Interferometric constellation orbit optimization method based on second order state transition tensor

Abstract

The application discloses an interferometric constellation orbit optimization method based on a second-order state transition tensor and belongs to the field of space technology. The method of the application is as follows: an orbit dynamics model and a configuration stability index model of an interferometric constellation spacecraft are established, an orbit deviation propagation expression is given based on a second-order state transition tensor, and a second-order analytical mapping expression of configuration stability of the interferometric constellation and initial orbit deviation is derived; an iterative deviation of the initial state of the spacecraft is given; an initial value of the constellation configuration with strong stability is obtained through iteration, the constellation configuration satisfying long-term stability is obtained through recursive initial value, the interferometric constellation is realized to be long-term stable according to the constellation configuration, and the detection precision of the interferometric constellation is improved. The application has the advantages of high-precision space measurement constellation configuration stability, high efficiency, is favorable for fast iterative optimization of the high-precision space measurement constellation configuration, and is favorable for improving the stability and detection performance of the high-precision space measurement constellation configuration.

Description

Technical Field

[0001] This invention relates to a method for optimizing the orbit of a high-precision space interferometric constellation, belonging to the field of space technology. Background Technology

[0002] Observing outer space is crucial for understanding the origin of the universe, exploring space, and discovering extraterrestrial life and Earth-like planets. It is of great significance for the development of space science and technology, planetary physics, and the exploration of the universe. Due to the vast distances and weak signals from targets in outer space, interferometry is typically used to improve observational sensitivity. However, ground-based interferometry methods have limited applicability due to atmospheric obstruction, ground vibration noise, and the influence of surface gravity gradients. Therefore, deploying multiple interferometric spacecraft to form a space interferometric constellation has become a feasible solution for future high-precision interferometry. High-precision space interferometric constellations have long mission cycles and require high configuration stability. Traditional intelligent optimization methods suffer from low optimization efficiency and poor configuration stability. Therefore, it is necessary to develop iterative optimization methods for the orbits of high-precision space interferometric constellations to improve optimization efficiency and enhance their long-term stability. Summary of the Invention

[0003] The main objective of this invention is to provide an interferometric constellation orbit optimization method based on a second-order state transition tensor. This method establishes an orbital dynamics model and a configuration stability index model for the interferometric constellation spacecraft. Based on the second-order state transition tensor, an expression for orbital deviation propagation is derived, followed by a second-order analytical mapping expression between the configuration stability of the interferometric constellation and the initial orbital deviation. Based on this second-order analytical mapping expression, an iterative deviation of the spacecraft's initial state is given. Iteration yields initial values ​​for the constellation configuration with strong stability. By recursively calculating these initial values, a constellation configuration that satisfies long-term stability is obtained. Based on this constellation configuration, the interferometric constellation achieves long-term stability, thereby improving the detection accuracy of the interferometric constellation and solving related technical problems in the field of high-precision space measurement constellations. This invention has the advantages of good configuration stability and high efficiency for high-precision space measurement constellations, facilitating rapid iterative optimization of high-precision space measurement constellation configurations and improving their stability and detection performance.

[0004] The objective of this invention is achieved through the following technical solutions.

[0005] This invention discloses an interferometric constellation orbit optimization method based on a second-order state transition tensor. It establishes a dynamic model of the spacecraft and a stability index model for the high-precision interferometric constellation configuration, providing initial values ​​for the spacecraft's orbital states. Then, based on these initial values, a second-order state transition tensor for orbital deviation prediction is recursively derived, leading to a second-order expression for predicting the orbital deviation of a single spacecraft within the constellation. Next, based on this second-order expression, a second-order expression for predicting the total orbital deviation of multiple spacecraft within the constellation is established. Finally, based on the obtained state transition tensor of the orbital deviations of multiple spacecraft within the constellation, a second-order analytical expression for the constellation's stability index and initial orbital states is established. Using a preset stability index as the expectation, this invention iterates the initial orbital values ​​of the spacecraft based on the obtained stability index of the space high-precision interferometry constellation configuration and the second-order analytical expression of the initial orbital state. This achieves long-term stability of the interferometry constellation, thereby improving the detection accuracy of the interferometry constellation and solving related technical problems in the field of space high-precision measurement constellations. This invention has the advantages of good stability and high efficiency in space high-precision measurement constellation configurations, which is conducive to rapid iterative optimization of space high-precision measurement constellation configurations and improves their stability and detection performance.

[0006] This invention discloses an interferometric constellation orbit optimization method based on a second-order state transition tensor, comprising the following steps:

[0007] Step 1: Establish the dynamic model of the spacecraft and the stability index model f(x) of the high-precision interferometry constellation configuration in space. i ,t), given the initial value x of the spacecraft orbital state in a high-precision space interferometry constellation configuration. i,0 .

[0008] The dynamic model of the spacecraft in the high-precision interferometry constellation configuration is as follows:

[0009]

[0010] Where x i (t)=[r i (t) T ,v i (t) T ] T This represents the state of spacecraft i at time t, where the state includes position and velocity, f(x). i ,t) represents the dynamic equation of the spacecraft.

[0011] The stability indices of a high-precision space interferometry constellation configuration include arm length, breathing angle, and relative velocity, and their models are as follows:

[0012] l ij (t)=||r ij (t)|| (2)

[0013]

[0014]

[0015] Among them l ij (t) represents the arm lengths corresponding to spacecraft i and spacecraft j, θ i (t) represents the breathing angle with spacecraft i as the vertex. r represents the relative velocity between spacecraft i and spacecraft j. ij (t)=r i (t)-r j (t) represents the relative position vector between spacecraft i and spacecraft j, v ij (t)=v i (t)-v j (t) represents the relative velocity vector between spacecraft i and spacecraft j.

[0016] The initial values ​​of the spacecraft's orbital state in a given high-precision space interferometry constellation configuration are as follows:

[0017] x i (t0)=x i,0 (5)

[0018] Where x i,0 Let t be the initial state given to spacecraft i at the initial time t0.

[0019] Step 2: Based on the initial value x of the spacecraft orbital state in the high-precision interferometry constellation configuration given in Step 1. i,0 The second-order state transition tensor used for orbit deviation prediction is obtained recursively. Furthermore, a second-order expression for predicting the orbital deviation of a single spacecraft in a high-precision space interferometry constellation is established.

[0020] Based on the initial value x of the spacecraft orbital state in the high-precision interferometry constellation configuration given in step 1. i,0 By integrating differential equations (6) and (7), the second-order state transition tensor used for orbital deviation prediction is recursively obtained.

[0021]

[0022]

[0023] in and Represents the dynamic model f(x) i The first and second order Jacobian matrices of t). The superscripts in formulas (6) and (7) denote Einstein summation notations.

[0024] The second-order expression for predicting the orbital deviation of a single spacecraft in a high-precision space interferometry constellation is established as follows:

[0025]

[0026] Step 3: Based on the second-order expression for the prediction of the orbital deviation of a single spacecraft in the high-precision interferometry constellation in step 2, establish the second-order expression for the prediction of the total orbital deviation of multiple spacecraft in the high-precision interferometry constellation.

[0027] Based on the second-order expression for the orbital deviation prediction of a single spacecraft in the high-precision interferometry constellation in step 2, the second-order expression for the overall orbital deviation prediction of multiple spacecraft in the high-precision interferometry constellation in space is established as follows:

[0028]

[0029] Where X(t) = [x1(t); x2(t); x3(t)] is the state vector of multiple spacecraft, and X0 = [x 1,0 ;x 2,0 ;x 3,0 ] represents the initial state vector of multiple spacecraft. and The state transition tensor is used to simultaneously predict orbital deviations of multiple spacecraft.

[0030] Step 4: Based on the state transition tensor of the orbital deviations of multiple spacecraft in the space high-precision interferometry constellation in Step 3, establish a second-order analytical expression for the configuration stability index and initial orbital state of the space high-precision interferometry constellation.

[0031] First, the second-order analytical expression for the stability index of the space high-precision interferometry constellation configuration and the spacecraft orbital state X(t) is established as follows:

[0032]

[0033] in Ω represents the spatial high-precision interferometric constellation configuration stability index vector at time t. k,a With Ω k,abThese are the first and second partial derivatives of the spatial high-precision interferometry constellation configuration stability index y(t) at time t with respect to the spacecraft orbital state X(t) at time t.

[0034] Furthermore, based on the second-order expression for the prediction of the total orbital deviation of multiple spacecraft in the high-precision interferometry constellation established in step 3, the second-order analytical expression for the configuration stability index and initial orbital state of the high-precision interferometry constellation is established as follows:

[0035]

[0036] Among them Ξ k,a With Ξ k,ab The expression is derived from the formula.

[0037] Ξ k,a =Ω k,p Ξ p,a (12)

[0038] Ξ k,ab =Ω k,p Ξ p,ab +Ω k,pq Ξ p,a Ξ q,b (13)

[0039] Step 5: Using the preset stability index as the expectation, iterate the initial value of the spacecraft orbit based on the second-order analytical expression of the space high-precision interferometry constellation configuration stability index and the initial orbit state obtained in Step 4.

[0040] Using a preset stability index as the expectation, the initial orbital value X0 of the spacecraft is iterated based on the second-order analytical expression of the space high-precision interferometry constellation configuration stability index and the initial orbital state obtained in step 4. The iterative expression is as follows:

[0041] X0←X0+ΔX0 (14)

[0042] Wherein ΔX0 is the correction amount for the initial value of the spacecraft orbit calculated based on the second-order analytical expression of the space high-precision interferometry constellation configuration stability index and the initial orbit state obtained in step 4, as well as the preset stability index. ΔX0 is obtained by solving the nonlinear equation shown in formula (15).

[0043]

[0044] in This is a stability index for the desired high-precision spatial interferometry constellation configuration.

[0045] Step 6: Determine if convergence has occurred. If convergence has occurred, output the initial orbit values ​​of the spacecraft in the high-precision interferometry constellation corresponding to the iterative optimization, i.e., realize the orbit optimization of the interferometry constellation based on the second-order state transition tensor. If convergence has not occurred, return to step 2.

[0046] Determine if convergence has occurred. If ||ΔX0|| < η, where η is a preset convergence threshold, indicating convergence, then output the initial orbital value X0 of the spacecraft in the corresponding space high-precision interferometry constellation for iterative optimization. If convergence has not occurred, return to step 2.

[0047] The invention also includes step 7, which, based on the optimized initial orbit values, recursively calculates the constellation configuration that satisfies long-term stability. This constellation configuration enables the interferometric constellation to achieve long-term stability, thereby improving the detection accuracy of the interferometric constellation and solving related technical problems in the field of high-precision space measurement constellations. This invention has the advantages of good stability and high efficiency in high-precision space measurement constellation configurations, facilitating rapid iterative optimization of high-precision space measurement constellation configurations and improving their stability and detection performance.

[0048] Beneficial effects:

[0049] 1. This invention discloses an interferometric constellation orbit optimization method based on a second-order state transition tensor. It establishes an orbital dynamics model and a configuration stability index model for the interferometric constellation spacecraft. Based on the second-order state transition tensor, it derives an expression for orbital deviation propagation, and then derives a second-order analytical mapping expression between the configuration stability of the interferometric constellation and the initial orbital deviation. Based on this second-order analytical mapping expression, iterative deviations of the spacecraft's initial state are given. Iteration yields initial values ​​for the constellation configuration with strong stability. By recursively calculating these initial values, a constellation configuration satisfying long-term stability is obtained. Based on this constellation configuration, the interferometric constellation achieves long-term stability, thereby improving the detection accuracy of the interferometric constellation and solving related technical problems in the field of high-precision space measurement constellations. This invention has the advantages of good configuration stability and high efficiency in high-precision space measurement constellations, facilitating rapid iterative optimization of high-precision space measurement constellation configurations and improving their stability and detection performance. The related technical problems in the field of high-precision space measurement constellations include constellation configuration maintenance and reconstruction, and high-precision constellation orbit determination.

[0050] 2. The present invention discloses an interferometric constellation orbit optimization method based on second-order state transition tensor. Based on configuration stability and initial orbit deviation, a second-order analytical mapping expression for the configuration stability of the interferometric constellation is constructed. Through iterative optimization of the analytical expression, the computational load is small, which helps to reduce the computation time of high-precision spatial interferometric constellation orbit optimization.

[0051] 3. The present invention discloses an interferometric constellation orbit optimization method based on second-order state transition tensor. In the process of constructing the second-order analytical mapping expression for the stability of the interferometric constellation configuration, it does not rely on the dynamic model assumptions, nor on the dynamic model and constellation configuration stability index model. It can be extended to any dynamic and configuration stability requirements and has wide applicability.

[0052] 4. The interferometric constellation orbit optimization method based on second-order state transition tensor disclosed in this invention has the advantages of good stability and high efficiency of the configuration obtained by optimizing the configuration of high-precision space measurement constellation, based on the above three beneficial effects. It is conducive to the rapid iterative optimization of the configuration of high-precision space measurement constellation and to improving the stability and detection performance of the configuration of high-precision space measurement constellation.

[0053] 5. This invention discloses an interferometric constellation orbit optimization method based on second-order state transition tensors. It adopts a second-order analytical approximation and iterative optimization method, and expands its application to near-Earth spacecraft orbit stability analysis, deep-space transfer orbit stability analysis, and near-small celestial body probe orbit stability analysis by replacing the high-precision space measurement constellation configuration with near-Earth spacecraft dynamics, deep-space spacecraft dynamics, and near-small celestial body spacecraft dynamics. It also solves related technical problems in the fields of near-Earth spacecraft dynamics, deep-space spacecraft dynamics, and near-small celestial body spacecraft. Attached Figure Description

[0054] Figure 1 This is a flowchart of an interferometric constellation orbit optimization method based on a second-order state transition tensor disclosed in this invention;

[0055] Figure 2 To optimize the evolution diagram of the stability index of the "Lyra" constellation configuration corresponding to the initial orbit values, where: Figure 2 (a) Evolution diagram of the breathing angle of the Lyra constellation configuration corresponding to the initial orbit value before optimization. Figure 2 (b) Evolution of stability index of the "Lyra" constellation configuration corresponding to the initial orbit value before optimization. Figure 2 (c) The relative velocity evolution diagram of the "Lyra" constellation configuration corresponding to the initial orbit value before optimization.

[0056] Figure 3 The evolution diagram of the stability index of the "Lyra" constellation configuration corresponding to the optimized initial orbit value is shown, where: Figure 3 (a) is the evolution diagram of the breathing angle of the Lyra constellation configuration corresponding to the optimized initial orbit value. Figure 3 (b) is a graph showing the evolution of the stability index of the "Lyra" constellation configuration corresponding to the optimized initial orbit values. Figure 3 (c) is a diagram showing the relative velocity evolution of the "Lyra" constellation configuration corresponding to the optimized initial orbit values. Detailed Implementation

[0057] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0058] This example uses the geocentric gravitational wave detection configuration as an example to optimize the orbit of the "Tianqin" space high-precision interferometry constellation configuration using the method proposed in this invention.

[0059] like Figure 1 As shown in the figure, the specific implementation steps of the interferometric constellation orbit optimization method based on the second-order state transition tensor disclosed in this example are as follows:

[0060] Step 1: Establish the dynamic model of the spacecraft in the "Tianqin" constellation configuration and the stability index model of the "Tianqin" constellation configuration, and give the initial value of the orbital state of the spacecraft in the high-precision space interferometry constellation configuration.

[0061] The "Tianqin" space-based high-precision interferometry constellation consists of three spacecraft. In this example, the high-precision dynamic model used includes the Earth's J2-order gravitational field, the Moon's gravitational pull, and the Sun's central gravity. Considered stability parameters include arm length, breathing angle, and arm length variation rate. The initial orbital date was chosen as May 22, 2034. The initial orbital values ​​corresponding to this date are shown in Table 1. Table 1 shows the evolution of the "Tianqin" constellation configuration stability parameters corresponding to the initial orbital values. Figure 2 As shown, the arm length changes by more than 30%, the breathing angle changes by more than 20°, the relative velocity changes by more than 6 m / s, and the configuration stability is poor.

[0062] Table 1. Initial orbit values ​​of the Lyra constellation before optimization

[0063]

[0064] Step 2: Based on the initial values ​​of the spacecraft orbital state in the high-precision interferometry constellation configuration given in Step 1, the second-order state transition tensor for orbital deviation prediction is recursively obtained, and then the second-order expression for the orbital deviation prediction of a single spacecraft in the high-precision interferometry constellation is established.

[0065] Step 3: Based on the second-order expression for the orbital deviation prediction of a single spacecraft in the high-precision interferometry constellation in Step 2, establish the second-order expression for the total orbital deviation prediction of the three spacecraft in the high-precision interferometry constellation.

[0066] Step 4: Based on the state transition tensor of the orbital deviation of the three spacecraft in the high-precision interferometry constellation in Step 3, establish a second-order analytical expression for the configuration stability index and initial orbital state of the high-precision interferometry constellation.

[0067] Step 5: Using a preset stability index as the expectation, iterate the initial values ​​of the spacecraft orbit based on the second-order analytical expression of the space high-precision interferometry constellation configuration stability index and the initial orbit state obtained in Step 4. In this example, a genetic algorithm is used to solve the nonlinear equations.

[0068] Step 6: Determine if convergence has occurred. If convergence has occurred, output the initial orbit values ​​of the spacecraft in the corresponding high-precision interferometry constellation for iterative optimization. If convergence has not occurred, return to Step 2. In this example, the convergence threshold is set to η = 10. -3 .

[0069] Step 7: Based on the optimized initial orbit values, long-term stability of the interferometric constellation is achieved, thereby improving the detection accuracy of the interferometric constellation and solving related technical problems in the field of high-precision space measurement constellations. This invention has the advantages of good stability and high efficiency in the configuration of high-precision space measurement constellations, which is conducive to rapid iterative optimization of the configuration of high-precision space measurement constellations and to improving the stability and detection performance of the configuration.

[0070] The initial orbit values ​​of spacecraft in the "Tianqin" constellation obtained after optimization using the interferometric constellation orbit optimization method based on second-order state transition tensor disclosed in this embodiment are shown in Table 2.

[0071] Figure 3 The stability indices of the "Lyra" constellation configuration after optimization using an interferometric constellation orbit optimization method based on a second-order state transition tensor disclosed in this invention are presented. The arm length change is less than 0.2%, the breathing angle change is less than 0.12°, and the relative velocity change is less than 5 m / s, representing a significant improvement in configuration stability compared to the unoptimized configuration.

[0072] Table 2. Initial orbital values ​​of the Lyra constellation after optimization

[0073]

[0074] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the orbit of an interferometric constellation based on a second-order state transition tensor, characterized in that: Includes the following steps, Step 1: Establish the dynamic model of the spacecraft and the stability index model f(x) of the high-precision interferometry constellation configuration in space. i ,t), given the initial value x of the spacecraft orbital state in a high-precision space interferometry constellation configuration. i,0 ; Step 2: Based on the initial value x of the spacecraft orbital state in the high-precision interferometry constellation configuration given in Step 1. i,0 The second-order state transition tensor used for orbit deviation prediction is obtained recursively. Furthermore, a second-order expression for predicting the orbital deviation of a single spacecraft in a high-precision space interferometry constellation is established; Step 3: Based on the second-order expression for the orbital deviation prediction of a single spacecraft in the space high-precision interferometry constellation in Step 2, establish the second-order expression for the total orbital deviation prediction of multiple spacecraft in the space high-precision interferometry constellation; Step 4: Based on the state transition tensor of the orbital deviations of multiple spacecraft in the high-precision interferometry constellation in Step 3, establish a second-order analytical expression for the configuration stability index and initial orbital state of the high-precision interferometry constellation. Step 5: Using the preset stability index as the expectation, iterate the initial value of the spacecraft orbit based on the second-order analytical expression of the space high-precision interferometry constellation configuration stability index and the initial orbit state obtained in Step 4; Step 6: Determine if convergence has occurred. If convergence has occurred, output the initial orbit values ​​of the spacecraft in the high-precision interferometry constellation corresponding to the iterative optimization, i.e., realize the orbit optimization of the interferometry constellation based on the second-order state transition tensor. If convergence has not occurred, return to step 2.

2. The interferometric constellation orbit optimization method based on second-order state transition tensor as described in claim 1, characterized in that: It also includes step 7, which, based on the optimized initial orbit values, obtains a constellation configuration that satisfies long-term stability by recursively calculating the initial values. According to the constellation configuration, the interferometric constellation achieves long-term stability, thereby improving the detection accuracy of the interferometric constellation and enhancing the stability and detection performance of the high-precision space measurement constellation configuration.

3. The interferometric constellation orbit optimization method based on second-order state transition tensor as described in claim 1 or 2, characterized in that: Step 1 is implemented as follows: The dynamic model of the spacecraft in the high-precision interferometry constellation configuration is as follows: Where x i (t)=[r i (t) T ,v i (t) T ] T This represents the state of spacecraft i at time t, where the state includes position and velocity, f(x). i ,t) represents the dynamic equations of the spacecraft; The stability indices of a high-precision space interferometry constellation configuration include arm length, breathing angle, and relative velocity, and their models are as follows: l ij (t)=||r ij (t)|| (2) Among them l ij (t) represents the arm lengths corresponding to spacecraft i and spacecraft j, θ i (t) represents the breathing angle with spacecraft i as the vertex. r represents the relative velocity between spacecraft i and spacecraft j. ij (t)=r i (t)-r j (t) represents the relative position vector between spacecraft i and spacecraft j, v ij (t)=v i (t)-v j (t) represents the relative velocity vector between spacecraft i and spacecraft j; The initial values ​​of the spacecraft's orbital state in a given high-precision space interferometry constellation configuration are as follows: x i (t0)=x i,0 (5) Where x i,0 Let t be the initial state given to spacecraft i at the initial time t0.

4. The interferometric constellation orbit optimization method based on second-order state transition tensor as described in claim 3, characterized in that: Step 2 is implemented as follows: Based on the initial value x of the spacecraft orbital state in the high-precision interferometry constellation configuration given in step 1. i,0 By integrating the differential equations, the second-order state transition tensor used for orbit deviation prediction is recursively obtained. Where f i k,a with f i k,ab Represents the dynamic model f(x) i First-order and second-order Jacobian matrices of t; superscripts in the formula and symbols represent Einstein summation notation; The second-order expression for predicting the orbital deviation of a single spacecraft in a high-precision space interferometry constellation is established as follows:

5. The interferometric constellation orbit optimization method based on second-order state transition tensor as described in claim 4, characterized in that: Step 3 is implemented as follows: Based on the second-order expression for the orbital deviation prediction of a single spacecraft in the high-precision interferometry constellation in step 2, the second-order expression for the overall orbital deviation prediction of multiple spacecraft in the high-precision interferometry constellation in space is established as follows: Where X(t) = [x1(t); x2(t); x3(t)] is the state vector of multiple spacecraft, and X0 = [x 1,0 ;x 2,0 ;x 3,0 ] represents the initial state vector of multiple spacecraft; and The state transition tensor is used to simultaneously predict orbital deviations of multiple spacecraft.

6. The interferometric constellation orbit optimization method based on second-order state transition tensor as described in claim 5, characterized in that: Step 4 is implemented as follows: First, the second-order analytical expression for the stability index of the space high-precision interferometry constellation configuration and the spacecraft orbital state X(t) is established as follows: in Ω represents the spatial high-precision interferometric constellation configuration stability index vector at time t. k,a With Ω k,ab These are the first and second partial derivatives of the spatial high-precision interferometry constellation configuration stability index y(t) at time t with respect to the spacecraft orbital state X(t) at time t, respectively. Furthermore, based on the second-order expression for the prediction of the total orbital deviation of multiple spacecraft in the high-precision interferometry constellation established in step 3, the second-order analytical expression for the configuration stability index and initial orbital state of the high-precision interferometry constellation is established as follows: Among them Ξ k,a With Ξ k,ab The expression is derived from the formula. X k,a =Oh k,p X p,a (12) X k,ab =Oh k,p X p,ab +Oh k,pq X p,a X q,b (13)。 7. The interferometric constellation orbit optimization method based on second-order state transition tensor as described in claim 6, characterized in that: Step 5 is implemented as follows: Using a preset stability index as the expectation, the initial value X0 of the spacecraft orbit is iterated based on the second-order analytical expression of the space high-precision interferometry constellation configuration stability index obtained in step 4 and the initial orbit state; the iterative expression is as follows: X0←X0+ΔX0 (14) Where ΔX0 is the correction amount of the initial value of the spacecraft orbit calculated based on the second-order analytical expression of the space high-precision interferometry constellation configuration stability index and the initial orbit state obtained in step 4, as well as the preset stability index; ΔX0 is obtained by solving the nonlinear equation shown in the formula; in This is a stability index for the desired high-precision spatial interferometry constellation configuration.

8. The interferometric constellation orbit optimization method based on second-order state transition tensor as described in claim 7, characterized in that: In step 6, Determine if convergence has occurred. If ||ΔX0|| < η, where η is a preset convergence threshold, indicating convergence, then output the initial orbital value X0 of the spacecraft in the corresponding space high-precision interferometry constellation for iterative optimization. If convergence has not occurred, return to step 2.

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