A method for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging

Abstract

The present invention discloses a method for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging, the method comprising: setting initial parameters for a central satellite or a virtual central satellite and N formation companion satellites; generating an expected baseline arithmetic progression for the N formation companion satellites and determining a corresponding position progression; calculating the initial phase angle of each companion satellite based on the obtained position progression; obtaining the relative orbital element of each companion satellite based on the obtained initial phase angle and the initial parameters; calculating the absolute orbital element of each companion satellite based on the relative orbital element; predicting the position of each companion satellite based on the absolute orbital element and calculating a detection baseline; and performing imaging inversion based on the detection baseline and the interferometric imaging principle. The detection baseline formed by the method of the present invention has length invariance, is circularly sampled, and is continuous and uniform in both radial and circumferential directions, effectively improving the density of baseline coverage.

Description

Technical Field

[0001] The present invention belongs to the technical field of passive microwave interferometric imaging based on satellite formations, and in particular relates to a method for determining an initial phase angle of sub-satellite point circle satellite formation interferometric imaging. Background Art

[0002] Interferometric imaging detection using multiple satellites flying in formation is an important means of improving spatial resolution. Formation flying creates a detection baseline, enabling imaging detection based on the principles of interferometric imaging. The effective detection baseline is the two-dimensional vector resulting from the projection of the three-dimensional baseline formed by the formation satellites onto the observation plane—that is, the projection of the three-dimensional baseline onto the subsatellite point circle. Therefore, the direction of the baseline is primarily determined by the initial phase angles of the satellites on the circle. A reasonable distribution of phase angles determines the detection baseline for multiple satellites and directly impacts imaging quality.

[0003] Satellites orbit around a central satellite or virtual satellite. Based on the relative motion equation, when there is no long-term relative drift, the trajectory of the companion satellite relative to the central satellite is a spatial ellipse. A subsatellite point circle configuration means that the projection of the subsatellite point is a circle. If multiple companion satellites orbit the same spatial ellipse, they have the same angular velocity and period on the subsatellite point circle, differing only in their initial phase angles.

[0004] Based on 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 in the direction of the subsatellite point is called the projected detection baseline (abbreviated as "baseline"). The baseline formed between the accompanying satellites is circular and has a constant length; the baseline rotates as the satellites orbit one revolution.

[0005] Conventional methods for determining the initial phase of interferometric imaging satellite formation configurations usually use various optimization search algorithms to achieve uniform coverage of long and short baselines, but the optimization results are often uncertain. Summary of the Invention

[0006] To address the uncertainty in optimization results from existing techniques, the present invention aims to overcome these shortcomings by proposing a method for determining the initial phase angle for sub-satellite point circle formation interferometric imaging. This method calculates the initial phase angle by calculating the desired baseline sequence, ensuring uniqueness. The resulting detection baseline is continuous and uniform in both radial and circumferential directions, effectively improving the density of baseline coverage.

[0007] To achieve the above object, the present invention proposes a method for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging, the method comprising:

[0008] Step 1) setting the initial parameters of the central satellite or virtual central satellite and N formation companion satellites;

[0009] Step 2) generating an expected baseline arithmetic sequence for the N formation companion satellites and determining the corresponding position sequence;

[0010] Step 3) calculating the initial phase angle of each companion satellite based on the position sequence obtained in step 2);

[0011] Step 4) obtaining the relative orbital elements of each companion satellite based on the initial phase angle obtained in step 3) and the initial parameters;

[0012] Step 5) calculating the absolute orbital elements of each companion satellite based on the relative orbital elements obtained in step 4);

[0013] Step 6) Using the absolute orbital elements obtained in step 5), the position of each companion satellite is predicted and the detection baseline is calculated;

[0014] Step 7) Perform imaging inversion based on the detection baseline obtained in step 6) based on the principle of interferometric imaging.

[0015] As an improvement to the above method, the initial parameters of step 1) include:

[0016] The six orbital elements of the central satellite or virtual central star: semi-major axis a0, eccentricity e0, orbital inclination i0, perihelion argument ω0, ascending node ecliptic longitude Ω0, mean anomaly M0;

[0017] The accompanying flight mode is a sub-satellite point circle with a radius of R.

[0018] As an improvement to the above method, step 2) specifically includes:

[0019] Generate the expected baseline arithmetic sequence for N companion satellites {b n}, the difference is 2R / s, s = N × (N-1) / 2, where s is the number of baselines generated by N companion satellites, and n∈[2,s] is a positive integer;

[0020] According to the number of companion satellites N, combined with the pre-established lookup table corresponding to the number of companion satellites and the recommended distribution positions, the expected baseline arithmetic sequence {b n} select N values ​​closest to the recommended distribution position in the lookup table and record them as position sequence {d k},k=1,...,N。

[0021] As an improvement to the above method, step 3) specifically includes:

[0022] According to the position sequence {d k},Depend on Get the initial phase angle of the kth companion satellite Among them, the position of the first companion satellite is d1 = 0, and the initial phase angle is The position d of the Nth satellite N =2R, initial phase angle

[0023] As an improvement to the above method, step 4) specifically includes:

[0024] According to the radius R of the subsatellite point circle, the initial phase angle Get the relative orbital elements of the kth companion satellite:

[0025]

[0026] Where Δa k ,Δe xk ,Δe yk ,Δi xk ,Δi yk ,ΔM k They represent the relative semi-major axis, relative eccentricity in the x-direction, relative eccentricity in the y-direction, relative orbital inclination in the x-direction, relative orbital inclination in the y-direction and relative mean anomaly.

[0027] As an improvement to the above method, step 5) specifically includes:

[0028] The absolute orbital elements of the kth companion satellite are obtained by the following formula:

[0029]

[0030] Among them, a k 、e k 、i k 、ω k ,Ω k and M k They represent the semi-major axis, eccentricity, orbit inclination, perihelion argument, ascending node ecliptic longitude and mean anomaly of the kth companion satellite respectively.

[0031] As an improvement to the above method, step 6) specifically includes:

[0032] Step 6-1) Initial phase angles of the kth companion satellite and the ith companion satellite The angular velocity of the two accompanying satellites is the same, so the phase angle that changes with time is The projection positions of the kth companion satellite and the ith companion satellite in the x-direction and y-direction (r k (x),r k (y))、(r i (x),r i (y)):

[0033]

[0034] The detection baseline formed by the two satellites satisfies the following formula and is continuous and uniform:

[0035]

[0036] Where (u, v) represents any point on the detection baseline formed by the kth companion satellite and the ith companion satellite;

[0037] Step 6-2) Repeat step 6-1) until the detection baseline of every two companion satellites is obtained.

[0038] As an improvement to the above method, step 7) specifically includes:

[0039] According to the (u, v) obtained in step 6), the corresponding visibility function Viss(u, v) is calculated by the following formula:

[0040]

[0041] According to the basic principle of interferometric imaging, the inversion image T is obtained by the following formula: B (ξ,η):

[0042]

[0043] Among them, (ξ,η) is the position coordinate of each point in the image.

[0044] On the other hand, the present invention proposes a system for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging, the system comprising:

[0045] The initial parameter setting module is used to set the initial parameters of the central satellite or virtual central satellite and N formation companion satellites;

[0046] The position sequence determination module is used to generate an expected baseline arithmetic sequence for the N formation companion satellites and determine the corresponding position sequence;

[0047] An initial phase angle calculation module is used to calculate the initial phase angle of each companion satellite based on the position sequence obtained by the position sequence determination module;

[0048] The relative orbit element calculation module is used to obtain the relative orbit element of each companion satellite based on the initial phase angle obtained by the initial phase angle calculation module and the initial parameters;

[0049] The absolute orbit element calculation module is used to calculate the absolute orbit element of each companion satellite based on the relative orbit element obtained by the relative orbit element calculation module;

[0050] A detection baseline calculation module is used to predict the position of each companion satellite using the absolute orbit elements obtained by the absolute orbit element calculation module to calculate the detection baseline; and

[0051] The imaging inversion module is used to perform imaging inversion based on the interference imaging principle according to the detection baseline obtained by the detection baseline calculation module.

[0052] Compared with the prior art, the advantages of the present invention are:

[0053] 1. The method of the present invention calculates the initial phase angle by calculating the expected baseline sequence, which is unique;

[0054] 2. The detection baseline formed by the method of the present invention has length invariance, is circular sampling, and has continuity and uniformity in both radial and circumferential directions, effectively improving the density of baseline coverage. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart of the method for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging of the present invention;

[0056] Figure 2 This is a schematic diagram of the subsatellite point circle configuration of the companion satellite;

[0057] Figure 3 It is a schematic diagram of the relative trajectory of the subsatellite point projection plane (XY plane);

[0058] Figure 4 It is a schematic diagram of the short-term baseline distribution;

[0059] Figure 5 It is a schematic diagram of the orbital period baseline distribution;

[0060] Figure 6 is the input graph of the simulation;

[0061] Figure 7 is the inversion image of interferometric imaging. DETAILED DESCRIPTION

[0062] This paper proposes a method for determining initial satellite phase angles and calculating satellite orbital elements for interferometric imaging using a circular satellite formation at a sub-satellite point. Given the central satellite, orbital radius, and number of satellites, a method for determining the initial phase angles of companion satellites on the circle and calculating the corresponding orbital elements is proposed to obtain a uniformly distributed baseline.

[0063] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0064] Example 1

[0065] like Figure 1The embodiment of the present invention proposes a method for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging, which is specifically described as follows:

[0066] Step 1) Set the orbital elements (a0, e0, i0, ω0, Ω0, M0) of the center satellite (or virtual center satellite). Assume that there are N satellites in formation flying, the flying mode is the subsatellite point circle, and the radius of the subsatellite point circle is R. The phase angle of the N satellite distribution is Figure 2 This is a schematic diagram of the subsatellite point circle configuration of the companion satellite.

[0067] Step 2) The baselines formed by N satellites are s=N×(N-1) / 2 in total. Generate the desired baseline arithmetic sequence {b n}, satisfying b n -b n-1 = 2R / s, n∈[2s] positive integer. According to the number of satellites, combined with the following lookup table, from the expected baseline {b n}Select N values ​​closest to the recommended distribution position in the lookup table from the sequence, and record them as the position sequence {d k},k=1,...,N。

[0068] The lookup table is as follows:

[0069]

[0070]

[0071] Step 3) According to the position sequence {d k}, generate the phase angles of N satellites Among them, the first satellite is d1=0, The Nth satellite is d N =2R,

[0072] Step 4) According to the radius R of the subsatellite circle and the initial phase Calculate the relative orbital elements (Δa, Δe) of all satellites x ,Δe y ,Δi x ,Δi y ,ΔM), the formation is a subsatellite point circle, and the satellites fly together in the same direction.

[0073] The relative orbital element of the kth satellite is: Δa k ,Δe xk ,Δe yk ,Δi xk ,Δi yk ,ΔM k .

[0074]

[0075] Step 5) According to the relative orbital elements (Δa, Δe) of all satellites x ,Δe y ,Δi x ,Δi y ,ΔM), calculate the absolute orbit elements (a,e,i,Ω,ω,M).

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

[0077]

[0078] Step 6) Calculate the satellite position r according to the absolute orbital elements of the companion satellite obtained in step 5) 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. The detection baseline is continuous and uniform in both radial and circumferential directions.

[0079] Assume that the initial phase angles of the two satellites are Since the two satellites have the same angular velocity, the phase angle changes with time. The same. Then the projected positions of the two satellites are:

[0080]

[0081] The baseline formed by the two satellites is:

[0082]

[0083] From the above formula, we can see that

[0084]

[0085] Step 7) Based on the detection baseline obtained in step 6), imaging inversion can be performed based on the principle of interferometric imaging.

[0086] T B is the brightness temperature of the two-dimensional simulated image, (ξ,η) is the position coordinate 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:

[0087]

[0088] According to the basic principle of interferometric imaging, the inversion image is obtained by the following formula:

[0089]

[0090] Example 2

[0091] Embodiment 2 of the present invention proposes a system for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging, which is implemented based on the method of embodiment 1. The system includes:

[0092] The initial parameter setting module is used to set the initial parameters of the central satellite or virtual central satellite and N formation companion satellites;

[0093] The position sequence determination module is used to generate an expected baseline arithmetic sequence for the N formation companion satellites and determine the corresponding position sequence;

[0094] An initial phase angle calculation module is used to calculate the initial phase angle of each companion satellite based on the position sequence obtained by the position sequence determination module;

[0095] The relative orbit element calculation module is used to obtain the relative orbit element of each companion satellite based on the initial phase angle obtained by the initial phase angle calculation module and the initial parameters;

[0096] The absolute orbit element calculation module is used to calculate the absolute orbit element of each companion satellite based on the relative orbit element obtained by the relative orbit element calculation module;

[0097] A detection baseline calculation module is used to predict the position of each companion satellite using the absolute orbit elements obtained by the absolute orbit element calculation module to calculate the detection baseline; and

[0098] The imaging inversion module is used to perform imaging inversion based on the interference imaging principle according to the detection baseline obtained by the detection baseline calculation module.

[0099] Simulation example:

[0100] Take the 9 satellites subsatellite point circle formation as an example to simulate the situation. Figure 3 As shown, Figure 4 is a diagram of the short-term baseline distribution. Figure 5 This is a diagram of the orbital period baseline distribution. Figure 6 is the simulation input image, and the interference imaging inversion simulation results are as follows Figure 7 shown.

[0101] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art 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 are intended to be encompassed by the claims of the present invention.

Claims

1. A method for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging, the method comprising: Step 1) setting the initial parameters of the central satellite or virtual central satellite and N formation companion satellites; Step 2) generating an expected baseline arithmetic sequence for the N formation companion satellites and determining the corresponding position sequence; Step 3) calculating the initial phase angle of each companion satellite based on the position sequence obtained in step 2); Step 4) obtaining the relative orbital elements of each companion satellite based on the initial phase angle obtained in step 3) and the initial parameters; Step 5) calculating the absolute orbital elements of each companion satellite based on the relative orbital elements obtained in step 4); Step 6) Using the absolute orbital elements obtained in step 5), the position of each companion satellite is predicted and the detection baseline is calculated; Step 7) Perform imaging inversion based on the detection baseline obtained in step 6) based on the principle of interferometric imaging.

2. The method for determining the initial phase angle of sub-satellite point circle satellite formation interferometry imaging according to claim 1, characterized in that: The initial parameters of step 1) include: The six orbital elements of the central satellite or virtual central star: semi-major axis a0, eccentricity e0, orbital inclination i0, perihelion argument ω0, ascending node ecliptic longitude Ω0, mean anomaly M0; The accompanying flight mode is a sub-satellite point circle with a radius of R.

3. The method for determining the initial phase angle of sub-satellite point circle satellite formation interferometry imaging according to claim 2, characterized in that: The step 2) specifically includes: Generate the expected baseline arithmetic sequence for N companion satellites {b n }, the difference is 2R / s, s = N × (N-1) / 2, where s is the number of baselines generated by N companion satellites, and n∈[2,s] is a positive integer; According to the number of companion satellites N, combined with the pre-established lookup table corresponding to the number of companion satellites and the recommended distribution positions, the expected baseline arithmetic sequence {b n } select N values ​​closest to the recommended distribution position in the lookup table and record them as position sequence {d k },k=1,...,N。 4. The method for determining the initial phase angle of sub-satellite point circle satellite formation interferometry imaging according to claim 3, characterized in that: The step 3) specifically includes: According to the position sequence {d k },Depend on Get the initial phase angle of the kth companion satellite Among them, the position of the first companion satellite is d1 = 0, and the initial phase angle is The position d of the Nth satellite N =2R, initial phase angle 5. The method for determining the initial phase angle of sub-satellite point circle satellite formation interferometry imaging according to claim 4, characterized in that: The step 4) specifically includes: According to the radius R of the subsatellite point circle, the initial phase angle Get the relative orbital elements of the kth companion satellite: Where Δa k ,Δe xk ,Δe yk ,Δi xk ,Δi yk ,ΔM k They represent the relative semi-major axis, relative eccentricity in the x-direction, relative eccentricity in the y-direction, relative orbital inclination in the x-direction, relative orbital inclination in the y-direction and relative mean anomaly.

6. The method for determining the initial phase angle of sub-satellite point circle satellite formation interferometry imaging according to claim 5, characterized in that: The step 5) specifically includes: The absolute orbital elements of the kth companion satellite are obtained by the following formula: Among them, a k 、e k 、i k 、ω k ,Ω k and M k They represent the semi-major axis, eccentricity, orbit inclination, perihelion argument, ascending node ecliptic longitude and mean anomaly of the kth companion satellite respectively.

7. The method for determining the initial phase angle of sub-satellite point circle satellite formation interferometry imaging according to claim 6, characterized in that: The step 6) specifically includes: Step 6-1) Initial phase angles of the kth companion satellite and the ith companion satellite The angular velocity of the two accompanying satellites is the same, so the phase angle that changes with time is The projection positions of the kth companion satellite and the ith companion satellite in the x-direction and y-direction (r k (x),r k (y))、(r i (x),r i (y)): The detection baseline formed by the two satellites satisfies the following formula and is continuous and uniform: Where (u, v) represents any point on the detection baseline formed by the kth companion satellite and the ith companion satellite; Step 6-2) Repeat step 6-1) until the detection baseline of every two companion satellites is obtained.

8. The method for determining the initial phase angle of sub-satellite point circle satellite formation interferometry imaging according to claim 7, characterized in that: The step 7) specifically includes: According to the (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): Among them, (ξ,η) is the position coordinate of each point in the image.

9. A system for determining the initial phase angle of sub-satellite point circle satellite formation interferometric imaging, characterized in that: The system comprises: The initial parameter setting module is used to set the initial parameters of the central satellite or virtual central satellite and N formation companion satellites; The position sequence determination module is used to generate an expected baseline arithmetic sequence for the N formation companion satellites and determine the corresponding position sequence; An initial phase angle calculation module is used to calculate the initial phase angle of each companion satellite based on the position sequence obtained by the position sequence determination module; The relative orbit element calculation module is used to obtain the relative orbit element of each companion satellite based on the initial phase angle obtained by the initial phase angle calculation module and the initial parameters; The absolute orbit element calculation module is used to calculate the absolute orbit element of each companion satellite based on the relative orbit element obtained by the relative orbit element calculation module; A detection baseline calculation module is used to predict the position of each companion satellite using the absolute orbit elements obtained by the absolute orbit element calculation module to calculate the detection baseline; and The imaging inversion module is used to perform imaging inversion based on the interference imaging principle according to the detection baseline obtained by the detection baseline calculation module.

Images