A dynamic water level inversion method based on low-orbit satellite multi-band signal fusion

Abstract

The application discloses a kind of dynamic water level inversion methods based on low-orbit satellite multi-band signal fusion, belong to satellite remote sensing monitoring technical field, comprising: obtaining multi-satellite multi-band observation data, according to the signal-to-noise ratio arc section of the azimuth of monitored water area environment screening;Phase center correction is carried out to the sequence, and the troposphere is corrected in combination with Ulich approximation method;Variational mode decomposition method with priori physical constraint is used to extract the interference term of multi-band observation data;Interference term is carried out spectrum analysis, and high-order dynamic height correction is carried out in combination with height angle change rate, and the initial value of each frequency band water level inversion is obtained;The peak signal-to-noise ratio and the mean value of signal-to-noise ratio amplitude are integrated, and the initial value of multi-satellite multi-band water level inversion is adaptively weighted and fused to obtain the final water level inversion result.The application realizes the accurate separation of low-frequency trend term and high-frequency interference term in low-orbit satellite complex signal, and improves the calculation accuracy of single-band water level inversion.

Description

Technical Field

[0001] This invention belongs to the field of satellite remote sensing monitoring technology, specifically relating to a dynamic water level inversion method based on the fusion of multi-band signals from low Earth Orbit (LEO) satellites. Background Technology

[0002] The Global Navigation Satellite System (GNSS) was initially designed to provide high-precision navigation, positioning, and timing (PNT) services to users worldwide. However, with the rapid development of Low Earth Orbit (LEO) satellite constellations (such as LEO navigation augmentation satellites and LEO internet satellites), LEO satellites are no longer merely a supplement to traditional medium and high orbit navigation systems, but have evolved into an independent and powerful positioning augmentation and space remote sensing system. Compared to medium and high orbit satellites operating at altitudes above 20,000 kilometers (such as GPS and BeiDou), LEO satellites typically orbit at altitudes between several hundred and two thousand kilometers. This significantly enhances the signal strength reaching the ground, effectively mitigating the vulnerability of traditional satellite signals to interference in complex environments. From a remote sensing perspective, LEO satellites possess extremely high speeds and very short revisit periods, meaning that a single station can observe a greater number of satellites passing by per unit of time, providing unprecedented spatiotemporal sampling density. Low Earth Orbit (LEO) satellite infrared (LEO-IR) technology utilizes the rich frequency bands (covering L, S, C, Ku, and Ka bands) broadcast by these LEO satellites as external radiation sources. Ground receivers capture the direct signal and the interference signal generated by reflection from the water surface, extracting the signal-to-noise ratio (SNR) observations carrying the physical characteristics of the Earth's surface. This high-frequency signal coverage not only fills the gap in the observation arc of traditional GNSS-IR within specific time periods but also provides a solid physical foundation for achieving tidal level inversion at the minute level or even shorter periods.

[0003] High-precision, real-time water level monitoring is the cornerstone of modern water conservancy engineering, disaster prevention and mitigation, and marine scientific research. In inland river environments, water level monitoring is crucial for flood and drought early warning, water resource allocation, and navigation safety; especially during the flood season, river water levels are highly susceptible to drastic fluctuations caused by heavy rainfall, necessitating automated monitoring methods with high-frequency response capabilities. In coastal and nearshore areas, water level monitoring is not only an important safeguard against threats to residents' lives from extreme weather events such as storm surges and waves, but also a key data source for studying long-term ecological issues such as sea-level rise and ocean thermal expansion caused by global warming. However, traditional monitoring methods face serious challenges in complex, all-encompassing environments: while tide gauges and contact water level gauges are technically mature, their installation is highly dependent on the physical structure of the shoreline, and in inland rivers they are susceptible to high-speed water flow, riverbed siltation, impact from floating debris, or chemical corrosion, resulting in high maintenance costs and insufficient deployment flexibility; while satellite altimetry technology can achieve wide-area coverage, when facing narrow and long river channels, near-shore shoals, or inland waters with complex topography, the echo signal is easily contaminated by shoreline buildings or vegetation, resulting in a significant decrease in accuracy and an excessively long revisit time period, making it difficult to capture instantaneous water level peaks.

[0004] In contrast, LEO-IR technology demonstrates exceptional environmental adaptability and technological superiority: it employs a non-contact observation mode, capturing satellite signals using receivers deployed at high altitudes along riverbanks or coastlines, effectively avoiding physical damage to the hardware caused by the aquatic environment. Benefiting from the frequent transits of low-Earth orbit satellites, this technology can provide observation sequences with extremely high temporal resolution, accurately capturing flood peak changes in inland rivers or subtle tidal fluctuations along the coast. This low-cost, all-weather monitoring solution with high spatial coverage not only significantly improves the monitoring accuracy of existing water level monitoring systems in complex inland and near-shore terrains but also provides irreplaceable technical support for building a global-scale digital hydrological monitoring network. Summary of the Invention

[0005] The purpose of this invention is to address the problems of difficulty in separating signal trend terms and frequency shifts in the high-dynamic environment of low-Earth orbit (LEO) satellites, inversion altitude drift caused by the rapid operation of LEO satellites, and low absolute solution accuracy of single-band inverted water levels. This invention provides a dynamic water level inversion method based on the fusion of multi-band signals from LEO satellites. Utilizing the advantages of high signal strength, short revisit period, and abundant frequency resources of LEO satellites, this method employs epoch-level antenna phase center correction, atmospheric curvature angle correction, variational mode decomposition (VMD), and a high-order dynamic correction model. Through robust estimation and weighted fusion of multi-band signals from various satellites, a highly reliable instantaneous water level inversion sequence is obtained, providing high-frequency, high-precision reliable data support for water level monitoring in inland rivers and coastal areas.

[0006] According to one aspect of the present invention, a dynamic water level inversion method based on multi-band signal fusion from low-Earth orbit satellites is provided, comprising:

[0007] Based on the acquired raw observation data of various low-orbit satellites in multiple frequency bands, the satellite elevation angle and satellite azimuth angle are calculated. Combined with the geographical environment of the monitored water area, the effective water surface reflection area and signal-to-noise ratio arc are determined.

[0008] Based on the epoch-by-epoch correction of the phase center deviation and phase center change errors in the elevation angle calculation from the antenna calibration file, the corrected elevation angle is obtained. The Ulich approximation method is used, combined with real-time meteorological data from the station, to perform tropospheric correction on the corrected elevation angle, and the tropospheric corrected elevation angle is obtained.

[0009] By combining the elevation angle after tropospheric correction, the a priori central angular frequency within the short-time observation window of the signal-to-noise ratio arc is calculated. The variational mode decomposition method with a priori physical constraints is used to calculate the high-frequency interferometric terms containing water level change information.

[0010] Lom-Skageller spectrum analysis was performed on the high-frequency interferometric terms containing water level change information to obtain the dominant frequency, and the initial inversion height was calculated. The initial inversion height was then input into a high-order dynamic correction model, and the initial water level inversion values ​​for each satellite and frequency band were obtained by combining the receiver antenna reference plane elevation.

[0011] Based on the initial water level inversion values ​​of each satellite and each frequency band, the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude are calculated to determine the initial fused water level of each frequency band. Through adaptive weighting, the water level inversion results are obtained through iterative convergence.

[0012] As a further technical solution, the prior center angular frequency within the short-time observation window of the signal-to-noise ratio arc is calculated by combining the tropospheric corrected elevation angle, including:

[0013] Based on the tropospheric correction of the elevation angle and the rate of change of the elevation angle, and according to the principle of spatial geometric interference, the theoretical interference frequency within the short-time observation window of the current signal-to-noise ratio arc is calculated;

[0014] The a priori central angular frequency is obtained by averaging the theoretical interference frequencies within a short observation window over a period of time.

[0015] As a further technical solution, a variational mode decomposition method with prior physical constraints is adopted to calculate high-frequency interferometric terms containing water level change information, including:

[0016] A quadratic penalty constraint term with respect to the central angular frequency is introduced into the objective function of the standard variational mode decomposition to form the objective function of the variational mode decomposition with prior physical constraints.

[0017] The objective function of variational mode decomposition with prior physical constraints is solved by alternating direction multiplier method. When the modal component variables of the two iterations are less than the set value, the signal decomposition is considered to have converged and completed, and two modal components are obtained.

[0018] Calculate the correlation coefficient and kurtosis of the two modal components with the signal-to-noise ratio arc;

[0019] Based on the correlation coefficient and kurtosis, high-frequency interferometric terms containing water level change information are selected.

[0020] As a further technical solution, based on the correlation coefficient and kurtosis, high-frequency interferometric terms containing water level change information are selected, including:

[0021] Remove features with low kurtosis and high correlation coefficients, i.e., low-frequency trend terms;

[0022] Features with high kurtosis and moderate correlation coefficients are extracted, namely high-frequency interferometric terms that contain information about water level changes.

[0023] As a further technical solution, Lom-Skageller spectral analysis is performed on the high-frequency interferometric terms containing water level change information to obtain the dominant frequency, and the initial inversion height is calculated. The initial inversion height is then input into a higher-order dynamic correction model, including:

[0024] Lom-Skageller spectral analysis was performed on the interferometric terms containing water level change information to extract the dominant frequency, and the initial reflection height was calculated by combining it with the satellite elevation angle change rate.

[0025] The initial reflection height is input into the high-order dynamic correction model, and the instantaneous reflection height is obtained by combining the star altitude angle change rate and the preset altitude change rate.

[0026] As a further technical solution, based on the initial water level inversion values ​​of each satellite and each frequency band, the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude are calculated to determine the initial fused water level for each frequency band, including:

[0027] Extract the initial values ​​of water level inversion for each frequency band of each satellite, calculate the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude, and assign initial weights to the initial values ​​of water level inversion for each frequency band.

[0028] The initial fused water level is obtained by weighted fusion based on the initial weights, and the residual of the initial value of the water level inversion for each frequency band is calculated.

[0029] As a further technical solution, the water level inversion results are obtained through adaptive weighting and iterative convergence, including:

[0030] Calculate the unit weighted mean error based on the residuals of the initial values ​​of water level inversion for each frequency band;

[0031] Based on the initial weights, residuals, and unit weight error of the initial water level inversion values, a weighting function is used to adaptively assign weights to the initial water level inversion values, and the water level inversion results are obtained through iterative convergence.

[0032] As a further technical solution, the satellite elevation angle and satellite azimuth angle are calculated based on the acquired multi-band raw observation data of various low-orbit satellites, including:

[0033] Based on the original observation data of each low-orbit satellite in multiple frequency bands, the on-orbit position coordinates of the low-orbit satellites are calculated using ephemeris files. The coordinates of the station are calculated using high-low orbit joint single-point positioning technology. Combining the spatial position relationship between the satellite and the station, the satellite elevation angle and satellite azimuth angle of each sampling epoch are obtained.

[0034] According to one aspect of the present invention, a dynamic water level inversion system based on low-Earth orbit satellite multi-band signal fusion is provided, for implementing the dynamic water level inversion method based on low-Earth orbit satellite multi-band signal fusion, comprising:

[0035] The first processing module is used to calculate the satellite elevation angle and satellite azimuth angle based on the acquired raw observation data of each low-orbit satellite multi-band, and determine the effective water surface reflection area and signal-to-noise ratio arc segment by combining the geographical environment of the monitored water area.

[0036] The second processing module is used to correct the errors in the calculation of the elevation angle caused by the phase center deviation and phase center change based on the antenna calibration file epoch by epoch, and obtain the corrected elevation angle. The Ulich approximation method is used to combine the real-time meteorological data of the station to perform tropospheric correction on the corrected elevation angle, and obtain the tropospheric corrected elevation angle.

[0037] The third processing module is used to calculate the prior center angular frequency within the short-time observation window of the signal-to-noise ratio arc segment by combining the elevation angle after tropospheric correction, and to obtain the high-frequency interferometric terms containing water level change information by using the variational mode decomposition method with prior physical constraints.

[0038] The fourth processing module is used to perform Lom-Skageller spectrum analysis on the high-frequency interferometric terms containing water level change information to obtain the dominant frequency, and calculate the initial inversion height. The initial inversion height is then input into a high-order dynamic correction model, and combined with the receiver antenna reference plane elevation, the initial water level inversion values ​​for each satellite and each frequency band are obtained.

[0039] The fifth processing module is used to calculate the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude based on the initial values ​​of water level inversion for each frequency band of each satellite, determine the initial fused water level for each frequency band, and obtain the water level inversion result through adaptive weighting and iterative convergence.

[0040] According to one aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the dynamic water level inversion method based on low-orbit satellite multi-band signal fusion.

[0041] Compared with the prior art, the beneficial effects of the present invention are:

[0042] 1. This invention introduces a variational mode decomposition method with prior physical constraints, which can force the algorithm to accurately lock the real water level interference frequency band, effectively avoid mode aliasing during the decomposition of high dynamic non-stationary signals, and achieve more accurate separation of low-frequency trend terms and high-frequency interference terms in complex signals of low-orbit satellites.

[0043] 2. By introducing a high-order dynamic correction model for the rate of change of elevation angle, this invention can use satellite dynamic parameters to perform strict velocity normalization compensation on the extracted time domain dominant frequency, thereby eliminating the elevation drift caused by the extremely fast operation of low-orbit satellites and improving the absolute solution accuracy of single-band inverted water level.

[0044] 3. This invention, by introducing a micro-window robust estimation weighted fusion strategy with a signal strength gain factor, can fully leverage the physical advantage of the high-power signals of low-orbit satellites in resisting multipath interference, and adaptively reduce weights to eliminate gross errors caused by sudden environmental conditions. This enables the reliable reconstruction of the initial inversion values ​​of multiple frequency bands of each satellite into a dynamic water level monitoring sequence with minute-level high temporal resolution. It is suitable for nearshore water level monitoring based on interferometric reflection remote sensing of low-orbit satellite navigation signals. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 The flowchart of a dynamic water level inversion method based on multi-band signal fusion of low-orbit satellites provided by the present invention is shown.

[0047] Figure 2 The SNR sequence provided by this invention is obtained by VMD decomposition of the IMF and the original SNR plot.

[0048] Figure 3 The image shows the LS spectrum analysis and screening results provided by this invention.

[0049] Figure 4The water level inversion result diagram provided by the present invention.

[0050] Figure 5 This is a schematic diagram of the geometric model for the multipath effect of water level inversion provided by the present invention. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] like Figure 1 As shown, this invention proposes a dynamic water level inversion method based on multi-band signal fusion from low-Earth orbit satellites, including: Step 1, acquiring multiple original observation data from multiple low-Earth orbit satellites and calculating the satellite elevation angle and azimuth angle, and determining the effective water surface reflection area and signal-to-noise ratio arc based on the geographical environment of the monitored water area; Step 2, correcting the errors in elevation angle calculation caused by phase center deviation and phase center change based on the antenna calibration file epoch by epoch, obtaining the corrected elevation angle, and using the Ulich approximation method, combined with real-time meteorological data from the station, to perform tropospheric correction on the corrected elevation angle, obtaining the tropospheric corrected elevation angle; Step 3, combining the tropospheric corrected elevation angle... Step 4: Calculate the prior center angular frequency within the short-time observation window of the signal-to-noise ratio arc segment, and use the variational mode decomposition method with prior physical constraints to obtain the high-frequency interferometric term containing water level change information; Step 5: Perform Lom-Skageller spectrum analysis on the high-frequency interferometric term containing water level change information to obtain the dominant frequency, and calculate the initial inversion height. Input the initial inversion height into the high-order dynamic correction model, and combine it with the receiver antenna reference plane elevation to obtain the initial water level inversion value for each satellite and each frequency band; Step 6: Based on the initial water level inversion value for each satellite and each frequency band, calculate the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude, determine the initial fused water level for each frequency band, and obtain the water level inversion result through adaptive weighting and iterative convergence.

[0053] Specifically, step 1 includes the following:

[0054] Low-Earth orbit (LEO) satellite signal receivers were deployed at high elevations along the monitored waters, ensuring unobstructed antennas facing the water to stably acquire multi-band raw observation data from LEO satellites. The sampling frequency of the LEO satellite signal receivers was set to 1 Hz. Multi-band raw observation data (navigation messages and raw observation values) was collected and converted to standard RINEX format. Continuous acquisition was maintained for at least 24 hours to ensure data integrity. The on-orbit coordinates of the LEO satellites were calculated using the ephemeris files in the navigation messages. The coordinates of the station were calculated using the Low Earth Orbit-High Earth Orbit Combined Single Point Positioning (LEO-PPP) technology. Simultaneously extract signal-to-noise ratio data for each frequency band. By combining the spatial relationship between the low-orbit satellite and the station, the satellite elevation angle for each sampling epoch is obtained through spatial geometric calculations. and satellite azimuth .

[0055] Based on the geographical environment of the monitored water area (such as river course and coastline distribution), and combined with satellite azimuth and elevation angles, the effective water surface reflection area (the area where water surface reflected signal energy is most concentrated) is delineated, and the effective azimuth range is set as follows: (Adaptively adjustable based on actual water area distribution), effective range of elevation angle. The signal-to-noise ratio (SNR) arcs within the effective water surface reflection area are selected, and arcs corresponding to invalid signals such as land reflection, building obstruction, and vegetation interference are removed.

[0056] Specifically, step 2 includes the following:

[0057] 1. Due to the high speed of low-orbit satellites (approximately 7-8 km / s), receiver antenna phase center deviation (PCO) and phase center variation (PCV) will cause systematic errors in the calculation of satellite elevation angle. It is necessary to correct the errors caused by phase center deviation and phase center variation in elevation angle calculation on an epoch-by-epoch basis based on the antenna calibration file to obtain the corrected elevation angle.

[0058] 1.1 The formula for calculating the elevation angle correction caused by phase center deviation is:

[0059] (1)

[0060] in, The elevation angle correction amount caused by phase center deviation (unit: rad). This is the unit vector for satellite observation direction.

[0061] 1.2 Corrected elevation angle for:

[0062] (2)

[0063] in, The elevation angle correction (unit: rad) caused by phase center changes is obtained by interpolation based on the PCV data corresponding to different elevation angles in the antenna calibration file, using a linear interpolation method. This correction process eliminates systematic elevation errors at the hardware level caused by antenna phase center drift, ensuring the accuracy of geometric parameters.

[0064] 2. Due to the tropospheric refraction causing signal bending during the propagation of low-Earth orbit satellite signals, the calculated elevation angle deviates from the actual value, affecting the inversion accuracy. Therefore, the Ulich approximation method (an approximation method for calculating the change of the equilibrium constant with temperature) is adopted, combined with real-time meteorological data from the station (surface temperature). 25℃, ground dry air pressure 1013 hPa, water vapor pressure (21 hPa), the elevation angle is corrected for tropospheric elevation to obtain the tropospheric corrected elevation angle, as shown in the following formula:

[0065] (3)

[0066] in, This is the tropospheric corrected elevation angle. The refractive index of the ground is contributed by dry air and water vapor.

[0067] (4)

[0068] The numerical difference method was used to simultaneously calculate the rate of change of satellite elevation angle at each epoch. This serves as the input for subsequent dynamic corrections.

[0069] Specifically, step 3 includes the following:

[0070] In low-Earth orbit satellite interferometry, the large rate of change of satellite elevation angle leads to a non-stationary characteristic in the measured signal-to-noise ratio arc, where the frequency varies with time. Traditional variational mode decomposition (VMD), when processing such non-stationary signals, is prone to mode aliasing if it relies solely on empirically set decomposition parameters. This results in the inability to completely separate the low-frequency direct component (trend term) from the high-frequency reflected component (interference term). Therefore, a variational mode decomposition method incorporating prior physical constraints is used.

[0071] 1. Before performing signal decomposition, the prior reflection height is obtained using the approximate water surface elevation around the station. Combining the elevation angle and the rate of change of the elevation angle, and based on the principle of spatial geometric interference, short-time micro-window resampling is performed on the signal-to-noise ratio arc segment, i.e., the theoretical interference frequency within the short-time observation window of the current measured SNR sequence is calculated. :

[0072] (5)

[0073] in, For the carrier wavelength of the corresponding satellite signal, For the prior reflection height, The rate of change of satellite elevation angle (equivalent to) ), The satellite elevation angle (equivalent to) ).

[0074] 2. Calculate the time average of the theoretical interference frequencies within the short-time observation window to obtain the a priori central angular frequency. :

[0075] (6)

[0076] in, This represents the total number of epochs within the window. This prior center angular frequency reflects the expected frequency band distribution of the water level interference signal within the current arc segment.

[0077] 3. The standard VMD algorithm aims to decompose the input signal into K (K=7 in this embodiment) center angular frequencies. Discrete modes To ensure one of the modes (let the target interference mode be...) Its corresponding target center angular frequency is This invention can accurately converge to the frequency band of the water level interference signal. In this embodiment, a quadratic penalty constraint term regarding the center angular frequency is introduced into the objective function of standard VMD. The objective function of the variational mode decomposition constituting the a priori physical constraints (unconstrained augmented Lagrangian function) The expression is:

[0078] (7)

[0079] Where K represents the signal decomposed into K modes, For the k-th mode component sequence obtained from the decomposition, The central angular frequency (in rad / s) corresponds to the k-th modal component. For carrier wavelength, The Dirac function (dimensionless) This represents the convolution operation (dimensionless). The time partial derivative (unit: 1 / s) It is an imaginary unit (dimensionless). This is the measured SNR sequence. These are time-domain Lagrange multipliers, and this term is a constraint correction term. It is a secondary penalty factor (with a value of 2000). Prior constraint weight coefficients ; Indicates the target's central angular frequency. It represents the prior central angular frequency.

[0080] 4. Solve Equation 7 using the Alternating Direction Multiplier Method (ADMM) and update iteratively. , and The number of iterations is set to 100. When the change in modal components between two iterations is less than... When the signal converges, the signal decomposition is complete, resulting in two modal components. Figure 2 The diagram shows the IMF, residuals, and original SNR of the SNR sequence decomposed by VMD. The diagram clearly distinguishes the low-frequency trend term dominated by satellite trajectory and the high-frequency interferometric term containing water level change information.

[0081] 5. After completing the signal decomposition, calculate the correlation coefficients between the two modal components and the SNR sequence. and kurtosis The formula for calculating the correlation coefficient is:

[0082] (8)

[0083] The formula for calculating kurtosis is:

[0084] (9)

[0085] in, Modal components The mean, The mean of the SNR sequence is... Modal components The standard deviation is given by n, where n is the data length. The correlation coefficient and kurtosis are used to accurately identify and separate the trend term representing the direct component from the interference term representing the reflected component: the correlation coefficient reflects the consistency between the modal component and the overall trend of the SNR sequence, and the kurtosis reflects the fluctuation characteristics of the modal component, where high kurtosis indicates that the signal contains significant oscillatory components, and low kurtosis indicates that the signal is stable.

[0086] Based on the calculation results of formulas (8) and (9), features with low kurtosis and high correlation coefficients, i.e., low-frequency trend terms dominated by satellite trajectory changes or environmental noise, are removed; features with high kurtosis and medium correlation coefficients, i.e., high-frequency interferometric terms containing water level change information, are extracted and used as input interferometric terms for subsequent processing. By using quantitative indicators for screening, the subjectivity of human judgment can be avoided, ensuring the accuracy and stability of interference item extraction.

[0087] Specifically, step 4 includes the following:

[0088] 1. Due to the SNR sequence corresponding to low-orbit satellites For non-uniform sampling, the Lomb-Scargle spectral analysis (LSP) method was used to analyze the interference terms. Perform spectral analysis. The formula for calculating the LSP power spectrum is:

[0089] (10)

[0090] in, Interference term The variance (dimensionless). Sampling time (unit: s) Interference term exist The value at time (dimensionless). Interference term The mean (dimensionless). The time offset (in seconds) satisfies the orthogonality condition:

[0091] (11)

[0092] The dominant frequency is determined by searching for the frequency corresponding to the peak value of the LSP power spectrum. . Figure 3 The image shows the LS spectrum analysis and screening results. The location of the main frequency peak can be clearly identified from the image.

[0093] 2. Based on the principle of interferometric reflection measurement (IR) altimetry, the satellite elevation angle variation rate is introduced. A dynamic frequency compensation model was established to obtain the initial reflection height. (Unit: m) The calculation formula is:

[0094] (12)

[0095] in, The carrier wavelength of the signal in the corresponding frequency band. The elevation angle after tropospheric correction (unit: rad).

[0096] 3. To address the high dynamic characteristics of low-Earth orbit (LEO) satellites, the initial reflection altitude is input into a high-order dynamic correction model to compensate for frequency offset errors caused by the high-speed motion of LEO satellites, combined with the satellite elevation angle change rate. (Unit: rad / s) and preset altitude change rate (Unit: m / s) The initial reflection height is corrected to obtain the instantaneous reflection height. The formula is:

[0097] (13)

[0098] in, The corrected elevation angle is shown below. The elevation angle rate is obtained by adaptively adjusting the elevation angle sequence using the water level change trend between adjacent time points, with a value range of -0.1 to 0.1 m / s, and by performing a first-order difference calculation.

[0099] 4. Based on the elevation of the receiver antenna reference plane (Unit: m, determined by second-order leveling, accuracy better than ±2 mm), calculate the initial value for water level inversion. (Unit: m):

[0100] (14)

[0101] This yields the initial value sequence for water level inversion for each satellite and each frequency band. , where i is the inversion result of one frequency for one satellite.

[0102] Specifically, step 5 includes the following:

[0103] Set the width of the time sliding window to (Set to 5 minutes), sliding step size is (Set to 5 minutes), for each target fusion time Extracting data falling within the time window Use all valid water level inversion initial values ​​within the range to construct the dataset to be merged for the current window. ,in This represents the total number of initial values ​​for water level inversion within the window.

[0104] For each water level inversion initial value within the window Calculate its peak signal-to-noise ratio (PSNR) As a quality scoring factor, It reflects the significance of the main frequency peak value, and the calculation formula is:

[0105] (15)

[0106] in, This represents the maximum amplitude corresponding to the dominant frequency in the frequency domain. Let j be the amplitude at the j-th frequency point in the frequency domain. This represents the total number of frequency points in the discrete frequency sequence.

[0107] Because low-Earth orbit satellites exhibit significant differences in transmission power and spatial attenuation across different frequency bands (such as L, S, and Ku), higher absolute signal strength results in stronger resistance to interference from water surface wave scattering. Therefore, the mean signal-to-noise ratio amplitude of the i-th observation arc segment is extracted. As a signal strength gain factor, combined with the peak signal-to-noise ratio of each frequency band ( Initial weights were assigned to the initial values ​​of water level inversion for different satellite frequency bands. :

[0108] (16)

[0109] in, This represents the mean original signal-to-noise ratio amplitude of the i-th observation arc segment. The larger this value, the stronger the signal power when it is dropped. This represents the peak signal-to-noise ratio of the i-th observation arc segment. The total number of epochs within the window, with the denominator being the sum of all observed arcs within the window. and The sum of products.

[0110] Weighted fusion is performed based on the initial weights to obtain the initial fusion water level. And calculate the residuals of the initial values ​​of water level inversion for each frequency band. (Reflecting the degree of deviation from the fusion result):

[0111] (17)

[0112] (18)

[0113] in, This is the initial value for the i-th water level inversion within the window. The window reference water level is obtained through weighted fusion. Let be the residual of the i-th inversion result.

[0114] Calculate the unit weighted mean error using the median method :

[0115] (19)

[0116] For each water level inversion result within the time window, the standardized residual is calculated, and the initial weights are adjusted based on the IGG3 weighting function. Adaptive weighting, during the first iteration After five iterations, the final water level inversion result is obtained through convergence:

[0117] (20)

[0118] (twenty one)

[0119] (twenty two)

[0120] in, The error is the unit weight. To standardize the residuals, The equivalent weights after the IGG3 weight function update. , For the robust estimation threshold constant, take... , , The final water level inversion result obtained by merging the windows is as follows: Figure 4 As shown.

[0121] By redundancy compensation of multi-satellite and multi-frequency band information, errors caused by environmental fluctuations and noise interference in a single frequency band are suppressed, and finally, an equally spaced water level inversion monitoring sequence with high frequency (minute level) and high precision is output, providing reliable data support for dynamic water level monitoring.

[0122] Specifically, the embodiments of the present invention realize water level inversion based on the interferometric reflection principle of low-orbit satellite navigation signals. Its core is to accurately infer water level changes by analyzing the interferometric information in the multi-band signal-to-noise ratio (SNR) sequence and combining geometric models and signal processing algorithms.

[0123] First, the core geometric foundation of water level inversion will be explained: Figure 5 This is a schematic diagram of the geometric model for the multipath effect in water level inversion. The phase center A of the receiver antenna is fixed at a high point along the shore of the monitored water area, and its reflection height from the water surface is... The signal transmitted by a low-Earth orbit satellite arrives at the receiver in two parts: a direct signal and a reflected signal. The direct signal propagates directly from the satellite to the antenna phase center A, while the reflected signal is reflected by the specular reflection point B in the first Fresnel zone of the water surface before reaching point A. The satellite elevation angle... This is the angle between the line connecting the phase centers of the satellite and the antenna and the ground plane. The reflected signal has a path delay Δ compared to the direct signal; this delay is related to... , The existence of a strict geometric correlation is the key basis for inferring water levels.

[0124] Based on the above geometric model and combined with the propagation characteristics of electromagnetic waves, the geometric model for measuring reflection height is derived using the following formula.

[0125] a. Path delay Δ (unit: m) can be obtained from geometric relationships:

[0126] (twenty three)

[0127] b. Phase difference between direct and reflected signals The relationship between (unit: rad) and path delay Δ is as follows:

[0128] (twenty four)

[0129] c. Combining the two equations and rearranging, we obtain the reflection height. The core calculation formula (unit: m) is as follows:

[0130] (25)

[0131] d. The dominant frequency extracted by combining SNR sequence spectral analysis (Unit: Hz), since the dominant frequency is directly related to the phase change rate, a simplified formula for engineering applications is further derived:

[0132] (26)

[0133] In the formula, The carrier wavelength (in meters) for low-Earth orbit satellite signals is fixed across different frequency bands. The dominant frequency is obtained through spectrum analysis. Then, by substituting the values ​​into the formula, the reflection height of the antenna above the water surface can be calculated. Then, by combining the elevation of the antenna reference surface, the actual water level can be calculated.

[0134] In this embodiment of the invention, the nearshore waters of the Yangtze River were selected as the monitoring area. Low-orbit satellite receivers were deployed to continuously collect multi-band data for 10 days. The water level inversion results were compared with measured data from jointly located tide gauge stations. Experimental results show that the root mean square error between the water level inversion method of this invention and the measured data is within 3 cm, and the time resolution reaches 5 minutes.

[0135] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a dynamic water level inversion system based on low-orbit satellite multi-band signal fusion. This system is used to execute a dynamic water level inversion method based on low-orbit satellite multi-band signal fusion from the above method embodiments.

[0136] The system comprises: a first processing module, used to calculate the satellite elevation angle and azimuth angle based on the acquired raw observation data of various low-orbit satellites in multiple frequency bands, and to determine the effective water surface reflection area and signal-to-noise ratio arc band by combining the geographical environment of the monitored water area; a second processing module, used to correct the errors in elevation angle calculation caused by phase center deviation and phase center change based on the antenna calibration file epoch by epoch, to obtain the corrected elevation angle, and to perform tropospheric correction on the corrected elevation angle using the Ulich approximation method combined with real-time meteorological data from the station, to obtain the tropospheric corrected elevation angle; and a third processing module, used to calculate the short-time observation window of the signal-to-noise ratio arc band by combining the tropospheric corrected elevation angle. The first processing module uses a priori center angular frequency and a variational mode decomposition method with prior physical constraints to obtain high-frequency interferometric terms containing water level change information. The second processing module performs Lom-Skageller spectrum analysis on the high-frequency interferometric terms containing water level change information to obtain the dominant frequency and calculates the initial inversion height. The initial inversion height is then input into a high-order dynamic correction model and combined with the receiver antenna reference plane elevation to obtain the initial water level inversion values ​​for each satellite and each frequency band. The third processing module calculates the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude based on the initial water level inversion values ​​for each satellite and each frequency band, determines the initial fused water level for each frequency band, and obtains the water level inversion results through adaptive weighting and iterative convergence.

[0137] The dynamic water level inversion system based on multi-band signal fusion of low-Earth orbit (LEO) satellites provided in this invention addresses the challenges of separating signal trend terms and frequency shifts in the high-dynamic environment of LEO satellites, the inversion altitude drift caused by the rapid operation of LEO satellites, and the low absolute accuracy of single-band inverted water level. It employs several modules, leveraging the advantages of LEO satellites' high signal strength, short revisit period, and abundant frequency resources. Through epoch-level antenna phase center correction, atmospheric curvature angle correction, variational mode decomposition (VMD), and a high-order dynamic correction model, and through robust estimation and weighted fusion of multi-band signals from various satellites, a highly reliable instantaneous water level inversion sequence is obtained. This provides high-frequency, high-precision reliable data support for water level monitoring in inland rivers and coastal areas.

[0138] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides an electronic device, including a memory and a processor. The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize a dynamic water level inversion method based on low-orbit satellite multi-band signal fusion as proposed in the above embodiments.

[0139] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A dynamic water level inversion method based on low-orbit satellite multi-band signal fusion, characterized in that, include: Based on the acquired raw observation data of various low-orbit satellites in multiple frequency bands, the satellite elevation angle and satellite azimuth angle are calculated. Combined with the geographical environment of the monitored water area, the effective water surface reflection area and signal-to-noise ratio arc are determined. Based on the epoch-by-epoch correction of the phase center deviation and phase center change errors in the elevation angle calculation from the antenna calibration file, the corrected elevation angle is obtained. The Ulich approximation method is used, combined with real-time meteorological data from the station, to perform tropospheric correction on the corrected elevation angle, and the tropospheric corrected elevation angle is obtained. By combining the elevation angle after tropospheric correction, the a priori central angular frequency within the short-time observation window of the signal-to-noise ratio arc is calculated. The variational mode decomposition method with a priori physical constraints is used to calculate the high-frequency interferometric terms containing water level change information. Lom-Skageller spectrum analysis was performed on the high-frequency interferometric terms containing water level change information to obtain the dominant frequency, and the initial inversion height was calculated. The initial inversion height was then input into a high-order dynamic correction model, and the initial water level inversion values ​​for each satellite and frequency band were obtained by combining the receiver antenna reference plane elevation. Based on the initial water level inversion values ​​of each satellite and each frequency band, the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude are calculated to determine the initial fused water level of each frequency band. Through adaptive weighting, the water level inversion results are obtained through iterative convergence.

2. The dynamic water level inversion method based on low-orbit satellite multi-band signal fusion according to claim 1, characterized in that, Based on the tropospheric corrected elevation angle, the prior center angular frequency within the short-time observation window of the signal-to-noise ratio arc is calculated, including: Based on the tropospheric correction of the elevation angle and the rate of change of the elevation angle, and according to the principle of spatial geometric interference, the theoretical interference frequency within the short-time observation window of the current signal-to-noise ratio arc is calculated; The a priori central angular frequency is obtained by averaging the theoretical interference frequencies within a short observation window over a period of time.

3. The dynamic water level inversion method based on low-orbit satellite multi-band signal fusion according to claim 1, characterized in that, Using a variational mode decomposition method with prior physical constraints, high-frequency interferometric terms containing water level change information are calculated, including: A quadratic penalty constraint term with respect to the central angular frequency is introduced into the objective function of the standard variational mode decomposition to form the objective function of the variational mode decomposition with prior physical constraints. The objective function of variational mode decomposition with prior physical constraints is solved by alternating direction multiplier method. When the modal component variables of the two iterations are less than the set value, the signal decomposition is considered to have converged and completed, and two modal components are obtained. Calculate the correlation coefficient and kurtosis of the two modal components with the signal-to-noise ratio arc; Based on the correlation coefficient and kurtosis, high-frequency interferometric terms containing water level change information are selected.

4. The dynamic water level inversion method based on low-orbit satellite multi-band signal fusion according to claim 1, characterized in that, Based on the correlation coefficient and kurtosis, high-frequency interferometric terms containing water level change information were selected, including: Remove features with low kurtosis and high correlation coefficients, i.e., low-frequency trend terms; Features with high kurtosis and moderate correlation coefficients are extracted, namely high-frequency interferometric terms that contain information about water level changes.

5. The dynamic water level inversion method based on low-orbit satellite multi-band signal fusion according to claim 1, characterized in that, Lom-Skageller spectral analysis is performed on the high-frequency interferometric term containing water level change information to obtain the dominant frequency, and the initial inversion height is calculated. The initial inversion height is then input into a higher-order dynamic correction model, including: Lom-Skageller spectral analysis was performed on the interferometric terms containing water level change information to extract the dominant frequency, and the initial reflection height was calculated by combining it with the satellite elevation angle change rate. The initial reflection height is input into the high-order dynamic correction model, and the instantaneous reflection height is obtained by combining the star altitude angle change rate and the preset altitude change rate.

6. The dynamic water level inversion method based on low-orbit satellite multi-band signal fusion according to claim 1, characterized in that, Based on the initial water level inversion values ​​for each satellite and each frequency band, the peak signal-to-noise ratio (PSNR) and mean SNR amplitude are calculated to determine the initial fused water level for each frequency band, including: Extract the initial values ​​of water level inversion for each frequency band of each satellite, calculate the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude, and assign initial weights to the initial values ​​of water level inversion for each frequency band. The initial fused water level is obtained by weighted fusion based on the initial weights, and the residual of the initial value of the water level inversion for each frequency band is calculated.

7. The dynamic water level inversion method based on low-orbit satellite multi-band signal fusion according to claim 6, characterized in that, Through adaptive weighting, the water level inversion results are obtained through iterative convergence, including: Calculate the unit weighted mean error based on the residuals of the initial values ​​of water level inversion for each frequency band; Based on the initial weights, residuals, and unit weight error of the initial water level inversion values, a weighting function is used to adaptively assign weights to the initial water level inversion values, and the water level inversion results are obtained through iterative convergence.

8. The dynamic water level inversion method based on low-orbit satellite multi-band signal fusion according to claim 1, characterized in that, The satellite elevation angle and azimuth angle are calculated based on the acquired raw observation data of various low-orbit satellites in multiple frequency bands, including: Based on the original observation data of each low-orbit satellite in multiple frequency bands, the on-orbit position coordinates of the low-orbit satellites are calculated using ephemeris files. The coordinates of the station are calculated using high-low orbit joint single-point positioning technology. Combining the spatial position relationship between the satellite and the station, the satellite elevation angle and satellite azimuth angle of each sampling epoch are obtained.

9. A dynamic water level inversion system based on low-orbit satellite multi-band signal fusion, characterized in that, The method for implementing the dynamic water level inversion method based on low-orbit satellite multi-band signal fusion as described in any one of claims 1-8 includes: The first processing module is used to calculate the satellite elevation angle and satellite azimuth angle based on the acquired raw observation data of each low-orbit satellite multi-band, and determine the effective water surface reflection area and signal-to-noise ratio arc segment by combining the geographical environment of the monitored water area. The second processing module is used to correct the errors in the calculation of the elevation angle caused by the phase center deviation and phase center change based on the antenna calibration file epoch by epoch, and obtain the corrected elevation angle. The Ulich approximation method is used to combine the real-time meteorological data of the station to perform tropospheric correction on the corrected elevation angle, and obtain the tropospheric corrected elevation angle. The third processing module is used to calculate the prior center angular frequency within the short-time observation window of the signal-to-noise ratio arc segment by combining the elevation angle after tropospheric correction, and to obtain the high-frequency interferometric terms containing water level change information by using the variational mode decomposition method with prior physical constraints. The fourth processing module is used to perform Lom-Skageller spectrum analysis on the high-frequency interferometric terms containing water level change information to obtain the dominant frequency, and calculate the initial inversion height. The initial inversion height is then input into a high-order dynamic correction model, and combined with the receiver antenna reference plane elevation, the initial water level inversion values ​​for each satellite and each frequency band are obtained. The fifth processing module is used to calculate the peak signal-to-noise ratio and the mean signal-to-noise ratio amplitude based on the initial values ​​of water level inversion for each frequency band of each satellite, determine the initial fused water level for each frequency band, and obtain the water level inversion result through adaptive weighting and iterative convergence.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the dynamic water level inversion method based on low-orbit satellite multi-band signal fusion as described in any one of claims 1 to 8.

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