A method and system for enhanced detection of platoon offset frequency planning for a phase-locked topology

Abstract

This application provides a method and system for frequency offset planning of a detection formation with enhanced phase-locked topology. The detection formation includes three satellites arranged in a triangular array: Satellite 1, Satellite 2, and Satellite 3. Each satellite is equipped with two optical platforms, and each optical platform has a laser. The phase-locked topology selects one laser as the master laser and the others as slave lasers. The method includes: acquiring orbital information of a space-based gravitational wave detector, calculating time-varying inter-satellite Doppler frequency shift data, establishing an enhanced phase-locked topology structure and a general representation model, and using the Attempt-Update optimization method to achieve frequency offset planning within an N-year period. The advantages of this application are: expanding the feasible phase-locked topologies to 144 types; and improving the efficiency of phase-locked topology selection and calculation during the optimization process.

Description

Technical Field

[0001] This application belongs to the field of aerospace, and specifically relates to a detection formation offset frequency planning method and system for enhancing phase-locked loop topology. Background Technology

[0002] Gravitational wave detection is one of the new windows for observing the universe. To detect gravitational waves in the [0.1 mHz, 1 Hz] frequency band, space missions such as LISA, Taiji, and Tianqin employ an equilateral triangle formation of three spacecraft, measuring the arm length changes through laser interferometry. Since the relative motion between spacecraft generates a Doppler frequency shift, affecting the measurement of the interferometric signal, phase-locked loop (PLL) technology is typically used: one laser beam is used as a reference, and the other lasers are phase-locked with it through a PLL, with an offset frequency inserted during this process to compensate for the Doppler effect, thus ensuring continuous measurability of the signal. Therefore, setting a reasonable and stable offset frequency for interferometry has become a key research focus. Existing research has proposed various PLL topologies for current space-based gravitational wave detection missions and constructed corresponding algorithms to solve for the offset frequency between lasers. Currently, under the constraint of a detection bandwidth of [5, 25 MHz], the Taiji mission, based on an arm length of 3 million kilometers, can achieve a stable offset frequency for a maximum of 5 years. In the actual operation of space-based gravitational wave detection missions, the offset frequency is required to remain unchanged for at least 10 years. To address this requirement, existing phase-locked loop (PLL) topologies and corresponding offset frequency calculation methods cannot provide a stable offset frequency configuration over a decade. To ensure continuous and uninterrupted interferometry for the Taiji mission, it is essential to develop new PLL topologies, offset frequency calculation methods, and systems. Summary of the Invention

[0003] The purpose of this application is to overcome the shortcomings of existing technologies in achieving a stable offset frequency for the required duration.

[0004] To achieve the above objectives, this application proposes a detection formation offset frequency planning method for enhanced phase-locked topology. The detection formation includes three satellites in a triangular array: satellite 1, satellite 2, and satellite 3. Each satellite is equipped with two optical platforms, and each optical platform has a laser. In phase-locked topology, one laser is selected as the master laser, and the other lasers are used as slave lasers. The method includes: The orbital information of the space-based gravitational wave detector is obtained, the time-varying inter-satellite Doppler frequency shift data is calculated, an enhanced phase-locked topology and a general representation model are established, and the offset frequency planning within an N-year period is realized using the Attempt-Update optimization method.

[0005] As an improvement to the above method, the orbital information of the space-based gravitational wave detector is the orbital position and velocity information of the space-based gravitational wave detector within an N-year period.

[0006] As an improvement to the above method, the calculation of time-varying inter-satellite Doppler frequency shift data involves using orbital information to calculate the relative motion information between satellites, and then converting the relative motion information into inter-satellite Doppler frequency shift data. ; in, v 12 , v 13 , v 23 These represent the relative velocities between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3, respectively. f d12 , f d13 , f d23 The Doppler frequency shifts between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3 are shown respectively. c Represents the speed of light. f 0 Indicates the laser frequency.

[0007] As an improvement to the above method, the enhanced phase-locked loop (PLL) topology and general representation model include 144 enhanced PLL topologies and a general representation model for beat frequency; wherein, the 144 enhanced PLL topologies include: Phase-locked loop (PLL) topologies include four types: non-switched PLL topology, switched PLL topology, enhanced non-switched PLL topology, and enhanced switched PLL topology. The lasers are numbered from 1 to 6 in clockwise order of their spatial location, resulting in a total of 6 non-switched phase-locked loop topologies, 6 switched phase-locked loop topologies, 6 enhanced non-switched phase-locked loop topologies, and 6 enhanced switched phase-locked loop topologies. Set the main laser number to 1; The six non-switching phase-locked loop topologies are: Topology A1: [2->1, 6->5, 5->4, 4->3, 3->2]; Topology A2: [2->1, 6->1, 5->4, 4->3, 3->2]; Topology A3: [2->1, 6->1, 5->6, 4->3, 3->2]; Topology A4: [2->1, 6->1, 5->6, 4->5, 3->2]; Topology A5: [2->1, 6->1, 5->6, 4->5, 3->4]; Topology A6: [2->3, 6->1, 5->6, 4->5, 3->4]; Where 2->1 indicates that laser 2 is phase-locked to laser 1; The six types of switch-locked loop topologies are: Topology B1: [2->1, 4->1, 3->4, 6->3, 5->6]; Topology B2: [5->2, 2->1, 4->1, 3->4, 6->3]; Topology B3: [6->5, 5->2, 2->1, 4->1, 3->4]; Topology B4: [3->6, 6->5, 5->2, 2->1, 4->1]; Topology B5: [4->3, 3->6, 6->5, 5->2, 2->1]; Topology B6: [2->5, 4->1, 3->4, 6->3, 5->6]; Compared to the non-switched phase-locked loop topology, the enhanced non-switched phase-locked loop topology, and the enhanced switched phase-locked loop topology, both involve adding an acousto-optic frequency shifter during laser beam emission in the inter-satellite phase-locking process to achieve fixed frequency shifting of the emitted beam. The six enhanced non-switching phase-locked loop topologies are: Topology C1: [2->1, 6->5, 5->5*, 5*->4, 4->3, 3->3*, 3*->2]; Topology C2: [2->1, 6->6*, 6*->1, 5->5*, 5*->4, 4->3, 3->3*, 3*->2]; Topology C3: [2->1, 6->6*, 6*->1, 5->6, 4->3, 3->3*, 3*->2]; Topology C4: [2->1, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->3*, 3*->2]; Topology C5: [2->1, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->4]; Topology C6: [2->2*, 2*->3, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->4]; Wherein, 5* represents the frequency shift when laser 5 is emitted from the optical platform of the satellite; The six enhanced switching phase-locked loop topologies are: Topology 1: [2->1, 4->4*, 4*->1, 3->4, 6->6*, 6*->3, 5->6]; Topology 2: [5->5*, 5*->2, 2->1, 4->4*, 4*->1, 3->4, 6->6*, 6*->3]; Topology 3: [6->5, 5->5*, 5*->2, 2->1, 4->4*, 4*->1, 3->4]; Topology 4: [3->3*, 3*->6, 6->5, 5->5*, 5*->2, 2->1, 4->4*, 4*->1]; Topology 5: [4->3, 3->3*, 3*->6, 6->5, 5->5*, 5*->2, 2->1]; Topology 6: [2->2*, 2*->5, 4->4*, 4*->1, 3->4, 6->6*, 6*->3, 5->6]; By selecting different lasers as the master laser, a total of 144 phase-locked loop topologies were formed.

[0008] As an improvement to the above method, the general expression model for the beat frequency is as follows: ; in, B 11 , B 22 and B 33 These represent the beat frequencies between lasers from different optical platforms on the same satellite. B 12 , B 13 , B 21 , B 23 , B 31 , B 32 These represent the beat frequencies between the lasers of the optical platforms of different satellites represented by the subscripts; D 12 , D 13 and D 23 These represent the Doppler frequencies between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3, respectively. Δf 11 , Δf 22 , Δ f 33 These represent the offset frequencies introduced during the laser phase-locked loop process within the same satellite; Δf 12 ,Δf 13 , Δf 23 These represent the offset frequencies introduced between the satellites represented by the subscripts during the laser phase-locking process, respectively. Δf 12β , Δf 13β , Δf 23β These represent the offset frequencies introduced between the satellites represented by the subscripts during the laser phase-locking process, where the subscripts contain... β The satellite number indicates that when the laser is emitted from the optical platform of that satellite, an offset frequency is added through an acousto-optic frequency shifter; This represents the beat frequency signal coefficient matrix.

[0009] As an improvement to the above method, the beat frequency signal coefficient matrix for: ; in, x 11 ~ x 99 , β 12 , β 13 , β 21 , β 23 , β 31 and β 32 These represent the coefficient settings after selecting a specific phase-locked topology; where, x 11 ~ x 99 Depending on the selected phase-locked topology, the value range is [-2, -1, 0, 1, 2]; β 12 , β 13 , β 21 , β 23 , β 31 and β 32 Depending on the selected phase-locked topology, the value range is [0,1].

[0010] As an improvement to the above method, the The methods for setting the coefficients in a matrix include: Step 1: Select the desired phase-locked topology type; Step 2: Obtain the frequencies of the 5 slave lasers and 1 master laser; Step 3: In each phase-locked topology, each laser has only two phase-locked sequences, namely, locked to a laser on another optical platform of the same satellite or locked to a laser on a certain optical platform of another satellite; When from laser x and laser y Located on the same satellite i The corresponding beat frequency The calculation formula is as follows: ; After phase locking, from the laser x The frequency is f y + f ii , f y For laser y The frequency; When from laser x and laser y Located in satellite i and j The corresponding beat frequency and The calculation formula is as follows: ; If an enhanced phase-locked loop topology is used, then M is 1; otherwise, M is 0. After phase locking, from the laser x The frequency is f y + D ij + f ij ; After obtaining the calculation formula for each beat frequency, extract its coefficients and fill them in sequentially. In the matrix.

[0011] As an improvement to the above method, the Attempt-Update optimization method includes an Attempt phase and an Update phase, and execution begins first in the Attempt phase, wherein: The Attempt phase includes: Step A1: Set the task start time t_start = 1, Task end time t_end = 1, the unit is days; Step A2: Select either a switched phase-locked loop (PLL) topology or a non-switched PLL topology, according to the current... t_start andt_end Using the general expression model of beat frequency, beat frequency constraints are set, and a set of constraint equations is established; Step A3: If the constraint boundary check passes, proceed to step A4; otherwise, proceed to the Update phase. Step A4: Solve the constraint equations established in step A2 using a genetic algorithm or a linear programming algorithm; Step A5: If the optimal solution is found, proceed to step A6; otherwise, proceed to the Update stage. Step A6: If t_end =If the satellite mission lifespan is determined, proceed to step A8; otherwise, proceed to step A7. Step A7: Settings t_end Add 1 day and proceed to step A2; Step A8: Optimization terminated; Update phase: Step B1: Select the enhanced phase-locked topology corresponding to the phase-locked topology selected in the Attempt stage, and based on this topology, according to the current... [[ID= and ​ Using the general representation model of beat frequency, beat frequency constraints are set, and a set of constraint equations is established. Step B2: Solve the constraint equations established in Step B1 using a genetic algorithm or a linear programming algorithm; Step B3: If the optimal solution is found, proceed to step B4; otherwise, proceed to step B5. Step B4: If ​ = Satellite mission lifespan, proceed to step B6, otherwise set ​ Add 1 day and proceed to step B2; Step B5: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] ​ Set to with ​ If the values ​​are the same, set ​ Add 1 day and proceed to step 2; Step B6: Optimization terminated.

[0012] As an improvement to the above method, the constraint boundary check includes: Setting all offset frequencies to 0, and substituting all inter-satellite Doppler frequency shift data under the current conditions into the general representation model of beat frequency, the extreme values ​​of each beat frequency are calculated, and it is determined whether the extreme values ​​exceed the boundary of the constraint conditions. The formula is as follows: ; in, and These represent the upper and lower limits of the beat frequency, respectively; To determine the duration of a single offset frequency, the optimization objective is to maximize... ; Indicates duration T At that time, satellite i Accepted satellites j The beat frequency of the interference signal obtained by interfering the emitted laser with the local laser.

[0013] This application also provides a detection formation offset frequency planning system for enhanced phase-locked loop topology, implemented based on the above method, the system comprising: The data acquisition module is used to acquire orbital information of the space-based gravitational wave detector; The frequency shift calculation module is used to calculate time-varying inter-satellite Doppler frequency shift data; The modeling module is used to build enhanced phase-locked topologies and general representation models; The frequency planning module is used to implement offset frequency planning over an N-year period using the Attempt-Update optimization method.

[0014] Compared with existing technologies, the advantages of this application are: 1. Exchanged phase-locked loop (PLL) topology and non-exchanged PLL topology were proposed, and enhanced exchanged PLL topology and enhanced non-exchanged PLL topology were obtained based on these, expanding the number of feasible PLL topologies to 144.

[0015] 2. A general beat frequency representation model was established to improve the efficiency of phase-locked loop topology selection and calculation during the optimization process.

[0016] 3. An Attempt-Update two-stage optimization algorithm is adopted. During the solution process, non-enhanced phase-locked loop (PLL) topologies are prioritized to reduce the complexity of setting the offset frequency in the detector formation. When the selected non-enhanced PLL topology cannot meet the constraints, its corresponding enhanced PLL topology is selected to obtain a feasible offset frequency. Attached Figure Description

[0017] ​ The diagram shows six non-switched phase-locked loop topologies when laser 1 is set as the main laser. ​ The diagram shows six different phase-locked loop topologies when laser 1 is set as the main laser. ​ The flowchart shown is for the detection formation offset frequency planning method of enhanced phase-locked loop topology; ​ The result shown is the beat frequency solution for Example 1. Detailed Implementation

[0018] The technical solution of this application will be described in detail below with reference to the accompanying drawings.

[0019] This invention proposes a detection formation offset frequency planning method for enhanced phase-locked loop topology, comprising: To acquire orbital information of a space-based gravitational wave detector, calculate time-varying inter-satellite Doppler frequency shift data, establish an enhanced phase-locked topology and a general representation model, and establish an Attempt-Update optimization method to achieve the goal of changing the offset frequency within a 10-year cycle; Among them, the orbital information of the space-based gravitational wave detector is the orbital position and velocity information of the space-based gravitational wave detector (such as the Taiji constellation) within a 10-year cycle, which is used as input; Inter-satellite Doppler shift calculation involves using orbital information to calculate the relative motion information between satellites, and then converting the relative motion information into inter-satellite Doppler shift data. The enhanced phase-locked topology and general representation model represent 144 enhanced phase-locked topologies built upon the existing 36 traditional phase-locked topologies across the entire probe constellation, as well as a general representation model for beat frequency.

[0020] The three-satellite constellation for space-based gravitational wave detection comprises three satellites, each equipped with two optical platforms. Each platform contains a laser, numbered from 1 to 6 in clockwise order of their spatial location: Laser 1, Laser 2, Laser 3, Laser 4, Laser 5, and Laser 6. Lasers 1 and 2 are located on Satellite 1, Lasers 3 and 4 on Satellite 2, and Lasers 5 and 6 on Satellite 3. Phase-locked loop (PLL) topology selects one laser as the master laser, with the others serving as slave lasers. There are four core PLL topologies: non-switched PLL, switched PLL, enhanced non-switched PLL, and enhanced switched PLL.

[0021] Non-commutative phase-locked loop topology: With laser 1 as the master laser, there are 6 possible phase-locked loop topologies. They are represented as follows: Topology 1: [2->1, 6->5, 5->4, 4->3, 3->2]; Topology 2: [2->1, 6->1, 5->4, 4->3, 3->2]; Topology 3: [2->1, 6->1, 5->6, 4->3, 3->2]; Topology 4: [2->1, 6->1, 5->6, 4->5, 3->2]; Topology 5: [2->1, 6->1, 5->6, 4->5, 3->4]; Topology 6: [2->3, 6->1, 5->6, 4->5, 3->4].

[0022] Where 2->1 indicates that laser 2 is phase-locked to laser 1, and so on. Setting laser 1 as the master laser, the six phase-locked topologies are as follows: ​ As shown.

[0023] Switched Phase-Locked Topology: With laser 1 as the master laser, there are 6 possible switched phase-locked topologies. They are represented as follows: Topology 1: [2->1, 4->1, 3->4, 6->3, 5->6]; Topology 2: [5->2, 2->1, 4->1, 3->4, 6->3]; Topology 3: [6->5, 5->2, 2->1, 4->1, 3->4]; Topology 4: [3->6, 6->5, 5->2, 2->1, 4->1]; Topology 5: [4->3, 3->6, 6->5, 5->2, 2->1]; Topology 6: [2->5, 4->1, 3->4, 6->3, 5->6].

[0024] Six types of phase-locked topologies, such as ​ As shown.

[0025] Compared to the non-switched phase-locked loop (PLL) topology, the enhanced non-switched PLL topology adds an acousto-optic frequency shifter during inter-satellite phase-locking to achieve a fixed frequency shift of the emitted laser beam. For example, when laser 6 is emitted from the satellite's optical platform, it is first frequency-shifted to 6*, and then phase-locked to laser 1. Therefore, the enhanced non-switched PLL topology introduces an additional offset frequency during inter-satellite laser transmission.

[0026] Using laser 1 as the master laser, the enhanced non-switched phase-locked loop topology is shown below: Topology 1: [2->1, 6->5, 5->5*, 5*->4, 4->3, 3->3*, 3*->2]; Topology 2: [2->1, 6->6*, 6*->1, 5->5*, 5*->4, 4->3, 3->3*, 3*->2]; Topology 3: [2->1, 6->6*, 6*->1, 5->6, 4->3, 3->3*, 3*->2]; Topology 4: [2->1, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->3*, 3*->2]; Topology 5: [2->1, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->4]; Topology 6: [2->2*, 2*->3, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->4].

[0027] Using laser 1 as the main laser, the enhanced switching phase-locked loop topology is shown below: Topology 1: [2->1, 4->4*, 4*->1, 3->4, 6->6*, 6*->3, 5->6]; Topology 2: [5->5*, 5*->2, 2->1, 4->4*, 4*->1, 3->4, 6->6*, 6*->3]; Topology 3: [6->5, 5->5*, 5*->2, 2->1, 4->4*, 4*->1, 3->4]; Topology 4: [3->3*, 3*->6, 6->5, 5->5*, 5*->2, 2->1, 4->4*, 4*->1]; Topology 5: [4->3, 3->3*, 3*->6, 6->5, 5->5*, 5*->2, 2->1]; Topology 6: [2->2*, 2*->5, 4->4*, 4*->1, 3->4, 6->6*, 6*->3, 5->6].

[0028] There are 6 types of non-switched phase-locked loop topologies and 6 types of switched phase-locked loop topologies, each corresponding to an enhanced phase-locked loop topology.

[0029] Non-switched phase-locked loop topology, switched phase-locked loop topology, enhanced non-switched phase-locked loop topology, and enhanced switched phase-locked loop topology can all select any one of the 6 lasers as the master laser, thus there are a total of 144 phase-locked loop topology structures.

[0030] Inter-satellite Doppler shift calculation involves obtaining inter-satellite Doppler shift data based on the relative motions of satellites 1, 2, and 3. The relationship between Doppler shift and the relative motion of the spacecraft is shown below: (1) In the formula, v 12 , v 13 , v 23 This indicates the relative velocities between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3. f d12 , f d13 , f d23 This indicates the Doppler shift between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3.c Represents the speed of light. f 0 Indicates the laser frequency.

[0031] The general representation model of beat frequency is shown below.

[0032] (2) in, B 11 , B 22 and B 33 These represent the beat frequencies between lasers from different optical platforms on the same satellite. B 12 , B 13 , B 21 , B 23 , B 31 , B 32 These represent the beat frequencies between lasers from different satellites and different optical platforms, for example... B 12 This represents the beat frequency of the interference signal obtained by interfering the laser emitted by satellite 2 and the local laser received by satellite 1. D 12 , D 13 and D 23 These represent the Doppler frequencies between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3, respectively. ​ 11 , ​ 22 , ​ 33 These represent the offset frequencies introduced during the laser phase-locking process within the same satellite. ​ 12 , ​ 13 , ​ 23 These represent the offset frequencies introduced between different satellites during the laser phase-locking process of the main laser. ​ 12β , ​ 13β , ​ 23β These represent the offset frequencies added by the acousto-optic frequency shifter when the laser is emitted from the optical platform. This represents the beat frequency signal coefficient matrix.

[0033] The general formula for representing the beat frequency signal coefficient matrix is ​​as follows:

[0034] middle x 11 ~ x 99 , β 12 , β 13 , β 21 , β 23 , β 31 and β 32 These represent the coefficient settings after selecting a specific phase-locked loop topology. Among them, x 11 ~ x 99 Depending on the selected phase-locked topology, the value range is [-2,-1,0,1,2]. β 12 , β 13 , β 21 , β 23 , β 31 and β 32 Depending on the selected phase-locked topology, the value range is [0,1].

[0035] The setting of each coefficient in the matrix follows these steps: Step 1: Select a specific phase-locked loop topology; Step 2: Obtain the frequencies of the 5 slave lasers and 1 master laser; Step 3: Obtain the coefficients in each beat frequency. In each phase-locked topology, each slave laser has only two phase-locking sequences: locked to a laser on another optical platform of the same satellite, or locked to a laser on a specific optical platform of another satellite. Assume the current slave laser... x and laser y Located on the same satellite①, including lasers y If the signal can be from a laser or a main laser, the corresponding beat frequency calculation formula is as follows:

[0036] After phase locking, from the laser x The frequency is f y + f ①① ,in f y For laser y The frequency.

[0037] Assuming the current laser x and laser y Located on satellites ① and ② respectively, among which y If the signal can be from a laser or a main laser, the corresponding beat frequency calculation formula is as follows:

[0038] If an enhanced phase-locked loop topology is used, then M is 1; otherwise, M is 0.

[0039] After phase locking, from the laser x The frequency is f y + D ①② + f ①② ,in f y For laser y The frequency.

[0040] Therefore, through steps 1-3, the calculation formula for each beat frequency can be obtained. Finally, the coefficients are extracted and filled in sequentially. In the matrix.

[0041] The optimization model is represented by the objective function and corresponding constraints, as shown below: (4) in, To determine the duration of a single offset frequency, the optimization objective is to maximize... . and These represent the upper and lower limits of the beat frequency, respectively. |·| indicates the absolute value sign. T Represents [0, Any time within ]

[0042] The Attempt-Update optimization method refers to using an optimization algorithm to solve a given traditional phase-locked loop topology once that topology has been selected. The solution process is described below: Attempt stage: Step A1: Set the task start time ​ = 1, Task end time ​ = 1, the unit is days.

[0043] Step A2: Select either a switched phase-locked loop (PLL) topology or a non-switched PLL topology, based on... ​ Set beat frequency constraints with t_end.

[0044] Step A3: If the constraint boundary check passes, proceed to step A4; otherwise, proceed to the Update phase.

[0045] Step A4: Solve the constraint equations established in step A2 using a genetic algorithm or a linear programming algorithm.

[0046] Step A5: If the optimal solution is found, proceed to step A6; otherwise, proceed to the Update stage.

[0047] Step A6: If ​ =Satellite mission lifespan, proceed to step A8; otherwise, proceed to step A7.

[0048] Step A7: Let ​ = ​ +1, and proceed to step A2.

[0049] Step A8: Optimization terminated.

[0050] Update phase: Step B1: Select the enhanced phase-locked topology corresponding to the phase-locked topology selected in the Attempt stage, and based on this topology, according to... ​ and ​ Set constraints.

[0051] Step B2: Solve the constraint equations established in Step B1 using a genetic algorithm or a linear programming algorithm.

[0052] Step B3: If the optimal solution is found, proceed to step B4; otherwise, proceed to step B5.

[0053] Step B4: If ​ = Satellite mission lifespan, proceed to step B6; otherwise, set... ​ = ​ +1, and proceed to try step B2.

[0054] Step B5: Let ​ = ​ , ​ = ​ +1, and proceed to try step 2.

[0055] Step B6: Optimization terminated.

[0056] The Attempt stage constraint boundary check involves setting all offset frequencies to 0 before solving for the constraints. Under the current conditions, all inter-satellite Doppler frequency shift data are substituted into beat frequency calculation formula 2 to calculate the extreme value of each beat frequency. The check then determines whether the extreme value exceeds the constraint boundary. The formula is as follows:

[0057] The algorithm flow is as follows ​ As shown.

[0058] Example 1 The three-satellite constellation for space-based gravitational wave detection comprises three satellites and six optical platforms. Each optical platform contains one laser, designated Laser 1, Laser 2, Laser 3, Laser 4, Laser 5, and Laser 6. Lasers 1 and 2 are located on Satellite 1, Lasers 3 and 4 on Satellite 2, and Lasers 5 and 6 on Satellite 3. The phase-locked loop topology selects one laser as the master laser and the others as slave lasers.

[0059] In the solution process, a set of three-satellite formation orbits of space gravitational wave detectors with an operating time of 10 years were used. Inter-satellite Doppler shift data were calculated using inter-satellite Doppler shift, and the relationship between the Doppler shift and the relative motion of the spacecraft is shown below:

[0060] In the formula, D 12 , D 13 , D 23 This indicates the relative velocities between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3. c Represents the speed of light. f 0 Indicates the laser frequency.

[0061] In the solution process, a non-switched phase-locked loop (PLL) topology 1 [2->1, 4->1, 3->4, 6->3, 5->6] is selected as an example. The beat frequency calculation formula for PLL topology 1 is as follows:

[0062] The formula for calculating the beat frequency corresponding to phase-locked topology 1 can be rewritten using a general expression model as follows:

[0063] Among them, in non-exchangeable phase-locked topology 1 M 9×12 for:

[0064] The enhanced non-switched phase-locked loop topology 1 corresponding to non-switched phase-locked loop topology 1 M 9×12 for:

[0065] First, the upper and lower limits of the beat frequency are set to 25MHz and 5MHz respectively, with the goal of maximizing the longest duration. The optimization algorithm is set to a genetic algorithm with a random initial seed.

[0066] Next, we proceed to the Attempt solution phase: Step A1: Let ​ = 1, ​ = 1.

[0067] Step A2: Select non-switched phase-locked loop topology 1, according to ​ and ​ The beat frequency constraint is set as shown in the following formula:

[0068] Step A3: If the constraint boundary check passes, proceed to step A4; otherwise, proceed to the Update phase.

[0069] Step A4: Use a genetic algorithm to solve the set of constraint equations established in step A2.

[0070] Step A5: If the optimal solution is found, proceed to step A6; otherwise, proceed to the Update stage.

[0071] Step A6: If ​ = Satellite mission lifespan, proceed to step A8; otherwise, proceed to step A7.

[0072] Step A7: Let ​ = ​ +1, and proceed to step A2.

[0073] Step A8: Optimization terminated.

[0074] Update phase: Step B1: Select the non-switched phase-locked loop topology 1 chosen in the Attempt phase, and based on this topology, according to... ​ and ​ Set the constraints for enhanced non-exchangeable phase-locked loop topology 1 as follows:

[0075] Step B2: Use a genetic algorithm to solve the set of constraint equations established in step B1.

[0076] Step B3: If the optimal solution is found, proceed to step B4; otherwise, proceed to step B5.

[0077] Step B4: If ​ = Satellite mission lifespan, proceed to step B6; otherwise, set... ​ = ​ +1, and proceed to try step B2.

[0078] Step 5: Let t ​ = ​ , ​ = ​ +1, and proceed to try step B2.

[0079] Step B6: Optimization terminated.

[0080] Following the above solution process, the beat frequency is calculated as follows:

[0081] During actual operation of the detection formation, one of the two topologies, non-switched phase-locked loop (PLL) or switched PLL, is selected first, and its corresponding beat frequency setting scheme is obtained. In the beat frequency setting scheme, the system dynamically switches between non-enhanced and enhanced PLL topologies based on whether the beat frequency exceeds the detector bandwidth to ensure uninterrupted inter-satellite laser interferometry measurements: for example, initially, the non-enhanced topology is preferred; if its beat frequency exceeds the bandwidth, it switches to the enhanced topology; if the enhanced topology still exceeds the bandwidth, it switches back to the non-enhanced topology; if the system experiences frequent switching within a short period, a fault signal is automatically sent.

[0082] Example 2 This application also provides a detection formation offset frequency planning system for enhanced phase-locked loop topology, implemented based on the above method, the system comprising: The data acquisition module is used to acquire orbital information of the space-based gravitational wave detector; The frequency shift calculation module is used to calculate time-varying inter-satellite Doppler frequency shift data; The modeling module is used to build enhanced phase-locked topologies and general representation models; The frequency planning module is used to implement offset frequency planning over an N-year period using the Attempt-Update optimization method.

[0083] This application may also provide a computer device, including: at least one processor, memory, at least one network interface, and a user interface. The various components in this device are coupled together via a bus system. It is understood that the bus system is used to implement communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0084] The user interface can include a display, keyboard, or clicking device. Examples include a mouse, trackball, touchpad, or touchscreen.

[0085] It is understood that the memory in the embodiments disclosed in this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0086] In some implementations, the memory stores elements such as executable modules or data structures, or subsets thereof, or extended sets thereof: operating systems and applications.

[0087] The operating system includes various system programs, such as the framework layer, core library layer, and driver layer, used to implement various basic business functions and handle hardware-based tasks. The application programs include various applications, such as media players and browsers, used to implement various application functions. Programs implementing the methods of the embodiments of this disclosure can be included in the application programs.

[0088] In the above embodiments, the processor can also invoke programs or instructions stored in memory, specifically programs or instructions stored in an application program, for the following purposes: Follow the steps described above.

[0089] The above methods can be applied to or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above methods can be completed by integrated logic circuits in the processor's hardware or by software instructions. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic diagrams disclosed above. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the disclosed methods can be directly implemented by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0090] It is understood that the embodiments described in this application can be implemented using hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0091] For software implementation, the technology of this application can be implemented by executing the functional modules (e.g., procedures, functions, etc.) of this application. The software code can be stored in memory and executed by a processor. The memory can be implemented in the processor or outside the processor.

[0092] This application may also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, it can implement the steps in the above method embodiments.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application, and should all be covered within the scope of the claims of this application.

Claims

1. A method for planning the offset frequency of a detection formation in an enhanced phase-locked topology, wherein the detection formation comprises three satellites in a triangular array: satellite 1, satellite 2 and satellite 3, each satellite is equipped with two optical platforms, each optical platform has a laser, and the phase-locked topology selects one laser as the master laser and the other lasers as slave lasers; The method includes: The orbital information of the space-based gravitational wave detector is obtained, the time-varying inter-satellite Doppler frequency shift data is calculated, an enhanced phase-locked topology and a general representation model are established, and the offset frequency planning within an N-year period is realized using the Attempt-Update optimization method.

2. The detection formation offset frequency planning method for enhanced phase-locked loop topology according to claim 1, characterized in that, The orbital information of the space-based gravitational wave detector refers to the orbital position and velocity information of the space-based gravitational wave detector within an N-year period.

3. The detection formation offset frequency planning method for enhanced phase-locked loop topology according to claim 1, characterized in that, The calculation of time-varying inter-satellite Doppler frequency shift data involves using orbital information to calculate the relative motion information between satellites, and then converting the relative motion information into inter-satellite Doppler frequency shift data. ； in, v 12 , v 13 , v 23 These represent the relative velocities between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3, respectively. f d12 , f d13 , f d23 The Doppler frequency shifts between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3 are shown respectively. c Represents the speed of light. f 0 Indicates the laser frequency.

4. The detection formation offset frequency planning method for enhanced phase-locked loop topology according to claim 1, characterized in that, The enhanced phase-locked loop (PLL) topology and general representation model include 144 enhanced PLL topologies and a general representation model for beat frequency; wherein, the 144 enhanced PLL topologies include: Phase-locked loop (PLL) topologies include four types: non-switched PLL topology, switched PLL topology, enhanced non-switched PLL topology, and enhanced switched PLL topology. The lasers are numbered from 1 to 6 in clockwise order of their spatial location, resulting in a total of 6 non-switched phase-locked loop topologies, 6 switched phase-locked loop topologies, 6 enhanced non-switched phase-locked loop topologies, and 6 enhanced switched phase-locked loop topologies. Set the main laser number to 1; The six non-switching phase-locked loop topologies are: Topology A1: [2->1, 6->5, 5->4, 4->3, 3->2]; Topology A2: [2->1, 6->1, 5->4, 4->3, 3->2]; Topology A3: [2->1, 6->1, 5->6, 4->3, 3->2]; Topology A4: [2->1, 6->1, 5->6, 4->5, 3->2]; Topology A5: [2->1, 6->1, 5->6, 4->5, 3->4]; Topology A6: [2->3, 6->1, 5->6, 4->5, 3->4]; Where 2->1 indicates that laser 2 is phase-locked to laser 1; The six types of switch-locked loop topologies are: Topology B1: [2->1, 4->1, 3->4, 6->3, 5->6]; Topology B2: [5->2, 2->1, 4->1, 3->4, 6->3]; Topology B3: [6->5, 5->2, 2->1, 4->1, 3->4]; Topology B4: [3->6, 6->5, 5->2, 2->1, 4->1]; Topology B5: [4->3, 3->6, 6->5, 5->2, 2->1]; Topology B6: [2->5, 4->1, 3->4, 6->3, 5->6]; Compared to the non-switched phase-locked loop topology, the enhanced non-switched phase-locked loop topology, and the enhanced switched phase-locked loop topology, both involve adding an acousto-optic frequency shifter during laser beam emission in the inter-satellite phase-locking process to achieve fixed frequency shifting of the emitted beam. The six enhanced non-switching phase-locked loop topologies are: Topology C1: [2->1, 6->5, 5->5*, 5*->4, 4->3, 3->3*, 3*->2]; Topology C2: [2->1, 6->6*, 6*->1, 5->5*, 5*->4, 4->3, 3->3*, 3*->2]; Topology C3: [2->1, 6->6*, 6*->1, 5->6, 4->3, 3->3*, 3*->2]; Topology C4: [2->1, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->3*, 3*->2]; Topology C5: [2->1, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->4]; Topology C6: [2->2*, 2*->3, 6->6*, 6*->1, 5->6, 4->4*, 4*->5, 3->4]; Wherein, 5* represents the frequency shift when laser 5 is emitted from the optical platform of the satellite; The six enhanced switching phase-locked loop topologies are: Topology 1: [2->1, 4->4*, 4*->1, 3->4, 6->6*, 6*->3, 5->6]; Topology 2: [5->5*, 5*->2, 2->1, 4->4*, 4*->1, 3->4, 6->6*, 6*->3]; Topology 3: [6->5, 5->5*, 5*->2, 2->1, 4->4*, 4*->1, 3->4]; Topology 4: [3->3*, 3*->6, 6->5, 5->5*, 5*->2, 2->1, 4->4*, 4*->1]; Topology 5: [4->3, 3->3*, 3*->6, 6->5, 5->5*, 5*->2, 2->1]; Topology 6: [2->2*, 2*->5, 4->4*, 4*->1, 3->4, 6->6*, 6*->3, 5->6]; By selecting different lasers as the master laser, a total of 144 phase-locked loop topologies were formed.

5. The detection formation offset frequency planning method for enhanced phase-locked topology according to claim 4, characterized in that, The general representation model for the beat frequency is as follows: ； in, B 11 , B 22 and B 33 These represent the beat frequencies between lasers from different optical platforms on the same satellite. B 12 , B 13 , B 21 , B 23 , B 31 , B 32 These represent the beat frequencies between the lasers of the optical platforms of different satellites represented by the subscripts; D 12 , D 13 and D 23 These represent the Doppler frequencies between satellite 1 and satellite 2, satellite 1 and satellite 3, and satellite 2 and satellite 3, respectively. Δf 11 , Δf 22 , Δf 33 These represent the offset frequencies introduced during the laser phase-locked loop process within the same satellite; Δf 12 , Δf 13 , Δf 23 These represent the offset frequencies introduced between the satellites represented by the subscripts during the laser phase-locking process, respectively. Δf 12β , Δf 13β , Δ f 23β These represent the offset frequencies introduced between the satellites represented by the subscripts during the laser phase-locking process, where the subscripts contain... β The satellite number indicates that when the laser is emitted from the optical platform of that satellite, an offset frequency is added through an acousto-optic frequency shifter; This represents the beat frequency signal coefficient matrix.

6. The detection formation offset frequency planning method for enhanced phase-locked topology according to claim 5, characterized in that, The beat frequency signal coefficient matrix for: ； in, x 11 ~ x 99 , β 12 , β 13 , β 21 , β 23 , β 31 and β 32 These represent the coefficient settings after selecting a specific phase-locked topology; where, x 11 ~ x 99 Depending on the selected phase-locked topology, the value range is [-2, -1, 0, 1, 2]; β 12 , β 13 , β 21 , β 23 , β 31 and β 32 Depending on the selected phase-locked loop topology, the value range is [0,1].

7. The detection formation offset frequency planning method for enhanced phase-locked loop topology according to claim 6, characterized in that, The The methods for setting the coefficients in a matrix include: Step 1: Select the desired phase-locked topology type; Step 2: Obtain the frequencies of the 5 slave lasers and 1 master laser; Step 3: In each phase-locked topology, each laser has only two phase-locked sequences, namely, locked to a laser on another optical platform of the same satellite or locked to a laser on a certain optical platform of another satellite; When from laser x and laser y Located on the same satellite i The corresponding beat frequency The calculation formula is as follows: ； After phase locking, from the laser x The frequency is f y + f ii , f y For laser y The frequency; When from laser x and laser y Located in satellite i and j The corresponding beat frequency and The calculation formula is as follows: ； If an enhanced phase-locked loop topology is used, then M is 1; otherwise, M is 0. After phase locking, from the laser x The frequency is f y + D ij + f ij ; After obtaining the calculation formula for each beat frequency, extract its coefficients and fill them in sequentially. In the matrix.

8. The detection formation offset frequency planning method for enhanced phase-locked topology according to claim 4, characterized in that, The Attempt-Update optimization method includes an Attempt phase and an Update phase, and execution begins with the Attempt phase, wherein: The Attempt phase includes: Step A1: Set the task start time t_start = 1, Task end time t_end = 1, the unit is days; Step A2: Select either a switched phase-locked loop (PLL) topology or a non-switched PLL topology, according to the current... t_start and t_ end Using the general expression model of beat frequency, beat frequency constraints are set, and a set of constraint equations is established; Step A3: If the constraint boundary check passes, proceed to step A4; otherwise, proceed to the Update phase. Step A4: Solve the constraint equations established in step A2 using a genetic algorithm or a linear programming algorithm; Step A5: If the optimal solution is found, proceed to step A6; otherwise, proceed to the Update stage. Step A6: If t_end =If the satellite mission lifespan is determined, proceed to step A8; otherwise, proceed to step A7. Step A7: Settings t_end Add 1 day and proceed to step A2; Step A8: Optimization terminated; Update phase: Step B1: Select the enhanced phase-locked topology corresponding to the phase-locked topology selected in the Attempt stage, and based on this topology, according to the current... t_start and t_end Using the general expression model of beat frequency, beat frequency constraints are set, and a set of constraint equations is established; Step B2: Solve the constraint equations established in Step B1 using a genetic algorithm or a linear programming algorithm; Step B3: If the optimal solution is found, proceed to step B4; otherwise, proceed to step B5. Step B4: If t_end = Satellite mission lifespan, proceed to step B6, otherwise set t_end Add 1 day and proceed to step B2; Step B5: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full t_start Set to with t_end If the values ​​are the same, set t_end Add 1 day and proceed to step 2; Step B6: Optimization terminated.

9. The detection formation offset frequency planning method for enhanced phase-locked topology according to claim 8, characterized in that, The constraint boundary check includes: Setting all offset frequencies to 0, and substituting all inter-satellite Doppler frequency shift data under the current conditions into the general representation model of beat frequency, the extreme values ​​of each beat frequency are calculated, and it is determined whether the extreme values ​​exceed the boundary of the constraint conditions. The formula is as follows: ； in, and These represent the upper and lower limits of the beat frequency, respectively; To determine the duration of a single offset frequency, the optimization objective is to maximize... ; Indicates duration T At that time, satellite i Accepted satellites j The beat frequency of the interference signal obtained by interfering the emitted laser with the local laser.

10. A detection formation offset frequency planning system for enhanced phase-locked topology, implemented based on the method described in any one of claims 1-9, characterized in that, The system includes: The data acquisition module is used to acquire orbital information of the space-based gravitational wave detector; The frequency shift calculation module is used to calculate time-varying inter-satellite Doppler frequency shift data; The modeling module is used to build enhanced phase-locked loop topologies and general representation models; and The frequency planning module is used to implement offset frequency planning over an N-year period using the Attempt-Update optimization method.

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