EMD-SSA combined filtering method for Beidou multipath error elimination

Abstract

The invention discloses an EMD-SSA combined filtering method for Beidou multipath error elimination, and the method combines an EMD method and an SSA method, extracts multipath errors in single-difference observation value residual errors, builds a single-difference hemisphere model according to the spatial repeatability of the multipath errors, an elevating angle and an azimuth angle, eliminates the multipath errors in deformation monitoring, and improves the precision of Beidou multipath error elimination. And the precision of deformation monitoring by using the BDS is improved.

Description

Technical Field

[0001] This invention relates to an EMD-SSA joint filtering method for BeiDou multipath error elimination. Background Technology

[0002] With the development of the BeiDou Navigation Satellite System (BDS), BDS has acquired high-precision positioning capabilities, and its application in deformation monitoring in engineering projects is gradually increasing. When using BDS for deformation monitoring, due to the close distance between the monitoring station and the reference station, the observation difference method can reduce most of the impact of errors such as tropospheric delay and ionospheric delay. However, multipath error, as an environment-related error source, still seriously affects positioning accuracy. In reservoir dam monitoring environments, the BDS signal received by the receiver is more easily blocked by surrounding trees, and the multipath effect caused by the water surface is also more pronounced. These factors all affect positioning accuracy. Therefore, in deformation monitoring, it is necessary to select appropriate multipath attenuation methods to improve the accuracy of BDS deformation monitoring.

[0003] Currently, many scholars have conducted in-depth research on multipath reduction, mainly reducing the impact of multipath errors from three aspects. First, selecting suitable monitoring stations, avoiding environmental obstructions, and choosing open environments for station placement; second, resisting multipath interference from the receiver hardware perspective, selecting receiver antennas with strong multipath resistance; and third, reducing the impact of multipath through data post-processing. For the application environment of deformation monitoring of reservoir dams using BDS, some degree of obstruction is unavoidable in station selection, and choosing better receiver hardware will increase the cost of deformation monitoring. Therefore, it is more appropriate to reduce the impact of multipath errors in deformation monitoring through data post-processing. The main method of reducing multipath errors in data post-processing is to establish corresponding correction models in the time and spatial domains based on the spatiotemporal repetition characteristics of multipath errors, and then subtract the corresponding multipath error value from the current observation value to obtain a more accurate positioning result. The sidereal filtering method was first proposed to suppress the impact of multipath errors. It primarily establishes a filtering model in the time domain based on the time repeatability of multipath errors, extracts the multipath error model of the previous period using an appropriate filtering method, and subtracts the time-aligned multipath error value during the current epoch calculation to correct the multipath error before baseline calculation. Many researchers have focused on improving the multipath error extraction process of the sidereal filtering method, studying suitable methods to separate noise and multipath error information, and improving the multipath error correction effect by obtaining high-precision multipath error values. These methods can weaken the impact of BDS multipath errors and have been applied in many engineering projects, improving positioning accuracy and BDS deformation monitoring capabilities to some extent. However, in long-term deformation monitoring, the matching results of time-related multipath errors become inaccurate as the observation time increases, thus affecting the multipath error mitigation effect. To address this, some scholars have developed a multipath hemispherical model based on the spatial repeatability of multipath errors, using the elevation and azimuth angles of the observed satellites from the previous period. This method avoids errors in time matching and corrects multipath errors, improving the accuracy of BDS positioning. This method has been further optimized to obtain the optimal multipath matching value through trend surface fitting, thus improving the matching fit. Other scholars have combined the EMD method with the hemispherical method to refine the multipath error purification process in hemispherical modeling, achieving a more effective multipath error reduction.

[0004] Current research on multipath reduction methods mainly involves artificially adding strong reflective surfaces to construct multipath environments or conducting simulation experiments. While the single-difference hemispherical modeling method is an effective approach, there is limited verification of its application in engineering. Furthermore, before implementing single-difference hemispherical modeling, it is necessary to refine the extraction method of multipath error values ​​to obtain better multipath modeling results. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes an EMD-SSA joint filtering method for BeiDou multipath error elimination.

[0006] To achieve the above objectives, the solution of the present invention is:

[0007] An EMD-SSA joint filtering method for BeiDou multipath error elimination, the specific steps of which are as follows:

[0008] Step 1: Process the obtained raw observation data using the EMD method to obtain each IMF and residual component;

[0009] Step 2: Use the maximum inter-class variance method to determine the boundary IMF between the IMF information components and the mixed components;

[0010] Step 3: Extract the signal component from the mixed components;

[0011] Step 4: Accumulate the signal component and the IMF information component in the mixed components to obtain the final signal, which is the multipath error.

[0012] Furthermore, step 2 specifically includes:

[0013] The first IMF component obtained by the EMD method is regarded as the noise IMF component.

[0014] Iterate through the inter-class variances of high-frequency and low-frequency information for all potential thresholds except the first IMF component, select the maximum value of the inter-class variance as the threshold, and determine the IMF component corresponding to the threshold as the boundary IMF between the IMF information component and the mixed component.

[0015] Furthermore, the calculation method for the inter-class variance v is as follows:

[0016] v=ω lf ω hf (h lf -h hf ) 2

[0017] In the formula, ω lf ω hf This indicates the proportion of low-frequency and high-frequency information in all IMF data; h lf h hf These are the average values ​​of low-frequency and high-frequency information, respectively.

[0018] Furthermore, step 3 specifically includes:

[0019] All IMFs from the second IMF component to the boundary IMF are the mixed components;

[0020] The singular spectrum of the mixed components is performed to extract the signal portion.

[0021] This invention also proposes a method for eliminating BeiDou multipath errors, the specific steps of which are as follows:

[0022] Step 1: Use the EMD-SSA joint filtering method described above to obtain the multipath error;

[0023] Step 2: Establish a single-difference hemispherical model;

[0024] Step 3: Use the average value of the multipath error in each grid point as the multipath error correction value in the grid corresponding to the elevation angle and azimuth angle to construct the ES-MHM model;

[0025] Step 4: Obtain the elevation angle and azimuth angle information of the observed satellite at the current epoch, query the corresponding half-sky grid in the ES-MHM model, and obtain the multipath error correction value within the corresponding grid.

[0026] Step 5: Based on the multipath error correction value obtained from the query, perform epoch-by-epoch correction on the current observation data to complete the elimination of BeiDou multipath error.

[0027] This invention also proposes a method for monitoring dam deformation based on BeiDou positioning. The specific steps of this method are as follows:

[0028] Step 1: Receive real-time observation data from BeiDou satellites;

[0029] Step 2: Use the BeiDou multipath error elimination method described above to eliminate multipath errors in the observation data;

[0030] Step 3: Perform location calculations on the observation data after eliminating multipath errors to obtain deformation monitoring results.

[0031] This invention also proposes a dam deformation monitoring system based on BeiDou positioning, the system comprising:

[0032] The receiver is used to receive real-time observation data from BeiDou satellites.

[0033] The error elimination unit is used to perform multipath error elimination on the observation data using the BeiDou multipath error elimination method described above.

[0034] The positioning and calculation unit is used to perform positioning and calculation on the observation data after eliminating multipath errors, and obtain deformation monitoring results.

[0035] The significant advantages of this invention compared to existing technologies are:

[0036] The method of this invention uses the EMD-SSA joint filtering method to extract multipath error values. Based on the spatial repeatability of multipath errors, a single-difference hemispherical model is established according to the elevation angle and azimuth angle. This method can effectively reduce the influence of multipath errors in BeiDou deformation monitoring, improve the accuracy of deformation monitoring using BDS, and obtain highly reliable and accurate deformation monitoring results, which has broad application prospects. Attached Figure Description

[0037] Figure 1 The flowchart of the EMD-SSA joint filtering algorithm.

[0038] Figure 2 This is a time series of the original signal and the mixed signal after adding noise.

[0039] Figure 3 This is the EMD decomposition result of the mixed signal.

[0040] Figure 4 The results are obtained by filtering the mixed signal using three different methods.

[0041] Figure 5 The results are the residuals between the filtered results and the original signal under different filtering schemes.

[0042] Figure 6 This is a flowchart for correcting multipath errors based on the ES-MHM model.

[0043] Figure 7 The images show the installation distribution and environmental conditions of the base station and monitoring stations, where (a) is the left base station, (b) is the right base station, (c) shows the relative positions of the stations, and (d) shows the reservoir area environment.

[0044] Figure 8 The images show the satellite multipath error sky maps for different dates during reservoir dam deformation monitoring, where (a) is DOY103, (b) is DOY109, and (c) is DOY110.

[0045] Figure 9 The residual sequences of observations before and after ES-MHM correction for satellites C11 and C13 are shown, where (a) is for C11 and (b) is for C13.

[0046] Figure 10 The frequency domain results of C11 and C13 satellites before and after ES-MHM correction are compared. (a) is C11 and (b) is C13.

[0047] Figure 11 The RMS residuals and improvement rates of observations before and after applying ES-MHM correction to all observation satellites are given, where (a) is the RMS residual and (b) is the improvement rate.

[0048] Figure 12For all satellites, residual sky maps of observations before and after ES-MH correction are provided. Among them, (a) is the residual sky map of observations before DOY110 correction, and (b) is the residual sky map of observations after DOY110 correction.

[0049] Figure 13 The coordinate deviation sequence and frequency domain result of the positioning results in the E direction are compared, where (a) is the coordinate deviation sequence and (b) is the frequency domain result.

[0050] Figure 14 The coordinate deviation sequence and frequency domain result of the N-direction positioning are compared, where (a) is the coordinate deviation sequence and (b) is the frequency domain result.

[0051] Figure 15 The coordinate deviation sequence and frequency domain result of the positioning results in the U direction are compared, where (a) is the coordinate deviation sequence and (b) is the frequency domain result. Detailed Implementation

[0052] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0053] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0054] Multipath error is a significant and unavoidable error in dam deformation monitoring using the BeiDou Navigation Satellite System (BDS), severely impacting BDS monitoring accuracy. The single-difference hemispherical model is an effective way to mitigate the multipath effect; however, its effectiveness is currently mostly verified through simulated obstruction environments, lacking experimental validation in practical engineering applications. Furthermore, refining multipath error extraction before single-difference hemispherical modeling can also enhance the multipath error mitigation effect. Therefore, this paper utilizes BDS observation data of a reservoir dam, employs the EMD-SSA joint filtering method to extract multipath error values, and then establishes a single-difference hemispherical model based on elevation and azimuth angles according to the spatial repeatability of multipath errors. This eliminates multipath errors in deformation monitoring, improving the accuracy of deformation monitoring using BDS. Experimental results show that after correcting multipath errors using the EMD-SSA-based single-difference hemispherical modeling method, the positioning accuracy in the east, north, and elevation directions is improved by 16.72%, 17.70%, and 19.29%, respectively.

[0055] This paper proposes an EMD-SSA joint filtering method for BeiDou multipath error elimination. Combining EMD and SSA methods, the multipath error is first extracted from the residual of single-difference observations. Then, an ES-MHM model is established based on elevation and azimuth information. Finally, the positioning accuracy of the method is evaluated using measured BDS deformation monitoring data from a reservoir dam.

[0056] 1.1 EMD-SSA Joint Filtering Method

[0057] The residual sequences of BDS double-difference and single-difference observations exhibit highly nonlinear characteristics, exhibiting the properties of non-stationary time series. If EMD decomposition is used alone to extract multipath error information from observations, some information components will be discarded due to the lack of a unified standard for high-frequency component partitioning. Therefore, the maximum inter-class variance method is used to reasonably partition the information components, noise components, and mixed components obtained from EMD decomposition. Then, combining the data analysis capabilities of SSA decomposition for nonlinear time series, SSA is applied to the mixed information IMFs to obtain the denoised information IMF components. Finally, all information components are reconstructed. Based on the above analysis, a joint EMD-SSA filtering algorithm is used for multipath error extraction, with the specific steps as follows:

[0058] (1) The original observation data were processed using the EMD method to obtain each IMF and residual component.

[0059] (2) The maximum inter-class variance (MOL) method is used as the criterion for dividing the information component and the mixed component of the IMF. This method treats the first IMF component obtained after EMD processing as a noisy IMF component. After eliminating noise, it iterates through the inter-class variances of high-frequency and low-frequency information for all potential thresholds, selects the maximum inter-class variance as the final threshold, and determines the IMF component corresponding to the maximum inter-class variance value as the boundary IMF between the mixed IMF and the information IMF. The calculation method for the inter-class variance v is as follows:

[0060] v=ω lf ω hf (h lf -h hf ) 2

[0061] In the formula, ω lf ω hf This indicates the proportion of low-frequency and high-frequency IMFs among all IMFs; h lf h hf These are the average values ​​of the low-frequency and high-frequency IMFs, respectively.

[0062] (3) All IMFs from the second IMF component to the boundary IMF component are considered mixed components, requiring singular spectrum analysis to further extract their information IMFs. First, a suitable window length is selected based on the length of the observation sequence; in this paper, 1 / 4 of the data length is chosen for the IMFs. k Perform singular value decomposition (SVD) to calculate the singular values ​​of the autocovariance matrix (ACM), arrange them in ascending order, determine the subset X consisting of the SVD components of the signal, and transform it into a time series g. n The mixed information component IMF is obtained. k Signal section G k .

[0063] (4) Accumulate all G values. k The final signal is obtained from the information IMFs obtained by EMD decomposition. The process is as follows Figure 1 As shown.

[0064] 1.2 Simulation Experiment

[0065] Using Matlab for simulation to obtain the original signal and noise signal can effectively verify the effectiveness of the filtering method. The data type of the noisy simulation is as follows:

[0066] s t =y t +u t

[0067] In the formula, s t For a mixed signal containing noise, y t The original signal without noise, ut This represents a noise signal. A simulation experiment was conducted using Matlab, where the original signal without noise was set to the following form:

[0068]

[0069] The total epoch length of the generated simulation data was set to 8000, and noise signals following the patterns N(0,0.52), B(0,1.02), B(0,1.52), and N(0,2.02) were added, with standard deviations in cm. Four schemes were designed to compare the denoising effects of the EMD-SSA joint filtering algorithm. Scheme 1 did not perform any noise processing, representing the mixed signal itself; Scheme 2 used wavelet denoising with the wavelet basis function db5 and a decomposition level of 3; Scheme 3 used EMD decomposition and reconstruction; and Scheme 4 used the EMD-SSA joint filtering method.

[0070] The experiment uses the root mean square (RMS) value S of the filtered signal. RMS The RMS value N of the filtered noise component RMS The three metrics used to evaluate the filtering effect are: the correlation coefficient R between the filtered signal and the original signal.

[0071]

[0072] In the formula: N is the total length of the signal. For the filtered signal, Let be the covariance between the filtered signal and the original signal. σ y These are the standard deviations of the filtered signal and the original signal, respectively. The R-value measures the similarity between the filtered signal and the original signal; a higher R-value indicates that the signal is closest to the true signal.

[0073] To clearly demonstrate the composition of the analog signal sequence, Figure 2 Taking the addition of a noise signal conforming to N(0, 0.52) as an example, the results of the original signal and the mixed signal after adding noise are given. Figure 3 The results of EMD decomposition of mixed signals are presented.

[0074] Depend on Figure 3It can be seen that the EMD decomposition scale is 5, and the signal trend is more obvious in the low-frequency IMFs. The noise in the original data is concentrated in the high-frequency components. The inter-class variances between each IMF were calculated using the maximum inter-class variance method, and they are 0.0153, 0.0049, 0.1452, 0.0185, and 0.0023, respectively. Therefore, IMF3 is the boundary component of the IMFs. Thus, IMF1 and IMF2 are considered as high-frequency noise, and IMF3, 4, and 5 are considered as mixed information components. Singular spectrum analysis is used to further denoise these components, and the results are reconstructed from the residual signal to obtain the EMD-SSA joint filtering result. Figure 4 The signals obtained after processing using three methods are presented. Figure 5 The residual results between four schemes and the original signal are presented.

[0075] Depend on Figure 4 It can be seen that the EMD-SSA joint filtering method has the best extraction effect on information components. Figure 5 The residual results show that all three methods can filter out some noise signals and effectively filter noisy sequences. The signal sequence processed by the EMD-SSA joint filtering method is the smoothest and has the highest similarity to the original signal without noise. The closer the residual value is to zero, the closer the filtered result is to the real signal. The residual value of the EMD-SSA joint filtering method is significantly smaller than that of the other two methods and fluctuates within a certain range. Table 1 further statistically analyzes the S values ​​calculated by wavelet transform, EMD decomposition, and EMD-SSA joint filtering algorithms for noise levels of N(0,0.52), N(0,1.02), N(0,1.52), and N(0,2.02). RMs N RMs R value.

[0076] Table 1 shows the statistical results of filtering using different methods.

[0077]

[0078]

[0079] Table 1 shows that regardless of the noise level, the EMD-SSA joint filtering algorithm consistently exhibits the lowest SRMS and the highest NRMS at the same noise level. This indicates that the EMD-SSA joint filtering method produces the closest result to the real signal, demonstrating its superior performance. The R-value of the EMD-SSA algorithm is significantly higher than the other two methods. While the R-values ​​of the other two methods decrease significantly with increasing noise levels, reducing the similarity between the filtered signal and the real signal, the EMD-SSA joint filtering method exhibits the smallest variation in R-value, consistently maintaining a level greater than 0.94 and retaining excellent similarity to the noise-free original signal. Therefore, the SRMS, NRMS, and R-values ​​all indicate that the EMD-SSA joint filtering method offers the best noise reduction performance, making it suitable for purifying multipath errors.

[0080] 1.3 Construction of a Single-Difference Hemispherical Model Based on EMD-SSA

[0081] Based on the spatial repeatability of multipath errors, a single-difference hemispherical model grid can be established according to elevation and azimuth angles. The grid range is typically set to 1°×1°. The hemispherical model, centered on the station, divides the spatial multipath effect of the station into grids according to elevation and azimuth angles. The average value of all multipath errors within the same grid is used as the grid model value for subsequent multipath correction. By calculating the average value within each grid point as the correction value for multipath errors, the influence of noise can be further reduced, improving the modeling accuracy. Based on this, this section introduces the EMD-SSA method to first obtain accurate multipath error values. Then, a single-difference hemispherical model is established. Finally, the average value of the multipath error within each grid point is used as the multipath error correction value within the corresponding grid for that elevation and azimuth angle. During matching, this value is used to perform multipath correction on the carrier observations of the current epoch, achieving the purpose of eliminating multipath errors.

[0082] The single-difference hemispherical algorithm based on EMD-SSA described above is defined as the ES-MHM method. This method does not require calculating the time lead; it only needs to match the elevation and azimuth angles, making it more suitable for situations with long sampling intervals, discontinuous observation data, and poor time-domain matching. First, the elevation and azimuth angles of the observed satellite at the current epoch are obtained. Then, the hemispherical grid corresponding to that location is queried in the ES-MHM model, and the average value of all multipath error model values ​​within the corresponding grid is calculated as the final multipath correction value. Finally, the positioning solution is performed to obtain the deformation monitoring results after multipath correction. The specific process is as follows: Figure 6 Show.

[0083] This embodiment uses deformation monitoring data from the Xin'anjiang Reservoir project for experimental verification. The BDS deformation monitoring system used in the project was installed to monitor the deformation of the Xin'anjiang Reservoir dam.

[0084] 2.1 Experimental Data and Solution Strategies

[0085] The Xin'anjiang Reservoir is located in Chun'an County, Hangzhou City, Zhejiang Province. The dam is built on the upper reaches of the Qiantang River and the main stream of the Xin'anjiang River in Linghou, Jiande City. It is the largest water body in Hangzhou City, Zhejiang Province, and carrying out deformation monitoring of the Xin'anjiang Reservoir dam is of great significance.

[0086] Two monitoring stations from the BDS dam monitoring system in the Xin'anjiang Reservoir project were selected to form a short baseline of approximately 18m for the experiment. The distribution of the two selected monitoring stations, their relative positions, and the surrounding environment are as follows: Figure 7 As shown.

[0087] from Figure 7 It can be seen that the overall environment of the station receivers is relatively open, but there is some obstruction from the mountains and trees to the west of both stations. At the same time, the multipath effect from the water surface will be quite obvious during deformation monitoring. Among them, B1 is the base station, installed on a stable mountain platform, and R1 is the monitoring station, installed in the dam deformation zone.

[0088] This experiment selected 8 days of data from the BDS reservoir dam deformation monitoring (covering the shortest MEO satellite orbital period), collected from April 12th to April 19th, 2020 (DOY103 to DOY110). To ensure the validity of the experimental results, the period of reservoir flood discharge was avoided. Research showed that no flood storage or drainage occurred during the selected period, resulting in relatively stable water levels and meeting the basic conditions for modeling based on multipath spatial repeatability. The satellite cutoff elevation angle was set to 10° during the calculation.

[0089] The experiment used a Trimble receiver to receive the B1 single-frequency satellite signal from BDS, and selected observation data from days 103-110 of the 2020 Doyota Observatory (DOY) for multipath correction experiments. To enable real-time and rapid deformation detection and enhance the ability to detect sudden deformations, the solution mode was set to dynamic relative positioning, weakening the relationship between preceding and following positions. The data sampling interval was 30 seconds, the cutoff elevation angle was set to 10°, the ionospheric delay was corrected using the broadcast ionospheric model, and the tropospheric delay was corrected using the Saastamonin model.

[0090] 2.2 Multipath Error Extraction and Spatial Correlation Analysis

[0091] The double-difference residuals are converted to single-difference residuals using a transformation matrix. The EMD-SSA joint filtering method is then used to decompose and reconstruct the multipath error values ​​from the residual sequence. Finally, an ES-MHM model is established based on the observed satellite elevation and azimuth angles. To visually demonstrate the spatial distribution of the multipath error, Figure 8The spatial distribution of multipath errors for all satellites obtained using the ES-MHM method on different dates is presented.

[0092] Depend on Figure 8 It can be seen that multipath errors are mainly concentrated in the elevation angle range of 10° to 30°. The spatial distribution of multipath errors in DOY103 and DOY110 is basically consistent, indicating that the spatial correlation of multipath errors is relatively obvious in the environment of reservoir dam deformation monitoring. ES-MHM modeling can be used to reduce the influence of multipath effects in deformation monitoring. However, the spatial distribution of DOY109 and DOY110 is different, mainly because for MEO satellites, multipath errors spaced seven days apart have spatial repeatability.

[0093] As can be seen from the above analysis, in order to obtain the best ES-MHM modeling effect, minimize the impact of observation noise, and better correct the multipath effect of MEO satellites, the ES-MHM model should be established using the observation data of DOY103 for MEO satellites, and the ES-MHM multipath error model should be established using all the observation data of the first 7 days for IGSO satellites. After the modeling is completed, the multipath error correction experiment analysis is carried out on the original observation data of DOY110.

[0094] 2.3 Analysis of Observation Filtering Results

[0095] To clearly demonstrate the effect of ES-MHM multipath error modeling on the residuals of observations from each satellite, we will take satellites C11 and C13 as examples. Figure 9 The residual sequences of the original observations from the two satellites are presented, as well as the residual results after correcting for multipath errors using ES-MHM modeling. Figure 9 The solid blue line represents the residuals without multipath correction, while the solid red line represents the residuals after multipath correction using the ES-MHM model. It can be seen that the residual sequence without multipath correction exhibits non-stationary behavior, frequent low-frequency fluctuations, and high-frequency noise. After ES-MHM correction, most of the low-frequency fluctuations are removed, and the remaining residual sequence is more concentrated near 0, with almost all residuals within the 1cm range, tending towards Gaussian-distributed white noise. For the C11 satellite, the proportion of residuals smaller than 8mm before multipath correction was 92.2%, which increased to 97.4% after ES-MHM correction. The calculated RMS value of the C11 satellite residuals before correction was 8.13mm, and after correction, it was 4.75mm, achieving an improvement rate of 41.57%. For the C13 satellite, the proportion of residuals smaller than 8mm before multipath correction was 92.5%, which increased to 98.5% after ES-MHM correction. The RMS of the C13 satellite before correction was 5.56 mm, and the RMS after correction was 3.97 mm, representing an improvement rate of 28.6%.

[0096] The residuals of the two satellites before and after correction were further transformed to the frequency domain using Fourier transform, such as... Figure 10 As shown. Figure 10 The frequency domain results show that the low-frequency multipath of the residual sequences of the two satellites after multipath correction is effectively suppressed, which is consistent with the results of the coordinate domain analysis.

[0097] Figure 11 The changes in the RMS values ​​of the observation residual sequences before and after multipath correction for all satellites are further shown, as well as the change curves of the improvement rate before and after multipath correction for each satellite. Figure 11 The results show that the RMS of the single-difference residuals of all satellites was significantly reduced after multipath correction using the ES-MHM model, with the overall improvement rate remaining within the range of 20% to 50%. Calculations show that the average RMS value of the observation residuals of all BDS observation satellites before correction was 6.32 mm, which decreased to 4.31 mm after correction, resulting in an average improvement rate of 31.80%.

[0098] Figure 12 A sky map plotted in elevation and azimuth angles is provided, showing the residual values ​​of all satellite observations before and after multipath error correction. Figure 12 It is evident that the residuals of the observed values ​​are significantly reduced within the low elevation angle range, indicating that the ES-MHM model has a significant effect on suppressing multipath effects.

[0099] 2.4 Analysis of Positioning Results

[0100] The ultimate goal of correcting multipath errors is to improve the accuracy of deformation monitoring results. Therefore, we will discuss the deformation monitoring results of the selected baselines before and after the correction of the ES-MHM model, namely the positioning results in the east, north, and sky directions. In the experiment, the average value of the fixed solution calculated by BDS for all epochs is used as the true value. Figure 13 , 14 Figures 1 and 15 provide the positioning results for the east, north, and sky directions, as well as the corresponding spectrum analysis results.

[0101] Figure 13 , 14 The results in Table 15 show that after ES-MHM correction of multipath errors, the coordinate sequences in the three directions are closer to zero overall compared to the results before correction, and the fluctuation amplitude is significantly reduced. The deviation sequences in the three directions are stabilized within the range of 5mm, 5mm, and 10mm, respectively, and the deviation range is also significantly reduced. From the frequency domain results, the low-frequency multipath components in the three directions are also effectively suppressed. Table 2 further calculates the RMS and corresponding improvement percentage of the results in the E, N, and U directions of DOY110 before and after multipath error correction using the ES-MHM model.

[0102] Table 2. RMS values ​​and corresponding improvement rates of E, N, and U direction localization results before and after multipath correction in the ES-MHM model.

[0103]

[0104] The results in Table 2 show that the ES-MHM modeling method can improve the accuracy of BDS reservoir dam deformation monitoring results to a certain extent, with the accuracy of positioning in the three directions improving by 16.72%, 17.70%, and 19.29%, respectively.

[0105] This paper conducts an experimental study on multipath error correction for a reservoir dam BDS monitoring project in a practical engineering project. Before single-difference hemispherical modeling, simulation experiments were first conducted to compare and analyze the results with traditional wavelet and EMD methods, demonstrating the effectiveness of the EMD-SSA joint filtering method for multipath error extraction and its advantages in refining multipath error extraction. Compared with traditional wavelet transform and EMD decomposition methods, it has the highest NRMS and R values ​​and the lowest SRMS. Subsequently, since most current multipath method verifications are based on simulated occlusion environment experiments, we used general monitoring data collected from actual engineering projects to establish an ES-MHM multipath correction model based on the multipath error values ​​extracted by the EMD-SSA joint filtering method. Experimental results show that this method has a certain suppression effect on the multipath effect in the BDS reservoir dam deformation monitoring environment, improving the positioning accuracy in the E, N, and U directions by 16.72%, 17.70%, and 19.29%, respectively.

[0106] This invention conducts an experimental study on multipath error correction for BDS monitoring projects of reservoir dams in practical engineering. Before single-difference hemispherical modeling, simulation experiments were first conducted to compare and analyze the results with traditional wavelet and EMD methods, demonstrating the effectiveness of the EMD-SSA joint filtering method for multipath error extraction and its advantages in refining multipath error extraction. Compared with traditional wavelet transform and EMD decomposition methods, it has the highest NRMS and R values ​​and the lowest SRMS. Subsequently, since most current verification of multipath methods is based on simulated occlusion environment experiments, we used general monitoring data collected from actual engineering projects to establish an ES-MHM multipath correction model based on the multipath error values ​​extracted by the EMD-SSA joint filtering method. Experimental results show that this method has a certain suppression effect on the multipath effect in the BDS reservoir dam deformation monitoring environment, and the positioning accuracy in the E, N, and U directions can be improved by 16.72%, 17.70%, and 19.29%, respectively.

[0107] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any transformations or substitutions that can be conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An EMD-SSA combined filtering method for Beidou multipath error elimination, characterized in that, The method comprises the following steps: Step 1, the obtained original observation data is processed by using the EMD method to obtain each IMF and a residual component; Step 2, the maximum inter-class variance method is used to determine the boundary IMF of the IMF information component and the mixed component; Step 3, the signal part in the mixed component is extracted; Step 4, the signal part in the mixed component and the IMF information component are accumulated to obtain a final signal, that is, the multipath error.

2. The EMD-SSA combined filtering method for Beidou multipath error elimination according to claim 1, characterized in that, The step 2 specifically comprises: The first IMF component obtained by the EMD method is regarded as a noise IMF component; The inter-class variance of the high-frequency and low-frequency information of all potential thresholds except the first IMF component is traversed, the maximum value of the inter-class variance is selected as the threshold, and the IMF component corresponding to the threshold is determined as the boundary IMF of the IMF information component and the mixed component. 3.The EMD-SSA joint filtering method for Beidou multipath error elimination according to claim 2, characterized in that, The calculation method of the inter-class variance v is as follows: v = ω 1f ω hf (h 1f -h hf ) 2 In the formula, ω lf , ω hf represent the proportion of low frequency and high frequency information in all IMFs; h lf , h hf are the average values of low frequency and high frequency information, respectively.

4. The EMD-SSA combined filtering method for Beidou multipath error elimination according to claim 1, characterized in that, The step 3 specifically comprises: All IMFs from the second IMF component to the boundary IMF are the mixed component; The singular spectrum of the mixed component is obtained, and the signal part is extracted.

5. A method for removing multi-path errors of Beidou, characterized in that, The method comprises the following steps: Step1, the EMD-SSA joint filtering method is used to obtain the multipath error according to claim 1; Step2, a single difference half-sphere model is established; Step3, the average value of the multipath error values in each grid point is taken as the multipath error correction value in the grid corresponding to the elevation angle and the azimuth angle, and an ES-MHM model is constructed; Step4, the elevation angle and the azimuth angle information of the observed satellite at the current epoch are obtained, the corresponding half-sphere grid in the ES-MHM model is queried, and the multipath error correction value in the corresponding grid is obtained; Step5, based on the queried multipath error correction value, the current observation data is corrected in each epoch, and the Beidou multipath error is eliminated.

6. A dam deformation monitoring method based on Beidou positioning, characterized in that, The method comprises the following steps: Step 1, real-time receiving of the observation data of the Beidou satellite; Step 2, the Beidou multipath error elimination method is used to eliminate the multipath error of the observation data according to claim 5; Step 3, the observation data after the multipath error is eliminated is positioned and solved to obtain a deformation monitoring result.

7. A dam deformation monitoring system based on Beidou positioning, characterized in that, The system comprises: A receiver is configured to receive the observation data of the Beidou satellite in real time; An error elimination unit is configured to eliminate the multipath error of the observation data by using the Beidou multipath error elimination method according to claim 5; A positioning and solving unit is configured to position and solve the observation data after the multipath error is eliminated to obtain a deformation monitoring result.

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