A time-varying gravity field model inversion method, system, electronic equipment and medium

Abstract

The present invention discloses a time-varying gravity field model inversion method, system, electronic equipment and medium, and relates to the field of gravity field inversion. The method comprises acquiring satellite gravity observation data; inverting the satellite gravity observation data according to the time-varying gravity field model, constructing an orbit observation equation and a corresponding satellite spacing rate variation observation equation for each arc segment with an integration time of one day as an arc segment; inverting the orbit observation equation and the corresponding satellite spacing rate variation observation equation according to the time-varying gravity field model of each arc segment, and obtaining a normal equation for each arc segment by using a weighted least squares method; performing Gaussian elimination on the normal equation of each arc segment to obtain a time-varying gravity field model potential coefficient. The present invention suppresses high-frequency mass change noise in the time-varying gravity field inversion process, and improves the accuracy of the inverted time-varying gravity field model.

Description

Technical Field

[0001] The present invention relates to the field of gravity field inversion, and in particular to a time-varying gravity field model inversion method, system, electronic equipment and medium. Background Art

[0002] The accuracy of the atmospheric and oceanic de-aliasing model is the primary factor limiting improvements in the accuracy of time-varying gravity fields from gravity satellites. During gravity field inversion, de-aliasing involves using a priori information to construct high-frequency mass variations of the Earth, such as high-frequency non-tidal variations in the atmosphere and ocean, with a temporal resolution less than one day. These high-frequency gravity signals are pre-deducted during the inversion of the monthly average time-varying gravity field to mitigate signal aliasing caused by insufficient sampling rates. According to the Nyquist sampling theorem, signal aliasing occurs when the sampling frequency is less than twice the signal frequency. Therefore, existing gravity field inversion processes contain significant high-frequency components. Therefore, developing a model that suppresses high-frequency mass variation noise during the time-varying gravity field inversion process and improves the accuracy of the inverted time-varying gravity field is of great significance to relevant earth science research, including geodesy, geophysics, geodynamics, and ocean-related sciences, as well as to the development of national defense and military science. Summary of the Invention

[0003] The purpose of the present invention is to provide a time-varying gravity field model inversion method, system, electronic equipment and medium, which can suppress the high-frequency mass change noise in the time-varying gravity field inversion process and improve the accuracy of the inverted time-varying gravity field.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A time-varying gravity field model inversion method, the method comprising:

[0006] Acquiring satellite gravity observation data; the satellite gravity observation data includes orbit data and inter-satellite moment variation data of the gravity satellite;

[0007] Based on the satellite gravity observation data, the orbit observation equation of each arc segment and the corresponding satellite spacing variation rate observation equation are constructed with one day of integration time as one arc segment;

[0008] According to the orbit observation equation of each arc segment and the corresponding satellite spacing variation observation equation, a weighted least squares method is used to obtain the normal equation of each arc segment;

[0009] Gaussian elimination is performed on the normal equation of each arc segment to obtain the potential coefficients of the time-varying gravity field model.

[0010] Optionally, before constructing the orbit observation equations and the satellite spacing variation rate observation equations of each arc segment based on the satellite gravity observation data with one day of integration time as one arc segment, the method further includes:

[0011] According to satellite events, outliers in the satellite gravity observation data are eliminated; the outliers include satellite gravity observation data in a maneuvering time period and satellite gravity observation data in an invalid payload observation time period.

[0012] Optionally, based on the satellite gravity observation data, with one day of integration time as one arc segment, the orbit observation equation of each arc segment and the satellite spacing variation rate observation equation of each arc segment are constructed, specifically including:

[0013] The initial observation equation is constructed with one day of integration time as an arc segment, accelerometer parameters, initial state parameters, empirical parameters and 2-8 order gravity field potential coefficients as local variables, and 9-60 order gravity field potential coefficients as global variables.

[0014] According to the satellite gravity observation data, numerical calculation is applied to obtain the orbit observation equation of each arc segment and the satellite distance variation rate observation equation of each arc segment.

[0015] Optionally, Gaussian elimination is performed on the normal equation of each arc segment to obtain the potential coefficients of the time-varying gravity field model, specifically including:

[0016] Performing Gaussian elimination on the normal equation of each arc segment to obtain the normal equation of each arc segment after elimination;

[0017] Combining the normal equations after elimination of the variables of each arc segment, eliminating the local variables, and obtaining the global variable normal equation;

[0018] Solving the global variable method equation to obtain 9-60 order gravity field potential coefficients;

[0019] Solving the normal equation after elimination of each arc segment according to the 9th to 60th order gravity field potential coefficients to obtain local variables of each arc segment;

[0020] Calculating the average value of the local variables of all arc segments according to the number of arc segments and the local variables of each arc segment to obtain the averaged gravity field potential coefficient;

[0021] The combination of the averaged gravity field potential coefficient and the 9th to 60th order gravity field potential coefficient is used as the time-varying gravity field model potential coefficient.

[0022] A time-varying gravity field model inversion system is applied to the above-mentioned time-varying gravity field model inversion method, and the system comprises:

[0023] An acquisition module is used to acquire satellite gravity observation data; the satellite gravity observation data includes orbit data and inter-satellite moment variation data of the gravity satellite;

[0024] A construction module is used to construct the orbit observation equation and the corresponding satellite spacing variation rate observation equation of each arc segment based on the satellite gravity observation data, with one day of integration time as one arc segment;

[0025] According to the orbit observation equation of each arc segment and the corresponding satellite spacing variation observation equation, a weighted least squares method is used to obtain the normal equation of each arc segment;

[0026] The coefficient determination module is used to perform Gaussian elimination on the normal equation of each arc segment to obtain the potential coefficients of the time-varying gravity field model.

[0027] An electronic device includes a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the above-mentioned time-varying gravity field model inversion method.

[0028] A computer-readable storage medium stores a computer program, which implements the above-mentioned time-varying gravity field model inversion method when executed by a processor.

[0029] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0030] The present invention provides a time-varying gravity field model inversion method. According to the influence characteristics of frequency mixing, during the gravity field inversion process, low-order gravity field potential coefficients are estimated at high frequency in the form of multiple days, and the time-varying gravity field model is estimated on a monthly time scale at the same time, thereby suppressing high-frequency noise in the gravity field inversion and improving the accuracy of the inverted time-varying gravity field model. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0032] Figure 1 A flow chart of the time-varying gravity field model inversion method provided by the present invention;

[0033] Figure 2 This is a module diagram of the time-varying gravity field model inversion system provided by the present invention.

[0034] Description of reference numerals:

[0035] Acquisition module—1, construction module—2, normal equation determination module—3, coefficient determination module—4. DETAILED DESCRIPTION

[0036] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0037] The purpose of the present invention is to provide a time-varying gravity field model inversion method, system, electronic equipment and medium, which can suppress the high-frequency mass change noise in the time-varying gravity field inversion process and improve the accuracy of the inverted time-varying gravity field.

[0038] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] like Figure 1 As shown, the present invention provides a time-varying gravity field model inversion method, the method comprising:

[0040] Step S1: Acquire satellite gravity observation data; the satellite gravity observation data includes orbit data and inter-satellite moment variation data of the gravity satellite.

[0041] Specifically, between step S1 and step S2, the following steps are also included:

[0042] Based on satellite events, outliers in the satellite gravity observation data are removed. These outliers include satellite gravity observation data during maneuvering periods and during periods when payload observations are invalid. Specifically, gravity satellite orbit and intersatellite moment variability data are read from the satellite system to remove outliers. Satellite gravity observation data includes the orbital data and intersatellite moment variability data of the gravity satellite, as well as accelerometer data and attitude data. Auxiliary data primarily includes Earth rotation data, AOD1B data, static gravity field models, tidal models, ephemeris files, and satellite event files such as satellite attitude adjustment and calibration. Outliers include satellite gravity observation data during maneuvering periods and during periods when payload observations are invalid, and these data are derived from satellite events.

[0043] Step S2: Based on the satellite gravity observation data, with one day of integration time as one arc segment, construct the orbit observation equation of each arc segment and the corresponding satellite distance variation rate observation equation.

[0044] S2 specifically includes:

[0045] Step S21: Taking one day of integration time as an arc segment, accelerometer parameters, initial state parameters, empirical parameters and 2-8 order gravity field potential coefficients as local variables, and 9-60 order gravity field potential coefficients as global variables, construct the initial observation equation.

[0046] As a specific implementation method, according to Newton's laws of kinematics, for a GRACE satellite, its orbital perturbation observation equation can be written as follows:

[0047]

[0048] Among them, H 3×3 is the Hessian matrix, ρ represents the orbital perturbation, and are the first and second derivatives of the orbital perturbation with respect to time, T k represents the gravity field potential coefficient to be solved (orders 2-8 are solved by day, and orders 9-60 are solved by month), b k is the basis function, ρ0 and η0 are the initial states, and the parameters to be estimated are solved for each arc segment. Assume that Equation (1) is about T k The response matrix of the parameters to be estimated is The state transfer matrices of the estimated parameters ρ0 and η0 are and The solution to the differential equation group (1) can be obtained through numerical calculation.

[0049] Step S22: applying numerical calculation based on the satellite gravity observation data to obtain the orbit observation equation of each arc segment and the satellite distance variation rate observation equation of each arc segment.

[0050] As a specific implementation, since the accelerometer has scale factors and bias drift parameters during the observation process, the correction of the accelerometer parameters can be expressed as follows:

[0051]

[0052] in, is the bias parameter of the accelerometer, is the scale factor of the accelerometer, q is the quaternion derived from the satellite’s attitude data, is the observed value of the accelerometer, where and is the parameter to be estimated. Replace the formula (2) in the formula (1) The solution of equation (1) is and The response matrix of the parameters to be estimated is assumed to be and

[0053] Due to the existence of perturbation model errors and unmodeled errors, the empirical formula form of formula (3) is used for absorption:

[0054]

[0055] Where t is time, ω is the angular velocity of the satellite, and a0 to a6 are the parameters to be evaluated. During the gravity field inversion process, the parameters a0 to a6 are evaluated every three hours. Assume that the parameter response matrix is ​​Φ a .

[0056] In the gravity field inversion process, the orbit and intersatellite distance variation observation equations are established for formula (1) with one day of integration time as one arc segment. The unknown quantities of the observation equations are the initial state, accelerometer parameters, empirical parameters, 2nd to 8th order gravity fields as coefficients, and 9th to 60th order gravity field potential coefficients as global variables. The local parameter design matrix of the i-th arc segment can be written as:

[0057]

[0058] The global parameter design matrix of the i-th arc segment can be written as:

[0059]

[0060] The orbit and intersatellite distance variability observation equations for the i-th arc segment can be written as follows:

[0061]

[0062] in, represents the local variables of the i-th arc segment (initial state, accelerometer parameters, empirical parameters, 2-8 low-order gravity field coefficients), A1i represents the design matrix of the local parameters of the i-th arc segment, x2 represents the global parameters (9-60 order monthly time-varying gravity field parameters, which do not change with the arc segment), A2i represents the global parameter design matrix of the i-th arc segment, b i Represents the observation value of the i-th arc segment.

[0063] The orbital observation equation is

[0064]

[0065] in, It represents the bit coefficient matrix of the local parameters established for the track data of the i-th arc segment, Represents the bit coefficient matrix of the global parameters established for the orbit data of the i-th arc segment, represents track data, represents the local variables of the i-th arc segment (initial state, accelerometer parameters, empirical parameters, 2-8 low-order gravity field potential coefficients), and x2 represents the global parameters (9-60 order monthly scale time-varying gravity field parameters, which do not change with the arc segment).

[0066] The observation equation for the interstellar distance variability is:

[0067]

[0068] in, It represents the bit coefficient matrix of the local parameters established for the satellite spacing variability data of the i-th arc segment, It represents the bit coefficient matrix of the global parameters established for the ith arc segment based on the intersatellite distance variation data, represents the intersatellite distance variability data, represents the local variables of the i-th arc segment (initial state, accelerometer parameters, empirical parameters, 2-8 low-order gravity field potential coefficients), and x2 represents the global parameters (9-60 order monthly scale time-varying gravity field parameters, which do not change with the arc segment).

[0069] Step S3: According to the orbit observation equation of each arc segment and the corresponding satellite spacing variation rate observation equation, the weighted least squares method is used to obtain the normal equation of each arc segment.

[0070] As a specific implementation method, the orbit and inter-satellite distance variation observation equations of the i-th arc segment are combined according to certain weights to form the i-th normal equation. Specifically, it is assumed that the weights of the orbit and inter-satellite distance observation equations are According to weighted least squares, the normal equation of the i-th arc segment is shown in formula (9):

[0071]

[0072] in

[0073] Step S5: Perform Gaussian elimination on the normal equation of each arc segment to obtain the potential coefficients of the time-varying gravity field model.

[0074] S4 specifically includes:

[0075] Step S41: performing Gaussian elimination on the normal equation of each arc segment to obtain the normal equation of each arc segment after elimination.

[0076] As a specific implementation method, Gaussian elimination is performed on the i-th normal equation to eliminate the low-order gravity field coefficients, accelerometer parameters, initial state, empirical parameters, etc. as the coefficient design matrix, and all arc segments are combined to form only the 9-60 order monthly time-varying gravity field coefficient normal equations, and then solved. Specifically, multiply the first line of formula (9) by Second row minus Multiplying by the first row, we get

[0077]

[0078] Simplified to get

[0079]

[0080] in,

[0081] Step S42: combining the normal equations after elimination of the variables of each arc segment, eliminating the local variables, and obtaining the global variable normal equation.

[0082] As a specific implementation method, for N arc segments, all arc segments are combined to form a normal equation of the global parameter The left and right sides are:

[0083]

[0084]

[0085] Step S43: Solve the global variable normal equation to obtain the 9th to 60th order gravity field potential coefficients. Specifically, according to formula (12) and formula (13), the solution of the 9th to 60th order gravity field potential coefficients is:

[0086]

[0087] Step S44: Solve the normal equations after elimination of each arc segment according to the 9th to 60th order gravity field potential coefficients to obtain the local variables of each arc segment.

[0088] As a specific implementation method, the calculated 9th-60th order gravity field coefficients are substituted into the normal equation for each arc segment, that is, formula (11) is used to solve the 2nd-8th order gravity field coefficients, accelerometer parameters, empirical parameters, and accelerometer initial state. Specifically, the 9th-60th order gravity field coefficient x2 is substituted into formula (11), and the parameter solution for the i-th arc segment is as follows:

[0089]

[0090] Step S45: Calculate the average value of the local variables of all arc segments according to the number of arc segments and the local variables of each arc segment to obtain the averaged gravity field potential coefficient.

[0091] Step S46: taking the combination of the averaged gravity field potential coefficient and the 9th to 60th order gravity field potential coefficient as the time-varying gravity field model potential coefficient.

[0092] As a specific implementation method, the 2nd to 8th order daily time-varying gravity field potential coefficients obtained for each arc segment are averaged and then combined with the 9th to 60th order gravity field potential coefficients to obtain the standard monthly time-varying gravity field model. Specifically, for the 2nd to 8th order gravity field potential coefficients x′ in the local parameter x1 of formula (11), 1,i Take the average

[0093]

[0094] Where x′ 1,i is the gravity field potential coefficient of the 2nd to 8th order of the i-th arc segment, and N represents the number of arc segments. The gravity field potential coefficient after averaging the 2nd to 8th order is Combined with the 9-60 order gravity field potential coefficients by x2, that is:

[0095]

[0096] in, represents the local variables of the i-th arc segment (initial state, accelerometer parameters, empirical parameters, 2-8 low-order gravity field coefficients), x2 represents the global parameters (9-60 order monthly time-varying gravity field parameters, which do not change with the arc segment), [.] represents the combination of the two sequences and outputs the standard monthly time-varying gravity field.

[0097] Compared with the prior art, the time-varying gravity field model inversion method provided by the present invention is superior to the prior art in that, in order to suppress the influence of high-frequency noise on the accuracy of time-varying gravity field solution, the time-varying gravity field model inversion method provided by the present invention estimates low-order gravity field potential coefficients at a high frequency in the form of multiple days during the gravity field inversion process based on the influence characteristics of mixing, and simultaneously estimates the time-varying gravity field model on a monthly time scale, thereby suppressing the high-frequency noise in the gravity field inversion and improving the accuracy of the inverted time-varying gravity field model.

[0098] Example 2

[0099] In order to execute the method corresponding to the above embodiment 1 and achieve the corresponding functions and technical effects, a time-varying gravity field model inversion system is provided below. Figure 2 As shown, the system includes:

[0100] The acquisition module 1 is used to acquire satellite gravity observation data; the satellite gravity observation data includes orbit data and inter-satellite moment variation data of the gravity satellite.

[0101] Construction module 2 is used to construct the orbit observation equation and the corresponding satellite distance variation rate observation equation of each arc segment based on the satellite gravity observation data, with one day of integration time as one arc segment.

[0102] The normal equation determination module 3 is used to obtain the normal equation of each arc segment using the weighted least squares method based on the orbit observation equation of each arc segment and the corresponding satellite spacing variation observation equation.

[0103] The coefficient determination module 4 is used to perform Gaussian elimination on the normal equation of each arc segment to obtain the potential coefficients of the time-varying gravity field model.

[0104] Example 3

[0105] An embodiment of the present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the time-varying gravity field model inversion method of embodiment 1.

[0106] Optionally, the above-mentioned electronic device may be a server.

[0107] In addition, an embodiment of the present invention further provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the time-varying gravity field model inversion method of embodiment 1.

[0108] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0109] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A time-varying gravity field model inversion method, characterized in that: The method comprises: Acquiring satellite gravity observation data; the satellite gravity observation data includes orbit data and inter-satellite moment variation data of the gravity satellite; Based on the satellite gravity observation data, the orbit observation equation of each arc segment and the corresponding satellite spacing variation rate observation equation are constructed with one day of integration time as one arc segment; According to the orbit observation equation of each arc segment and the corresponding satellite spacing variation observation equation, a weighted least squares method is used to obtain the normal equation of each arc segment; Performing Gaussian elimination on the normal equation of each arc segment to obtain the potential coefficients of the time-varying gravity field model; Based on the satellite gravity observation data, with one day of integration time as one arc segment, the orbit observation equations and the satellite distance variation rate observation equations of each arc segment are constructed, specifically including: The initial observation equation is constructed with one day of integration time as an arc segment, accelerometer parameters, initial state parameters, empirical parameters and 2-8 order gravity field potential coefficients as local variables, and 9-60 order gravity field potential coefficients as global variables. According to the satellite gravity observation data, numerical calculation is applied to obtain the orbit observation equation of each arc segment and the satellite distance variation rate observation equation of each arc segment; Gaussian elimination is performed on the normal equation of each arc segment to obtain the time-varying gravity field model potential coefficients, which specifically include: Performing Gaussian elimination on the normal equation of each arc segment to obtain the normal equation after elimination of each arc segment; Combining the normal equations after elimination of the variables of each arc segment, eliminating the local variables, and obtaining the global variable normal equation; Solving the global variable method equation to obtain 9-60 order gravity field potential coefficients; Solving the normal equation after elimination of each arc segment according to the 9th to 60th order gravity field potential coefficients to obtain local variables of each arc segment; Calculating the average value of the local variables of all arc segments according to the number of arc segments and the local variables of each arc segment to obtain the averaged gravity field potential coefficient; The combination of the averaged gravity field potential coefficient and the 9th to 60th order gravity field potential coefficient is used as the time-varying gravity field model potential coefficient.

2. The time-varying gravity field model inversion method according to claim 1, characterized in that: Before constructing the orbit observation equations and the satellite distance variation rate observation equations of each arc segment based on the satellite gravity observation data and taking one day of integration time as one arc segment, the method further includes: Eliminating abnormal values ​​in the satellite gravity observation data according to satellite events; The abnormal values ​​include satellite gravity observation data during the maneuvering period and satellite gravity observation data during the payload observation invalid period.

3. A time-varying gravity field model inversion system, used to implement the time-varying gravity field model inversion method according to any one of claims 1-2, characterized in that: The system comprises: An acquisition module is used to acquire satellite gravity observation data; the satellite gravity observation data includes orbit data and inter-satellite moment variation data of the gravity satellite; A construction module is used to construct the orbit observation equation and the corresponding satellite spacing variation rate observation equation of each arc segment based on the satellite gravity observation data, with one day of integration time as one arc segment; a normal equation determination module, configured to obtain the normal equation of each arc segment using a weighted least squares method based on the orbit observation equation of each arc segment and the corresponding satellite spacing variation observation equation; The coefficient determination module is used to perform Gaussian elimination on the normal equation of each arc segment to obtain the potential coefficients of the time-varying gravity field model.

4. An electronic device, characterized in that: The device comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the time-varying gravity field model inversion method according to any one of claims 1 to 2.

5. A computer-readable storage medium, characterized in that It stores a computer program, which, when executed by a processor, implements the time-varying gravity field model inversion method according to any one of claims 1 to 2.

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