A two-step method for precise correction of GNSS-IR anomalous phases

Abstract

The application discloses a two-step method for accurately correcting GNSS-IR abnormal phase, and belongs to the technical field of microwave remote sensing. The method is characterized in that: the GNSS observation data is preprocessed, and the modulation term in the signal-to-noise ratio is extracted; then, the nonlinear least square method is used to fit the modulation term, and the phase of each satellite is obtained; finally, the abnormal phase is accurately corrected through the two-step method: in the first step, a signal-to-noise ratio period method is constructed to correct the phase of the whole period and half period jump caused by the limitation of the nonlinear least square method itself; in the second step, the standard fraction method is combined with the Savitzky-Golay filter to accurately detect and repair the phase of less than half period jump caused by the multipath environmental factors. The method can effectively improve the phase quality of each satellite, improve the shortcomings of the traditional phase solving method, and solve the problems in the prior art.

Description

Technical Field

[0001] This invention belongs to the field of GNSS interferometric reflection remote sensing and soil moisture monitoring technology, and more specifically relates to a two-step method for accurately correcting GNSS-IR anomalous phase. Background Technology

[0002] Soil moisture is a crucial parameter in agricultural, meteorological, and hydrological research. Accurate soil moisture data is essential for agricultural irrigation, weather forecasting, and flood warning. Global navigation satellite system interferometric reflectometry (GNSS-IR) is a novel microwave remote sensing technology that utilizes the interference effect caused by the direct and reflected satellite signals at a receiver to acquire surface parameters. Currently, this technology has enabled effective monitoring of parameters such as vegetation cover, soil moisture, sea level, and snow depth.

[0003] Currently, existing research on soil moisture retrieval using GNSS-IR mainly employs the nonlinear least squares (NLS) method to fit the modulation term in the signal-to-noise ratio (SNR), solving for its characteristic parameters (phase and amplitude), and then establishing a mapping relationship between these characteristic parameters and soil moisture. The accuracy of these characteristic parameters directly affects the reliability of soil moisture retrieval. Existing methods primarily improve the quality of characteristic parameters by removing outlier data or satellite orbits with poor quality. However, this not only reduces the number of available satellite orbits but also disrupts the continuity of time-series characteristic parameters. Furthermore, the rationale for using NLS to solve for characteristic parameters lacks in-depth research. This invention aims to address the limitation imposed on current GNSS-IR soil moisture retrieval by poor phase quality. By analyzing the causes of anomalous phases, a data quality control method is proposed, which can accurately detect and correct various anomalous phases, increase the number of available satellite orbits, and improve the phase quality of each satellite orbit. This invention lays a data foundation for high-precision real-time soil moisture monitoring using multi-source GNSS, enabling it to better serve applications such as precision agriculture. Summary of the Invention

[0004] This invention proposes a two-step method for accurately correcting anomalous GNSS-IR phase. The proposed method mainly consists of two steps: First, based on the periodicity of the cosine function, the standard fitting formula for GNSS-IR is extended to construct a signal-to-noise ratio periodic method to correct phase jumps of both integer and half-cycle caused by the limitations of the nonlinear least squares method. Second, by combining the Z-score method with Savitzky-Golay filtering, phase jumps of less than half-cycle caused by multipath environmental factors are accurately detected and repaired. The combination of these two steps accurately corrects anomalous phase, thereby improving the correlation between phase and soil moisture.

[0005] The present invention achieves the above objectives through the following technical solution, specifically including the following steps:

[0006] Step 1: Satellite Phase Determination. The modulation term in the SNR is obtained by preprocessing the GNSS observation data. After resampling the satellite modulation term, NLS is used to fit the modulation term, and the characteristic parameters (phase, amplitude) corresponding to each satellite are solved. The fitting formula is as follows:

[0007]

[0008] Among them, SNR r This is the modulation term of the satellite, f is the frequency corresponding to the maximum power amplitude, and A r and These are the amplitude and phase of the modulation term, respectively.

[0009] Step Two: Exploring the Limitations of NLS. As a commonly used mathematical optimization technique, NLS finds the optimal solution by minimizing the sum of squares of the function residuals. However, due to limitations in the choice of search direction and step size, this method is susceptible to local information, easily getting trapped in local optima, resulting in parameter results that are local minima.

[0010] Step 3: Analysis of the Causes and Characteristics of Anomalous Phases: The SNR modulation term fitting formula for GNSS-IR is a periodic standard cosine function. Therefore, when using NLS fitting to solve for the phase, if the obtained phase is a local minimum of the cosine function, the phase will fall on the minimum or maximum point of the cosine function, resulting in an anomalous phase jump of the whole period or half period. Furthermore, multipath environmental factors can also directly affect the NLS fitting accuracy, leading to phase jumps smaller than half a period.

[0011] Step 4: Phase correction for full-cycle or half-cycle jumps. Based on the periodicity of the cosine function and the inherent limitations of NLS, this invention proposes an SNR periodic method to correct abnormal phase jumps of full-cycle and half-cycle caused by the inherent limitations of NLS fitting.

[0012] Step 5: Phase detection and repair for transitions smaller than half a cycle. Z-score and SGF are used to detect and repair phases with transitions smaller than half a cycle caused by multipath environmental factors, resulting in more accurate phases.

[0013] Step Six: Correlation Analysis. Based on the corrected, detected, and repaired satellite orbital phase, the correlation between it and soil moisture is analyzed.

[0014] Compared with existing technologies, this invention proposes a two-step method for accurately correcting GNSS-IR anomalous phase. This method addresses anomalous phases caused by the limitations of NLS itself and multipath environmental factors. The two-step approach corrects and repairs anomalous phases: First, a signal-to-noise ratio periodic method is constructed to correct phase jumps of both integer and half-cycle due to the limitations of the nonlinear least squares method. Second, by combining the Z-score method with Savitzky-Golay filtering, phase jumps of less than half-cycle caused by multipath environmental factors are accurately detected and repaired. This two-step method increases the number of available satellites, significantly improves phase quality, and ensures phase continuity over time. Furthermore, compared with the original phase, the correlation between the phase accurately corrected using this method and soil moisture is significantly improved, laying a data foundation for high-precision real-time soil moisture monitoring of GNSS-IR and better serving applications such as precision agriculture. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the process of the present invention.

[0016] Figure 2 This section presents the original phase fitting process and results for different years of satellite orbits.

[0017] Figure 3 Linear regression analysis of phase and soil moisture before and after SNR periodicity correction.

[0018] Figure 4 Correlation analysis was performed between the original phase, the phase corrected by the SNR periodic method, and the phase precisely corrected by the two-step method, and soil moisture. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0020] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0021] Figure 1 The diagram illustrates the implementation process of this invention, with the specific steps as follows:

[0022] Step 1: Satellite Phase Determination. The raw observation data acquired by the GNSS receiver is converted into observation files (O files) and hybrid navigation files (P files) using ToRinex4 format conversion software; the SNR, elevation angle, and azimuth angle of all satellites are extracted using TEQC software. Specifically, the multipath effect in SNR can be expressed as:

[0023]

[0024] Among them, A d and A r Here, ψ represents the amplitudes of the direct and reflected components, respectively, and ψ is the phase difference between the two components. This invention uses wavelet transform to decompose the SNR of each satellite into direct and reflected signals, and then removes the trend term to obtain the SNR modulation term. After resampling the satellite reflected signals, NLS is used to fit the reflected signals, and the characteristic parameters (phase, amplitude) corresponding to each satellite orbit are obtained. The fitting formula is as follows:

[0025]

[0026] Where SNRr is the reflected signal from the satellite, f is the frequency corresponding to the maximum power amplitude, and Ar and These are the amplitude and phase of the reflected component, respectively.

[0027] Step Two: Exploring the Limitations of NLS. NLS is a commonly used mathematical optimization technique that aims to minimize the sum of squared residuals of a function. The objective function is:

[0028]

[0029] During the optimization process, the choice of search direction and step size can easily lead to being limited by local information at the current point, thus getting trapped in a local optimum. That is, the desired parameter becomes a local minimum.

[0030] F′(t * )=0 (5)

[0031] Among them, t * Let t be the stationary point of the function F(t). * There are three possible scenarios: minimum point, maximum point, and saddle point.

[0032] Step 3: Analysis of the causes and characteristics of anomalous phase. The fitting formula for the SNR modulation term is a standard periodic cosine function, the periodicity of which is defined as:

[0033] cosα=cos(α+2lπ) ​​(6)

[0034] Where l∈Z and l≠0. This means that it completes a full cycle every 2π. When the cosine function has passed half a cycle π:

[0035] cosα=-cos(α+lπ) (7)

[0036] Therefore, the fitting formula can be transformed to obtain the following formula:

[0037]

[0038] When using NLS fitting to solve for the phase, if the obtained phase is a local minimum, then the value will fall on the minimum or maximum point of the cosine function, that is, a phase solution with a full-cycle (2π) or half-cycle (π) jump will appear. Figure 2 The original phase fitting process and results for some satellite orbits are shown. The modulation terms of PRN 02(S) show no significant change in DOY 110 and DOY 111, and their fitting lines are quite similar. However, the solved phase magnitudes differ by approximately 2π, indicating that PRN 02(S) experiences an anomalous phase jump of an integer period in DOY 111. For PRN 25(J), the solved amplitudes in DOY 124 and DOY 125 are opposite in sign, and their phase difference is approximately π, indicating that PRN 25(J) experiences an anomalous phase jump of half a period in DOY 125. Furthermore, multipath environmental factors can directly affect the NLS fitting accuracy, leading to phase jumps smaller than half a period.

[0039] Step 4: Phase Correction for Full-Period or Half-Period Jumps. Based on the limitations of NLS phase fitting and the periodicity of the cosine function, this invention proposes an SNR periodic method. In the process of solving the phase using NLS fitting, a threshold range of full periods is first set to determine whether the solved phase has a full-period (2π) jump. When the solved phase exceeds this threshold range, it can be determined that a full-period jump has occurred, and it needs to be corrected. The phase formula for correcting full-period jumps is:

[0040] phase1 = phase0 ± 2lπ (9)

[0041] Where phase1 is the phase after correcting for a full-cycle jump, and phase0 is the original phase, i.e., the local minimum. Repeat the above steps until phase1 falls within the range. Then, determine if a half-cycle (π) jump exists in the phase. When the calculated amplitude A... r When the value is less than 0, it can be determined that a half-cycle anomalous phase transition has occurred. Therefore, the formula for correcting this phase half-cycle anomalous transition is:

[0042] phase=phase1±lπ (10)

[0043] Where phase is the correct phase after correcting the half-cycle jump.

[0044] Step 5: Phase detection and repair for transitions less than half a cycle. Based on the linear regression analysis of the corrected phase from Step 1 and soil moisture parameters (…),… Figure 3 As can be seen, some corrected phases exhibit anomalous phase jumps, primarily due to multipath environmental factors. Therefore, Z-score is used to detect anomalous phases for each satellite. This method detects anomalous phases by calculating the standardized distance between sample values ​​and the overall mean. The calculation formula is as follows:

[0045]

[0046] Where x is the sample value, and μ and σ are the population mean and standard deviation, respectively. By pre-setting a threshold for Z, abnormal phases can be effectively detected. This invention uses 3.5 as the threshold for Z-score anomaly determination. That is, when the absolute value of Z in a sample is greater than 3.5, we determine it as an abnormal phase. Furthermore, SGF is used to fit and smooth the abnormal phases detected by Z-score, further improving phase quality. The calculation formula is:

[0047]

[0048] Where, p x Here, x is the output data, and a is the input data. m These are the fitting coefficients.

[0049] Step Six: Correlation Analysis. The correlation between the original phase, the phase corrected using the SNR periodic method, and the phase after two-step precise correction, and soil moisture is analyzed separately. Figure 4 As shown.

Claims

1. A two-step method for accurately correcting anomalous phases in GNSS-IR, characterized in that, Includes the following steps: Step 1: Preprocess the GNSS observation data to obtain the modulation term in the SNR; after resampling the modulation term of each satellite, use the non-linear least squares (NLS) method to fit it to obtain the characteristic parameters corresponding to each satellite, including phase and amplitude. Step 2: Explore the limitations of NLS; As a commonly used mathematical optimization technique, NLS finds the optimal solution by minimizing the sum of squares of the function residuals; however, due to the limitations in the choice of search direction and step size, this method is easily affected by local information and gets trapped in local optima, resulting in the parameter results being local minima. Step 3: Analysis of the Causes and Characteristics of Anomalous Phases: The SNR modulation term fitting formula for GNSS-IR is a standard cosine function with periodicity. Therefore, when using NLS fitting to solve for the phase, if the obtained phase is a local minimum of the cosine function, the phase will fall on the minimum or maximum point of the cosine function, resulting in a full-cycle or half-cycle phase jump. A full-cycle jump is a phase deviation of 2. A jump that is an integer multiple of a phase shift, a half-cycle jump is a phase deviation of 0. The jump is an odd multiple of the jump; in addition, multipath environmental factors can also directly affect the NLS fitting accuracy, resulting in a phase jump of less than half a cycle. Step 4: Phase correction of full-cycle or half-cycle jumps; Based on the periodicity of the cosine function and the limitations of NLS itself, an SNR periodic method is constructed to correct the phase jumps of full-cycle and half-cycles caused by NLS fitting. Step 5: Detection and repair of phase transitions smaller than half a cycle; Z-score and SGF are used to detect and repair phase transitions smaller than half a cycle caused by multipath environmental factors, so as to obtain more accurate phases for each satellite. Step Six: Correlation Analysis; Based on the corrected, detected and repaired satellite orbit phase, compare and analyze its correlation with soil moisture.

2. The two-step method for accurately correcting GNSS-IR anomalous phase according to claim 1, characterized in that... In step two, NLS is a commonly used mathematical optimization technique. This optimization method achieves its objective by minimizing the sum of squares of the function residuals; the objective function is: (2) in, For the first The residual sum of squares function of satellite signals, The time variable is used; during the optimization process, due to the choice of search direction and step size, it is easy to be limited by the local information of the current point, thus getting trapped in a local optimum; that is, the parameter to be found is a local minimum, i.e.: (3) for Stationary points of a function, stationary points There are three possible scenarios: minimum point, maximum point, and saddle point.

3. The two-step method for accurately correcting GNSS-IR anomalous phase according to claim 1, characterized in that... In step three, the fitting formula for the SNR modulation term is a periodic cosine function, defined as: (4) in For angle, It is an integer. ,and This means that it completes a full cycle of the cosine graph every 2 μ; when the cosine function has passed half a cycle μ: (5) Therefore, the fitting formula can be transformed to obtain the following formula: (6) in, The amplitude of the reflected signal. For phase, For frequency, The time variable is used. When NLS fitting is used to solve the phase, if the obtained phase is a local minimum, then the value will fall on the minimum or maximum point of the cosine function, resulting in an integer cycle jump or a half cycle jump. In addition, multipath environmental factors will also directly affect the NLS fitting accuracy, resulting in a phase jump of less than half a cycle.

4. The two-step method for accurately correcting GNSS-IR anomalous phase according to claim 1, characterized in that... In step four, based on the limitations of NLS fitting in solving the phase and the periodicity of the cosine function, an SNR periodic method is constructed; in the NLS phase solution process, a threshold range of an integer period [-2] is first set. ,2 This is used to determine whether the solved phase has an integer-cycle jump; when the solved phase exceeds this threshold range, it can be determined that an integer-cycle jump has occurred, and it needs to be corrected; the phase formula for correcting integer-cycle jumps is: (9) in, To correct the phase jump after the whole cycle, This is the original phase, i.e., the local minimum; repeat the above steps until... Falling in [-2 ,2 Within the range; then, begin to determine whether there is a half-cycle jump in the phase; when the amplitude is being solved When <0, it can be determined that a half-cycle phase transition has occurred; therefore, the formula for correcting the half-cycle phase is: (10) Where phase is the correct phase after correcting the half-cycle jump.

5. The two-step method for accurately correcting GNSS-IR anomalous phase according to claim 1, characterized in that... In step five, for phase jumps of less than half a period caused by multipath environmental factors, Z-score is used to detect phase jumps for each satellite. This method detects outliers by calculating the standardized distance between sample values ​​and the population mean. The calculation formula is as follows: (11) in, For sample values, and These represent the population mean and standard deviation, respectively. By pre-setting a threshold for Z-score, outliers can be effectively detected. This paper uses 3.5 as the threshold for Z-score anomaly detection; that is, when the absolute value of Z in a sample is greater than 3.5, the phase is judged to be abnormal. Furthermore, SGF is used to fit and smooth the phases detected by Z-score anomalies, further improving phase quality. The calculation formula is: (12) in, It is the output data. It is the input data. These are the fitting coefficients.

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