A method and system for interferometric imaging detection of satellite formations flying in the same direction in space.

Abstract

This invention discloses a method and system for interferometric imaging detection of satellite formations flying in the same direction in space. The method includes: setting initial parameters for a central satellite or virtual central satellite and N accompanying satellites in a formation; calculating the relative orbital elements of the N accompanying satellites; calculating the absolute orbital elements based on the relative orbital elements; predicting the position of each accompanying satellite based on the absolute orbital elements, and calculating the detection baseline formed by every two accompanying satellites; calculating the baseline distribution uniformity measurement function based on the detection baseline, using it as the objective function, and exploring optimization using an optimization algorithm to obtain the optimal solution; repeating the above steps based on the optimal solution to obtain a detection baseline with continuity and uniformity in both the radial and circumferential directions; and performing imaging inversion based on the detection baseline and the principle of interferometric imaging. This invention effectively improves the density of baseline coverage and reduces the deployment difficulty compared to deploying multiple satellites in a circle.

Description

Technical Field

[0001] This invention belongs to the field of passive microwave interferometric imaging technology based on satellite formations, and particularly relates to a method and system for interferometric imaging detection of satellite formations flying in the same direction in space. Background Technology

[0002] Using multiple satellites in formation for interferometric imaging is an important method to improve spatial resolution. Each satellite carries a microwave radiometer, and by forming an interferometric baseline using multiple satellites in formation, imaging inversion is performed based on the principles of interferometric imaging.

[0003] Centered on a central or virtual satellite, satellites orbit and accompany each other. According to the equations of relative motion, without long-term relative drift, the relative trajectory of the accompanying satellites relative to the central satellite is a spatial ellipse, and the orbital period is equal to the orbital period of the central satellite. Circular nadir alignment means that the projection plane of the nadir point is a circle. With several satellites of different radii and initial phases, using the nadir point method as a reference, the relative motion of the accompanying satellites is either counterclockwise or clockwise rotation in the same direction.

[0004] According to the principle of interferometric imaging, the relative position vectors of every two satellites form a detection baseline in the spatial frequency domain. The projection vector of the relative position vectors onto the nadir point is called the projected detection baseline (or simply "baseline"). The relative motion of the companion satellites relative to the central satellite is a projection circle, with different satellites distributed on different radii, having the same angular velocity, and rotating in the same direction. Based on baseline analysis, the baselines formed by companion satellites flying in the same direction in space are also circularly distributed. The baseline length is invariant, and the baseline direction rotates once with each satellite's companion flight.

[0005] A multi-ring, co-directional escort satellite formation in space provides a detection baseline that is continuous and uniform in both the radial and circumferential directions.

[0006] Conventional interferometric imaging satellite formation configurations, such as multi-satellite linear formations, T-formations, cross formations, spatial circles of the same radius, or nadir circles, require optimization and improvement in the continuity and uniformity of the detection baseline in both the radial and circumferential directions. Summary of the Invention

[0007] To address the shortcomings of existing technologies in improving the continuity and uniformity of detection baselines in both the radial and circumferential directions, this invention proposes a spatial satellite formation interferometric imaging detection method and system that utilizes satellites flying in the same direction. Different satellites are distributed at different radii, resulting in a detection baseline with invariant length, circular sampling, and continuity and uniformity in both the radial and circumferential directions, effectively improving the density of baseline coverage. Compared to deploying multiple satellites in a single circle, this method also reduces deployment complexity.

[0008] To achieve the above objectives, this invention proposes a space-based satellite formation interferometric imaging detection method, the method comprising:

[0009] Step 1) Set the initial parameters for the central satellite or virtual central satellite and N accompanying satellites in the same direction;

[0010] Step 2) Calculate the relative orbital parameters of the N escort satellites in formation;

[0011] Step 3) Calculate the absolute orbital elements based on the relative orbital elements obtained in Step 2);

[0012] Step 4) Based on the absolute orbital elements obtained in Step 3), predict the position of each companion satellite and calculate the detection baseline formed by each pair of companion satellites;

[0013] Step 5) Calculate the baseline distribution uniformity measurement function based on the probe baseline obtained in Step 4), use it as the objective function, and use an optimization algorithm to explore for optimization and obtain the optimal solution;

[0014] Step 6) Based on the optimal solution, repeat steps 2)-4) to obtain a detection baseline that is continuous and uniform in both the radial and circumferential directions;

[0015] Step 7) Based on the detection baseline obtained in Step 6), perform imaging inversion based on the principle of interferometric imaging.

[0016] As an improvement to the above method, the initial parameters in step 1) include:

[0017] The six orbital elements of a central satellite or virtual central star are: semi-major axis a0, eccentricity e0, orbital inclination i0, perihelion argument ω0, ascending node longitude Ω0, and mean apogee angle M0.

[0018] N satellites are distributed on K sub-satellite points, each circle containing N satellites. k For each satellite, the initial value of the radius of the k-th circle is r. k Given k = 1, 2, ..., K, with a maximum circle radius of R, the initial phase angle of the j-th companion satellite is... And determine whether the escort direction is counterclockwise or clockwise.

[0019] As an improvement to the above method, step 2) specifically includes:

[0020] When the escort direction is clockwise, the relative orbital elements of the j-th escort satellite satisfy the following formula:

[0021]

[0022] Where, Δa j ,Δe xj ,Δeyj ,Δi xj ,Δi yj ,ΔM j These represent the relative semi-major axis, the relative eccentricity in the x-direction, the relative eccentricity in the y-direction, the relative orbital inclination in the x-direction, the relative orbital inclination in the y-direction, and the relative angle of abduction.

[0023] When the escort direction is counterclockwise, the relative orbital elements of the j-th escort satellite satisfy the following formula:

[0024]

[0025] As an improvement to the above method, step 3) specifically includes:

[0026] The absolute orbital elements of the j-th companion satellite are obtained from the following formula:

[0027]

[0028] Among them, a j e j i j ω j Ω j and M j Let represent the semi-major axis, eccentricity, orbital inclination, perihelion argument, ascending node longitude, and mean apogee angle of the j-th companion satellite, respectively.

[0029] As an improvement to the above method, step 4) specifically includes:

[0030] Based on the absolute orbital features of the companion satellite obtained in step 3), calculate the position r of the j-th companion satellite. j (x,y,z), the position r of the i-th companion satellite i (x,y,z), i,j=1,...,N, and calculate the detection baseline formed by every two satellites, denoted as b(u,v,w).

[0031] As an improvement to the above method, step 5) specifically includes:

[0032] Based on the detection baseline obtained in step 4), the Cornwell index M, a measure of distribution uniformity, is calculated. cs (b1,b2,...,b s ):

[0033]

[0034] Where s is the number of detection baselines formed by N companion satellites, s=N×(N-1) / 2, b1,b2,...,b s This represents the s detection baselines at a certain moment;

[0035] Using the Cornwell index as the objective function, and the radius of each circle, the number of satellites on each circle, and the initial phase angle of each satellite distribution as optimization variables, an optimization search is performed to obtain the optimal solution.

[0036] As an improvement to the above method, the detection baseline in step 6) includes:

[0037] The detection baselines formed by the same ring are circularly distributed, satisfying the following equation:

[0038]

[0039] Where (u,v) represents the projection of any point on the detection baseline formed by the i-th and j-th companion satellites;

[0040] The detection baselines formed between different rings satisfy the following equation:

[0041]

[0042] As an improvement to the above method, step 7) specifically includes:

[0043] Based on (u,v) obtained in step 6), the corresponding visibility function Viss(u,v) is calculated using the following formula:

[0044]

[0045] Based on the fundamental principles of interferometric imaging, the inverted image T is obtained using the following formula. B (ξ,η):

[0046]

[0047] Where (ξ,η) are the position coordinates of each point in the image.

[0048] On the other hand, this invention proposes a space-based satellite formation interferometric imaging detection system for coordinated flight in space, the system comprising:

[0049] The initial parameter setting module is used to set the initial parameters of the central satellite or virtual central satellite and N accompanying satellites in formation;

[0050] The relative orbital element calculation module is used to calculate the relative orbital elements of N formation companion satellites;

[0051] The absolute orbital element calculation module is used to calculate the absolute orbital element based on the relative orbital element obtained from the relative orbital element calculation module.

[0052] The detection baseline calculation module is used to obtain absolute orbital features, predict the position of each companion satellite, and calculate the detection baseline formed by each pair of companion satellites.

[0053] The optimization module is used to calculate the baseline distribution uniformity metric function based on the probe baseline obtained by the probe baseline calculation module. This function serves as the objective function, and the optimization algorithm is used to explore and find the optimal solution.

[0054] A detection baseline calculation module based on the optimal solution is used to obtain a detection baseline that is continuous and uniform in both the radial and circumferential directions, based on the optimization module; and

[0055] The imaging inversion module is used to perform imaging inversion based on the detection baseline obtained by the detection baseline calculation module based on the optimal solution and the principle of interferometric imaging.

[0056] Compared with the prior art, the advantages of the present invention are:

[0057] The interferometric imaging detection method of satellite formation flying in the same direction in space, with the flying method being a point circle below the satellite, forms a detection baseline with invariant length. It is a circular sampling method with continuity and uniformity in both radial and circumferential directions, effectively improving the density of baseline coverage. Compared with deploying multiple satellites on a circle for flying together, it also reduces the difficulty of deployment. Attached Figure Description

[0058] Figure 1 This is a flowchart of the space-based satellite formation interferometric imaging detection method of the present invention;

[0059] Figure 2 This is a schematic diagram of a multi-satellite, multi-ring, co-directional sub-satellite point circular configuration;

[0060] Figure 3 This is a schematic diagram of the relative trajectory of the projection plane (XY plane) of the sub-satellite point;

[0061] Figure 4 This is a schematic diagram of the baseline distribution over a period of time;

[0062] Figure 5 This is a schematic diagram of the baseline distribution of an orbital period;

[0063] Figure 6 It simulates the original image;

[0064] Figure 7 It is an interference inversion diagram. Detailed Implementation

[0065] This invention proposes a space-based satellite formation interferometric imaging detection method with a nadir circle configuration. To obtain a uniformly distributed baseline and optimal interferometric imaging results, given the central satellite, maximum orbital radius, and number of satellites, an optimization calculation method for the orbital elements of the accompanying satellites is proposed.

[0066] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0067] Example 1

[0068] like Figure 1 As shown, Embodiment 1 of the present invention provides a method for detecting interferometric imaging of satellite formations flying in the same direction in space, which is described in detail below:

[0069] Step 1) Set the orbital parameters (a0, e0, i0, ω0, Ω0, M0) of the central satellite (or virtual central satellite). Assume there are N satellites flying in formation, distributed across K circles, with N satellites on each circle. k One satellite. The initial radius of each circle is r. k (j=1,2,...,K), the initial phase angle of each satellite is initially set to... The maximum ring radius is R, and the escort direction is determined to be either counterclockwise or clockwise. For example... Figure 2 The diagram shows a multi-ring, co-directional sub-satellite point circular configuration of multiple satellites.

[0070] Step 2) Based on the K circles obtained in Step 1), N k The flight radius r of the satellite k Initial phase Follow-up direction, calculate the relative orbital elements (Δa) of all satellites. j ,Δe xj ,Δe yj ,Δi xj ,Δi yj ,ΔM j The formation is a circular pattern with multiple rings flying in the same direction in space.

[0071] The relative orbital elements of the j-th satellite are: (Δa) j ,Δe xj ,Δe yj ,Δi xj ,Δi yj ,ΔM j If the flight is clockwise, the calculation is as follows:

[0072]

[0073] If the flight is counter-clockwise, the calculation is as follows:

[0074]

[0075] Step 3) Based on Step 2), the relative orbital elements (Δa) of all satellites j ,Δe xj ,Δe yj ,Δi xj ,Δi yj,ΔM j ), calculate the absolute orbital elements (a,e,i,Ω,ω,M).

[0076] Calculate the absolute orbital elements from the satellite's relative orbital elements:

[0077]

[0078] Step 4) Calculate the satellite position r based on the absolute orbital features of the orbiting satellite obtained in Step 3). j (x,y,z), and calculate the detection baseline Δr formed by every two satellites. i,j (u,v,w). The spatial frequency baseline is: Δr i,j =r i -r j , where i,j=1,...,N, denoted as b(u,v,w).

[0079] Step 5) Calculate the Cornwell index, a measure of distribution uniformity, based on the baseline. Using the Cornwell index as the objective function, and the radius of each circle, the number of satellites on each circle, and the initial phase angle of each satellite distribution as optimization variables, perform an optimization search. The optimal solution is then obtained.

[0080] The baselines formed by N satellites total s = N × (N-1) / 2. At a given time, the s baselines are Δr1, Δr2, ..., Δr s The distribution uniformity measure function is calculated as follows:

[0081]

[0082] Step 6): Based on the optimal solution, repeat steps 2), 3), and 4). The probe baseline is continuous and uniform in both the radial and circumferential directions.

[0083] Baseline characteristics analysis is as follows:

[0084] (1) Baseline formed by the same ring

[0085] Assuming the radius of the first ring is r1, and both satellites are deployed on this ring, with initial phases of the two satellites respectively... Within the same ring, rotation can only occur in the same direction. Therefore, the projected positions of the two satellites are:

[0086]

[0087] Since the two satellites have the same flight angular velocity, therefore, the change over time... The angles are the same. The baseline formed by the two satellites is:

[0088]

[0089] From the above formula, we can see that

[0090]

[0091] This shows that satellites rotating in the same direction on the same ring have a circular baseline distribution.

[0092] (2) Baselines formed between different rings

[0093] Assuming the radius of the first ring is r1 and the radius of the second ring is r2, and the initial phases of the two satellites are respectively... The two space rings rotate in the same direction. Therefore, the projected position of the satellite located in the first ring is:

[0094]

[0095] The projected position of the satellite located in the second ring is:

[0096]

[0097] Since the two satellites have the same flight angular velocity, therefore, the change over time... The angles are the same. The baseline formed by the two satellites is:

[0098]

[0099] From the above formula, we can see that

[0100]

[0101] Therefore, the baselines formed by satellites in different rings are circularly distributed. The radius of the circle is related to the radii of the two rings and the initial phase difference of the satellites. When the initial phase difference of the satellites is 0, the baseline length is the shortest, which is |r1-r2|; when the initial phase difference of the satellites is pi, the baseline length is the longest, which is |r1+r2|.

[0102] Step 7) Based on the interferometric baseline obtained in step 6), imaging inversion can be performed based on the principle of interferometric imaging.

[0103] Assume T B Let (ξ,η) be the brightness temperature of the two-dimensional simulated image, and (ξ,η) be the position coordinates of each point in the image. The projection detection baseline is (u,v), and the visibility function Viss corresponding to (u,v) is calculated according to the following formula:

[0104]

[0105] Based on the fundamental principles of interferometric imaging, the inverted image is obtained using the following formula:

[0106]

[0107] Example 2

[0108] Embodiment 2 of the present invention proposes a space-based satellite formation interferometric imaging detection system, implemented based on the method of Embodiment 1. The system includes:

[0109] The initial parameter setting module is used to set the initial parameters of the central satellite or virtual central satellite and N accompanying satellites in formation;

[0110] The relative orbital element calculation module is used to calculate the relative orbital elements of N formation companion satellites;

[0111] The absolute orbital element calculation module is used to calculate the absolute orbital element based on the relative orbital element obtained from the relative orbital element calculation module.

[0112] The detection baseline calculation module is used to obtain absolute orbital features, predict the position of each companion satellite, and calculate the detection baseline formed by each pair of companion satellites.

[0113] The optimization module is used to calculate the baseline distribution uniformity metric function based on the probe baseline obtained by the probe baseline calculation module. This function serves as the objective function, and the optimization algorithm is used to explore and find the optimal solution.

[0114] The detection baseline calculation module based on the optimal solution is used to obtain a detection baseline that is continuous and uniform in both the radial and circumferential directions based on the optimization module.

[0115] The imaging inversion module is used to perform imaging inversion based on the detection baseline obtained by the detection baseline calculation module based on the optimal solution, and on the principle of interferometric imaging.

[0116] Simulation Example

[0117] Taking a circular formation of 9 satellites below the satellite as an example, the simulation process is as follows:

[0118] 1) An example of 9 satellites distributed across 3 rings, such as... Figure 3 The diagram shows the relative trajectory of the projection plane (XY plane) of the sub-satellite point;

[0119] 2) A schematic diagram of the baseline distribution over a period of time, such as... Figure 4 As shown;

[0120] 3) A schematic diagram of the baseline distribution over one orbital period is shown below. Figure 5 As shown;

[0121] 4) The original simulation image is as follows Figure 6 As shown;

[0122] 5) Interferometric imaging inversion diagram as shown Figure 7 As shown.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for interferometric imaging detection of a spatial co-orbiting satellite formation, the method comprising: Step 1) setting initial parameters of a central satellite or a virtual central satellite and N co-orbiting formation satellites; The initial parameters include six elements of the orbit of the central satellite or virtual central satellite: semi-major axis a0, eccentricity e0, orbit inclination i0, perihelion argument ω0, ascending node argument Ω0 and mean anomaly M0; N satellites are distributed on K lower point circles, each circle has N k satellites, the initial value of the radius of the kth circle is r k ,k = 1, 2,..., K, the maximum circle radius is R, the initial value of the initial phase angle of the jth satellite is j = 1, 2,..., N, and the direction of the satellite is determined to be counterclockwise or clockwise. Step 2) calculating relative orbital elements of the N formation satellites; Step 3) calculating absolute orbital elements according to the relative orbital elements obtained in Step 2); Step 4) predicting the position of each formation satellite according to the absolute orbital elements obtained in Step 3), and calculating detection baselines formed by each two formation satellites; Step 5) calculating a baseline distribution uniformity metric function according to the detection baselines obtained in Step 4) as an objective function, and performing optimization exploration using an optimization algorithm to obtain an optimal solution; Step 6) repeating Steps 2) to 4) based on the optimal solution to obtain detection baselines with continuity and uniformity in both radial and circumferential directions; Step 7) performing imaging inversion based on the detection baselines obtained in Step 6) according to the principle of interferometric imaging. The Step 2) specifically comprises: When the co-orbiting direction is clockwise, the relative orbital elements of the jth formation satellite satisfy the following formula: wherein, Δa j , Δe xj , Δe yj , Δi xj , Δi yj , ΔM j respectively represent the relative semi-major axis, the relative eccentricity in the x direction, the relative eccentricity in the y direction, the relative inclination in the x direction, the relative inclination in the y direction and the relative mean anomaly; When the co-orbiting direction is counterclockwise, the relative orbital elements of the jth formation satellite satisfy the following formula: The Step 5) specifically comprises: The Cornwell indicator M is calculated from the probe baseline obtained according to step 4) as a measure of the uniformity of the distribution cs (b1,b2,...,b s ) : Wherein, s is the number of detection baselines formed by N chaser satellites, s=N×(N-1) / 2, b1, b2,..., bs represent s detection baselines at a certain moment. s s detection baselines at a certain moment; Taking the Cornwell index as the objective function, and taking each circle radius, the number of satellites on each circle, and the initial phase angle of each satellite distribution as optimization variables, the optimal solution is obtained by optimization search.

2. The method according to claim 1, wherein, The Step 3) specifically comprises: The absolute orbital elements of the jth formation satellite are obtained by the following formula: where a j , e j , i j , ω j , Ω j , and M j represent the semi-major axis, eccentricity, inclination, argument of perigee, longitude of the ascending node, and mean anomaly of the jth co-orbital satellite, respectively.

3. The method according to claim 2, wherein, The Step 4) specifically comprises: From the absolute orbital elements of the formation satellites obtained in step 3), the position r of the jth formation satellite is calculated j (x,y,z), the position r of the ith formation satellite i (x,y,z), i,j = 1,...,N, and the probe baseline formed by each pair of satellites is calculated, denoted as b(u,v,w).

4. The method according to claim 1, wherein, The detection baselines of the Step 6) comprise: The detection baselines formed by the same ring are circularly distributed, satisfying the following formula: Where (u, v) represents the projection coordinates of any point on the detection baseline formed by the ith formation satellite and the jth formation satellite; The detection baselines formed between different rings satisfy the following formula:

5. The method according to claim 4, wherein, The Step 7) specifically comprises: According to (u, v) obtained in Step 6), the corresponding visibility function Viss(u, v) is calculated by the following formula: According to the basic principle of interferometric imaging, the inversion image T is obtained by the following formula B (ξ,η): Where (ξ, η) is the position coordinates of each point in the image.

6. A system for interferometric imaging detection of a satellite formation flying based on the spatial co- flight of claim 1, characterized in that, The system comprises: An initial parameter setting module for setting initial parameters of a central satellite or a virtual central satellite and N formation satellites; A relative orbital element calculation module for calculating relative orbital elements of the N formation satellites; An absolute orbital element calculation module for calculating absolute orbital elements according to the relative orbital elements obtained by the relative orbital element calculation module; A detection baseline calculation module for obtaining absolute orbital elements, predicting the position of each formation satellite, and calculating detection baselines formed by each two formation satellites; An optimization module for calculating a baseline distribution uniformity metric function according to the detection baselines obtained by the detection baseline calculation module as an objective function, and performing optimization exploration using an optimization algorithm to obtain an optimal solution; A detection baseline calculation module based on the optimal solution for obtaining detection baselines with continuity and uniformity in both radial and circumferential directions based on the optimal solution obtained by the optimization module; and An imaging inversion module for performing imaging inversion based on the principle of interferometric imaging according to the detection baselines obtained by the detection baseline calculation module based on the optimal solution.

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