A method for predicting the orbit insertion allowable domain boundary of a space high-precision interferometric measurement constellation

Abstract

The application discloses a space high-precision interferometric measurement constellation orbit insertion allowable domain boundary prediction method and belongs to the field of space technology.The third-order semi-analytic expression of the space high-precision interferometric measurement constellation configuration stability index deviation propagation is established, the space high-precision interferometric measurement constellation configuration stability index deviation propagation calculation precision is greatly improved, and then the space high-precision interferometric measurement constellation orbit insertion allowable domain boundary prediction calculation precision is improved.The semi-analytic expression of the space high-precision interferometric measurement constellation configuration stability index deviation propagation is established, the space high-precision interferometric measurement constellation configuration stability index deviation propagation calculation amount is greatly reduced, and the space high-precision interferometric measurement constellation orbit insertion allowable domain boundary prediction calculation speed is improved.The application has the advantages of high prediction precision and fast calculation speed, is favorable for improving the space high-precision interferometric measurement constellation configuration stability and improving the space high-precision interferometric measurement constellation observation efficiency.

Description

Technical Field

[0001] This invention relates to a method for predicting the boundary of the orbital allowable domain of a high-precision space interferometry constellation, belonging to the field of space technology. Background Technology

[0002] Interferometry is a crucial tool for detecting gravitational waves, observing Earth-like planets, and conducting high-precision cosmological observations. Compared to a single measurement unit, interferometry significantly improves observational accuracy by deploying multiple observers. However, the range of interferometry is limited by the arm lengths between the observers. For ground-based interferometry, due to the constraint of the Earth's radius, it typically only measures high-frequency signals. In contrast, deploying interferometric spacecraft in space to form a high-precision space interferometric constellation significantly expands the measurement range, enabling the measurement of low-frequency signals. High-precision space interferometric constellations have extremely high requirements for configuration stability. Although optimized design typically ensures that the nominal orbits of high-precision space interferometric constellations meet these stability requirements, orbital insertion deviations can cause spacecraft within the constellation to deviate from their pre-set nominal orbits, thus compromising the constellation's configuration stability. Therefore, it is necessary to predict the allowable range boundary of the orbit insertion deviation of the high-precision interferometry constellation in space, so as to provide a reference for the orbit insertion control of the high-precision interferometry constellation in space. The allowable range boundary of the orbit insertion deviation of the high-precision interferometry constellation in space is the allowable domain boundary of the orbit insertion of the high-precision interferometry constellation in space. Summary of the Invention

[0003] The main objective of this invention is to provide a method for predicting the boundary of the orbital allowable region of a high-precision space interferometry constellation. It establishes a reduced-order semi-analytical expression for the propagation of deviations in the configuration stability index of a high-precision space interferometry constellation, and predicts the boundary of the orbital allowable region. This invention has the advantages of high accuracy and fast computation speed in predicting the boundary of the orbital allowable region of a high-precision space interferometry constellation, which is beneficial for improving the configuration stability of high-precision space interferometry constellations and enhancing their observational efficiency.

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

[0005] This invention discloses a method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation. The method sets the orbital insertion time and mission termination time of the high-precision space interferometry constellation, establishes the spacecraft dynamics equations, sets the initial state of the spacecraft, establishes a configuration stability characterization model for the high-precision space interferometry constellation, establishes the mapping relationship between the configuration stability index and the state vector of the spacecraft in the high-precision space interferometry constellation, and sets the number of discrete variables. Based on the set orbital insertion time, mission termination time, initial state of the spacecraft, and established spacecraft dynamics equations, the method calculates the spacecraft state transition tensor and establishes a semi-analytical expression for the propagation of orbital deviations. Based on this semi-analytical expression, a further semi-analytical expression for the propagation of orbital deviations within the high-precision space interferometry constellation is established. Based on analytical expressions and the established mapping relationship between the configuration stability index of the high-precision interferometry constellation and the state vector of the spacecraft in the constellation, a semi-analytical expression for the propagation of the configuration stability index deviation of the high-precision interferometry constellation is established. According to this semi-analytical expression, the characteristic direction of the propagation of the configuration stability index deviation is calculated, and a reduced-order semi-analytical expression is established. Based on this reduced-order semi-analytical expression, and with the set number of discrete elements, the orbit insertion time of the high-precision interferometry constellation, and the mission termination time, the boundary of the allowable orbit insertion domain of the high-precision interferometry constellation is predicted. Based on the predicted boundary of the allowable orbit insertion domain, an orbit insertion control strategy is designed to achieve high-precision orbit insertion, thereby enabling space gravitational wave measurement, observation of Earth-like planets, and high-precision cosmological observation.

[0006] This invention discloses a method for predicting the boundary of the orbital allowable domain of a high-precision space interferometry constellation, comprising the following steps:

[0007] Step 1: Set the orbit insertion time t0 of the high-precision space interferometry constellation, and set the mission termination time t0 of the high-precision space interferometry constellation. fEstablish the dynamic equation f of the spacecraft for the high-precision interferometry constellation, and set the initial state x of the spacecraft for the high-precision interferometry constellation. 1,0 x 2,0 x 3,0 A stability characterization model for the configuration of a high-precision interferometry constellation in space is established, and the mapping relationship between the stability index of the configuration of the high-precision interferometry constellation and the state vector of the spacecraft in the high-precision interferometry constellation in space is established, with a set number of discrete elements N.

[0008] Set the orbit insertion time t0 of the high-precision space interferometry constellation, and set the mission termination time t of the high-precision space interferometry constellation. f The dynamic equations for the spacecraft of the high-precision interferometry constellation are established as follows:

[0009]

[0010] Where t∈[t0,t f [x] represents any time interval. i =[r i ;v i ] represents the state vector of the i-th spacecraft in the high-precision interferometry constellation at time t, where i belongs to {1,2,3}, r i v represents the position vector of the i-th spacecraft in the high-precision interferometry constellation at time t. i Let f represent the velocity vector of the i-th spacecraft in the high-precision interferometry constellation at time t, and let f be the dynamic equation of the spacecraft in the high-precision interferometry constellation.

[0011] The initial state of the first spacecraft in the high-precision interferometry constellation is set as x. 1,0 The initial state of the second spacecraft in the high-precision interferometry constellation is set as x. 2,0 The initial state of the third spacecraft in the high-precision interferometry constellation is set as x. 3,0 .

[0012] A stability characterization model for a high-precision space interferometry constellation configuration is established. This stability includes the arm length l between the i-th and j-th spacecraft in the constellation. ij The breathing angle θ corresponding to the i-th spacecraft in the high-precision interferometry constellation of space i The relative velocity between the i-th and j-th spacecraft in a high-precision interferometry constellation. The stability characterization model for the high-precision space interferometry constellation configuration is as follows:

[0013]

[0014] in

[0015] r ij =r i -r j (3)

[0016] v ij =v i -v j (4)

[0017] Based on equation (2), the mapping relationship between the stability index of the space high-precision interferometry constellation configuration and the state vector of the spacecraft in the space high-precision interferometry constellation is established as follows:

[0018]

[0019] Where z = [l 12 ,l 13 ,l 23 ,θ1,θ2,θ3,l 12 ,l 13 ,l 23 ] T X = [x1; x2; x3] represents the stability index vector of the high-precision interferometry constellation configuration in space, and X = [x1; x2; x3] represents the spacecraft state vector in the high-precision interferometry constellation in space.

[0020] Set the number of discrete numbers N.

[0021] Step Two: Based on the orbit insertion time t0 and mission termination time t0 of the high-precision space interferometry constellation set in Step One... f Initial state of spacecraft in high-precision interferometry constellation x 1,0 x 2,0 x 3,0 In addition to the space high-precision interferometry constellation spacecraft dynamic equation f established in step one, the state transition tensor of the space high-precision interferometry constellation spacecraft is calculated, and a semi-analytical expression for the propagation of orbital deviation of the space high-precision interferometry constellation spacecraft is established.

[0022] Based on the orbit insertion time t0 and mission termination time t0 of the space high-precision interferometry constellation set in step one... f Initial state of spacecraft in high-precision interferometry constellation x 1,0 x 2,0 x 3,0 And based on the space high-precision interferometry constellation spacecraft dynamic equation f established in step one, the state transition tensor of the space high-precision interferometry constellation spacecraft is calculated as follows:

[0023]

[0024]

[0025]

[0026] in This represents the first-order state transition tensor of the spacecraft in the high-precision interferometry constellation. This represents the second-order state transition tensor of spacecraft in a high-precision interferometry constellation. This represents the third-order state transition tensor of a spacecraft in a high-precision interferometry constellation. (Superscript x) i The superscript represents the i-th element of the state vector x. Represents the k-th state vector x0 p Each element.

[0027] First-order state transition tensor of space high-precision interferometry constellation spacecraft Second-order state transition tensor of space high-precision interferometry constellation spacecraft Third-order state transition tensor of space high-precision interferometry constellation spacecraft We obtain the following by integrating the following three expressions:

[0028]

[0029]

[0030]

[0031] in:

[0032]

[0033] The semi-analytical expression for the propagation of orbital deviations of spacecraft in a high-precision space interferometry constellation is established as follows:

[0034]

[0035] Since equations (6)-(13) hold true for all spacecraft in the high-precision interferometry constellation, the subscripts used to distinguish different spacecraft in the high-precision interferometry constellation are removed in equations (6)-(13), and the subscripts are the subscripts i in equation (1).

[0036] Step 3: Based on the semi-analytical expression for the propagation of orbital deviations of spacecraft in the high-precision interferometry constellation established in Step 2, establish a semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation.

[0037] Based on the semi-analytical expression for the propagation of orbital deviations of spacecraft in the high-precision interferometry constellation established in step two, the semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation in space is established as follows:

[0038]

[0039] in δx 1,0 δx represents the initial orbital deviation of the first spacecraft in the high-precision interferometry constellation in space. 2,0 δx represents the initial orbital deviation of the second spacecraft in the high-precision interferometry constellation. 3,0 δX represents the initial orbital deviation of the third spacecraft in the high-precision interferometry constellation. i This represents the i-th element of the deviation vector δX. The k-th term of the deviation vector δX0 p Each element. and The expression is as follows:

[0040]

[0041]

[0042] The superscripts 1, 2, and 3 represent the state transition tensors of the first, second, and third spacecraft of the high-precision interferometry constellation, respectively, with Δ′ = Δ-6 and Δ″ = Δ-12.

[0043] Step 4: Based on the semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation established in Step 3, and the mapping relationship between the configuration stability index of the high-precision interferometry constellation and the spacecraft state vector in the high-precision interferometry constellation established in Step 1, establish a semi-analytical expression for the propagation of deviations in the configuration stability index of the high-precision interferometry constellation.

[0044] Based on the semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation established in step three, and the mapping relationship between the configuration stability index of the high-precision interferometry constellation and the spacecraft state vectors in the high-precision interferometry constellation established in step one, the semi-analytical expression for the propagation of deviations in the configuration stability index of the high-precision interferometry constellation is established as follows:

[0045]

[0046] in:

[0047]

[0048]

[0049]

[0050] in:

[0051]

[0052]

[0053]

[0054] Step 5: Based on the semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation established in Step 4, calculate the characteristic direction of the propagation of the stability index deviation of the space high-precision interferometry constellation, and establish a reduced-order semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation based on the characteristic direction of the propagation of the stability index deviation of the space high-precision interferometry constellation.

[0055] Based on the semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation established in step four, the characteristic direction of the propagation of the stability index deviation of the space high-precision interferometry constellation is calculated. First, based on the semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation established in step four, the first-order matrix is ​​obtained as follows:

[0056]

[0057] Here, A is a first-order matrix. The Cauchy-Green matrix is ​​then constructed as follows:

[0058] CGT=A T A(25)

[0059] Where CGT is the Cauchy-Green matrix. The eigenvalues ​​and eigendirections of the Cauchy-Green matrix are calculated, and the eigendirection corresponding to the largest eigenvalue is denoted as R. This eigendirection R is the eigendirection of the deviation propagation in the stability index of the high-precision interferometry constellation configuration.

[0060] Based on the characteristic direction of the propagation of the stability index deviation of the high-precision space interferometry constellation configuration, a reduced-order semi-analytical expression for the propagation of the stability index deviation of the high-precision space interferometry constellation configuration is established as follows:

[0061]

[0062] in The expression is:

[0063]

[0064]

[0065]

[0066] Step Six: Based on the reduced-order semi-analytical expression for the propagation of the stability index deviation of the high-precision interferometry constellation configuration established in Step Five, and the discrete number N, the orbit insertion time t0 of the high-precision interferometry constellation, and the mission termination time t0 of the high-precision interferometry constellation set in Step One, f Predict the boundary of the orbital allowable domain for high-precision interferometry constellations in space.

[0067] Based on the discrete number N, the orbit insertion time t0 of the high-precision interferometry constellation, and the mission completion time of the high-precision interferometry constellation set in step one, the discrete time sequence is obtained as follows:

[0068]

[0069] For each discrete moment, the following cubic inequality is solved based on the reduced-order semi-analytical expression for the propagation of the deviation index of the spatial high-precision interferometric constellation configuration established in step five:

[0070]

[0071] in Indicates the nominal configuration at time t k The deviation of the i-th configuration stability index from the desired configuration stability index Let represent the maximum permissible deviation of the i-th configuration stability index. By merging the solutions at all discrete times, we obtain the following permissible domain with respect to δY0:

[0072]

[0073] The This refers to the predicted boundary of the orbital allowable domain for the high-precision interferometry constellation in space.

[0074] It also includes step seven, which involves constructing a high-precision interferometry constellation orbit insertion control strategy based on the predicted orbit insertion allowable domain boundary of the high-precision interferometry constellation, thereby achieving high-precision orbit insertion of the high-precision interferometry constellation, improving the configuration stability of the high-precision interferometry constellation, and enhancing the observation efficiency of the high-precision interferometry constellation.

[0075] Beneficial effects:

[0076] 1. This invention discloses a method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation. The method sets the orbital insertion time and mission termination time of the high-precision space interferometry constellation, establishes the spacecraft dynamics equations, sets the initial state of the spacecraft, establishes a configuration stability characterization model for the high-precision space interferometry constellation, establishes the mapping relationship between the configuration stability index and the state vector of the spacecraft in the high-precision space interferometry constellation, and sets the number of discrete variables. Based on the set orbital insertion time, mission termination time, initial state of the spacecraft, and established spacecraft dynamics equations, the method calculates the spacecraft state transition tensor and establishes a semi-analytical expression for the propagation of orbital deviations. Based on this semi-analytical expression, a semi-analytical expression for the propagation of orbital deviations in the high-precision space interferometry constellation is established. Based on the semi-analytical expression and the established mapping relationship between the configuration stability index of the high-precision interferometry constellation and the state vector of the spacecraft in the constellation, a semi-analytical expression for the propagation of the configuration stability index deviation of the high-precision interferometry constellation is established. According to this semi-analytical expression, the characteristic direction of the propagation of the configuration stability index deviation is calculated, and a reduced-order semi-analytical expression for the propagation of the configuration stability index deviation is established. Based on this reduced-order semi-analytical expression, and with the set number of discrete elements, the orbit insertion time of the high-precision interferometry constellation, and the mission termination time, the boundary of the allowable orbit insertion domain of the high-precision interferometry constellation is predicted. Based on the predicted boundary of the allowable orbit insertion domain, an orbit insertion control strategy is designed to achieve high-precision orbit insertion of the high-precision interferometry constellation, thereby enabling space gravitational wave measurements, observation of Earth-like planets, and high-precision cosmological observations.

[0077] 2. The present invention discloses a method for predicting the boundary of the orbital allowable domain of a high-precision space interferometry constellation. By establishing a third-order semi-analytical expression for the propagation of the configuration stability index deviation of a high-precision space interferometry constellation, the calculation accuracy of the propagation of the configuration stability index deviation of a high-precision space interferometry constellation is greatly improved, which in turn helps to improve the calculation accuracy of the prediction of the boundary of the orbital allowable domain of a high-precision space interferometry constellation.

[0078] 3. The present invention discloses a method for predicting the boundary of the orbital allowable domain of a high-precision space interferometric constellation. By establishing a reduced-order semi-analytical expression for the propagation of the configuration stability index deviation of a high-precision space interferometric constellation, the computational load of the propagation of the configuration stability index deviation of a high-precision space interferometric constellation is significantly reduced, which is beneficial to improving the computational speed of predicting the boundary of the orbital allowable domain of a high-precision space interferometric constellation.

[0079] 4. The method for predicting the boundary of the orbital allowable region of a high-precision space interferometry constellation disclosed in this invention, while achieving the above three beneficial effects, has the advantages of high accuracy and fast calculation speed in predicting the boundary of the orbital allowable region of a high-precision space interferometry constellation. This is beneficial for improving the configuration stability of high-precision space interferometry constellations and enhancing their observation efficiency. Attached Figure Description

[0080] Figure 1 This is a flowchart of a method for predicting the boundary of the orbital allowable domain of a high-precision space interferometry constellation, as disclosed in this invention. Detailed Implementation

[0081] 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.

[0082] This example uses the problem of predicting the boundary of the orbital allowable region of a heliocentric high-precision interferometric constellation as an example, and uses the method proposed in this invention to predict the boundary of the orbital allowable region of a high-precision interferometric constellation.

[0083] like Figure 1 As shown in the figure, this example discloses a method for predicting the boundary of the orbital allowable domain of a high-precision space interferometry constellation. The specific implementation steps are as follows:

[0084] Step 1: Set the orbit insertion time t0 of the high-precision space interferometry constellation, and set the mission termination time t0 of the high-precision space interferometry constellation. f Establish the dynamic equation f of the spacecraft for the high-precision interferometry constellation, and set the initial state x of the spacecraft for the high-precision interferometry constellation. 1,0 x 2,0 x 3,0 A stability characterization model for the configuration of a high-precision interferometry constellation in space is established, and the mapping relationship between the stability index of the configuration of the high-precision interferometry constellation and the state vector of the spacecraft in the high-precision interferometry constellation in space is established, with a set number of discrete elements N.

[0085] The launch time t0 of the high-precision space interferometry constellation is set to January 1, 2015, and the mission end time t0 of the high-precision space interferometry constellation is set to... fThe dynamic equations for the spacecraft of the high-precision interferometry constellation are established as follows, with a target date of December 31, 2025:

[0086]

[0087] Where μ e μ represents the Earth's gravitational constant. s The gravitational constant of the Sun, r e This represents the Earth's position vector in a heliocentric inertial frame.

[0088] The initial state of the first spacecraft in the high-precision interferometry constellation is set as x. 1,0 The initial state of the second spacecraft in the high-precision interferometry constellation is set as x. 2,0 The initial state of the third spacecraft in the high-precision interferometry constellation is set as x. 3,0 The corresponding initial states are shown in Table 1.

[0089] Table 1 Initial state of spacecraft in the high-precision interferometry constellation

[0090]

[0091] Set the number of discrete numbers N = 366.

[0092] Step Two: Based on the orbit insertion time t0 and mission termination time t0 of the high-precision space interferometry constellation set in Step One... f Initial state of spacecraft in high-precision interferometry constellation x 1,0 x 2,0 x 3,0 In addition to the space high-precision interferometry constellation spacecraft dynamic equation f established in step one, the state transition tensor of the space high-precision interferometry constellation spacecraft is calculated, and a semi-analytical expression for the propagation of orbital deviation of the space high-precision interferometry constellation spacecraft is established.

[0093] Step 3: Based on the semi-analytical expression for the propagation of orbital deviations of spacecraft in the high-precision interferometry constellation established in Step 2, establish a semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation.

[0094] Step 4: Based on the semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation established in Step 3, and the mapping relationship between the configuration stability index of the high-precision interferometry constellation and the spacecraft state vector in the high-precision interferometry constellation established in Step 1, establish a semi-analytical expression for the propagation of deviations in the configuration stability index of the high-precision interferometry constellation.

[0095] Step 5: Based on the semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation established in Step 4, calculate the characteristic direction of the propagation of the stability index deviation of the space high-precision interferometry constellation, and establish a reduced-order semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation based on the characteristic direction of the propagation of the stability index deviation of the space high-precision interferometry constellation.

[0096] Step Six: Based on the reduced-order semi-analytical expression for the propagation of the stability index deviation of the high-precision interferometry constellation configuration established in Step Five, and the discrete number N, the orbit insertion time t0 of the high-precision interferometry constellation, and the mission termination time t0 of the high-precision interferometry constellation set in Step One, f The boundary of the orbital insertion allowable domain of a high-precision interferometry constellation in space was predicted. The calculated boundary of the orbital insertion allowable domain was 0.00073848. The calculation took only 1 second.

[0097] Step 7: Based on the predicted orbital insertion allowable domain boundary of the high-precision space interferometry constellation, construct the orbital insertion control strategy of the high-precision space interferometry constellation to achieve high-precision orbital insertion, improve the configuration stability of the high-precision space interferometry constellation, and improve the observation efficiency of the high-precision space interferometry constellation by at least 30%.

[0098] 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 predicting the boundary of the orbital allowable domain of a high-precision space interferometry constellation, characterized in that: Includes the following steps, Step 1: Set the orbit insertion time t0 of the high-precision space interferometry constellation, and set the mission termination time t0 of the high-precision space interferometry constellation. f Establish the dynamic equation f of the spacecraft for the high-precision interferometry constellation, and set the initial state x of the spacecraft for the high-precision interferometry constellation. 1,0 x 2,0 x 3,0 Establish a stability characterization model for the configuration of a high-precision interferometry constellation in space, establish the mapping relationship between the stability index of the high-precision interferometry constellation configuration and the state vector of the spacecraft in the high-precision interferometry constellation in space, and set the number of discrete elements N; Step Two: Based on the orbit insertion time t0 and mission termination time t0 of the high-precision space interferometry constellation set in Step One... f Initial state of spacecraft in high-precision interferometry constellation x 1,0 x 2,0 x 3,0 And the space high-precision interferometry constellation spacecraft dynamic equation f established in step one, calculate the space high-precision interferometry constellation spacecraft state transition tensor, and establish a semi-analytical expression for the propagation of the space high-precision interferometry constellation spacecraft orbital deviation; Step 3: Based on the semi-analytical expression for the propagation of orbital deviations of spacecraft in the high-precision interferometry constellation established in Step 2, establish a semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation. Step 4: Based on the semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation established in Step 3, and the mapping relationship between the configuration stability index of the high-precision interferometry constellation and the spacecraft state vector in the high-precision interferometry constellation established in Step 1, establish a semi-analytical expression for the propagation of deviations in the configuration stability index of the high-precision interferometry constellation. Step 5: Based on the semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation established in Step 4, calculate the characteristic direction of the propagation of the stability index deviation of the space high-precision interferometry constellation, and establish a reduced-order semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation based on the characteristic direction of the propagation of the stability index deviation of the space high-precision interferometry constellation. Step Six: Based on the reduced-order semi-analytical expression for the propagation of the stability index deviation of the high-precision interferometry constellation configuration established in Step Five, and the discrete number N, the orbit insertion time t0 of the high-precision interferometry constellation, and the mission termination time t0 of the high-precision interferometry constellation set in Step One, f Predict the boundary of the orbital allowable domain for high-precision interferometry constellations in space.

2. The method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation as described in claim 1, characterized in that: It also includes step seven, which involves constructing a high-precision interferometry constellation orbit insertion control strategy based on the predicted orbit insertion allowable domain boundary of the high-precision interferometry constellation, thereby achieving high-precision orbit insertion of the high-precision interferometry constellation, improving the configuration stability of the high-precision interferometry constellation, and enhancing the observation efficiency of the high-precision interferometry constellation.

3. A method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation as described in claim 1 or 2, characterized in that: The implementation method for step one is as follows: Set the orbit insertion time t0 of the high-precision space interferometry constellation, and set the mission termination time t of the high-precision space interferometry constellation. f The dynamic equations for the spacecraft of the high-precision interferometry constellation are established as follows: Where t∈[t0,t f [x] represents any time interval. i =[r i ;v i ] represents the state vector of the i-th spacecraft in the high-precision interferometry constellation at time t, where i belongs to {1,2,3}, r i v represents the position vector of the i-th spacecraft in the high-precision interferometry constellation at time t. i Let f represent the velocity vector of the i-th spacecraft in the high-precision interferometry constellation at time t, and let f be the dynamic equation of the spacecraft in the high-precision interferometry constellation. The initial state of the first spacecraft in the high-precision interferometry constellation is set as x. 1,0 The initial state of the second spacecraft in the high-precision interferometry constellation is set as x. 2,0 The initial state of the third spacecraft in the high-precision interferometry constellation is set as x. 3,0 ; A stability characterization model for a high-precision space interferometry constellation configuration is established. This stability includes the arm length l between the i-th and j-th spacecraft in the constellation. ij The breathing angle θ corresponding to the i-th spacecraft in the high-precision interferometry constellation of space i The relative velocity between the i-th and j-th spacecraft in a high-precision interferometry constellation. The stability characterization model for the high-precision space interferometry constellation configuration is as follows: in r ij ＝r i -r j (3) v ij =v i -v j (4) Based on equation (2), the mapping relationship between the stability index of the space high-precision interferometry constellation configuration and the state vector of the spacecraft in the space high-precision interferometry constellation is established as follows: in X = [x1; x2; x3] represents the stability index vector of the high-precision interferometry constellation configuration in space, and X = [x1; x2; x3] represents the spacecraft state vector in the high-precision interferometry constellation in space. Set the number of discrete numbers N.

4. The method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation as described in claim 3, characterized in that: The second step is implemented as follows: Based on the orbit insertion time t0 and mission termination time t0 of the space high-precision interferometry constellation set in step one... f Initial state of spacecraft in high-precision interferometry constellation x 1,0 x 2,0 x 3,0 And based on the space high-precision interferometry constellation spacecraft dynamic equation f established in step one, the state transition tensor of the space high-precision interferometry constellation spacecraft is calculated as follows: in This represents the first-order state transition tensor of the spacecraft in the high-precision interferometry constellation. This represents the second-order state transition tensor of spacecraft in a high-precision interferometry constellation. This represents the third-order state transition tensor of a spacecraft in a high-precision interferometry constellation; the superscript x i The superscript represents the i-th element of the state vector x. Represents the k-th state vector x0 p One element; First-order state transition tensor of space high-precision interferometry constellation spacecraft Second-order state transition tensor of space high-precision interferometry constellation spacecraft Third-order state transition tensor of space high-precision interferometry constellation spacecraft We obtain the following by integrating the following three expressions: in: The semi-analytical expression for the propagation of orbital deviations of spacecraft in a high-precision space interferometry constellation is established as follows: Since equations (6)-(13) hold true for all spacecraft in the high-precision interferometry constellation, the subscripts used to distinguish different spacecraft in the high-precision interferometry constellation are removed in equations (6)-(13).

5. The method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation as described in claim 4, characterized in that: The method for implementing step three is as follows: Based on the semi-analytical expression for the propagation of orbital deviations of spacecraft in the high-precision interferometry constellation established in step two, the semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation in space is established as follows: in δx 1,0 δx represents the initial orbital deviation of the first spacecraft in the high-precision interferometry constellation in space. 2,0 δx represents the initial orbital deviation of the second spacecraft in the high-precision interferometry constellation. 30 δX represents the initial orbital deviation of the third spacecraft in the high-precision interferometry constellation. i This represents the i-th element of the deviation vector δX. The k-th term of the deviation vector δX0 p One element; and The expression is as follows: The superscripts 1, 2, and 3 represent the state transition tensors of the first, second, and third spacecraft of the high-precision interferometry constellation, respectively, with Δ′ = Δ-6 and Δ″ = Δ-12.

6. The method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation as described in claim 5, characterized in that: Step four is implemented as follows: Based on the semi-analytical expression for the propagation of orbital deviations of the high-precision interferometry constellation established in step three, and the mapping relationship between the configuration stability index of the high-precision interferometry constellation and the spacecraft state vectors in the high-precision interferometry constellation established in step one, the semi-analytical expression for the propagation of deviations in the configuration stability index of the high-precision interferometry constellation is established as follows: in: in:

7. The method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation as described in claim 6, characterized in that: Step five is implemented as follows: Based on the semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation established in step four, the characteristic direction of the propagation of the stability index deviation of the space high-precision interferometry constellation is calculated. First, based on the semi-analytical expression for the propagation of the stability index deviation of the space high-precision interferometry constellation established in step four, the first-order matrix is ​​obtained as follows: Where A is a first-order matrix; the Cauchy-Green matrix is ​​then constructed as follows: CGT=A T A (25) Where CGT is the Cauchy-Green matrix; calculate the eigenvalues ​​and eigendirections of the Cauchy-Green matrix, where the eigendirection corresponding to the largest eigenvalue is denoted as R, and the eigendirection R corresponding to the largest eigenvalue is the eigendirection of the deviation propagation of the stability index of the spatial high-precision interferometry constellation configuration. Based on the characteristic direction of the propagation of the stability index deviation of the high-precision space interferometry constellation configuration, a reduced-order semi-analytical expression for the propagation of the stability index deviation of the high-precision space interferometry constellation configuration is established as follows: in The expression is:

8. The method for predicting the boundary of the orbital insertion allowable domain of a high-precision space interferometry constellation as described in claim 7, characterized in that: Step six is ​​implemented as follows: Based on the discrete number N, the orbit insertion time t0 of the high-precision interferometry constellation, and the mission completion time of the high-precision interferometry constellation set in step one, the discrete time sequence is obtained as follows: For each discrete moment, the following cubic inequality is solved based on the reduced-order semi-analytical expression for the propagation of the deviation index of the spatial high-precision interferometric constellation configuration established in step five: in Indicates the nominal configuration at time t k The deviation of the i-th configuration stability index from the desired configuration stability index Let represent the maximum permissible deviation of the i-th configuration stability index; by merging the solutions at all discrete times, we obtain the following permissible domain with respect to δY0: The This refers to the predicted boundary of the orbital allowable domain for the high-precision interferometry constellation in space.

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