies in the orbital plane and is perpendicular to the X-axis, pointing towards the direction of the satellite's motion. Furthermore, by designing a transformation matrix, the satellite's coordinates in a stationary geocentric coordinate system can be obtained. coordinates in ; 2) Calculate the latitude and longitude of the point on the ground that the antenna is pointing to, based on the antenna's orientation; 3) Calculation of the nadir point and beam coverage area of ​​spaceborne SAR; By setting different perspectives to calculate the latitude and longitude of the point on the ground pointed to by the beam, and further calculating the real-time position of the satellite according to the simulation time series given in 1), the points are continuously drawn to form the final coverage image; Step 3: Perform latitude revisit time analysis for spaceborne SAR; 1) Set the target geographical location to be analyzed, and convert the latitude and longitude coordinates of the target location into coordinates in the geocentric coordinate system; 2) Calculate arbitrary simulation time Real-time position of the satellite in a non-rotating geocentric coordinate system Subtracting the coordinates of the satellite and the target point yields the relative radius vector between them. ; 3) Perform coordinate system transformation, successively transforming the relative radius vector to the non-rotating geocentric coordinate system, the orbital plane coordinate system, the satellite platform coordinate system, the satellite body coordinate system, and finally to the antenna coordinate system; 4) Perform visibility assessment to determine whether the target is within the antenna beam; 5) Calculate the single irradiation time and the revisit time; Set a simulation period and select a time step Δt; starting from the simulation start time... By the end time Repeat steps 2) to 4), and record all time points that meet the judgment conditions. The continuous visible time points are combined into a visible time window, and then the duration of a single irradiation is calculated. Revisit time: ; and These are the start and end times for each window.

2. The method and system for analyzing and simulating spaceborne SAR coverage performance as described in claim 1, characterized in that: In step 1, the standard TLE parameter is parsed as follows: Input a standard TLE file and read the data line by line and field by field according to the TLE format definition: The first line extracts: satellite number, international code, epoch year, date within the year and its decimal part, first derivative of mean motion, second derivative, and BSTAR drag term; The second line extracts: orbital inclination i, right ascension of the ascending node Ω, eccentricity e, argument of perigee ω, angle of average anomaly M0, and average number of orbits around the Earth. ; Then, the angle units were uniformly converted to radians, and Kepler's third law was used to calculate the semi-major axis of the orbit from the average motion. The calculation method is as follows: in, is the Earth's gravitational constant.

3. The method and system for analyzing and simulating spaceborne SAR coverage performance as described in claim 1, characterized in that: In step 2, sub-step 1), a series expansion is used to approximate the angle of the near point at each time step.

4. The method and system for analyzing and simulating spaceborne SAR coverage performance as described in claim 1, characterized in that: The specific method for sub-step 2 of step two is as follows: Let the Earth's semi-major axis be The minor semi-axis is In a stationary geocentric coordinate system, the antenna points as follows: The antenna phase center is The coordinates of the point on the ground pointed to by the antenna are: The relationship between the three is as follows: In the formula, R is the distance from the satellite to the ground; Substitute the coordinates of the point where the antenna points to the ground into the equation of the Earth's surface. In the middle, we get: Based on the requirement that the antenna pointing vector must be parallel to the direction vector from the phase center of the satellite antenna to the point where the antenna points to the ground, we obtain: Combining the above three equations, we obtain the quadratic equation as follows: The coefficients of each term in the equation are as follows: Calculate the distance from the satellite to the ground using the quadratic equation formula: Then, based on the antenna pointing vector Calculate the coordinates of the ground observation point pointed to by the antenna in a stationary geocentric coordinate system. ; make The normal length of the satellite beam pointing point. For satellite altitude, These are the coordinates of the ground observation point. Latitude For longitude; first calculate the square of the first eccentricity of the Earth's ellipsoid. Then calculate and latitude and longitude: 。 5. The method and system for analyzing and simulating spaceborne SAR coverage performance as described in claim 1, characterized in that: The judgment method for sub-step 4) of step 3 is as follows: Based on the definition of the antenna coordinate system (with the Y-axis pointing in the direction of the aiming line), visibility is determined by calculating the included angles, including the front and side view included angles. Distance deviation angle The specific judgment is divided into: A: According to radar wavelength and antenna length The antenna azimuth main lobe width is obtained as follows: Then the angle between the front and side views must satisfy: B: Based on the maximum angle of incidence in the distance direction and minimum angle of incidence The distance deviation angle must satisfy: When conditions A and B are met, the target is located within the beam antenna.

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