CN113532397B - Regional elevation anomaly fitting method based on expansion algorithm - Google Patents

Regional elevation anomaly fitting method based on expansion algorithm Download PDF

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CN113532397B
CN113532397B CN202110769067.1A CN202110769067A CN113532397B CN 113532397 B CN113532397 B CN 113532397B CN 202110769067 A CN202110769067 A CN 202110769067A CN 113532397 B CN113532397 B CN 113532397B
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赵鹏宇
侯春萍
侯永宏
王致芃
刘洪琛
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Abstract

The invention relates to an extension algorithm-based regional elevation anomaly fitting method, which comprises the following steps: the method comprises the steps of obtaining GNSS leveling data, combining plane coordinates and elevation abnormal data of GNSS control points, and obtaining sample data for model training; dividing a fitting point and a check point, preprocessing fitting point data, and adding at least one random disturbance to increase the fitting point so as to expand sample data; for each small area, utilizing the expanded sample data, and respectively adopting at least more than two fitting schemes to fit the elevation anomaly model; for each small area, evaluating the model precision, and selecting an elevation anomaly model with the best performance; normal high data for unknown points are calculated.

Description

Regional elevation anomaly fitting method based on expansion algorithm
Technical Field
The invention relates to the technical field of geodetic surveying and neural networks, in particular to a regional elevation anomaly fitting technology based on an extended algorithm.
Background
Since the advent of GNSS measurement, the GNSS measurement method has the advantages of being fast, real-time, accurate in positioning, simple and efficient, and can be widely applied to the field of engineering measurement. Although the plane network distribution of the GNSS is very flexible and the accuracy completely meets the requirements of engineering tests, the elevation data measured by the GNSS is the geodetic height elevation based on a WGS-84 ellipsoid, and the elevation datum adopted in engineering application is the normal height elevation obtained by level leveling, so that the elevation measured by the GNSS cannot be directly applied to engineering tasks, wherein the difference between the geodetic height and the normal height is called elevation abnormity, and the elevation abnormity is not a constant value and can change along with different regional and geological conditions. Therefore, how to fit elevation anomaly models in different regions so as to smoothly convert the geodetic height measured by the GNSS into the normal height which can be directly applied by engineering tasks is a current research hotspot.
Currently, methods for fitting elevation anomalies can be roughly divided into two main categories: gravity method and geometric method. The gravity method fitting needs a large amount of gravity data, the gravity data still belongs to the blank in most areas in the northwest of China, the gravity data is difficult to measure, and a large amount of manpower and material resources are consumed. Data required by the geometric method are GNSS leveling data, leveling measurement is required, the difficulty of obtaining the GNSS leveling data is far less than that of obtaining gravity data, and therefore the geometric method fitting elevation anomaly becomes a research hotspot in the future. However, the engineering quantity of leveling measurement is still not small, and a large amount of manpower and material resources are consumed, so that the problem of needing to measure a large amount of leveling data is also an urgent need to be solved; and researches show that the influence of the terrain of a measuring area on the fitting of a geometric method is large, and the fitting precision of partial areas is low due to the fact that the terrain is difficult to simulate by a mathematical surface model, and the adverse effect is also brought to engineering measurement.
An artificial neural network is a nonlinear network of simple processing units (neurons) connected in some way. The method can automatically extract the relation between learning samples through learning, has good performance in the aspect of nonlinear mapping, can achieve global approximation to expected mapping, and has better generalization capability. Therefore, the appearance of the artificial neural network provides a new idea for fitting the elevation anomaly model.
Disclosure of Invention
In order to solve the problems of low precision and large leveling workload of a single mathematical surface fitting model, the invention provides an extension algorithm-based regional elevation anomaly fitting method. The technical scheme is as follows:
an extension algorithm-based regional elevation anomaly fitting method comprises the following steps:
s1: the method comprises the steps of obtaining GNSS leveling data, combining plane coordinates and elevation abnormal data of GNSS control points, and obtaining sample data for model training; the method for obtaining GNSS level data comprises the following steps: selecting a measuring area, dividing the measuring area according to the relief degree of the terrain, and dividing a place with a small relief degree difference into small areas; arranging GNSS control points in each cell;
s2: dividing a fitting point and a check point according to sample data for model training, preprocessing the fitting point data, and adding at least one random disturbance to increase the fitting point so as to expand the sample data;
(1) uniformly distributed disturbance is added to the plane coordinate and elevation abnormity;
(2) increasing disturbance of normal distribution to the plane coordinate and elevation abnormity;
(3) uniformly distributed disturbance is added to the plane coordinate, and the elevation is abnormal and unchanged;
(4) uniformly distributed disturbance is added to the plane coordinate, and normal distributed disturbance is added to the elevation abnormity;
s3: for each small area, utilizing the expanded sample data, and respectively adopting at least more than two fitting schemes to fit the elevation anomaly model;
s4: for each small area, the accuracy of the model is evaluated by two parameters, so that an elevation anomaly model with the best performance is selected, and the method comprises the following steps:
(1) the internal coincidence precision mu is calculated as follows:
Vi＝ξ′i-ξi
Figure BDA0003151934020000021
wherein, ξ'iObtaining an elevation abnormal value xi for a fitting point participating in fitting through an elevation abnormal modeliFor true elevation outliers, V, of fitted points participating in the fittingiFitting residual errors are obtained, and n is the number of fitting points;
(2) the external coincidence precision M is as follows:
Vi＝ξ′i-ξi
Figure BDA0003151934020000022
wherein xi isi' the elevation abnormal value, xi, obtained by an elevation abnormal model for the check point participating in the checkiTrue elevation outliers, V, for check points involved in the checkiThe fitting residual error is obtained, and n is the number of check points participating in check;
(3) for each small area, whether the internal coincidence precision of each elevation abnormity model meets the engineering requirement is verified, and then an elevation abnormity model with the best performance is selected from the elevation abnormity models of which the internal coincidence precision meets the engineering requirement according to the external coincidence precision;
s5: normal high data for unknown points are calculated.
Wherein, step S1 specifically includes:
s1.1: selecting a measuring area, dividing the measuring area according to the relief degree of the terrain, and dividing a place with a small relief degree difference into small areas;
s1.2: distributing GNSS control points in each cell;
s1.3: performing level measurement on the distributed GNSS control points to obtain normal high data;
s1.4: performing GNSS measurement on the distributed GNSS control points to obtain plane coordinates and geodetic height data;
s1.5: performing difference on the geodetic height and the normal height to obtain elevation abnormal data of the GNSS control point;
s1.6: and combining the plane coordinates and the elevation abnormal data of the GNSS control points to obtain sample data for model training.
Further, the types of the elevation anomaly models include:
a polynomial surface model;
a BP neural network model;
RBF neural network model.
Furthermore, the polynomial surface model adopts a least square method to solve coefficients, and is further divided into a quadratic polynomial surface model and a cubic polynomial surface model.
Furthermore, the BP neural network model is a 5-layer network structure, the activation functions all adopt sigmoid functions, the first layer is an input layer, and two neurons are arranged and respectively input the longitude and the latitude of the control point; the second layer is an input data optimization layer, which is provided with two neurons, and carries out unified reduction on input data to construct standard input data; the third hidden layer is used for processing the nonlinear relation; the fourth layer is an output data conversion layer, corresponds to the function of the second layer and is used for carrying out unified reduction on output data; and the fifth layer is an output layer and is used for outputting standard elevation anomaly data. The data for training the model includes longitude, latitude, and elevation anomaly for a control point.
Furthermore, the RBF neural network model is a three-layer neural network, wherein the first layer is an input layer and consists of two neurons, and the longitude and the latitude of a control point are respectively input; the second layer is a radial basis function layer, and a Gaussian radial basis kernel function is adopted as an activation function; the third layer is an output layer and outputs elevation anomaly data, and the data of the training model comprises longitude and latitude of the control point and elevation anomaly of the point.
The method adopts a data expansion algorithm to preprocess data, namely, random disturbance is added to original data to amplify the number of samples so as to enhance the generalization capability of a fitting model; the invention adopts a zoning method to zone the terrain so as to better reflect the local characteristics of the terrain and reduce the problems of over-fitting and under-fitting; the method combines the traditional method with the neural network, carries out model fitting on the partitions, synthesizes the terrain model according to the precision of the fitting model of each partition, and improves the precision of the final fitting model.
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FIG. 1 is a basic block diagram of the present invention;
FIG. 2 is a block diagram of the present invention for acquiring GNSS level data;
FIG. 3 is a classification chart of the method for adding a perturbation matrix according to the present invention;
FIG. 4 is a model classification chart of the fitted elevation anomaly of the present invention;
FIG. 5 is a schematic diagram of the BP neural network structure of the present invention;
FIG. 6 is a schematic diagram of the RBF neural network structure of the present invention;
FIG. 7 is a diagram of the accuracy assessment method of the present invention;
FIG. 8 is a basic block diagram of normal high of the unknown point measured by the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, a sub-regional elevation anomaly fitting technique based on an extended algorithm specifically includes the following steps:
s1: the method comprises the steps of obtaining GNSS leveling data, combining plane coordinates and elevation abnormal data of GNSS control points to obtain sample data for model training, selecting a measurement area, dividing the measurement area according to the topographic relief degree, and dividing a place with a small relief degree difference into small areas; and 15 to 20 GNSS control points are distributed in each cell area.
The partition idea of the invention is as follows: the polynomial degree selected by the polynomial surface fitting model is related to the terrain relief, the relief is more, the terrain changes rapidly, and then the polynomial degree is higher, and vice versa. Therefore, when the area of the measurement region is large, part of the region has much fluctuation, and part of the region is flat, none of the polynomial surfaces can be considered, so that the fitting by only one polynomial surface can be considered. If the measurement areas are divided according to the topographic features, and the polynomial curved surfaces are selected to be fitted according to the topographic features of the areas, good fitting effects can be achieved.
The GNSS control points distributed by the invention are points with large elevation abnormal values difference and are generally arranged at places with higher terrain and lower terrain.
S2: preprocessing original GNSS level data, dividing fitting points and check points, preprocessing the fitting point data, and expanding sample data;
the idea of the extended algorithm of the invention is: because the mass distribution, geological conditions and the like of the earth in a small range are slightly different, the elevation anomaly is not greatly different in a small range. Based on the control method, the longitude and latitude of the selected control point are slightly deviated (controlled within a small range), and the elevation abnormity of the point is slightly deviated, so that a plurality of effective control points can be generated. Since the selected control points are all the points which can reflect the local features most in each small area, the points expanded from the points can well reflect the terrain features. Therefore, the extension algorithm can enable the terrain features to be more fully reflected.
S3: for each small area, fitting a plurality of elevation anomaly models by different fitting methods according to sample data expanded by different methods in S2;
s4: evaluating the accuracy of the elevation anomaly model of each small area fitted by different schemes according to the internal coincidence accuracy and the external coincidence accuracy;
s5: selecting an elevation anomaly fitting model with highest precision for each small area, combining an elevation anomaly model of the whole measurement area, and substituting unknown points to obtain the elevation anomaly of the unknown points, so that normal high data of the unknown points are calculated through the measurement data of the GNSS;
the specific steps for acquiring GNSS level data from fig. 2 include:
s1.1: selecting a measuring area, dividing the measuring area according to the relief degree of the terrain, and dividing a place with a small relief degree difference into small areas;
s1.2: 15 to 20 GNSS control points are distributed in each cell;
s1.3: performing grade leveling on the distributed GNSS control points to obtain normal high data;
s1.4: performing GNSS measurement on the distributed GNSS control points to obtain plane coordinates and geodetic height data;
s1.5: the method comprises the steps of obtaining elevation abnormal data of a GNSS control point by subtracting two kinds of data of the earth height and the normal height;
s1.6: combining the plane coordinates and the elevation abnormal data of the GNSS control points to obtain sample data for model training;
preprocessing raw GNSS data includes:
s2.1: dividing fitting points (points participating in model fitting) and checking points (points for checking);
s2.2: adding a random disturbance matrix to the fitting points to expand the number of samples and enhance the generalization capability of the fitting model;
the random perturbation matrix is added as shown in FIG. 3:
s2.2.1: uniformly distributed disturbance is added to the plane coordinate and elevation abnormity;
s2.2.2: increasing disturbance of normal distribution to the plane coordinate and elevation abnormity;
s2.2.3: uniformly distributed disturbance is added to the plane coordinate, and the elevation is abnormal and unchanged;
s2.2.4: uniformly distributed disturbance is added to the plane coordinate, and normal distributed disturbance is added to the elevation abnormity;
the S2.2.1 method specifically comprises the following steps of increasing uniformly distributed disturbance to the plane coordinate and elevation abnormity:
s2.2.1.1: the plane coordinate (x) of each fitting point ii,yi) And elevation anomaly data xi thereofiCombine to form a sample data Ai＝(xi,yi,ξi)；
S2.2.1.2: combining sample data formed by all fitting points i into a sample matrix An×3Comprises the following steps:
Figure BDA0003151934020000061
s2.2.1.3: generating a uniformly distributed random perturbation matrix Bn×3(matrix B is the same as matrix A) is shown by the following formula:
Figure BDA0003151934020000062
s2.2.1.4: generating expanded data C as shown in the following equation:
Figure BDA0003151934020000063
s2.2.1.5: adding the element in the C into the A to generate final extension data A', which is shown as the following formula:
Figure BDA0003151934020000064
the specific steps of S2.2.2 disturbance on the abnormal increase normal distribution of plane coordinates and elevations are as follows:
s2.2.2.1: the plane coordinate (x) of each fitting point ii,yi) And elevation anomaly data xi thereofiCombine to form a sample data Ai＝(xi,yi,ξi)；
S2.2.2.2: combining sample data formed by all fitting points i into a sample matrix An×3Comprises the following steps:
Figure BDA0003151934020000071
s2.2.2.3: generating a normally distributed random disturbance matrix Bn×3(matrix B is of the same type as matrix A) is shown by the following formula:
Figure BDA0003151934020000072
s2.2.2.4: generating expanded data C as shown below:
Figure BDA0003151934020000076
s2.2.2.5: adding the element in the C into the A to generate final extension data A' as shown in the following formula:
Figure BDA0003151934020000073
s2.2.3 only adds uniformly distributed disturbance to the plane coordinate, and the elevation is abnormal and unchanged, the method comprises the following steps:
s2.2.3.1: the plane coordinate (x) of each fitting point ii,yi) And elevation anomaly data xi thereofiCombine to form a sample data Ai＝(xi,yi,ξi)；
S2.2.3.2: combining sample data formed by all fitting points i into a sample matrix An×3Comprises the following steps:
Figure BDA0003151934020000074
s2.2.3.3: generating a uniformly distributed random perturbation matrix Bn×2As shown in the following formula:
Figure BDA0003151934020000075
wherein B isi＝(Δxi,Δyi)
S2.2.3.4: generating an all-zero matrix On×1As shown in the following formula:
Figure BDA0003151934020000081
s2.2.3.5: combined out and An×3Perturbation matrix B 'of the same type'n×3As shown in the following formula:
Figure BDA0003151934020000082
s2.2.3.6: generating expanded data Cn×3As shown in the following formula:
C＝A+B′
s2.2.3.7: adding the element in the C into the A to generate final extension data A' as shown in the following formula:
Figure BDA0003151934020000083
s2.2.4, wherein the specific steps of increasing uniformly distributed disturbance to the plane coordinate and increasing normally distributed disturbance abnormally in elevation are as follows:
s2.2.4.1: the plane coordinates P of all the fitting points ii＝(xi,yi) Combined into a matrix P, as shown in the following equation:
Figure BDA0003151934020000084
s2.2.4.2: and combining the elevation abnormal values of all fitting points i into a vector xi, which is shown as the following formula:
Figure BDA0003151934020000085
s2.2.4.3: the matrix P and the vector ξ are combined to form the original data sample a as shown in the following equation:
A＝[P,ξ]
s2.2.4.4: generating a uniformly distributed random perturbation matrix Bn×2As shown in the following formula:
Figure BDA0003151934020000091
wherein B isi＝(Δxi,Δyi)
S2.2.4.5: generating a perturbed plane coordinate P' as shown in the following equation:
P′＝P+B
s2.2.4.6: generating a normally distributed random disturbance matrix Δ ξn×1As shown in the following formula:
Figure BDA0003151934020000092
s2.2.4.7: generating a perturbed elevation anomaly vector ξ' as follows:
ξ′＝ξ+Δξ
s2.2.4.8: the combination of P 'and xi' constitutes the extended sample data Cn×3As shown in the following formula:
C＝[P′,ξ′]
s2.2.4.9: adding the element in the C into the A to generate final extension data A' as shown in the following formula:
Figure BDA0003151934020000093
for each small region partitioned by S1, fitting the elevation anomaly model by using the fitting scheme shown in fig. 4 using sample data expanded by S2 respectively includes:
s3.1: a polynomial surface model;
s3.2: a BP neural network model;
s3.3: an RBF neural network model;
wherein, the polynomial surface model adopts the least square method to solve the coefficient, and the polynomial surface model further divide into:
s3.1.1: the second order polynomial surface model is shown as the following formula:
ξ＝a0+a1x+a2y+a3x2+a4y2+a5xy
in the formula, xi is an elevation anomaly, aiAnd x and y are plane coordinates of the fitting points.
S3.1.2: the cubic polynomial surface model is shown as the following formula:
ξ＝a0+a1x+a2y+a3x2+a4y2+a5xy+a6x2y+a7xy2+a8x3+a9y3
in the formula, xi is an elevation anomaly, aiAnd x and y are plane coordinates of the fitting point.
As shown in fig. 5, in order to improve the BP neural network model, which is a 5-layer network structure, sigmoid functions are adopted for activation functions. The first layer is an input layer, and the first layer is provided with two neurons which respectively input the longitude and the latitude of the control point; the second layer is an input data optimization layer, which is provided with two neurons and is used for carrying out unified reduction on input data and constructing standard input data; the third hidden layer can process the nonlinear relation, plays a role in adjusting and refining nonlinear mapping, and can increase the number of neurons according to actual engineering, so that the learning ability is stronger when the number of the neurons is larger; the fourth layer is an output data conversion layer, corresponds to the function of the second layer and is used for carrying out unified reduction on output data; and the fifth layer is an output layer and is used for outputting standard elevation abnormal data. The data for training the model includes longitude and latitude as control points and elevation anomalies for the points.
As shown in fig. 6, the RBF neural network model is a fixed three-layer neural network. The first layer is an input layer, consists of two neurons and respectively inputs the longitude and the latitude of a control point; the second layer is a radial basis function layer, a Gaussian radial basis kernel function is adopted as an activation function, the number of the neurons selected in the second layer is positively correlated with the learning capacity of the network, and the number of the neurons can be determined according to engineering requirements; the third layer is an output layer and outputs elevation abnormal data. The data for training the model includes longitude, latitude, and elevation anomaly for a control point.
As shown in fig. 7, the method of assessing the accuracy of the model has an inner coincidence accuracy and an outer coincidence accuracy:
the internal coincidence precision reflects the coincidence degree of a real elevation abnormal value of a fitting point for constructing the model and an elevation abnormal value of the fitting point fitted after modeling, and the reliability of the model is reflected in a certain sense; the external conformity precision reflects the conformity of the real elevation abnormal value of the checking point used for checking the model and the elevation abnormal value of the checking point fitted after modeling, and the usability of the model is reflected in a certain sense. Therefore, the invention firstly verifies whether the internal coincidence precision of each model meets the engineering requirement, and then selects the model with the best performance from the models with the internal coincidence precision meeting the engineering requirement according to the external coincidence precision.
S4.1: the calculation formula of the internal coincidence accuracy μ is shown below
Vi＝ξ′i-ξi
Figure BDA0003151934020000101
Wherein, ξ'iObtaining an elevation abnormal value xi obtained by an elevation abnormal model for a known point participating in fittingiFor true elevation outliers of known points participating in the fitting, ViTo fit the residual, n is the number of known points involved in the fit.
S4.2 calculation of the out-of-compliance accuracy M is shown below
Vi＝ξ′i-ξi
Figure BDA0003151934020000111
Wherein, ξ'iObtaining an elevation abnormal value xi for the check point participating in the check through an elevation abnormal modeliTrue elevation outliers, V, for the examination points involved in the examinationiM is the number of check points participating in check for fitting residual errors.
FIG. 8 shows a method of measuring the normal height of an unknown point:
s5.1: according to the evaluation result of S4, selecting the highest-precision model from all the fitting models of the subareas, and combining to form an elevation anomaly model of the whole measuring area;
s5.2: measuring the plane coordinates and geodetic height data of unknown points by utilizing GNSS;
s5.3: substituting the plane coordinates of the unknown points into the model which accords with the precision standard to obtain elevation abnormal data;
s5.4: combining the geodetic height data H and the elevation abnormal data xi to obtain the normal height data HrAs shown in the following formula:
Hr＝H-ξ
the problem that the accuracy of the fitting model is low in a local area can be solved through a zoning method; the current situation that a large amount of manpower and material resources are consumed for carrying out a large amount of leveling measurement can be improved through the expansion algorithm; the engineering implementation efficiency is improved, the engineering implementation cost is saved, and the method has practical significance for actual engineering measurement.
The foregoing shows and describes the general principles, principal features, and advantages of the invention. For those skilled in the art, it is possible to modify the above technical solutions or replace the models thereof to adapt to their own items according to actual engineering requirements, and all modifications and substitutions that are within the spirit and principle of the present invention fall within the protection scope of the present invention.

Claims (6)

1. An extension algorithm-based regional elevation anomaly fitting method comprises the following steps:
s1: the method comprises the steps of obtaining GNSS leveling data, combining plane coordinates and elevation abnormal data of GNSS control points, and obtaining sample data for model training; the method for obtaining the GNSS level data comprises the following steps: selecting a measuring area, dividing the measuring area according to the relief degree of the terrain, and dividing a place with a small relief degree difference into small areas; distributing GNSS control points in each cell;
s2: dividing a fitting point and a check point according to sample data for model training, preprocessing the fitting point data, and adding at least one random disturbance to increase the fitting point so as to expand the sample data;
(1) uniformly distributed disturbance is added to the plane coordinate and elevation abnormity;
(2) increasing disturbance of normal distribution to the plane coordinate and elevation abnormity;
(3) uniformly distributed disturbance is added to the plane coordinate, and the elevation is abnormal and unchanged;
(4) uniformly distributed disturbance is added to the plane coordinate, and normal distributed disturbance is added to the elevation anomaly;
s3: for each small area, utilizing the expanded sample data, and respectively adopting at least more than two fitting schemes to fit the elevation anomaly model;
s4: for each small area, the accuracy of the model is evaluated by adopting two parameters, so that an elevation anomaly model with the best performance is selected, and the method comprises the following steps:
(1) the internal coincidence precision mu is calculated as follows:
Vi＝ξ′i-ξi
Figure FDA0003151934010000011
wherein, ξ'iObtaining an elevation abnormal value xi for a fitting point participating in fitting through an elevation abnormal modeliFor true elevation outliers, V, of fitted points participating in the fittingiFitting residual errors, wherein n is the number of fitting points;
(2) and (3) the external coincidence precision M is calculated as follows:
Vi＝ξ′i-ξi
Figure FDA0003151934010000012
wherein, ξ'iObtaining an elevation abnormal value xi for a check point participating in the check through an elevation abnormal modeliTrue elevation outliers, V, for check points involved in the checkiFitting residual errors, wherein n is the number of check points participating in check;
(3) for each small area, whether the internal conforming precision of each elevation abnormity model meets the engineering requirement is verified, and then an elevation abnormity model with the best performance is selected from the elevation abnormity models of which the internal conforming precision meets the engineering requirement according to the external conforming precision;
s5: normal high data for unknown points are calculated.
2. The sub-regional elevation anomaly fitting method according to claim 1, wherein the step S1 is specifically:
s1.1: selecting a measuring area, dividing the measuring area according to the relief degree of the terrain, and dividing a place with a small relief degree difference into small areas;
s1.2: arranging GNSS control points in each cell;
s1.3: performing grade leveling on the distributed GNSS control points to obtain normal high data;
s1.4: performing GNSS measurement on the distributed GNSS control points to obtain plane coordinates and geodetic height data;
s1.5: performing difference on the geodetic height and the normal height to obtain elevation abnormal data of the GNSS control point;
s1.6: and combining the plane coordinates and the elevation abnormal data of the GNSS control points to obtain sample data for model training.
3. The method according to claim 1, wherein the elevation anomaly model comprises:
a polynomial surface model;
a BP neural network model;
RBF neural network model.
4. The method for fitting elevation anomaly across regions according to claim 3, wherein the polynomial surface model is solved for coefficients using a least squares method, and is further divided into a quadratic polynomial surface model and a cubic polynomial surface model.
5. The method according to claim 3, wherein the BP neural network model is a 5-layer network structure, the activation functions are sigmoid functions, the first layer is an input layer, and two neurons are provided for respectively inputting the longitude and latitude of the control point; the second layer is an input data optimization layer, which is provided with two neurons and is used for carrying out unified reduction on input data and constructing standard input data; the third hidden layer is used for processing the nonlinear relation; the fourth layer is an output data conversion layer, corresponds to the function of the second layer and is used for carrying out unified reduction on output data; the fifth layer is an output layer and is used for outputting standard elevation abnormal data; the data for training the model includes longitude, latitude, and elevation anomaly for a control point.
6. The method for fitting elevation anomaly of divided regions according to claim 3, wherein the RBF neural network model is a three-layer neural network, the first layer is an input layer and consists of two neurons, and the longitude and the latitude of the control point are respectively input; the second layer is a radial basis function layer, and a Gaussian radial basis kernel function is adopted as an activation function; the third layer is an output layer and outputs elevation anomaly data, and the data of the training model comprises longitude and latitude of the control point and elevation anomaly of the point.
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