Method and device for determining lunar modulation parameters of GNSS observation of M2 tidal components

Abstract

The present invention discloses a method and apparatus for determining lunar modulation parameters for the M2 component of the tide observed by GNSS. The method comprises: resolving GNSS data under conditions where first and second noise levels are optimized to obtain a GNSS coordinate time series; extracting the M2 component of the tide harmonic constant from the GNSS coordinate time series; constructing a first model and a second model based on the M2 component of the tide harmonic constant; determining the optimal model based on the coefficient of determination of the first and second models; and resolving the optimal model to obtain lunar modulation parameters for the M2 component of the tide. The method obtains lunar modulation parameters for the M2 component of the tide based on GNSS data, and is more accurate than theoretical values ​​calculated using equilibrium tide theory.

Description

Technical Field

[0001] The present invention relates to a method and device for determining lunar modulation parameters for GNSS observation of the M2 tidal component, 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 ocean tide. The elastic response of the solid earth to the redistribution of seawater mass caused by ocean tide is called the ocean tide load effect. In some coastal areas, the vertical ocean tide 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 ocean tide 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 interior properties, such as the anelastic dispersion effect of the asthenosphere and the buoyancy of the Earth's deep mantle.

[0003] Harmonic analysis is commonly used to extract tidal load displacement parameters, namely the harmonic constants (amplitude and Greenwich phase delay) of the main tidal components, from long-term GNSS coordinate time series. The lunar node period (18.61 years) and perigee period (8.85 years) modulate tidal components on an interannual scale. To account for these effects, node corrections (also known as lunar modulations) calculated using equilibrium tide theory are often used in harmonic analysis and are widely adopted in tidal analysis software. However, equilibrium tide theory is not applicable in some coastal areas where seafloor friction and nonlinear tidal interactions exist. In such cases, node corrections calculated using equilibrium tide theory are bound to introduce systematic errors in harmonic analysis.

[0004] In some coastal shallow waters, the M2 tidal intersection 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 seabed friction on tidal signals, the intersection 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 lunar perigee modulation has also been found in the Gulf of Maine. 3 M2 and resonance-enhanced 3 Unlike the aforementioned ocean tides, it remains unknown whether GNSS-observed ocean load displacements are modulated by the lunar nodes and perigee. If so, this bias could lead to erroneous geophysical interpretations. As one of the primary components of ocean load displacements, the M2 tide has a wide range of scientific applications. Therefore, accurately determining the lunar modulation parameters of the M2 tide (i.e., the node and perigee modulation parameters) is crucial. Summary of the Invention

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

[0006] According to one aspect of the present disclosure, a method for determining lunar modulation parameters for GNSS observation of the M2 tidal component is provided, comprising:

[0007] Under the condition that 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;

[0008] Extract the M2 tidal harmonic constant from the GNSS coordinate time series;

[0009] 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;

[0010] Determine the optimal model based on the coefficient of determination of the first model and the second model;

[0011] The optimal model is solved to obtain the intersection point modulation parameters, or the intersection point modulation parameters and the perigee modulation parameters.

[0012] Furthermore, the method further includes a step of optimizing the first noise and the second noise, the step comprising:

[0013] Fix the second noise, adjust the first noise, and solve the GNSS data to obtain the GNSS coordinate time series after each first noise adjustment. The first noise corresponding to the GNSS coordinate time series with the lowest standard deviation is taken as the optimal first noise.

[0014] 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. The second noise corresponding to the GNSS coordinate time series with the lowest standard deviation is used as the optimal second noise.

[0015] Furthermore, a sliding time window method is used to extract the M2 tidal harmonic constant, and within each time window, the median value in the time window corresponds to the time of the M2 tidal harmonic constant.

[0016] Furthermore, the time window is two years, sliding once every year.

[0017] Furthermore, the formula of the first model is:

[0018] H′(t)=β1+β2t+β3cos(N′)+β4sin(N′);

[0019] The formula for the second model is:

[0020] H(t)=β1+β2t+β3cos(N′)+β4sin(N′)+β5cos(P)+β6sin(P);

[0021] where H′(t) is the M2 tidal harmonic constant at time t in the first model, H(t) is the M2 tidal harmonic constant at time t in the second model, β1, β2, β3, β4, β5, and β6 are the constant term, the linear trend term, the amplitude of the node cosine function, the amplitude of the node sine function, the amplitude of the perigee cosine function, and the amplitude of the perigee sine function, respectively. The parameter N′=-N, N is the mean longitude of the lunar ascending node, and P is the mean longitude of the lunar perigee.

[0022] Furthermore, determining the optimal model based on the coefficient of determination of the first model and the second model includes:

[0023] If the coefficient of determination of model M is greater than the threshold, the coefficient of determination of model M is greater than the coefficient of determination 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.

[0024] Furthermore, the optimal model is solved to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters, including:

[0025] 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

[0026] According to another aspect of the present disclosure, a device for determining lunar modulation parameters for GNSS observation of the M2 tidal component is provided, comprising:

[0027] The coordinate time series acquisition module solves the GNSS data under the conditions of optimal first noise and second noise to obtain the GNSS coordinate time series. The first noise is the zenith tropospheric delay process noise, and the second noise is the horizontal tropospheric gradient process noise.

[0028] Harmonic constant extraction module, extracts the M2 tidal harmonic constant from the GNSS coordinate time series;

[0029] A model construction module constructs a first model and a second model based on 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;

[0030] A model determination module determines the optimal model based on the determination coefficients of the first model and the second model;

[0031] The solving module solves the optimal model to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters.

[0032] 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 performs a method for determining lunar modulation parameters of GNSS observations of the M2 tidal component.

[0033] 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 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.

[0034] The beneficial effects achieved by the present invention are as follows: 1. The present invention solves GNSS data to obtain a GNSS coordinate time series, obtains the M2 tidal harmonic constant 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 coefficient of determination, and solves the optimal model to obtain lunar modulation parameters. The lunar modulation parameters are modulation parameters obtained based on measured GNSS data and are more accurate than the theoretical values ​​calculated by equilibrium tide theory. 2. The present invention obtains the GNSS coordinate time series under the condition of optimal noise, which is beneficial to reducing the noise of the GNSS coordinate time series and further ensuring the accuracy of the lunar modulation parameters. 3. The present invention obtains the M2 tidal harmonic constant by a sliding time window. The time window is two years and slides once every year. This not only can extract a more accurate M2 tidal harmonic constant, but also can ensure that the time interval of the M2 tidal harmonic constant is one year, thereby improving data availability. 4. After the accurate lunar modulation parameters are obtained by the present invention, they can be compared and analyzed with the equilibrium tide theoretical values ​​to further identify the deficiencies of the equilibrium tide theoretical values, which is beneficial to further improving the accuracy of GNSS estimation of the M2 tidal. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Flowchart of the method for determining lunar modulation parameters for GNSS observations of the M2 tidal component;

[0036] Figure 2Schematic diagram of the least squares fitting of the first model of the vertical M2 harmonic constant of the TERS station;

[0037] Figure 3 Schematic diagram of the least squares fitting of the second model of the vertical M2 harmonic constant of the TERS station;

[0038] Figure 4 Block diagram of the apparatus for determining lunar modulation parameters for GNSS observations of the M2 tidal component. DETAILED DESCRIPTION

[0039] 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 in no way 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 making creative work are within the scope of protection of the present disclosure.

[0040] 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.

[0041] 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.

[0042] 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.

[0043] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0044] It should be noted that like symbols and letters refer to like items in the following figures, so once an item is defined in one figure, it does not need to be further discussed in subsequent figures.

[0045] At the same time, in the description of the embodiments of this application, the terms "first" and "second" are used only to distinguish the description and should not be understood as indicating or implying relative importance. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more features.

[0046] 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 nodal modulation parameters, or the nodal modulation parameters and the perigee modulation parameters based on the measured GNSS data.

[0047] See Figure 1 , Figure 1 This is a flowchart of a method for determining lunar modulation parameters of an M2 tidal component provided by 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. The terminal device can include but is not limited to a mobile phone, a computer, a smart wearable device, a smart vehicle-mounted device, etc., which is not limited by the embodiment 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 is not limited by the embodiment of the present application. Optionally, the method can also be collaboratively executed 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.

[0048] like Figure 1 As shown, in step 1 of the embodiment, the GNSS data is solved to obtain a 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.

[0049] 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.

[0050] In some embodiments, the process of optimizing the first noise and the second noise may be as follows:

[0051] 11) Fixing the second noise, adjusting the first noise, and solving the GNSS data to obtain the GNSS coordinate time series after each first noise adjustment, and taking the first noise corresponding to the GNSS coordinate time series with the lowest standard deviation as the optimal first noise.

[0052] The second noise can be fixed using 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 uses the default value as a reference value. Each time it is reduced, it is divided by 2, and each time it is increased, it is multiplied by 2. This is repeated 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, this corresponds to the optimal value of the first noise.

[0053] GNSS data is resolved using dynamic point positioning (PPP). Dynamic PPP uses GNSS data for real-time positioning, using precise point positioning (PPP) technology to accurately calculate the position of dynamic targets. Dynamic PPP plays an important role in various applications, including but not limited to vehicle navigation, drone flight control, and mobile communication base station positioning.

[0054] 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. The second noise corresponding to the GNSS coordinate time series with the lowest standard deviation is used as the optimal second noise.

[0055] The optimal first noise is fixed, and the second noise is also determined according to the above process. Similarly, the optimal value of the second noise can be obtained.

[0056] Under the condition of optimal first and second noise, dynamic PPP solution is performed on GNSS data (without correction for tidal load displacement), which can obtain high-precision and high-temporal-resolution GNSS coordinate time series, which is conducive to reducing the noise of GNSS coordinate time series and further ensuring the accuracy of the lunar modulation parameters of the M2 tidal component.

[0057] GPS observation data from the TERS station (5.2194°E, 56.0957°N) in the European EUREF Permanent GNSS Network from January 1, 2001, to November 26, 2022, were used as an example. PRIDE PPP-AR v3.0 software was used to dynamically calculate the GPS data using PPP. GPS precise orbit and clock products were then processed using the third reprocessing of the IGS from CODE. Floating-point ambiguities were then undifferenced and fixed. The recommended values ​​for both the first and second noise values ​​are 0.4 mm / sqrt(s). Therefore, the second noise was initially fixed at 0.4 mm / sqrt(s). The first noise values ​​were then set to 0.05, 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, and 6.4 mm / sqrt(s). The optimal value, 1.6 mm / sqrt(s), was found to minimize the standard deviation of the GNSS three-dimensional coordinate time series. Next, the first noise factor is fixed at 1.6 mm / sqrt(s), and the second noise factor is varied similarly, achieving an optimal value of 0.1 mm / sqrt(s). Finally, with the noise factor optimized, a dynamic PPP solution is performed without correcting for tidal load displacement to obtain the final GNSS coordinate time series.

[0058] return Figure 1 In step 2 of the embodiment, the M2 tidal harmonic constant is extracted 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.

[0059] Currently, the M2 tidal harmonic constant is often extracted using annual data, with each year being considered as a time period. However, in some embodiments, a sliding time window approach is used to extract the M2 tidal harmonic constant, and within each time window, the median value corresponds to the time of the M2 tidal harmonic constant. The time window can be set to two years, sliding once each year. This not only allows for the extraction of more accurate M2 tidal harmonic constants, but also ensures that the time interval for the M2 tidal harmonic constant is one year, thereby improving data availability.

[0060] When the length of the GNSS coordinate time series is less than four years, increasing the length of the time series can improve the accuracy of tidal load displacement parameter estimation to a certain extent. Taking the TERS station mentioned above as an example, the sliding time window is two years, sliding once a year, that is, 2001-2002, 2002-2003, ..., 2021-2022. The M2 harmonic constant time is extracted as the middle moment of each time window, that is, 2002.0, 2003.0, ..., 2022.0, and the time interval is still one year. This improves M2 accuracy while ensuring data availability.

[0061] It should be noted that when using harmonic analysis to extract the M2 tidal harmonic constant, it is necessary to consider the effects of the four semi-weekly main tides (M2, S2, N2 and K2) and the four weekday main tides (K1, O1, P1 and Q1).

[0062] return Figure 1 In step 3 of the embodiment, a first model and a second model are constructed 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.

[0063] It should be noted that the first model considers the 18.61-year node period change, while the second model considers both the 18.61-year node period change and the 8.85-year perigee period change. Therefore, the formula of the first model can be expressed as:

[0064] H′(t)=β1+β2t+β3cos(N′)+β4sin(N′);

[0065] The formula of the second model can be expressed as:

[0066] H(t)=β1+β2t+β3cos(N′)+β4sin(N′)+β5cos(P)+β6sin(P);

[0067] where H′(t) is the M2 tidal harmonic constant at time t in the first model, H(t) is the M2 tidal harmonic constant at time t in the second model, the unit of time t is year, β1, β2, β3, β4, β5, and β6 are the constant term, the linear trend term, the amplitude of the node cosine function, the amplitude of the node sine function, the amplitude of the perigee cosine function, and the amplitude of the perigee sine function, respectively. The parameter N′=-N, N is the mean longitude of the ascending node, and P is the mean longitude of the lunar perigee.

[0068] N′=100.8432°+1934.142°T-0.0021°T 2 ;

[0069] P=334.3853°+4069.034°T-0.0103°T 2 ;

[0070] Where T is the Julian century, specifically the Julian century from the early morning of January 1, 1990 to time t. A Julian century is 36,525 days.

[0071] return Figure 1 In step 4 of the embodiment, the optimal model is determined based on the determination coefficients of the first model and the second model.

[0072] It should be noted that the coefficient of determination R of the least squares fitting of the model 2It 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:

[0073] If the coefficient of determination of model M is greater than the threshold (i.e., 0.5 mentioned above), the coefficient of determination of model M is greater than the coefficient of determination 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.

[0074] 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 coefficients R obtained by the second model are 2 The fitted curves are 0.91 and 0.84, respectively, significantly higher than the first model's 0.79 and 0.81. The fitted curves are more consistent with the time-varying M2 tidal harmonic constant, particularly the amplitude fit. This is also true for the easterly direction, as shown in the figure. The northerly M2 amplitude is relatively small, at only 1.9 mm. The fitting results of all models are relatively poor. In summary, the second model is the optimal model.

[0075] 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.

[0076] Step 5 can specifically use least square fitting to solve the optimal model to obtain the intersection modulation parameter, or the intersection modulation parameter and the perigee modulation parameter; wherein the intersection modulation parameter is The perigee modulation parameter is The modulation parameters are amplitude or phase delay modulation.

[0077] If the optimal model is the first model, the perigee modulation parameter can be ignored and only the intersection modulation parameter can be calculated. If it is the second model, both the intersection modulation parameter and the perigee modulation parameter can be calculated simultaneously.

[0078] Taking the TERS station above as an example, the results of the M2 tidal intersection and perigee modulation parameters are listed in Table 1. Note: The units of amplitude in the table are mm, the units of amplitude ratio are %, and the units of phase are degrees. The formal errors are listed with 95% confidence intervals.

[0079] Table 1. Modulation parameters of the intersection and perigee of the M2 tide

[0080]

[0081] As shown in Table 1, the above method can accurately extract the lunar node and perigee modulation parameters 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.

[0082] 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 can be 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.

[0083] Taking the TERS station above as an example, the difference between the modulation parameters obtained by the above method and the theoretical values ​​can be seen in Table 2.

[0084] Table 2 Differences between the intersection and perigee modulation parameters of the M2 tide component

[0085]

[0086] Table 2 shows that in the vertical and easting directions, where the GNSS estimates (i.e., the values ​​obtained by the above method) have relatively small formal errors, the nodal amplitude modulation is significantly lower than the theoretical equilibrium tide value by 3% and 1.5%, while the perigee amplitude modulation is higher by 1.7% and 1.8%. The phase delay deviations between the nodal and perigee points are both small, less than 0.7°. The average vertical M2 amplitude of TERS is 8.5 mm. Therefore, the deviation in amplitude modulation between the nodal and perigee points can result in M2 amplitude errors of up to 0.26 mm and 0.14 mm, respectively. Ignoring these errors can lead to erroneous geophysical interpretations and applications.

[0087] The above method dynamically solves GNSS data with PPP to obtain the GNSS coordinate time series, obtains the M2 tidal harmonic constant from the GNSS coordinate time series, constructs the intersection modulation estimation model and the intersection 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 the lunar modulation parameters. The lunar modulation parameters are modulation parameters obtained based on the measured GNSS data, which are more accurate than the theoretical values ​​calculated by the equilibrium tide theory. The obtained modulation parameters can be further compared with the equilibrium tide theoretical values. The shortcomings of the equilibrium tide theoretical values ​​are found, which is conducive to further improving the accuracy of GNSS estimation of the M2 tidal.

[0088] See also Figure 4 , Figure 4 This is a block diagram of a device for determining lunar modulation parameters for GNSS observation of the M2 component tide 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, may:

[0089] 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.

[0090] The harmonic constant extraction module is configured to extract the M2 tidal harmonic constant from the GNSS coordinate time series.

[0091] The model construction 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.

[0092] The model determination module is configured to determine the optimal model according to the determination coefficients of the first model and the second model.

[0093] 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.

[0094] The above-mentioned device uses dynamic PPP to solve GNSS data to obtain GNSS coordinate time series, obtains the M2 tidal harmonic constant from the GNSS coordinate time series, constructs an intersection modulation estimation model and an intersection 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 the lunar modulation parameters. The lunar modulation parameters are modulation parameters obtained based on measured GNSS data and are more accurate than the theoretical values ​​calculated by equilibrium tide theory.

[0095] The present disclosure also relates to a computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions that, when executed by a computing device, cause the computing device to perform a method for determining lunar modulation parameters of GNSS observations of the M2 tidal component.

[0096] 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 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.

[0097] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely 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 magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] 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 flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, 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 flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0099] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work 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 The function specified in one or more boxes.

[0100] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0101] 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 lunar modulation parameters for GNSS observations of the M2 tidal component, characterized in that: include: Under the condition that 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; If the coefficient of determination of model M is greater than the threshold, the coefficient of determination of model M is greater than the coefficient of determination 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; where model M is the first model or the second model; Solving the optimal model to obtain intersection point modulation parameters, or intersection point modulation parameters and perigee modulation parameters; The formula for the first model above is: H′(t)=β1+β2t+β3cos(N′)+β4sin(N′); The formula for the second model is: H(t)=β1+β2t+β3cos(N′)+β4sin(N′)+β5cos(P)+β6sin(P); where H′(t) is the M2 tidal harmonic constant at time t in the first model, H(t) is the M2 tidal harmonic constant at time t in the second model, β1, β2, β3, β4, β5, and β6 are the constant term, the linear trend term, the amplitude of the node cosine function, the amplitude of the node sine function, the amplitude of the perigee cosine function, and the amplitude of the perigee sine function, respectively; the parameter N′=-N, N is the mean longitude of the lunar ascending node, and P is the mean longitude of the lunar perigee; The method further includes a step of optimizing the first noise and the second noise, the step comprising: Fix the second noise, adjust the first noise, and solve the GNSS data to obtain the GNSS coordinate time series after each first noise adjustment. 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. The second noise corresponding to the GNSS coordinate time series with the lowest standard deviation is used as the optimal second noise.

2. 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.

3. The method according to claim 2, characterized in that The time window is two years, sliding once every year.

4. The method according to claim 1, wherein Solve the optimal model 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 5. A device for determining lunar modulation parameters for GNSS observation of the M2 tidal component, comprising: The coordinate time series acquisition module solves the GNSS data under the conditions of optimal first noise and second noise to obtain the GNSS coordinate time series. The first noise is the zenith tropospheric delay process noise, and the second noise is the horizontal tropospheric gradient process noise. Harmonic constant extraction module, extracts the M2 tidal harmonic constant from the GNSS coordinate time series; A model construction module constructs a first model and a second model based on 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; The model determination module determines that if the coefficient of determination of model M is greater than a threshold, the coefficient of determination of model M is greater than the coefficient of determination 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; A solution module solves the optimal model to obtain the intersection modulation parameters, or the intersection modulation parameters and the perigee modulation parameters; The formula for the first model above is: H′(t)=β1+β2t+β3cos(N′)+β4sin(N′); The formula for the second model is: H(t)=β1+β2t+β3cos(N′)+β4sin(N′)+β5cos(P)+β6sin(P); where H′(t) is the M2 tidal harmonic constant at time t in the first model, H(t) is the M2 tidal harmonic constant at time t in the second model, β1, β2, β3, β4, β5, and β6 are the constant term, the linear trend term, the amplitude of the node cosine function, the amplitude of the node sine function, the amplitude of the perigee cosine function, and the amplitude of the perigee sine function, respectively; the parameter N′=-N, N is the mean longitude of the lunar ascending node, and P is the mean longitude of the lunar perigee; The apparatus further includes a module for optimizing the first noise and the second noise, configured to: Fix the second noise, adjust the first noise, and solve the GNSS data to obtain the GNSS coordinate time series after each first noise adjustment. 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. The second noise corresponding to the GNSS coordinate time series with the lowest standard deviation is used as the optimal second noise.

6. 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 the method according to any one of claims 1 to 4.

7. Computer equipment, characterized in that include: One or more processors and one or more memories, one or more programs stored in the one or more memories and configured to be executed by the one or more processors, the one or more programs including instructions for executing any one of the methods of claims 1 to 4.

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