Earth free oscillation waveform rapid generation method and system for geocentric orbit space gravitational wave detection

Abstract

The invention discloses a geocentric orbit space gravitational wave detection-oriented earth free oscillation waveform rapid generation method and system, which are used for solving the problems that the calculation process of the existing earth free oscillation waveform generation method is complicated, the time consumption is serious, the requirements of rapid noise evaluation and elimination in a task are difficult to meet, and the reliability is poor. And the calculation efficiency of the earth free oscillation waveform is low. The method comprises the following steps: acquiring earth gravitational field parameters and an inter-satellite instantaneous distance, and constructing an inter-satellite distance measurement acceleration analysis model by adopting a Couwurah linear perturbation method; correcting based on an earth free oscillation model, and determining a corrected inter-satellite distance measurement acceleration analysis model; when satellite orbit parameters, a simulation time sequence and earth free oscillation mode parameters are received, distance measurement acceleration signals among multiple satellites are calculated through the correction model; and selecting a target ranging acceleration signal, performing earth oscillation signal extraction on the target ranging acceleration signal by adopting a time delay interference method, and finally outputting a target earth oscillation signal.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method and system for rapidly generating free oscillation waveforms of the Earth for geocentric orbit space gravitational wave detection. Background Technology

[0002] The time-varying Earth gravitational field is a key physical quantity for understanding the Earth's internal structure, material transport, and global mass redistribution. It has significant scientific value for studying fundamental geophysical theories such as Earth's free oscillations and solid-state geophysical processes.

[0003] High-orbit space gravitational wave detection missions, such as the Tianqin project, are mainly achieved through laser interferometry, which requires extremely high detection accuracy. Against this backdrop, noise generated by geophysical effects such as Earth's free oscillation has become an important factor restricting detection accuracy. Accurate modeling and rapid evaluation of this noise is one of the key challenges currently facing space gravitational wave detection missions.

[0004] Currently, in the data processing and noise assessment of space gravitational wave missions, the assessment of the interference of the Earth-Moon system's gravitational field on inter-satellite ranging acceleration relies entirely on high-precision numerical calculations. This method is complex and time-consuming, making it difficult to meet the needs of rapid noise assessment and elimination in missions, resulting in low computational efficiency for Earth's free oscillation waveforms. Summary of the Invention

[0005] This invention provides a method and system for rapidly generating Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection. It addresses the technical problem that existing methods for generating Earth's free oscillation waveforms are complex and time-consuming, making it difficult to meet the needs of rapid noise assessment and elimination in missions, resulting in low computational efficiency of Earth's free oscillation waveforms.

[0006] The first aspect of this invention provides a method for rapidly generating Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection, comprising:

[0007] The Earth's gravitational field parameters and instantaneous inter-satellite distances are obtained, and an analytical model of inter-satellite ranging acceleration is constructed based on the Earth's gravitational field parameters and instantaneous inter-satellite distances using the Koula linear perturbation method.

[0008] The analytical model of inter-satellite ranging acceleration is modified based on the Earth free oscillation model, and the modified analytical model of inter-satellite ranging acceleration is determined.

[0009] When satellite orbit parameters, simulation time series, and Earth free oscillation mode parameters are received, the modified inter-satellite ranging acceleration analytical model is used to calculate the ranging acceleration signals between multiple satellites based on the satellite orbit parameters, the simulation time series, and the Earth free oscillation mode parameters.

[0010] The target ranging acceleration signal is selected from the ranging acceleration signals of each of the satellites, and the Earth oscillation signal is extracted from the target ranging acceleration signal using the time delay interferometry method, and the target Earth oscillation signal is output.

[0011] Optionally, the step of constructing an analytical model for inter-satellite ranging acceleration using the Koula linear perturbation method based on the Earth's gravitational field parameters and the instantaneous inter-satellite distance includes:

[0012] Based on the Earth's gravitational field parameters, a spherical coordinate spherical harmonic function model is constructed;

[0013] The spherical coordinate spherical harmonic function model is converted into a satellite orbital element model using the Koula linear perturbation method;

[0014] The satellite orbital element model is simplified to determine a simplified Earth gravitational field model under a reference circular orbit;

[0015] The satellite's gravitational potential is calculated based on the simplified Earth gravitational field model under the aforementioned reference circular orbit.

[0016] An analytical model for inter-satellite ranging acceleration is constructed based on the satellite's gravitational potential and the instantaneous inter-satellite distance.

[0017] Optionally, the analytical model of inter-satellite ranging acceleration based on the Earth free oscillation model is modified to determine the modified analytical model of inter-satellite ranging acceleration, including:

[0018] Based on the Earth free oscillation model, the time-varying perturbation of the gravitational field coefficients is solved;

[0019] The analytical model of inter-satellite ranging acceleration is modified by using the time-varying perturbation of the gravitational field coefficients, and the modified analytical model of inter-satellite ranging acceleration is determined.

[0020] Optionally, the step of using the modified inter-satellite ranging acceleration analytical model to calculate the ranging acceleration signals between multiple satellites based on the satellite orbital parameters, the simulation time series, and the Earth free oscillation mode parameters includes:

[0021] The order of the modified inter-satellite ranging acceleration analytical model is simplified to determine the order-simplified inter-satellite ranging acceleration analytical model.

[0022] The simplified inter-satellite ranging acceleration analytical model is used to solve for satellite acceleration based on the satellite orbital parameters, the simulation time series, and the Earth free oscillation mode parameters, and outputs ranging acceleration signals between multiple satellites.

[0023] Optionally, the step of extracting the Earth oscillation signal from the target ranging acceleration signal using the time-delay interferometry method and outputting the target Earth oscillation signal includes:

[0024] The target ranging acceleration signal is optically delayed, and the delayed target ranging acceleration signal is output.

[0025] The target ranging acceleration signal after the optical path delay is expanded to determine the expanded target ranging acceleration signal.

[0026] The laser phase noise in the deployed target ranging acceleration signal is sorted and matched to determine the initial Earth oscillation signal;

[0027] The initial Earth oscillation signal is subjected to a Fourier transform and then filtered by a high-pass filter to output the target Earth oscillation signal.

[0028] Optionally, it also includes:

[0029] Numerical simulation data is acquired, and Bayesian analysis and MCMC parameter estimation methods are used to extract estimated values ​​of Earth's free oscillation parameters from the numerical simulation data.

[0030] The simplified inter-satellite ranging acceleration analytical model is used to output a simulated ranging acceleration signal based on the satellite orbital parameters, the simulation time series, and the estimated values ​​of the Earth's free oscillation parameters.

[0031] The time-delay interferometry method is used to extract the Earth oscillation signal from the simulated ranging acceleration signal to determine the simulated Earth oscillation signal;

[0032] The simulated Earth oscillation signal is subjected to Fourier transform and filtered by a high-pass filter to determine the target simulated Earth oscillation signal.

[0033] The matching factor is used to measure the degree of curve conformity. The simplified inter-satellite ranging acceleration analytical model is verified based on the target simulated Earth oscillation signal and the target Earth oscillation signal, and the verification results are output.

[0034] The second aspect of this invention provides a rapid generation system for Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection, comprising:

[0035] The acquisition module is used to acquire the Earth's gravitational field parameters and the instantaneous inter-satellite distance, and to construct an analytical model of inter-satellite ranging acceleration based on the Earth's gravitational field parameters and the instantaneous inter-satellite distance using the Koula linear perturbation method;

[0036] The correction module is used to correct the analytical model of the inter-satellite ranging acceleration based on the Earth free oscillation model, and to determine the corrected analytical model of the inter-satellite ranging acceleration.

[0037] The calculation module is used to calculate the ranging acceleration signals between multiple satellites based on the satellite orbit parameters, the simulation time series, and the Earth free oscillation mode parameters when satellite orbit parameters, simulation time series, and Earth free oscillation mode parameters are received.

[0038] The output module is used to select the target ranging acceleration signal among the ranging acceleration signals of each of the satellites, and to extract the earth oscillation signal from the target ranging acceleration signal using the time delay interferometry method, and output the target earth oscillation signal.

[0039] A computer device provided in a third aspect of the present invention includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor causes the processor to perform the steps of the method for rapidly generating free oscillation waveforms of the Earth for geocentric orbit space gravitational wave detection as described in any of the preceding claims.

[0040] The fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed, it implements the steps of the method for rapidly generating Earth free oscillation waveforms for geocentric orbit space gravitational wave detection as described in any of the preceding claims.

[0041] The fifth aspect of the present invention provides a computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, wherein, when the program instructions are executed by a computer, the computer performs the steps of the method for rapidly generating Earth free oscillation waveforms for geocentric orbit space gravitational wave detection as described in any of the preceding claims.

[0042] As can be seen from the above technical solutions, the present invention has the following advantages:

[0043] The above-mentioned technical solution of the present invention provides a method for rapidly generating Earth free oscillation waveforms for geocentric orbit space gravitational wave detection. It obtains Earth's gravitational field parameters and inter-satellite instantaneous distances, and uses the Koula linear perturbation method to construct an analytical model of inter-satellite ranging acceleration based on the Earth's gravitational field parameters and inter-satellite instantaneous distances. Based on the Earth free oscillation model, the analytical model of inter-satellite ranging acceleration is modified to determine the modified analytical model. When satellite orbital parameters, simulation time series, and Earth free oscillation mode parameters are received, the modified analytical model of inter-satellite ranging acceleration is used to calculate... The method calculates the ranging acceleration signals between multiple satellites; selects the target ranging acceleration signal among the ranging acceleration signals between satellites, and uses time-delay interferometry to extract the Earth oscillation signal from the target ranging acceleration signal, outputting the target Earth oscillation signal; based on the above scheme, this invention breaks through the limitations of traditional reliance on high-precision numerical calculations by innovatively combining the Koula linear perturbation method with analytical model construction, transforming the complex problem of generating Earth free oscillation waveforms into efficient analytical calculations. With targeted time-varying perturbation correction and signal purification by time-delay interferometry, the calculation process is greatly simplified, the waveform generation time is shortened, and the calculation efficiency of Earth free oscillation waveforms is significantly improved. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart illustrating the steps of a method for rapidly generating Earth's free oscillation waveform for geocentric orbit space gravitational wave detection, as provided in Embodiment 1 of the present invention.

[0046] Figure 2 This is a schematic diagram showing the distribution of satellite 1, satellite 2, and satellite 3 according to Embodiment 1 of the present invention;

[0047] Figure 3 This is a schematic diagram of the signal detected at the photodetector provided in Embodiment 1 of the present invention;

[0048] Figure 4 This is a schematic diagram illustrating TDI-X, TDI-Y, and TDI-Z as provided in Embodiment 1 of the present invention;

[0049] Figure 5 This is a schematic diagram illustrating TDI-X, TDI-Y, and TDI-Z as provided in Embodiment 1 of the present invention;

[0050] Figure 6 This is an overall framework diagram of a method for rapidly generating Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection, provided in Embodiment 1 of the present invention.

[0051] Figure 7 This is a flowchart illustrating the steps for verifying the simplified inter-satellite ranging acceleration analytical model according to Embodiment 2 of the present invention.

[0052] Figure 8 This is a structural block diagram of a rapid generation system for Earth's free oscillation waveforms for geocentric orbital space gravitational wave detection, provided in Embodiment 3 of the present invention. Detailed Implementation

[0053] This invention provides a method and system for rapidly generating Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection. It addresses the technical problem that existing methods for generating Earth's free oscillation waveforms are computationally complex and time-consuming, failing to meet the requirements for rapid noise assessment and elimination in missions, resulting in low computational efficiency. This invention is applicable to noise assessment and elimination in space gravitational wave detection.

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that in the optional embodiments of the present invention, the object information and other related data involved require the permission or consent of the object when the embodiments of the present invention are applied to specific products or technologies, and the collection, use, and processing of related data must comply with the relevant laws, regulations, and standards of the relevant countries and regions. That is to say, if the embodiments of the present invention involve data related to the object, it needs to be obtained with the authorization and consent of the object, the authorization and consent of the relevant departments, and in compliance with the relevant laws, regulations, and standards of the country and region. If personal information is involved in the embodiments, the acquisition of all personal information requires the consent of the individual. If sensitive information is involved, the separate consent of the information subject is required, and the embodiments also need to be implemented with the authorization and consent of the object.

[0055] Please see Figure 1 , Figure 1 The flowchart illustrates the steps of a method for rapidly generating Earth's free oscillation waveforms for geocentric orbital space gravitational wave detection, as provided in Embodiment 1 of the present invention.

[0056] This invention provides a method for rapidly generating Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection, comprising:

[0057] Step 101: Obtain the Earth's gravitational field parameters and the instantaneous inter-satellite distance, and use the Koula linear perturbation method to construct an analytical model of inter-satellite ranging acceleration based on the Earth's gravitational field parameters and the instantaneous inter-satellite distance.

[0058] Earth's gravitational field parameters: physical quantities describing the spatial distribution of Earth's gravitational field, including the product of the gravitational constant and the Earth's mass (GM), the Earth's average radius (R), and the normalized spherical harmonic coefficients (GMC). , And the order of spherical harmonic expansion, truncation order, etc.

[0059] Inter-satellite instantaneous distance: the straight-line distance between any two satellites in a probe constellation at the same moment, mathematically expressed as the magnitude of the difference in the position vectors of the two satellites ( ), This is the position vector of another satellite, used to describe its position in space. This is the position vector of one of the satellites, used to describe its position in space.

[0060] Koula linear perturbation method: A classic method in orbital mechanics used to convert gravitational field models into orbital element functions. It establishes the relationship between gravitational field parameters and satellite orbital parameters (semi-major axis, inclination, etc.) by linearizing the gravitational potential expansion.

[0061] Detector constellation equilateral triangle configuration: A space detection system consisting of three satellites arranged in an equilateral triangle in orbit, with equal distances between them, which is a typical configuration for space gravitational wave detection.

[0062] Reference circular orbit assumption: An ideal orbital condition set to simplify orbital calculations, assuming that the satellite orbital eccentricity is 0, that is, the satellite moves along a circular orbit with the Earth's center as the center.

[0063] Earth's gravitational field spherical harmonic function model: A model that describes the spatial distribution of Earth's gravitational potential using the expansion of spherical harmonic functions. By superimposing spherical harmonic terms of different orders and degrees, it accurately characterizes the non-spherical features of Earth's gravitational field.

[0064] Satellite orbital elements: Parameters describing the shape of a satellite's orbit, its spatial orientation, and its position in orbit, including semi-major axis, eccentricity, inclination, longitude of the ascending node, argument of perigee, and mean perigee.

[0065] Inter-satellite ranging acceleration analytical model: the second derivative of inter-satellite distance with respect to time expressed mathematically ( The relationship model between the satellite and related parameters (gravitational field parameters, orbital parameters, etc.) can be used to directly calculate the inter-satellite ranging acceleration by substituting the parameters.

[0066] It should be noted that after obtaining the Earth's gravitational field parameters and the instantaneous inter-satellite distances, and combining the equilateral triangle configuration of the detector constellation (the three satellites are spatially distributed in an equilateral triangle with equal inter-satellite distances) and the assumption of a reference circular orbit (the satellites operate along a circular orbit with zero eccentricity), the spherical harmonic function model of the Earth's gravitational field is first mapped to a function of the satellite orbital elements through coordinate transformation. Then, the Koula linear perturbation method is used to linearize the function model, and the geometric relationship of the instantaneous inter-satellite distances is simultaneously incorporated. Finally, an analytical model of the inter-satellite ranging acceleration between the three satellites is constructed.

[0067] Specifically, step 101 may include the following sub-steps:

[0068] S11. Construct a spherical coordinate spherical harmonic function model based on the Earth's gravitational field parameters;

[0069] S12. The Koula linear perturbation method is used to convert the spherical coordinate spherical harmonic function model into a satellite orbital element model;

[0070] S13. Simplify the satellite orbital element model and determine the simplified Earth gravitational field model under the reference circular orbit;

[0071] S14. Calculate the satellite's gravitational potential based on a simplified Earth gravitational field model under a reference circular orbit;

[0072] S15. Based on the satellite's gravitational potential and the instantaneous inter-satellite distance, construct an analytical model for inter-satellite ranging acceleration.

[0073] It should be noted that, based on the Earth's gravitational field parameters, a spherical coordinate spherical harmonic function model (i.e., the spherical coordinate spherical harmonic expansion of the Earth's gravitational field) is constructed in the Conventional Earth Reference System. Then, using the Koula linear perturbation method, this spherical coordinate spherical harmonic function model is converted into a satellite orbital element model with satellite orbital elements as variables. Combining this with the equilateral triangle configuration of the probe constellation, the actual satellite motion is approximated as the motion of a reference circular orbit generated by the Earth's central gravitational potential, simplifying the satellite orbital element model and determining the simplified Earth gravitational field model under the reference circular orbit. Based on this, the satellite gravitational potential is calculated using this simplified model. Finally, considering the instantaneous inter-satellite distance, its second derivative with respect to time is taken, and through coordinate transformation and differentiation, an analytical model of inter-satellite ranging acceleration is constructed.

[0074] Among them, the Conventional Earth Reference System is an internationally recognized Earth reference frame used to unify the coordinate system for describing the Earth and its surrounding space, and to provide a reference coordinate system for gravitational field models.

[0075] Spherical coordinate spherical harmonic expansion: In a spherical coordinate system (radius, colatitude, longitude), the mathematical form of the Earth's gravitational field is represented by spherical harmonic functions (including Legendre functions and trigonometric function terms), which can accurately characterize the spatial distribution of the gravitational field.

[0076] Satellite orbital elements model: A model of Earth's gravitational field that uses satellite orbital elements (semi-major axis, eccentricity, inclination, etc.) as variables, and can directly reflect the influence of the gravitational field on satellite orbital motion.

[0077] Satellite gravitational potential: The gravitational potential energy generated by the Earth's gravitational field at the satellite's location is a physical quantity that describes the strength of the gravitational field's effect on the satellite. It is determined by both the Earth's gravitational field model and the satellite's location.

[0078] Specifically, the Earth's gravitational field model is represented in spherical coordinates in the Common Earth Reference System. That is, based on the Earth's gravitational field model, the spherical coordinate spherical harmonic expansion of the Earth's gravitational field in the Common Earth Reference System is obtained (spherical coordinate spherical harmonic function model).

[0079] ;

[0080] in, It is the gravitational constant. It is the total mass of the Earth. It is the Earth's average radius. It is a spherical harmonic expansion Step Second-rate, Here, n is the truncation order, n is the order of the spherical harmonic expansion, and m is the degree of the spherical harmonic expansion. These are the radius, coplanar latitude, and longitude in a spherical coordinate system. These are the normalized spherical harmonic coefficients. It is the normalized associated Legendre function; The gravitational potential of Earth is the position of a unit mass object in Earth's gravitational field. The gravitational potential energy at that location.

[0081] Furthermore, based on the Kalua linear perturbation method, the Earth's gravitational field is represented by satellite orbital elements, i.e., the satellite orbital element model:

[0082] ;

[0083] in, Let be the Earth's gravitational potential expressed in terms of satellite orbital elements, describing the gravitational potential energy effect of the Earth's gravitational field on the satellite's orbital motion. It is an angle function, derived from the argument of perigee. , and the near point angle Longitude of ascending node Greenwich true sidereal time angle Together, these angular parameters constitute and describe the combined effect of gravitational potential. , This is an auxiliary degree parameter used in spherical harmonic expansion and orbital perturbation analysis, for series expansion of function terms, to help characterize the complex distribution characteristics of the gravitational field. 'a' is the semi-major axis of the satellite orbit. It is the satellite orbital eccentricity. It is the satellite's orbital inclination. It is the longitude of the ascending node. It is the perigee argument. It is a near-point angle. It is the satellite orbital eccentricity The function;

[0084] It is the satellite orbital inclination. Functions:

[0085] ;

[0086] in, is a function of the satellite's orbital inclination i, and is a core function term of the Koula linear perturbation method, describing the perturbation effect of the non-spherical distribution of the Earth's gravitational field on the satellite's orbital inclination; p is an auxiliary degree parameter in orbital perturbation analysis, used for the series expansion of the function term, and helps characterize the complex influence of the gravitational field on the orbital inclination. , , , , , , , It serves as an auxiliary parameter for series expansion, used to decompose complex orbital inclination functions into multi-level summation terms, simplifying mathematical expression and calculation process; , , Let be the combination number (binomial coefficient), representing selecting s elements from m elements, and selecting s elements from m elements respectively. Select c elements from 1. Select from the elements The number of combinations of terms used in series expansion; Let i be the sine power term of the satellite orbital inclination, which describes the contribution of higher powers of the sine of the orbital inclination to the perturbation of the Earth's gravitational field. Let i be the cosine power of the satellite orbital inclination, which describes the contribution of higher powers of the cosine of the orbital inclination to the perturbation of the Earth's gravitational field. , , The factorial term is used for calculating the coefficients of combinatorial numbers and series expansions, ensuring the mathematical rigor of function expansions. , The sign and power terms are used to adjust the sign and magnitude of the series expansion terms, accurately characterizing the spatial symmetry of the non-spherical distribution of the Earth's gravitational field.

[0087] It is the perigee argument. , and the near point angle Longitude of ascending node Greenwich true sidereal time angle Functions:

[0088] ;

[0089] Where the coefficient It is the Earth's gravitational field coefficient Rearrangement:

[0090] ;

[0091] In the formula, The rearrangement coefficients of the Earth's gravitational field coefficients; These are the normalized spherical harmonic coefficients (cosine term) and the normalized spherical harmonic coefficients (sine term), respectively. To combine angles, from the perigee argument. , and the near point angle Longitude of ascending node Greenwich true sidereal time angle Angle variables, which are combined according to specific relationships, are used to integrate multiple orbital angle parameters into a single angle term, simplifying the function form. Even numbers indicate The case where the coefficients are even is used to distinguish the recombination of spherical harmonic coefficients; If it is an odd number, it means The case where the number is odd.

[0092] Furthermore, by approximating the actual motion of the three satellites as the motion of a reference circular orbit generated by the gravitational potential at the Earth's center, a simplified representation of the Earth's gravitational field is obtained, namely, a simplified model of the Earth's gravitational field under a reference circular orbit:

[0093] ;

[0094] in, To describe the gravitational potential energy effect of the Earth's gravitational field on a satellite (based on the assumption that the satellite moves along a circular orbit), a simplified Earth gravitational potential is used as a reference. It is a function of the satellite's orbital radius. 'a' is the semi-major axis of the satellite orbit. The length of the semi-major axis of the satellite's elliptical orbit determines the spatial scale of the orbit. It is a function of the satellite orbital inclination i, belonging to the inclination function term of the Koula linear perturbation method. The superscript k is an auxiliary parameter that describes the perturbation effect of the orbital inclination on the Earth's gravitational potential. The combined angle is composed of the angle parameters of the satellite orbit (perigee argument, mean perigee angle, etc.) and is used to integrate the influence of orbital angle on gravitational potential; n is the order of the spherical harmonic expansion; m is the degree of the spherical harmonic expansion; k is an auxiliary degree parameter used for the series expansion of the function term to help characterize the complex distribution characteristics of the gravitational field; n1 and n2 are the series expansion range parameters, controlling the upper and lower limits of the summation, and belong to auxiliary index variables.

[0095] function Represented as:

[0096] ;

[0097] Where k is an auxiliary degree parameter in orbital perturbation analysis, used for the series expansion of the function term to help characterize the complex influence of the gravitational field on the orbital inclination; s, t, c, and g are auxiliary parameters for the series expansion, used to decompose the complex orbital inclination function into multi-level summation terms, simplifying the mathematical expression and calculation process (controlling the level and range of the summation, and participating in the combination of signs and the number of terms). , , Let be the combination number (binomial coefficient), representing the combinations from m, ... indivual, The number of combinations of elements selected from a given number of elements is used to determine the number of terms in a series expansion. Let i be the sine power term of the satellite orbital inclination, which describes the contribution of higher powers of the sine of the orbital inclination to the perturbation of the Earth's gravitational field. Let i be the cosine power of the satellite's orbital inclination, describing the contribution of higher powers of the cosine of the orbital inclination to the perturbation of Earth's gravitational field.

[0098] Auxiliary parameters Represented as:

[0099] ;

[0100] Combination of angles ,in and These represent angles related to Earth's rotation and satellite orbital motion, respectively:

[0101] ;

[0102] Furthermore, regarding the instantaneous distance between stars... Taking the second derivative with respect to time, we obtain the inter-satellite ranging acceleration of the satellite under the existence of Earth's gravitational potential:

[0103] ;

[0104] First item = It is the interstellar line-of-sight gravitational acceleration difference. and These are the gravitational potentials of Earth at satellite 2 (the precursor satellite) and satellite 1 (the follower satellite), respectively. It is the unit vector in the direction (line of sight) from satellite 1 to satellite 2;

[0105] Second item Represents centrifugal acceleration. , , , These are the positions and velocities of Satellite 2 and Satellite 1, and the rate of change of inter-satellite distance, respectively. The values ​​of each quantity can be determined by geometric relationships.

[0106] Through coordinate transformation and differentiation, the analytical expression for inter-satellite ranging acceleration is obtained, i.e., the analytical model of inter-satellite ranging acceleration:

[0107] ;

[0108] in, It is the amplitude. It is the Earth's rotation frequency. It is the satellite's orbital frequency. It is the initial phase of Earth's rotation. It is the initial phase of the satellite's revolution. It is the angle subtended by the two satellites relative to the Earth's center; is the inter-satellite ranging acceleration, which is the second derivative of the inter-satellite distance with respect to time, describing the accelerated change of the inter-satellite distance over time; N is ; m and k are auxiliary parameters for spherical harmonic expansion and orbital perturbation analysis, where m is related to the Earth's rotation and k is related to the satellite's revolution, and their values ​​are limited by the truncation order N; t is the time variable; The inherent phase is determined by the Earth's gravitational field and the inherent characteristics of the satellite orbit; it is the phase offset term of the inter-satellite ranging acceleration component. The semi-major axis of the satellite orbit is the length of the semi-major axis of the elliptical orbit, which determines the spatial scale of the orbit.

[0109] It is worth mentioning that the same applies to Satellite 2 and Satellite 3, and Satellite 1 and Satellite 3.

[0110] Step 102: Based on the Earth free oscillation model, the analytical model of inter-satellite ranging acceleration is modified, and the modified analytical model of inter-satellite ranging acceleration is determined.

[0111] Earth Free Oscillation Model: A model describing the overall elastic vibration of the Earth under the excitation of earthquakes and other stimuli. It includes parameters such as oscillation frequency, attenuation factor, and gravitational potential change coefficient, and is used to characterize the time-varying characteristics of the Earth's gravitational field.

[0112] Time-varying perturbations of Earth's gravitational field coefficients: Factors such as earthquakes cause changes in the spherical harmonic coefficients of Earth's gravitational field over time, which are divided into permanent correction terms (long-term stable changes after earthquakes) and damped oscillation terms (oscillating changes that decay over time).

[0113] The revised analytical model for inter-satellite ranging acceleration incorporates the time-varying perturbation of Earth's free oscillations, and can more accurately reflect the characteristics of inter-satellite ranging acceleration including the influence of Earth's free oscillations.

[0114] It should be noted that, based on the Earth free oscillation model, the time-varying perturbations of the Earth's gravitational field and the inter-satellite ranging acceleration formula are solved to obtain an analytical correction model of the inter-satellite ranging acceleration formula (i.e., the corrected analytical model of inter-satellite ranging acceleration).

[0115] Specifically, step 102 may include the following sub-steps:

[0116] S21. Solve for the time-varying perturbation of the gravitational field coefficients based on the Earth's free oscillation model;

[0117] S22. The analytical model of inter-satellite ranging acceleration is modified by using time-varying perturbations of gravitational field coefficients, and the modified analytical model of inter-satellite ranging acceleration is determined.

[0118] It should be noted that, based on the Earth's free oscillation model, the time-varying perturbation of the Earth's gravitational field coefficient after an earthquake-induced free oscillation is obtained, i.e., the time-varying perturbation of the gravitational field coefficient:

[0119] ;

[0120] in, It is the free oscillation harmonic number. It is the maximum harmonic number. It is the moment the earthquake occurred; For is the time-varying normalized spherical harmonic coefficient (cosine term), used to describe the time-varying perturbation characteristics of cosine-like spherical harmonic coefficients in the Earth's gravitational field after an earthquake; The normalized spherical harmonic coefficients (sine terms) vary with time and are used to describe the time-varying perturbation characteristics of sinusoidal spherical harmonic coefficients in the Earth's gravitational field after an earthquake. , Together, they constitute the time-varying perturbation of the Earth's gravitational field coefficient, reflecting the dynamic changes in the gravitational field after the Earth's free oscillations are triggered by an earthquake; For the initial normalized spherical harmonic coefficients (cosine terms), the inherent cosine-like spherical harmonic coefficients of the Earth's gravitational field before the earthquake; For the initial normalized spherical harmonic coefficients (sine term), the inherent sinusoidal spherical harmonic coefficients of the Earth's gravitational field before the earthquake; Let l be the perturbation amplitude of the l-th free oscillation harmonic on the m-th normalized spherical harmonic coefficient (cosine term) of the n-th order, used to quantify the change intensity of the l-th order harmonic induced by the earthquake on the cosine-like spherical harmonic coefficient of the Earth's gravitational field, l is the free oscillation harmonic number, representing the index of the l-th order harmonic component of the Earth's free oscillation, used to distinguish different oscillation components; Let be the perturbation amplitude of the l-th order free oscillation harmonic on the nth order m-th normalized spherical harmonic coefficients (sine term), used to quantify the intensity of the change in the l-th order harmonic induced by the earthquake on the sinusoidal spherical harmonic coefficients of the Earth's gravitational field. , The values ​​of are shown in Table 1, representing the permanent correction of the spherical harmonic coefficients; Let be a time function, representing the l-th order free oscillating harmonic as a function of time difference under the n-th order spherical harmonic. The decaying oscillation behavior is used to quantify the influence of the time dynamics of Earth's free oscillations on time-varying perturbations of the gravitational field.

[0121] Table 1 , The value of

[0122]

[0123] Furthermore, the time function is expressed as:

[0124] ;

[0125] in, It is the time function of free oscillation, which is the time response function corresponding to the l-th harmonic and the n-th spherical harmonic. It describes the decaying oscillation characteristics of the Earth's free oscillation over time and is a function of time t. Let be the decay function, representing the decay time characteristic of the l-th order free oscillation harmonic under the n-th order spherical harmonic. It is used to quantify the decay law of the amplitude of the Earth's free oscillation over time, reflecting the dissipation process of oscillation energy. , As the attenuation factor, The oscillation frequency; The time variable describes the dynamic time process of free oscillation.

[0126] Furthermore, after introducing a time-varying term, the analytical model of inter-satellite ranging acceleration (i.e., the modified analytical model of inter-satellite ranging acceleration) is as follows:

[0127] ;

[0128] in, and The same as DA and CA in the case of Earth's gravitational field.

[0129] The second term in the revised analytical model of inter-satellite ranging acceleration (representing the permanent change in the gravitational acceleration difference between inter-satellites after the earthquake):

[0130] ;

[0131] Where m and k are auxiliary parameters for spherical harmonic expansion and orbital perturbation analysis, used to characterize the complex distribution characteristics of the Earth's gravitational field and satellite orbits, and their value range is limited by the truncation order N; The amplitude of the permanently altered component, which characterizes the magnitude of the permanently altered component of the interstellar gravitational acceleration difference, is determined by factors such as the spherical harmonic coefficients of the permanent perturbation of the Earth's gravitational field. The combined angle of the permanently changed part varies with time t and is composed of angle parameters such as Earth's rotation and satellite orbit, describing the dynamic characteristics of the angle of the permanently changed part. The permanent phase shift term is determined by the inherent characteristics of the Earth's gravitational field and the satellite's orbit, and is a phase shift term of the permanently altered component.

[0132] ;

[0133] ;

[0134] ;

[0135] ;

[0136] ;

[0137] in, The amplitude of the cosine component of the permanently changed part is the amplitude of the cosine term in the permanently changed component. The amplitude of the sinusoidal component of the permanently altered part is the amplitude of the sinusoidal term in the permanently altered component; m is the spherical harmonic order; n is the order of the spherical harmonic expansion, which characterizes the complexity of the spatial distribution of the Earth's gravitational field; n1 and n2 are the upper and lower limits of the summation of the spherical harmonic orders, which help determine the summation range of the spherical harmonic expansion; L is the maximum harmonic number, the maximum value of the free oscillation harmonic number, which determines the accuracy of the model. To align with the semi-major axis of the satellite orbit Track inclination Angle of satellite to Earth And a function related to the harmonic number l, used to correlate the permanent changes in the Earth's gravitational field perturbation and the interstellar acceleration difference; Let be the perturbation amplitude of the cosine-type spherical harmonic coefficients of the nth order spherical harmonic, describing the intensity of the change in cosine-type spherical harmonic coefficients induced by the earthquake; Let be the perturbation amplitude of the sinusoidal spherical harmonic coefficients of the nth order spherical harmonic, describing the intensity of the change in sinusoidal spherical harmonic coefficients induced by the earthquake.

[0138] The third term in the corrected inter-satellite ranging acceleration analytical model (representing the decaying oscillation component of the inter-satellite gravitational acceleration difference after the earthquake):

[0139] ;

[0140] ;

[0141] ;

[0142] ;

[0143] ;

[0144] Where N is the upper limit of the summation of spherical harmonic orders, which determines the accuracy of the model; The combined amplitude of the l-th harmonic, the n-th spherical harmonic, and parameters m and k is synthesized from the amplitudes of the cosine and sine components. The positive combination angle under the l-th harmonic varies with time t, integrating the time dynamics of free oscillation frequency, Earth's rotation, and satellite revolution; The inherent phase of the l-th harmonic, n-th spherical harmonic, and parameters m and k is determined by the ratio of the sine and cosine components and is the phase offset term of the damped oscillation component. The reverse combination angle under the lth harmonic varies with time t, integrating the time dynamics of free oscillation frequency, Earth's rotation, and satellite revolution. The amplitude of the cosine component under the l-th harmonic, n-th spherical harmonic, and parameters m and k is related to the cosine perturbation coefficient of the gravitational field. The amplitude of the sinusoidal component under the l-th harmonic, n-th spherical harmonic, and parameters m and k is related to the sinusoidal perturbation coefficient of the gravitational field.

[0145] It is worth mentioning that the Earth's gravitational field model and satellite orbital element parameters in this embodiment can be freely selected, thus making it applicable to satellite orbital element representations for all Earth's gravitational fields.

[0146] For example, the parameters of the Earth's free oscillation mode are calculated using the open-source MINOS program: considering an earthquake of magnitude 6.0 that occurs 30 days after the initial time, the period of the Earth's free oscillation mode excited by the earthquake is obtained. Attenuation factor and the coefficient of change of Earth's gravitational potential and Earthquake-induced free oscillation mode period Attenuation factor The specific parameters are shown in Table 2:

[0147] Table 2 , parameters

[0148]

[0149] In this embodiment, based on the Earth's free oscillation model, the time-varying perturbation of the Earth's gravitational field coefficient after the earthquake-induced Earth's free oscillation is obtained; after introducing the time-varying term of the Earth's gravitational field coefficient, the time-varying correction of the inter-satellite ranging acceleration is obtained. Based on the analytical expression of the inter-satellite ranging acceleration and the time-varying correction, the analytical model of the inter-satellite ranging acceleration is obtained.

[0150] Step 103: When the satellite orbit parameters, simulation time series and Earth free oscillation mode parameters are received, the modified inter-satellite ranging acceleration analytical model is used to calculate the ranging acceleration signals between multiple satellites based on the satellite orbit parameters, simulation time series and Earth free oscillation mode parameters.

[0151] Satellite orbital parameters: Key parameters describing the orbital characteristics of a satellite around the Earth, including the semi-major axis, orbital inclination, orbital frequency, and initial phase, used to determine the satellite's spatial position and motion. See also... Figure 2 The satellite orbital parameters of satellite 1 (SC1, Spacecraft 1), satellite 2 (SC2, Spacecraft 2), and satellite 3 (SC3, Spacecraft 3) differ in that they have different phase differences, with values ​​of 0°, 120°, and -120° respectively. The other parameters are the same.

[0152] Simulation time series: A set of time points arranged at fixed time intervals, covering the complete time range from before the earthquake to the end of the observation, used to characterize the dynamic changes of physical quantities over time.

[0153] Earth Free Oscillation Mode Parameters: Core parameters characterizing the Earth's free oscillation characteristics, including free oscillation harmonics, oscillation frequency, damping ratio, decay time function, and disturbance amplitude, used to quantify time-varying disturbances in the Earth's gravitational field caused by earthquakes.

[0154] Inter-satellite ranging acceleration signals: These are the second derivative signals of the distance between two satellites with respect to time. They directly reflect the acceleration characteristics of the relative motion between satellites and are core data for satellite ranging accuracy analysis and gravitational field inversion. Ranging acceleration signals between multiple satellites include those between satellite 1 and satellite 2, satellite 2 and satellite 3, and satellite 1 and satellite 3.

[0155] It should be noted that when satellite orbital parameters, simulation time series, and Earth free oscillation mode parameters are received, a modified inter-satellite ranging acceleration analytical model is used. The orbital semi-major axis and orbital inclination from the satellite orbital parameters are substituted into the orbital-related function terms of the model. The simulation time series corresponds to the time variables in the model to characterize the dynamic change process. The Earth free oscillation mode parameters (including harmonics, oscillation frequency, attenuation factor, etc.) empower the time-varying perturbation terms of the model. Through the coupling calculation of the original basic terms in the model, the permanent changes after the earthquake, and the attenuated oscillation part, the ranging acceleration signal between multiple satellites containing the influence of Earth free oscillation is finally obtained. This signal can be directly used for subsequent satellite ranging accuracy calibration or analysis of the time-varying characteristics of the Earth's gravitational field.

[0156] It is worth mentioning that the analytical model in this embodiment assumes that the Earth rotates at a constant speed. The satellite orbital parameters selected in the subsequent steps are shown in Table 3. The 12th order EGM2008 is used as the Earth's gravitational field model, and the initial Greenwich mean sidereal time is set to the actual initial Greenwich mean sidereal time at the initial time UTC 00:00:000 on June 6, 2004.

[0157] Table 3 Satellite orbital parameters

[0158]

[0159] Furthermore, step 103 may include the following sub-steps:

[0160] S31. Simplify the order of the modified inter-satellite ranging acceleration analytical model and determine the order-simplified inter-satellite ranging acceleration analytical model.

[0161] S32. The simplified inter-satellite ranging acceleration analytical model is used to solve for satellite acceleration based on satellite orbital parameters, simulation time series and Earth free oscillation mode parameters, and outputs ranging acceleration signals between multiple satellites.

[0162] It should be noted that the order of the modified inter-satellite ranging acceleration analytical model was simplified by removing high-order spherical harmonic terms and low-contribution free oscillation harmonic components that have little impact on the calculation results. Using this simplified model, combined with satellite orbital parameters, simulation time series, and Earth free oscillation mode parameters received uniformly through a standardized parameter input / output interface, multiple satellite ranging acceleration signals were output. These signals were processed using the Time Delay Interferometry (TDI) method and calculated under the same parameter settings. The resulting Earth oscillation signal was compared and verified with the simulated Earth oscillation signal obtained through a high-precision numerical orbit simulation program. Deviation analysis confirmed the rationality of the order simplification, ensuring that core accuracy was preserved while simplifying computational complexity, providing efficient and reliable data support for subsequent applications.

[0163] Step 104: Select the target ranging acceleration signal among the ranging acceleration signals of each satellite, and use the time delay interferometry method to extract the earth oscillation signal from the target ranging acceleration signal, and output the target earth oscillation signal.

[0164] It should be noted that, by combining satellite orbital parameters (high orbit), simulation time series, and Earth free oscillation mode parameters, the analytical model order is simplified and processed by TDI. Then, Fourier transform and high-pass filter are used to generate a fast waveform of Earth free oscillation expressed as inter-satellite ranging acceleration. The degree of conformity between the traditional numerical simulation waveform and the analytical model waveform is compared, and the Earth free oscillation mode is extracted.

[0165] Among them, TDI, or time-delayed interferometry, is used to construct a virtual equal-arm length interference, which removes laser phase noise while retaining the desired signal. The TDI empty channel is insensitive to gravitational wave response and can effectively separate the Earth's free oscillation signal (i.e., the Earth oscillation signal) from the signal.

[0166] Specifically, step 104 may include the following sub-steps:

[0167] S41. Delay the target ranging acceleration signal optically and output the target ranging acceleration signal after optical delay.

[0168] S42. Expand the target ranging acceleration signal after optical path delay and determine the expanded target ranging acceleration signal.

[0169] S43. The laser phase noise in the deployed target ranging acceleration signal is sorted and matched to determine the initial Earth oscillation signal;

[0170] S44. Perform a Fourier transform on the initial Earth oscillation signal and filter it using a high-pass filter to output the target Earth oscillation signal.

[0171] Optical path delay: Simulates the time delay process of laser propagation in the inter-satellite interferometer arm. The delay parameters are set according to the length of the interferometer arm, the speed of light and the relative motion of the satellites to make the signal more closely match the actual propagation physical process.

[0172] The unfolded target ranging acceleration signal: The signal after optical path delay is decomposed into multiple components (such as earth oscillation term, noise term, etc.) according to the time dimension and physical causes, which facilitates subsequent targeted processing.

[0173] Laser phase noise: Random fluctuations in the phase of the laser itself, caused by the characteristics of the laser source or the influence of the propagation environment, can mask the true characteristics of the Earth's oscillation signal.

[0174] Initial Earth Oscillation Signal: After laser phase noise sorting, pairing and elimination, the signal that initially retains the core information of Earth's free oscillation may still contain a small amount of residual interference.

[0175] It should be noted that optical path delay is applied to the target ranging acceleration signal. Based on the propagation path length of the laser in the interferometer arm between satellites and the speed of light, a matching delay parameter is set to simulate the time delay effect of the actual laser propagation, and the target ranging acceleration signal after optical path delay is output. Further, the target ranging acceleration signal after optical path delay is expanded according to time sequence and signal components, decomposing the Earth oscillation contribution, laser phase noise, and other environmental interference components to determine the expanded target ranging acceleration signal. For each expanded signal component, it is sorted and paired according to the propagation delay law of laser phase noise and signal correlation characteristics. Most of the laser phase noise interference is eliminated through noise cancellation or separation algorithms to determine the initial Earth oscillation signal that initially retains the core information of Earth oscillation. Fourier transform is performed on the initial Earth oscillation signal to convert the time-domain signal into a frequency-domain signal to highlight the characteristic frequency components corresponding to the Earth's free oscillation. Then, a high-pass filter with a preset reasonable cutoff frequency is used to filter out low-frequency background noise and residual interference signals, finally outputting a target Earth oscillation signal with high purity that accurately reflects the time-varying characteristics of the Earth's free oscillation.

[0176] Specifically, regarding the principle of time delay interference processing methods, such as... Figure 3 As shown, in a Michelson interferometer with unequal arm lengths, the signal detected at the photodetector can be expressed as:

[0177] ;

[0178] ;

[0179] in, The output signal of the first photoelectric detector (PD) varies with time t and includes gravitational wave phase shift, laser phase noise, and secondary noise. The output signal of the second photodetector varies with time t and includes gravitational wave phase shift, laser phase noise, and secondary noise. = 2L1 / c, = 2L2 / c represents the time it takes for the laser to travel back and forth between the two arms, where L1 is the length of the first arm of the laser interferometer and L2 is the length of the second arm. , These represent the phase shifts caused by gravitational waves in the first and second arms, respectively. This represents the laser phase noise, which varies with time t. , These represent the secondary noise introduced during the readings of the first and second photodetectors, respectively. Subtracting the two equations eliminates the noise in either equation. :

[0180] ;

[0181] right and Delaying for T2 and T1 respectively, we can obtain:

[0182] ;

[0183] ;

[0184] Subtracting the two equations above will eliminate the error. item:

[0185] ;

[0186] Subtracting again, constructing a combination of the form x(t), we finally obtain a signal that contains only the desired signal and other noise, with all laser phase noise removed:

[0187] ;

[0188] This is the output signal after time delay processing.

[0189] Furthermore, if we choose equal arm lengths, then the time it takes for the laser to travel back and forth through the two arms is equal, denoted as T. Then we have:

[0190] ;

[0191] In the formula, the two terms in the first bracket represent the optical path represented by the blue solid line, and the two terms in the second bracket represent the optical path represented by the black solid line. This is equivalent to constructing a virtual Michelson interferometer with equal arm length to naturally cancel out laser phase noise.

[0192] Two operators, “:” and “;”, are specifically defined to address laser phase noise. For example, the specific explanation is as follows:

[0193] ;

[0194] in, This is the signal after the laser phase noise has been delayed by the j-th fixed-length interferometer arm (the operator ":" indicates a constant delay on the variable it acts on, the specific delay amount is equal to the arm length represented by the number after the operator divided by the speed of light). This is the fixed length of the j-th laser interferometer arm (such as the inherent length of a certain arm of a laser interferometer). The speed of light; Let be the propagation time delay of the laser in the j-th fixed-length interferometer arm; t is a time variable describing the temporal dynamics of the laser phase noise. Let be the total propagation time delay of the laser in the k-th and j-th fixed-length interferometer arms; Let be the time-varying length of the j-th laser interferometer arm (e.g., the length changes with time t due to gravitational waves, satellite orbit changes, etc.). The length of the k-th laser interferometer arm varies with time t (e.g., due to gravitational waves, changes in satellite orbit, etc.). Let be the time-varying propagation time delay of the laser in the j-th time-varying length interferometer arm; This is the signal after the laser phase noise has been delayed by the total time of the k-th and j-th fixed-length interferometer arms; This is the signal after the laser phase noise has been delayed by the time-varying length of the j-th interferometer arm (the operator ";" indicates a delay of the variable it acts on, which varies with time; the delay is equal to the length of the laser link at that moment, represented by the number after the operator, divided by the speed of light). The signal is the laser phase noise after the total time-varying time delay of the k-th and j-th time-varying length interferometer arms.

[0195] The derivation of the TDI formula uses the delay operator D, which is defined as follows:

[0196] ;

[0197] or

[0198] ;

[0199] in, This is the signal after the laser phase noise has been delayed by the i-th interferometer arm; For the i-th interferometer arm, there is a delay operator used to represent the time delay operation of laser propagation in the i-th interferometer arm; For the j-th interferometer arm, there is a delay operator used to represent the time delay operation of laser propagation in the j-th interferometer arm; This is a composite operation that first applies a time delay operation to the signal in the i-th interferometer arm and then applies a time delay operation to the j-th interferometer arm, used to describe the total time delay composite operation of the laser propagating continuously in the i-th and j-th interferometer arms; This is the signal after the laser phase noise has been delayed by the total time of the i-th and j-th interferometer arms; To address laser phase noise The i-th interferometer arm delay operator is used to... Apply a time delay operation to the i-th interferometer arm.

[0200] The first step in subtracting laser phase noise using TDI (Through-Diverter) interferometry requires constructing intermediate variables using scientific interferometry signals, verification quality interferometry signals, and reference interferometry signals. :

[0201] ;

[0202] ;

[0203] in, , This is an intermediate variable constructed in the TDI process, used for subsequent calculations to subtract laser phase noise, and serves as a transitional quantity in signal combination processing; , An intermediate processing signal, composed of scientific signals, reference signals, etc., is used to construct... The basis of a series of variables, used to integrate information from multi-channel signals; For scientific interference signals (such as scientific channel interference signals for gravitational wave detection), it includes target physical signals (such as gravitational waves) and noise interference; To test the mass interference signal (interference signal related to the motion of the test mass), it is used to assist signal processing to extract effective physical information; , , , It serves as a reference interference signal (or auxiliary interference signal) to provide a calibration or reference standard for signal processing; , , , It is a time delay quantity, reflecting the time shift of the laser propagation or signal in the interferometer arm, which varies with time t (e.g., affected by gravitational waves or equipment dynamics). , These are delay operators, representing the application of time delay operations to the second and third interferometer arms of the signal, respectively, used to characterize the time delay effect of the signal passing through the corresponding interferometer arm.

[0204] Furthermore, Optical platform displacement noise can be deducted ,and This further eliminates half of the laser phase noise, namely all laser phase noise with “′”, namely p1′, p2′, p3′ and all their delay terms.

[0205] Based on the equilateral triangle configuration of the detector constellation, the inter-satellite distances are equal, so the time it takes for the laser to travel back and forth between the two arms is equal.

[0206] To avoid excessively long formulas and to emphasize the key aspect of laser phase noise, this invention temporarily ignores secondary noise and clock noise in the derivation. It can be approximated as:

[0207] ;

[0208] ;

[0209] At this point, the formula only includes laser phase noise and gravitational wave signals; various combinations of TDI are then used. A linear combination of the laser's phase noise and its delay term is used to construct a virtual equal-arm-length interference to eliminate laser phase noise while preserving the desired signal. In the formula, , The phase shift signal caused by gravitational waves corresponds to the modulation of the laser phase by gravitational waves in different interference channels; The signal is the laser phase noise of MOSA2 after being delayed by three interferometer arms; The laser phase noise of MOSA1; The signal is the laser phase noise of MOSA3 after being delayed by the 2' interferometer arm. MOSA stands for Movable Optical Sub-Assembly.

[0210] Based on the above, such as Figures 4-5 This invention utilizes the ranging acceleration signals between satellite 1 and satellite 2, between satellite 2 and satellite 3, and between satellite 1 and satellite 3 output from the modified inter-satellite ranging acceleration analytical model, combined with the TDI-Michelson combination formula, and uses TDI-X, TDI-Y, and TDI-Z to represent the results, as follows:

[0211] ;

[0212] in, The ranging acceleration signal between satellite 1 and satellite 3 represents the output signal of the TDI-X combination. It is used to extract the effective signal (such as time-varying gravitational field or Earth free oscillation signal) related to the X direction in the ranging acceleration between satellites after eliminating laser phase noise. The ranging acceleration signal between satellite 1 and satellite 2 represents the output signal of the TDI-Y combination, which is used to extract the effective signal related to the Y direction in the ranging acceleration between satellites after eliminating laser phase noise. The ranging acceleration signal between satellite 2 and satellite 3 represents the output signal of the TDI-Z combination, which is used to extract the effective signal related to the Z direction in the ranging acceleration between satellites after eliminating laser phase noise; For MOSA 2' The signal after the intermediate variable is delayed by the 3', 2', 2' interferometer arms; The signal is the intermediate variable at MOSA1 after being delayed by the interferometer arms 2 and 2'. The signal is the intermediate variable at MOSA3 after being delayed by the 2' interferometer arm; For MOSA 1' Intermediate variable; The signal at MOSA3 is delayed by the 2', 3', and 3 interferometer arms; The signal is the intermediate variable at MOSA1 after being delayed by the 3' and 3' interferometer arms; For MOSA 2' The signal after the intermediate variable is delayed by three interferometer arms; This is an intermediate variable at MOSA1; For MOSA 3' The signal after the intermediate variable is delayed by the 1', 3', and 3' interferometer arms; The signal of the intermediate variable at MOSA2 after being delayed by the 3' and 3' interferometer arms; The signal is the intermediate variable at MOSA1 after being delayed by the 3' interferometer arm; For MOSA 2' Intermediate variable; The signal at MOSA1 is delayed by the 3', 1', and 1 interferometer arms; For MOSA 2' The signal after the intermediate variable is delayed by interferometer arms 1' and 1'; For MOSA 3' The signal after the intermediate variable is delayed by one interferometer arm; This is an intermediate variable at MOSA2; For MOSA 1' The signal after the intermediate variable is delayed by the 2', 1', and 1' interferometer arms; The signal of the intermediate variable at MOSA3 after being delayed by the interferometer arms 1 and 1'; The signal is the intermediate variable at MOSA2 after being delayed by the 1' interferometer arm; For MOSA 3' Intermediate variable; The signal at MOSA2 is delayed by interferometer arms 1', 2', and 2; For MOSA 3' The signal after the intermediate variable is delayed by the 2' and 2' interferometer arms; For MOSA 1' The signal after the intermediate variable is delayed by two interferometer arms; This is an intermediate variable at MOSA3.

[0213] Furthermore, among the ranging acceleration signals between satellite 1 and satellite 2, between satellite 2 and satellite 3, and between satellite 1 and satellite 3, any one signal is selected as the target ranging acceleration signal. This invention uses... For example:

[0214] ;

[0215] in The content within the first set of parentheses in the corresponding expression is The delay combination of laser number 1 with respect to the other lasers, and the content in the second parenthesis is the delay combination of laser number 1 with respect to the other lasers.

[0216] by For example:

[0217] ;

[0218] This expression represents: For L3, L2 and The optical path is delayed. Among other things, For MOSA 2' The phase shift signal caused by the gravitational wave measured at the location; The signal is the laser phase noise of MOSA1 after being delayed by the 3' interferometer arm; This is the laser phase noise signal of MOSA2; This is the signal after the above three signals are combined and delayed by the 3', 2', and 2' interferometer arms.

[0219] by For example:

[0220] ;

[0221] This expression represents: For L2 and The optical path is delayed. Among other things, The phase shift signal caused by the gravitational wave measured at MOSA1; The signal is the laser phase noise of MOSA2 after being delayed by three interferometer arms; This is the laser phase noise signal of MOSA1; This is the signal after the above three signals are combined and delayed by the 2' and 2' interferometer arms;

[0222] by For example:

[0223] ;

[0224] This expression represents: right The optical path is delayed. Among other things, The phase shift signal caused by the gravitational wave measured at MOSA3; The signal is the laser phase noise of MOSA1 after being delayed by two interferometer arms; This is the laser phase noise signal of MOSA3; The signal is the result of the combination of the three signals mentioned above, after being delayed by the 2' interferometer arm.

[0225] right Expanding, we get:

[0226] ;

[0227] Further refine the pairings:

[0228] ;

[0229] in, The signal is the laser phase noise of MOSA1 after being delayed by interferometer arms 3', 3', 2', 2'. The signal is the laser phase noise of MOSA3 after being delayed by the 2', 3', and 3 interferometer arms; The signal is the laser phase noise of MOSA1 after being delayed by the 3' and 3' interferometer arms; The signal is the laser phase noise of MOSA2 after being delayed by three interferometer arms; This is the laser phase noise signal of MOSA1; The signal is the phase shift caused by the gravitational wave at MOSA2, and is delayed by the interferometer arms 3, 2, and 2'. The signal is the phase shift caused by the gravitational wave at MOSA1, after being delayed by the interferometer arms 2 and 2'. The signal is the phase shift caused by the gravitational wave at MOSA3, and is delayed by the 2' interferometer arm.

[0230] The above equation shows that laser phase noise almost always occurs in pairs, and except for the two terms within the first set of parentheses, the others can cancel each other out. Therefore, we can obtain... The final expression is:

[0231] ;

[0232] for and Similarly, the combined expression ultimately retains only the gravitational wave signal and has no laser phase noise term.

[0233] Furthermore, for the TDI-X combination, because:

[0234] ;

[0235] in, To delay the gravitational wave response signal by a time factor of T; This is the gravitational wave response signal; is the time shift factor; i is the imaginary unit; f is the frequency; T is the time delay; F denotes the Fourier transform of the function. For a Michelson interferometer with equal arm lengths, assuming all delay times are equal, the Fourier transform is:

[0236] ;

[0237] in, , , It is a time shift factor; This is the delay time; , This is the gravitational wave response signal; The difference is the gravitational wave response signal; This is the initial Earth oscillation signal after Fourier transform.

[0238] Based on the above, the transfer function of TDI-X is:

[0239] ;

[0240] in, For TDI response transfer function; The output is an interference signal with unequal arm lengths in the frequency domain.

[0241] The same applies to TDI-Y and TDI-Z. Therefore, after TDI processing, the signal contains only the desired signal and other noise, while laser phase noise is completely eliminated.

[0242] Finally, a high-pass filter is used to process the data obtained from numerical simulation and analytical model respectively, and the Earth free oscillation waveform expressed in terms of inter-satellite ranging acceleration is obtained, that is, the target Earth oscillation signal.

[0243] It is worth mentioning that, since the filter will truncate the data before and after it when it is working, the earthquake time is set to 5000 seconds after the earliest time (177300s) that the filter can tolerate, and the data duration is set to allow high-pass filtering to produce a data segment of 5000 seconds before the earthquake plus 1 day after the earthquake.

[0244] In this embodiment, data processing is performed using time-delay interferometry (TDI) by combining satellite orbital parameters, simulated time series, and Earth free oscillation mode parameters, and a high-pass filter is used to generate a fast waveform of Earth free oscillation expressed as inter-satellite ranging acceleration.

[0245] For comparison of technical effectiveness, existing technologies can be used as a reference. Currently, in data processing and noise assessment for space gravitational wave missions, evaluating the interference of the Earth-Moon system's gravitational field on inter-satellite ranging acceleration relies entirely on high-precision numerical calculations. While these methods are highly accurate, the calculation process is complex and time-consuming, making it difficult to meet the needs of rapid noise assessment and elimination in missions, especially when dealing with global, multimodal, time-varying signals such as earthquake-induced free oscillations of the Earth.

[0246] To address the above problems, this invention proposes a method for rapidly generating Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection, such as... Figure 6 As shown, based on the equilateral triangle configuration of the detector constellation and the assumption of a reference circular orbit, the spherical harmonic function model of the Earth's gravitational field is expressed as a function model of the satellite orbital elements through coordinate transformation, resulting in the ranging acceleration formula between the three satellites. Based on the Earth's free oscillation model, the time-varying perturbation of the Earth's gravitational field and the time-varying correction of the inter-satellite ranging acceleration formula are solved, resulting in an analytical correction model for the inter-satellite ranging acceleration formula. Combining satellite orbital parameters and simulation time series, and based on the principles of eliminating laser frequency noise through time-delay interferometry and the insensitivity of TDI empty channel combinations to gravitational wave response, the ranging acceleration data between the three satellites are combined and processed to quickly generate an Earth free oscillation waveform based on the analytical model. This waveform can be directly used for scientific data processing. The matching degree between the rapidly generated waveform and the numerical simulation results can be analyzed. In addition, it can also be used to extract Earth free oscillation modes.

[0247] In summary, this invention establishes a unified analytical model of the Earth's gravitational field, enabling the rapid generation of the Earth's free oscillation waveform represented by inter-satellite ranging acceleration. This effectively overcomes the problems of low computational efficiency and difficulty in evaluating and eliminating noise in traditional numerical simulation methods.

[0248] Furthermore, this invention significantly shortens the generation time of the Earth's free oscillation waveform by transforming the complex numerical simulation problem into analytical calculation, thereby improving computational efficiency. Through the above process, this method rapidly generates the Earth's free oscillation waveform while ensuring consistency with high-precision numerical simulation results, significantly reducing the demand for computational resources. Therefore, it can be widely applied to rapid noise assessment and real-time data processing in space gravitational wave detection missions.

[0249] In this embodiment of the invention, a method for rapidly generating Earth free oscillation waveforms for geocentric orbit space gravitational wave detection is provided. The method acquires Earth's gravitational field parameters and instantaneous inter-satellite distances, and uses the Koula linear perturbation method to construct an analytical model of inter-satellite ranging acceleration based on these parameters. The analytical model of inter-satellite ranging acceleration is then modified based on the Earth free oscillation model to determine the modified analytical model. When satellite orbital parameters, simulation time series, and Earth free oscillation mode parameters are received, the modified analytical model of inter-satellite ranging acceleration is used to generate the waveforms based on these parameters. The invention calculates ranging acceleration signals between multiple satellites; selects a target ranging acceleration signal from among the ranging acceleration signals of each satellite, and extracts the Earth oscillation signal from the target ranging acceleration signal using the time-delay interferometry method, outputting the target Earth oscillation signal; based on the above scheme, this invention breaks through the limitations of traditional reliance on high-precision numerical calculations by innovatively combining the Koula linear perturbation method with analytical model construction, transforming the complex problem of generating Earth free oscillation waveforms into efficient analytical calculations. Combined with targeted time-varying perturbation correction and signal purification using the time-delay interferometry method, the calculation process is greatly simplified, the waveform generation time is shortened, and the calculation efficiency of Earth free oscillation waveforms is significantly improved.

[0250] The conformity between the waveforms obtained from traditional numerical calculations and those from analytical models is compared to verify the correctness and computational accuracy of the analytical model. Furthermore, the obtained waveforms are used to extract the Earth's free oscillation modes, enabling the rapid generation of Earth's free oscillation waveforms based on the analytical model. Specifically, refer to... Figure 7 , Figure 7 To verify the simplified inter-satellite ranging acceleration analytical model of the present invention, the following steps are also included:

[0251] Step 701: Obtain numerical simulation data, and use Bayesian analysis and MCMC parameter estimation methods to extract estimated values ​​of Earth's free oscillation parameters from the numerical simulation data;

[0252] Step 702: Using the simplified inter-satellite ranging acceleration analytical model, the simulated ranging acceleration signal is output based on the estimated values ​​of satellite orbital parameters, simulation time series, and Earth free oscillation parameters.

[0253] Step 703: Use the time-delay interferometry method to extract the Earth oscillation signal from the simulated ranging acceleration signal and determine the simulated Earth oscillation signal;

[0254] Step 704: Perform Fourier transform on the simulated Earth oscillation signal and filter it using a high-pass filter to determine the target simulated Earth oscillation signal;

[0255] Step 705: Using a matching factor to measure the degree of curve conformity, the simplified inter-satellite ranging acceleration analytical model is verified based on the target simulated Earth oscillation signal and the target Earth oscillation signal, and the verification results are output.

[0256] It should be noted that after acquiring the numerical simulation data, Bayesian analysis and MCMC parameter estimation methods are used. By modeling and iteratively sampling the probability distribution of the Earth's free oscillation characteristics in the numerical simulation data, estimated values ​​of the Earth's free oscillation parameters are extracted from the numerical simulation data. First, the gravitational field changes caused by dynamic free oscillations are injected into the static Earth model. Based on this, numerical simulation is performed to output the orbital changes of the satellite affected by this effect. Then, the time-delay interferometry is used to process the simulated ranging acceleration signal to extract the simulated Earth oscillation signal containing only Earth free oscillation information. Next, the simulated Earth oscillation signal is Fourier transformed to convert it into a frequency domain signal. After filtering out low-frequency interference through a high-pass filter, the target simulated Earth oscillation signal is determined. Finally, a matching factor mechanism is used to measure the degree of curve conformity, calculating the matching degree between the target simulated Earth oscillation signal and the target Earth oscillation signal in amplitude, frequency, and phase. This verifies the accuracy and reliability of the analytical model, and outputs the verification results including the model error range and parameter confidence levels.

[0257] Bayesian analysis, in particular, is a statistical analysis method that uses Bayes' theorem, combined with prior knowledge and observational data, to infer the posterior probability distribution of parameters and is used to quantify the uncertainty of Earth's free oscillation parameters.

[0258] MCMC parameter estimation (Markov Chain Monte Carlo): A numerical method that approximates the posterior probability distribution of parameters by constructing a Markov chain and performing Monte Carlo sampling. It is used to extract estimated values ​​and confidence intervals of Earth's free oscillation parameters from numerical simulation data.

[0259] Numerical simulation data: Virtual data generated by numerical simulation software to simulate the Earth's free oscillations and satellite ranging acceleration response, used for model training and validation.

[0260] Simulated ranging acceleration signal: The simulated inter-satellite ranging acceleration signal is calculated by substituting satellite orbital parameters, simulation time series and estimated values ​​of Earth's free oscillation parameters into the simplified analytical model, and is used for simulation analysis.

[0261] Matching factor: A quantitative indicator that measures the degree of similarity between the simulated Earth oscillation signal and the target Earth oscillation signal in terms of amplitude, frequency, phase, etc. The closer the value is to 1, the higher the degree of similarity.

[0262] Validation results: The conclusions on the accuracy and reliability of the model are evaluated through indicators such as matching factors, including information such as model error range and parameter confidence, which are used to determine whether the model meets the application requirements.

[0263] It is worth mentioning that the matching factor mechanism introduced in this invention measures the degree of curve conformity. By comparing and analyzing the consistency of the waveform characteristics of the numerical simulation results with those of the analytical model's Earth's free oscillation waveform, the correctness and computational accuracy of the analytical model are verified. This mechanism is specifically as follows:

[0264] ;

[0265] Where, x num and x ana Representing numerical and analytical time-domain sequences respectively. The amplitude of the simulated Earth oscillation signal at the i-th sampling point (generated by the simplified analytical model, which includes the simulated response of the Earth's free oscillation). Let be the amplitude of the observed Earth oscillation signal at the i-th sampling point (such as a reference signal obtained from actual satellite observation or high-precision numerical simulation); M is the matching factor, used to quantify the degree of fit between the simulated Earth oscillation signal and the target Earth oscillation signal in dimensions such as amplitude, frequency, and phase. The value of M is between 0 and 1, with a better fit indicating a higher degree of conformity. The correctness and calculation accuracy of the analytical model are verified by comparing the waveform characteristics of the Earth's free oscillation waveforms from numerical simulation and analytical models; p and q are the start and end indices of the summation interval, defining the range of signal sampling points participating in the matching calculation (covering the complete characteristic period of Earth's free oscillation).

[0266] Furthermore, this invention uses Bayesian analysis and MCMC parameter estimation methods to extract estimated values ​​of Earth's free oscillation parameters from numerical simulation data, verifying the practicality of the analytical model.

[0267] The Bayesian formula used for parameter estimation is:

[0268] ;

[0269] in, The vector to be estimated represents the core parameters of Earth’s free oscillation (such as harmonic number, oscillation frequency, and disturbance amplitude), which is the target quantity to be inferred through Bayesian analysis and the MCMC method. This refers to already obtained data, such as observational signals of inter-satellite ranging acceleration, and simulation data generated by numerical simulation, which are used to infer parameters. The basis for observation; It is signal background information, covering prior knowledge such as laser interferometry principles and satellite orbit dynamics, providing theoretical and scenario support for parameter estimation; For posterior probabilities, given observed data and background information At that time, the Earth's free oscillation parameter vector to be estimated The probability distribution reflects the parameters after combining data and prior knowledge. The degree of credibility (such as the probability distribution of oscillation frequency, amplitude, attenuation factor, etc.); As evidence (marginal likelihood), in the context information Below, observation data The total probability of occurrence is over all possible parameters. The weighted average is used to normalize the posterior probability; Let be the likelihood function, given the Earth's free oscillation parameters. and background information At that time, the observed data The probability of occurrence (such as inter-satellite ranging acceleration signals, numerical simulation data) reflects the parameter. With data The degree of compatibility; For prior probability, when only background information is known... (e.g., geophysical models, satellite orbit theories, etc.) regarding the parameters of Earth's free oscillations The probability distribution reflects prior knowledge of the parameters (such as assumptions about the parameter range based on theory).

[0270] Assuming a prior uniform distribution and that the noise is Gaussian and stationary, the likelihood function is:

[0271] ;

[0272] in, It is the likelihood function; This represents the wave pattern of Earth's free oscillation. This refers to the actual measured quantity.

[0273] The specific definition of the sign of the inner product is as follows: for two signals g and h, we have... Indicates the inner product:

[0274] ;

[0275] The Fourier transform of the signal; The conjugate of the Fourier transform of the signal; The noise one-sided power spectral density; To take the real part; For frequency.

[0276] In summary, this invention employs an integrated sampling (MCMC) algorithm for posterior distribution sampling to derive estimated values ​​of the Earth's free oscillation mode parameters. This enables the rapid generation of Earth's free oscillation waveforms based on an analytical model.

[0277] It is worth mentioning that, based on the parameters shown in Tables 1, 2, and 3 of Embodiment 1, this invention retains the third order of the Earth's gravitational field and the third order of the Earth's free oscillation modes in the analytical model, while keeping the harmonic number to 2. In this specific embodiment, generating the unfiltered analytical waveform takes only about 2 minutes, and the time-domain waveform matching factor M between the numerical simulation and the analytical model is >99%, indicating that the Earth's free oscillation waveform generated by the analytical model is fast, accurate, and computationally precise. In this specific example, taking the OS2 Earth free oscillation mode as an example, six free oscillation modes that split due to the Earth and satellite rotation were extracted, and the oscillation frequencies of the split modes were predicted, demonstrating that the Earth's free oscillation waveform generated by the analytical model has good practicality.

[0278] In this embodiment of the invention, the present invention effectively solves the technical bottleneck of existing methods for generating Earth free oscillation waveforms, which suffer from complex and time-consuming calculation processes, making it difficult to meet the needs of rapid noise assessment and elimination, resulting in low computational efficiency. Its core technical effects are reflected in the following: First, by eliminating low-contribution terms through a simplified inter-satellite ranging acceleration analytical model, the computational complexity is significantly reduced, and the computation time is decreased. Then, by combining Bayesian analysis and MCMC parameter estimation methods, the Earth free oscillation parameters are extracted quickly and accurately, avoiding the iterative inefficiency caused by redundant parameters in traditional methods. Subsequently, a time-delay interferometry method is used to specifically extract the Earth oscillation signal from the simulated ranging acceleration signal, combined with Fourier transform and high-pass filtering. The system employs efficient noise separation and processing to rapidly assess and eliminate laser phase noise and low-frequency interference, precisely matching the task's need for rapid noise handling. Finally, a matching factor measurement mechanism achieves an efficient closed-loop model validation process. The entire technical workflow, from parameter extraction, signal generation, noise processing to model validation, forms a highly efficient connection. While ensuring the accuracy of Earth's free oscillation waveform generation, it significantly improves overall computational efficiency, overcoming the existing method's challenge of balancing complexity and time consumption. This results in efficient, accurate, and noise-fast noise processing-adaptive Earth free oscillation waveform generation, providing efficient and reliable technical support for subsequent applications such as geophysical characteristic analysis and satellite ranging accuracy calibration. This demonstrates systematic R&D innovation from model optimization to workflow design.

[0279] Please see Figure 8 , Figure 8 This is a structural block diagram of a rapid generation system for Earth's free oscillation waveforms for geocentric orbital space gravitational wave detection, provided in Embodiment 3 of the present invention.

[0280] This invention provides a rapid generation system for Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection, comprising:

[0281] The acquisition module 801 is used to acquire the Earth's gravitational field parameters and the instantaneous inter-satellite distance, and to construct an analytical model of inter-satellite ranging acceleration based on the Earth's gravitational field parameters and the instantaneous inter-satellite distance using the Koula linear perturbation method.

[0282] The correction module 802 is used to correct the analytical model of inter-satellite ranging acceleration based on the Earth free oscillation model, and to determine the corrected analytical model of inter-satellite ranging acceleration.

[0283] The calculation module 803 is used to calculate the ranging acceleration signal between multiple satellites based on the satellite orbit parameters, simulation time series and Earth free oscillation mode parameters when satellite orbit parameters, simulation time series and Earth free oscillation mode parameters are received.

[0284] The output module 804 is used to select the target ranging acceleration signal among the ranging acceleration signals of each satellite, and to extract the earth oscillation signal from the target ranging acceleration signal using the time delay interferometry method, and output the target earth oscillation signal.

[0285] In one optional system embodiment, it further includes:

[0286] The first module is used to acquire numerical simulation data. It uses Bayesian analysis and MCMC parameter estimation methods to extract estimated values ​​of Earth's free oscillation parameters from the numerical simulation data.

[0287] The second module is used to output the simulated ranging acceleration signal based on the estimated values ​​of satellite orbit parameters, simulation time series and Earth free oscillation parameters using the simplified inter-satellite ranging acceleration analytical model.

[0288] The third module is used to extract the Earth oscillation signal from the simulated ranging acceleration signal using the time-delay interferometry method, and to determine the simulated Earth oscillation signal.

[0289] The fourth module is used to perform Fourier transform on the simulated Earth oscillation signal and filter it through a high-pass filter to determine the target simulated Earth oscillation signal.

[0290] The fifth module is used to verify the simplified inter-satellite ranging acceleration analytical model based on the target simulated Earth oscillation signal and the target Earth oscillation signal using a matching factor to measure the degree of curve conformity, and outputs the verification results.

[0291] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system and modules described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0292] This invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program; when the computer program is executed by the processor, the processor performs the steps of the method for rapidly generating free oscillation waveforms of the Earth for geocentric orbit space gravitational wave detection as described in any of the above embodiments.

[0293] This invention also provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the method for rapidly generating Earth free oscillation waveforms for geocentric orbit space gravitational wave detection as described in any of the above embodiments.

[0294] This invention also provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of the method for rapidly generating Earth free oscillation waveforms for geocentric orbit space gravitational wave detection as described in any of the above embodiments.

[0295] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0296] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0297] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for rapidly generating Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection, characterized in that, include: The Earth's gravitational field parameters and instantaneous inter-satellite distances are obtained, and an analytical model of inter-satellite ranging acceleration is constructed based on the Earth's gravitational field parameters and instantaneous inter-satellite distances using the Koula linear perturbation method. The analytical model of inter-satellite ranging acceleration is modified based on the Earth free oscillation model, and the modified analytical model of inter-satellite ranging acceleration is determined. When satellite orbit parameters, simulation time series, and Earth free oscillation mode parameters are received, the modified inter-satellite ranging acceleration analytical model is used to calculate the ranging acceleration signals between multiple satellites based on the satellite orbit parameters, the simulation time series, and the Earth free oscillation mode parameters. The target ranging acceleration signal is selected from the ranging acceleration signals of each of the satellites, and the Earth oscillation signal is extracted from the target ranging acceleration signal using the time delay interferometry method, and the target Earth oscillation signal is output.

2. The method for rapid generation of Earth's free oscillation waveforms for geocentric orbital gravitational wave detection according to claim 1, characterized in that, The analytical model for inter-satellite ranging acceleration, constructed using the Koula linear perturbation method based on the Earth's gravitational field parameters and the instantaneous inter-satellite distance, includes: Based on the Earth's gravitational field parameters, a spherical coordinate spherical harmonic function model is constructed; The spherical coordinate spherical harmonic function model is converted into a satellite orbital element model using the Koula linear perturbation method; The satellite orbital element model is simplified to determine a simplified Earth gravitational field model under a reference circular orbit; The satellite's gravitational potential is calculated based on the simplified Earth gravitational field model under the aforementioned reference circular orbit. An analytical model for inter-satellite ranging acceleration is constructed based on the satellite's gravitational potential and the instantaneous inter-satellite distance.

3. The method for rapidly generating Earth's free oscillation waveforms for geocentric orbital space gravitational wave detection according to claim 1, characterized in that, The analytical model of inter-satellite ranging acceleration based on the Earth free oscillation model is modified to determine the modified analytical model of inter-satellite ranging acceleration, including: Based on the Earth free oscillation model, the time-varying perturbation of the gravitational field coefficients is solved; The analytical model of inter-satellite ranging acceleration is modified by using the time-varying perturbation of the gravitational field coefficients, and the modified analytical model of inter-satellite ranging acceleration is determined.

4. The method for rapid generation of Earth's free oscillation waveforms for geocentric orbital space gravitational wave detection according to claim 1, characterized in that, The modified inter-satellite ranging acceleration analytical model calculates ranging acceleration signals between multiple satellites based on the satellite orbital parameters, the simulation time series, and the Earth's free oscillation mode parameters, including: The order of the modified inter-satellite ranging acceleration analytical model is simplified to determine the order-simplified inter-satellite ranging acceleration analytical model. The simplified inter-satellite ranging acceleration analytical model is used to solve for satellite acceleration based on the satellite orbital parameters, the simulation time series, and the Earth free oscillation mode parameters, and outputs ranging acceleration signals between multiple satellites.

5. The method for rapid generation of Earth's free oscillation waveforms for geocentric orbital space gravitational wave detection according to claim 1, characterized in that, The step of extracting the Earth oscillation signal from the target ranging acceleration signal using the time-delay interferometry method and outputting the target Earth oscillation signal includes: The target ranging acceleration signal is optically delayed, and the delayed target ranging acceleration signal is output. The target ranging acceleration signal after the optical path delay is expanded to determine the expanded target ranging acceleration signal. The laser phase noise in the deployed target ranging acceleration signal is sorted and matched to determine the initial Earth oscillation signal; The initial Earth oscillation signal is subjected to a Fourier transform and then filtered by a high-pass filter to output the target Earth oscillation signal.

6. The method for rapid generation of Earth's free oscillation waveforms for geocentric orbital space gravitational wave detection according to claim 4, characterized in that, Also includes: Numerical simulation data is acquired, and Bayesian analysis and MCMC parameter estimation methods are used to extract estimated values ​​of Earth's free oscillation parameters from the numerical simulation data. The simplified inter-satellite ranging acceleration analytical model is used to output a simulated ranging acceleration signal based on the satellite orbital parameters, the simulation time series, and the estimated values ​​of the Earth's free oscillation parameters. The time-delay interferometry method is used to extract the Earth oscillation signal from the simulated ranging acceleration signal to determine the simulated Earth oscillation signal; The simulated Earth oscillation signal is subjected to Fourier transform and filtered by a high-pass filter to determine the target simulated Earth oscillation signal. The matching factor is used to measure the degree of curve conformity. The simplified inter-satellite ranging acceleration analytical model is verified based on the target simulated Earth oscillation signal and the target Earth oscillation signal, and the verification results are output.

7. A rapid generation system for Earth's free oscillation waveforms for geocentric orbit space gravitational wave detection, characterized in that, include: The acquisition module is used to acquire the Earth's gravitational field parameters and the instantaneous inter-satellite distance, and to construct an analytical model of inter-satellite ranging acceleration based on the Earth's gravitational field parameters and the instantaneous inter-satellite distance using the Koula linear perturbation method; The correction module is used to correct the analytical model of the inter-satellite ranging acceleration based on the Earth free oscillation model, and to determine the corrected analytical model of the inter-satellite ranging acceleration. The calculation module is used to calculate the ranging acceleration signals between multiple satellites based on the satellite orbit parameters, the simulation time series, and the Earth free oscillation mode parameters when satellite orbit parameters, simulation time series, and Earth free oscillation mode parameters are received. The output module is used to select the target ranging acceleration signal among the ranging acceleration signals of each of the satellites, and to extract the earth oscillation signal from the target ranging acceleration signal using the time delay interferometry method, and output the target earth oscillation signal.

8. A computer device, characterized in that, The system includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor causes the processor to perform the steps of the method for rapidly generating Earth free oscillation waveforms for geocentric orbit space gravitational wave detection as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the method for rapid generation of Earth's free oscillation waveforms for geocentric orbital space gravitational wave detection as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, wherein when the program instructions are executed by a computer, the computer performs the method for rapid generation of Earth free oscillation waveforms for geocentric orbit space gravitational wave detection as described in any one of claims 1-6.

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