GNSS-IR water level refined inversion method based on dynamic correction and bayesian fusion

Abstract

The application discloses a GNSS-IR water level refining inversion method based on dynamic correction and Bayesian fusion, and the method comprises the following steps: a satellite interferometric reflectometry system is arranged in a research water area, and SNR data and carrier phase data in the satellite interferometric reflectometry system are acquired; the SNR data is subjected to polynomial fitting, and water level inversion height under SNR static state is calculated; the carrier phase data is subjected to three-frequency carrier phase combination expression and multi-path information separation, and water level inversion height under carrier phase static state is calculated; dynamic geometric correction is performed on the water level inversion height, and a Bayesian fusion model is constructed to obtain a fused water level time sequence. The application realizes high-precision, high-stability and high-applicability inversion of water level change, has the advantages of high calculation efficiency, strong anti-interference ability, good real-time performance and the like, and provides efficient, accurate and reliable water level result time sequence data for application scenarios such as hydrological monitoring, flood control and disaster reduction and water resource scheduling.

Description

Technical Field

[0001] This invention relates to the field of interferometric reflection measurement of global navigation satellite systems, and in particular to a GNSS-IR water level refinement inversion method based on dynamic correction and Bayesian fusion. Background Technology

[0002] Water level changes are crucial parameters characterizing the evolution of hydrological processes and ecosystem responses, playing a key role in flood control and disaster reduction, water resource allocation, and environmental monitoring. Traditional water level monitoring methods largely rely on contact sensors, which suffer from high installation and maintenance costs and limited spatial coverage. In recent years, global navigation satellite system interferometric reflectometry (GRS) technology has emerged as a non-contact method for retrieving water level changes by analyzing the interference characteristics formed by direct signals at the receiver and reflected signals from the ground surface. This method offers significant advantages such as continuous observation, low cost, and strong adaptability, and is gradually becoming the development direction in the field of water level monitoring. Global Navigation Satellite System (GNSS) interferometric reflection measurement data includes signal-to-noise ratio (SNR) signals and carrier phase observation signals. In current research, if only SNR-based inversion methods are used, they offer high time resolution and are easy to implement. However, their interferometric oscillation characteristics are easily affected by environmental noise, changes in scatterers around the antenna, and disturbances in observation conditions, leading to unstable spectral characteristics and thus limiting the accuracy of water level inversion. If only carrier phase-based inversion methods are used, although they have high measurement accuracy, they are sensitive to phase cycle slips and anomalous observations, which can easily affect the reliability and stability of the inversion results.

[0003] Currently, interferometric reflection measurement technology for global navigation satellite systems faces significant challenges in water level inversion. Problems such as low accuracy, insufficient reliability and stability occur during water level retrieval. Existing reflection geometry models fail to fully consider the time-varying characteristics of reflection geometry caused by water level changes. Moreover, since the effective reflection point position, reflection path length and phase offset change dynamically over time due to water level fluctuations, the lack of reasonable dynamic correction for reflection geometry offsets easily introduces systematic errors into the water level inversion process. These errors have a cumulative effect in long-term continuous observations, further restricting the improvement of water level inversion accuracy and stability. Summary of the Invention

[0004] The purpose of this invention is to provide a GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion. This method utilizes SNR data and carrier phase data to obtain their respective static water level inversion heights using corresponding methods, and then performs dynamic geometric correction to obtain the dynamic vertical reflection distance. A Bayesian fusion model is constructed using the mean and variance of tide gauge records or actual water levels as the prior distribution, and the refined water level result after inverse variance weighting of the dynamic vertical reflection distance as the posterior distribution. This achieves high-precision, high-stability, and high-applicability inversion of water level changes, providing efficient and reliable time-series water level data for applications such as hydrological monitoring, flood control and disaster reduction, and water resource allocation.

[0005] The objective of this invention is achieved through the following technical solution: A GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion, the method comprising: S1. A satellite interferometric reflection measurement system is deployed for the study water area. The satellite interferometric reflection measurement system consists of a satellite and a network of GNSS-IR ground-based equipment deployed along the edge of the study water area; the SNR data and carrier phase data of the satellite interferometric reflection measurement system are acquired. The original expressions for S2 and SNR data are as follows: , ,in and These represent the amplitudes of the direct signal and the reflected signal, respectively. This represents the phase difference between two signals. The wavelength of the GNSS signal for GNSS-IR ground-based equipment. The elevation angle is corrected for the troposphere; polynomial fitting is performed on the original expression of the SNR data; the static water level inversion height is obtained according to the following expression. : ,in The frequency of the signal.

[0006] S3. Combine the carrier phase data into three-frequency carrier phase representations and separate multipath information. Obtain the water level inversion height under static carrier phase conditions according to the following expression. : ,in The dominant frequency is obtained from multipath information through power spectrum analysis. and For coefficients; S4. Retrieve water level height , Dynamic vertical reflection distance is obtained by performing dynamic geometric corrections separately. and ; S5. Construct a prior distribution using the mean and variance of tide gauge records or actual water levels, and using dynamic vertical reflection distance... and After inverse variance weighted fusion, the refined water level result is a Bayesian fusion model with a posterior distribution. The fused water level time series is obtained according to the following formula. : ,in This represents the variance of the merged water level time series. Let be the posterior mean of the water level estimate for observation type j at time t. Let $\begin{pmatrix} \ ... and Data source types, including those mentioned above.

[0007] To better realize the present invention, the tropospheric correction elevation angle The elevation angle error compensation expression of the model is obtained by constructing an elevation angle error compensation model that incorporates tropospheric refraction and delay. ; ; ; ,in This refers to the zenith delay difference between the antenna location of the GNSS-IR ground-based equipment and its location on the ground surface. , Elevation angles The corresponding dry and wet delay mapping functions, For tropospheric delay, For the prior reflection height, Temperature in Celsius Atmospheric pressure, The atmospheric curvature angle, For the prior elevation angle, This is an elevation angle correction caused by tropospheric delay.

[0008] Preferably, the water or sea surface is set to remain stationary, and the phase difference between the direct signal and the reflected signal is... The phase difference is derived from the path delay using geometric relationships. The expression.

[0009] Preferably, in method S3, the phase shift associated with the interferometric signal in the multipath effect of the carrier phase can be modeled as follows: ;in Expressed as the amplitude attenuation factor; when Greater than At that time, including phase shift The carrier wave can be expressed as: ;in, , , These represent the geometric distance, ionospheric error, and tropospheric error between the satellite and GNSS-IR ground-based equipment, respectively. The GNSS signal wavelength for GNSS-IR ground-based equipment. This is the phase shift factor caused by multipath propagation. For integer ambiguity, For noise measurement, dual-frequency carrier The combined expression is as follows: Dual-frequency carrier carrier With carrier Multipath combination expression, , These are the first frequency carriers in GNSS for GNSS-IR ground-based equipment. With the second frequency carrier wavelength, , The first frequency carrier With the second frequency carrier The amplitude attenuation factor is then expressed by combining the phases of the three-frequency carrier waves.

[0010] Preferably, in method S4, the water level inversion height and All tidal wave curves are fitted based on harmonic analysis, and the curve fitting equations are as follows: ,in Indicates the height of water level inversion or sequence; and They represent tides. The sine and cosine functions, The number of tidal factors, For tidal frequency, For tidal phase, This is the amplitude adjustment factor.

[0011] Preferably, the rate of change of the reflection path is obtained by taking the time derivative of the curve fitting equation. Dynamic vertical reflection distance and Dynamic geometric correction is performed according to the following formula: ,in The corrected or adjusted dynamic vertical reflection distance, including the dynamic vertical reflection distance. and , This refers to the satellite elevation angle.

[0012] Preferably, the prior distribution is constructed using the mean and variance recorded by the tide gauge, and is expressed as follows: ; , The prior mean of the tide gauge records. The prior variance of the tide gauge records. This represents the observation record of the tide gauge at time t.

[0013] Preferably, the fused water level time series The conditional probability density is modeled as a normal distribution, and the expression is as follows: ,in Indicates the deadline All historical information.

[0014] Preferably, the posterior distribution expression for the water level to be merged is as follows: ; ,in Let be the error variance of observation type j relative to the tide gauge at time t. Let j be the water level time series to be merged at time t.

[0015] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) This invention utilizes SNR data and carrier phase data to perform inversion according to corresponding methods to obtain the corresponding static water level inversion heights and performs dynamic geometric correction to obtain the dynamic vertical reflection distance. Through a Bayesian fusion model, the mean and variance of the water level recorded by the tide gauge or the actual water level are used as the prior distribution, and the water level refinement result after inverse variance weighting fusion of the dynamic vertical reflection distance is used as the posterior distribution. This achieves high-precision, high-stability and high-applicability inversion of water level changes, providing efficient and reliable water level result time series data for application scenarios such as hydrological monitoring, flood control and disaster reduction and water resource scheduling.

[0016] (2) The Bayesian fusion model of this invention performs joint modeling and probabilistic consistency fusion of multi-source GNSS observation information such as signal-to-noise ratio (SNR) signal and carrier phase under the Bayesian probabilistic framework. By using the uncertainty characteristics of different observation information, it avoids the complex iterative optimization and empirical weighting process in traditional multi-source fusion methods. While ensuring computational efficiency and real-time performance, it improves the robustness and reliability of water level inversion results.

[0017] (3) This invention fully considers the complementary characteristics between the signal-to-noise ratio (SNR) signal and carrier phase observation data in the GNSS-IR water level inversion process. It introduces a dynamic reflection geometric correction mechanism in the water level inversion process, fully considers the time-varying characteristics of the reflection point position and signal propagation path caused by water level changes, and dynamically corrects the reflection geometric relationship, thereby effectively reducing the systematic bias caused by static geometric assumptions. By constructing a Bayesian fusion framework, it jointly models the water level results obtained from the inversion based on SNR and carrier phase observation data, comprehensively utilizes the posterior distribution information of various inversion results, and adopts an inverse variance weighting strategy to achieve optimal fusion. Compared with existing fusion methods, which usually require a complex iterative process to gradually optimize multi-source data, the Bayesian fusion framework of this invention significantly reduces the computational complexity by directly utilizing the posterior probability information of each observation result, while ensuring the high accuracy and high stability of the fused inversion results. This invention effectively improves the GNSS-IR water level by organically combining dynamic reflection geometric correction with Bayesian multi-source data fusion method. The water level inversion exhibits high accuracy, stability, and anti-interference capabilities, along with good generalization ability and strong environmental adaptability, making it suitable for various water areas and observation scenarios.

[0018] (4) This invention has the advantages of high computational efficiency and strong anti-interference ability, and can be widely used in hydrological monitoring scenarios such as coastal water level monitoring, lake water level measurement, flood warning and water resource management. Attached Figure Description

[0019] Figure 1 This is a flowchart of the GNSS-IR water level refinement and inversion method of the present invention; Figure 2 This is a schematic diagram illustrating the principle of the GNSS-IR water level refinement and inversion method in the embodiment. Figure 3 This is a schematic diagram illustrating the deployment of a satellite interferometric reflection measurement system in a selected water area as an example in this embodiment. Figure 4 Numerical curves of the elevation angle compensation optimization effect under tropospheric modeling were selected for the study of water area cases; Figure 5 This is a schematic diagram of signal oscillations during signal extraction from SNR data in a selected study water area case. Figure 6 for Figure 5 A schematic diagram showing the result of extracting interference components from a portion of the signal. Figure 7 To select the SNR static water level inversion height time series results from the case study water area; Figure 8 To select the time series results of water level inversion height under static carrier phase in the case study water area; Figure 9 for Figure 7 Timing results of dynamic vertical reflection distance (SNR) after dynamic reflection geometric correction; Figure 10 for Figure 8 Timing result of dynamic vertical reflection distance of carrier phase after dynamic reflection geometric correction; Figure 11 This is a schematic diagram comparing the water level change curves of the merged water level result and the actual water level in a selected case study water area. Detailed Implementation

[0020] The present invention will be further described in detail below with reference to embodiments: Example like Figure 1 As shown, a GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion is proposed, the method comprising: S1. A satellite interferometric reflection measurement system is deployed for the study water area. This system consists of a satellite and GNSS-IR ground-based equipment deployed along the shore of the study water area (the GNSS-IR ground-based equipment acts as shore-based GNSS-IR ground-based receiving equipment, deployed along the shore of the study water area). SNR data and carrier phase data from the satellite interferometric reflection measurement system are acquired. See [link to relevant documentation]. Figure 2 The data from the satellite interferometric reflection measurement system consists of multi-source GNSS observation information or data, which includes SNR data (i.e., signal-to-noise ratio SNR data) and carrier phase data.

[0021] like Figure 3As shown, the study water area in this embodiment is a location in San Michael, Alaska, USA (latitude and longitude: 63.4840°N, 162.0064°W). A GNSS-IR ground-based device (also known as the AT01 station) was deployed in the study water area. The GNSS-IR ground-based device is equipped with a high-precision GNSS receiver and antenna system. The vertical distance from the phase center of the receiver antenna to the water surface is approximately 12 m. A tide gauge station numbered 9468333 is located approximately 74 km away from this station. In the example study water area, considering the surrounding environmental conditions of the AT01 station, GNSS observation data with an azimuth range of 0° to 220° and an elevation range of 5° to 15° were selected. Taking the GNSS observation data acquired from February 1st to March 3rd of a certain year as an example, water level inversion based on SNR observations and three-frequency carrier phase combination was carried out. During this period, the obtained SNR inversion results and the three-frequency carrier phase combination inversion results are used as multi-source water level information. On this basis, a dynamic water level correction model is introduced, and a Bayesian fusion model is constructed by integrating multi-source water level information to achieve weighted fusion of water level inversion results.

[0022] S2 and SNR data observations are highly sensitive to multipath interference, which manifests as an oscillating component superimposed on the direct signal. After one reflection from the water surface, the reflected signal introduces an additional phase delay compared to the direct signal, thus producing interference. In a case study using a body of water in the St. Michael region as the research area, signal extraction from the SNR data is performed as follows: Figure 5 As shown, from Figure 5 The significant oscillation characteristics caused by reflection interference can be clearly identified in the SNR data signal. The original expression for SNR data (the original SNR data can be represented by the following expression) is as follows: ,in and The amplitudes of the direct and reflected signals are respectively used. Polynomial fitting (preferably, quadratic polynomial fitting) of the original expression for the SNR data can effectively extract the interference components. See [link to relevant documentation]. Figure 6 This can effectively extract interference components. This represents the phase difference between two signals (i.e., the direct signal and the reflected signal); to extract the interference components, the water or sea surface is assumed to be stationary, and the phase difference between the direct signal and the reflected signal is... The phase difference is derived from the path delay using geometric relationships. The expression: , The wavelength of the GNSS signal for GNSS-IR ground-based equipment. This is the elevation angle corrected for the troposphere.

[0023] In some embodiments, the elevation angle of tropospheric correction The elevation angle error compensation was calculated by constructing an elevation angle error compensation model that incorporates tropospheric refraction and delay. The elevation angle error compensation model (corresponding to...) was used to calculate the elevation angle error compensation. Figure 2 The expression for altitude angle error compensation is as follows: ; ; ; ,in This refers to the zenith delay difference between the antenna location of the GNSS-IR ground-based equipment and its location on the ground surface. , , Elevation angles The corresponding dry and wet delay mapping functions, Indicates the antenna height as The zenith dry delay, This represents the zenith interference delay when the antenna height is 0 (close to the ground). For tropospheric delay (corresponding to) Figure 2 (delay mapping function correction in the middle) For the prior reflection height, Temperature in Celsius Atmospheric pressure, The atmospheric curvature angle (the elevation angle deviation caused by tropospheric refraction, corresponding to...) Figure 2 The refraction angle correction is expressed as follows: ; For the prior elevation angle, For elevation angle correction caused by tropospheric delay (corresponding to) Figure 2 The expression for the elevation angle error compensation is as follows: In the case study of a body of water in the St. Michael region, the tropospheric corrected elevation angle was determined. Optimization effect such as Figure 4 As shown, Figure 4 Numerical curves show the effect of elevation angle compensation optimization under tropospheric modeling.

[0024] signal frequency Includes reflection height The information is used to obtain the static water level inversion height under SNR according to the following expression. (Also known as SNR static water level inversion height): ,in The frequency of the signal is given. In a case study using a body of water in the St. Michael area as the research area, the obtained static SNR-based water level inversion height is as follows: Figure 7 As shown.

[0025] S3. In the multipath effect of carrier phase, the phase shift associated with the interference signal can be modeled as follows: ;in Expressed as the amplitude attenuation factor; when Greater than At that time, including phase shift The carrier wave can be expressed as: ;in, , , These represent the geometric distance, ionospheric error, and tropospheric error between the satellite and GNSS-IR ground-based equipment, respectively. The GNSS signal wavelength for GNSS-IR ground-based equipment. This is the phase shift factor caused by multipath propagation. For integer ambiguity, For noise measurement, dual-frequency carrier The combined expression is as follows: Dual-frequency carrier carrier With carrier Multipath combination expression, , These are the first frequency carriers in GNSS for GNSS-IR ground-based equipment. With the second frequency carrier wavelength, , The first frequency carrier With the second frequency carrier The amplitude attenuation factor is then used for the three-frequency carrier phase combination expression, which is based on the dual-frequency carrier... The third frequency carrier in the middle combination The multipath signals are further separated by weighted combination. The expression for the three-frequency carrier phase combination is as follows: , , , These are three frequencies in GNSS for GNSS-IR ground-based equipment. , , The wavelength, of which for , Multipath combinations, for , Multipath combinations, for , Multipath combination. Carrier phase data is expressed by combining three-frequency carrier phases and separating multipath information. The multipath information can be used to determine the dominant frequency through Lomb-Scargle power spectrum analysis. The water level inversion height under static carrier phase is obtained according to the following expression. (Also known as carrier phase static water level inversion height): ,in The dominant frequency is obtained from multipath information through power spectrum analysis. and The coefficient is used. In a case study using a body of water in the St. Michael area as the research area, the water level inversion height under static carrier phase is obtained as follows: Figure 8 As shown.

[0026] S4. Retrieve water level height (i.e., SNR static water level inversion height) (i.e., carrier phase static water level inversion height) are dynamically geometrically corrected to obtain the dynamic vertical reflection distance. (i.e., SNR dynamic vertical reflection distance) and (i.e., carrier phase dynamic vertical reflection distance), in a case study using a body of water in the St. Michael area as the research area, the SNR dynamic vertical reflection distance... like Figure 9 As shown, the carrier phase dynamic vertical reflection distance like Figure 10 As shown. Water level inversion (including SNR static water level inversion height and carrier phase static water level inversion height) is modeled and inverted under the assumption that the reflecting surface remains stationary. However, since the water level height changes continuously over time, the reflection geometry exhibits dynamic characteristics, making this type of static assumption difficult to hold in actual water level monitoring scenarios, thus affecting the accuracy and stability of the water level inversion results. Considering the dynamic nature of water level changes, this invention preferably adopts the following method: water level inversion height (i.e., SNR static water level inversion height) and (i.e., carrier phase static water level inversion height) are all based on harmonic analysis fitting of tidal wave curves, and the curve fitting equation is as follows: ,in Indicates the height of water level inversion or sequence; and They represent tides. The sine and cosine functions, The number of tidal factors, For tidal frequency, For tidal phase, This is the amplitude adjustment factor.

[0027] The rate of change of the reflection path is obtained by taking the time derivative of the curve fitting equation. Rate of change of reflection path It can be represented as: Dynamic vertical reflection distance and Dynamic geometric correction is performed according to the following formula: ,in The corrected or adjusted dynamic vertical reflection distance, including the dynamic vertical reflection distance. and Dynamic vertical reflection distance and All adopt the above dynamic geometric correction formula. Satellite elevation rate, satellite elevation rate .

[0028] S5. Construct a prior distribution using the mean and variance of tide gauge records or actual water levels, and using dynamic vertical reflection distance... and The refined water level result after inverse variance weighted fusion is a Bayesian fusion model with a posterior distribution. After obtaining the water level result after dynamic reflection geometric correction, the uncertainty of water level height measurement obtained from the inversion of different types of observation data can be calculated by the standard deviation of the difference between the inverted historical water level time series and the corresponding tide gauge observation water level: ;in, This represents the historical water level time series obtained for the j-th type of observation under time index t. This represents the observation record of the tide gauge at time index t, where N is the number of valid inversion points using this method. denoted as the standard deviation of the measurement error of the water level retrieved from the j-th type of observation at time index t relative to the tide gauge record.

[0029] Preferably, the initial conditions for Bayesian fusion are defined, and the prior mean and variance are calculated based on historical tide gauge records; the prior distribution is constructed using the mean and variance of the tide gauge records, as expressed below: , , The prior mean of the tide gauge records. The prior variance of the tide gauge records. This represents the water level observation record at time t. Given a prior distribution, the merged water level time series... The conditional probability density is modeled as a normal distribution, and the expression is as follows: ,in Indicates the deadline All historical information. The posterior distribution expression of the water level estimate to be fused, obtained from SNR data inversion and carrier phase inversion, is as follows: , ,in Let j be the variance of the error relative to the tide gauge at time t (preferably two observation types, i.e., j=2, the two observation types being SNR data and carrier phase data). For observation type j, the posterior mean of the water level estimate is obtained. Let j be the water level time series to be merged at time t.

[0030] The posterior estimates of water level obtained from SNR data inversion and carrier phase data inversion are fused using the inverse variance weighting method to obtain the fused water level time series according to the following formula. : ,in This represents the variance of the merged water level time series. Let be the posterior mean of the water level estimate for observation type j at time t. Let $\begin{pmatrix} \ ... and Data source types, including those related to the fusion of water level time series variance. The expression is as follows: In a case study using a body of water in the St. Michael area, the merged water level time series was obtained as follows: Figure 11 As shown, from Figure 11 It can be seen that the merged water level time series is not significantly different from the actual water level (obtained by actual water level measurement at the study area), with the high and low points of the water level curve being quite close. The merged water level time series curve also closely matches the actual water level time series curve. Figure 11 This demonstrates that the fused water level time series data obtained in this invention closely approximates the actual water level time series data, exhibiting high inversion accuracy, stability, and reliability. The Bayesian fusion-based GNSS-IR multi-source water level inversion method of this invention can fully integrate the dynamic vertical reflection distance after dynamic reflection geometric correction. and This significantly improves the accuracy, stability, and reliability of water level monitoring results.

[0031] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion, characterized in that: The methods include: S1. A satellite interferometric reflection measurement system is deployed for the study water area. The satellite interferometric reflection measurement system consists of a satellite and a network of GNSS-IR ground-based equipment deployed along the edge of the study water area; the SNR data and carrier phase data of the satellite interferometric reflection measurement system are acquired. The original expressions for S2 and SNR data are as follows: , ,in and These represent the amplitudes of the direct signal and the reflected signal, respectively. This represents the phase difference between two signals. The wavelength of the GNSS signal for GNSS-IR ground-based equipment. The tropospheric corrected elevation angle, the tropospheric corrected elevation angle The elevation angle error compensation expression of the model is obtained by constructing an elevation angle error compensation model that incorporates tropospheric refraction and delay. ； ； ； ,in This refers to the zenith delay difference between the antenna location of the GNSS-IR ground-based equipment and its location on the ground surface. , Elevation angles The corresponding dry and wet delay mapping functions, For tropospheric delay, For the prior reflection height, Temperature in Celsius Atmospheric pressure, The atmospheric curvature angle, For the prior elevation angle, To correct the elevation angle caused by tropospheric delay, a polynomial fit was performed on the original expression of the SNR data; the static water level inversion height under SNR was obtained according to the following expression. : ,in The frequency of the signal; S3. Combine the carrier phase data into three-frequency carrier phase representations and separate multipath information. Obtain the water level inversion height under static carrier phase conditions according to the following expression. : ,in The dominant frequency is obtained from multipath information through power spectrum analysis. and For coefficients; S4, Retrieve water level height , Dynamic vertical reflection distance is obtained by performing dynamic geometric corrections separately. and ; S5. Construct a prior distribution using the mean and variance of tide gauge records or actual water levels, and using dynamic vertical reflection distance... and After inverse variance weighted fusion, the refined water level result is a Bayesian fusion model with a posterior distribution. The fused water level time series is obtained according to the following formula. : ,in This represents the variance of the merged water level time series. Let be the posterior mean of the water level estimate for observation type j at time t. Let $\begin{pmatrix} \ ... and Data source types, including those mentioned above.

2. The GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion as described in claim 1, characterized in that: Assuming the water or sea surface remains stationary, the phase difference between the direct signal and the reflected signal... The phase difference is derived from the path delay using geometric relationships. The expression.

3. The GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion as described in claim 1, characterized in that: In method S3, the phase shift associated with the interferometric signal in the multipath effect of the carrier phase can be modeled as follows: ;in Expressed as the amplitude attenuation factor; when Greater than At that time, including phase shift The carrier wave can be expressed as: ;in, , , These represent the geometric distance, ionospheric error, and tropospheric error between the satellite and GNSS-IR ground-based equipment, respectively. The GNSS signal wavelength for GNSS-IR ground-based equipment. This is the phase shift factor caused by multipath propagation. For integer ambiguity, For noise measurement, dual-frequency carrier The combined expression is as follows: Dual-frequency carrier carrier With carrier Multipath combination expression, , These are the first frequency carriers in GNSS for GNSS-IR ground-based equipment. With the second frequency carrier wavelength, , The first frequency carrier With the second frequency carrier The amplitude attenuation factor is then expressed by combining the phases of the three-frequency carrier waves.

4. The GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion as described in claim 1, characterized in that: In method S4, the water level inversion height and All tidal wave curves are fitted based on harmonic analysis, and the curve fitting equations are as follows: ,in Indicates the height of water level inversion or sequence; and They represent tides. The sine and cosine functions, The number of tidal factors, For tidal frequency, For tidal phase, This is the amplitude adjustment factor.

5. The GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion according to claim 4, characterized in that: The rate of change of the reflection path is obtained by taking the time derivative of the curve fitting equation. Dynamic vertical reflection distance and Dynamic geometric correction shall be performed according to the following formula: ,in The corrected or adjusted dynamic vertical reflection distance, including the dynamic vertical reflection distance. and , This refers to the satellite elevation angle.

6. The GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion according to claim 1, characterized in that: The prior distribution is constructed using the mean and variance of the tide gauge records, and is expressed as follows: ； , The prior mean of the tide gauge records. The prior variance of the tide gauge records. This represents the observation record of the tide gauge at time t.

7. The GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion as described in claim 6, characterized in that: Merged water level time series The conditional probability density is modeled as a normal distribution, and the expression is as follows: ,in Indicates the deadline All historical information.

8. The GNSS-IR water level refinement and inversion method based on dynamic correction and Bayesian fusion according to claim 6 or 7, characterized in that: The posterior distribution expression for the estimated water level to be merged is as follows: ； ,in Let be the variance of the error of observation type j relative to the tide gauge at time t. Let j be the water level time series to be merged at time t.

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