Method for measuring water level height by using NMEA data of low-cost GNSS module

Abstract

The invention discloses a method for measuring a water level height by using NMEA data of a low-cost GNSS module. The method comprises the following steps: receiving NMEA observation data output by a low-cost navigation type GNSS module; carrying out the preprocessing of the GNSS NMEA data; a GNSS satellite elevation angle sine value is used as an independent variable, a corresponding refined SNR interference signal observation value is used as a dependent variable, a satellite elevation angle sine value-SNR observation value sequence is constructed, the amplitude, the angular frequency and the phase of interference signal data are calculated respectively, and the GNSS reflection height H is calculated finally; and fusing the multiple groups of GNSS NMEA water level observation values by adopting a velocity pause particle swarm optimization (VPPSO) algorithm, and substituting the reflection height H in the optimal parameter value to obtain a water level height value h. Through joint innovation of a plurality of key links such as water level calculation data source, observation data modeling, fusion measurement and intelligent optimization, the water level measurement precision of the GNSS technology under the conditions of low cost and low power consumption equipment is systematically improved.

Description

Technical Field

[0001] The invention relates to a method for measuring water level height by utilizing NMEA data of a low-cost GNSS module, and belongs to the technical field of non-contact water level monitoring. Background Art

[0002] Water level monitoring plays an irreplaceable and important role in disaster prevention, engineering safety, and ecological protection. It is a fundamental technical means for achieving dynamic perception of the water environment and scientific decision-making. In terms of flood prevention and disaster reduction, water level data can reflect changes in water bodies in rivers, lakes, reservoirs, and offshore areas, and plays an important supporting role in flood warning, emergency dispatch, and disaster response. Through continuous monitoring of key water areas, abnormal water level fluctuations can be identified in advance, effectively improving the ability to respond to extreme hydrological events and reducing the risks and losses caused by flood disasters. In terms of the ecological environment, ecosystems such as lakes, wetlands, and estuaries are highly sensitive to water level conditions. The fluctuation of water levels is directly related to the stability of aquatic habitats and the maintenance of ecosystem functions. Long-term water level monitoring can provide a scientific basis for ecological water level regulation, ecological water replenishment, and wetland protection.

[0003] Currently, acoustic and pressure-based water level measurement technologies are the two most widely used. The former primarily relies on the propagation characteristics of high-frequency sound waves in a medium. By transmitting an acoustic signal into the water and receiving the reflected echo, the round-trip propagation time of the sound wave is measured to infer the water level. However, the measurement accuracy of this method significantly depends on the stability of the sound wave's propagation velocity in water. This velocity is significantly affected by environmental factors such as water temperature, salinity, and water pressure, and is prone to nonlinear fluctuations, which can lead to systematic measurement errors. Pressure-based water level measurement technology deploys underwater pressure sensors to measure the hydrostatic pressure exerted by the water column on the sensor. The water level is then inferred based on the known physical relationship between water pressure and water depth. However, because the equipment operates underwater for a long time, it is susceptible to environmental factors such as biofouling, material corrosion, and aging, which can lead to degradation of sensor performance and increased measurement errors, making long-term, high-precision, and stable monitoring difficult. In addition, whether it is the acoustic or pressure method, its system construction generally has problems such as high cost, complex installation and maintenance, and long site construction cycle, which makes it difficult to meet the current actual needs of large-scale, intensive networking and remote autonomous monitoring.

[0004] GNSS is a global positioning infrastructure composed of multiple satellite navigation constellations, including the United States' GPS, Russia's GLONASS, Europe's Galileo, and China's BeiDou Navigation Satellite System (BDS). NMEA data is a globally adopted GNSS information output standard with high versatility and cross-platform compatibility. The data is encoded in ASCII text and has a standardized structure. It can be directly output by most low-cost navigation-type GNSS receiver chips (or modules), avoiding dependence on proprietary data formats or high-end equipment, significantly reducing system deployment and application costs. Key information such as satellite elevation angle, signal-to-noise ratio (SNR), and timestamp provided in the NMEA GSV sentence provides the data foundation for water level inversion based on GNSS interferometric reflection.

[0005] In the process of realizing the present invention, the inventors discovered that the current water level measurement based on GNSS interferometric reflection mainly uses high-resolution SNR, carrier phase or pseudo-range observations recorded in RINEX format files to achieve water level inversion; however, low-cost navigation GNSS modules do not have the function of outputting RINEX format files, and the resolution of the NMEA observation data they output is low. Specifically, SNR, satellite altitude angle, etc. are integer data and cannot be directly used for water level measurement. Summary of the Invention

[0006] The purpose of the present invention is to propose a method for measuring water level height using NMEA data from a low-cost GNSS module, so as to solve the problems raised in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] GNSS interference signal reception: Receive NMEA observation data output by low-cost navigation GNSS modules;

[0009] GNSS NMEA data preprocessing: The satellite elevation angle, satellite azimuth angle, and SNR observation values ​​in the NMEA observation data output by the GNSS module in real time are refined. The sine value of the GNSS satellite elevation angle is used as the independent variable, and the corresponding refined SNR interference signal observation value is used as the dependent variable. A "satellite elevation angle sine value - SNR observation value" sequence is constructed, and a data subset with an elevation angle range of 10° to 25° is selected as the valid data interval.

[0010] Single-frequency GNSS NMEA water level solution: Use a low-order polynomial fitting method to remove the direct component in the SNR observation value sequence to obtain the interference component. Calculate the amplitude, angular frequency, and phase of the interference signal data, and finally calculate the GNSS reflection height H.

[0011] Multi-frequency GNSS NMEA water level data fusion: The velocity-paused particle swarm optimization (VPPSO) algorithm is used to fuse multiple sets of GNSS NMEA water level observations. The water level height h is obtained by substituting the reflection height H from the optimal parameter value into h = H0 - H; where H0 is the GNSS antenna orthometric height determined by leveling.

[0012] As a further solution of the present invention, the satellite elevation angle, satellite azimuth angle, and SNR observation value in the NMEA observation data output by the GNSS module in real time are refined, specifically, (1) refinement of the satellite elevation angle: the relationship between the integer satellite elevation angle θ and time t in NMEAGSV is simplified to a first-order linear function form, that is:

[0013] θ = a × t + b (Formula 1)

[0014] Where a represents the rate at which the satellite elevation angle changes over time, and b is the initial angle.

[0015] Since the NMEA satellite elevation angle data output by the GNSS chip in real time is a rounded integer value, the first and last measured integer satellite elevation angles can be restored to floating point data using (Formula 2):

[0016]

[0017] Where θ a The satellite elevation angle value measured for the period;

[0018] (2) Refinement of satellite azimuth angle: The relationship between the integer satellite azimuth angle α and time t in the NMEA GSV sentence is expressed using a first-order linear function, that is:

[0019] α=c×t+d (Formula 3)

[0020] Where c represents the rate of change of the satellite azimuth angle over time, and d is the initial angle. Since the NMEA satellite azimuth angle data output by the GNSS chip in real time is a rounded integer value, the first and last measured satellite azimuth angles are restored to floating-point type using (Formula 4):

[0021]

[0022] Where α a The satellite azimuth angle value measured for the period;

[0023] (3) Refinement of SNR observation value: Each refined elevation angle data corresponds to an SNR observation value. Since the elevation angle data retains the value of three decimal places, there are multiple elevation angles with the same value in a short continuous time period, and the SNR observation values ​​corresponding to these data are different. The multiple SNR observation values ​​SNR1~sNR of the same elevation angle value θ are calculated using (Formula 5). n Perform averaging:

[0024]

[0025] Where SNR(θ) represents the unique SNR observation value corresponding to the altitude angle value, and n is the number of valid SNR samples at the altitude angle.

[0026] As a further solution of the present invention, the GNSS NMEA data includes interference signal information obtained by superimposing the signal from the water surface and the direct signal. The interference component can be obtained by removing the direct component from the SNR sequence using a low-order polynomial fitting method:

[0027]

[0028] Where A is the amplitude of the interference signal. Expand (Formula 7) using (Formula 8):

[0029]

[0030] Where ω is the angular frequency, t ave is the average time of the time series. τ is the phase offset parameter. Use (Formula 9), (Formula 10), and (Formula 11) to calculate the amplitude, angular frequency, and phase in (Formula 8):

[0031]

[0032]

[0033]

[0034] Where, ofac is the oversampling factor. j ·t ave and -ω j ·τ is the phase delay caused by time translation and phase offset respectively. After obtaining the angular frequency of the GNSS interferometer signal according to (Formula 10), the GNSS reflection height is calculated using (Formula 12).

[0035] As a further solution of the present invention: the specific implementation process of this step using the velocity pause particle swarm optimization algorithm (VPPSO) to fuse multiple groups of GNSS NMEA water level observations is as follows:

[0036] S1. Multi-frequency GNSS interferometric signal modeling.

[0037] According to the amplitude A extracted from (Formula 13) LSS , frequency f LSS and phase φ LSS , build the GNSS SNR interference signal model:

[0038] SNR LSS (θ)=A LSS cos(2π·f LSS sinθ+φ LSS ) (Formula 13)

[0039] For the interference signals of different frequency bands (such as L1 and L2, or B1 and B2) in the same satellite system at the same time, a multi-frequency fusion model is constructed using (Formula 14).

[0040]

[0041] Where H is the vertical height of the water surface relative to the GNSS antenna, λ L1 and λ L2 are the wavelengths of L1 and L2 frequency band signals, A L1 、A L2 and φ L1 、φ L2 are the amplitude and phase parameters corresponding to each frequency band.

[0042] S2. Initial value estimation and search boundary construction:

[0043] The amplitude, phase, and water level of (Formula 14) are considered as unknowns and optimized by VPPSO. The parameters to be estimated are the amplitude parameters A of the reflected signal in different frequency bands. L1 、A L2 , phase parameter φ L1 、φ L2 , and the final reflection height value H used for water level calculation. The initial particle position and search boundary of the VPPSO algorithm are determined by the values ​​obtained by (Formula 13).

[0044] S3. Parameter optimization and fitness evaluation:

[0045] A fitness evaluation mechanism based on the GNSS interferometric signal reconstruction accuracy is constructed as the core metric for VPPSO algorithm convergence. Specifically, a physically interpretable and mathematically operable objective function is defined to measure the quality of the fit of the parameter combination represented by the current particle in the GNSS interferometric signal model, as shown in (Equation 15).

[0046]

[0047] The objective function is continuous and differentiable, and reflects the fitting error between the parameter model output and the actual observation data. The smaller the objective function value is, the closer the estimated parameter value is to the true value.

[0048] S4. Output optimal parameters and water level inversion:

[0049] After processing through steps S1, S2, and S3, a set of optimal parameter values ​​is obtained, achieving high-precision reconstruction of the GNSS reflection model. Substituting the reflection height H from the optimal parameter values ​​into (Equation 16) yields the water level height h.

[0050] h=H0-H (Formula 16)

[0051] Where H0 is the orthometric height of the GNSS antenna determined by leveling.

[0052] The beneficial effects of the present invention are:

[0053] 1. This invention establishes a key technical approach for high-precision GNSS interferometric water level measurement using low-resolution NMEA-formatted data, achieving centimeter-level water level measurement using a low-cost, low-power navigation-grade GNSS chip. This solution effectively addresses the high economic costs, difficult deployment, and complex operations and maintenance associated with existing GNSS interferometric technology applications, which rely on high-performance equipment. This significantly reduces the technical complexity and economic costs of water level monitoring systems, providing a practical and feasible path for their widespread application.

[0054] 2. The present invention proposes a collaborative modeling and fusion measurement mechanism based on multi-system and multi-band interference signals, which achieves consistency in parameter solution, complementary utilization of inter-frequency information, and refined integration of observation redundancy; effectively solves the problems of modeling fragmentation and solution conflicts between frequency bands, thereby enhancing the robustness and reliability of GNSS water level measurement.

[0055] This invention systematically improves the water level measurement accuracy of GNSS technology under low-cost, low-power equipment conditions through joint innovation in multiple key links such as water level solution data source, observation data modeling, fusion measurement and intelligent optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is an example result of refining the satellite altitude angle sequence in the NMEA data in the method of the present invention;

[0057] Figure 2 This is an example result after refining the satellite azimuth angle sequence in NMEA using the method of the present invention;

[0058] Figure 3The figure is a comparison chart of the original NMEA SNR observation value of the present invention and the SNR observation value sequence after being refined using the above method;

[0059] Figure 4 This is a flow chart of the method for measuring water level using NMEA data from a low-cost GNSS module according to the present invention;

[0060] Figure 5 This is a flow chart of the multi-frequency GNSS NMEA water level data fusion of the present invention;

[0061] Figure 6 Specific implementation methods of the present invention Multiple GNSS interferometric water level monitoring prototype architecture;

[0062] Figure 7 This is a picture of the GNSS interferometric water level monitoring experimental station and its surrounding environment;

[0063] Figure 8 Comparison chart of the water level measurement results of the solution disclosed in the present invention and the measurement results of the radar water level meter.

[0064] Glossary: ​​Global Navigation Satellite System (GNSS): Global Satellite Navigation System; GNSS interferometric reflectometry: GNSS interferometric reflectometry; National Marine Electronics Association (NMEA): A standard protocol developed by the National Marine Electronics Association of the United States for exchanging information between GNSS and other devices; SNR, Signal-to-Noise: Signal-to-Noise Ratio; Water level, the vertical distance from the water surface to the measurement antenna. DETAILED DESCRIPTION

[0065] Example 1

[0066] The GNSS receiver is installed in an open area near the shore, away from tall obstructions, and the horizontal distance between the antenna and the water's edge is kept within 10 meters. The GNSS antenna is tilted toward the water surface, with an inclination angle of 30° to 45° relative to the horizontal plane to enhance sensitivity to signals reflected from the water. The receiver receives and analyzes NMEA data, which is the interference signal generated by the superposition of GNSS signals reflected from the water and the direct signal.

[0067] Since the apparent motion of GNSS satellites in the sky is relatively slow, starting from a fixed observation point on the Earth's surface, within a certain time window (about 30 minutes), multiple satellites can be continuously tracked, and their corresponding elevation and azimuth change information can be obtained. During this observation period, for a specific satellite, its geometric position relative to the ground receiving point shows good temporal continuity, and the trajectory of the satellite elevation and azimuth changing with time can be regarded as a linear change in a short time scale. Therefore, the relationship between the integer satellite elevation angle θ and time t in the NMEA GSV is simplified to a first-order linear function form, that is:

[0068] θ = a × t + b (Formula 1)

[0069] Where a represents the rate at which the satellite elevation angle changes over time, and b is the initial angle.

[0070] Since the NMEA satellite elevation angle data output by the GNSS chip in real time is a rounded integer value, the first and last measured integer satellite elevation angles can be restored to floating point data using (Formula 2):

[0071]

[0072] Where θ a The satellite altitude angle value measured during this time period. For example, if the NMEA satellite altitude angle is 19 degrees from the 1st second to the 50th second, then using (Formula 2) to recover the satellite altitude angle, the 1st second's altitude angle is 18.445 degrees, and the 50th second's altitude angle is 19.444 degrees. Substituting the recovered floating-point satellite altitude angle and the corresponding time into (Formula 1) yields the function coefficients a and b. Substituting other moments and coefficients into (Formula 1) within this time period yields the satellite altitude angle at any point within that time period. Figure 1 The figure shows an example result after refining the satellite elevation angle sequence in NMEA using this method.

[0073] The relationship between the integer satellite azimuth angle α and time t in the NMEA GSV sentence is expressed using a first-order linear function, namely:

[0074] α=c×t+d (Formula 3)

[0075] Where c represents the rate of change of the satellite azimuth angle over time, and d is the initial angle. Since the NMEA satellite azimuth angle data output by the GNSS chip in real time is a rounded integer value, the first and last measured satellite azimuth angles are restored to floating-point type using (Formula 4):

[0076]

[0077] Where α aThe satellite azimuth angle value measured during this period. For example, if the NMEA satellite azimuth angle is 60 degrees from the 1st second to the 50th second, the recovered satellite angle value (Formula 4) is 59.445 degrees at the 1st second and 60.444 degrees at the 50th second. Substituting the recovered floating-point satellite angle and the corresponding time into Formula 3 yields the function coefficients c and d. Substituting other times and coefficients within this period into Formula 3 yields the satellite azimuth angle at any point during this period. Figure 2 The figure shows an example result after refining the satellite azimuth angle sequence in NMEA using this method.

[0078] For the integer SNR data in the NMEA GSV sentence, it is necessary to match and refine it with the satellite altitude angle; then, it is mapped and normalized to ensure that each altitude angle value uniquely corresponds to an SNR observation value. Each refined altitude angle data corresponds to an SNR observation value. Since the altitude angle data retains three decimal places, there are multiple altitude angles with the same value in a short continuous time period, and the SNR observation values ​​corresponding to these data are different. The multiple SNR observation values ​​SNR1~SNR of the same altitude angle value θ are calculated using (Formula 5). n Perform averaging:

[0079]

[0080] Where SNR(θ) represents the unique SNR observation value corresponding to the altitude angle value, and n is the number of valid SNR samples at the altitude angle. Figure 3 The following is a comparison of the original NMEA SNR observations and the refined SNR observations using the above method. This processed data sequence achieves a one-to-one correspondence between elevation angles and SNR values, preserving the fine resolution of elevation angles while eliminating errors caused by inaccurate observation data.

[0081] To improve the interferometric characteristics of GNSS signals during water level measurement, noise suppression and signal enhancement are required for the raw observation data. This method uses the sine of the GNSS satellite elevation angle as the independent variable and the corresponding, refined SNR interferometric signal observation as the dependent variable. A "satellite elevation angle sine value - SNR observation value" sequence is constructed, and a data subset with elevation angles between 10° and 25° is selected as the valid data interval.

[0082] GNSS NMEA data includes interference signal information obtained by superimposing the signal from the water surface and the direct signal. The interference component can be obtained by removing the direct component from the SNR sequence using a low-order polynomial fitting method:

[0083]

[0084] Where A is the amplitude of the interference signal. Expand (Formula 7) using (Formula 8):

[0085]

[0086] Where ω is the angular frequency, t ave is the average time of the time series. τ is the phase offset parameter. Use (Formula 9), (Formula 10), and (Formula 11) to calculate the amplitude, angular frequency, and phase in (Formula 8):

[0087]

[0088]

[0089] Where, ofac is the oversampling factor. j ·t ave and -ω j ·τ is the phase delay caused by time translation and phase offset respectively. After obtaining the angular frequency of the GNSS interferometer signal according to (Formula 10), the GNSS reflection height is calculated using (Formula 12).

[0090]

[0091] Since the satellite elevation angle has a significant impact on the interference signal in NMEA, when the satellite elevation angle is low (less than 40°), the interference pattern of NMEA data is clearer and more stable; therefore, the present invention sets the upper limit of the NMEA data satellite altitude value used to calculate the GNSS reflection height to 40°.

[0092] The velocity pause particle swarm optimization algorithm (VPPSO) is used to fuse multiple sets of GNSS NMEA water level observations to achieve high-precision water level measurement. The specific implementation process of data fusion is as follows: Figure 5 shown.

[0093] S1. Multi-frequency GNSS interferometric signal modeling:

[0094] According to the amplitude A extracted from (Formula 13) LSS , frequency f LSS and phase φ LSS , build the GNSS SNR interference signal model:

[0095] SNR LSS (θ)=A LSS cos(2π·f LSS sinθ+φ LSS ) (Formula 13)

[0096] For the interference signals of different frequency bands (such as L1 and L2, or B1 and B2) in the same satellite system at the same time, a multi-frequency fusion model is constructed using (Formula 14).

[0097]

[0098] Where H is the vertical height of the water surface relative to the GNSS antenna, λ L1 and λ L2 are the wavelengths of L1 and L2 frequency band signals, A L1 、A L2 and φ L1 、φ L2 are the amplitude and phase parameters corresponding to each frequency band.

[0099] S2. Initial value estimation and search boundary construction:

[0100] The amplitude, phase, and water level of (Formula 14) are considered as unknowns and optimized by VPPSO. The parameters to be estimated are the amplitude parameters A of the reflected signal in different frequency bands. L1 、A L2 , phase parameter φ L1 、φ L2 , and the final reflection height value H used for water level calculation. The initial particle position and search boundary of the VPPSO algorithm are determined by the values ​​obtained by (Formula 13).

[0101] S3. Parameter optimization and fitness evaluation:

[0102] This paper constructs a fitness evaluation mechanism based on the reconstruction accuracy of GNSS interferometric signals as a core metric for VPPSO convergence. Specifically, it defines a physically interpretable and mathematically feasible objective function to measure the quality of the fit of the parameter combination represented by the current particle in the GNSS interferometric signal model, as shown in (Equation 15).

[0103]

[0104] The objective function is continuous and differentiable, and reflects the fitting error between the parameter model output and the actual observation data. The smaller the objective function value is, the closer the estimated parameter value is to the true value.

[0105] S4. Output optimal parameters and water level inversion:

[0106] After processing through steps S1, S2, and S3, a set of optimal parameter values ​​is obtained, achieving high-precision reconstruction of the GNSS reflection model. Substituting the reflection height H from the optimal parameter values ​​into (Equation 16) yields the water level height h.

[0107] h=H0-H (Formula 16)

[0108] Where H0 is the orthometric height of the GNSS antenna determined by leveling.

[0109] Example 2

[0110] Figure 6 This demonstration showcases the hardware structure and physical implementation of a GNSS water level monitoring system based on this invention. The prototype integrates five core modules: a control module, a 2G wireless network relay module, a 4G wireless network communication module, an RS485 protocol hub, and a u-blox F9P GNSS chip. This GNSS chip provides NMEA data. The control module uses an H616 chip, which is programmed with the GNSS NMEA water level measurement solution disclosed in this invention.

[0111] The hardware uses an SMA interface to connect to an external antenna, supporting both geodetic and low-cost ceramic antennas, offering excellent adaptability. To enable comparative observations between the prototype system and traditional water level sensors, the device also integrates an RS485 communication interface for easy expansion and connection of water level sensors. The main control module can also configure measurement intervals and output parameters.

[0112] The prototype realizes remote data transmission through the built-in 4G wireless communication module, and can upload the daily generated GNSSNMEA water level data and sensor observation data to the back-end server in real time, supporting online monitoring and centralized management.

[0113] The experimental station environment is as follows Figure 7 The experimental station was located in a typical underground coal mining subsidence area in the Luxi mining district of Shandong Province. The GNSS interferometric water level monitoring prototype was installed atop a 2.5m-high support pole. The system is powered by an 80W solar panel and a 100Ah lead-zinc battery, which can provide approximately 168 hours of continuous power in the absence of sunlight, ensuring stable operation in the field.

[0114] To further verify the accuracy of GNSS interferometric measurements, a high-frequency water level radar was also installed in the experiment. The radar used was the KLJ-039 model produced by Keluojia Environmental Protection Technology Co., Ltd., with an operating frequency of 26GHz, a maximum range of 30 meters, and a measurement accuracy of ±5mm. In this experiment, the radar measurement interval was set to 60 seconds. Figure 7 As shown, the radar is mounted below a horizontal crossbar, which is bolted to the center of the GNSS bracket. Using a manual steel ruler, the vertical distance between the phase centers of the radar antenna and the GNSS antenna is 0.742 meters.

[0115] The observation period of this experiment is from May 1, 2024 to September 30, 2024, a total of 153 days. During this period, GPS (L1 / L2), GLONASS (G1 / G2) and Galileo (E1 / E5) multi-system multi-band NMEA data are used for water level inversion.

[0116] In this experiment, based on the spatial relationship between the GNSS station and the water surface, a satellite orbit arc segment with an azimuth range of 270° to 360° and an elevation range of 10° to 25° was selected as the observation window for interferometric signal extraction. Within this range, dual-frequency GNSS NMEA observations were acquired, and GNSS water level measurements were performed using the proposed method. Water level radar measurements were used as the true values ​​for comparative analysis.

[0117] During the experiment (May to September 2024), the maximum change in the water level in the monitoring area was 99.7 cm. The comparison of the water level measurement results of the scheme disclosed in this invention with the measurement results of the high-frequency water level radar is shown in Figure 8 The minimum absolute error between the measurement results and the true value of the disclosed solution is 0.005 cm, and the maximum absolute error is 14.64 cm. The relative error range is -4.7% to 5.1%, and the average relative error is 0.0%. The average error of the water level measurement results of the disclosed solution is 0.0353 cm, the standard deviation is 5.453 cm, and the root mean square error is 5.453 cm.

[0118] The key improvements of the present invention compared to the prior art are as follows:

[0119] (1) Existing GNSS interferometric water level measurement methods rely on high-precision SNR and elevation angle observation data in the RINEX format. This paper discloses a method for measuring water level using NMEA data from a low-cost GNSS module. This method uses the NMEA data output by a low-cost navigation GNSS module as the data source and measures water level by extracting the interferometric signal from the NMEA data.

[0120] (2) Aiming at the low resolution and integer discreteness of satellite elevation angle and SNR observation values ​​in NMEA format data, the present invention proposes a method for refining NMEA observation values ​​based on a linear model. The core steps of this method are: first, by constructing a satellite-receiver geometric model and combining it with a time series, the original integer elevation angle data is subjected to piecewise linear interpolation processing to achieve refined reconstruction of the elevation angle; second, for multiple SNR observation values ​​corresponding to the same elevation angle, a statistical averaging strategy is used to perform mean filtering on them to eliminate the influence of observation noise and enhance the periodic characteristics of the interference signal.

[0121] (3) To address the problems of complex reflection signal modeling and insufficient parameter estimation accuracy in GNSS interferometry under multi-frequency observation conditions, a high-precision, multi-frequency GNSS interferometry water level inversion algorithm strategy was constructed, integrating fusion modeling, key parameter extraction, and intelligent optimization. The key steps include: first, using the cosine function to construct a data fusion model suitable for multi-system and multi-band GNSS signals; second, using the trigonometric function expansion method to calculate the angular frequency, amplitude, and initial phase information of the NMEASNR interferometry signal under non-uniform sampling conditions. Finally, using VPPSO to jointly estimate the amplitude, phase, and reflection height in the model.

[0122] The above is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solutions and inventive concepts of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for measuring water level using NMEA data from a low-cost GNSS module, characterized by: The steps include: GNSS interference signal reception: Receive NMEA observation data output by low-cost navigation GNSS modules; GNSS NMEA data preprocessing: fine-tune the satellite altitude angle, satellite azimuth angle, and SNR observation values ​​in the NMEA observation data output by the GNSS module in real time; The sine value of the GNSS satellite elevation angle is used as the independent variable, and the corresponding refined SNR interference signal observation value is used as the dependent variable. A "satellite elevation angle sine value - SNR observation value" sequence is constructed, and a data subset with an elevation angle range of 10° to 25° is selected as the valid data interval. Single-frequency GNSS NMEA water level solution: Use a low-order polynomial fitting method to remove the direct component in the SNR observation value sequence to obtain the interference component. Calculate the amplitude, angular frequency, and phase of the interference signal data, and finally calculate the GNSS reflection height H. Multi-frequency GNSS NMEA water level data fusion: The velocity-paused particle swarm optimization (VPPSO) algorithm is used to fuse multiple sets of GNSS NMEA water level observations. The water level height h is obtained by substituting the reflection height H from the optimal parameter value into h = H0 - H; where H0 is the GNSS antenna orthometric height determined by leveling.

2. The method for measuring water level height using NMEA data from a low-cost GNSS module according to claim 1, characterized in that: The GNSS receiver was installed in an open area near the shore, away from tall obstructions, and the horizontal distance between the antenna and the water's edge was kept within 10 meters. The GNSS antenna was tilted toward the water surface, with an inclination angle of 30° to 45° to the horizontal plane to enhance sensitivity to signals reflected from the water surface.

3. The method for measuring water level using NMEA data from a low-cost GNSS module according to claim 1, characterized in that: The satellite elevation angle, satellite azimuth angle, and SNR observation value in the NMEA observation data output by the GNSS module in real time are refined. Specifically, (1) refinement of the satellite elevation angle: the relationship between the integer satellite elevation angle θ and time t in the NMEA GSV is simplified to a first-order linear function form, that is: θ = a × t + b (Formula 1) Where a represents the rate at which the satellite elevation angle changes over time, and b is the initial angle; Since the NMEA satellite elevation angle data output by the GNSS chip in real time is a rounded integer value, the first and last measured integer satellite elevation angles can be restored to floating point data using (Formula 2): Where θ a The satellite elevation angle value measured for the period; (2) Refinement of satellite azimuth angle: The relationship between the integer satellite azimuth angle α and time t in the NMEA GSV sentence is expressed using a first-order linear function, that is: α=c×t+d (Formula 3) Where c represents the rate of change of the satellite azimuth angle over time, and d is the initial angle. Since the NMEA satellite azimuth angle data output by the GNSS chip in real time is a rounded integer value, the first and last measured satellite azimuth angles are restored to floating-point type using (Formula 4): Where α a The satellite azimuth angle value measured for the period; (3) Refinement of SNR observation value: Each refined altitude angle data corresponds to an SNR observation value. Since the altitude angle data retains three decimal places, there are multiple altitude angles with the same value in a short continuous time period, and the SNR observation values ​​corresponding to these data are different. The multiple SNR observation values ​​SNR1~SNR n Perform averaging: Where SNR(θ) represents the unique SNR observation value corresponding to the altitude angle value, and n is the number of valid SNR samples at the altitude angle.

4. The method for measuring water level using NMEA data from a low-cost GNSS module according to claim 1, characterized in that: GNSS NMEA data includes interference signal information obtained by superimposing the signal from the water surface and the direct signal. The interference component can be obtained by removing the direct component from the SNR sequence using a low-order polynomial fitting method: Where A is the amplitude of the interference signal. Expand (Formula 7) using (Formula 8): Where ω is the angular frequency, t ave is the average time of the time series. τ is the phase offset parameter. Use (Formula 9), (Formula 10), and (Formula 11) to calculate the amplitude, angular frequency, and phase in (Formula 8): Where, ofac is the oversampling factor. j ·t ave and -ω j ·τ is the phase delay caused by time translation and phase offset respectively. After obtaining the angular frequency of the GNSS interferometer signal according to (Formula 10), the GNSS reflection height is calculated using (Formula 12).

5. The method for measuring water level using NMEA data from a low-cost GNSS module according to claim 1, characterized in that: In this step, the specific implementation process of fusing multiple sets of GNSS NMEA water level observations using the velocity pause particle swarm optimization algorithm (VPPSO) is as follows: S1. Multi-frequency GNSS interferometric signal modeling: According to the amplitude A extracted from (Formula 13) LSS , frequency f LSS and phase φ LSS , build the GNSS SNR interference signal model: SNR LSS (θ) = A LSS cos(2π·f LSS ·sinθ + φ LSS ) (Equation 13) For the interference signals of different frequency bands (such as L1 and L2, or B1 and B2) in the same satellite system at the same time, a multi-frequency fusion model is constructed using (Formula 14). Where H is the vertical height of the water surface relative to the GNSS antenna, λ L1 and λ L2 are the wavelengths of L1 and L2 frequency band signals, A L1 、A L2 and φ L1 、φ L2 are the amplitude and phase parameters corresponding to each frequency band; S2. Initial value estimation and search boundary construction: The amplitude, phase, and water level of (Formula 14) are considered as unknowns and optimized by VPPSO. The parameters to be estimated are the amplitude parameters A of the reflected signal in different frequency bands. L1 、A L2 , phase parameter φ L1 、φ L2 , and the final reflection height value H used for water level calculation; the initial particle position and search boundary of the VPPSO algorithm are determined by the values ​​obtained by (Formula 13); S3. Parameter optimization and fitness evaluation: A fitness evaluation mechanism based on the reconstruction accuracy of GNSS interferometric signals is constructed as the core indicator for VPPSO algorithm convergence. Specifically, a physical interpretability and mathematical operability objective function is defined to measure the fitting quality of the parameter combination represented by the current particle in the GNSS interferometric signal model, as shown in (Formula 15) The objective function is continuous and differentiable, and reflects the fitting error between the parameter model output and the actual observed data. The smaller the objective function value, the closer the estimated parameter value is to the true value. S4. Output optimal parameters and water level inversion After processing steps ①, ②, and ③, a set of optimal parameter values ​​can be obtained, and high-precision reconstruction of the GNSS reflection model can be achieved. Substituting the reflection height H in the optimal parameter value into (Formula 16) can obtain the water level height value h h=H0-H (Formula 16) Where H0 is the orthometric height of the GNSS antenna determined by leveling.

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