Water level measurement method based on multi-antenna reverse modeling

Abstract

The invention provides a water level measurement method based on multi-antenna reverse modeling. The water level measurement method comprises the following steps that a GNSS multi-antenna array observation system is established; constructing a mathematical model about the reflection height and determining an initial value of the reflection height; carrying out reverse modeling and fitting water level change by adopting a B-spline curve; and carrying out multi-antenna water level fusion and precision evaluation. Compared with the prior art, the multi-antenna array monitoring system has the remarkable advantages that by constructing the low-cost multi-antenna array monitoring system, the construction and operation cost of a monitoring station is remarkably reduced, the monitoring precision is remarkably improved, and the monitoring stability is ensured; an efficient and economical solution is provided for the fields of water resource management, environment monitoring, natural disaster early warning and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of global navigation satellite system reflectometry, and particularly to a water level measurement method based on satellites such as Beidou, specifically a water level measurement method based on multi-antenna inverse modeling. Background Art

[0002] GNSS-R (Global Navigation Satellite System Reflectometry) is an emerging remote sensing technology, whose core concept is based on the concept of bistatic radar. GNSS satellites continuously transmit L-band signals to the ground. After these signals are reflected by the ground, they are received by spaceborne, airborne or ground-based receivers. By extracting relevant parameters from the reflected signals, the characteristics of the reflector can be inverted. GNSS-R technology has significant advantages such as global coverage, good penetrability, all-weather, all-day, and high temporal resolution. Especially its high temporal resolution makes it show broad application prospects in fields such as water level dynamic monitoring and environmental change assessment.

[0003] However, due to the relatively high installation and maintenance costs of traditional geodetic receivers, their popularization and application in large-scale monitoring are limited. In contrast, the unit price of low-cost GNSS receiving devices (such as u-blox positioning modules) is only about 100 to 200 yuan, and the power consumption is only 1W. They have characteristics such as low production cost and low energy consumption, which can significantly reduce the construction and maintenance costs of monitoring stations, thereby improving the economy and feasibility of the system. In addition, existing research has shown that in order to obtain high-precision positioning results, the design of geodetic receivers will suppress the multipath effect, while low-cost receiving devices lack effective means to suppress the multipath effect and are more significantly affected by the multipath effect. Their water level inversion results may be better than those of geodetic receivers, further enhancing their applicability in GNSS-R water level monitoring. Nevertheless, due to their relatively simple design, low-cost devices are vulnerable to noise interference in complex environments such as cities, and there are performance limitations, and there are certain problems with the inversion accuracy and stability.

[0004] Moreover, in the common methods of GNSS-R water level inversion, Lomb-Scargle spectral analysis is a typical method. This method realizes inversion by analyzing the spectral characteristics of the SNR signal observed by the receiver, but its results largely depend on the selection of satellite arcs, resulting in uneven temporal distribution of the output results. In addition, Lomb-Scargle spectral analysis is vulnerable to random noise, and low-cost devices are more susceptible to noise interference. Therefore, the application of this method on low-cost devices will lead to a decrease in inversion accuracy. Summary of the Invention

[0005] To solve the above problems, the present technology proposes a water level measurement method based on multi-antenna inverse modeling, so as to achieve a low-cost water level monitoring means and improve the accuracy and stability of water level monitoring. The object of the present invention is achieved by the following technical solutions:

[0006] A water level measurement method based on multi-antenna inverse modeling includes the following steps:

[0007] Step 1: Establish a GNSS multi-antenna array observation system: Arrange more than 2 low-cost GNSS receiving antennas vertically at equal intervals to form an antenna array for receiving GNSS satellite signals; the low-cost GNSS receiving antenna is any one of ceramic antennas or smartphone GNSS positioning modules;

[0008] Step 2: Construct a mathematical model for the reflection height and determine the initial value of the reflection height: Receive GNSS satellite signal data, extract the signal-to-noise ratio data contained therein, remove the direct signal part in the signal-to-noise ratio data, and only retain the reflected signal part, and construct a mathematical model between the signal-to-noise ratio data after removing the direct signal and the reflection height, as shown in Equation (1):

[0009]

[0010] In the formula, δSNR is the signal-to-noise ratio data after removing the direct signal; λ is the satellite signal wavelength; h is the reflection height; θ is the satellite elevation angle; k is the wave number; s is the roughness parameter of the reflecting surface; C1 and C2 are in-phase and out-of-phase components, used to replace the amplitude A and phase

[0011] Use the LSP spectrum analysis method to preliminarily analyze the δSNR data to determine the initial values of the parameters C1, C2, h, and s in the mathematical model 2 ;

[0012] Step 3: Perform inverse modeling and use B-spline curve fitting to fit the water level change: Select n curve nodes at equal time intervals, and the nodes are represented as P i ; Use the observation data and the mathematical model established in Step 2 to fit a function y i (x) to estimate the undetermined parameters, where x is the undetermined parameter, and the undetermined parameters are: C1, C2, P i , s 2 , P i , and this function can be expressed as:

[0013]

[0014] In the formula: i represents any integer between 1 and n, representing the ordinal number of the node; δSNR i is the observation data, that is, the node P iThe SNR data after removing the direct signal at this point; Based on the initial parameter values determined in step two, use the non-linear least squares method to estimate the undetermined parameters. Through repeated iteration, when the sum of the squared residuals of y i (x) is minimized, the optimal parameter solution is obtained, that is:

[0015]

[0016] where n is the number of δSNR data. After the iteration is completed, using the estimated h at the nodes for B-spline interpolation can obtain a uniform water surface height change sequence;

[0017] Step four: Multi-antenna inversion result fusion: Select any one of the antennas as the reference antenna, eliminate the average interval caused by position deviation between different antennas, and fuse the inversion results of each antenna and output them as the final water level result.

[0018] For further optimization, in step one: The arrangement position of the antenna array is selected in the open area by the water area to ensure that the antenna can effectively receive signals from different satellites.

[0019] Furthermore, in step one: Vertically arrange 2 - 5 low-cost GNSS receiving antenna devices at equal intervals and combine them into an antenna array. Preferably 4.

[0020] In step two, the conversion relationship between C1 and C2 and the amplitude A and phase is:

[0021]

[0022] In step three: Use B-spline curve to fit the water level change. The function expression of the B-spline curve of the water level change is:

[0023]

[0024] where h(t) is the B-spline curve of the water surface changing with time t; is the B-spline basis function of order p.

[0025] The specific content of step four is:

[0026] The interval Δh between the average reflection height of the reference antenna and the other antennas i can be expressed as:

[0027]

[0028] where is the average reflection height of the reference antenna; is the average reflection height of the i-th antenna; Then eliminate the average interval between the antennas, that is:

[0029]

[0030] where h i (t) represents the water level change curve of the i-th antenna; represents the corrected water level change curve of the i-th antenna; after eliminating the offset caused by different vertical spacings, the reflection heights of all antennas can be unified to the same reference, and then the water levels at the same time are averaged as the final fused water level, improving the accuracy and consistency of the multi-antenna array observation data:

[0031]

[0032] where N is the number of antennas; is the fused water level curve. Finally, the obtained water level result is compared with the measured result of the water level gauge to evaluate the accuracy.

[0033] Applying the technical solution of the present invention has the following beneficial effects:

[0034] Compared with the traditional method, the multi-antenna inverse modeling method adopted by the present invention can more accurately fit the observation data, significantly reduce the influence of noise interference, and thus improve the accuracy and stability of the inversion result. Especially for low-cost devices, this method can still provide reliable water level monitoring results in complex environments, significantly enhancing its application potential. This technology not only effectively improves the application value of low-cost devices in GNSS-R water level monitoring, but also ensures the high precision and high stability of the monitoring system, providing a more economical and efficient solution for water level monitoring. The specific advantages can be summarized as follows:

[0035] (1) Cost reduction: The antennas and receivers adopted by the present invention are both low-cost devices, with a simple design structure, convenient production and maintenance. Its power consumption is only 1W, far lower than that of traditional geodetic receivers, so it shows significant cost advantages in equipment procurement and later operation and maintenance. Specifically, not only the initial equipment purchase cost is greatly reduced, but also the cost expenditure can be significantly reduced during operation and maintenance. In addition, the low-power design effectively reduces energy consumption, especially in the scenario of long-term continuous monitoring, and the advantage of operation cost is more obvious.

[0036] (2) Accuracy improvement: The present invention adopts a multi-antenna combination method for water level monitoring. Compared with the traditional single-antenna configuration, it significantly increases the amount of observation data and the density of inversion points, thus expanding the spatial coverage of water level monitoring. Low-cost antennas can also use a wider elevation angle range for water level inversion, further improving the accuracy and comprehensiveness of the data. Multi-antenna synchronous observation increases the diversity and reliability of the data, and in areas with complex terrain or drastic water level changes, it can more accurately capture the water level change trend, greatly improving the monitoring accuracy.

[0037] (3) Improvement in stability: Through the co-location design of multiple antennas, the present invention significantly improves the fault tolerance of the system, effectively avoiding data loss problems caused by single device failures or signal interference. The complementarity of multiple antennas can compensate for temporary interference or signal quality degradation that a single antenna may encounter during the data acquisition process. In addition, this technology uses an optimized algorithm to fit the water level changes into a smooth curve, significantly reducing the impact of noise interference, while clearly reflecting the changing trend of the water level over time, ensuring the stability of data in long-term monitoring, thereby enhancing the reliability of the system.

[0038] (4) Easy to promote and apply: With the characteristics of low cost, low energy consumption, and easy operation, the present invention reduces the application threshold of GNSS-R water level monitoring technology, and has high promotability and universality. The device design is simple, and the installation and maintenance processes are more efficient, suitable for deployment under various environmental conditions. Combined with a specially designed high-precision inversion algorithm, the present invention can meet the vast majority of water level monitoring requirements and is more suitable for applications in diverse monitoring scenarios. Therefore, this technology has broad application potential and is expected to promote the large-scale popularization and development of GNSS-R water level monitoring technology.

[0039] The present invention will be further described in detail below with reference to the drawings. Description of the Drawings

[0040] The drawings forming a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0041] Figure 1 is a schematic diagram of a multi-antenna array in Embodiment 1. Among them, h1 and h2 represent any two antennas;

[0042] Figure 2 is the SNR data sequence and the corresponding spectrum analysis results of a low-cost GNSS receiving antenna (a) and a geodetic receiver (b) in Embodiment 1;

[0043] Figure 3 is the water level inversion curve of a low-cost GNSS receiving antenna (a) and a geodetic receiver (b) in Embodiment 1;

[0044] Figure 4 is the water level measurement results output by 4 antennas respectively in Embodiment 1;

[0045] Figure 5 is the water level measurement results output after the fusion of 4 antennas in Embodiment 1. Detailed Description of the Preferred Embodiments

[0046] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered by the claims.

[0047] Embodiment 1:

[0048] See Figure 1 and Figure 1 , a water level inversion method using a multi - antenna inverse modeling method, comprising the following steps:

[0049] Step 1: Establish a GNSS multi - antenna array observation system: Combine multiple low - cost GNSS receiving antennas vertically at equal intervals to form a multi - antenna array. The layout position of the antenna array is selected in an open area by the water area to ensure that the antennas can effectively receive signals from different satellites. The low - cost GNSS receiving antenna in this embodiment is a ceramic antenna, mainly composed of an antenna module, a signal receiving module, and a data transmission module. The antenna model is ST - 35 - AGH1, the signal receiving module uses a Kaixinwei A8P board, and the signal transmission uses a YouRen 4G module. A smartphone GNSS positioning module can also be used. A smartphone GNSS positioning module is an integrated device, generally including: an antenna; a receiver; a processor; a memory, and a transmission system.

[0050] As Figure 1 shown, four receiving antennas are arranged vertically at equal intervals. There is an offset constant value Δh between the actual reflection heights of each receiving antenna from the water surface. To eliminate this offset and ensure the consistency of the observation data of different antennas, calibration can be performed by selecting a reference antenna. The reference antenna can be any one of the antennas, and its reflection height is specified as the reference value.

[0051] Step 2: Construct a mathematical model for the reflection height and determine the initial value of the reflection height: After receiving the GNSS satellite signal data, extract the signal - to - noise ratio data contained therein, use a low - order polynomial to remove the direct - signal part from the signal - to - noise ratio data, only retain the reflected - signal part, and establish a mathematical model between it and the reflection height. First, model the signal - to - noise ratio data after removing the trend term as:

[0052]

[0053] In the formula, δSNR is the signal - to - noise ratio data after removing the direct signal; λ is the satellite signal wavelength; h is the reflection height; θ is the satellite elevation angle; k is the wave number; s is the roughness parameter of the reflecting surface; in the formula, C1 and C2 are in - phase and out - of - phase components, used to replace the amplitude A and phase Its conversion relation formula is:

[0054]

[0055] Before calculating using the inverse modeling method, it is necessary to preliminarily analyze the δSNR data using the LSP spectral analysis method to determine the initial values of C1, C2, h, and s in the mathematical model. 2 Initial values of each parameter.

[0056] Step 3: Inverse modeling and using B-spline curve to fit water level changes: Before using the B-spline curve to fit the water level change curve, n curve nodes need to be selected at equal time intervals, and the nodes are represented as P i . Use the observation data and the δSNR mathematical model established in Step 2 to fit a function y i (x) to estimate the undetermined parameters, where x is the undetermined parameter, namely C1, C2, P i , the roughness parameter s 2 , the node P i , and this function can be expressed as:

[0057]

[0058] In the formula, i represents any integer between 1 and n, indicating the ordinal number of the node; δSNR i is the observation data, that is, the signal-to-noise ratio data after removing the direct signal. Use the LSP spectral analysis in Step 2 to calculate the initial reflection height, then determine the node spacing of the B-spline curve, initialize the parameters at the nodes according to the results of LSP, use the nonlinear least squares method to estimate the undetermined parameters, and through repeated iteration, make the sum of the squared residuals of y i (x) the smallest to obtain the optimal parameter solution, that is:

[0059]

[0060] In the formula, n is the number of δSNR data. After the iteration is completed, using the estimated value h at the node for B-spline interpolation can obtain a uniform water surface height change sequence. In the present invention, the function of the B-spline curve of the water level change can be expressed as:

[0061]

[0062] In the formula, h(t) is the B-spline curve of the water surface changing with time t; is the B-spline basis function of order p, and this basis function can be expressed as:

[0063]

[0064] In the formula, u is the parameter in the node space, that is, u ∈ [t0, t n ; t i represents the time window [t0, t nThe moment within; p represents the order of the spline curve. Since the water surface height changes continuously with time, the order of the B-spline basis function in the present invention is selected as the second order.

[0065] Step 4: Multi-antenna water level fusion and accuracy evaluation. By smoothing the inversion results, the accuracy and stability of the inversion results are improved, and noise interference is effectively avoided. Select one as the reference antenna to eliminate the average interval caused by position deviation between different antennas, and fuse the inversion results of each antenna to further optimize the data accuracy. The interval between the average reflection height of the reference antenna and the average reflection heights of the other antennas can be expressed as:

[0066]

[0067] In the formula, is the average reflection height of the reference antenna; is the average reflection height of the i-th antenna. Then eliminate the average interval between the antennas, that is:

[0068]

[0069] In the formula, h i (t) represents the water level change curve of the i-th antenna. After eliminating the offset caused by different vertical intervals, the reflection heights of all antennas can be unified to the same reference, and then the water levels at the same moment are averaged as the final fused water level to improve the accuracy and consistency of the multi-antenna array observation data:

[0070]

[0071] In the formula, N is the number of antennas. Finally, the obtained water level results are compared with the measured results of the water level gauge to evaluate the accuracy.

[0072] See Figure 2 、 Figure 3 and Table 1, which show the comparison of water level inversion cases of low-cost GNSS receiving antennas and geodetic receivers at the same site. Figure 2 is the SNR data sequence and the corresponding spectrum analysis results of the low-cost GNSS receiving antenna (a) and the geodetic receiver (b). Figure 3 is the water level inversion curve corresponding to the two receivers, and Table 1 is the accuracy statistical analysis of the two receivers. The results show that due to the stronger influence of the multipath effect, the periodic oscillation of the SNR data of the low-cost GNSS receiving antenna is more intense and the elevation angle range is larger. The peak amplitude of the corresponding LSP spectrogram is also higher than that of the geodetic receiver, and the corresponding GNSS-R water level inversion effect is also better, and the accuracy and correlation coefficient are both better than those of the geodetic receiver.

[0073] Table 1

[0074]

[0075] See Figure 4 and Figure 5 Table 2, which shows an example of a water level measurement method based on multiple antennas. The results show that a single low-cost device may have data loss due to insufficient hardware stability, thus unable to achieve continuous and reliable water level monitoring. By juxtaposing multiple devices, not only is the problem of data loss in a single device effectively solved, but also the inversion accuracy is significantly improved to a certain extent. The accuracy analysis results show that the juxtaposition scheme of four devices can provide higher inversion accuracy while ensuring the stable operation of the water level monitoring system. Considering the construction cost and device power consumption factors comprehensively, the present invention recommends adopting the juxtaposition scheme of four devices as the best configuration scheme to achieve a balance between performance and cost.

[0076] Table 2

[0077]

[0078] Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A water level measurement method based on multi-antenna inverse modeling, characterized in that: The following steps are involved: Step 1: Establish a GNSS multi-antenna array observation system: Arrange two or more low-cost GNSS receiving antennas at equal intervals vertically to form an antenna array for receiving GNSS satellite signals; The low-cost GNSS receiving antenna is any one of a ceramic antenna or a smartphone GNSS positioning module; Step 2: Construct a mathematical model for the reflection height and determine the initial value of the reflection height: Receive GNSS satellite signal data, extract the signal-to-noise ratio data contained therein, remove the direct signal part of the signal-to-noise ratio data, retain only the reflected signal part, and construct a mathematical model between the signal-to-noise ratio data after removing the direct signal and the reflection height, as shown in formula (1): In the formula, δSNR is the signal-to-noise ratio data after removing the direct signal; λ is the wavelength of the satellite signal; h is the reflection height; θ is the satellite altitude angle; k is the wave number; s is the roughness parameter of the reflecting surface; C1 and C2 are the in-phase and out-of-phase components, which are used to replace the amplitude A and phase The LSP spectrum analysis method is used to perform a preliminary analysis of the δSNR data and determine the parameters C1, C2, h, and s in the mathematical model. 2 The initial value of Step 3: Reverse modeling and use B-spline curve to fit water level changes: select n curve nodes at equal time intervals, and the nodes are represented by P i ; Use the observed data and the mathematical model established in step 2 to fit a function y i (x) Estimate the unknown parameters, where x is the unknown parameters, and the unknown parameters are: C1, C2, P i ,s 2 , P i , the function can be expressed as: Where: i represents any integer between 1 and n, indicating the ordinal number of the node; δSNR i is the observed data, that is, node P i The signal-to-noise ratio data after removing the direct signal; Based on the initial parameter values ​​determined in step 2, the nonlinear least squares method is used to estimate the unknown parameters. Through repeated iterations, y i The optimal parameter solution is obtained when the residual sum of squares of (x) is minimized, namely: After the iteration is completed, the uniform water surface height variation sequence can be obtained by using the estimated value h at the node for B-spline interpolation; Step 4: Fusion of multi-antenna inversion results: Select any one of the antennas as the reference antenna, eliminate the average interval between different antennas due to position deviation, and fuse the inversion results of each antenna as the final water level result output.

2. The water level measurement method based on multi-antenna inverse modeling according to claim 1 is characterized in that: In step 1: the antenna array is located in an open area near the water to ensure that the antenna can effectively receive signals from different satellites.

3. The water level measurement method based on multi-antenna inverse modeling according to claim 1 is characterized in that: In step 1: 2 to 5 low-cost GNSS receiving antenna devices are arranged vertically at equal intervals to form an antenna array.

4. The water level measurement method based on multi-antenna inverse modeling according to claim 3 is characterized in that: In step 1: four low-cost GNSS receiving antenna devices are arranged vertically at equal intervals to form an antenna array.

5. The water level measurement method based on multi-antenna inverse modeling according to claim 1 is characterized in that: In step 2, C1, C2, amplitude A and phase The conversion relationship is:

6. The water level measurement method based on multi-antenna inverse modeling according to claim 1 is characterized in that: In step 3: use the B-spline curve to fit the water level change. The function expression of the B-spline curve of the water level change is: Where h(t) is the B-spline curve of the water surface changing with time t; is the B-spline basis function of order p.

7. The water level measurement method based on multi-antenna inverse modeling according to claim 1 is characterized in that: In step 4, the specific operation of fusing the inversion results of each antenna is as follows: The distance Δh between the reference antenna and the average reflection height of the remaining antennas i It can be expressed as: In the formula, is the average reflection height of the reference antenna; is the average reflection height of the ith antenna; then the average interval between the antennas is eliminated, that is: In the formula, h i (t) represents the water level variation curve of the i-th antenna; represents the water level variation curve of the ith antenna after correction; Where N is the number of antennas; This is the water level curve after fusion.

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