Joint observation fusion method and system for slope radar and GNSS three-dimensional deformation data

Abstract

The present invention discloses a joint observation and fusion method and system for slope radar and GNSS three-dimensional deformation data. The method comprises: S1, obtaining slope radar data and performing discrete value elimination processing, and obtaining GNSS three-dimensional deformation data and performing discrete value elimination processing and spatial interpolation processing; S2, calculating the displacement data of the slope radar data and converting it to the BLH coordinate system; S3, constructing a joint observation model for the slope radar data and the GNSS three-dimensional deformation data in the BLH coordinate system; S4, taking the weights after iterative optimization from the joint observation model to perform data fusion of the slope radar data and the GNSS three-dimensional deformation data according to the weights. The present invention jointly constructs a joint observation model for multi-source data based on the slope radar observation equation and the GNSS observation equation, and introduces a weighted residual algorithm based on the least squares method to minimize the sum of the weighted residuals, thereby generating a high-precision three-dimensional deformation fusion result, providing reliable technical support for subsequent slope deformation analysis.

Description

Technical Field

[0001] The present invention relates to the field of mining slope deformation monitoring, and in particular to a joint observation and fusion method and system for slope radar and GNSS three-dimensional deformation data. Background Art

[0002] Both slope radar and GNSS technologies are applicable to slope deformation detection. Slope radar transmits microwave signals, which are reflected by the slope surface and then received by the radar. Based on information such as the time difference and frequency change between the transmitted and received signals, the change in distance between the slope surface and the radar can be calculated. GNSS technology utilizes satellite signals transmitted by systems such as GPS and Beidou satellite navigation systems. By receiving these signals, the three-dimensional position of the receiver (installed at the slope monitoring point) is determined, including longitude, latitude, and elevation.

[0003] In open-pit mine slope safety monitoring, slope radar uses coherent synthesis radar imaging technology to efficiently monitor large-scale slope displacement and deformation. This technology can acquire high-resolution displacement information in a short period of time, making it suitable for high-frequency, large-scale monitoring tasks. However, noise interference in mining environments can reduce its accuracy. Furthermore, radar data typically only provides one-dimensional displacement information along the line of sight, which is difficult to directly reflect deformation characteristics in three dimensions. GNSS technology provides high-precision, continuous displacement data and is also suitable for slope monitoring. (In slope deformation monitoring, multiple GNSS receivers are installed at key locations on the slope. As the slope deforms, the positions of these receivers change. By comparing position information at different time points, slope deformation data can be obtained.) GNSS technology is suitable for long-term monitoring tasks and can accurately reflect the changes in the three-dimensional coordinates of monitoring points. However, GNSS monitoring points are often scattered and have limited coverage, making it difficult to provide comprehensive regional displacement information.

[0004] Both slope radar and GNSS technologies are applicable to slope deformation detection. How to combine slope radar and GNSS technologies for slope deformation detection is a current research direction; however, how to use the data obtained by slope radar and GNSS technology respectively to achieve the fusion of the two data (to achieve the complementary advantages of the two technologies); and to build a complementary fusion of multi-source data advantages of slope radar and GNSS technology. This is of great significance to slope deformation detection and can provide more comprehensive technical support for slope safety monitoring in complex environments. Summary of the Invention

[0005] The purpose of the present invention is to overcome the data fusion problem of existing slope radar and GNSS deformation monitoring, and provide a joint observation fusion method of slope radar and GNSS three-dimensional deformation data, which utilizes the data complementarity of slope radar data and GNSS three-dimensional deformation data. The slope radar data and GNSS three-dimensional deformation data respectively constitute the slope radar observation equation and GNSS observation equation. Based on the two types of observation equations, a joint observation model of multi-source data is jointly constructed, and a weighted residual algorithm based on the least squares method is introduced. During the fusion process, the weights of the slope radar data and the GNSS three-dimensional deformation data are adjusted and the weighted residual sum is minimized, thereby finally generating a high-precision three-dimensional deformation fusion result. The present invention combines multi-source observation data, effectively utilizes the complementary advantages of different source data and fused observations, and can obtain high-precision three-dimensional displacement data of the target, providing reliable technical support for subsequent slope deformation analysis.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A joint observation and fusion method for slope radar and GNSS three-dimensional deformation data, the method comprising:

[0008] S1. Obtain slope radar data and perform discrete value elimination processing, and obtain GNSS three-dimensional deformation data and perform discrete value elimination processing and spatial interpolation processing;

[0009] S2. Calculate the displacement data of the slope radar data and convert it into the BLH coordinate system;

[0010] S3. Construct a joint observation model of slope radar data and GNSS 3D deformation data in the BLH coordinate system. The weighted iterative optimization expression of the two types of observation data in the joint observation model is as follows: , Indicates the category of observation data, Represents the weight corresponding to the observed data category i after iteration, Represents the weight corresponding to the observed data category i before iteration, until the weight variances of the two types of observed data are approximately equal, that is, ;

[0011] S4. The joint observation model takes the weights after iterative optimization to fuse the slope radar data and the GNSS three-dimensional deformation data according to the weights.

[0012] In order to better implement the present invention, in method S3, the joint observation model solves the residual minimization process based on the least squares principle, and the result expression is as follows:

[0013] ,in is the coefficient matrix, is the transpose of the coefficient matrix, is the weight matrix, is the observation matrix of the joint observation model.

[0014] Preferably, the joint observation model is composed of the slope radar observation equation and the GNSS observation equation.

[0015] The slope radar observation equation is expressed as follows:

[0016] ;in, is the radar line of sight direction deformation value, are the projection vectors of the longitude, latitude and elevation directions of the slope radar data, are the deformation values ​​in the longitude, latitude and elevation directions to be calculated, is the initial displacement of the radar line of sight, are the initial deformation values ​​in longitude, latitude, and elevation directions respectively;

[0017] The GNSS observation equation is expressed as follows:

[0018] ,in are the deformation values ​​in the longitude, latitude and elevation directions decomposed from the GNSS three-dimensional deformation data. are the deformation values ​​in the longitude, latitude and elevation directions to be calculated, They are the residuals in the east-west, north-south, and vertical directions respectively;

[0019] Joint observation model combines the observation matrix of slope radar observation equation and GNSS observation equation The expression is as follows:

[0020] ;

[0021] is the fusion result X of the joint observation model.

[0022] Preferably, in method S1, the discrete value elimination processing method of GNSS three-dimensional deformation data is as follows:

[0023] The GNSS 3D deformation data is standardized, and the mean of the GNSS 3D deformation data within the window is calculated using a sliding window. Data points that deviate from the sliding window mean are preliminarily determined to be discrete values.

[0024] The discrete values ​​that are initially separated are classified by the support vector machine with the purpose of maximizing the classification interval. The label +1 is used to represent normal data points and -1 is used to represent discrete data points. The constraint expression of the support vector machine is: , Represents the displacement, velocity, and acceleration vector combination of each data point input, Indicates the category of the sample after rough separation, is the hyperplane normal vector, perpendicular to the decision hyperplane; It is a bias term and is used to adjust the position of the decision hyperplane. The constraints of the vector machine ensure that each data point is classified on one side of the hyperplane and the distance from the decision hyperplane is at least 1.

[0025] By the hyperplane normal vector and bias The distance between each data point and the hyperplane is calculated. If the distance is less than or equal to -1, the data point is determined to be a discrete value and is removed.

[0026] Preferably, for discrete values ​​that are initially separated but cannot be completely separated, a soft interval is introduced by introducing a slack variable ,by As a purpose, the constraint expression is as follows:

[0027] ,in It is a hyperparameter used to control the soft interval maximization and error penalty, and further separate and eliminate discrete values ​​that cannot be completely separated.

[0028] Preferably, the discrete value removal processing method of slope radar data is as follows:

[0029] Use proximity analysis to initially detect discrete values, then use Euclidean distance to calculate the neighborhood set of each data point and the mean and standard deviation of the line of sight displacement within the area, and use the following formula to determine suspected discrete values:

[0030] ,in , are the mean and variance in the domain, is the displacement of data point j; Parameters preset based on the characteristics of historical slope radar data;

[0031] The random forest decision tree model is constructed by using the split node to select the optimal split feature and threshold through the Gini index to maximize the reduction of the Gini index after splitting. , 、 They are normal value nodes and discrete value nodes after the slope radar data is split. 、 are the number of samples of normal value and discrete value nodes respectively, is the total number of samples of slope radar data, The Gini index is the normal value, is the Gini index of discrete values;

[0032] The random forest decision tree model determines the discrete values ​​in the slope radar data by majority voting of all decision trees and eliminates them.

[0033] Preferably, in method S1, the spatial interpolation processing of the GNSS three-dimensional deformation data is performed by using the Kriging method and spatial correlation. The Kriging interpolation formula is as follows:

[0034] ,in Unknown bit The predicted value of is the known data point numbered i The value on is the kriging weight numbered i.

[0035] Preferably, in method S2, the three-dimensional displacement conversion relationship expression is as follows:

[0036] ,in are the projection vectors of the longitude, latitude and elevation directions of the slope radar data, are the coordinates in geocentric rectangular coordinates, The BLH coordinates of the center point of the radar device for slope radar data.

[0037] A joint observation and fusion system for slope radar and GNSS three-dimensional deformation data includes a slope radar data processing module, a GNSS three-dimensional deformation data processing module, and a joint observation model. The slope radar data processing module is used to obtain slope radar data and perform discrete value elimination processing. The GNSS three-dimensional deformation data processing module is used to obtain GNSS three-dimensional deformation data and perform discrete value elimination processing and spatial interpolation processing. The joint observation model includes a coordinate conversion calculation module, which is used to calculate the displacement data of the slope radar data and convert it to a BLH coordinate system. The coordinate conversion calculation module calibrates the slope radar data and the GNSS three-dimensional deformation data to the same BLH coordinate system. The weighted iterative optimization expression of the two types of observation data, slope radar data and GNSS three-dimensional deformation data, in the joint observation model is as follows: , Indicates the category of observation data, Represents the weight corresponding to the observed data category i after iteration, Represents the weight corresponding to the observed data category i before iteration, until the weight variances of the two types of observed data are approximately equal, that is, The joint observation model takes the iteratively optimized weights to fuse the slope radar data and the GNSS three-dimensional deformation data according to the weights.

[0038] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0039] (1) The present invention combines threshold classification, support vector machine classification interval maximization characteristics and random forest decision tree integration capabilities to achieve accurate identification and elimination of outliers in the data, showing stronger accuracy and classification efficiency when processing complex data, and significantly improving the accuracy and reliability of outlier processing; the slope radar data is modeled and decomposed in three-dimensional space, and the slope radar line of sight direction displacement is converted into a BLH coordinate system. The maximum likelihood optimization method is combined to optimize the variation function parameters. By optimizing key parameters such as the nugget value, base value and range in the variation function, the accuracy of the Kriging interpolation results is significantly improved.

[0040] (2) The present invention utilizes the data complementarity between slope radar data and GNSS three-dimensional deformation data. The slope radar data and GNSS three-dimensional deformation data respectively constitute the slope radar observation equation and GNSS observation equation. Based on the two types of observation equations, a joint observation model of multi-source data is jointly constructed, and a weighted residual algorithm based on the least squares method is introduced. During the fusion process, the weights of the slope radar data and the GNSS three-dimensional deformation data are adjusted and the weighted residual sum is minimized, finally generating a high-precision three-dimensional deformation fusion result; the present invention combines multi-source observation data, effectively utilizes the complementary advantages of different source data and fusion observation, and can obtain high-precision three-dimensional displacement data of the target, providing reliable technical support for subsequent slope deformation analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Flowchart of the joint observation fusion method of the present invention;

[0042] Figure 2 Schematic diagram of the principle of the joint observation fusion method of the embodiment;

[0043] Figure 3 For example, the displacement data of a mining area in Xinjiang from January to April in GNSS three-dimensional deformation data changes over time;

[0044] Figure 4 As an example, the GNSS 3D deformation data of a mining area in Xinjiang from January to April is screened and classified by support vector machine;

[0045] Figure 5 The following is a schematic diagram of grid point data of a slope radar data of a 100x100 grid in a mining area in Xinjiang as an example;

[0046] Figure 6 for Figure 5 Schematic diagram of grid point data after standardization of mid-slope radar data;

[0047] Figure 7 for Figure 6 Schematic diagram of the separation results of adjacent value analysis of mid-slope radar data;

[0048] Figure 8 for Figure 7 Schematic diagram of random forest separation results of mid-slope radar data;

[0049] Figure 9 This is a schematic diagram of the principle of slope radar data decomposition and conversion;

[0050] Figure 10 RMSE variation diagram during the maximum likelihood optimization process of Kriging parameters in the embodiment;

[0051] Figure 11 This is a schematic diagram of the visualization result after the fusion of part of the slope radar data and part of the GNSS 3D deformation data as an example of the embodiment;

[0052] Figure 12 This is a comparison of the detection accuracy of slope radar data, GNSS three-dimensional deformation data, and data after joint observation fusion. DETAILED DESCRIPTION

[0053] Below in conjunction with embodiment, the present invention is described in further detail:

[0054] Example

[0055] like Figure 1 、 Figure 2 As shown, a joint observation fusion method for slope radar and GNSS three-dimensional deformation data includes:

[0056] S1. Obtain slope radar data and perform discrete value elimination processing. In some embodiments, the discrete value elimination processing method of slope radar data of the present invention is as follows:

[0057] Use proximity analysis to preliminarily detect discrete values. Then use Euclidean distance to calculate the neighborhood set of each data point and the mean and standard deviation of the line-of-sight displacement within the area. Use the following formula to determine suspected discrete values ​​(based on the information of radar center, illumination point, and line-of-sight displacement in the slope radar data, and based on the principle that this information and the displacement values ​​of adjacent illumination points have a certain degree of spatial consistency, the proximity analysis method is used to make a preliminary judgment on discrete values):

[0058] ,in , are the mean and variance in the domain, is the displacement of data point j. The parameters are preset based on the characteristics of the slope radar historical data (in the example of a mining area in Xinjiang, The value is 3).

[0059] The present invention constructs a random forest decision tree model and uses the split node to select the optimal split feature and threshold through the Gini index to maximize the reduction of the Gini index after splitting. , 、 They are normal value nodes and discrete value nodes after the slope radar data is split. 、 are the number of samples of normal value and discrete value nodes respectively, is the total number of samples of slope radar data, The Gini index is the normal value, is the Gini index of discrete values. The expression of the Gini index is as follows: , is the sample ratio of normal value or discrete value in the current slope radar normal value and discrete value classification, The radar data is classified into normal points and discrete values. Figure 5 As shown, calculate the neighborhood mean and variance:

[0060] =2.04; =1.161.

[0061] The slope radar data is standardized according to the neighborhood mean and variance to obtain the following Figure 6 As shown, a proximity analysis is then performed on each data point in the slope radar data (using Euclidean distance to calculate the neighborhood set of each data point and the mean and standard deviation of the sight direction displacement within the area). The mean and variance conditions are used to determine whether the sight direction displacement deviates from the neighborhood statistical value, and the normal value and discrete value are preliminarily separated, as shown in Figure 7 As shown in the figure. Based on the proximity analysis, the initially marked outlier points are merged with other normal data points into a single dataset. A label column is added to the dataset to indicate whether the outlier points are marked by the proximity analysis, with 0 indicating normal data and 1 indicating a preliminary outlier. A decision tree is constructed based on the average proximity distance and local distance mean of the radar data, and the Gini index is used to select the optimal splitting feature and threshold.

[0062] The random forest decision tree model uses the majority vote of all decision trees to determine and eliminate discrete values ​​in the slope radar data. The majority vote expression is as follows: , is the total judgment of whether the tree in the random forest is a discrete value, After constructing the optimal separation tree for each decision tree, the discrete values ​​of the slope radar data are removed according to the separation tree standard. Because random forests greatly enhance the recognition of discrete values ​​in slope radar through multiple feature selection and splitting, they can accurately extract discrete values ​​in slope radar data that meet the conditions, providing an accurate data basis for subsequent function construction. In the example of slope radar data from a mining area in Xinjiang, the random forest decision tree model constructs a decision tree, selects the optimal splitting feature and threshold value through the Gini index to separate discrete values, and the random forest separation results of slope radar data are as follows: Figure 8 shown.

[0063] Obtain GNSS three-dimensional deformation data and perform discrete value elimination and spatial interpolation processing. In some embodiments, the discrete value elimination processing method of GNSS three-dimensional deformation data is as follows:

[0064] The GNSS 3D deformation data is standardized, and the mean of the GNSS 3D deformation data within the window is calculated using a sliding window. Data points that deviate from the sliding window mean are initially determined to be discrete values. A simple example is as follows: The dataset of GNSS 3D deformation data is represented as ..., standardize the data, then use the sliding window technology to detect GNSS outliers within a continuous time period, set the sliding window and anomaly detection settings, consider the overall changes in GNSS data, set an appropriate window size, and calculate the mean of the GNSS data within the window; judge each GNSS data point, and preliminarily determine the data points that deviate from the sliding window mean as discrete values:

[0065] ; is the normalized GNSS displacement data over time, is the mean calculated for the window, is the standard deviation calculated for the window, is a variable that controls the discrete value threshold (determined according to the characteristics of GNSS historical data). If the above formula conditions are met, it is considered a discrete value. This example takes the displacement data (displacement among displacement, velocity, and acceleration) in the GNSS three-dimensional deformation data of a mining area in Xinjiang as an example, and intercepts the time range from January 1 to April 1, and obtains Figure 3 The displacement data in the GNSS 3D deformation data shown in the figure changes with time. and ,In the example of a mining area in Xinjiang, the ,sliding window size is set to 20 data points, and the mean and ,variance of the sliding window are calculated to filter ,discrete value points.

[0066] The initially separated discrete values ​​are classified using a support vector machine with the goal of maximizing the classification interval, using a label of +1 to represent a normal data point and -1 to represent a discrete data point. In some embodiments, the displacement, velocity, and acceleration of the separated data are selected as input values, and then the support vector machine classification is performed. The data is mapped to a high-dimensional feature space using a radial basis function kernel, and a hyperplane is found in the space to separate the normal data points from the discrete values. The support vector machine (SVM) can maximize the interval between the two types of samples while ensuring that the sample points are correctly classified. The classification optimization is expressed as: .

[0067] The constraint expression of the support vector machine is: , Represents the displacement, velocity, and acceleration vector combination of each data point input, Indicates the category of the sample after rough separation, is the hyperplane normal vector, perpendicular to the decision hyperplane. is a bias term and is used to adjust the position of the decision hyperplane; the constraints of the support vector machine ensure that each data point is classified on one side of the hyperplane and the distance from the decision hyperplane is at least 1. In the example of a mining area in Xinjiang, the GNSS 3D deformation data is filtered and classified by the support vector machine. Figure 4 As shown, the black solid line represents the classification hyperplane, the dotted line represents the boundary interval, the shaded area is the interval range, and the points close to the interval boundary are support vectors.

[0068] By the hyperplane normal vector and bias The distance between each data point and the hyperplane is calculated. If the distance is less than or equal to -1, the data point is determined to be a discrete value and is removed.

[0069] For discrete values ​​that cannot be completely separated after initial separation, soft intervals are introduced by introducing relaxation variables. ,by As a purpose, the constraint expression is as follows:

[0070] ,in is a hyperparameter used to control the soft interval maximization and error penalty, and further separate and eliminate discrete values ​​that cannot be completely separated; in the example of a mining area in Xinjiang, Take 10, In some embodiments, by different and After determining the optimal classification standard through the combination of Calculate the distance from each sample point to the hyperplane and determine whether it is a discrete value. If , then the data point is determined to be a discrete value; if It is a normal data point; after the detection is completed, all samples with discrete values ​​are eliminated, and only normal value data are retained to obtain a new data set after elimination.

[0071] In some embodiments, the spatial interpolation processing of the GNSS three-dimensional deformation data in method S1 is performed by using the Kriging method and spatial correlation; the Kriging interpolation formula is as follows:

[0072] ,in Unknown bit The predicted value of is the known data point numbered i The value on is the kriging weight numbered i.

[0073] In a further embodiment, the maximum likelihood method is introduced into the Kriging interpolation process of the Kriging method to perform parameter optimization. By calculating the partial derivative and optimizing the parameters in the negative gradient direction, the optimized interpolation model can effectively process the characteristics of the GNSS data, thereby providing more accurate results for the GNSS spatial difference. When the Kriging method uses spatial correlation for interpolation, it is necessary to model the spatial variability of the GNSS data; this variability is quantified by calculating the variogram. For two different station locations (the station location is the station location of the GNSS data), and , variogram for:

[0074] ;in and There are two measuring stations and The observation value on is the spatial distance between locations, and the Gaussian model is used to fit the variogram. The Gaussian model expression is as follows: Where is the range, It's the base. The three parameters of the structure part, range, base and structure part, are the key parameters that affect the Kriging interpolation fitting effect. In order to reduce uncertainty and increase the accuracy of model space interpolation, it is necessary to fit the variation function parameters and set The initial parameter range is then calculated, and the covariance under the initial parameters describes the correlation between each pair of data points; for two data points and , the covariance between them for: ;in, is a data point and The spatial distance between them.

[0075] Compute the likelihood function: ;in are the Gaussian model parameters, yes The covariance matrix of is a vector of GNSS station observations.

[0076] The log-likelihood function is simplified as follows:

[0077] Calculate the gradient of the log-likelihood function with respect to the parameters and update the parameters

[0078] ,

[0079] in It is The parameter value of the iteration, is the learning rate, which controls the magnitude of the update, The log-likelihood function is The gradient at .

[0080] In each round of iteration, by calculating the current parameter combination The gradient of the log-likelihood function with respect to each parameter is obtained, and then the parameters are updated along the direction of the negative gradient, thereby gradually approaching the maximum value of the log-likelihood function and obtaining the optimal Parameter combination for Kriging interpolation, is the unknown bit to be predicted The value of is a known data point The values ​​on . The Kriging equations are as follows: , Where It is a GNSS station To the destination The variation function value between It is a GNSS station To the GNSS station The variation function value between Interpolate the regional mean for the target point. Finally, solve the Kriging equations to obtain the target 3D deformation result.

[0081] An example of performing Kriging interpolation of a target point using 10 GNSS station coordinates is as follows:

[0082] Table 1 GNSS station coordinates

[0083]

[0084] In order to minimize the error of the Kriging interpolation model, the optimization objective is the variation function parameter The initial parameter range is set to the nugget value. :(0,0.1), sill value : (0.5, 2.0), variable range : (10,100), calculate the covariance matrix to find the partial derivative, optimize the parameters along the negative gradient direction, and finally get the optimized Kriging interpolation result after MSE no longer decreases significantly

[0085] Table 2 , , ) Iterative process and its mse results

[0086]

[0087] Kriging interpolation of 6 points using the optimal variance function parameter values

[0088] Table 3 Kriging interpolation results of target points

[0089]

[0090] This embodiment uses Kriging parameter maximum likelihood optimization interpolation iteration, Figure 10 The figure shows the results of multiple optimizations of the Kriging interpolation method variation function parameters using the maximum likelihood method. It can be seen from the figure that the rmse gradually decreases with the increase in the number of optimization iterations, showing that maximum likelihood optimization can effectively improve the performance of the interpolation model.

[0091] S2. Calculate the displacement data of the slope radar data and convert it to the BLH coordinate system. In some embodiments, the displacement data of the slope radar data of the present invention can be converted using the following three-dimensional displacement conversion relationship, which is expressed as follows:

[0092] ,in are the projection vectors of the longitude, latitude and elevation directions of the slope radar data, are the coordinates in geocentric rectangular coordinates, The BLH coordinates of the center point of the radar device for slope radar data.

[0093] In some embodiments, the method for converting slope radar data into displacement data is as follows:

[0094] First, the BLH coordinates of the center point of the radar device Convert ECEF coordinates , the expression is as follows: ;

[0095] in is the semi-major axis of the WGS84 ellipsoid, is the square of the first eccentricity.

[0096] According to the polar coordinates of the slope radar pixel points Calculate the displacement of the pixel in the ENU coordinate system . The expression is as follows:

[0097]

[0098] Convert ENU coordinates to ECEF coordinates

[0099]

[0100] The local coordinates Convert to geocentric rectangular coordinates .

[0101]

[0102] According to the geocentric rectangular coordinates , calculate the slope radar pixel .

[0103]

[0104] The process of converting the slope radar pixel points to the BLH coordinate system is completed. The present invention can construct the following three-dimensional displacement conversion relationship for conversion: ,in The polar coordinates are converted into radar pixel BLH coordinates through polar coordinate parameters, and the positions of slope radar pixels are converted into GNSS coordinate system. The positions of GNSS monitoring points are matched with radar pixels, and the spatial correspondence between GNSS and radar images is established. This provides conversion coefficients for converting slope radar line of sight displacement into three-dimensional displacement in the subsequent fusion of slope radar and GNSS data. In the example of slope radar data in a mining area in Xinjiang, according to Figure 9 The calibration and decomposition conversion principle (by converting radial distance and angle into X, Y, and Z coordinates in three-dimensional space, the spatial distribution and height variation of radar signals can be analyzed). An example is as follows:

[0105] Table 4 Slope radar example data

[0106]

[0107] The calculation results of three-dimensional space calibration are as follows:

[0108] Table 5 Pixel 3D calibration results

[0109]

[0110] S3. Construct a joint observation model of slope radar data and GNSS 3D deformation data in the BLH coordinate system. The weighted iterative optimization expression of the two types of observation data in the joint observation model is as follows: , Indicates the category of observation data, Represents the weight corresponding to the observed data category i after iteration, Represents the weight corresponding to the observed data category i before iteration, until the weight variances of the two types of observed data are approximately equal, that is, The weight iterative optimization process of this embodiment is as follows:

[0111] Table 6 Iterative change process

[0112]

[0113] Calculate the convergence conditions and complete the convergence after the convergence conditions are met. .

[0114] In some embodiments, the joint observation model solves the residual minimization process based on the least squares principle, and the result expression is as follows:

[0115] ,in is the coefficient matrix, is the transpose of the coefficient matrix, is the weight matrix, is the observation matrix of the joint observation model.

[0116] The joint observation model of the present invention is composed of the slope radar observation equation and the GNSS observation equation.

[0117] The slope radar observation equation is expressed as follows:

[0118] .in, is the radar line of sight direction deformation value, are the projection vectors of the longitude, latitude and elevation directions of the slope radar data, are the deformation values ​​in the longitude, latitude and elevation directions to be calculated, is the initial displacement of the radar line of sight, are the initial deformation values ​​in longitude, latitude, and elevation directions respectively.

[0119] The GNSS observation equation is expressed as follows:

[0120] ,in are the deformation values ​​in the longitude, latitude and elevation directions decomposed from the GNSS three-dimensional deformation data. are the deformation values ​​in the longitude, latitude and elevation directions to be calculated, They are the residuals in the east-west, north-south, and vertical directions respectively.

[0121] S4. The joint observation model takes the weights after iterative optimization to fuse the slope radar data and GNSS 3D deformation data according to the weights. The joint observation model combines the observation matrix of the slope radar observation equation and the GNSS observation equation. The expression is as follows:

[0122] .

[0123] is the fusion result X of the joint observation model.

[0124] This embodiment takes a mining area in Xinjiang as an example, and the visualization results after the fusion of part of the slope radar data and part of the GNSS three-dimensional deformation data are shown as follows: Figure 11 As shown, Figure 11 The visualization results of the 3D displacement field after the fusion of GNSS and slope radar data are shown. In the example of a mining area in Xinjiang, the comparison results of the detection accuracy of slope radar data, GNSS 3D deformation data and the combined observation fusion data are as follows: Figure 12 As shown in the figure, it can be seen that the RMSE of the data after the joint observation fusion of the present invention is significantly better than that of using GNSS three-dimensional deformation data or slope radar data alone, indicating that compared with GNSS three-dimensional deformation data or slope radar data, the data after the joint observation fusion can more accurately reflect the three-dimensional deformation field of the slope, thereby improving the monitoring quality.

[0125] A joint observation and fusion system for slope radar and GNSS three-dimensional deformation data includes a slope radar data processing module, a GNSS three-dimensional deformation data processing module, and a joint observation model. The slope radar data processing module is used to obtain slope radar data and perform discrete value elimination processing. The GNSS three-dimensional deformation data processing module is used to obtain GNSS three-dimensional deformation data and perform discrete value elimination processing and spatial interpolation processing. The joint observation model includes a coordinate conversion calculation module, which is used to calculate the displacement data of the slope radar data and convert it to a BLH coordinate system. The coordinate conversion calculation module calibrates the slope radar data and the GNSS three-dimensional deformation data to the same BLH coordinate system. The weighted iterative optimization expression of the two types of observation data, slope radar data and GNSS three-dimensional deformation data, in the joint observation model is as follows: , Indicates the category of observation data, Represents the weight corresponding to the observed data category i after iteration, Represents the weight corresponding to the observed data category i before iteration, until the weight variances of the two types of observed data are approximately equal, that is, The joint observation model uses the iteratively optimized weights to fuse the slope radar data and the GNSS three-dimensional deformation data according to the weights.

[0126] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A joint observation and fusion method for slope radar and GNSS three-dimensional deformation data, characterized by: The methods include: S1. Obtain slope radar data and perform discrete value elimination processing, and obtain GNSS three-dimensional deformation data and perform discrete value elimination processing and spatial interpolation processing; S2. Calculate the displacement data of the slope radar data and convert it into the BLH coordinate system; S3. Construct a joint observation model of slope radar data and GNSS 3D deformation data in the BLH coordinate system. The weighted iterative optimization expression of the two types of observation data in the joint observation model is as follows: , Indicates the category of observation data, Represents the weight corresponding to the observed data category i after iteration, Represents the weight corresponding to the observed data category i before iteration, until the weight variances of the two types of observed data are approximately equal, that is, ; S4. The joint observation model takes the weights after iterative optimization to fuse the slope radar data and the GNSS three-dimensional deformation data according to the weights.

2. The joint observation and fusion method of slope radar and GNSS 3D deformation data according to claim 1 is characterized by: In method S3, the joint observation model is solved based on the least squares principle to minimize the residual error, and the result expression is as follows: ,in is the coefficient matrix, is the transpose of the coefficient matrix, is the weight matrix, is the observation matrix of the joint observation model.

3. The joint observation and fusion method of slope radar and GNSS 3D deformation data according to claim 2 is characterized by: The joint observation model consists of the slope radar observation equation and the GNSS observation equation. The slope radar observation equation is expressed as follows: ;in, is the radar line of sight direction deformation value, are the projection vectors of the longitude, latitude and elevation directions of the slope radar data, are the deformation values ​​in the longitude, latitude and elevation directions to be calculated, is the initial displacement of the radar line of sight, are the initial deformation values ​​in longitude, latitude, and elevation directions respectively; The GNSS observation equation is expressed as follows: ,in are the deformation values ​​in the longitude, latitude and elevation directions decomposed from the GNSS three-dimensional deformation data. are the deformation values ​​in the longitude, latitude and elevation directions to be calculated, They are the residuals in the east-west, north-south, and vertical directions respectively; Joint observation model combines the observation matrix of slope radar observation equation and GNSS observation equation The expression is as follows: ； is the fusion result X of the joint observation model.

4. The joint observation and fusion method of slope radar and GNSS 3D deformation data according to claim 1 is characterized by: In method S1, the discrete value removal processing method of GNSS 3D deformation data is as follows: The GNSS 3D deformation data is standardized, and the mean of the GNSS 3D deformation data within the window is calculated using a sliding window. Data points that deviate from the sliding window mean are preliminarily determined to be discrete values. The discrete values ​​that were initially separated were classified by support vector machine with the purpose of maximizing the classification interval, using labels +1 to represent normal data points and -1 to represent discrete data points; The constraint expression of the support vector machine is: , Represents the displacement, velocity, and acceleration vector combination of each data point input, Indicates the category of the sample after rough separation, is the hyperplane normal vector, perpendicular to the decision hyperplane; It is a bias term and is used to adjust the position of the decision hyperplane. The constraints of the vector machine ensure that each data point is classified on one side of the hyperplane and the distance from the decision hyperplane is at least 1. By the hyperplane normal vector and bias The distance between each data point and the hyperplane is calculated. If the distance is less than or equal to -1, the data point is determined to be a discrete value and is removed.

5. The joint observation and fusion method of slope radar and GNSS 3D deformation data according to claim 4 is characterized by: For discrete values ​​that cannot be completely separated after initial separation, soft intervals are introduced by introducing relaxation variables. ,by As a purpose, the constraint expression is as follows: ,in It is a hyperparameter used to control the soft interval maximization and error penalty, and further separate and eliminate discrete values ​​that cannot be completely separated.

6. The joint observation and fusion method of slope radar and GNSS 3D deformation data according to claim 1 is characterized by: The discrete value removal processing method of slope radar data is as follows: Use proximity analysis to initially detect discrete values, then use Euclidean distance to calculate the neighborhood set of each data point and the mean and standard deviation of the line of sight displacement within the area, and use the following formula to determine suspected discrete values: ,in , are the mean and variance in the domain, is the displacement of data point j; Parameters preset based on the characteristics of historical slope radar data; The random forest decision tree model is constructed by using the split node to select the optimal split feature and threshold through the Gini index to maximize the reduction of the Gini index after splitting. , 、 They are normal value nodes and discrete value nodes after the slope radar data is split. 、 are the number of samples of normal value and discrete value nodes respectively, is the total number of samples of slope radar data, The Gini index is the normal value, is the Gini index of discrete values; The random forest decision tree model determines the discrete values ​​in the slope radar data by majority voting of all decision trees and eliminates them.

7. The joint observation and fusion method of slope radar and GNSS 3D deformation data according to claim 1 is characterized by: In method S1, the spatial interpolation of GNSS 3D deformation data is performed using the Kriging method using spatial correlation. The Kriging interpolation formula is as follows: ,in Unknown bit The predicted value of is the known data point numbered i The value on is the kriging weight numbered i.

8. The joint observation and fusion method of slope radar and GNSS three-dimensional deformation data according to claim 1 is characterized by: In method S2, the three-dimensional displacement conversion relationship is expressed as follows: ,in are the projection vectors of the longitude, latitude and elevation directions of the slope radar data, are the coordinates in geocentric rectangular coordinates, The BLH coordinates of the center point of the radar device for slope radar data.

9. A joint observation and fusion system for slope radar and GNSS three-dimensional deformation data, characterized by: It includes a slope radar data processing module, a GNSS three-dimensional deformation data processing module and a joint observation model. The slope radar data processing module is used to obtain slope radar data and perform discrete value elimination processing. The GNSS three-dimensional deformation data processing module is used to obtain GNSS three-dimensional deformation data and perform discrete value elimination processing and spatial interpolation processing. The joint observation model includes a coordinate conversion calculation module. The coordinate conversion calculation module is used to calculate the displacement data of the slope radar data and convert it to the BLH coordinate system. The coordinate conversion calculation module calibrates the slope radar data and the GNSS three-dimensional deformation data to the same BLH coordinate system. The weighted iterative optimization expression of the two types of observation data, slope radar data and GNSS three-dimensional deformation data, in the joint observation model is as follows: , Indicates the category of observation data, Represents the weight corresponding to the observed data category i after iteration, Represents the weight corresponding to the observed data category i before iteration, until the weight variances of the two types of observed data are approximately equal, that is, ; The joint observation model takes the iteratively optimized weights to fuse the slope radar data and the GNSS three-dimensional deformation data according to the weights.

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