Positioning measurement data gross error elimination system and method based on wavelet analysis

Abstract

The application discloses a wavelet analysis-based positioning measurement data gross error elimination system and method in the technical field of GNSS RTK measurement data processing, and comprises the following steps: acquiring GNSS RTK measurement data; performing wavelet transformation on the GNSS RTK measurement data through a wavelet base function and a decomposition layer number to obtain high-frequency information and low-frequency information; determining a high-frequency coefficient layer subjected to wavelet threshold processing based on the high-frequency information, and performing gross error elimination on the determined high-frequency coefficient layer by using an algorithm based on a 3sigma criterion; performing wavelet inverse transformation and recombination on the decomposed low-frequency information and the processed high-frequency information to obtain data from which gross errors are eliminated; and removing noise components in the observation data in the height direction after the gross errors are eliminated by using a hard threshold method. The application can effectively and accurately eliminate the gross errors of the GNSS RTK measurement data, and can also retain effective high-frequency information of the measurement data.

Description

TECHNICAL FIELD

[0001] The present application relates to a positioning measurement data gross error elimination system and method based on wavelet analysis, belonging to the technical field of GNSS RTK measurement data processing. BACKGROUND

[0002] Global Navigation Satellite System (GNSS) precise dynamic real-time relative positioning, simply referred to as GNSS RTK (Real Time Kinematic), eliminates satellite orbit error, atmospheric propagation delay error, and satellite and receiver clock error and other error sources by difference between receivers and between satellites, and then uses high-precision carrier phase observations to achieve centimeter-level or even millimeter-level positioning. At the same time, GNSS RTK positioning technology integrates GPS, GLONASS, BDS and Galileo four satellite navigation systems, greatly improves the number of visible satellites, gets better satellite distribution, and greatly improves the positioning accuracy of RTK.

[0003] The key of RTK positioning technology lies in solving the phase integer ambiguity. Two prerequisites must be met to accurately and quickly solve the integer ambiguity: first, the ambiguity float solution must be accurately solved, mainly using least squares estimation; second, a good ambiguity search strategy is used for ambiguity fixing. LAMBDA method (Leastsquare Ambiguity Decorrelation Adjustment) is currently considered to be a fast and reliable ambiguity solution algorithm, and is theoretically relatively rigorous. LAMBDA method first obtains the float solution of ambiguity by least squares method or Kalman filter method, and then establishes a search space according to the float solution. LAMBDA method performs decorrelation processing on the float solution of ambiguity, establishes an integer ambiguity search space, and then searches for the integer ambiguity in the established search space according to certain judgment criteria.

[0004] In actual engineering applications, RTK will be affected by satellite conditions, sky environment, data link transmission interference and restrictions, large operation distance, precision and stability, etc. In the case of fast positioning, when the observation time is short, the ill-conditioned nature of the double-difference equation system is serious, and the precision of the ambiguity float solution is poor, which cannot correctly search and fix the integer ambiguity. With the increase of observation time, the station-geometry structure changes, and the ill-conditioned nature of the equation system is improved, so that a higher precision ambiguity float solution can be obtained. Therefore, the measurement data of GNSS RTK will have gross error data different from the actual data, which needs to be eliminated to meet the actual engineering needs.

[0005] Wavelet analysis has the function of band-pass filtering, can effectively frequency division of original signal, realize the separation of gross error and noise in different scales. Wavelet analysis also has the characteristics of multi-resolution, can obtain the localization characteristics of signal well, focus more details of signal, and the detection of local signal mutation signal is very effective. Therefore, in the case of unclear data statistical law, wavelet analysis can detect and eliminate gross error of data sequence containing gross error. In the process of gross error elimination of GNSS RTK measurement data, the observation value can be regarded as a group of signals, and the gross error is the mutation point in the group of signals. The wavelet analysis is used to eliminate these mutation points. GNSS RTK measurement data belongs to non-stationary signal, and the precision is high. Therefore, after the wavelet transform of GNSS RTK measurement data, the high frequency signal of high layer has high signal-to-noise ratio, and the direct use of wavelet analysis threshold denoising will affect the effective high frequency signal of original signal. SUMMARY

[0006] The purpose of the present application is to overcome the deficiencies in the prior art, provide a positioning measurement data gross error elimination system and method based on wavelet analysis, which can effectively and accurately eliminate the gross error of GNSS RTK measurement data, and also can retain the effective high frequency information of measurement data.

[0007] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0008] In a first aspect, the present application provides a positioning measurement data gross error elimination method based on wavelet analysis, comprising:

[0009] Obtaining GNSS RTK measurement data;

[0010] Wavelet transforming the GNSS RTK measurement data through wavelet base function and decomposition layer, to obtain high frequency information and low frequency information;

[0011] Determining the high frequency coefficient layer for wavelet threshold processing based on the high frequency information, and using the algorithm based on 3σ criterion for gross error elimination in the determined high frequency coefficient layer;

[0012] Recombining the decomposed low frequency information and the processed high frequency information through wavelet inverse transform, to obtain the data after eliminating gross error;

[0013] Using hard threshold method to remove the noise component in the observation data in the height direction after eliminating gross error.

[0014] Further, the GNSS RTK measurement data is:

[0015]

[0016] In the formula, f(t) is GNSS RTK measurement data, s(t) is true measurement data, n(t) is noise, and t is gross error point.

[0017] Wavelet transform is performed on GNSS RTK measurement data by using wavelet base function and decomposition layer to obtain high frequency information and low frequency information, including representing GNSS RTK measurement data as multi-resolution as follows:

[0018] f(t)=f j-1 (t)+d j-1 (t)=f j-2 (t)+d j-2 (t)+d j-1 (t)=…=f M (t)+d M (t)+d M+1 (t)+…+d j-1 (t)

[0019] Wherein:

[0020]

[0021]

[0022] f M (t) represents the low frequency component of f j (t), while d M (t), d M+1 (t)…d j-1 (t) represent the high frequency component of f j (t) at different resolutions, is a scale coefficient, is a wavelet coefficient, is a scale function at the l scale of signal multi-resolution analysis, d j (t) is an expansion coefficient at the l scale of signal multi-resolution analysis, V j is a subspace of multi-resolution analysis, W j is a wavelet subspace of multi-resolution analysis.

[0023] Further, the high frequency coefficient layer for wavelet threshold processing is determined based on the high frequency information, including:

[0024] Wavelet threshold denoising is performed by taking different decomposition layers and high frequency coefficient layers, and the signal to noise ratio SNR and the root mean square error RMSE of the signal after removing gross errors and the original signal are calculated, and the combination of the decomposition layer and the high frequency coefficient layer with the maximum signal to noise ratio and the minimum root mean square error is selected, wherein:

[0025] The formula for calculating the signal to noise ratio SNR is:

[0026]

[0027] The formula for calculating the root mean square error (RMSE) is:

[0028]

[0029] where f(i) represents the original signal, and N represents the signal length.

[0030] Further, the algorithm based on the 3σ criterion is used for gross error rejection in the determined high-frequency coefficient layer, including:

[0031] Calculate the mean square value of the wavelet coefficient:

[0032]

[0033] where σ represents the mean square value of the wavelet coefficient, d i represents the i-th wavelet coefficient in a certain wavelet decomposition layer, and N represents the signal length.

[0034] Set the coefficients greater than 3σ in the wavelet transform coefficients to 0, and the others remain unchanged. At this time, 3σ is the threshold value of the wavelet coefficient at each decomposition scale.

[0035] Recalculate the mean square value of the high-frequency coefficient to determine whether there is a value greater than 3σ in the wavelet coefficient.

[0036] In response to the existence of a value greater than 3σ in the wavelet coefficient, the mean square value of the wavelet coefficient is recalculated, the coefficients greater than 3σ in the wavelet transform coefficients are set to 0, and then the mean square value of the high-frequency coefficient is recalculated and it is determined whether there is still a value greater than 3σ in the wavelet coefficient.

[0037] In response to the absence of a value greater than 3σ in the wavelet coefficient, the gross error rejection is completed.

[0038] Further, the low-frequency information after decomposition and the high-frequency information after processing are subjected to wavelet inverse transform and recombination to obtain the data with gross error rejection, including:

[0039] The data with gross error rejection in three directions obtained by recombining the low-frequency information after decomposition and the high-frequency information after processing is subjected to wavelet inverse transform, and the filter coefficient {h n ,n∈Z} and {g n ,n∈Z} corresponding to the bi-scale equation are used to reconstruct the j-th layer wavelet coefficient and the scale coefficient using the j-1-th layer coefficient, and the wavelet reconstruction algorithm is recursively applied to obtain the wavelet transform recovery signal. The calculation formula of the j-th layer scale coefficient is:

[0040]

[0041] wherein, is the j-th layer scale coefficient, is the j-1th layer scale coefficient, is the j-1th layer wavelet coefficient.

[0042] Further, the jth layer coefficient of wavelet transform Through the filter coefficient The decomposition formula of the j-1th layer coefficient is obtained, and the calculation is as follows:

[0043]

[0044] In the formula, is the scale function under the j scale, and ψ j,n is the wavelet function under the j scale.

[0045] Further, the hard threshold method is used to remove the noise components in the height direction observation data after removing the gross errors, including:

[0046] The hard threshold method is used to remove the noise components in the height direction observation data, a wavelet base function is selected, the optimal decomposition layer is determined by a trial method, and the threshold value of each scale coefficient is calculated by an empirical formula. Wavelet threshold processing is performed at each layer of wavelet transform, and the empirical formula is:

[0047] σ j = median(d j,k ) / 0.6745

[0048] Wherein, λ j is the threshold value of wavelet denoising, median is the median function in calculation, d j,k The jth layer high-frequency coefficient layer wavelet coefficient;

[0049] Each scale new wavelet coefficient is estimated by the wavelet threshold denoising method, and each scale new wavelet coefficient is reconstructed by using wavelet inverse transform to obtain the denoised height direction measurement data, and each scale new wavelet coefficient is:

[0050]

[0051] Wherein, is each scale new wavelet coefficient, sign is a sign function, w j,k is each scale old wavelet coefficient.

[0052] Secondly, the application provides a positioning measurement data gross error elimination system based on wavelet analysis, comprising:

[0053] The data acquisition module is used for acquiring GNSS RTK measurement data.

[0054] A wavelet transform module is configured to perform wavelet transform on GNSS RTK measurement data by using a wavelet base function and a decomposition layer number to obtain high-frequency information and low-frequency information;

[0055] A gross error elimination module is configured to determine a high-frequency coefficient layer for wavelet threshold processing based on the high-frequency information, and perform gross error elimination on the determined high-frequency coefficient layer by using an algorithm based on a 3σ criterion;

[0056] A recombination module is configured to perform wavelet inverse transform recombination on the decomposed low-frequency information and the processed high-frequency information to obtain data with eliminated gross errors;

[0057] A noise removal module is configured to remove noise components in the highly-directional observation data after eliminating the gross errors by using a hard threshold method.

[0058] Compared with the prior art, the present application has the following beneficial effects:

[0059] The present application applies wavelet analysis technology to GNSS RTK measurement data processing, uses an algorithm based on a 3σ criterion to determine a wavelet denoising threshold for gross error elimination, and performs gross error processing on GNSS RTK data in three directions, which can accurately eliminate gross errors in GNSS RTK observation data, effectively and accurately eliminate gross errors in GNSS RTK measurement data, and retain effective high-frequency information of the measurement data, thereby meeting the requirements of high-precision positioning in engineering and making the positioning data meet the requirements of actual engineering applications. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 FIG. 1 is a flowchart of a positioning measurement data gross error elimination method based on wavelet analysis according to an embodiment of the present application;

[0061] Figure 2 FIG. 2 is a diagram of original signals and decomposed signals at different wavelet decomposition layers according to an embodiment of the present application;

[0062] Figure 3 FIG. 3 is a flowchart of an algorithm based on a 3σ criterion for determining a threshold for gross error elimination according to an embodiment of the present application;

[0063] Figure 4 FIG. 4 is a comparison diagram of differences between signals after eliminating gross errors in the longitude direction by using three methods and corresponding original signals according to an embodiment of the present application;

[0064] Figure 5 FIG. 5 is a comparison diagram of differences between signals after eliminating gross errors in the latitude direction by using three methods and corresponding original signals according to an embodiment of the present application;

[0065] Figure 6 FIG. 6 is a diagram of differences between signals after eliminating gross errors in the height direction and corresponding original signals according to an embodiment of the present application;

[0066] Figure 7 is a high direction wavelet denoising effect figure provided by the embodiment one of the present application. DETAILED DESCRIPTION

[0067] The present application will be further described below in conjunction with the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, and cannot be used to limit the protection scope of the present application.

[0068] Embodiment one:

[0069] The method for removing gross errors of positioning measurement data based on wavelet analysis, please refer to Figure 1 , comprising the following steps,

[0070] I. Selecting a wavelet base function and a decomposition layer number to perform wavelet transform on GNSS RTK measurement data to obtain high frequency information and low frequency information. Wherein:

[0071] Selecting a suitable wavelet base function, the wavelet function suitable for detecting singular signals can consider the following four conditions: ψ(t) has a compact support; ψ(t) is continuous and differentiable; ψ(t) has a vanishing moment order; ψ(t) has symmetry. In practice, a wavelet function with good regularity and compactness is often selected, which can meet the smoothness, stability and good locality of signal description. The dbN wavelet meets the above requirements, and its characteristics are that as the value of N increases, the order of vanishing moment is larger, the higher the smoothness, the stronger the frequency domain locality, but it does not have symmetry. The symN wavelet is an improvement of the dbN wavelet base function, which has better symmetry, can reduce the phase distortion when analyzing and reconstructing the signal to a certain extent, and ensures that the data after removing gross errors will not lose effective high frequency information;

[0072] Selecting a wavelet base function to perform wavelet transform on GNSS RTK measurement data to obtain high frequency information and low frequency information of wavelet transform. The GNSS RTK measurement data is described by a function as follows:

[0073]

[0074]

[0075] In the formula, f(t) is GNSS RTK measurement data, s(t) is true measurement data; n(t) is noise; Otherwise For any f(t), there is a multi-resolution representation as shown in the following formula:

[0076] f(t) = f j-1 (t) + d j-1 (t) = f j-2 (t) + dj-2 (t)+d j-1 (t)=…=f M (t)+d M (t)+d M+1 (t)+…+d j-1 (t)

[0077] in:

[0078]

[0079]

[0080] In the formula, f M (t) represents f j The low-frequency components of (t), while d M (t), d M+1 (t)…d j-1 (t) represents f j High-frequency components at different resolutions of (t) It is the scaling factor. These are wavelet coefficients. It is the scaling function at the l-scale of multiresolution analysis, d j (t) are the l-scale expansion coefficients of the signal, V j It is a subspace for multiresolution analysis, W j It is a wavelet subspace for multiresolution analysis.

[0081] The j-th level coefficients of the wavelet transform Through filter coefficients The decomposition formula of the coefficients of the (j-1)th layer is obtained, and the calculation is shown in the following formula:

[0082]

[0083] In the formula, Let ψ be the scaling function of the j-th layer. j,n Let be the wavelet function of the j-th layer, and let... Then c j-1 and d j-1 They can be viewed as c respectively. j The low-frequency signal and detail signals, namely low-frequency coefficients and high-frequency coefficients, are obtained by recursively applying the wavelet decomposition algorithm. j low-frequency signal c M and detail signals d at different resolutions M d M+1 d j-1 c M d M d M+1 , ...d j-1 For cj Wavelet transform.

[0084] II. Based on high-frequency information, determine the high-frequency coefficient layer for wavelet thresholding. Then, use an algorithm based on the 3σ criterion to remove gross errors from this determined high-frequency coefficient layer. Wherein:

[0085] Input measurement data from an RTK rover over a period of time, including gross errors in the longitude, latitude, and altitude directions.

[0086] Wavelet basis function selection: The longitude data was decomposed into 5 levels using sym8. The results are shown below. Figure 2 Comparison revealed that gross errors were clearly reflected in the first, second, and third layers of the high-frequency coefficients of wavelet decomposition in sym4, sym6, sym7, and sym8, with sym8 showing the clearest and best identification of gross errors.

[0087] Determine the number of decomposition layers and high-frequency coefficient layers: Take different numbers of decomposition layers and high-frequency coefficient layers, perform wavelet threshold denoising, calculate the signal-to-noise ratio (SNR) and mean square error (RMSE) of the signal after removing gross errors and the original signal, and select the combination of decomposition layers and high-frequency coefficient layers with the largest SNR and the smallest RMSE.

[0088] The formula for calculating the signal-to-noise ratio (SNR) is:

[0089]

[0090] The formula for calculating the mean squared error (RMSE) is:

[0091]

[0092] Where f(i) represents the original signal, This represents the recombined signal, and N represents the signal length.

[0093] In this embodiment, the decomposition levels are 4, 5, 6, and 7. For each decomposition level, different numbers of high-frequency coefficient layers are used for gross error removal. The signal-to-noise ratio (SNR) and mean square error (MSE) of the signals after gross error removal are shown in Table 1. Table 1 shows that for different decomposition levels, the SNR and MSE of the signals after removing gross errors are the same as the original signals starting with the same number of high-frequency coefficient layers. Comparing the SNR and MSE, a decomposition level of 4 and a high-frequency coefficient layer of 3 show the best results in removing gross errors. Using SNR and MSE to determine the decomposition level and the number of high-frequency coefficient layers ensures that while effectively and accurately removing gross errors from GNSSRTK measurement data, the effective high-frequency information of the measurement data is also preserved.

[0094]

[0095]

[0096] Table 1 signal-to-noise ratio, mean square error, smoothness and normalization of the signal after removing gross errors and the original signal

[0097] Select sym8 wavelet basis function, decomposition layer is 4, wavelet decomposition is carried out on the data in three directions, and the threshold value is determined based on 3σ criterion algorithm to carry out wavelet threshold processing on the high frequency coefficient of the 3rd, 2nd and 1st layer.

[0098] The threshold value determination algorithm based on 3σ criterion carries out wavelet threshold processing on the high frequency coefficient layer, including:

[0099] Step 1) calculate the mean square value of wavelet coefficient:

[0100]

[0101] In the formula, σ represents the mean square value of wavelet coefficient, d i represents the i-th wavelet coefficient in a certain wavelet decomposition layer, and N represents the length of the signal.

[0102] Step 2) set the coefficient greater than 3σ in the wavelet transform coefficient to 0, and keep the others unchanged, at this time, 3σ is the threshold value of the wavelet coefficient at each decomposition scale.

[0103] Step 3) return to step 1) to recalculate the mean square value of the high frequency coefficient, if there are still values greater than 3σ in the wavelet coefficient, then loop step 1) and step 2), until all wavelet coefficients of this layer are less than 3σ.

[0104] III. The decomposed low frequency information and the processed high frequency information are inversely transformed and recombined to obtain the data after removing gross errors. Among them:

[0105] In this embodiment, the decomposed low frequency information and the processed high frequency information are inversely transformed and recombined to obtain the data after removing gross errors in three directions, through the filter coefficient corresponding to the bi-scale equation {h n ,n∈Z}, {g n ,n∈Z}, using the j-1 layer coefficient to reconstruct the j layer scale coefficient The wavelet transform recovery signal is obtained by recursively applying the wavelet reconstruction algorithm, The calculation formula is:

[0106]

[0107] Among them, is the j layer scale coefficient, is the j-1 layer scale coefficient, is the j-1 layer wavelet coefficient.

[0108] IV. The noise component in the observation data in the height direction after removing gross errors is removed by using hard threshold method.

[0109] The hard threshold method is used to remove the noise component in the height direction observation data, the sym6 wavelet base function is selected, the optimal decomposition layer is determined to be 3 through the trial method, and the threshold value of each scale coefficient is calculated by using the following empirical formula. The wavelet threshold processing is performed on each layer of the wavelet transform.

[0110] σ j = median(d j,k ) / 0.6745

[0111] Wherein, λ j is the threshold value of wavelet denoising, median is the median function in calculation, d j,k is the wavelet coefficient of the high-frequency coefficient layer of the jth layer.

[0112] The new wavelet coefficient of each scale is estimated by the threshold method The following formula is used to calculate the new wavelet coefficient of each scale. The inverse wavelet transform is used for reconstruction to obtain the denoised height direction measurement data.

[0113]

[0114] Wherein, is the new wavelet coefficient of each scale, sign is a sign function, w j,k is the old wavelet coefficient of each scale.

[0115] Embodiment two:

[0116] The positioning measurement data gross error elimination system based on wavelet analysis can realize the positioning measurement data gross error elimination method based on wavelet analysis in embodiment one, and includes:

[0117] The positioning data acquisition module is used for real-time parsing the longitude, latitude and height of the GNSS RTK flow station.

[0118] The wavelet decomposition signal module is used for wavelet decomposition of the positioning data in a period of time to obtain the high-frequency signal and the low-frequency signal of the positioning data.

[0119] The gross error elimination module is used for processing the high-frequency coefficient by using the 3σ criterion-based gross error elimination algorithm.

[0120] The wavelet signal reconstruction module is used for wavelet signal reconstruction of the low-frequency coefficient and the processed high-frequency coefficient to obtain the positioning data with the eliminated gross error.

[0121] The height direction filtering module is used for denoising filtering of the height direction by using the wavelet threshold denoising method.

[0122] Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0123] The present application is described in reference to the flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0124] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0125] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0126] The above description is only preferred embodiments of the application. It should be pointed out that for those skilled in the art, some improvements and modifications can be made without departing from the technical principles of the application, and these improvements and modifications should also be considered as falling within the scope of the application.

Claims

1. A method for removing gross errors in positioning measurement data based on wavelet analysis, characterized by: include: Acquire GNSSRTK measurement data; Wavelet transform is performed on GNSSRTK measurement data by wavelet basis functions and decomposition level to obtain high-frequency and low-frequency information; The high-frequency coefficient layer for wavelet thresholding is determined based on high-frequency information, and an algorithm based on the 3σ criterion is used to remove gross errors in the determined high-frequency coefficient layer. The decomposed low-frequency information and the processed high-frequency information are recombined by inverse wavelet transform to obtain data with gross errors removed. The hard thresholding method was used to remove noise components from the height direction observation data after gross errors were eliminated. The decomposed low-frequency information and the processed high-frequency information are recombined using inverse wavelet transform to obtain data with gross errors removed, including: The decomposed low-frequency information and the processed high-frequency information are reconstructed using inverse wavelet transform to obtain data with gross errors removed in three directions. This data is then processed using the filter coefficients {h} corresponding to the dual-scale equation. n ,n∈Z},{g n For the scale coefficients of the (j-1)th layer (n∈Z), the wavelet transform is used to reconstruct the scale coefficients of the jth layer. The wavelet transform is then recursively applied to obtain the wavelet-reconstructed signal. The formula for calculating the scale coefficients of the jth layer is: in, Let be the scaling factor of the j-th layer. The scaling factor for the (j-1)th layer is... For the (j-1)th layer wavelet coefficients.

2. The method for removing gross errors in positioning measurement data based on wavelet analysis according to claim 1, characterized in that, Assume the GNSSRTK measurement data is as follows: In the formula, f(t) represents GNSSRTK measurement data, s(t) represents actual measurement data, n(t) represents noise, and t represents gross errors. Wavelet transform is performed on GNSSRTK measurement data using wavelet basis functions and decomposition levels to obtain high-frequency and low-frequency information, including multi-resolution representation of GNSSRTK measurement data as follows: f(t)=f j-1 (t)+d j-1 (t)=f j-2 (t)+d j-2 (t)+d j-1 (t)=… =f M (t)+d M (t)+d M+1 (t)+…+d j-1 (t) in: f M (t) represents f j The low-frequency components of (t), while d M (t), d M+1 (t)…d j-1 (t) represents f j High-frequency components at different resolutions of (t) It is the scaling factor. These are wavelet coefficients. It is the scaling function at the l-scale in multiresolution signal analysis, d j (t) is the expansion coefficient of the signal at the l-scale in multiresolution analysis, V j It is a subspace for multiresolution analysis, W j It is a wavelet subspace for multiresolution analysis.

3. The method for removing gross errors in positioning measurement data based on wavelet analysis according to claim 1, characterized in that, The high-frequency coefficient layer for wavelet thresholding is determined based on high-frequency information, including: Different decomposition levels and high-frequency coefficient levels are selected for wavelet threshold denoising. The signal-to-noise ratio (SNR) and mean square error (RMSE) of the signal after removing gross errors are calculated compared to the original signal. The combination of decomposition level and high-frequency coefficient level with the highest SNR and lowest RMSE is selected, where: The formula for calculating the signal-to-noise ratio (SNR) is: The formula for calculating the mean squared error (RMSE) is: Where f(i) represents the original signal, This represents the recombined signal, and N represents the signal length.

4. The method for removing gross errors in positioning measurement data based on wavelet analysis according to claim 1, characterized in that, Gross error removal is performed using an algorithm based on the 3σ criterion at the defined high-frequency coefficient layer, including: Calculate the mean square value of wavelet coefficients: In the formula, σ represents the mean square value of the wavelet coefficients, and d i represents the i-th wavelet coefficient in a certain wavelet decomposition layer, and N represents the signal length; Set the coefficients greater than 3σ in the wavelet transform coefficients to 0, and leave the others unchanged. At this time, 3σ is the threshold of the wavelet coefficients at each decomposition scale. Recalculate the mean square value of the high-frequency coefficients and determine whether there are values ​​greater than 3σ in the wavelet coefficients; If there are values ​​greater than 3σ in the wavelet coefficients, the mean square value of the wavelet coefficients is recalculated. After setting the coefficients greater than 3σ in the wavelet transform coefficients to 0, the mean square value of the high-frequency coefficients is recalculated and it is determined whether there are still values ​​greater than 3σ in the wavelet coefficients. The outlier is eliminated when there are no values ​​greater than 3σ in the wavelet coefficients.

5. The method for removing gross errors in positioning measurement data based on wavelet analysis according to claim 1, characterized in that, The j-th level coefficients of the wavelet transform Through filter coefficients The decomposition formula of the coefficients of the (j-1)th layer is obtained, and the calculation is shown in the following formula: In the formula, Let ψ be a wavelet function. j,n It is a scaling function.

6. The method for removing gross errors in positioning measurement data based on wavelet analysis according to claim 1, characterized in that, The noise component in the height-direction observation data after removing gross errors is removed using a hard thresholding method, including: A hard thresholding method is used to remove noise components from the height-direction observation data. A wavelet basis function is selected, and the optimal number of decomposition levels is determined through a trial-and-error approach. The threshold for each scale coefficient is calculated using an empirical formula. Wavelet thresholding is performed at each level of the wavelet transform. The empirical formula is as follows: s j =median(d j,k ) / 0.6745 Where, λ j d is the threshold for wavelet denoising, median is the function for calculating the median, and d j,k The wavelet coefficients of the j-th high-frequency coefficient layer; The new wavelet coefficients at each scale are estimated using wavelet threshold denoising. The new wavelet coefficients at each scale are then reconstructed using inverse wavelet transform to obtain the denoised height measurement data. The new wavelet coefficients at each scale are: in, New wavelet coefficients for each scale, where sign is the sign function, w j,k The old wavelet coefficients for each scale.

7. A system for removing gross errors in positioning measurement data based on wavelet analysis, characterized in that: include: Data acquisition module: used to acquire GNSSRTK measurement data; Wavelet transform module: Used to perform wavelet transform on GNSSRTK measurement data using wavelet basis functions and decomposition levels to obtain high-frequency and low-frequency information; Gross error removal module: This module is used to determine the high-frequency coefficient layer for wavelet thresholding based on high-frequency information, and to remove gross errors in the determined high-frequency coefficient layer using an algorithm based on the 3σ criterion. Reconstruction module: Used to reconstruct the decomposed low-frequency information and the processed high-frequency information by performing inverse wavelet transform, so as to obtain data with gross errors removed; Noise Removal Module: Used to remove noise components from height-direction observation data after gross error removal using a hard thresholding method; The decomposed low-frequency information and the processed high-frequency information are recombined using inverse wavelet transform to obtain data with gross errors removed, including: The decomposed low-frequency information and the processed high-frequency information are reconstructed using inverse wavelet transform to obtain data with gross errors removed in three directions. This data is then processed using the filter coefficients {h} corresponding to the dual-scale equation. n ,n∈Z},{g n For the scale coefficients of the (j-1)th layer (n∈Z), the wavelet transform is used to reconstruct the scale coefficients of the jth layer. The wavelet transform is then recursively applied to obtain the wavelet-reconstructed signal. The formula for calculating the scale coefficients of the jth layer is: in, Let be the scaling factor of the j-th layer. The scaling factor for the (j-1)th layer is... For the (j-1)th layer wavelet coefficients.

8. A device for removing gross errors in positioning measurement data based on wavelet analysis, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1 to 6.

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