Sea surface altimetry method based on ionospheric layered elevation angle correction model

Abstract

The present invention relates to the technical field of sea surface height measurement based on the signal-to-noise ratio of satellite signals. Specifically, it is a sea surface height measurement method based on an ionospheric layered altitude angle correction model, which can overcome the problem that the measured value of the satellite altitude angle deviates from the true value due to the influence of the ionosphere during the propagation of navigation satellite signals. Compared with the existing technology, the present invention constructs a new ionospheric layered altitude angle correction model for the altitude angle refraction of the ionosphere on the propagation path of satellite signals. The satellite altitude angle, azimuth angle and signal-to-noise ratio (SNR) data are calculated using the GNSS observation data file acquired by the receiver. The correction value of the altitude angle is calculated using the ray tracing method. Finally, the accurate sea surface height after correction by the new ionospheric layered altitude angle correction model is obtained. Experimental results show that the ISEACM correction can effectively improve the accuracy of GNSS-IR sea surface height measurement, which is of great significance for accurately measuring sea surface height.

Description

Technical field:

[0001] The present invention relates to the technical field of sea surface height measurement based on the signal-to-noise ratio of satellite signals, and more specifically to a sea surface height measurement method based on an ionospheric layered altitude angle correction model, which can overcome the problem that the measured value of the satellite altitude angle deviates from the true value due to the influence of the ionosphere during the propagation of navigation satellite signals. Background technology:

[0002] The ocean gravity field is essential data for seafloor topography inversion, marine resource development, and elevation datum unification. Satellite altimetry can directly measure the ocean geoid and infer ocean gravity anomalies using the functional relationship between the geoid and gravity anomalies. Therefore, satellite altimetry has become one of the primary methods for inferring the ocean gravity field. Over the past few decades, sea surface altimetry has evolved from traditional ship-based data collection and tide gauge measurements to satellite altimeter measurements and, now, the developing Global Navigation Satellite System-reflectometry (GNSS-R). These technological advancements have not only expanded the accuracy and coverage of sea surface altimetry but also provided rich data support for fields such as marine science, climate research, and ocean management. In short, sea surface height inversion provides a quantitative and qualitative description of ocean surface height variations and is a key ocean observation technology with significant implications for various marine activities and research.

[0003] GNSS-IR technology utilizes only traditional geodetic receivers to monitor altitude. Based on the frequency characteristics of the signal-to-noise ratio (SNR), it can monitor changes in the height of reflecting surfaces. This technology offers advantages such as full automation, low cost, long-term continuity, and a fixed frame. In 2013, Larson et al. proposed a LSP analysis method for sea surface height measurement. The calculated results were compared with those from nearby tide gauges, demonstrating good consistency. In 2014, Loefgren et al. analyzed SNR observations from five GPS stations at Onsala GTGU, Sweden, and obtained highly accurate sea surface height measurements with correlations of 0.89-0.99 with sea level heights observed using co-located traditional tide gauges. Signal propagation is inevitably affected by the ionosphere and troposphere, resulting in refraction of the satellite signal, which affects the accuracy of GNSS-IR altitude measurements. They subsequently discovered that changes in the SNR oscillation frequency at low elevation angles are primarily related to the geometric bending of radio waves passing through the troposphere. Correction for this effect improves the accuracy of the results. In 2017, Larson et al. calculated the effect of tropospheric refraction on the altitude angle of GNSS-IR sea surface altimetry and found a root mean square error of 12 cm between tide gauge and GNSS-IR data. Although existing GNSS-IR sea surface altimetry has a number of mature inventions for satellite-side error correction, signal propagation error correction, and ground receiver error correction, the presence of ionized charged particles in the ionosphere inevitably affects the traveling electromagnetic waves, causing them to undergo refraction and group delay. Atmospheric refraction bends the propagation path of radio waves, causing the apparent distance and elevation angle of the satellite-measured target to differ from the true distance and elevation angle. Therefore, to achieve accurate sea surface altimetry, it is necessary to correct GNSS-IR altitude measurements for ionospheric refraction errors. Summary of the invention:

[0004] In view of the shortcomings and deficiencies in the prior art, the present invention proposes a sea surface altimetry method based on an ionospheric layered altitude angle correction model, which can overcome the problem that the measured value of the satellite altitude angle deviates from the true value due to the influence of the ionosphere during the propagation of navigation satellite signals.

[0005] The present invention is achieved by the following measures:

[0006] A sea surface altimetry method based on an ionospheric stratification altitude angle correction model is characterized in that an ionospheric stratification altitude angle correction model (ISEACM) is constructed, and specifically comprises the following steps:

[0007] Step 1: Using the GNSS observation data file and satellite orbit data, calculate the satellite's azimuth and elevation angles, and extract the interference signal-to-noise ratio data of the direct signal and reflected signal in the observation data. At the same time, record the satellite's azimuth, elevation angle, satellite PRN number of the signal-to-noise ratio data, and the corresponding time. These parameters are combined in units of days to generate a signal-to-noise ratio data file;

[0008] Step 2: Considering the uneven distribution of electron content density in the ionosphere, an ionospheric altitude range of 100-450 km was selected, and the ionosphere was divided into eight layers with a step size of 50 km. The ionospheric penetration point, including longitude and latitude data, was calculated using the satellite's altitude and azimuth angles, as well as the height of each layer after ionospheric stratification. The electron content density of each layer was then obtained using the International Reference Ionosphere Model (IRI).

[0009] Step 3: Using the electron density values ​​obtained from the International Reference Ionosphere Model (IRI), the altitude correction for each layer of the ionosphere is calculated. The refraction model of the troposphere is introduced to correct the refraction angle of the satellite signal. The sea surface altitude around the station is obtained through LSP spectrum analysis, and the altitude inversion results are quality controlled.

[0010] Step 4: Obtain tide data from tide gauges near the observation station and GNSS-IR sea surface inversion height, and remove outliers.

[0011] In step 1 of the present invention, the GNSS-IR receiver receives the direct signal and the reflected signal from the satellite. The direct signal and the reflected signal interfere with each other, and the interference signal composed of the direct signal and the reflected signal is recorded by the receiver in the signal-to-noise ratio. The signal-to-noise ratio can be described as:

[0012]

[0013] in, and denote the direct signal amplitude and the reflected signal amplitude respectively, represents the phase difference between the direct signal and the reflected signal, and the obtained signal-to-noise ratio oscillation term is approximately:

[0014]

[0015] Where A represents the signal amplitude, f represents the oscillation frequency, φ represents the phase, and D is the additional distance of the reflected signal relative to the direct signal. From the additional distance D, the phase difference between the direct signal and the reflected signal can be calculated.

[0016]

[0017] Where λ represents the carrier wavelength, and θ is the angle between the direct signal and the sea level, that is, the satellite elevation angle. From formula (4), we can see that there is a linear relationship between the phase difference and the sine value of the satellite elevation angle sin(θ), that is:

[0018]

[0019] After simplifying formula (5), we can get SNR m The relationship between the height h of the reflecting surface and the frequency is:

[0020]

[0021] Here, λ represents the wavelength and f represents the frequency.

[0022] In steps 2 and 3 of the present invention, the ionospheric refractive index is calculated based on the frequency of the satellite signal L1 band using the electron content density provided by the International Reference Ionosphere Model (IRI):

[0023]

[0024] Among them, N e Represents the electron content, f represents the satellite signal frequency, and the highest electron content density is layered into eight layers. From the top layer of 450 km downward according to the satellite signal propagation trajectory, the layers are layered with a step size of 50 km. The ray tracing method is used to correct and update the altitude angle of each layer, and finally the satellite altitude angle corrected by ionospheric refraction is obtained. First, the corresponding ionospheric refractive index is calculated according to the electron content density of the ionosphere layer i-1 and i-2, and the refractive index is used to solve the geocentric angle, and finally the corrected satellite altitude angle is calculated:

[0025]

[0026] β i =arcos(n i *r i *cos(z) / n i-1 *r i-1 ) (9),

[0027]

[0028] Among them, n i-1 represents the refractive index of the upper ionosphere, n i-2 represents the refractive index of the underlying ionosphere, r i-1 Indicates the height from the center of the earth to the target plane i-1 layer, r i-2 Indicates the height from the center of the earth to the target plane i-2 layer, e i-2 It represents the satellite elevation angle corresponding to the i-2 layer, i represents the corresponding layer number, and the highest layer i=8.

[0029] The present invention takes into account the influence of the earth's curvature and facilitates the layered iterative calculation of the satellite elevation angle along the direction of satellite signal propagation. Therefore, the elevation angle at the initial measuring station is calculated to the elevation angle at 450 km, the highest layer of the ionosphere. r0 represents the radius of the earth, r2 represents the sum of the height at 450 km and the radius of the earth, and e represents the satellite elevation angle at the initial measuring station. The refractive index of each layer of the ionosphere is calculated according to formula (3), and the corresponding refraction angles of the two adjacent layers are calculated according to Snell's refraction law. Combined with the refraction angle of the previous layer and the geocentric angle between the current layer and the previous layer, the elevation angle value of the iteratively updated layer is solved by the triangle internal angle theorem. The elevation angle is iteratively calculated to the next layer according to formulas (7)(8)(9)(10) to obtain the satellite elevation angle corrected by the ionosphere refraction, and finally the accurate satellite elevation angle value corrected by the ionosphere is calculated.

[0030] In step 4 of the present invention, RMSE and PCC are used to evaluate the accuracy of GNSS-IR sea surface height measurement after ISEACM correction and the accuracy of original GNSS-IR height measurement without model correction. The root mean square error is calculated as follows:

[0031]

[0032] Where Y represents the sea level height measurement sequence of the tide gauge station, X represents the GNSS-IR sea surface height inversion result, and RMSE is used to evaluate the discrete deviation between the inversion result and the true value. The smaller the root mean square error of the calculated ISEACM-corrected inversion height, the more accurate the inversion result after model correction.

[0033] The Pearson correlation coefficient calculation formula is as follows:

[0034]

[0035] in, and They represent the average values ​​of the sea level height measurement sequence of the tide gauge station and the GNSS-IR sea surface height inversion result sequence, respectively, and n represents the number of discrete points in the data sequence.

[0036] Compared with the existing technology, the present invention constructs a new ionospheric layered altitude angle correction model based on the altitude angle refraction of the ionosphere on the propagation path of satellite signals. The satellite altitude angle, azimuth angle and signal-to-noise ratio (SNR) data are calculated using the GNSS observation data file obtained by the receiver. The correction amount of the altitude angle is calculated using the ray tracing method. Finally, the accurate sea surface height after correction by the new ionospheric layered altitude angle correction model is obtained. The sea surface height is compared with the measurement station and the nearby tidal measurement station that have not been corrected with the new ionospheric layered altitude angle correction model. The root mean square error and Pearson correlation coefficient are used to evaluate the reliability of the new method proposed in the present invention. Experimental results show that the ISEACM correction can effectively improve the accuracy of GNSS-IR sea surface height measurement, which is of great significance for accurately measuring sea surface height. Description of the drawings:

[0037] The attached figure shows the ionospheric electron content density of the selected GNSS stations in the present invention. Figure 1 (a) Electron content density map of the United States; (b) Electron content density map of Spain; (c) Electron content surface density distribution map of Australia.

[0038] Attachment Figure 2 This is a flow chart of the new ionospheric layered altitude angle correction model in the present invention.

[0039] Attachment Figure 3 This is the basic principle diagram of GNSS-IR measurement.

[0040] Attachment Figure 4 This is a map of GNSS station distribution and Fresnel reflection area.

[0041] Attachment Figure 5 This is a diagram of the station angle correction of the novel ionospheric layered altitude angle correction model of the present invention.

[0042] Attachment Figure 6 This is a comparison diagram of the altitude inversion sequence and the tidal observation value sequence after correction by the new ionospheric stratification altitude angle correction model in an embodiment of the present invention.

[0043] Attachment Figure 7 3. This is a Pearson correlation coefficient diagram of the altitude inversion series and the tidal observation value series of the four observation stations after correction by the new ionospheric layered altitude angle correction model in an embodiment of the present invention.

[0044] Attachment Figure 8 3. This is a comparison diagram of the altitude inversion sequence and the tidal observation value sequence of four stations before and after correction of the new ionospheric layered altitude angle correction model in an embodiment of the present invention.

[0045] Attachment Figure 9This is a comparison diagram of the residuals of the altitude inversion series and the tidal observation value series of the four stations after correction by the new ionospheric layered altitude angle correction model in the embodiment of the present invention. Specific implementation method:

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] The purpose of the present invention is to establish a sea surface altimetry method based on an ionospheric layered altitude angle correction model.

[0048] The Earth's ionosphere refers to the area of ​​Earth's atmosphere from approximately 60 km above the Earth's magnetosphere. This portion of the atmosphere is partially ionized due to the influence of polar ultraviolet rays, X-rays, and other factors. The ionosphere is generally divided into four layers, depending on the degree of ionization and electron density: the D layer (60-90 km, typically disappearing at night), the E layer (90-140 km), the F1 layer (140-210 km, often disappearing at night), and the F2 layer (above 210 km, where the atmospheric density is the lowest, the particle collision and combination rate is the lowest, and the maximum electron density typically occurs. This layer is also the primary region that reflects and affects satellite signal propagation). The IRI, recognized as the international standard for electron density and temperature specifications, is an empirical model of the ionosphere jointly established by the Committee for Space Research (COSPAR) and the International Union of Radio Science (URSI). By inputting parameters such as time, latitude, longitude, and altitude, users can obtain a wide range of physically important ionospheric parameters, including electron density from 60 to 2000 km, peak F2 density (NmF2), peak F2 height (HmF2), ion temperature, and TEC. The ionosphere can be divided into the D layer, E layer, and F layer, from low to high. The F layer can be further divided into the F1 layer and the F2 layer. The electron content density is primarily concentrated near the F layer.

[0049] Since the subsequent scheme of this invention mainly selects GNSS stations in Spain, Australia and the United States, the electron content density of the ionosphere is mainly affected by day and night and seasons in the time series. Excessive stratification will lead to a long time to extract the electron content density data. Figure 1The electron density distribution of the ionosphere is shown to be primarily concentrated around 100-450 km. Considering that the refraction of satellite signals by the ionosphere is primarily related to the electron density, and that ionosphere regions with lower electron density have less impact on satellite signal refraction, for the sake of computational time and efficiency, the present invention subsequently investigated the refraction of the ionosphere in the region with higher electron density at altitudes between 100 and 450 km. Using the International Reference Ionosphere Model (IRI), the model was divided into eight layers with a step size of 50 km. The subsequent invention investigated the impact of ionospheric refraction on the accuracy of GNSS-IR sea level inversion.

[0050] The ray tracing method calculates the distance and angle of refraction of satellite signals during propagation. It is based on Snell's law and Fermat's principle, and is strictly derived based on mathematical geometric relationships. It has high accuracy and has therefore become a correction method widely used in engineering. For GNSS-IR shore-based sea surface height measurement, there is still a lack of a better solution to the impact of ionospheric refraction on satellite signal propagation. At the same time, since the electron content density within the ionosphere is affected by day and night, seasons and other environmental factors, the electron content density is unevenly distributed at the vertical height level. The traditional ray tracing method has limited improvement in the accuracy of sea surface height inversion when calculating satellite altitude angle refraction under a single layer of ionosphere. Therefore, based on the idea of ​​traditional ray tracing, the present invention introduces the concept of ionospheric stratification and constructs a new ionospheric stratification altitude angle correction model.

[0051] The construction ideas of ISEACM of the present invention are as follows:

[0052] First, using the GNSS observation data file and satellite orbit file, the satellite azimuth and elevation angle are calculated, and the interference signal-to-noise ratio data of the direct signal and the reflected signal in the observation data file are extracted. At the same time, the satellite azimuth, elevation angle, satellite PRN number of the signal-to-noise ratio data and the corresponding time are recorded, and these parameters are combined in units of days to generate the signal-to-noise ratio data file;

[0053] Second, considering the uneven distribution of electron content density in the ionosphere, we selected an ionospheric altitude range of 100-450 km and divided the ionosphere into eight layers with a step size of 50 km. We calculated the ionospheric penetration point (longitude and latitude) using the satellite's altitude and azimuth angles, as well as the height of each layer after ionospheric stratification, and obtained the electron content density of each layer using the International Reference Ionosphere Model (IRI).

[0054] Third, using the electron density values ​​obtained from the International Reference Ionosphere Model (IRI) and the ray tracing method, the altitude correction for each layer of the ionosphere is calculated. To reduce the influence of the troposphere on the refraction of satellite signals, a tropospheric refraction model is introduced to correct the refraction angle of the satellite signal. The sea surface height around the observation station is obtained through LSP spectrum analysis, and the height inversion results are quality controlled to achieve the optimal accuracy of GNSS-IR sea surface height inversion.

[0055] Finally, the tide data of tide gauges near the measuring station and the GNSS-IR sea surface inversion height were obtained, the outliers were eliminated, and the tide data and inversion height data were compared and analyzed.

[0056] In GNSS-IR sea level inversion measurements, the signal received by the satellite receiver is primarily a combination of the direct signal from the satellite and the reflected signal after reflecting off the sea surface. The final signal obtained is the vector sum of the direct and reflected signals. The strength of the composite signal is expressed as the signal-to-noise ratio, which is primarily affected by factors such as multipath, signal transmission power, and antenna gain. Figure 2 The basic principle diagram of GNSS-IR sea surface height inversion, where H is the vertical distance from the phase center of the satellite receiver antenna to the sea surface; θ is the angle between the direct signal and the sea level, that is, the satellite elevation angle; and D is the additional distance of the reflected signal relative to the direct signal.

[0057] GNSS-IR means that the receiver receives the direct signal and reflected signal from the satellite, and the direct signal and reflected signal interfere with each other, such as Figure 2 The interference signal composed of the direct signal and the reflected signal is recorded by the receiver in the signal-to-noise ratio, which can be described as:

[0058]

[0059] in, and denote the direct signal amplitude and the reflected signal amplitude respectively, Indicates the phase difference between the direct signal and the reflected signal. In order to ensure accurate positioning, the antenna of a standard geodetic receiver is usually designed with specific features to reduce the impact of multipath effects so that the received signal meets Therefore, under the influence of direct signals, the signal-to-noise ratio sequence generally presents a parabolic trend.

[0060] At low elevation angles, the signal-to-noise ratio values ​​are smaller, they are more affected by multipath, and the periodic oscillation is more significant. Therefore, it is easier to extract the signal-to-noise ratio oscillation characteristic parameters at low elevation angles than at high elevation angles. Although the signal-to-noise ratio sequence with a larger elevation angle contains more complete information about the reflecting surface, the effective information is often submerged in complex noise and difficult to extract accurately. In the traditional GNSS-IR model, a quadratic polynomial is used to fit the signal-to-noise ratio arc trend. Then, the fitting term is subtracted from the signal-to-noise ratio arc to eliminate the direct signal and a small amount of reflected signal, that is, The resulting signal-to-noise ratio oscillation term can be approximated as:

[0061]

[0062] Where A represents the signal amplitude, f represents the oscillation frequency, and φ represents the phase. The phase difference between the direct signal and the reflected signal can be calculated from the additional distance D.

[0063]

[0064] Where λ represents the carrier wavelength. From Equation (4), we can see that there is a linear relationship between the phase difference and the sine value of the satellite elevation angle sin(θ), namely:

[0065]

[0066] After simplifying formula (5), we can get SNR m The relationship between the height h of the reflecting surface and the frequency is:

[0067]

[0068] Here, λ represents the wavelength and f represents the frequency.

[0069] The present invention uses the electron content density provided by the International Reference Ionosphere Model (IRI) and calculates the ionospheric refractive index based on the frequency of the satellite signal L1 band:

[0070]

[0071] Among them, N e represents the electron content, and f represents the satellite signal frequency.

[0072] The present invention mainly performs a six-layer stratification process at the highest electron content density, starting from the top 450km and following the satellite signal propagation trajectory, with a step size of 50km. The ray tracing method is used to correct and update the elevation angle of each layer, and finally the satellite elevation angle corrected for ionospheric refraction is obtained. First, the corresponding ionospheric refractive index is calculated based on the electron content density of the ionosphere layer i-1 and i-2. The refractive index is used to solve the geocentric angle, and finally the corrected satellite elevation angle is calculated:

[0073]

[0074] β i =arcos(n i *r i *cos(z) / n i-1 *r i-1 ) (9),

[0075]

[0076] Among them, n i-1 represents the refractive index of the upper ionosphere, n i-2 represents the refractive index of the underlying ionosphere, r i-1 Indicates the height from the center of the earth to the target plane i-1 layer, r i-2 Indicates the height from the center of the earth to the target plane i-2 layer, e i-2 Represents the satellite elevation angle corresponding to the i-2 layer, i represents the corresponding layer number, and the highest layer i=8. Taking into account the influence of the earth's curvature, it is convenient to perform layered iterative calculation of the satellite elevation angle along the direction of satellite signal propagation. Therefore, the invention calculates the elevation angle at the initial measuring station to the elevation angle at the highest layer of the ionosphere at 450km. r0 represents the radius of the earth, r2 represents the sum of the height at 450km and the radius of the earth, and e represents the satellite elevation angle at the initial measuring station. According to the refractive index of each layer of the ionosphere calculated by formula (3), the corresponding refraction angle of the two adjacent layers is calculated according to Snell's refraction law. Combined with the refraction angle of the previous layer and the geocentric angle between this layer and the previous layer, the elevation angle value after iterative update of this layer is solved by the triangle internal angle theorem. According to formulas (7)(8)(9)(10), the elevation angle is iteratively calculated to the next layer to obtain the satellite elevation angle corrected by the ionospheric refraction, and finally the accurate satellite elevation angle value corrected by the ionosphere is calculated.

[0077] In order to demonstrate the superiority of the new ionospheric layer elevation angle correction model, the present invention uses RMSE and PCC to evaluate the GNSS-IR sea surface height accuracy after ISEACM correction and the original GNSS-IR height accuracy without model correction.

[0078] The formula for calculating the root mean square error is as follows:

[0079]

[0080] Where Y represents the sea level height measurement sequence from the tide gauge station, and X represents the GNSS-IR sea surface height inversion result. The RMSE is used to assess the discrete deviation between the inversion result and the true value. The smaller the root mean square error of the calculated ISEACM-corrected inverted height, the more accurate the inversion result after model correction.

[0081] The Pearson correlation coefficient calculation formula is as follows:

[0082]

[0083] in, and represents the average of the tide gauge sea level measurement series and the GNSS-IR sea surface altimetry inversion results series, respectively, and n represents the number of discrete points in the data series. PCC primarily describes the linear correlation between the tide gauge sea level measurement series and the model-corrected GNSS-IR altimetry series, with PCC values ​​ranging from -1 to 1. A correlation coefficient closer to 1 indicates a more reliable inversion result; a correlation coefficient between 0.8 and 1.0 indicates an extremely strong correlation between the two series; between 0.6 and 0.8 indicates a strong correlation; and between 0.4 and 0.6 indicates a moderate correlation.

[0084] Example 1:

[0085] This example uses observation file data provided by the Global Shore-Based GNSS website and selects observation data from four stations: TAR0, GOM1, PTLD, and TPW2. The sampling interval is 30 seconds, and one month of continuous observation data is selected for each station. The TAR0 site (latitude and longitude: 36.00, -5.60) is located in Tarifa, Spain, and is equipped with a LEICA GR25 geodetic receiver and a LEIAR20 LEIM antenna. The GOM1 site (latitude and longitude: 28.08, -17.10) is located in San Sebastian de La Gomera, Spain, and is equipped with a LEICA GR50 geodetic receiver and a LEIAR20 LEIM antenna. The PTLD site (latitude and longitude: -38.34, 141.61) is located in Portland, Australia, and is equipped with a LEICA GR25 geodetic receiver and a LEIAT504GG SCIS antenna. The TPW2 site (latitude and longitude: 46.20, -123.77) is located in Puerto Morelos, USA, and is equipped with a SEPT POLARX5 geodetic receiver and a TRM59800.80 SCIS antenna. The selection of tide stations is based on the geographical location of the corresponding stations, and the tide stations closest to the GNSS-IR sea surface height measurement experimental sites are selected. Figure 4 The site distribution map of the four measuring stations is shown.

[0086] In order to verify the reliability of ISEACM, the adjacent tide gauge station was selected for each GNSS station to perform auxiliary verification of the GNSS-IR sea level height inversion. The GNSS single antenna interferometric measurement mode was used to measure and receive satellite data, so the satellite elevation angle was set as much as possible within 30°. Too large an elevation angle will affect the interference result of the data and increase the measurement error of the inverted sea level height. Regarding the setting of the satellite elevation angle, the present invention conducted a cut-off elevation angle experiment with a 10° interval on the four stations. The study found that stations in different regions may require different elevation angle settings, which may be related to the surrounding environment, such as ships docked on the nearby coast, tall objects adjacent to or far away from the station area, etc.

[0087] Therefore, this example selected different cutoff elevation angles for different stations for experimental comparison and analysis. Based on the satellite imagery in Google Maps, the station was divided into four quadrants, with settings for the four areas of 0-90°, 90°-180°, 180°-270°, and 270°-360°.

[0088] Currently, research on the electron content of the ionosphere is relatively mature, with a variety of calculation models available. For example, the Global Positioning System (GPS) used the Klobuchar model to correct for ionospheric delay when it was launched; the European Union's Galileo navigation system uses a three-dimensional electron density model (NeQuick G) to correct for ionospheric delay. In addition, IRI is a project initiated by the Committee on Space Research and the International Union of Radio Science, which aims to generate an empirical standard model of the ionosphere based on various available data sources. This model can provide the electron density of the auroral ionosphere at a specific time and location under geomagnetic quiet conditions. In this example, the International Reference Ionosphere Model (IRI) was used to extract the ionospheric electron density.

[0089] Example 2:

[0090] This example verifies the new ionospheric layer elevation angle correction model:

[0091] This example uses 30 consecutive days of GNSS signal-to-noise ratio data from four stations, TAR0, PTLD, GOM1, and TPW2, to obtain a 30-day time series of sea surface height inversion results using a novel ionospheric layer elevation correction model. Given that tide gauge benchmarks may vary across regions, the inverted sea surface height results were normalized and compared with sea surface data from nearby tide gauges.

[0092] The entire process of GNSS-IR sea level height measurement involves the transmission of satellite signals, the propagation of signals in space, and the final reception by GPS receivers. Each link will cause measurement errors of varying sizes. The ISEACM model of the present invention mainly corrects the changes in satellite signal elevation angles caused by the ionosphere. A lower satellite elevation angle means that the signal propagates farther in the horizontal direction, so the influence of the ionosphere is also longer, and the impact on the elevation angle is also greater. The present invention uses signal-to-noise ratio data at low elevation angles to focus on the impact of elevation angle correction on the accuracy of the final GNSS-IR sea level height inversion. For this purpose, one day's data results from each experimental station are selected for detailed analysis.

[0093] Figure 5 The deviation diagram of the altitude angle before and after correction by the IRI tomographic ray tracing model. The horizontal axis represents the altitude angle of the satellite, and the vertical axis represents the difference between the altitude angle corrected by ISEACM and the altitude angle without correction. The enlarged line graph shows the detailed refraction correction value for each angle. Figure 5 It can be seen that the elevation angle corrections of the four measuring stations are basically between 0.05° and 0.21°.

[0094] Due to the long distance between the ionosphere and the satellite receiver station, even small changes can have a significant impact on GNSS applications. Therefore, all error effects must be considered in the design. However, in the GNSS-IR sea surface height inversion experiment, the refraction of satellite signals in the ionosphere was not carefully considered, resulting in an offset between the calculated satellite elevation angle and the true elevation angle, reducing the accuracy of the GNSS-IR sea surface height inversion. The experimental results show that the larger the elevation angle, the smaller the angle corrected by ISEACM; and the smaller the elevation angle, the greater the correction to the satellite elevation angle. This is consistent with the relationship between elevation angle and propagation distance, and provides a reliable basis for the subsequent ionospheric refraction correction to improve the accuracy of GNSS-IR sea surface height measurements.

[0095] After error correction using the new ionospheric layered altitude angle correction model, the Figure 6 It is clearly observed that the water level inversion results at stations TAR0, PTLD, GOM1, and TPW2 correspond well to the measured water levels. The scattered GNSS-IR sea surface height data agrees well with the tidal observations, demonstrating the effectiveness of the ISEACM correction method. For these four stations, the root mean square error (RMS) between the height inversion results corrected using the new ionospheric layer height angle correction model and the tide gauge measurements is 0.1493 m for TAR0, 0.1732 m for PTLD, 0.2480 m for GOM1, and 0.2189 m for TPW2.

[0096] Among these results, the inversion results from the TAR0 station are superior, with the highest agreement with the tidal observations. This can be attributed to the station's location on a single shore, largely surrounded by sea, resulting in a high signal-to-noise ratio for the received satellite signal and a large amount of available data. Due to the relatively smooth sea surface, the observational root mean square error is small, as the station is less affected by wind and waves. In contrast, the PTLD station is located in an area of ​​Australia, surrounded by seawater and significantly affected by sea breezes. Therefore, the data obtained from the GNSS-IR sea surface altimetry inversion is more complex, with fewer valid altitude data points, and the overall altimetry inversion results are inferior to those of TAR0.

[0097] This example uses GNSS-IR sea surface height inversion experiments conducted at four stations around the world. Figure 7 The scatter plots of different colors represent the correlation analysis of the new ionospheric layer height angle correction model. The horizontal axis represents the tide observation value of the tide gauge station, and the vertical axis represents the height value of the GNSS-IR sea surface height inversion after ISEACM correction. Figure 7It can be seen that the Pearson correlation coefficients of each station are: 90.50% for TAR0 station, 76.34% for PTLD station, 84.70% for GOM1 station, and 83.84% for TPW2 station. Figure 5 and Figure 6 The results show that the sea surface height inversion values ​​corrected by the ISEACM method have a strong correlation with the tide observation values ​​at the tide gauge station, which indicates the reliability of the ISEACM in the invention of ionospheric refraction correction of GNSS-IR sea surface height measurement.

[0098] Example 3:

[0099] This example examines the application of a new ionospheric layering altitude angle correction model:

[0100] The invention was applied to the sea surface height measurement without ionospheric refraction correction and with ISEACM correction. Figure 7 The comparison of the height inversion results and tidal values ​​before and after correction using the new ISEACM method for one month at four stations is shown.

[0101] By observation Figure 8 It can be seen that the number of height series derived from GNSS-IR sea surface height retrievals without ISEACM is smaller than that derived from ionospheric refraction correction. Furthermore, the height retrievals corrected for ionospheric refraction are significantly closer to tidal observations, demonstrating a better correlation. A comparison of the root mean square error (RMS) and correlation coefficients before and after ISEACM correction at four stations reveals that the ISEACM model achieves a maximum 20% improvement in RMS error compared to traditional GNSS-IR sea surface height measurement, while the Pearson correlation coefficient improves by 4%.

[0102] according to Figure 9 The residual plots before and after the ionospheric refraction correction for elevation angles clearly show that the ISEACM correction significantly improves the GNSS-IR sea surface height accuracy at all four stations. This demonstrates the influence of ionospheric refraction on elevation angles, ultimately causing accuracy loss in the GNSS-IR sea surface height retrieval process. Therefore, using the ISEACM to correct satellite elevation angles is feasible and effective in improving the accuracy of the final GNSS-IR sea surface height retrieval.

[0103] Compared with the existing technology, the present invention constructs a new ionospheric layered altitude angle correction model based on the altitude angle refraction of the ionosphere on the propagation path of satellite signals. The satellite altitude angle, azimuth angle and signal-to-noise ratio (SNR) data are calculated using the GNSS observation data file obtained by the receiver. The correction amount of the altitude angle is calculated using the ray tracing method. Finally, the accurate sea surface height after correction by the new ionospheric layered altitude angle correction model is obtained. The sea surface height is compared with the measurement station and the nearby tidal measurement station that have not been corrected with the new ionospheric layered altitude angle correction model. The root mean square error and Pearson correlation coefficient are used to evaluate the reliability of the new method proposed in the present invention. Experimental results show that the ISEACM correction can effectively improve the accuracy of GNSS-IR sea surface height measurement, which is of great significance for accurately measuring sea surface height.

Claims

1. A sea surface altimetry method based on an ionospheric layered altitude angle correction model, characterized in that: The ionospheric layered elevation angle correction model (ISEACM) was constructed, which includes the following steps: Step 1: Using the GNSS observation data file and satellite orbit data, calculate the satellite's azimuth and elevation angles, and extract the interference signal-to-noise ratio data of the direct signal and reflected signal in the observation data. At the same time, record the satellite's azimuth, elevation angle, satellite PRN number of the signal-to-noise ratio data, and the corresponding time. These parameters are combined in units of days to generate a signal-to-noise ratio data file; Step 2: Considering the uneven distribution of electron content density in the ionosphere, an ionospheric altitude range of 100-450 km was selected, and the ionosphere was divided into eight layers with a step size of 50 km. The ionospheric penetration point, including longitude and latitude data, was calculated using the satellite's altitude and azimuth angles, as well as the height of each layer after ionospheric stratification. The electron content density of each layer was then obtained using the International Reference Ionosphere Model (IRI). Step 3: Using the electron density values ​​obtained from the International Reference Ionosphere Model (IRI), the altitude correction for each layer of the ionosphere is calculated. The refraction model of the troposphere is introduced to correct the refraction angle of the satellite signal. The sea surface altitude around the station is obtained through LSP spectrum analysis, and the altitude inversion results are quality controlled. Step 4: Obtain tide data from tide gauges near the station and GNSS-IR sea surface inversion height, and remove outliers; In step 1, the GNSS-IR receiver receives the direct signal and the reflected signal from the satellite. The direct signal and the reflected signal interfere with each other, and the interference signal composed of the direct signal and the reflected signal is recorded by the receiver in the signal-to-noise ratio. The signal-to-noise ratio can be described as: （1）， in, and denote the direct signal amplitude and the reflected signal amplitude respectively, represents the phase difference between the direct signal and the reflected signal, and the obtained signal-to-noise ratio oscillation term is approximately: （2）， in, A represents the signal amplitude, f represents the oscillation frequency, Indicates the phase, D is the additional distance of the reflected signal relative to the direct signal, from the additional distance D The phase difference between the direct signal and the reflected signal can be calculated : （3）， in, represents the carrier wavelength, θ is the angle between the direct signal and the sea level, that is, the satellite elevation angle. From formula (4), we can see that there is a linear relationship between the phase difference and the sine value of the satellite elevation angle sin(θ), that is: （4）， After simplifying formula (5), we can get Reflecting surface height h The relationship with frequency is: （5）， in, represents the wavelength, Indicates frequency; In steps 2 and 3, the electron content density provided by the International Reference Ionosphere Model (IRI) is used to calculate the ionospheric refractive index based on the frequency of the satellite signal's L1 band: （6）， in, represents the electron content, f It represents the satellite signal frequency. The highest electron content density is processed in eight layers. From the top layer of 450 km downwards, the satellite signal propagation trajectory is followed, and the layers are layered with a step length of 50 km. The ray tracing method is used to correct and update the elevation angle of each layer. Finally, the satellite elevation angle after ionospheric refraction correction is obtained. First, according to the first i -1 floor and i The electron content density of the -2 ionosphere layer is calculated to obtain the corresponding ionosphere refractive index, and the refractive index is used to solve the geocentric angle, and finally the corrected satellite altitude angle is calculated: (7)， (8)， (9)， (10)， in, represents the refractive index of the upper ionosphere, represents the refractive index of the underlying ionosphere, Represents the distance from the center of the earth to the target plane i -1 floor height, Represents the distance from the center of the earth to the target plane i -2 storeys in height, express i -2 layer corresponding to the satellite elevation angle, i Indicates the corresponding layer number, the highest layer i =8.

2. The method for measuring sea surface height based on the ionospheric layered altitude angle correction model according to claim 1, characterized in that: Taking into account the influence of the earth's curvature, it is convenient to perform layered iterative calculation of the satellite altitude angle along the direction of satellite signal propagation. Therefore, the altitude angle at the initial observation station is calculated to the altitude angle at the highest layer of the ionosphere at 450 km. represents the radius of the Earth, represents the sum of the altitude at 450 km and the radius of the Earth, = represents the initial satellite elevation angle at the observation station. The refractive index of each ionosphere layer is calculated according to formula (3). The corresponding refraction angles of the two adjacent layers are calculated according to Snell's refraction law. The refraction angle of the previous layer and the geocentric angle of the current layer and the previous layer are combined. The elevation angle value of the iteratively updated layer is solved by the triangle internal angle theorem. The elevation angle is iteratively calculated to the next layer according to formulas (7), (8), (9), and (10). The satellite elevation angle corrected for the ionosphere refraction is obtained, and finally the accurate satellite elevation angle value corrected for the ionosphere is calculated.

3. The method for measuring sea surface height based on the ionospheric layered altitude angle correction model according to claim 1, characterized in that: Utilize in step 4 RMSE and PCC The accuracy of GNSS-IR sea surface height measurement after ISEACM correction is evaluated against the accuracy of original GNSS-IR height measurement without model correction. The root mean square error is calculated as follows: （11）， Where, Y represents a sequence of sea level measurements at a tide gauge station, X Indicates the GNSS-IR sea surface height inversion result, RMSE It is used to evaluate the discrete deviation between the inversion result and the true value. The smaller the root mean square error of the ISEACM-corrected inversion height is, the more accurate the inversion result after the model correction is. The Pearson correlation coefficient calculation formula is as follows: （12）， in, and are the average values ​​of the sea level height measurement sequence of the tide gauge station and the GNSS-IR sea level height inversion result sequence, n Represents the number of discrete points in the data series.

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