Methods for reducing tide analysis errors when studying tidal load displacement using GNSS

Abstract

The present invention belongs to the field of ocean monitoring and provides a method for reducing tidal error when studying tidal load displacement using GNSS. The method comprises the following steps: determining tidal pairs N2 to M2, S2 to M2, K2 to M2, K2 to S2, P1 to K1, O1 to K1, Q1 to K1, and Q1 to O1; establishing relative relationships between each tidal pair to obtain the amplitude ratio and lag angle difference of each grid point; calculating the equilibrium tide harmonic constant to obtain the equilibrium tide amplitude of each tidal component corrected by geotidal correction; calculating the GPS data harmonic constant to obtain the amplitude of each tidal component obtained by harmonic analysis of GPS data; and correcting the estimation errors of K1 and K2 tidal components based on the results of the above steps and using relative admittance. The present invention establishes relative relationships between eight tidal pairs and can effectively obtain the relative admittance relationship of each tidal group. Combined with the ratio of the harmonic constant used in GPS data analysis to the corresponding equilibrium tide harmonic constant, the errors of K1 and K2 tidal components can be effectively corrected and the accuracy of K1 and K2 tidal components can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean monitoring, and in particular relates to a method for reducing tide analysis errors when studying tidal load displacement using GNSS. Background Art

[0002] With the rapid development of GNSS technology and data processing methods, GNSS can accurately measure the displacement deformation caused by tidal loading at observation stations and, in turn, derive the harmonic constants of tidal loading displacement, providing a new method for studying tidal loading effects. Generally, when using GNSS to study tidal loading displacement, GPS observations are primarily used. Harmonic analysis of GPS observations requires pre-estimation of the periods of the major tidal components. However, the GPS satellite orbit period (approximately 11.967 hours) is very close to the period of the K2 tidal component (approximately 11.9672 hours). The GPS constellation repetition period (approximately 23.9319 hours) is also very close to the period of the K1 tidal component (approximately 23.9345 hours), which can easily lead to coupling. When extracting tidal loading displacement parameters using GNSS technology, errors with similar periods are easily absorbed by the K1 / K2 tidal components corresponding to the same period, resulting in large errors in the K1 / K2 tidal components estimated by harmonic analysis. Therefore, how to solve the large error in K1 / K2 tide estimation has always been a difficult and hot issue in GNSS research on tidal load displacement. Summary of the Invention

[0003] The present invention utilizes the relative admittances of S2 to M2, N2 to M2, K2 to S2, O1 to K1, P1 to K1 and Q1 to O1 tidal components to correct the problem of excessive errors in the estimation of K1 and K2 tidal components obtained by GPS observation.

[0004] A first aspect of the present invention provides a method for reducing tide analysis errors when studying tidal load displacement using GNSS, characterized by comprising the following steps:

[0005] Step 1, determining tidal pairs; determining tidal pairs is determining tidal pairs of N2 to M2, S2 to M2, K2 to M2, K2 to S2, P1 to K1, O1 to K1, Q1 to K1 and Q1 to O1;

[0006] Step 2: Establish the relative relationship between each tide pair and obtain the amplitude ratio of each grid point. and delay angle difference

[0007] Step 3: Calculate the equilibrium tide harmonic constant and obtain the equilibrium tide amplitude of each component tide after correction by the ground tide.

[0008] Step 4: Calculate the GPS data harmonic constant and obtain the amplitude H of each tidal component obtained by the GPS data harmonic analysis. GpsiAccording to tidal theory, assuming that ζ is the instantaneous displacement of the tidal load in a certain direction of the observation station, the harmonic constant of the main tidal component can be expressed as,

[0009]

[0010] Where S0 is the average position of displacement; H and g are the harmonic constants of each tidal component; f i and u i is the intersection factor and intersection correction angle of the tidal component, V0 is the phase of the ith tidal component of the equilibrium tide at time t = 0; ω i is the tidal angular velocity; here f, ωt and ν0+u are related to time but not location; while H and g are related to location but not time; so the above formula can be written as

[0011]

[0012] in,

[0013]

[0014]

[0015] According to the principle of least squares, solve X i and Y i , and then calculate the harmonic constant H according to the following formula Gps and g Gps ,

[0016]

[0017] Step 5: Based on the results of steps 2, 3, and 4, the K1 and K2 tide estimation errors are corrected using relative admittance.

[0018] In a possible design, the specific process of step 1 is:

[0019] For a certain partial tide i, the admittance M i for

[0020]

[0021] in, H i and g i is the harmonic constant, amplitude and lag angle of the tidal component, C i is the tidal force coefficient. In the same tidal family, the relationship between the main tidal component n and the secondary tidal component m can be expressed as

[0022]

[0023] in

[0024]

[0025] a m / n =g m -g n (4)

[0026] In formula (3), H m / H n That is the amplitude ratio in traditional tidal science, g m -g n is the lag angle difference, A * m / n is the amplitude relationship of the major tidal component n relative to the minor tidal component m, a m / n is the retardation angle of the major tidal component n relative to the minor tidal component m; if the amplitude ratio of the actual tidal component is the same as the ratio of the tidal force, then Equal to 1; in the actual ocean It will not be exactly equal to 1, but it is close to 1 for most sea areas; if the retardation angles of the two tidal components are equal, then a m / n Equal to zero; in the actual ocean a m / n It is generally not equal to zero. For most sea areas, it is greater than zero or less than zero.

[0027] Determine the tidal pairs of N2 to M2, S2 to M2, K2 to M2, K2 to S2, P1 to K1, O1 to K1, Q1 to K1, and Q1 to O1;

[0028]

[0029] g m =a m / n +g n (6) Let the amplitude ratios be The delay angle differences are

[0030] For two tidal components, let the amplitude ratio be H, the lag angle difference be g, and let A = Hcosg, B = Hsing;

[0031] The specific process of step 2 is:

[0032] It is known that there are N observation points, represented by i (i = 1, 2..., N), and the longitude and latitude of each point are in Negative values are used for southern latitudes; λ, In degrees; and is the amplitude ratio and lag angle difference of each tide station observation point;

[0033] For observation station i, calculate its distance to other stations j as

[0034]

[0035] Find the weighted average of point i

[0036]

[0037]

[0038] in, represents the sum of all observation points, excluding point i; R i is the corrected Kelvin wavelength, which is determined based on the water depth near point i as follows:

[0039] Assume that the water depth values of each grid point in and around the sea area are known, that is, the longitude and latitude of point m are Water depth is D m ; For point i, the distance between grid point m and tide gauge station i is calculated as

[0040]

[0041] Select all r im <150×10 3 The water depth values of the points m are averaged and recorded as

[0042] Calculate the corresponding Kelvin wave velocity

[0043]

[0044] Kelvin wavelength

[0045] L i =u i T (13)

[0046] Among them, u i is the Kelvin wave speed, T is the tidal wave period, that is,

[0047] T=360° / ω (14)

[0048] ω is the tidal wave angular velocity;

[0049] Final selection

[0050] R i =κL i (κ=1 / 4) (15)

[0051] For all i=1,2......,N points calculate and and calculate

[0052]

[0053] and root mean square deviation

[0054]

[0055] like

[0056] δ i ≥mσ (18)

[0057] The data at point i is considered abnormal and needs to be discarded;

[0058] To verify the accuracy after removing outliers, and Back-calculate the amplitude ratio of each observation point and delay angle difference

[0059]

[0060]

[0061] Then by

[0062]

[0063]

[0064] Calculate the mean square error of the amplitude ratio and the delay angle difference

[0065]

[0066]

[0067] According to the method described in formula (18), unreasonable observation values are discarded first, and each grid point is set according to the predetermined resolution. The sequence number of each grid point is k (k = 1, 2, ...), and its corresponding longitude and latitude are The distance from the calculated point k to each observation point i is

[0068]

[0069] Find the weighted average of k points

[0070]

[0071]

[0072] where R k The calculation method is the same as that of R in the above formula (15) i The calculation method is the same as

[0073] Depend on and Back-calculate the amplitude ratio of each grid point and delay angle difference

[0074]

[0075]

[0076] In a possible design, the specific process of step 3 is:

[0077] For any observation point The corresponding equilibrium tide height ζ EQ It can be expressed as

[0078]

[0079] Where, f i and u i is the intersection factor and intersection correction angle of the tidal component, V0 is the phase of the ith tidal component of the equilibrium tide at time t = 0; ω i is the tidal angular rate; p is the family number, p = 1 for diurnal tides, p = 2 for semidiurnal tides; λ is the longitude; S = -8h is the Beijing standard time zone code; is the equilibrium tide amplitude of each component tide after correction by the ground tide,

[0080]

[0081]

[0082]

[0083]

[0084] Where, is the latitude.

[0085] In a possible design, the specific process of step 5 is as follows:

[0086] make

[0087] Where H Gpsi is the amplitude of each tidal component obtained by harmonic analysis of GPS data, is the equilibrium tidal amplitude of each component tide, ψ iAs the modulus, the ψ values of the semi-diurnal tides N2, M2, S2 and K2 are curve-fitted, and then the abnormal ψ values of the K2 tide are corrected to the normal fitting curve, thereby completing the correction of the K2 tide error and further improving the accuracy of the K2 tide harmonic constant; similarly, the ψ values of the diurnal tides K1, P1, O1 and Q1 are curve-fitted, and then the abnormal ψ values of the K1 tide are corrected to the normal fitting curve, thereby completing the correction of the K1 tide error and further improving the accuracy of the K1 tide harmonic constant.

[0088] The second aspect of the present invention also provides a device for reducing tidal analysis errors when using GNSS to study tidal load displacements, the device comprising at least one processor and at least one memory, the processor and memory being coupled; a computer program or instruction is stored in the memory; when the processor executes the computer program or instruction, the method for reducing tidal analysis errors when using GNSS to study tidal load displacements as described in the first aspect can be implemented.

[0089] The third aspect of the present invention also provides a computer-readable storage medium, which stores a computer program or instruction. When the computer program or instruction is executed by a processor, it can implement the method of reducing tidal analysis error when using GNSS to study tidal load displacement as described in the first aspect.

[0090] Compared with the prior art, the present invention provides a method for reducing tide analysis errors when studying tidal load displacement using GNSS, and produces the following beneficial effects:

[0091] 1. To address the problem of excessive errors in K2 and K1 tide estimates due to the coupling effect caused by the GPS orbital period being consistent with the K2 tide period, and the GPS constellation repetition period being consistent with the K1 tide period, this paper proposes a method for correcting the errors in K1 and K2 tide estimates obtained from GPS observations based on relative admittance. This method can effectively improve the errors in K1 and K2 tide estimates obtained from GPS observations and enhance their accuracy.

[0092] 2. By accurately obtaining the displacement deformation of the observation station caused by the tidal load through GNSS, and then obtaining the tidal load displacement harmonic constant, the present invention provides a new method for improving the accuracy of studying the tidal load effect.

[0093] 3. To improve the accuracy of studying tidal loading effects, the present invention establishes the relative relationships between eight tidal components, effectively determining the relative admittance relationships for each tidal family. By analyzing the ratio of the harmonic constants to the corresponding equilibrium tidal harmonic constants using GPS data, the present invention effectively corrects errors in the K1 and K2 tidal components and improves their accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 This is a flowchart of the method for correcting the K1 and K2 tide errors obtained from GPS observations according to the present invention.

[0095] Figure 2 This is a schematic diagram of the present invention correcting the K2 tide error.

[0096] Figure 3 This is a simplified schematic diagram of the device structure for correcting the K1 and K2 tidal errors obtained from GPS observations. DETAILED DESCRIPTION

[0097] The invention will be further described below with reference to specific embodiments.

[0098] Example 1:

[0099] In order to realize the calculation technology of K1 and K2 tide errors obtained by GPS observation based on relative admittance correction, it includes the calculation steps of relative admittance calculation and correction of K1 and K2 tide errors obtained by GPS observation. The general process is as follows: Figure 1 shown.

[0100] (1) Determine the tidal

[0101] For a certain partial tide i, the admittance M i for

[0102]

[0103] in H i and g i is the harmonic constant, amplitude and lag angle of the tidal component; C i is the tidal force coefficient. In the same tidal family, the relationship between the main tidal component n and the secondary tidal component m can be expressed as

[0104]

[0105] in

[0106]

[0107] a m / n =g m -g n (4) In formula (3), H m / H n That is the amplitude ratio in traditional tidal science, g m -g n If the amplitude ratio of the actual tidal component is the same as the ratio of the tidal force, then Equal to 1. In the actual ocean It will not be exactly equal to 1, but for most of the sea it is close to 1. If the retardation angles of the two tidal components are equal, then a m / n = zero. In the actual ocean m / n It is generally not equal to zero. For most sea areas, it is greater than zero or less than zero.

[0108] Determine the tidal pairs of N2 to M2, S2 to M2, K2 to M2, K2 to S2, P1 to K1, O1 to K1, Q1 to K1 and Q1 to O1.

[0109]

[0110] g m =a m / n +g n (6)

[0111] Let the amplitude ratios be The delay angle differences are

[0112] For two certain partial tides, let the amplitude ratio be H and the lag angle difference be g, and let A = Hcosg and B = Hsing.

[0113] (2) Establishing the relative relationship between each tide pair

[0114] It is known that there are N observation points, represented by i (i = 1, 2..., N), and the longitude and latitude of each point are in Negative values are used for south latitudes. The unit is degrees. H i and g i is the amplitude ratio and lag angle difference of the observation points at each tide station.

[0115] For observation station i, calculate its distance to other stations j as

[0116]

[0117] Find the weighted average of point i

[0118]

[0119]

[0120] in, Represents the sum of all observation points, excluding point i. i It is determined based on the water depth near point i as follows:

[0121] Assume that the water depth values of each grid point in and around the sea area are known, that is, the longitude and latitude of point m are Water depth is Dm For point i, the distance between grid point m and tide gauge station i is calculated as

[0122]

[0123] Select all r im <150×10 3 m points, and the average water depth values of these points are recorded as

[0124] Calculate the corresponding Kelvin wave velocity

[0125]

[0126] Kelvin wavelength

[0127] L i =u i T (13)

[0128] Where T is the tidal wave period, that is,

[0129] T=360° / ω (14)

[0130] Here ω is the tidal wave angular velocity.

[0131] Final selection

[0132] R i =κL i (κ=1 / 4) (15)

[0133] For all i=1,2......,N points calculate and and calculate

[0134]

[0135] and root mean square deviation

[0136]

[0137] like

[0138] δ i ≥mσ (18)

[0139] It is considered that the data at point i may be abnormal, and whether to discard it is considered. Here, m can be 2.

[0140] To verify the accuracy after removing outliers, and Back-calculate the amplitude ratio of each observation point and delay angle difference

[0141]

[0142]

[0143] Then by

[0144]

[0145]

[0146] Calculate the mean square error of the amplitude ratio and the delay angle difference

[0147]

[0148]

[0149] According to the above method, we first discard unreasonable observation values and set each grid point according to the pre-given resolution. The sequence number of each grid point is k (k = 1, 2, ...), and its corresponding longitude and latitude are The distance from the calculated point k to each observation point i is

[0150]

[0151] Find the weighted average of k points

[0152]

[0153]

[0154] R k The calculation method is similar to the above method.

[0155] Depend on and Back-calculate the amplitude ratio of each grid point and delay angle difference

[0156]

[0157]

[0158] (3) Calculation of equilibrium tidal harmonic constant

[0159] For any observation point The corresponding equilibrium tide height ζ EQ It can be expressed as,

[0160]

[0161] Where, f i and u iis the intersection factor and intersection correction angle of the tidal component, V0 is the phase of the ith tidal component of the equilibrium tide at time t = 0; ω i is the tidal angular rate; p is the family number, p = 1 for diurnal tides, p = 2 for semidiurnal tides; λ is the longitude; S = -8h is the Beijing standard time zone code; is the equilibrium tide amplitude of each component tide after correction by the ground tide,

[0162]

[0163]

[0164]

[0165]

[0166] Where, is the latitude.

[0167] (4) Calculating GPS data harmonic constants

[0168] Analyzing GPS observation data, according to tidal theory, assuming that ζ is the instantaneous displacement of the observation station in one of the east, north and radial directions due to the tidal load, the harmonic constant of the main tidal components can be expressed as:

[0169]

[0170] Where S0 is the average position of displacement; H and g are the harmonic constants of each tidal component; f i and u i is the intersection factor and intersection correction angle of the tidal component, V0 is the phase of the ith tidal component of the equilibrium tide at time t = 0; ω i is the tidal angular velocity; here f, ωt and ν0+u are related to time but not location; while H and g are related to location but not time; so the above formula can be written as

[0171]

[0172] in,

[0173]

[0174]

[0175] According to the principle of least squares, solve X i and Y i , and then calculate the harmonic constant H according to the following formula Gps and g Gps ,

[0176]

[0177] In actual calculations, the GPS satellite orbit period (approximately 11.967 hours) and the GPS constellation repetition period (approximately 23.9319 hours) are very close to the periods of some tidal components (K2 period is approximately 11.9672 hours, and K1 period is approximately 23.9345 hours), which easily leads to coupling. GPS satellite orbit errors are easily absorbed by these tidal components, resulting in large errors in the estimated displacements of the K1 / K2 tidal loads.

[0178] (V) Correction of K1 and K2 tide estimation errors using relative admittance

[0179] In the same tide family, there are main tides and secondary tides. The main tides account for a larger proportion, while the secondary tides account for a smaller proportion. However, the tidal characteristics of the tides in the same tide family are basically the same.

[0180] make

[0181]

[0182] Where H Gpsi is the amplitude of each tidal component obtained by harmonic analysis of GPS data; is the equilibrium tidal amplitude of each component tide, ψ i is the modulus.

[0183] For the same tidal family, the relative admittance characteristics of each tidal component have similar characteristics. For the semi-diurnal tidal family, the relative admittance characteristics of S2 to M2, N2 to M2, and K2 to S2 are similar, so the R values corresponding to the M2, N2, S2 and K2 tidal components are also similar. The ψ values of each semi-diurnal tidal component are curve fitted, and the abnormal ψ value of the K2 tidal component is corrected to the normal fitting curve. This solves the problem of large errors in the estimated results of the K2 tidal load displacement, such as Figure 2 Similarly, for the diurnal tide family, the relative admittance characteristics of O1 to K1, P1 to K1, and Q1 to O1 are similar, so the R values corresponding to the K1, P1, O1, and Q1 tides are also similar. By fitting the ψ values of each semi-diurnal tide and correcting the abnormal ψ value of the K1 tide to the normal fitting curve, the problem of large errors in the estimated results of the K1 tide load displacement is solved.

[0184] Example 2:

[0185] like Figure 3As shown, the present invention also provides a device for reducing tidal error when studying tidal load displacement using GNSS, the device including at least one processor and at least one memory, as well as a communication interface and an internal bus; the memory stores a computer program or instruction; when the processor executes the computer program or instruction, it can implement the method for reducing tidal error when studying tidal load displacement using GNSS as described in Example 1. The internal bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, the bus in the drawings of this application is not limited to only one bus or one type of bus. The memory may include high-speed RAM memory, and may also include non-volatile storage NVM, such as at least one disk memory, and can also be a USB flash drive, a mobile hard disk, a read-only memory, a disk, or an optical disk, etc.

[0186] The device may be provided as a terminal, a server, or other forms of devices.

[0187] Figure 3 is a block diagram of a device shown as an example. The device may include one or more of the following components: a processing component, a memory, a power component, a multimedia component, an audio component, an input / output (I / O) interface, a sensor component, and a communication component. The processing component typically controls the overall operation of the electronic device, such as operations associated with display, phone calls, data communications, camera operation, and recording operations. The processing component may include one or more processors to execute instructions to complete all or part of the steps of the above-mentioned method. In addition, the processing component may include one or more modules to facilitate interaction between the processing component and other components. For example, the processing component may include a multimedia module to facilitate interaction between the multimedia component and the processing component.

[0188] The memory is configured to store various types of data to support the operation of the electronic device. Examples of such data include instructions for any application or method operating on the electronic device, contact data, phone book data, messages, pictures, videos, etc. The memory can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk, or optical disk.

[0189] The power supply assembly provides power to various components of the electronic device. The power supply assembly may include a power management system, one or more power supplies, and other components associated with generating, managing, and distributing power for the electronic device. The multimedia assembly includes a screen that provides an output interface between the electronic device and the user. In some embodiments, the screen may include a liquid crystal display (LCD) and a touch panel (TP). If the screen includes a touch panel, the screen may be implemented as a touch screen to receive input signals from the user. The touch panel includes one or more touch sensors to sense touches, slides, and gestures on the touch panel. The touch sensor can not only sense the boundaries of a touch or slide action, but also detect the duration and pressure associated with the touch or slide action. In some embodiments, the multimedia assembly includes a front camera and / or a rear camera. When the electronic device is in an operating mode, such as a capture mode or a video mode, the front camera and / or the rear camera can receive external multimedia data. Each front camera and rear camera can be a fixed optical lens system or have focal length and optical zoom capabilities.

[0190] The audio component is configured to output and / or input audio signals. For example, the audio component includes a microphone (MIC), and when the electronic device is in an operating mode, such as a call mode, a recording mode, and a voice recognition mode, the microphone is configured to receive an external audio signal. The received audio signal can be further stored in a memory or sent via a communication component. In some embodiments, the audio component also includes a speaker for outputting audio signals. The I / O interface provides an interface between the processing component and the peripheral interface module, and the above-mentioned peripheral interface module can be a keyboard, a click wheel, a button, etc. These buttons may include but are not limited to: a home button, a volume button, a start button, and a lock button.

[0191] The sensor assembly includes one or more sensors for providing various aspects of status assessment for the electronic device. For example, the sensor assembly can detect the open / closed state of the electronic device, the relative positioning of components, such as the display and keypad of the electronic device. The sensor assembly can also detect changes in the position of the electronic device or a component of the electronic device, the presence or absence of user contact with the electronic device, the orientation or acceleration / deceleration of the electronic device and the temperature change of the electronic device. The sensor assembly may include a proximity sensor configured to detect the presence of nearby objects without any physical contact. The sensor assembly may also include a light sensor, such as a CMOS or CCD image sensor, for use in imaging applications. In some embodiments, the sensor assembly may also include an accelerometer, a gyroscope sensor, a magnetic sensor, a pressure sensor or a temperature sensor.

[0192] The communication component is configured to facilitate wired or wireless communication between the electronic device and other devices. The electronic device can access a wireless network based on a communication standard, such as WiFi, 2G or 3G, or a combination thereof. In an exemplary embodiment, the communication component receives a broadcast signal or broadcast-related information from an external broadcast management system via a broadcast channel. In an exemplary embodiment, the communication component further includes a near field communication (NFC) module to facilitate short-range communication. For example, the NFC module can be implemented based on radio frequency identification (RFID) technology, infrared data association (IrDA) technology, ultra-wideband (UWB) technology, Bluetooth (BT) technology and other technologies.

[0193] In an exemplary embodiment, the electronic device may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the above methods.

[0194] Example 3:

[0195] The present invention also provides a non-volatile computer-readable storage medium, which stores a computer program or instruction. When the computer program or instruction is executed by a processor, the method for reducing tidal analysis errors when studying tidal load displacement using GNSS as described in Example 1 can be implemented.

[0196] Specifically, a system, device, or apparatus equipped with a machine-readable storage medium may be provided, wherein the machine-readable storage medium stores software program code that implements the functions of any of the above-described embodiments, and the system, device, or apparatus is configured to read and execute the instructions stored in the machine-readable storage medium. In this case, the program code read from the machine-readable storage medium itself can implement the functions of any of the above-described embodiments, and thus the machine-readable code and the machine-readable storage medium storing the machine-readable code constitute part of the present invention.

[0197] The above-mentioned storage medium can be implemented by any type of volatile or non-volatile memory device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk (such as CD-ROM, CD-R, CD-RW, DVD-20ROM, DVD-RAM, DVD-RW, DVD-RW), magnetic tape, etc. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0198] It should be understood that the processor described above may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), or application-specific integrated circuits (ASICs). A general-purpose processor may be a microprocessor or any conventional processor. The steps of the method disclosed in the present invention may be directly executed by a hardware processor or by a combination of hardware and software modules within the processor.

[0199] It should be understood that the storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and storage medium can be located in an application-specific integrated circuit (ASIC). Of course, the processor and storage medium can also exist as discrete components in a terminal or server.

[0200] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions to be stored in the computer-readable storage medium in each computing / processing device.

[0201] The computer program instructions for performing the operations of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages such as Smalltalk, C++, and conventional procedural programming languages such as "C" language or similar programming languages. Computer-readable program instructions may be executed entirely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., utilizing an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be personalized by utilizing the state information of the computer-readable program instructions. The electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0202] The above description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

[0203] Although the above describes the specific implementation methods of the present invention, it does not limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for reducing tide analysis errors when studying tidal load displacement using GNSS, characterized in that: The following steps are involved: Step 1, determining tidal pairs; determining tidal pairs is determining tidal pairs of N2 to M2, S2 to M2, K2 to M2, K2 to S2, P1 to K1, O1 to K1, Q1 to K1 and Q1 to O1; Step 2: Establish the relative relationship between each tide pair and obtain the amplitude ratio of each grid point. and delay angle difference ; Step 3: Calculate the equilibrium tide harmonic constant and obtain the equilibrium tide amplitude of each component tide after correction by the ground tide. ; The specific process is: For any observation point , and its corresponding equilibrium tide height It can be expressed as （30） Where, and is the intersection factor and intersection correction angle of the tidal component, To balance the tide A tide in the phase of the moment; is the tidal angular rate; For the tribe, for the whole day tide , semidiurnal tide ; is the longitude; is the Beijing standard time zone code; is the equilibrium tide amplitude of each component tide after correction by the ground tide, （31） Where, is latitude; Step 4: Calculate the GPS data harmonic constant and obtain the amplitude of each tide obtained by the GPS data harmonic analysis. ; According to tidal theory, assuming is the instantaneous displacement of the tidal load in a certain direction of the observation station, then the harmonic constant of the main tidal component can be expressed as, （32） Where, is the average position of the displacement; and is the harmonic constant of each tide; and is the intersection factor and intersection correction angle of the tidal component, To balance the tide A tide in the phase of the moment; is the tidal angular rate; here 、 and It has nothing to do with place, but with time. and It is related to the location but not the time; so the above formula can be written as (33) in, (34) (35) According to the principle of least squares method, we can solve and , and then calculate the harmonic constant according to the following formula and , (36)； Step 5: Based on the results of steps 2, 3, and 4, the K1 and K2 tide estimation errors are corrected using relative admittance.

2. The method for reducing tide analysis error when studying tidal load displacement using GNSS as claimed in claim 1, characterized in that: The specific process of step 1 is: For a certain trend i , admittance M i for （1） in, , and are the harmonic constants, amplitude and lag angle of the tidal component, is the tidal force coefficient. In the same tidal family, the main tidal n Relative to the secondary tidal m The relationship can be expressed as: （2） in （3） （4） In formula (3) This is the amplitude ratio in traditional tidal science. is the retardation angle difference, The main tide n Relative to the secondary tidal m The amplitude relationship, The main tide n Relative to the secondary tidal m If the amplitude ratio of the actual tidal component is the same as the ratio of the tidal force, then is equal to 1; Determine the tidal pairs of N2 to M2, S2 to M2, K2 to M2, K2 to S2, P1 to K1, O1 to K1, Q1 to K1, and Q1 to O1; （5） （6） Let the amplitude ratios be The delay angle differences are (7) For two tidal components, let the amplitude ratio be , the delay angle difference is ,remember , ; The specific process of step 2 is: It is known that there are N observation points, respectively Represents, the longitude and latitude of each point is ,in Negative values are used for southern latitudes; , In degrees; and is the amplitude ratio and lag angle difference of each tide station observation point; For the observatory point, calculate its effect on other sites j The distance is （8） beg Weighted average of points （9） （10） in, represents the sum of all observation points, excluding point; is the corrected Kelvin wavelength, which is based on The water depth near the point is determined as follows: Assume that the water depth values of each grid point in and around the sea area are known, that is, Its longitude and latitude are , , water depth is D m ;right Point, calculation grid point Tide gauge stations The distance is （11） Select All The water depth values of the points are averaged and recorded as ; Calculate the corresponding Kelvin wave velocity （12） Kelvin wavelength （13） in, u i is the Kelvin wave velocity, T is the tidal wave period, （14） is the tidal wave angular velocity; Final selection （15） For all Calculate each point and , and calculate （16） and root mean square deviation （17） like （18） It is believed that The point data is abnormal and needs to be discarded; To verify the accuracy after removing outliers, and Back-calculate the amplitude ratio of each observation point and delay angle difference （19） （20） Then by （21） （22） Calculate the mean square error of the amplitude ratio and the delay angle difference （23） （24） According to the method described in formula (18), we first discard unreasonable observation values, set each grid point according to the predetermined resolution, and record the sequence number of each grid point as , and its corresponding longitude and latitude are , calculation point To each observation point The distance is （25） beg Weighted average of points （26） （27） in The calculation method is the same as that in the above formula (15) The calculation method is the same as Depend on and Back-calculate the amplitude ratio of each grid point and delay angle difference ; （28） （29）。 3. The method for reducing tide analysis error when studying tidal load displacement using GNSS as claimed in claim 1, characterized in that: The specific process of step 5 is as follows: make Where, is the amplitude of each tidal component obtained by harmonic analysis of GPS data, is the equilibrium tidal amplitude of each component tide, As the module, the semi-diurnal tides N2, M2, S2 and K2 The abnormal modulus value of K2 tide is then corrected to the normal fitting curve, thereby completing the correction of K2 tide error and improving the accuracy of K2 tide harmonic constant. Similarly, the values of K1, P1, O1 and Q1 of each full-day tide are corrected to the normal fitting curve. The value is used for curve fitting, and then the K1 tide anomaly is calculated. The value is corrected to the normal fitting curve, thereby completing the correction of the K1 tidal error and further improving the accuracy of the K1 tidal harmonic constant.

4. A device for reducing tide analysis errors when studying tidal load displacement using GNSS, characterized by: The device includes at least one processor and at least one memory, the processor and the memory are coupled; the memory stores a computer program or instruction; when the processor executes the computer program or instruction, it can implement the method for reducing tidal analysis error when studying tidal load displacement using GNSS as described in any one of claims 1 to 3.

5. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program or instruction. When the computer program or instruction is executed by the processor, the method for reducing tide analysis error when studying tidal load displacement using GNSS as described in any one of claims 1 to 3 can be implemented.

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