Small-area bds-3 real-time normal high intelligent measurement method and intelligent measurement system based on deep learning

Abstract

The application discloses a small-area BDS-3 real-time normal high intelligent measurement method and an intelligent measurement system based on deep learning, and comprises the following steps: 1, preprocessing and standardizing space remodeling of sampling point data measured by BDS-3 RTK; 2, stripping a wide-area background field component from original observation; 3, introducing a spatial correlation measure model with a second-order continuous characteristic, introducing an adaptive observation noise correction operator, and constructing a full-field covariance matrix to absorb random observation noise and constrain a fitting process; 4, introducing a super parameter group and constructing a target loss function of deep learning; 5, establishing a back propagation path under a deep learning architecture; performing deep optimization on an evidence function of the constructed model to obtain an optimal super parameter group; 6, performing multi-scale linear superposition on the wide-area background field component and a local refinement correction component to realize reconstruction; and 7, outputting a system result. The model constructed based on the Beidou positioning technology effectively improves the robustness of the model through deep learning.

Description

Technical Field

[0001] This invention relates to the field of elevation measurement technology, and in particular to a small-area BDS-3 real-time normal high-intelligence measurement method and intelligent measurement system based on deep learning. Background Technology

[0002] Normal height is an elevation system based on a quasi-geoid, used to describe the vertical position of points on the ground. While traditional leveling methods offer extremely high accuracy, they suffer from limitations such as low operational efficiency and high line-of-sight requirements in complex areas. With the full completion of the BeiDou-3 (BDS-3) system, using BeiDou positioning technology with BDS-3 RTK to obtain high-precision geodetic height and convert it into normal height required for engineering applications has become an efficient and real-time alternative. The accuracy of this elevation conversion largely depends on the quality of the constructed elevation anomaly model.

[0003] In practical surveying projects, control points are often scattered, and due to cost and geographical constraints, the number of known leveling control points is limited and their distribution is uneven. Therefore, existing methods for transforming highly anomalies mainly include plane fitting, quadratic surface fitting, and polynomial fitting. However, in application scenarios involving small, non-uniformly sparse areas:

[0004] First, because the measurement points are relatively scattered, and traditional polynomial fitting is a global parameter model, although it can capture the long-wave trend of the gravity field, it is weak in absorbing the nonlinear residuals caused by local terrain undulations or gravity anomalies. Forcibly increasing the order of the model for fitting can easily cause Runge phenomenon under sparse point distribution.

[0005] Second, when existing interpolation algorithms process sparse control points, due to the lack of spatial continuity constraints, the model surface often experiences slope jumps at control points, forming cusp phenomena (local numerical singularities), which seriously deviates from the physical characteristics of the geoid as a smooth gravity equipotential surface.

[0006] Third, while BDS-3 RTK observations offer high initial accuracy, they still contain multipath errors or residual tropospheric noise in complex environments. Traditional methods typically force the model surface to pass through every observation point, which amplifies local noise into model errors, affecting overall fitting accuracy and exhibiting poor robustness. Summary of the Invention

[0007] To address the aforementioned issues, this invention provides a real-time, normal, and highly intelligent measurement method and system for small-area BDS-3 based on deep learning. Based on BeiDou positioning technology using BDS-3 RTK, a real-time, normal, and highly intelligent measurement method is constructed in a sparse planar environment. This method can balance global stability, ensure physical second-order smoothness, and possess self-awareness of accuracy, effectively solving the accuracy problem of planar detection networks. The constructed model effectively improves its robustness through deep learning.

[0008] Definitions:

[0009] BDS-3: BeiDou-3 is a global satellite navigation system independently developed by China, providing services such as positioning, navigation, timing, and short message communication.

[0010] RTK: Real-time kinematic, a real-time dynamic carrier phase differential technology.

[0011] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0012] A deep learning-based method for real-time, normal, and highly intelligent measurement of small-area BDS-3 systems includes the following steps:

[0013] Step S1: Preprocess and standardize the spatial reshaping of the sampling point data within the measurement area obtained by BDS-3 RTK;

[0014] Step S2: Construct a nonlinear geometric feature space mapping operator to determine the global geometric shape of the measurement area, thereby extracting the wide-area background field component from the original observation, and simultaneously constructing the original feature expression of the local refined correction component.

[0015] Step S3: Calculate the standardized Euclidean distance between points in the feature space, introduce a spatial correlation measure model with second-order continuous characteristics to establish physical smoothing constraints for local refinement correction components, and introduce an adaptive observation noise correction operator to construct a full-field covariance matrix to absorb random observation noise and constrain the fitting process.

[0016] Step S4: Introduce a set of hyperparameters and construct a model evidence function based on minimizing structural risk as the target loss function for deep learning;

[0017] Step S5: Perform partial derivative analysis and gradient iteration for the hyperparameter set. By performing partial derivative analysis on the model evidence function with respect to the hyperparameter set, the backpropagation path under the deep learning architecture is established using the obtained gradient vector. The sensitivity of the prediction bias to each parameter is accurately calculated by iteratively solving the optimal solution in the hyperparameter set. In the process, the optimal gradient iteration direction for updating the model weights is determined, so as to shrink the model parameters from the data error. Deep optimization is performed on the constructed model evidence function to obtain the optimal hyperparameter set.

[0018] Step S6: Construct a cascaded reconstruction operator to reconstruct the wide-area background field component and the local refinement correction component by multi-scale linear superposition, and output the posterior variance index simultaneously.

[0019] Step S7: Calculate the RMSE and median deviation of the model residuals at the known points. If RTK gross errors are detected, the system automatically reduces the weight of the point using the adaptive observation noise correction operator, and the system outputs the results.

[0020] Preferably, step S1 specifically includes the following steps:

[0021] Step S101: Obtain the raw observation data measured by BDS-3 RTK, including data for each sampling point. Coordinates, normal elevation value, and geodetic elevation value;

[0022] Step S102: Subtract the geodetic elevation value from the normal elevation value of each sampling point to obtain the elevation anomaly value of the sampling points in the small area.

[0023] Step S103: Extract sampling points within the measurement area Using coordinates as input features, and extracting elevation outliers as observation targets, a raw feature space based on the data is constructed. ,in This indicates the number of measurements taken by BDS-3 RTK. The coordinates of the sampling points totaled [number]. One sampling point; For the first The geodetic elevation values ​​of each sampling point; For the first Normal elevation values ​​of each sampling point; For the first Elevation anomalies at individual sampling points;

[0024] Step S104: Read in the observation data of the measurement area to obtain the sample set. ; in the measurement area From the known points, the known points at the perimeter of the measurement area are selected as the control set to construct the spatial outer convex hull geometry; the relatively dispersed discrete points within the measurement area are selected as the test set; and the known points are... Each sampling point is divided into a control set. and test set ;

[0025] Step S105: Perform standardized spatial reshaping through standardized feature mapping of coordinates:

[0026] ;

[0027] In the formula, They are respectively sampling points Coordinate mean; They are respectively sampling points Coordinate standard deviation; and Represents the mapped coordinates.

[0028] Preferably, step S2 specifically includes the following steps:

[0029] Step S201: Construct a nonlinear geometric feature space mapping operator to determine the global geometric shape of the measurement area, targeting the first... Nonlinear geometric feature space mapping operator constructed from sampling points for:

[0030] ;

[0031] In the formula, 1 represents the regional translation reference; Indicates in Slope along the axial direction; Indicates in Slope along the axial direction; Indicates in The degree of concavity or convexity along the axial direction; Indicates when Axial direction and Coordinated changes when the axial direction is not independent; Indicates in The degree of concavity or convexity along the axial direction;

[0032] Step S202: Construct the spatial basis function measure matrix using the basis vector mapping rule. :

[0033] ;

[0034] In the formula, For the first Each sampling point is Slope along the axial direction; For the first Each sampling point is Slope along the axial direction;

[0035] Step S203: Construct the wide-area background field coefficient vector :

[0036] ;

[0037] In the formula, Represents the translation datum for the region; Indicates in Slope along the axial direction; Indicates in Slope along the axial direction; Indicates in The degree of concavity or convexity along the axial direction; Indicates when Axial direction and Coordinated changes when the axial direction is not independent; Indicates in The degree of concavity or convexity along the axial direction;

[0038] Step S204: Solve for the wide-area background field coefficient vector using the least squares algorithm. :

[0039] ;

[0040] In the formula, for An elevation outlier vector of each sampling point ;

[0041] Step S205: Strip away the wide-area background field and simultaneously construct the original feature representation of the local refined and corrected components:

[0042] Introducing nonlinear residual signals , ; Expanded to:

[0043] ;

[0044] In the formula, For wide-area background field components, This refers to the original feature representation of the locally refined and corrected components constructed synchronously.

[0045] Preferably, step S3 specifically includes the following steps:

[0046] Step S301: Calculate the two known points in the mapped space. Point and Standardized Euclidean distance between points :

[0047] Step S302: Construct a spatial correlation measurement model with second-order continuity properties. To establish physical smoothing constraints for local refinement correction components;

[0048] ;

[0049] In the formula, The process variance is used to represent the fluctuation energy of the residual component in the local refinement correction component; The relevant length parameter is introduced to determine the influence radius of local disturbances in the local refinement correction component;

[0050] Step S303: Introduce an adaptive observation noise correction operator. Construct the full-field covariance matrix containing the noisy operator. :

[0051] ;

[0052] In the formula, It is an identity matrix.

[0053] Preferably, step S4 specifically includes the following steps:

[0054] Step S401: Introduce the set of hyperparameters to be solved. :

[0055] ;

[0056] Step S402: Construct a model evidence function based on structural risk minimization. :

[0057] ;

[0058] In the formula, det is a function that calculates the determinant of a matrix;

[0059] In a deep learning architecture, this function serves as the target loss function, measuring the degree of matching between the nonlinear residual signal and the full-field covariance matrix, and is used to guide the model to extract higher-order features from the original observation data.

[0060] Preferably, step S5 specifically includes the following steps:

[0061] Step S501: Define residual weight components For any hyperparameter Then the derivative of the model evidence function is:

[0062] ;

[0063] In the formula, ; To find the trace of the matrix;

[0064] Step S502: Perform partial derivative analysis of the model evidence function with respect to the hyperparameter set. Use the derivative of the model evidence function to establish the backpropagation path of deep learning. Use the gradient vector to quantify the sensitivity of the model prediction bias to the parameters of each neuron, thereby determining the optimal weight update path in the hyperparameter space.

[0065] For adaptive noise correction operators The expression can be represented as:

[0066] ;

[0067] For process variance The expression can be represented as:

[0068] ;

[0069] In the formula, For the correlation matrix, a spatial correlation measure model with second-order continuous properties. The relationship is ;

[0070] For the relevant length parameters The expression can be represented as:

[0071] ;

[0072] In the formula, It is a nonlinear residual signal The corrected residual weight components at this point; Represents the coordinates of an element in the overall covariance matrix;

[0073] When a non-uniform distribution of points in the detection area is detected, the model increases the correlation length to expand the radius of spatial influence and eliminate possible numerical faults in the blank areas of the points.

[0074] Non-physical jumps caused by observation noise were detected in local parts of the model, and an adaptive noise correction operator was added adaptively. Combining for nonlinear residual signals The adaptive adjustment allows the model to suppress and eliminate possible numerical singular cusps through mathematical mechanisms;

[0075] Step S503: Iteratively optimize the model evidence function based on minimizing structural risk. Minimize the hyperparameters to obtain the optimal set of hyperparameters.

[0076] Preferably, step S6 specifically includes the following steps:

[0077] Step S601: Obtain the optimal hyperparameter set Then, construct the cascaded reconstruction operator. Treatment of prediction points Perform full-field elevation anomaly modeling and cascade reconstruction operators. for:

[0078] ;

[0079] In the formula, For the prediction point Wide-area background field components, For local refinement and correction of components;

[0080] Step S602: Output each point to be predicted based on the posterior variance operator. Uncertainty indicators :

[0081] ;

[0082] In the formula, Points to be predicted With each known point The correlation vector between them .

[0083] Preferably, step S7 specifically includes the following steps:

[0084] Step S701: Calculate the model residuals at all known points. ,in For the corresponding number The elevation anomaly model value obtained by the cascaded reconstruction operator at each sampling point;

[0085] Step S702: Calculate the root mean square error (RMSE) and median deviation of all model residuals, identify outliers, and if residuals at individual points exceed the threshold due to RTK gross errors, then use the introduced adaptive observation noise correction operator. The model will automatically reduce the weight of that point;

[0086] Step S703: Output the result.

[0087] Correspondingly, a deep learning-based small-area BDS-3 real-time normal high-intelligence measurement system is provided. The measurement system includes a processor and a memory. The memory stores at least one instruction, which is loaded and executed by the processor to implement the deep learning-based small-area BDS-3 real-time normal high-intelligence measurement method described above.

[0088] The beneficial effects of this invention are:

[0089] First, the deep learning-based small-area BDS-3 real-time normal high-intelligence measurement method proposed in this invention constructs a hierarchical coupled fitting architecture, overcoming the limitation of traditional global parameter fitting in capturing nonlinear residuals in non-uniform scenarios. Unlike the single parameter fitting of traditional models, this invention utilizes deep learning to refine the modeling of local residuals and BeiDou positioning technology, significantly improving the feature perception capability of complex terrain. By constructing a nonlinear geometric feature space mapping operator as the input feature encoding, and strategically selecting edge points in the control set to construct the spatial outer envelope convex hull geometry, this deep learning strategy effectively suppresses the Runge phenomenon and extrapolation divergence problems that are easily caused by traditional deep neural networks under sparse point source constraints.

[0090] Secondly, this invention first utilizes nonlinear geometric feature operators to propose a global baseline, and then uses a deep training loop to fill in local details, enabling the model to possess self-awareness of accuracy. This coupled mode of "global trend + local depth correction" leverages the efficiency of deep learning in processing massive nonlinear residuals while preserving the geometric rigor required for surveying engineering. This invention effectively solves the problems of numerical singular cusps and Runge phenomenon in non-uniform point distribution environments, significantly improving the automation level of elevation measurement in engineering under discrete point source constraints while ensuring millimeter-level conversion accuracy.

[0091] Third, by introducing second-order continuous physical constraints and noise correction, this invention completely solves the problem of numerical singular cusps in modeling. In response to the slope jumps and cusps caused by the lack of spatial constraints at sparse points in existing interpolation algorithms, this invention constructs a spatial correlation measure model with second-order continuous characteristics, so that the surface physically conforms to the characteristics of a smooth equipotential surface. At the same time, by coupling an adaptive observation noise correction operator, the model can dynamically absorb the random observation noise of BDS-3 RTK, avoid the amplification of local errors, and ensure the smoothness and robustness of the reconstructed surface.

[0092] Fourth, this invention establishes an adaptive feedback control loop for the model evidence function based on minimizing structural risk using Gaussian process regression. It achieves automated hyperparameter locking through gradient optimization, solving the problem of reliance on manual weighting in traditional methods. The constructed cascaded reconstruction operator addresses the global instability issue. Furthermore, the model utilizes a posterior variance operator to synchronously output uncertainty indicators for predicted points. By quantifying information gain, it objectively reflects the accuracy degradation caused by missing control points, providing a digital and transparent quality assessment basis for successful elevation conversion under non-uniform point distribution conditions.

[0093] Fifth, the specific embodiments of this invention cite actual cases to prove the effectiveness and feasibility of this invention. The results show that among all 51 points, the root mean square (RMS) of the 40 measurement points selected as the control set is 5.98 mm, and the root mean square (RMS) of the 11 measurement points selected as the independent test set is 6.91 mm. Both are at the millimeter level and meet the specifications for high-precision measurement, which can replace third and fourth order leveling. Attached Figure Description

[0094] Figure 1 This is a refined model diagram of the model plane datum and elevation anomaly in an embodiment of the present invention;

[0095] Figure 2 This is a schematic diagram of the spatial weight field distribution in an embodiment of the present invention.

[0096] Figure 3 This is a schematic diagram illustrating the evaluation of the accuracy and stability of test sample points in an embodiment of the present invention. Detailed Implementation

[0097] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0098] A deep learning-based method for real-time, normal, and highly intelligent measurement of small-area BDS-3 systems includes the following steps:

[0099] Step S1: Preprocess and standardize the spatial reshaping of the sampling point data within the measurement area obtained by BDS-3 RTK.

[0100] Preferably, step S1 specifically includes the following steps:

[0101] Step S101: Obtain the raw observation data measured by BDS-3 RTK, including data for each sampling point. Coordinates, normal elevation value, and geodetic elevation value;

[0102] Step S102: Subtract the geodetic elevation value from the normal elevation value of each sampling point to obtain the elevation anomaly value of the sampling points in the small area.

[0103] Step S103: Extract sampling points within the measurement area Using coordinates as input features, and extracting elevation outliers as observation targets, a raw feature space based on the data is constructed. ,in This indicates the number of measurements taken by BDS-3 RTK. The coordinates of the sampling points totaled [number]. One sampling point; For the first The geodetic elevation values ​​of each sampling point; For the first Normal elevation values ​​of each sampling point; For the first Elevation anomalies at individual sampling points;

[0104] Step S104: Read in the observation data of the measurement area to obtain the sample set. ; in the measurement area To ensure the baseline stability of the subsequent cascaded reconstruction operator among the known points, the known points at the perimeter of the measurement area are selected as the control set to construct the spatial outer envelope convex hull geometry. This point selection effectively avoids the divergence problem caused by extrapolation. Discrete points with relatively dispersed known points within the measurement area are selected as the test set. This selection strategy aims to simulate extreme engineering situations that may occur when points are dispersed within a non-uniform small region. Following the above point selection strategy, Each sampling point is divided into a control set. and test set control set Used to calculate the wide-area background field coefficient vector and optimizing hyperparameter sets In step S201, sampling points from the control set (i.e., control points, which are sampling points in the control set whose locations are known within the measurement area, whose elevation anomalies are determined, and which are included in the model training process) are used to construct a nonlinear geometric feature space mapping operator. The wide-area background field coefficient vector is solved by the least squares method to establish a global benchmark describing the wide-area geometry and to provide sampling point data for subsequent matrix and model construction.

[0105] test set It can be used to independently verify the generalization ability and extrapolation stability of the model, and can also be used in conjunction with the verification of accuracy self-awareness and robustness mechanisms.

[0106] Step S105: Due to different coordinate systems The scale differences are significant, so standardization is necessary to ensure the accuracy of subsequent correlation measurement calculations. This is achieved through standardized spatial reshaping using coordinate-standardized feature mapping.

[0107] ;

[0108] In the formula, They are respectively sampling points Coordinate mean; They are respectively sampling points Coordinate standard deviation; and This represents the mapped coordinates. This step has two purposes: first, to eliminate the singularity of the covariance matrix that is easily caused by large numerical coordinates under different coordinate systems; and second, to reconstruct the spatial feature benchmark by constructing a near-square region in the feature space. Through mean shifting and standard deviation scaling, large numerical coordinates under different coordinate systems are mapped to a near-square standardized feature region to solve potential numerical singularity problems.

[0109] Step S2: Construct a nonlinear geometric feature space mapping operator to determine the global geometric shape of the measurement area, and then extract the wide-area background field component from the original observation, and simultaneously construct the original feature expression of the local refinement correction component.

[0110] Preferably, step S2 specifically includes the following steps:

[0111] Step S201: Construct a nonlinear geometric feature space mapping operator to determine the global geometric shape of the measurement area, targeting the first... Nonlinear geometric feature space mapping operator constructed from sampling points for:

[0112] ;

[0113] The geoid anomaly on the Earth's surface appears as a smooth curved surface. Using a nonlinear geometric feature space mapping operator, a global framework can be established against a wide-area background field. Six components accurately describe the geometric perception of the region. These six components represent: 1 represents the regional translation datum, reflecting the average level of the geoid anomaly in the survey area; Indicates in Slope along the axial direction; Indicates in Slope along the axial direction, This represents a spatial tilting trend; Indicates in The degree of concavity or convexity along the axial direction; Indicates when Axial direction and Coordinated changes when the axial direction is not independent are used to simulate irregular background undulations in regions; Indicates in The degree of concavity or convexity along the axial direction; It represents the curvature characteristics of the landform.

[0114] Step S202: Construct the spatial basis function measure matrix using the basis vector mapping rule. :

[0115] ;

[0116] In the formula, For the first Each sampling point is Slope along the axial direction; For the first Each sampling point is Slope along the axial direction; the survey area has Given several points, the spatial basis function measure matrix is ​​constructed. for .

[0117] Step S203: Construct the wide-area background field coefficient vector :

[0118] ;

[0119] In the formula, the parameter definition of each term corresponds to the equation in step S201: The regional translation datum reflects the average level of elevation anomalies in the survey area; Indicates in Slope along the axial direction; Indicates in Slope along the axial direction, Corresponding spatial tilt trend; Indicates in The degree of concavity or convexity along the axial direction; Indicates when Axial direction and Coordinated changes when the axial direction is not independent are used to simulate irregular background undulations in regions; Indicates in The degree of concavity or convexity along the axial direction; Corresponding to the curvature characteristics of the landform.

[0120] Step S204: Solve for the wide-area background field coefficient vector using the least squares algorithm. :

[0121] ;

[0122] In the formula, for An elevation outlier vector of each sampling point ;

[0123] Step S205: Strip away the wide-area background field and simultaneously construct the original feature representation of the local refined and corrected components:

[0124] Introducing nonlinear residual signals , ; Expanded to:

[0125] ;

[0126] In the formula, The wide-area background field components are obtained by introducing the wide-area background field coefficient vector after the solution is completed in step S201. The obtained nonlinear geometric feature space mapping operator in the th Theoretical estimate of each sampling point. This refers to the original feature representation of the locally refined and corrected components constructed synchronously, which is also the nonlinear residual signal obtained after stripping. This serves as the data foundation for the subsequent construction of local refinement and correction components.

[0127] Step S3: Calculate the standardized Euclidean distance between points in the feature space, introduce a spatial correlation measure model with second-order continuous characteristics to establish physical smoothing constraints for local refinement correction components, and introduce an adaptive observation noise correction operator to construct a full-field covariance matrix to absorb random observation noise and constrain the fitting process.

[0128] Preferably, step S3 specifically includes the following steps:

[0129] Step S301: Calculate the two known points in the mapped space. Point and Standardized Euclidean distance between points :

[0130] In this invention and It is not a static definition, but rather has a phased interchangeable characteristic, as described here. and The known control set is traversed collaboratively to characterize the autocorrelation topology of the elevation anomaly signal in the survey area, so as to support the spatial correlation measurement model with second-order continuity proposed in step S302.

[0131] Step S302: Construct a spatial correlation measurement model with second-order continuity properties. To establish physical smoothing constraints for local refinement correction components;

[0132] ;

[0133] In the formula, The process variance is used to represent the fluctuation energy of the residual component in the local refinement correction component; the quadratic term in the above equation ensures that the spatial correlation measure model is second-order continuous at the origin, so that the fitting model fully conforms to the physical property that the level surface is a smooth equipotential surface. The relevant length parameter is introduced to determine the influence radius of local disturbances in the local refinement correction component;

[0134] Step S303: Introduce an adaptive observation noise correction operator. Construct the full-field covariance matrix containing the noisy operator. :

[0135] ;

[0136] Adaptive observation noise correction operator It can absorb random observation noise from BDS-3 RTK and eliminate singular cusps (sharp points on the 3D surface caused by overfitting due to errors in some observations during model fitting). In the formula, It is an identity matrix. This is a noise correction term. Its purpose is to address significant errors at a given observation point by increasing the adaptive observation noise correction operator. To identify error points.

[0137] Step S4: Introduce a set of hyperparameters and construct a model evidence function based on minimizing structural risk as the target loss function for deep learning.

[0138] Preferably, step S4 specifically includes the following steps:

[0139] Step S401: Introduce the set of hyperparameters to be solved. :

[0140] ;

[0141] Step S402: According to the Gaussian process regression model theory, the nonlinear residual signal Follows a multivariate normal distribution Construct a model evidence function based on structural risk minimization. :

[0142] ;

[0143] In the formula, det is a function to calculate the determinant of a matrix; N refers to multiple random variables that exhibit normality in their joint distribution, and there may be correlations between the variables.

[0144] Specifically, in this method, there are n known control points. The nonlinear residual signals at each point constitute an n-dimensional random vector that follows a zero-mean multivariate normal distribution and has core features such as zero mean, covariance structure integrity, adaptive embedding of observation noise, and physical consistency.

[0145] In a deep learning architecture, this function serves as the target loss function, measuring the degree of matching between the nonlinear residual signal and the full-field covariance matrix, and is used to guide the model to extract higher-order features from the original observation data.

[0146] Step S5: Perform partial derivative analysis and gradient iteration for the hyperparameter set. By performing partial derivative analysis on the model evidence function with respect to the hyperparameter set, the backpropagation path under the deep learning architecture is established using the obtained gradient vector. The sensitivity of the prediction bias to each parameter is accurately calculated by iteratively solving the optimal solution in the hyperparameter set. In the process, the optimal gradient iteration direction for updating the model weights is determined, so as to shrink the model parameters from the data error. Deep optimization is performed on the constructed model evidence function to obtain the optimal hyperparameter set.

[0147] Preferably, step S5 specifically includes the following steps:

[0148] Step S501: By introducing intermediate variables to perform parameter reshaping, establish the weight component mapping of the nonlinear residual signal after precision matrix correction, and define the residual weight components. According to the principles of calculus, for any hyperparameter Then the derivative of the model evidence function is:

[0149] ;

[0150] In the formula, ; To find the trace of the matrix;

[0151] Step S502: Perform partial derivative analysis of the model evidence function with respect to the hyperparameter set. Use the derivative of the model evidence function to establish the backpropagation path of deep learning. Use the gradient vector to quantify the sensitivity of the model prediction bias to the parameters of each neuron, thereby determining the optimal weight update path in the hyperparameter space.

[0152] The backpropagation path refers to using the chain rule to backpropagate the gradient of the model evidence function with respect to the hyperparameters to the covariance matrix construction layer, thereby achieving adaptive optimization of the hyperparameters.

[0153] The gradient vector represents a vector of the first-order partial derivatives of a multivariate function with respect to all independent variables at a given point, indicating the direction of the function's fastest increase at that point. In this invention, the gradient vector indicates the direction of the fastest change in the model evidence function in the hyperparameter space. During optimization, the gradient vector guides the parameters to be updated in the direction that reduces the model evidence function.

[0154] The optimal weight update path refers to the parameter update sequence in the parameter space that, through optimization algorithms, allows the model's evidence function to converge to a local or global minimum as quickly as possible. In this invention, the hyperparameter set is updated via gradient vectors, and the update path is adaptively adjusted by the curvature of the model's evidence function. This ensures that when sparse regions or noise points are detected, the path automatically biases towards increasing the correlation length. Or adaptive noise correction operator To smooth the surface and suppress overfitting.

[0155] This invention constructs an adaptive feedback control loop for a refined elevation anomaly model by performing partial derivative analysis on the model evidence function with respect to the hyperparameter set. Its purpose is to use gradient vectors to guide parameters to perform self-organized optimization iteration in nonlinear space, thereby achieving automatic absorption of observation noise and accurate capture of spatial topology through mathematical mechanisms.

[0156] For adaptive noise correction operators The expression can be represented as:

[0157] ;

[0158] For process variance The expression can be represented as:

[0159] ;

[0160] In the formula, For the correlation matrix, a spatial correlation measure model with second-order continuous properties. The relationship is ;

[0161] For the relevant length parameters The expression can be represented as:

[0162] ;

[0163] In the formula, It is a nonlinear residual signal The corrected residual weight components at this point; Represents the coordinates of elements in the overall covariance matrix, and represents the uncertainty structure of the model prediction;

[0164] When a non-uniform distribution of points in the detection region is detected, the model increases the correlation length to expand the spatial influence radius, eliminating potential numerical discontinuities in the point blank areas. Alternatively, when the input sample is detected to be in a sparsely distributed spatial region, the model automatically increases the correlation length through gradient guidance to expand the receptive field of the hidden layer neurons, enhancing the correlation length parameter of the spatial autocorrelation topology, thereby physically eliminating potential numerical discontinuities caused by point blank areas. Here, expanding the receptive field of the hidden layer neurons in this invention means, in the spatial correlation measurement model, increasing the correlation length... This allows any known point to have a wider spatial influence on the prediction of elevation anomalies in its surrounding area, which is mathematically equivalent to expanding the input sensing area and enhancing the generalization ability of the constructed model under sparse point conditions.

[0165] When a non-physical jump caused by observation noise is detected in the local model, an adaptive noise correction operator is added adaptively. Combining for nonlinear residual signals The adaptive adjustment allows the model to suppress and eliminate possible numerical singular cusps through mathematical mechanisms;

[0166] Step S503: Iteratively optimize the model evidence function based on minimizing structural risk. Minimize the hyperparameters to obtain the optimal set of hyperparameters.

[0167] Step S6: After obtaining the optimal hyperparameter set, construct a cascaded reconstruction operator to perform multi-scale linear superposition of the wide-area background field components and the local refinement correction components to achieve reconstruction, and simultaneously output the posterior variance index.

[0168] Preferably, step S6 specifically includes the following steps:

[0169] Step S601: Obtain the optimal hyperparameter set Then, construct the cascaded reconstruction operator. Treatment of prediction points Perform full-field elevation anomaly modeling and cascade reconstruction operators. for:

[0170] ;

[0171] In the formula, For the prediction point Wide-area background field components, The local refinement correction component is used; the elevation anomaly model value can be obtained by cascading reconstruction operators.

[0172] Step S602: Output each point to be predicted based on the posterior variance operator. Uncertainty indicators Used to evaluate the reliability of results under non-uniform sampling conditions:

[0173] ;

[0174] In the formula, Points to be predicted With each known point The correlation vector between them Here, the elements within the vector are values ​​from a spatial correlation measure model possessing second-order continuity. In the equation... The information gain term represents the sampling points in the known control set (i.e., Figure 1 The information gain provided by the control points (in the control points) to the prediction points. When the point to be predicted... The closer to the known control point, the stronger the correlation, the greater the information gain, and the lower the uncertainty index. The smaller the value, the better. Therefore, in the blank areas of non-uniform point distribution, this equation reveals the contribution of control point distribution to prediction quality through the information gain term, and can objectively reflect the accuracy degradation caused by the lack of control sets.

[0175] Step S7: Calculate the RMSE and median deviation of the model residuals at known points. If RTK gross errors (40mm or more under high-precision conversion) are detected, the system automatically reduces the weight of the point using the adaptive observation noise correction operator, and the system outputs the results.

[0176] Preferably, step S7 specifically includes the following steps:

[0177] Step S701: Perform closed-loop validation of the model based on statistical principles. The results can be visualized, and the model residuals at all known points can be statistically analyzed. ,in For the corresponding number The elevation anomaly model value obtained by the cascaded reconstruction operator at each sampling point;

[0178] Step S702: Calculate the root mean square error (RMSE) and median deviation of all model residuals, identify outliers, and if residuals at individual points exceed the threshold due to RTK gross errors, then use the introduced adaptive observation noise correction operator. The model will automatically reduce the weight of that point;

[0179] Step S703, Output Results: For example, the model values, actual values, and residuals can be fully output in the console for easy comparison and verification.

[0180] like Figure 1 The diagram visually demonstrates the reconstruction effect from global to local. The X and Y axes represent coordinates, and the Z axis represents the geoid. The units are meters. The upper plane represents the wide-area geometric background field calculated by the least squares method, corresponding to the model plane datum. It establishes a geometric datum framework within the wide area, reflecting the average translation and slope of the elevation in the survey area. The lower surface represents the final model after superimposing local refinement correction components, corresponding to the geoid refinement model. This surface reflects the constraint effect of the spatial correlation measurement model of second-order continuity, ensuring that the surface fully conforms to the characteristics of a smooth equipotential surface at the physical level, eliminating the slope jumps and cusp phenomena that are easily generated at sparse points in traditional interpolation algorithms.

[0181] like Figure 2The diagram illustrates the feature perception capability of this invention in a planar non-uniform point distribution environment. The X and Y axes represent coordinates, and the red rhombus lines illustrate the spatial outer envelope convex hull structure. By selecting edge points of the measurement area to construct the convex hull structure, a stable baseline edge constraint is provided for the model. The background cloud map represents the distribution of the weight energy field. When a non-uniform point distribution in the measurement area is detected, the model increases the correlation length to expand the spatial influence radius, thereby eliminating numerical discontinuities in the blank areas of the points.

[0182] like Figure 3 As shown, statistical data verified the robustness and accuracy self-awareness of the algorithm of this invention. It demonstrated that the elevation residuals of each sample point benefited from the adaptive observation noise correction operator. The model can dynamically absorb the random observation noise of BDS-3 RTK. Even if there are RTK gross errors at individual points, the system can automatically identify and reduce the weights to ensure that the overall accuracy remains stable within the excellent range. The error bar range of each point determined the uncertainty index. The quantitative information gain objectively reflected the accuracy decay caused by the lack of control points, providing a basis for quality assessment of the measurement results.

[0183] Correspondingly, a deep learning-based small-area BDS-3 real-time normal high-intelligence measurement system is provided. The measurement system includes a processor and a memory. The memory stores at least one instruction, which is loaded and executed by the processor to implement the deep learning-based small-area BDS-3 real-time normal high-intelligence measurement method described above.

[0184] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A small-area BDS-3 real-time normal high-intelligence measurement method based on deep learning, characterized in that, Includes the following steps: Step S1: Preprocess and standardize the spatial reshaping of the sampling point data within the measurement area obtained by BDS-3 RTK; Step S2: Construct a nonlinear geometric feature space mapping operator to determine the global geometric shape of the measurement area, thereby extracting the wide-area background field component from the original observation, and simultaneously constructing the original feature expression of the local refined correction component. Step S3: Calculate the standardized Euclidean distance between points in the feature space, introduce a spatial correlation measure model with second-order continuous characteristics to establish physical smoothing constraints for local refinement correction components, and introduce an adaptive observation noise correction operator to construct a full-field covariance matrix to absorb random observation noise and constrain the fitting process. Step S4: Introduce a set of hyperparameters and construct a model evidence function based on minimizing structural risk as the target loss function for deep learning; Step S5: Perform partial derivative analysis and gradient iteration calculation on the hyperparameter set. By performing partial derivative analysis on the model evidence function with respect to the hyperparameter set, the backpropagation path under the deep learning architecture is established using the obtained gradient vector. The sensitivity of the prediction bias to each parameter is accurately calculated by iteratively solving the optimal solution in the hyperparameter set. In the process, the optimal gradient iteration direction for updating the model weights is determined, so as to shrink the model parameters from the data error. Deep optimization is performed on the constructed model evidence function to obtain the optimal hyperparameter set; Step S6: Construct a cascaded reconstruction operator to reconstruct the wide-area background field component and the local refinement correction component by multi-scale linear superposition, and output the posterior variance index simultaneously. Step S7: Calculate the RMSE and median deviation of the model residuals at the known points. If RTK gross errors are detected, the system automatically reduces the weight of the point using the adaptive observation noise correction operator, and the system outputs the results.

2. The small-area BDS-3 real-time normal high-intelligence measurement method based on deep learning according to claim 1, characterized in that, Step S1 specifically includes the following steps: Step S101: Obtain the raw observation data measured by BDS-3 RTK, including data for each sampling point. Coordinates, normal elevation value, and geodetic elevation value; Step S102: Subtract the geodetic elevation value from the normal elevation value of each sampling point to obtain the elevation anomaly value of the sampling points in the small area. Step S103: Extract sampling points within the measurement area Using coordinates as input features, and extracting elevation outliers as observation targets, a raw feature space based on the data is constructed. ,in This indicates the number of measurements taken by BDS-3 RTK. The coordinates of the sampling points totaled [number]. One sampling point; For the first The geodetic elevation values ​​of each sampling point; For the first Normal elevation values ​​of each sampling point; For the first Elevation anomalies at individual sampling points; Step S104: Read in the observation data of the measurement area to obtain the sample set. ; in the measurement area From the known points, the known points at the perimeter of the measurement area are selected as the control set to construct the spatial outer convex hull geometry; the relatively dispersed discrete points within the measurement area are selected as the test set; and the known points are... Each sampling point is divided into a control set. and test set ; Step S105: Perform standardized spatial reshaping through standardized feature mapping of coordinates: ； In the formula, They are respectively sampling points Coordinate mean; They are respectively sampling points Coordinate standard deviation; and Represents the mapped coordinates.

3. The small-area BDS-3 real-time normal high-intelligence measurement method based on deep learning according to claim 2, characterized in that, Step S2 specifically includes the following steps: Step S201: Construct a nonlinear geometric feature space mapping operator to determine the global geometric shape of the measurement area, targeting the first... Nonlinear geometric feature space mapping operator constructed from sampling points for: ； In the formula, 1 represents the regional translation reference; Indicates in Slope along the axial direction; Indicates in Slope along the axial direction; Indicates in The degree of concavity or convexity along the axial direction; Indicates when Axial direction and Coordinated changes when the axial direction is not independent; Indicates in The degree of concavity or convexity along the axial direction; Step S202: Construct the spatial basis function measure matrix using the basis vector mapping rule. : ； In the formula, For the first Each sampling point is at Slope along the axial direction; For the first Each sampling point is at Slope along the axial direction; Step S203: Construct the wide-area background field coefficient vector : ； In the formula, Represents the translation datum for the region; Indicates in Slope along the axial direction; Indicates in Slope along the axial direction; Indicates in The degree of concavity or convexity along the axial direction; Indicates when Axial direction and Coordinated changes when the axial direction is not independent; Indicates in The degree of concavity or convexity along the axial direction; Step S204: Solve for the wide-area background field coefficient vector using the least squares algorithm. : ； In the formula, for An elevation outlier vector of each sampling point ; Step S205: Strip away the wide-area background field and simultaneously construct the original feature representation of the local refined and corrected components: Introducing nonlinear residual signals , ; Expanded to: ； In the formula, For wide-area background field components, This refers to the original feature representation of the locally refined and corrected components constructed synchronously.

4. The small-area BDS-3 real-time normal high-intelligence measurement method based on deep learning according to claim 3, characterized in that, Step S3 specifically includes the following steps: Step S301: Calculate the two known points in the mapped space. Point and Standardized Euclidean distance between points : Step S302: Construct a spatial correlation measurement model with second-order continuity properties. To establish physical smoothing constraints for local refinement correction components; ； In the formula, The process variance is used to represent the fluctuation energy of the residual component in the local refinement correction component; The relevant length parameter is introduced to determine the influence radius of local disturbances in the local refinement correction component; Step S303: Introduce an adaptive observation noise correction operator. Construct the full-field covariance matrix containing the noisy operator. : ； In the formula, It is an identity matrix.

5. The deep learning-based small-region BDS-3 real-time normal high-intelligence measurement method according to claim 4, characterized in that, Step S4 specifically includes the following steps: Step S401: Introduce the set of hyperparameters to be solved. : ； Step S402: Construct a model evidence function based on structural risk minimization. : ； In the formula, det is a function that calculates the determinant of a matrix; In a deep learning architecture, this function serves as the target loss function, measuring the degree of matching between the nonlinear residual signal and the full-field covariance matrix, and is used to guide the model to extract higher-order features from the original observation data.

6. The deep learning-based small-region BDS-3 real-time normal high-intelligence measurement method according to claim 5, characterized in that, Step S5 specifically includes the following steps: Step S501: Define residual weight components For any hyperparameter Then the derivative of the model evidence function is: ； In the formula, ; To find the trace of the matrix; Step S502: Perform partial derivative analysis of the model evidence function with respect to the hyperparameter set. Use the derivative of the model evidence function to establish the backpropagation path of deep learning. Use the gradient vector to quantify the sensitivity of the model prediction bias to the parameters of each neuron, thereby determining the optimal weight update path in the hyperparameter space. For adaptive noise correction operators The expression can be represented as: ； For process variance The expression can be represented as: ； In the formula, For the correlation matrix, a spatial correlation measure model with second-order continuous properties. The relationship is ; For the relevant length parameters The expression can be represented as: ； In the formula, It is a nonlinear residual signal The corrected residual weight components at this point; Represents the coordinates of an element in the overall covariance matrix; When a non-uniform distribution of points in the detection area is detected, the model increases the correlation length to expand the radius of spatial influence and eliminate possible numerical faults in the blank areas of the points. Non-physical jumps caused by observation noise were detected in local parts of the model, and an adaptive noise correction operator was added adaptively. Combining for nonlinear residual signals The adaptive adjustment allows the model to suppress and eliminate possible numerical singular cusps through mathematical mechanisms; Step S503: Iteratively optimize the model evidence function based on minimizing structural risk. Minimize the hyperparameters to obtain the optimal set of hyperparameters.

7. The deep learning-based small-region BDS-3 real-time normal high-intelligence measurement method according to claim 6, characterized in that, Step S6 specifically includes the following steps: Step S601: Obtain the optimal hyperparameter set Then, construct the cascaded reconstruction operator. Treatment of prediction points Perform full-field elevation anomaly modeling and cascade reconstruction operators. for: ； In the formula, For the prediction point Wide-area background field components, For local refinement and correction of components; Step S602: Output each point to be predicted based on the posterior variance operator. Uncertainty indicators : ； In the formula, Points to be predicted With each known point The correlation vector between them .

8. The deep learning-based small-region BDS-3 real-time normal high-intelligence measurement method according to claim 7, characterized in that, Step S7 specifically includes the following steps: Step S701: Calculate the model residuals at all known points. ,in For the corresponding number The elevation anomaly model value obtained by the cascaded reconstruction operator at each sampling point; Step S702: Calculate the root mean square error (RMSE) and median deviation of all model residuals, identify outliers, and if residuals at individual points exceed the threshold due to RTK gross errors, then use the introduced adaptive observation noise correction operator. The model will automatically reduce the weight of that point; Step S703: Output the result.

9. A small-area BDS-3 real-time normal high-intelligence measurement system based on deep learning, characterized in that, The measurement system includes a processor and a memory, the memory storing at least one instruction, which is loaded and executed by the processor to implement the deep learning-based small-area BDS-3 real-time normal high-intelligence measurement method as described in any one of claims 1-8.

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