Method and device for determining lunar modulation parameters of M2 partial tide observed by GNSS (Global Navigation Satellite System)

Abstract

The invention discloses a lunar modulation parameter determination method and device for observing M2 partial tide through a GNSS, and the method comprises the steps: resolving GNSS data under the condition that first noise and second noise are optimal, obtaining a GNSS coordinate time sequence, extracting an M2 partial tide harmonic constant in the GNSS coordinate time sequence, constructing a first model and a second model according to the M2 partial tide harmonic constant, and determining the lunar modulation parameter of the M2 partial tide observed by the GNSS. And determining an optimal model according to the decision coefficients of the first model and the second model, and resolving the optimal model to obtain the lunar modulation parameter of the M2 partial tide. According to the method, the lunar modulation parameters of the M2 partial tide are obtained based on the GNSS data, and compared with a theoretical value calculated by a balance tide theory, the theoretical value is more accurate.

Description

Technical Field

[0001] The present invention relates to a method and device for determining lunar modulation parameters of GNSS observation of M2 tidal components, belonging to the interdisciplinary field of GNSS precision positioning and tidal load displacement. Background Art

[0002] Under the influence of tidal forces from celestial bodies such as the sun and the moon, the sea level will rise and fall periodically. This phenomenon is called ocean tide, or simply sea tide. The elastic response of the solid earth to the redistribution of seawater mass caused by sea tide is called the tidal load effect. In some coastal areas, the vertical tidal load displacement can reach more than ten centimeters, and the horizontal direction is usually several times smaller than the vertical direction. High-precision global navigation satellite system (GNSS) observations can directly estimate the tidal load displacement parameters, and the estimation accuracy of the lunar tide (M2, N2, O1 and Q1) can even reach the sub-millimeter level. In particular, GNSS observations of the M2 tide have also been successfully applied to the detection of the Earth's internal properties, such as the anelastic dispersion effect of the asthenosphere and the buoyancy of the Earth's deep mantle.

[0003] The harmonic analysis method is usually used to extract the tidal load displacement parameters of the long-term GNSS coordinate time series, that is, the harmonic constants (amplitude and Greenwich phase delay) of the main tidal components. The lunar node period (18.61 years) and perigee period (8.85 years) modulate the tidal components on an interannual scale. In order to consider their influence, the node correction (or lunar modulation) calculated by the equilibrium tide theory is usually used in the harmonic analysis, and is widely used in tidal analysis software. However, in some coastal areas where seafloor friction and nonlinear tidal interactions exist, the equilibrium tide theory is not applicable. In this case, the node correction calculated by the equilibrium tide theory is bound to cause systematic errors in the harmonic analysis.

[0004] In some coastal shallow waters, the M2 tidal node and perigee modulation parameters observed by tide gauges have been shown to differ significantly from the equilibrium tide theoretical values. Due to the influence of seafloor friction on tidal signals, the node amplitude modulation in coastal areas such as the Bay of Fundy, the Gulf of Maine, the Bristol Channel and the west coast of Australia is significantly lower than the equilibrium tide theoretical value (amplitude correction factor is 3.7%). Although the third-order term of the spherical harmonic expansion of the astronomical tidal potential (indicated by a leading superscript 3) is very small, an effective perigee modulation has also been found in the Gulf of Maine. 3 M2 and resonance enhanced 3 N2. Unlike the above-mentioned ocean tides, it is still unknown whether there are lunar node and perigee modulation biases in the ocean tide load displacement observed by GNSS. If so, it may lead to incorrect geophysical interpretation. As one of the main tidal components of ocean tide load displacement, the M2 tidal component has a wide range of scientific applications. Therefore, it is particularly important to accurately determine the lunar modulation parameters of the M2 tidal component (i.e., node and perigee modulation parameters). Summary of the invention

[0005] The present invention provides a method and device for determining lunar modulation parameters of M2 tidal components observed by GNSS, which solves the problems disclosed in the background technology.

[0006] According to one aspect of the present disclosure, a method for determining lunar modulation parameters of M2 tidal components observed by GNSS is provided, comprising: When the first noise and the second noise are optimal, the GNSS data is solved to obtain the GNSS coordinate time series; wherein the first noise is the zenith tropospheric delay process noise, and the second noise is the horizontal tropospheric gradient process noise; Extract the M2 tidal harmonic constant from the GNSS coordinate time series; According to the M2 tidal harmonic constant, a first model and a second model are constructed; wherein the first model is a node modulation estimation model, and the second model is a node and perigee modulation estimation model; Determine the optimal model based on the determination coefficient of the first model and the second model; The optimal model is solved to obtain the intersection point modulation parameters, or the intersection point modulation parameters and the perigee modulation parameters.

[0007] Furthermore, the method further includes a step of optimizing the first noise and the second noise, the step comprising: The second noise is fixed, the first noise is adjusted, and the GNSS data is solved to obtain the GNSS coordinate time series after each adjustment of the first noise, and the first noise corresponding to the GNSS coordinate time series with the lowest standard deviation is taken as the optimal first noise; The optimal first noise is fixed, the second noise is adjusted, and the GNSS data is solved to obtain the GNSS coordinate time series after each second noise adjustment, and the second noise corresponding to the GNSS coordinate time series with the lowest standard deviation is taken as the optimal second noise.

[0008] Furthermore, a sliding time window method is used to extract the M2 tidal harmonic constant, and in each time window, the median value in the time window corresponds to the time of the M2 tidal harmonic constant.

[0009] Furthermore, the time window is two years, sliding once every year.

[0010] Furthermore, the formula of the first model is: ; The formula for the second model is: ; In the formula, H ( t ) is the timet The M2 tidal harmonic constant, They are the constant term, the linear trend term, the cosine function amplitude of the intersection point, the sine function amplitude of the intersection point, the cosine function amplitude of the perigee point, and the sine function amplitude of the perigee point. The parameters , N is the mean longitude of the lunar ascending node, P is the mean longitude of the lunar perigee.

[0011] Further, determining the optimal model according to the determination coefficients of the first model and the second model includes: If the determination coefficient of model M is greater than the threshold, the determination coefficient of model M is greater than the determination coefficient of another model, and the similarity between the least squares fitting curve of model M and the tidal harmonic constant of M2 is greater than the similarity between the least squares fitting curve of another model and the tidal harmonic constant of M2, then model M is the optimal model; wherein model M is the first model or the second model.

[0012] Further, the optimal model is solved to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters, including: The optimal model is solved by least square fitting to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters; wherein the intersection modulation parameters are , the perigee modulation parameter is .

[0013] According to another aspect of the present disclosure, a device for determining lunar modulation parameters of GNSS observation of M2 tidal components is provided, comprising: The coordinate time series acquisition module solves the GNSS data to obtain the GNSS coordinate time series when the first noise and the second noise are optimal; wherein the first noise is the zenith tropospheric delay process noise, and the second noise is the horizontal tropospheric gradient process noise; The harmonic constant extraction module extracts the M2 tidal harmonic constant from the GNSS coordinate time series; A model building module, constructing a first model and a second model according to the M2 tidal harmonic constant; wherein the first model is a node modulation estimation model, and the second model is a node and perigee modulation estimation model; A model determination module determines an optimal model according to the determination coefficients of the first model and the second model; The solving module solves the optimal model to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters.

[0014] According to another aspect of the present disclosure, a computer-readable storage medium is provided, which stores one or more programs, and the one or more programs include instructions. When the instructions are executed by a computing device, the computing device executes a method for determining lunar modulation parameters of GNSS observation of M2 tidal components.

[0015] According to another aspect of the present disclosure, a computer device is provided, comprising one or more processors and one or more memories, wherein one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors, and the one or more programs include instructions for executing a method for determining lunar modulation parameters of GNSS observations of the M2 tidal component.

[0016] The beneficial effects achieved by the present invention are as follows: 1. The present invention solves GNSS data to obtain GNSS coordinate time series, obtains M2 tidal harmonic constants from the GNSS coordinate time series, constructs an intersection modulation estimation model and an intersection and perigee modulation estimation model, obtains an optimal model from the two models based on the determination coefficient, solves the optimal model to obtain lunar modulation parameters, and the lunar modulation parameters are modulation parameters obtained based on measured GNSS data, which are more accurate than the theoretical values ​​calculated by equilibrium tide theory; 2. The present invention obtains GNSS coordinate time series under the condition of optimal noise, which is beneficial to reducing the noise of GNSS coordinate time series and further ensuring the accuracy of lunar modulation parameters; 3. The present invention obtains M2 tidal harmonic constants by means of a sliding time window, the time window is two years, and slides once every year, which can not only extract more accurate M2 tidal harmonic constants, but also ensure that the time interval of M2 tidal harmonic constants is one year, thereby improving data availability; 4. After obtaining accurate lunar modulation parameters, the present invention can compare and analyze with the equilibrium tide theoretical values, further discover the deficiencies of the equilibrium tide theoretical values, and is beneficial to further improve the accuracy of GNSS estimation of M2 tidal harmonic constants. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Flow chart of the method for determining the lunar modulation parameters for GNSS observations of the M2 tidal component; Figure 2 This is the least squares fitting diagram of the first model of the vertical M2 harmonic constant of the TERS station; Figure 3 This is the least squares fitting diagram of the second model of the vertical M2 harmonic constant of the TERS station; Figure 4 Block diagram of the apparatus for determining lunar modulation parameters for GNSS observations of the M2 tidal component. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of the present disclosure to clearly and completely describe the technical solutions in the embodiments of the present disclosure. It is obvious that the described embodiments are only part of the embodiments of the present disclosure, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present disclosure and its application or use. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure.

[0019] Unless specifically stated otherwise, the relative arrangement of components and steps, the numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present disclosure.

[0020] At the same time, it should be understood that for the convenience of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship.

[0021] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered part of the specification.

[0022] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0023] It should be noted that similar symbols and letters refer to similar items in the following figures, and therefore, once an item is defined in one figure, it does not require further discussion in subsequent figures.

[0024] At the same time, in the description of the embodiments of the present application, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance. Therefore, the features defined as "first" or "second" may explicitly or implicitly include one or more features.

[0025] In order to solve the problem of accurately determining the lunar modulation parameters of the M2 tidal component observed by GNSS, the present disclosure proposes a method and device for determining the lunar modulation parameters of the M2 tidal component observed by GNSS, which specifically determines the node modulation parameters, or the node modulation parameters and the perigee modulation parameters based on the measured GNSS data.

[0026] See also Figure 1 , Figure 1It is a flow chart of a method for determining lunar modulation parameters of an M2 tidal component provided in an embodiment of the present disclosure. The method can be executed by a modulation parameter determination device, which can be a terminal device or a server. Among them, the terminal device can include but is not limited to mobile phones, computers, smart wearable devices, smart vehicle-mounted devices, etc., which are not limited by the embodiments of the present application; the server can be an independent physical server, or a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, big data and artificial intelligence platforms, etc., which are not limited by the embodiments of the present application. Optionally, the method can also be executed collaboratively by multiple electronic devices with computing power. For the sake of ease of explanation, the subsequent embodiments are described as being executed by a modulation parameter determination device.

[0027] like Figure 1 As shown, step 1 of the embodiment is to solve the GNSS data to obtain the GNSS coordinate time series when the first noise and the second noise are optimal; wherein the first noise is the zenith tropospheric delay process noise, and the second noise is the horizontal tropospheric gradient process noise.

[0028] It should be noted that the GNSS data are GNSS observation data with a period greater than 18.61 years. Due to the presence of noise in the data, in order to reduce the impact of noise, it is possible to prioritize determining the optimal value of the zenith tropospheric delay process noise and the optimal value of the horizontal tropospheric gradient process noise, that is, optimizing the first noise and the second noise.

[0029] In some embodiments, the process of optimizing the first noise and the second noise may be as follows: 11) Fix the second noise, adjust the first noise, and solve the GNSS data to obtain the GNSS coordinate time series after each adjustment of the first noise, and take the first noise corresponding to the GNSS coordinate time series with the lowest standard deviation as the optimal first noise.

[0030] The second noise can be fixed by the default value of the GNSS precision data processing software, that is, the second noise is fixed to the default value, and the first noise takes the default value as the reference value. It is divided by 2 each time it becomes smaller, and multiplied by 2 each time it becomes larger. The reduction and increase are performed 3 to 4 times to determine the variation range of the first noise and the first noise of each adjustment. When the standard deviation of the GNSS coordinate time series is the lowest, the corresponding value is the optimal value of the first noise.

[0031] GNSS data is solved using dynamic PPP solution, which refers to the use of GNSS data for real-time positioning, and the precise position calculation of dynamic targets through precise point positioning (PPP) technology. Dynamic PPP solution plays an important role in various applications, including but not limited to vehicle navigation, drone flight control, mobile communication base station positioning, etc.

[0032] 12) Fix the optimal first noise, adjust the second noise, and solve the GNSS data to obtain the GNSS coordinate time series after each second noise adjustment, and take the second noise corresponding to the GNSS coordinate time series with the lowest standard deviation as the optimal second noise.

[0033] The optimal first noise is fixed, and the second noise is also selected according to the above process. Similarly, the optimal value of the second noise can be obtained.

[0034] Under the optimal conditions of the first and second noises, dynamic PPP solution is performed on the GNSS data (without correction of tidal load displacement), which can obtain high-precision and high-temporal-resolution GNSS coordinate time series, which is beneficial to reducing the noise of the GNSS coordinate time series and further ensuring the accuracy of the lunar modulation parameters of the M2 tidal component.

[0035] Taking the GPS observation data of TERS station (5.2194°E, 56.0957°N) of the European EUREF permanent GNSS network from January 1, 2001 to November 26, 2022 as an example, the PRIDE PPP-AR v3.0 software was used to dynamically PPP solve the GPS data, and the GPS precise orbit and clock products used the IGS third reprocessing products of CODE to fix the floating point ambiguity. The recommended values ​​of the first noise and the second noise are both 0.4 mm / sqrt(s). Therefore, the second noise is first fixed to 0.4 mm / sqrt(s), and the first noise is set to 0.05, 0.1, 0.2, 0.4, 0.8, 1.6, 3.2 and 6.4 mm / sqrt(s) respectively. It is found that the optimal value is 1.6 mm / sqrt(s), which can minimize the standard deviation of the GNSS three-dimensional coordinate time series. Then, the first noise is fixed at 1.6 mm / sqrt(s), and the second noise is also changed according to the above value. Similarly, the optimal value can be obtained to be 0.1 mm / sqrt(s). Finally, under the optimal noise condition, dynamic PPP solution is performed without correcting the tidal load displacement to obtain the final GNSS coordinate time series.

[0036] return Figure 1 , step 2 of the embodiment, extracting the M2 tidal harmonic constant from the GNSS coordinate time series; wherein the M2 tidal harmonic constant is the amplitude and Greenwich phase delay, which is a time-varying constant.

[0037] At present, annual data is often used to extract the M2 tidal harmonic constant, that is, each year is taken as a period and extracted once. However, in some embodiments, a sliding time window method is used to extract the M2 tidal harmonic constant, and in each time window, the median value in the time window corresponds to the time of the M2 tidal harmonic constant; wherein, the time window can be set to two years, and slide once every year. In this way, not only a more accurate M2 tidal harmonic constant can be extracted, but also the time interval of the M2 tidal harmonic constant can be guaranteed to be one year, thereby improving data availability.

[0038] When the length of the GNSS coordinate time series is less than 4 years, increasing the length of the time series can improve the estimation accuracy of the tidal load displacement parameters to a certain extent. Taking the TERS station above as an example, the sliding time window is two years, sliding once a year, that is, 2001~2002, 2002~2003, ..., 2021~2022, and the extracted M2 harmonic constant time is the middle moment of each time window, that is, 2002.0, 2003.0, ..., 2022.0, and the time interval is still 1 year, which ensures data availability while improving the M2 accuracy.

[0039] It should be noted that when using harmonic analysis to extract the M2 tidal harmonic constant, it is necessary to consider the influence of the four and a half weekly main tides (M2, S2, N2 and K2) and the four weekly main tides (K1, O1, P1 and Q1).

[0040] return Figure 1 In step 3 of the embodiment, a first model and a second model are constructed according to the M2 tidal harmonic constant; wherein the first model is an intersection modulation estimation model, and the second model is an intersection and perigee modulation estimation model.

[0041] It should be noted that the first model considers the 18.61-year node period change, and the second model considers both the 18.61-year node and the 8.85-year perigee period change. Therefore, the formula of the first model can be expressed as: ; The formula of the second model can be expressed as: ; In the formula, H ( t ) is the time t The M2 tidal harmonic constant, time t The unit is year, They are the constant term, the linear trend term, the cosine function amplitude of the intersection point, the sine function amplitude of the intersection point, the cosine function amplitude of the perigee point, and the sine function amplitude of the perigee point. The parameters , Nis the mean longitude of the lunar ascending node, P is the mean longitude of the lunar perigee.

[0042] ; ; In the formula, T The Julian century is the number from the early morning of January 1, 1990 to the time t A Julian century is 36525 days.

[0043] return Figure 1 , step 4 of the embodiment, determines the optimal model based on the determination coefficients of the first model and the second model.

[0044] It should be noted that the coefficient of determination of the least squares fitting model R 2 It is statistically significant only when it is greater than 0.5. 2 The model with a larger least squares fitting curve that better matches the original data is the optimal model, so the process of determining the optimal model can be as follows: If the determination coefficient of model M is greater than the threshold (i.e., 0.5 mentioned above), the determination coefficient of model M is greater than the determination coefficient of another model, and the similarity between the least squares fitting curve of model M and the tidal harmonic constant of M2 is greater than the similarity between the least squares fitting curve of another model and the tidal harmonic constant of M2, then model M is the optimal model; wherein model M is the first model or the second model.

[0045] Take the TERS station above as an example, see Figure 2 and 3 The first and second models are used to fit the M2 tidal harmonic constant of the TERS station. The amplitude and phase delay fitting determination coefficient R obtained by the second model is 2 They are 0.91 and 0.84 respectively, which are significantly higher than 0.79 and 0.81 of the first model, and the fitting curve is more consistent with the time-varying M2 tidal harmonic constant, especially the amplitude fitting. In addition to the vertical direction shown in the figure, the same is true for the east direction. The average amplitude of M2 in the north direction is small, only 1.9 mm. The fitting effects of each model are poor. In summary, the second model is the optimal model.

[0046] return Figure 1 In step 5 of the embodiment, the optimal model is solved to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters.

[0047] Step 5 can specifically use least square fitting to solve the optimal model to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters; wherein the intersection modulation parameters are , the perigee modulation parameter is , the modulation parameter is amplitude or phase delay modulation.

[0048] If the optimal model is the first model, the perigee modulation parameters can be ignored and only the intersection modulation parameters can be calculated. If it is the second model, both the intersection modulation parameters and the perigee modulation parameters can be calculated simultaneously.

[0049] Taking the TERS station above as an example, the intersection point of the M2 tidal component and the perigee modulation parameter results are listed in Table 1. Note: The amplitude unit in the table is mm, the amplitude ratio unit is %, the phase unit is degree, and the formal error with a 95% confidence interval is listed.

[0050] Table 1 The table of the modulation parameters of the intersection and perigee of the M2 tidal component

[0051] As shown in Table 1, the above method can accurately extract the modulation parameters of the lunar nodes and perigee of the M2 tidal component, especially in the vertical direction and east direction of the TERS station where the M2 amplitude is large, and the formal error of the estimated value is small. However, the M2 amplitude in the north direction is small, although the determination coefficient R 2 It is still greater than 0.5, but the formal error of the estimated value is large, which shows that when the M2 tidal signal is small, it is easily affected by the GNSS observation noise, making it difficult to obtain accurate intersection and perigee signals.

[0052] It should be noted that the calculation results of the above method can be further used to verify the insufficiency of the theoretical value of the equilibrium tide. Specifically, the lunar modulation parameters obtained by the above method are compared with the lunar modulation parameters obtained by the equilibrium tide theory (i.e., the theoretical value), so as to determine whether the theoretical value of the equilibrium tide is insufficient. This is conducive to further improving the accuracy of GNSS estimation of the M2 component tide and avoiding the erroneous geophysical interpretation or application of the M2 component tide that may be caused by the deviation of the theoretical value of the equilibrium tide.

[0053] Taking the above TERS station as an example, the difference between the modulation parameters obtained by the above method and the theoretical value can be seen in Table 2.

[0054] Table 2 The difference between the intersection point and perigee modulation parameters of the M2 tidal component

[0055] As shown in Table 2, in the vertical and east directions where the GNSS estimated values ​​(i.e., the values ​​obtained by the above method) have small formal errors, the intersection amplitude modulation is significantly lower than the theoretical value of the equilibrium tide by 3% and 1.5%, while the perigee amplitude modulation is higher than the theoretical value of the equilibrium tide by 1.7% and 1.8%, and the phase delay deviations between the intersection and the perigee are both small, less than 0.7°. The vertical M2 average amplitude of TERS is 8.5 mm, so the intersection and perigee amplitude modulation deviations will cause the M2 amplitude errors to be as high as 0.26 mm and 0.14 mm. Ignoring these errors may lead to incorrect geophysical interpretations and applications.

[0056] The above method dynamically PPP solves GNSS data to obtain GNSS coordinate time series, obtains M2 tidal harmonic constants from the GNSS coordinate time series, constructs node modulation estimation model and node and perigee modulation estimation model, obtains the optimal model from the two models based on the determination coefficient, and solves the optimal model to obtain lunar modulation parameters. The lunar modulation parameters are modulation parameters obtained based on measured GNSS data, which are more accurate than the theoretical values ​​calculated by equilibrium tide theory. The obtained modulation parameters can be further compared with the equilibrium tide theoretical values ​​for analysis, and the deficiencies of the equilibrium tide theoretical values ​​are found, which is conducive to further improving the accuracy of GNSS estimation of M2 tidal components.

[0057] See also Figure 4 , Figure 4 A block diagram of a device for determining lunar modulation parameters for GNSS observation of M2 tidal components provided in an embodiment of the present disclosure, the device is a virtual device that can be loaded and executed by a computer device, the computer device may include the above-mentioned modulation parameter determination device, Figure 4 The device may include a coordinate time series acquisition module, a harmonic constant extraction module, a model construction module, a model determination module and a solution module, which, when used to execute the above-mentioned method for determining the lunar modulation parameters of the GNSS observation of the M2 tidal component, can: The coordinate time series acquisition module is configured to solve the GNSS data and obtain the GNSS coordinate time series when the first noise and the second noise are optimal; wherein the first noise is the zenith tropospheric delay process noise, and the second noise is the horizontal tropospheric gradient process noise.

[0058] The harmonic constant extraction module is configured to extract the M2 tidal harmonic constant in the GNSS coordinate time series.

[0059] The model building module is configured to construct a first model and a second model based on the M2 tidal harmonic constant; wherein the first model is an intersection modulation estimation model, and the second model is an intersection and perigee modulation estimation model.

[0060] The model determination module is configured to determine the optimal model according to the determination coefficients of the first model and the second model.

[0061] The solving module is configured to solve the optimal model to obtain the intersection point modulation parameters, or the intersection point modulation parameters and the perigee modulation parameters.

[0062] The above-mentioned device uses dynamic PPP to solve GNSS data to obtain GNSS coordinate time series, obtains M2 tidal harmonic constants from the GNSS coordinate time series, constructs intersection modulation estimation models and intersection and perigee modulation estimation models, obtains the optimal model from the two models based on the determination coefficient, and solves the optimal model to obtain lunar modulation parameters. The lunar modulation parameters are modulation parameters obtained based on measured GNSS data, which are more accurate than the theoretical values ​​calculated by equilibrium tide theory.

[0063] The present disclosure also relates to a computer-readable storage medium, which stores one or more programs, and the one or more programs include instructions. When the instructions are executed by a computing device, the computing device executes a method for determining lunar modulation parameters of GNSS observation of M2 tides.

[0064] The present disclosure also relates to a computer device, comprising one or more processors and one or more memories, wherein one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors, and the one or more programs include instructions for executing a method for determining lunar modulation parameters of GNSS observations of the M2 tidal component.

[0065] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0066] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1A device that provides the functions specified in a block or multiple blocks.

[0067] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0068] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0069] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are included in the scope of the claims of the present invention to be approved.

Claims

1. A method for determining the lunar modulation parameters of the M2 tidal component observed by GNSS, characterized in that: include: When the first noise and the second noise are optimal, the GNSS data is solved to obtain the GNSS coordinate time series; wherein the first noise is the zenith tropospheric delay process noise, and the second noise is the horizontal tropospheric gradient process noise; Extract the M2 tidal harmonic constant from the GNSS coordinate time series; According to the M2 tidal harmonic constant, a first model and a second model are constructed; wherein the first model is a node modulation estimation model, and the second model is a node and perigee modulation estimation model; Determine the optimal model based on the determination coefficient of the first model and the second model; The optimal model is solved to obtain the intersection point modulation parameters, or the intersection point modulation parameters and the perigee modulation parameters.

2. The method according to claim 1, characterized in that The method further comprises the step of optimizing the first noise and the second noise, the step comprising: The second noise is fixed, the first noise is adjusted, and the GNSS data is solved to obtain the GNSS coordinate time series after each adjustment of the first noise, and the first noise corresponding to the GNSS coordinate time series with the lowest standard deviation is taken as the optimal first noise; The optimal first noise is fixed, the second noise is adjusted, and the GNSS data is solved to obtain the GNSS coordinate time series after each second noise adjustment, and the second noise corresponding to the GNSS coordinate time series with the lowest standard deviation is taken as the optimal second noise.

3. The method according to claim 1, characterized in that: The sliding time window method is used to extract the M2 tidal harmonic constant, and in each time window, the median value in the time window corresponds to the time of the M2 tidal harmonic constant.

4. The method according to claim 3, characterized in that The time window is two years, sliding once every year.

5. The method according to claim 1, characterized in that The formula for the first model is: ； The formula for the second model is: ； In the formula, H ( t ) is the time t The M2 tidal harmonic constant, They are the constant term, the linear trend term, the cosine function amplitude of the intersection point, the sine function amplitude of the intersection point, the cosine function amplitude of the perigee point, and the sine function amplitude of the perigee point. The parameters , N is the mean longitude of the lunar ascending node, P is the mean longitude of the lunar perigee.

6. The method according to claim 1, characterized in that According to the determination coefficients of the first model and the second model, the optimal model is determined, including: If the determination coefficient of model M is greater than the threshold, the determination coefficient of model M is greater than the determination coefficient of another model, and the similarity between the least squares fitting curve of model M and the tidal harmonic constant of M2 is greater than the similarity between the least squares fitting curve of another model and the tidal harmonic constant of M2, then model M is the optimal model; wherein model M is the first model or the second model.

7. The method according to claim 1, characterized in that The optimal model is solved to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters, including: The optimal model is solved by least square fitting to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters; wherein the intersection modulation parameters are , the perigee modulation parameter is .

8. A device for determining lunar modulation parameters of GNSS observation of M2 tidal components, characterized in that: include: The coordinate time series acquisition module solves the GNSS data to obtain the GNSS coordinate time series when the first noise and the second noise are optimal; wherein the first noise is the zenith tropospheric delay process noise, and the second noise is the horizontal tropospheric gradient process noise; The harmonic constant extraction module extracts the M2 tidal harmonic constant from the GNSS coordinate time series; A model building module, constructing a first model and a second model according to the M2 tidal harmonic constant; wherein the first model is a node modulation estimation model, and the second model is a node and perigee modulation estimation model; A model determination module determines an optimal model according to the determination coefficients of the first model and the second model; The solving module solves the optimal model to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores one or more programs, and the one or more programs include instructions. When the instructions are executed by a computing device, the computing device executes any one of the methods of claims 1 to 7.

10. A computer device, characterized in that include: One or more processors and one or more memories, one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors, and the one or more programs include instructions for executing any of the methods described in claims 1 to 7.

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