Non-parallel trajectory distributed spaceborne SAR space synchronization method

Abstract

The application provides a non-parallel trajectory distributed spaceborne SAR space synchronization method, which can firstly combine the velocity of the master and slave satellites and the observation scene to accurately calculate the master satellite aperture center time and obtain the azimuth angle and the elevation angle of the master satellite antenna; further, based on the criterion of making the geometric correlation of the master and auxiliary images optimal, the optimal aperture center time of the bistatic observation is calculated under the non-parallel trajectory condition; finally, based on the time, the azimuth angle and the elevation angle of the slave satellite antenna are obtained, and the space synchronization is completed. The application combines the velocity of the master and slave satellites and the scene elevation information, and can effectively improve the correlation of the master and auxiliary images compared with the traditional method.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture radar technology, and particularly relates to a non-parallel trajectory distributed spaceborne SAR space synchronization method. Background Technology

[0002] Distributed spaceborne synthetic aperture radar (SAR) utilizes close-range formations of two or more satellites to simultaneously or nearly simultaneously acquire multiple images of a scene, enabling single-flight interferometric altimetry of the scene. Because all satellites observe the same scene simultaneously or nearly simultaneously, the decorrelation between the images acquired by each satellite is negligible. Therefore, distributed spaceborne SAR can obtain ground digital elevation models (DEMs) with significantly higher accuracy than those obtained by heavy-orbit spaceborne SAR. Due to these advantages, distributed spaceborne SAR has become a research hotspot both domestically and internationally in recent years.

[0003] Distributed spaceborne SAR, due to the separate locations of transmitting and receiving satellites, requires addressing time, frequency, and spatial synchronization issues. Spatial synchronization refers to effectively controlling the antenna pointing of the transmitting and receiving platforms in real time, ensuring that the transmitting and receiving beams are simultaneously and precisely pointed at the same ground target, thereby maximizing the performance of the system products (such as interferometric altimetry accuracy).

[0004] Currently, in existing distributed spaceborne SAR systems (TanDEM-X, LuTan-1, etc.), the spatial synchronization method used involves both the primary and secondary satellites independently and sideways pointing towards the scene, ensuring that the images have the same Doppler center. Compared to the method where both primary and secondary satellites point towards the scene center, this spatial synchronization method, although slightly reducing the signal-to-noise ratio of the secondary image, guarantees that both primary and secondary images have the same Doppler center, thus achieving the highest Doppler correlation.

[0005] However, the existing distributed spaceborne SAR space synchronization methods mentioned above are all based on the assumption that the master and slave satellites have parallel trajectories. When the trajectories of the satellites are not parallel, even if the Doppler centers of the master and slave images are the same, it cannot be guaranteed that the Doppler correlation between the master and slave images will be the highest. For distributed spaceborne SAR, image geometric correlation is the primary factor determining elevation inversion. Therefore, it is urgent to break through the limitations of distributed spaceborne SAR space synchronization methods under non-parallel trajectories to improve the accuracy of single-flight altimetry. This has not been addressed in existing distributed spaceborne SAR space synchronization technologies. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a non-parallel trajectory distributed spaceborne SAR spatial synchronization method. This spatial synchronization method can accurately calculate the aperture center time of the master satellite, the azimuth and elevation angles of the master satellite antenna, and the azimuth and elevation angles of the slave satellite antenna by combining the velocities of the master and slave satellites and the observation scenario, thereby achieving spatial synchronization and improving the correlation between the master and slave images.

[0007] The non-parallel trajectory distributed spaceborne SAR space synchronization method of the present invention includes:

[0008] S1. Obtain the satellite's spatial parameters, including the primary satellite's operational time period Ω = [t]. beg ,t end ], the average velocity v1 of the primary star in the geocentric fixed (ECF) coordinate system during time Ω, the average velocity v2 of the secondary star, and the initial position s of the primary star. 1,0 From the starting position s of the star 2,0 And the average velocity v of the primary star in the geocentric inertial (ECI) coordinate system. 1,ECI The average velocity v of the star 2,ECI The starting position of the primary star s 1,0,ECI From the starting position s of the star 2,0,ECI ; Obtain information about the scene to be imaged, including the coordinates p of the scene center in the ECI and ECF coordinate systems at the midpoint of the time period during which the camera can be powered on. ECI and p, scene DEM, t beg The instantaneous velocity v of the scene center in the ECI coordinate system caused by the Earth's rotation. p Acquire satellite payload parameters, including wavelength λ, bandwidth B, and synthetic aperture time T. s ; Obtain the shortest vertical baseline b required for interferometry min .

[0009] S2. Calculate the average normal vector n of the scene in the ECI and ECF coordinate systems at the midpoint of the bootable time period. ECI And n. In the ECI coordinate system, construct the 3D coordinates of each point in the scene based on the scene DEM, form a 3D surface, and obtain the normals of the surface within each mesh. Take the average value of all normal directions and normalize to obtain the average normal vector n of the scene. ECI Similarly, performing this operation in the ECF coordinate system yields n.

[0010] S3. Calculate the optimal aperture center position s of the master and slave satellites at the midpoint of the power-on time period. 1,c s 2,c The specific steps include:

[0011] S31. Calculate the midpoint of the time period during which the system can be powered on, using the method t. 1,c =(t beg +t end ) / 2; Further, obtain the position of the primary star at this time, calculated as s 1,c =s 1,0 +v1·(t 1,c -t beg ).

[0012] S32, Calculate the ground equidistant direction ug⊥ First, calculate the line-of-sight vector, which is calculated as u = (s... 1,c -p) / ||s 1,c -p||; then the ground distance direction u g The calculation method is u g =P g u, where P g =I-nn T Let I be the projection matrix with n as the normal vector, and T be the identity matrix. The superscript T indicates the transpose operation. Further, the equidistant directions of the ground are calculated according to the following formula.

[0013] u g⊥ =u g ×n / ||u g ×n|| (1)

[0014] Where × represents the cross product of vectors.

[0015] S33. Calculate the optimal slave aperture center time t corresponding to the midpoint of the power-on time period. 2,c The calculation method is as follows

[0016]

[0017] Where P = I - uu T This represents the projection matrix with the line-of-sight vector as its normal vector.

[0018] S34. Calculate the time interval from the optimal aperture center position s of the satellite during the time period when it can be powered on. 2,c The calculation method is as follows

[0019] s 2,c =s 2,0 +v2·(t 2,c -t beg (3)

[0020] S4. Calculate if the actual vertical baseline is less than the shortest vertical baseline b. min The time interval Φ = [t1 + t 1,c ,t2+t 1,c The specific steps include:

[0021] S41. Calculate the vertical baseline between the master and slave satellites at any time t during the power-on period. The calculation method is as follows:

[0022]

[0023] in Indicates elevation direction. Δs c =s 1,c -s 2,c Indicates t 1,cThe inter-satellite baseline at time Δv = v1 - v2 represents the velocity deviation between the master and slave stars.

[0024] S42. Solve equation b ⊥ ≤b min The time interval Φ is obtained as Φ = [t1 + t2] 1,c ,t2+t 1,c ],in

[0025]

[0026] S5. Based on the available startup time period and the time period when the vertical baseline is less than the shortest vertical baseline, calculate the aperture center time t of the primary satellite. c The calculation method is as follows

[0027]

[0028] Where Ω-Φ represents the difference between sets Ω and Φ.

[0029] S6. Determine the azimuth angle α1 and elevation angle β1 of the antenna when the main satellite is powered on. The specific steps include:

[0030] S61. Calculate the positions of the master and slave stars and the scene center at the aperture center time in ECI coordinates. The calculation method is as follows:

[0031]

[0032] S62. Calculate the normal vector n1 of the primary star's reference horizontal plane based on the time position of the primary star's aperture center. The calculation method is as follows:

[0033]

[0034] The reference horizontal plane refers to the plane containing the velocity and is perpendicular to the line s connecting the Earth's center to the satellite. 1,cen,ECI A plane that is as vertical as possible.

[0035] S63. Determine the antenna azimuth angle α1 and elevation angle β1 when the main satellite is powered on. The calculation method is as follows:

[0036]

[0037] S7. Determine the antenna azimuth angle α2 and elevation angle β2 when the satellite is powered on. The specific steps include:

[0038] S71. Calculate the optimal aperture center time t of the master and slave stars during the acquisition of the auxiliary image. The calculation method is as follows:

[0039]

[0040] S72. Determine the wave foot center p of the primary star at time t. ECI,1Coordinates, calculated as follows

[0041]

[0042] Where s 1,bi,ECI =s 1,0,ECI +v 1,ECI ·(tt beg ) represents the position of the primary star at time t.

[0043] S73. Calculate the normal vector n2 of the reference horizontal plane from the satellite based on the position of the center of the satellite aperture at that time. The calculation method is as follows:

[0044]

[0045] Where s 2,bi,ECI =s 2,0,ECI +v 2,ECI ·(tt beg Let t be the position of the star at time t.

[0046] S74. Determine the antenna azimuth angle α2 and elevation angle β2 when the satellite is powered on. The calculation method is as follows:

[0047]

[0048] Where p ECI,2 Let p be the position from the center of the star beam at time t. ECI,2 =2p cen,ECI -p ECI,1 .

[0049] The beneficial effects of this invention are as follows:

[0050] This invention can combine the velocities of the master and slave stars with the observation scenario to accurately calculate the master star aperture center time, master star antenna azimuth and elevation angles, and slave star antenna azimuth and elevation angles to optimize the geometric correlation of the images, thereby achieving spatial synchronization and improving the correlation between the master and slave images. Attached Figure Description

[0051] Figure 1 This is a flowchart of the spatial synchronization method of the present invention;

[0052] Figure 2 This is a schematic diagram of the geometry of distributed spaceborne SAR observation;

[0053] Figure 3 A schematic diagram illustrating the method for calculating the aperture center time of the primary star;

[0054] Figure 4 A schematic diagram illustrating the method for calculating the optimal aperture center time in the auxiliary image;

[0055] Figure 5A schematic diagram illustrating the method for calculating the wave foot center when obtaining the auxiliary image;

[0056] Figure 6 This is a schematic diagram of the distributed spaceborne SAR observation geometry for an example.

[0057] Figure 7 The input scene DEM image is shown in the example.

[0058] Figure 8 The SAR image obtained from the simulation of the example;

[0059] Figure 9 A correlation coefficient diagram of the primary and secondary images obtained using this patent;

[0060] Figure 10 The primary and secondary image interferometric phase diagram obtained using this patent;

[0061] Figure 11 A graph showing the correlation coefficients of master and slave images obtained using the traditional iso-Doppler center spatial synchronization method;

[0062] Figure 12 This is the interferometric phase map of the master and slave images obtained using the conventional equal Doppler center spatial synchronization method. Detailed Implementation

[0063] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0064] The parameters required for space synchronization of distributed spaceborne SAR include the aperture center time t of the primary satellite. c The azimuth angle α1 and elevation angle β1 of the primary satellite antenna, and the azimuth angle α2 and elevation angle β2 of the secondary satellite antenna. The spatial synchronization method provided by this invention uses the maximum spatial correlation of image pairs as the criterion; specific steps are detailed below. Figure 1 ,include:

[0065] S1. Obtain the satellite's spatial parameters, including the primary satellite's operational time period Ω = [t]. beg ,t end ], the average velocity v1 of the primary star in the geocentric fixed (ECF) coordinate system during time Ω, the average velocity v2 of the secondary star, and the initial position s of the primary star. 1,0 From the starting position s of the star 2,0 And the average velocity v of the primary star in the geocentric inertial (ECI) coordinate system. 1,ECI The average velocity v of the star 2,ECI The starting position of the primary star s 1,0,ECI From the starting position s of the star 2,0,ECI ; Obtain information about the scene to be imaged, including the coordinates p of the scene center in the ECI and ECF coordinate systems at the midpoint of the time period during which the camera can be powered on. ECIand p, scene DEM, t beg The instantaneous velocity v of the scene center in the ECI coordinate system caused by the Earth's rotation. p Acquire satellite payload parameters, including wavelength λ, bandwidth B, and synthetic aperture time T. s ; Obtain the shortest vertical baseline b required for interferometry min In the ECF coordinate system, the observation geometry of distributed spaceborne SAR is as follows: Figure 2 As shown.

[0066] S2. Calculate the average normal vector n of the scene in the ECI and ECF coordinate systems at the midpoint of the bootable time period. ECI And n. In the ECI coordinate system, construct the 3D coordinates of each point in the scene based on the scene DEM, form a 3D surface, and obtain the normals of the surface within each mesh. Take the average value of all normal directions and normalize to obtain the average normal vector n of the scene. ECI Similarly, performing this operation in the ECF coordinate system yields n.

[0067] S3. Calculate the optimal aperture center position s of the master and slave satellites at the midpoint of the power-on time period. 1,c s 2,c The specific steps include:

[0068] S31. Calculate the midpoint of the time period during which the system can be powered on, using the method t. 1,c =(t beg +t end ) / 2; Further, obtain the position of the primary star at this time, calculated as s 1,c =s 1,0 +v1·(t 1,c -t beg ).

[0069] S32, Calculate the ground equidistant direction u g⊥ First, calculate the line-of-sight vector, which is calculated as u = (s... 1,c -p) / ||s 1,c -p||; then the ground distance direction u g The calculation method is u g =P g u, where P g =I-nn T Let I be the projection matrix with n as the normal vector, and T be the identity matrix. The superscript T indicates the transpose operation. Further, the equidistant directions of the ground are calculated according to the following formula.

[0070] u g⊥ =u g ×n / ||u g ×n|| (14)

[0071] Where × represents the cross product of vectors.

[0072] S33. Calculate the optimal slave aperture center time t corresponding to the midpoint of the power-on time period. 2,c The calculation method is as follows

[0073]

[0074] Where P = I - uu T This represents the projection matrix with the line-of-sight vector as its normal vector.

[0075] S34. Calculate the time interval from the optimal aperture center position s of the satellite during the time period when it can be powered on. 2,c The calculation method is as follows

[0076] s 2,c =s 2,0 +v2·(t 2,c -t beg (16)

[0077] S33 and S34 are based on selecting the optimal aperture center of the secondary star that maximizes the Doppler correlation between the primary and secondary images. The specific principle is as follows.

[0078] According to the literature: Z. Chen, Y. Li, C. Li, Y. Liu, X. Dong, and C. Hu, "Analysis of General Geometric Decorrelation in Interferometric SAR," IEEE Geoscience and Remote Sensing Letters, vol. 19, pp. 1-5, 2022, when the master and slave star trajectories are not parallel, the geometric correlation between the master and slave images can be expressed as the product of three parts, namely...

[0079] γ=γ B ·γ D ·γ unparallel (17)

[0080] Where γ B γ D γ unparallel These represent baseline correlation, Doppler correlation, and non-parallelism factor, respectively. The non-parallelism factor is introduced by the non-parallelism of the master and slave satellite trajectories; when the trajectories are parallel, this term is 1. This patent considers a distributed spaceborne SAR with one master and one slave satellite. Since only the master satellite transmits radar signals, the imaging time of the master and slave satellites is the same. Therefore, regardless of the orbital positions of the master and slave satellites, the synthetic aperture length is the same. That is, γ unparallelIt is a constant, independent of the selection of the aperture center of the master and slave stars. Therefore, the essence of the space synchronization method is to optimize γ. B ·γ D .

[0081] The main idea of ​​this patent is to first find γ within the time that the machine can be powered on. B The optimal orbital position that satisfies the shortest vertical baseline requirement is determined, and the corresponding time is used as the aperture center time of the primary satellite. The azimuth and elevation angles of the primary satellite's antenna are then determined. Then, based on γ... D The optimal criteria are used to obtain the positions of the master and slave satellites when acquiring auxiliary images. The beam center of the slave satellite is then obtained by further solving the problem, thereby obtaining the antenna azimuth and elevation angles of the slave satellite.

[0082] According to the literature: Z. Chen, Y. Li, C. Li, Y. Liu, X. Dong, and C. Hu, "Analysis of General Geometric Decorrelation in Interferometric SAR," IEEE Geoscience and Remote Sensing Letters, vol. 19, pp. 1-5, 2022, Doppler correlation γ D It can be represented as

[0083]

[0084] Where R0 = ||s 1,c -p|| represents the slant distance from the primary star to the center of the scene. Δu=(s 1,c -p) / ||s 1,c -p||-(s 2,c -p) / ||s 2,c -p|| indicates the difference in the line-of-sight direction between the primary and secondary stars. L g =P g P(v1+v2)T s / 2 represents the projection of the equivalent synthetic aperture onto the ground.

[0085] Midpoint t of the bootable time period 2,c From the optimal aperture center of the star s 2,c The selection criterion is to let γ D Maximum. Considering t 2,c The position of the primary star is fixed at any given time, therefore we need to determine the position of the aperture center of the secondary star. Since the satellite can be considered to be moving along a straight trajectory, we can assume that the time at the aperture center of the secondary star is t. 2,c The center position of the aperture can then be expressed as

[0086] s 2,c =s 2,0 +v2·(t2,c -t beg (19)

[0087] Since the distance between the master and slave satellites is much shorter than the slant range (typically on the order of kilometers in low-Earth orbit distributed spaceborne SAR, while the slant range is typically on the order of hundreds of kilometers), we can make a local approximation for Δu. Let Δs be the baseline of the aperture center position of the master and slave satellites. c =s 1,c -s 2,c ,but

[0088]

[0089] The second term on the right side of the equation can be approximated as:

[0090]

[0091] therefore

[0092]

[0093] Considering that current spaceborne SAR is usually a phased array antenna, the adjustable range of the azimuth beam is usually no more than 5°. Therefore, the adjustable range of the satellite line of sight is also usually no more than this angle. Hence, in equation (18), u g⊥ and L g It can be considered essentially unchanged. Therefore, γ D The maximum orbital position satisfies Δu T u g⊥ =0, combining (19) and (22) we can get

[0094]

[0095] Substituting back to (19) will yield s 2,c .

[0096] S4. Calculate if the actual vertical baseline is less than the shortest vertical baseline b. min The time interval Φ = [t1 + t 1,c ,t2+t 1,c The specific steps include:

[0097] S41. Calculate the vertical baseline between the master and slave satellites at any time t during the power-on period. The calculation method is as follows:

[0098]

[0099] in Indicates elevation direction. Δs c =s 1,c -s 2,c Indicates t 1,cThe inter-satellite baseline at time Δv = v1 - v2 represents the velocity deviation between the master and slave stars.

[0100] S42. Solve equation b ⊥ ≤b min The time interval Φ is obtained as Φ = [t1 + t2] 1,c ,t2+t 1,c ],in

[0101]

[0102] S5. Based on the available startup time period and the time period when the vertical baseline is less than the shortest vertical baseline, calculate the aperture center time t of the primary satellite. c The calculation method is as follows

[0103]

[0104] Where Ω-Φ represents the difference between sets Ω and Φ.

[0105] The main idea of ​​this formula is to satisfy the shortest baseline criterion as much as possible, and on this basis, to make the aperture center time of the primary star as close as possible to the middle of the time interval, so as to ensure that the signal-to-noise ratio of the image is as optimal as possible. Figure 3 As shown.

[0106] S6. Determine the azimuth angle α1 and elevation angle β1 of the antenna when the main satellite is powered on. The specific steps include:

[0107] S61. Calculate the positions of the master and slave stars and the scene center at the aperture center time in ECI coordinates. The calculation method is as follows:

[0108]

[0109] S62. Calculate the normal vector n1 of the primary star's reference horizontal plane based on the time position of the primary star's aperture center. The calculation method is as follows:

[0110]

[0111] The reference horizontal plane refers to the plane containing the velocity and is perpendicular to the line s connecting the Earth's center to the satellite. 1,cen,ECI A plane that is as vertical as possible.

[0112] The physical meaning of this formula is to project the direction of the line connecting the Earth's center to the satellite onto a plane with the velocity as the normal vector, and then find the direction vector.

[0113] S63. Determine the antenna azimuth angle α1 and elevation angle β1 when the main satellite is powered on. The calculation method is as follows:

[0114]

[0115] S7. Determine the antenna azimuth angle α2 and elevation angle β2 when the satellite is powered on. The specific steps include:

[0116] S71. Calculate the optimal aperture center time t of the master and slave stars during the acquisition of the auxiliary image. The calculation method is as follows:

[0117]

[0118] The main basis of the above calculation method is to ensure that the aperture center position of the main and auxiliary images meets the criterion of optimal Doppler correlation. The specific principle is as follows.

[0119] The aperture center time of the main image is t. c At this time, the positions of the master and slave stars in the ECF coordinate system are:

[0120]

[0121] With t c Centered on the axis, the ECF positions of the master and slave stars at time t are respectively

[0122]

[0123] The equivalent aperture center position of the auxiliary image is s. bi = [s1(t) + s2(t)] / 2, as shown Figure 4 As shown, therefore, according to (22), the line-of-sight difference between the main and auxiliary images can be expressed as:

[0124]

[0125] As described in step S3, the optimal equivalent of Doppler correlation is Δu. T u g⊥ =0 (The plane formed by vectors satisfying this condition is called the optimal plane, see...) Figure 4 Therefore, the solution can be obtained.

[0126]

[0127] S72. Determine the wave foot center p of the primary star at time t. ECI,1 Coordinates, calculated as follows

[0128]

[0129] The principle behind the above formula is as follows. The positions of the master and slave stars at time t can be written as:

[0130]

[0131] In the ECI coordinate system, the antenna beam direction is fixed in strip mode, therefore at time t, p ECI,1 With s 1,bi,ECIThe line connecting p is parallel to p cen,ECI With s 1,cen,ECI The connection, such as Figure 5 As shown, therefore we can assume

[0132] p ECI,1 -s 1,bi,ECI =k·(p cen,ECI -s 1,cen,ECI (37)

[0133] Furthermore, it can be known that p ECI,1 Located on the ground, that is, p ECI,1 With p cen,ECI The line connecting n is perpendicular to n ECI Therefore, there is It can be obtained

[0134]

[0135] Substituting into (37) will yield p. ECI,1 As shown in (11).

[0136] S73. Calculate the normal vector n2 of the reference horizontal plane from the satellite based on the position of the center of the satellite aperture at that time. The calculation method is as follows:

[0137]

[0138] S74. Determine the antenna azimuth angle α2 and elevation angle β2 when the satellite is powered on. The calculation method is as follows:

[0139]

[0140] Where p ECI,2 Let p be the position from the center of the star beam at time t. ECI,2 =2p cen,ECI -p ECI,1 .

[0141] The physical meaning of equation (13) is that, due to the position s shown in equation (36) 1,bi,ECI s 2,bi,ECI To achieve optimal Doppler correlation, the antenna beam center of the master-slave satellite synthesis must be located at p. cen,ECI Since the wave foot center of the primary star is located at p at this time... ECI,1 Since the antennas of master and slave stars typically have the same size and the same antenna pattern, it is only necessary to let p cen,ECI Located at the midpoint of the line connecting the centers of the primary and secondary star waves, such as Figure 5 As shown, p can be obtained. ECI,2 =2p cen,ECI -p ECI,1Furthermore, similar to equation (9), the antenna azimuth and elevation angles of the slave satellite can be calculated based on the slave satellite's velocity and position.

[0142] This completes all the steps.

[0143] The following provides an implementation example with specific parameters.

[0144] In this example, the satellite orbital altitude is 500km, and the primary star's inclination is 98°. For simplified calculations, this patent is implemented near the 0° meridian and the equator. The velocity angle between the primary and secondary stars is 1°, and their speeds are both 7.6km / s. The radar operates in the X-band, and the payload parameters are shown in Table 1. During the midpoint of the operational time period, the positional deviation of the secondary star relative to the primary star is [0, 200m, -1000m]. Note that at this time, the vertical baseline between the primary and secondary stars is greater than the minimum baseline requirement of 100m. The trajectories of the primary and secondary stars and the scenario are illustrated below. Figure 6 As shown. The DEM of the imaging area is as follows. Figure 7 As shown.

[0145] Table 1

[0146]

[0147]

[0148] After performing step S2, the scene average normal n = n is obtained. ECI = [0.9999; 0.0056; -0.0128].

[0149] After executing step S3, the midpoint time t of the bootable time period is obtained. 1,c =0s, and the optimal aperture center position of the master and slave stars at this time, the result is s 1,c =[6871km,0,0]、s 2,c = [6871km, 363.37m, 51.07m].

[0150] After performing step S4, the actual vertical baseline is found to be smaller than the shortest vertical baseline b. min The time interval Φ = [-1.0384s, 0.6676s].

[0151] Execute step S5. Note that the difference between the available power-on time period Ω = [-1s, 1s] and Φ is Ω - Φ = [0.6676s, 1s], which is not an empty set. This indicates that the inter-satellite vertical baseline is greater than b during this time period. min =100m. In the difference set Ω-Φ, with t 1,c The closest is 0.6676s, therefore the aperture center time t of the primary star is... c .

[0152] Execute step S6 to obtain t c The ECI coordinate system positions of the primary satellite and the center of the scene are [6871km, -0.705km, 5.019km] and [6367.6km, 262.23km, 36.81km], respectively. Based on the satellite velocity, the azimuth angle of the primary satellite beam is 91.1067° and the elevation angle is 27.7557°.

[0153] In step S7, the optimal startup time t = 0.7342s for acquiring the auxiliary image is obtained based on the optimal Doppler correlation, and the master and slave positions at this time are obtained as [6871km, -0.7756km, 5.5186km] and [6871km, -0.6718km, 4.5042km], respectively. Next, the coordinates of the master star's wave foot center are calculated as [6365.5km, 262.2km, 37.3km], and then the coordinates of the slave star's wave foot center are obtained as [6365.5km, 262.3km, 36.3km]. Finally, based on the slave star's ECI velocity, the slave star's beam azimuth angle is obtained as 92.1051°, and the elevation angle as 27.7594°.

[0154] Figure 8 The SAR image simulated based on the above parameters is shown. Figure 9 The correlation coefficient between the primary and secondary images after spatial synchronization using this method is shown, with an average correlation coefficient of 0.937. Figure 10 The interferometric phase diagrams of the primary and secondary images obtained using this method are shown, and the fringes are clearly visible. For comparison, Figure 11 The correlation coefficient between the primary and secondary images obtained by spatial synchronization using the traditional iso-Doppler method is shown, with an average value of 0.383, which is much lower than the result of our proposed method. Figure 12 The interferometric phase map obtained by the traditional space synchronization method is shown, revealing very strong phase noise that precludes subsequent interferometric processing. These results demonstrate that the proposed method can effectively improve the correlation between primary and secondary images of distributed spaceborne SAR with non-parallel trajectories, thus proving the effectiveness of the proposed method.

[0155] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A non-parallel trajectory distributed spaceborne SAR space synchronization method, characterized in that, Includes the following steps: S1. Obtain satellite spatial parameters; S2. Calculate the average normal vector of the scene in the ECI and ECF coordinate systems at the midpoint of the bootable time period. and ; In the ECI coordinate system, the three-dimensional coordinates of each point in the scene are constructed based on the scene DEM, forming a three-dimensional surface and obtaining the normals of the surface within each mesh; S3. Calculate the optimal aperture center position of the master and slave satellites at the midpoint of the power-on period. , ; S4. Calculate if the actual vertical baseline is less than the shortest vertical baseline. time period ; S5. Calculate the aperture center time of the primary satellite based on the available power-on time period and the time period when the vertical baseline is less than the shortest vertical baseline. ; S6. Determine the antenna azimuth angle when the main satellite is powered on. and pitch angle ; S7. Determine the antenna azimuth angle at the time of satellite power-on. and pitch angle .

2. The non-parallel trajectory distributed spaceborne SAR space synchronization method as described in claim 1, characterized in that... In step S3, the optimal slave aperture center time corresponding to the midpoint of the power-on time period is calculated. The calculation method is as follows: ； in Indicates equidistant directions on the ground. Indicates the starting position of the star. Represented by the line-of-sight vector Let be the projection matrix of the normal vector. This represents the average velocity of the star in the ECF coordinate system. This indicates the start time of the period during which the main star can be powered on.

3. The non-parallel trajectory distributed spaceborne SAR space synchronization method as described in claim 1, characterized in that... In step S7, the optimal aperture center time of the primary and secondary stars during the acquisition of the auxiliary image is calculated. The calculation method is as follows: ； in and These represent the initial position and average velocity of the primary star in the ECF coordinate system, respectively. This indicates the velocity deviation between the master and slave stars.

4. The non-parallel trajectory distributed spaceborne SAR space synchronization method as described in claim 1, characterized in that... In step S7, determine The wave foot center of the primary star Coordinates, calculated as follows: ； in for The position of the primary star in the ECI coordinate system at any given time. and These represent the initial position and average velocity of the primary star in the ECI coordinate system. and The positions of the primary star and the scene center at the time of aperture center are respectively.

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