Method for establishing gravity field model based on new generation of low-low satellite-to-satellite tracking satellite scheme with enhanced chinese area

Abstract

The application discloses a time-varying gravity field model establishment method of a new generation of low-low satellite tracking satellite scheme based on Chinese regional enhancement, belongs to the field of satellite gravitation, and refers to selection indexes of a global optimal double-track four-star formation scheme to determine multiple double-track four-star formation schemes in the Chinese region, select an optimal scheme from the multiple double-track four-star formation schemes, independently solve low-order and high-order gravity potential spherical harmonic coefficients by using different data in the optimal scheme, weaken the negative influence of time domain aliasing effect on the precision of the time-varying gravity field model, reduce the error of the high-order gravity potential spherical harmonic coefficients to a certain extent, and finally obtain a Chinese regional gravity field model with higher precision. The final result shows that, compared with an independent polar orbit formation, the application not only greatly weakens the north-south strip error caused by the north-south tracking mode in the Chinese region, but also avoids problems such as gravity signal leakage caused by a post-processing process, and finally obtains a Chinese regional gravity field model with smaller error and higher signal-to-noise ratio.

Description

Technical Field

[0001] This invention belongs to the field of satellite gravimetry, and more specifically, relates to a method for establishing a gravity field model for a new generation of low-low satellite tracking satellite scheme based on China's regional enhancement. Background Technology

[0002] Satellite gravity technology is a crucial tool for achieving high-precision global gravity field modeling. Launched gravity satellite missions include CNAMP, GRACE, GRACE Follow-On, and GOCE, all employing independent polar-orbiting formation (PSF). This means the satellite's orbital inclination is close to 90° from the equatorial plane. This results in gravity satellites being sensitive only to north-south gravity signals and insensitive to east-west gravity signals, ultimately causing north-south striping noise in the Earth's gravity field model (EGM). To obtain a more accurate Earth gravity field model, international research has focused on next-generation satellite gravity detection technologies. For example, the GRACE-FO satellite, in addition to the GRACE satellite, carries a laser ranging system to measure inter-satellite distances and their changes, improving inter-satellite observation accuracy by approximately 100 times. Furthermore, drag-free compensation systems can be used to compensate for non-conservative forces acting on the satellite in real time. However, despite this trend, the accuracy of the Earth's gravity field model has not improved significantly. This is because a significant error source affecting the accuracy of gravity field model solutions still exists in the new generation of gravity satellite missions: time-domain mixing error. Besides optimizing onboard instruments, many scholars have also conducted research on new satellite formation configurations. The aforementioned gravity satellites have significant shortcomings in their formation configurations: they can only detect gravity signals in the north-south direction, lacking detection of east-west signals; furthermore, due to the presence of only one group or a single satellite, their signal sampling frequency is low. According to the Nyquist sampling theorem, this makes it difficult to correctly model short-period time-varying gravity signals using the observation data from gravity satellites, thus affecting the accuracy of the gravity field model solution.

[0003] Currently, international efforts are considering a dual-orbit, four-satellite gravity satellite program to obtain more accurate global gravity field models. However, for high-precision regional gravity field models, the development of satellite programs with regional enhancement capabilities has not yet been fully considered. To further enhance my country's ability to characterize the Earth's gravity field, there is an urgent need to develop a new generation of gravity satellites with regional enhancement capabilities. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method for establishing a gravity field model based on a new generation of low-low satellite tracking satellite scheme with enhancements in the Chinese region, which can improve the accuracy of the gravity field model for the Chinese region. To achieve the above objective, according to a first aspect of this invention, a method for establishing a time-varying gravity field model based on a new generation of low-low satellite tracking satellite scheme with enhancements in the Chinese region is provided, comprising:

[0005] S1, determine the satellite tracking scheme; wherein, the satellite tracking scheme includes 6 dual-orbit four-satellite formations; in each formation, the combination of polar orbit inclination and inclined orbit inclination is respectively [ , , , , , ];

[0006] S2, the satellite trajectories of each formation scheme are processed to obtain the corresponding time-varying gravity field model;

[0007] S3, the formation scheme with the best uniformity of gravity satellite observations and the best accuracy of the time-varying gravity field model is selected as the optimal formation scheme; the final time-varying gravity field model is determined by a preset method based on the simulated observation data and reference observation data of the optimal formation scheme.

[0008] The preset method includes: based on the higher-order solution cycle. Highest order maximum solution order Low-order maximum solution order ,use The order obtained by solving the simulated observation data and reference observation data of the day is: The spherical harmonic coefficients; according to and low-order solution cycle respectively adopt The simulated observation data and reference observation data of the day were used to calculate the results. Group 2 to The spherical harmonic coefficients of order 2 are obtained by weighted averaging. The average spherical harmonic coefficients of order, and their relationship with the... The spherical harmonic coefficients of these factors are collectively used as the final spherical harmonic coefficients of the time-varying gravity field model; among them, .

[0009] According to a second aspect of the present invention, an electronic device is provided, comprising: a computer-readable storage medium and a processor;

[0010] The computer-readable storage medium is used to store executable instructions;

[0011] The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in the first aspect.

[0012] According to a third aspect of the invention, a computer-readable storage medium is provided, characterized in that the computer-readable storage medium stores computer instructions for causing a processor to perform the method as described in the first aspect.

[0013] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0014] Considering the inevitable systematic errors, such as north-south striping errors, when probing the Earth's gravity field using existing independent polar-orbiting formations, and given that the current spatiotemporal resolution and accuracy of gravity satellites are insufficient for refined gravity signal detection, coupled with the lack of high-precision local gravity field models, this invention proposes a gravity field model establishment method based on a new generation of low-low satellite tracking satellite schemes enhanced for the Chinese region. Referring to the selection criteria for global dual-orbit four-satellite formation schemes, multiple dual-orbit four-satellite formation schemes for the Chinese region are determined, and the optimal scheme is selected. Different data from the optimal scheme are then used to independently calculate the low- and high-order gravity potential spherical harmonic coefficients, mitigating the negative impact of temporal aliasing on the accuracy of the time-varying gravity field model. This reduces the error of the high-order gravity potential spherical harmonic coefficients to a certain extent, ultimately obtaining a higher-precision gravity field model for the Chinese region. Final results show that, compared with independent polar-orbiting formations, this invention not only significantly reduces the north-south striping errors caused by the north-south tracking mode within the Chinese region but also avoids problems such as gravity signal leakage during post-processing, ultimately obtaining a gravity field model for the Chinese region with smaller errors and a higher signal-to-noise ratio.

[0015] The method provided by this invention separately calculates the low-order diurnal time-varying gravity signal. In general gravity field calculations, the same set of data is usually used to simultaneously calculate the high- and low-order gravitational potential spherical harmonic coefficients. This can lead to aliasing effects between signals at different spatiotemporal scales. That is, the high-order long-period time-varying gravity signal will be severely contaminated by the low-order short-period time-varying signal. This invention uses different data to independently calculate the low- and high-order gravitational potential spherical harmonic coefficients, which weakens the negative impact of time-domain aliasing on the accuracy of the time-varying gravity field model and can reduce the error of the high-order gravitational potential spherical harmonic coefficients to a certain extent. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the gravity field inversion process provided in an embodiment of the present invention.

[0017] Figure 2 This is a flowchart illustrating how a final time-varying gravity field model is determined based on simulated observation data and reference observation data of the optimal formation scheme, as provided in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0019] This invention provides a method for establishing a gravity field model for a new generation of low-low satellite tracking satellite scheme based on China region enhancement, including:

[0020] S1, determine the satellite tracking scheme; wherein, the satellite tracking scheme includes 6 dual-orbit four-satellite formations; in each formation, the combination of polar orbit inclination and inclined orbit inclination is respectively [ , , , , , ].

[0021] Specifically, the dual-orbit four-satellite formation adds a group of inclined orbit satellites to the existing independent polar orbit formation. This not only increases the gravity satellites' ability to detect east-west gravity signals but also improves the sampling frequency of the satellites in areas of repeated observation. Furthermore, if applied on a global scale, then… The optimal dual-track four-star formation scheme.

[0022] Based on this, the orbital inclination of the polar-orbiting satellite group in the dual-orbit four-satellite formation is set as follows: To ensure that observational data are available globally, considering that the northernmost latitude of the China region is approximately The observation range of inclined orbit satellites depends on their orbital inclination, and considering that the orbital inclination range of an inclined orbit satellite group needs to be within [ Otherwise, the inversion performance of the dual-orbit four-satellite formation will be reduced. In view of the above two points, the orbital inclination range for the inclined orbit satellite group is determined to be […]. This is to ensure that inclined orbit satellites have observation data within the Chinese region.

[0023] The orbital inclination intervals for the inclined orbit satellite group are: Specifically: [ ], respectively forming a dual-orbit four-satellite formation with polar-orbiting satellites, thus obtaining 6 dual-orbit four-satellite formation schemes: [ , , , , , ].

[0024] According to the track height and orbital inclination Repeat period of satellite orbit (Considering the limitations of current gravity satellite spatiotemporal resolution, this invention sets the timeframe to 30 days) to confirm the satellite's orbital altitude. To obtain the satellite's semi-major axis of orbit , The calculation formula is shown below:

[0025]

[0026] in, The number of days for satellite flight repetition. This represents the number of orbits the satellite completes (geometrically, it represents the number of intersections between the satellite's trajectory and the equator). The average angular velocity of the orbit. The Earth's average angular velocity, The average radius of the Earth For the semi-major axis of the satellite orbit, The orbital inclination of the satellite, (here It is regularized. (The spherical harmonic coefficients characterizing the Earth's oblateness).

[0027] Finally, using 30 days as the inversion period for the gravity field model (i.e., the timescale of the gravity field model is 30 days), the […] were determined. The orbital altitudes of the corresponding inclined orbit satellites are respectively [ Polar-orbiting satellite constellation ( The corresponding orbital height is .

[0028] S2, process all satellite trajectories for each formation scheme to obtain the gravity field model corresponding to each formation scheme.

[0029] Specifically, the gravity field model corresponding to each formation scheme is obtained by processing all satellite trajectories of each formation scheme based on the orbit integrator.

[0030] Preferably, the processing includes: uniformly dividing the satellite's flight trajectory within a preset time period into N arc segments according to a preset duration; inputting the initial state of each arc segment into the first and second orbit integrators respectively to obtain simulated observation data and reference observation data of the satellite's orbit within the preset time period; and calculating the second order to third order of the gravity field model using the least squares adjustment method based on the simulated observation data and reference observation data. The spherical harmonic coefficients; wherein, the background force model of the first orbital integrator includes a static gravity field model, an ocean tide model, and a time-varying gravity field model, and the background force model of the second orbital integrator includes a static gravity field model, an ocean tide model, and a non-tidal atmospheric-ocean model.

[0031] Considering integration error, the preset duration is usually set to 6 hours.

[0032] The preset time can be set according to actual needs.

[0033] This embodiment of the invention uses a preset time of 60 months and a preset duration of 6 hours as an example for illustration. Specifically, step S2 includes:

[0034] S21, the satellite's flight trajectory within a preset time period is evenly divided into N arc segments according to a preset duration. Based on the orbital parameters of each scheme, the initial state vector of each orbital arc segment of the two groups of satellites in each scheme is calculated.

[0035] Since the integration error will increase over time, causing the orbit to gradually deviate from the set orbit parameters, this invention predetermines the initial state of each orbital arc segment. This initial state is obtained by a third Gaussian Jackson integrator (i.e., a third orbital integrator), where the background force model of the integrator is set to the Earth's central gravity, to ensure that the integrated orbit is always the pre-set orbit at the initial position of each arc segment (this can be achieved in practice by using a drag compensation system).

[0036] The initial state vector for each orbital arc segment is calculated as follows: The initial mean anomaly angle (i.e., the starting position of the first arc segment) of the satellite is set in the third Gaussian Jackson integrator (i.e., the third orbital integrator). Taking a preset duration of 6 hours and a preset time of 60 months as an example, the flight time of the two sets of satellites per day is divided into 4 segments. Correspondingly, the flight trajectories of the two sets of satellites within 60 months are divided into 4 × 60 × 30 = 7200 orbital arc segments. The Keplerian orbital six elements (including the semi-major axis, inclination, oblateness, right ascension of the ascending node, perigee distance, and mean anomaly angle, where the mean anomaly angle is used to determine the satellite's position in the orbit) are used to determine the initial state of the two sets of satellites within one month for a total of 7200 orbital arc segments. 5s and 5s are used as the arc length unit and integration step size for orbit integration, respectively; after setting the satellite orbit parameters (i.e., the initial Keplerian orbital root numbers for each arc segment), the integrator will be based on a pre-set background force model, with... Using 5s as the arc length unit and integration step size for orbital integration, respectively, the Kepler orbital six roots of the initial state for each arc segment (excluding the initial arc segment) are obtained. These roots are then converted into vector form, which is the initial state vector. 6h is used as the arc length unit for orbital integration to control the growth of the accumulated error in orbital integration.

[0037] S22, gravity field inversion is performed on each of the six schemes to obtain a monthly time-varying gravity field model (displayed in the form of spherical harmonic coefficients). The initial state vector of the orbital arc segment is used as the initial value of the orbital integral to invert a time-varying gravity field model for a total of 60 months from 2003 to 2007. The time-varying gravity field model is then converted into terrestrial water storage change according to equation (2), specifically in the form of equivalent water height (EWH: cm). Equivalent water height represents the gravity signal of the corresponding magnitude using the equivalent water thickness change. In this invention, the equivalent water height is... The water column, one grid point corresponds to one water column, that is, the equivalent water height.

[0038]

[0039] in, This represents the average density of the Earth. This indicates the density of water. and Let represent the truncation order and degree of the spherical harmonic coefficients, respectively. Represents the Love number, For full standardization Step The Legendre function, and Indicates the calculated Step Secondary gravitational potential spherical harmonic coefficients and This indicates full normalization. Step Secondary gravitational potential spherical harmonic coefficients and Represents the co-latitude and longitude of grid points. express( , The gravitational potential spherical harmonic coefficient corresponding to the grid point at ().

[0040] The above gravity field inversion includes both forward and inversion processes, such as... Figure 1 As shown.

[0041] During forward modeling, based on the initial state vector of the orbital arc segment, the first Gaussian Jackson integrator (i.e., the first orbital integrator) generates simulated values ​​of orbital observation data (including orbital coordinate data and inter-satellite distance variation data for both satellites at each sampling point), referred to as "real observation data." It can be understood that after setting the initial state vector of the orbital arc segment, the first orbital integrator, based on a pre-defined background force model, uses 6h and 5s as the arc length unit and integration step size for orbital integration, respectively, to obtain the Kepler orbital six elements at each sampling point of the arc segment, i.e., the "real observation data." The background force model of the first orbital integrator is a set of "real models."

[0042] The "realistic models" used in the aforementioned forward modeling process mainly include a static gravity field model, an ocean tidal model, and a time-varying gravity field model, employing GGM05s, EOT11a, and ESM AOHIS, respectively. The time-varying gravity field model, ESM AOHIS, includes components for the atmosphere ("A"), ocean ("O"), hydrology ("H"), ice ("I"), and solid Earth ("S"), with a time resolution of 6 hours. The simulation sampling interval and integration arc length are set to 5 seconds and 6 hours, respectively.

[0043] Furthermore, to simulate more realistic observation data, noise from sensors such as laser interferometers, accelerometers, and GNSS receivers needs to be added to the error-free simulated observation data. During the simulation, the laser interferometer observation data is obtained by differentiating satellite orbit data (including position and velocity); this data constitutes the simulated satellite observation data. The accelerometer observation data is taken from the actual accelerometer readings during satellite flight, used to simulate the non-conservative forces acting on the satellite. The GNSS receiver observation data corresponds to the satellite's orbit data (including position and velocity). This noise-contaminated observation data is the "simulated observation data."

[0044] During the inversion process, based on the initial state vector of the orbital arc segment, a second Gaussian Jackson integrator (i.e., the second orbital integrator) is used to generate simulated values ​​of the orbital observation data (including orbital coordinate data and inter-satellite distance variation data for both satellites at each sampling point), referred to as "reference observation data." It can be understood that after setting the initial state vector of the orbital arc segment, the second orbital integrator, based on a pre-defined background force model, uses 6h and 5s as the arc length unit and integration step size for orbital integration, respectively, to obtain the Kepler orbital six elements at each sampling point of the arc segment, i.e., the "reference observation data." The background force model of the second orbital integrator is a set of "reference models."

[0045] The "reference models" in the above inversion process mainly include a static gravity field model, an ocean tidal model, and a non-tidal atmospheric-ocean model. Specifically, the static gravity field model and the ocean tidal model employ the GGM05s model and the FES2004 model, respectively. For the non-tidal atmospheric-ocean model (AOD), this invention uses the DEAL model and the AOerr model, corresponding to the non-tidal mass variation signals and model errors of the time-varying gravity signal components of the atmosphere (A) and ocean (O), respectively.

[0046] Based on the above-mentioned "simulated observation data" and "reference observation data", the time-varying gravity field model is estimated using the least squares adjustment method:

[0047] Establish the least squares adjustment observation equations, and then establish the observation vectors sequentially. Design Matrix and unknown vectors As shown in formula (2), the spherical harmonic coefficients of the time-varying gravity field model are obtained. That is, the total amount of the three time-varying signal components in the time-varying gravity field model ESM AOHIS, namely hydrology ("H"), ice ("I") and solid soil ("S"), is estimated, and is referred to as "HIS".

[0048] Among them, the observation vector This represents the residual between the "actual observation data" and the "reference observation data";

[0049] Design Matrix From the variational equation (i.e., the partial derivative equation of the satellite instantaneous state vector with respect to the unsolved spherical harmonic coefficients) The derivative with respect to time is a function of... The solution to the first-order ordinary differential equation is obtained through numerical integration;

[0050] Unknown vector The local and global parameters of each arc segment (i.e., the unsolved spherical harmonic coefficients representing the Earth's gravity field model) are calculated using formula (3), where The weight matrix (in this invention, (For the identity matrix). Local parameters include the accelerometer's scale factor and bias correction, as well as the position and velocity corrections for the initial state of each arc segment. All directions need to be corrected. In this invention, the scale factor is set to 1, and the deviation includes corrections for constant terms, linear terms, and quadratic terms. Therefore, a total of 15 local parameters actually need to be corrected.

[0051] Finally, based on the principle of least squares adjustment, a set of spherical harmonic coefficients representing the Earth's time-varying gravity signal was calculated. The spherical harmonic coefficients calculated by this invention range from order 2 to 60.

[0052] (3)

[0053] (4)

[0054] The calculation process described above is shown below.

[0055] Due to the observation vector Its corresponding They cannot be completely equal, therefore a correction value needs to be added. As shown in equation (5):

[0056] (5)

[0057] The criteria for least squares adjustment are:

[0058] (6)

[0059] According to the least squares principle The above criteria must be met, therefore the above equation is applied to... Taking the partial derivative, we get:

[0060] (7)

[0061] Substituting equation (5) into equation (7), we get:

[0062] (8)

[0063] Finally calculated for:

[0064] (9)

[0065] S3, the formation scheme with the best uniformity of gravity satellite observations and the best accuracy of gravity field model is selected as the optimal formation scheme; the final gravity field model is determined by a preset method based on the simulated observation data and reference observation data of the optimal formation scheme;

[0066] The preset method includes: based on the higher-order solution cycle. n Highest order maximum solution order Low-order maximum solution order ,use The order obtained by solving the simulated observation data and reference observation data of the day is: The spherical harmonic coefficients; according to and low-order solution cycle respectively adopt The simulated observation data and reference observation data of the day were used to calculate the results. Group 2 to The spherical harmonic coefficients of order 2 are obtained by weighted averaging. The average spherical harmonic coefficients of order, and their relationship with the... The spherical harmonic coefficients of these factors are collectively used as the final spherical harmonic coefficients of the time-varying gravity field model; among them, .

[0067] The uniformity of gravity satellite observations is mainly reflected in the nadir trajectory of the dual-orbit four-satellite formation within the Chinese region.

[0068] Plot the nadir point trajectories of six dual-orbit four-satellite formation schemes within the Chinese region, and compare the distribution uniformity of each scheme within the Chinese region, i.e., observation uniformity.

[0069] The accuracy of the gravity field model is determined by the following methods:

[0070] The smaller the difference between the gravity field model and the "HIS" model, the higher the accuracy of the gravity field model.

[0071] Specifically, the accuracy of the time-varying gravity field model can be reflected by comparing the changes in terrestrial water storage under the dual-orbit four-star formation scheme over the five years from 2003 to 2007 with the "HIS" model.

[0072] The changes in terrestrial water storage under each scheme over the five years from 2003 to 2007 were compared with the "HIS" model (which can be understood as a set of spherical harmonic coefficients; converting it to equivalent water height allows for comparison with changes in terrestrial water storage) to evaluate the accuracy of the time-varying gravity field model. Specifically, the following steps were taken: 1) Calculate the fitted interannual amplitude and trend terms of the changes in terrestrial water storage and compare them with the fitted interannual amplitude and trend terms of the "HIS" model; 2) Calculate the RMS difference between the changes in terrestrial water storage and the "HIS" model.

[0073] The closer the fitted interannual amplitude and trend terms are to the "HIS" model, and the smaller the RMS difference with the "HIS" model, the higher the accuracy and reliability of the gravity field model.

[0074] Based on Equation (8), the fitting interannual amplitude term and fitting trend term of terrestrial water storage change are calculated:

[0075]

[0076] in, For a linear trend, i.e., a fitted trend term, ( ) represents the annual and semi-annual amplitude terms for fitting. and This represents the phase information of the annual time-varying gravity signal. and This represents the phase information of the semi-annual time-varying gravity signal. The calculation process of the RMS difference between the land water storage change at each grid point and the "HIS" model is as follows: First, remove the equivalent water high amplitude (including annual amplitude and semi-annual amplitude) and trend term of each grid point to obtain its monthly residual value, then calculate the RMS value for 60 months, and finally obtain the residual RMS value of each grid point.

[0077] After obtaining the optimal dual-track four-star formation scheme for the Chinese region, it is still necessary to further adopt a pre-defined method to weaken the negative impact of time-domain aliasing on the time-varying gravity field model.

[0078] The aforementioned preset method is as follows: the total arc length of the satellite's flight in one day is used as the smallest solution object, that is, one day is used as the unit of data for solution. The low-order daily solution gravity potential spherical harmonic coefficients and the corrections (including position and velocity) of the satellite's initial state vector, as well as the scale factor and deviation corrections of the accelerometer, are used as local parameters in the gravity field solution process for solution.

[0079] Solution period for higher-order long-period solutions ( This also refers to the timescale (30 days in this example) and the solution order of the time-varying gravity field model. Solution cycle of low-order daily solutions Summation order Assignment; the solution order based on the spherical harmonic coefficients of the low-order solar solution gravitational potential. ,use The "actual observation data" and "reference observation data" of the day are used to solve for a higher-order gravity field model, that is, to solve for a model of order [missing information]. The spherical harmonic coefficients of the gravity field model; then respectively using The "actual observation data" and "reference observation data" of one day in Tianzhong were calculated to obtain Group of daily solutions to the second order The first gravitational potential coefficient (e.g., when using a single-day solution), =1). Will A set of second-order to third-order harmonic coefficients is obtained by weighted averaging of the low-order gravitational potential spherical harmonic coefficients. The spherical harmonic coefficients of the first gravitational potential are finally compared with the calculated values. Average level Composition of spherical harmonic coefficients of gravitational potential Average level 2 to The spherical harmonic coefficient of the gravitational potential.

[0080] For example, after comparing the inversion capabilities of time-varying gravity field models of different schemes, the optimal dual-orbit four-satellite formation scheme was determined to be [ Based on this, the present invention further employs a preset method to reduce temporal aliasing errors. Therefore, for , , The solution cycle of low-order daily solutions (For example, a day) Assign a value, where The corresponding time scale of the time-varying gravity field model is a monthly scale in this invention, therefore the parameters... The value was assigned to 30; meanwhile, based on the excellent noise reduction performance of the dual-track four-star formation, In this invention, it is set to 60 (no spatial filtering is performed). Because... and The optimal value is unknown, and this invention will be based on and Set up different experimental groups, and utilize each experimental group and Dealiasing was performed, and the solution accuracy of the time-varying gravity field model for each experimental group was compared to determine... and The optimal value. Finally, using the determined... and The optimal value is dealiased during the time-varying gravity field solution process, thereby further improving the solution accuracy of the time-varying gravity field model.

[0081] Assumption and The optimal values ​​are 15 and 1, respectively. Using the optimal dual-track four-satellite formation scheme, the spherical harmonic coefficients of orders 16 to 60 are calculated from the "real observation data" and "reference observation data" for 30 days. Then, the "real observation data" and "reference observation data" for each day of the 30 days are used to calculate 30 sets of spherical harmonic coefficients of orders 2 to 15. These are then weighted and averaged to obtain a set of average spherical harmonic coefficients of orders 2 to 15. This average spherical harmonic coefficient is then used together with the aforementioned spherical harmonic coefficients of orders 16 to 60 as the final spherical harmonic coefficients of the time-varying gravity field model.

[0082] It is understood that the embodiments of the present invention perform integral processing on the satellite's flight trajectory over 60 months to obtain the corresponding "real observation data" and "reference observation data". Since the time scale of the time-varying gravity field model is 30 days, when calculating the spherical harmonic coefficients of the time-varying gravity field model, the "real observation data" and "reference observation data" for the first 60 months (approximately 30 days per month, with the actual number of days set according to the number of days in the month) are used to calculate the spherical harmonic coefficients of the time-varying gravity field model, and finally obtain the spherical harmonic coefficients of the time-varying gravity field model for the first 60 months.

[0083] Compared with independent polar-orbiting formations, the six dual-orbit four-satellite formation schemes provided in this invention all increase observations in the east-west direction; among the six schemes, the schemes... The nadir point trajectory is the densest and most uniform, resulting in the best observation uniformity. Compared to the "HIS" model, the gravity field models (without spatial filtering) of the six dual-orbit four-satellite formation schemes provided in this embodiment of the invention show the largest strip noise in the gravity field model corresponding to the independent polar orbit formation, with almost no visible gravity field signal. In the six dual-orbit four-satellite formation schemes, as the orbital inclination of the inclined orbit satellite group gradually increases, the time-varying gravity field model gradually exhibits strip noise. Compared to the interannual trend signal fitting of the "HIS" model, the six dual-orbit four-satellite formation schemes provided in this embodiment of the invention show that the […] , The model most closely resembles the "HIS" model; compared with the interannual amplitude signal fitting of the six dual-track four-star formation schemes provided in this embodiment of the invention, the changes in land water storage in China (without spatial smoothing filtering) are most similar to the "HIS" model. Among the six schemes, scheme [ , The model most closely resembles the "HIS" model; the embodiments of this invention provide six dual-track four-star formation schemes corresponding to changes in land water storage in China (without spatial smoothing filtering) compared to the fitting residuals of the "HIS" model. The fitted residual is the smallest; the embodiments of the present invention provide six dual-track four-star formation schemes for comparing the RMS difference between the changes in land water storage in China (without spatial smoothing filtering) and the "HIS" model, with the schemes having the smallest RMS. The difference from the "HIS" model is the smallest.

[0084] This invention provides an electronic device, including: a computer-readable storage medium and a processor;

[0085] The computer-readable storage medium is used to store executable instructions;

[0086] The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any of the above embodiments.

[0087] This invention provides a computer-readable storage medium storing computer instructions for causing a processor to perform the method described in any of the preceding embodiments.

[0088] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for establishing a time-varying gravity field model based on a new generation of low-low satellite tracking satellite scheme with enhanced coverage in the Chinese region, characterized in that, include: S1, determine the satellite tracking scheme; wherein, the satellite tracking scheme includes 6 dual-orbit four-satellite formation schemes; in each formation scheme, the combination of polar orbit inclination angle and inclined orbit inclination angle are [89° / 55°], [89° / 60°], [89° / 65°], [89° / 70°], [89° / 75°], [89° / 80°]; S2, the satellite trajectories of each formation scheme are processed to obtain the corresponding time-varying gravity field model; S3, the formation scheme with the best uniformity of gravity satellite observations and the best accuracy of the time-varying gravity field model is selected as the optimal formation scheme; the final time-varying gravity field model is determined by a preset method based on the simulated observation data and reference observation data of the optimal formation scheme; The preset method includes: based on the higher-order solution period n and the highest higher-order solution order n. max Low-order maximum solution order n int The order n is obtained by using n days of simulated observation data and reference observation data. int +1 to n max spherical harmonic coefficients; according to n int and low-order solution period T int T int The simulated observation data and reference observation data of the day were used to calculate n sets of second-order to n-order data. int The spherical harmonic coefficients of order n are obtained by weighted averaging, resulting in a set of 2nd to nth order coefficients. int The average spherical harmonic coefficients of order n are compared with those of n. int +1 to n max The spherical harmonic coefficients of T are collectively used as the final spherical harmonic coefficients of the time-varying gravity field model; where T int <n。 2. The method as described in claim 1, characterized in that, T int and n int The method of obtaining it is: Set T int and n int Multiple combinations of values, respectively based on T int and n int The various combinations of values ​​and T, n max Solve the second to nth order of the time-varying gravity field model max The spherical harmonic coefficients are the optimal combination of values ​​for the time-varying gravity field model, which determines the accuracy of T. int and n int The final value of .

3. The method as described in claim 1, characterized in that, In step S2, the processing includes: uniformly dividing the satellite's flight trajectory within a preset time period into N arc segments according to a preset duration; inputting the initial state of each arc segment into the first and second orbit integrators respectively to obtain simulated observation data and reference observation data of the satellite's orbit within the preset time period; and calculating the spherical harmonic coefficients of the time-varying gravity field model using the least squares adjustment method based on the simulated observation data and reference observation data. The background force model of the first orbit integrator includes a static gravity field model, an ocean tide model, and a time-varying gravity field model, while the background force model of the second orbit integrator includes a static gravity field model, an ocean tide model, and a non-tidal atmospheric-ocean model.

4. The method as described in claim 3, characterized in that, The initial state of each arc segment is obtained as follows: Set the initial mean anomaly angle of the satellite, which is the initial state of the starting arc segment. Input it into the third orbit integrator to obtain the initial state of other arc segments. The background force model of the third orbital integrator is the Earth's central gravitational model.

5. The method as described in claim 3, characterized in that, The initial state of each arc segment is characterized by the Kepler orbital six-root number.

6. The method as described in claim 3, characterized in that, The static gravity field model, ocean tide model, and time-varying gravity field model in the first orbital integrator adopt the GOCO05s model, EOT11a model, and ESM AOHIS model, respectively. The static gravity field model and ocean tide model in the second orbital integrator are the GGM05s model and the FES2004 model, respectively, while the non-tidal atmospheric and ocean model is the DEAL model, and the error of the non-tidal atmospheric and ocean model is the AOerr model.

7. The method as described in claim 1, characterized in that, The simulated observation data also includes noise data from the inter-satellite ranging system, accelerometers, and GNSS receivers.

8. The method as described in claim 1, characterized in that, The accuracy of the time-varying gravity field model is determined by the following methods: The smaller the difference between the time-varying gravity field model and the "HIS" model, the higher the accuracy of the gravity field model; where the "HIS" model is the total amount of the three time-varying signal components "H", "I" and "S" in the ESM AOHIS model.

9. An electronic device, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a processor to perform the method as described in any one of claims 1-8.

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