CN111274738A - Elevation abnormal value calculation method - Google Patents

Elevation abnormal value calculation method Download PDF

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CN111274738A
CN111274738A CN202010117015.1A CN202010117015A CN111274738A CN 111274738 A CN111274738 A CN 111274738A CN 202010117015 A CN202010117015 A CN 202010117015A CN 111274738 A CN111274738 A CN 111274738A
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胡伍生
李航
聂檄晨
董彦锋
戴一
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Southeast University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C5/00—Measuring height; Measuring distances transverse to line of sight; Levelling between separated points; Surveyors' levels
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Abstract

The invention discloses a method for calculating an elevation abnormal value, which comprises the following steps: 1: acquiring elevation abnormal values of a plurality of GPS level joint measuring points in a target area, performing pre-fitting by adopting a quadric surface method, taking an error in three times as a limit difference, and removing gross errors; s2: fitting the remaining N elevation abnormal values by using a quadratic polynomial; 3: calculating N elevation anomaly calculation values by utilizing a quadratic polynomial model, and calculating a fitting residual error; 4: constructing a wavelet neural network, wherein the input of the network is a plane coordinate and an elevation abnormal calculation value, and the output is a residual error; plane coordinates, elevation anomaly calculation values and residual error pairs of N GPS level joint measurement pointsTraining wave neural network, 5, calculating ξ abnormal calculation value of elevation of land to be measuredtCoordinates of the ground to be measured ξtInputting the data into the trained wavelet neural network to obtain the residual error of the land to be measured, and further calculating the elevation abnormal value of the land to be measured. The method has small error of the elevation abnormal value obtained in a large-area measuring area, and can calculate to obtain a more accurate elevation abnormal value.

Description

Elevation abnormal value calculation method
Technical Field
The invention relates to the field of regional quasi-geoid refinement, in particular to a calculation method based on an elevation abnormal value.
Background
In recent years, satellite positioning technology has been widely used due to its advantages of high efficiency, high precision, and strong real-time performance. The elevation abnormal value is the difference between the geodetic height of the GPS at the same point and the normal height of the precise level. And the elevation abnormal value at a certain point is obtained, and the conversion from the geodetic height to the normal height of the GNSS can be realized.
According to the specification of the 4.4 th item of the national standard engineering measurement Specification (GB50026-2007), when the GPS fitting elevation is calculated, a plane fitting method can be adopted to obtain an elevation abnormal value for a small measurement area with flat terrain, and a curved surface fitting method can be adopted to obtain the elevation abnormal value for a large-area measurement area with large terrain fluctuation. At present, a quadratic curve is usually adopted to carry out elevation outlier fitting on a large-area measuring area, and the error obtained by the method is usually large.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide an elevation abnormal value calculation method which is small in error of an elevation abnormal value obtained in a large-area measuring area and capable of calculating to obtain a more accurate elevation abnormal value.
The technical scheme is as follows: the invention adopts the following technical scheme:
an elevation outlier calculation method comprising:
s1: acquiring elevation abnormal values of a plurality of GPS level connection points in a target area, pre-fitting the acquired data by adopting a quadric surface method, taking an error in three times as a limit difference, and removing gross errors;
s2: eliminating the height abnormal values of the N GPS level combined measuring points after the gross errors of the S1
Figure BDA0002391804850000013
Fitting by using a quadratic polynomial:
ξ(x,y)＝a0+a1x+a2y+a3x2+a4xy+a5y2
wherein ξ (x, y) is an elevation anomaly at planar coordinates (x, y); a0,a1,…,a5Is a fitting coefficient; n is 1,2, …, N;
s3: calculating the elevation abnormity calculation values of the N GPS level joint measurement points by utilizing the quadratic polynomial model obtained in the step S2
Figure BDA0002391804850000011
Calculating the fitting residual:
Figure BDA0002391804850000012
s4, constructing a wavelet neural network, wherein the input of the wavelet neural network is plane coordinates (X, Y) and an elevation anomaly calculation value ξ1The output is residual △ξ;
connecting the plane coordinates (x) of N GPS level measuring pointsn,yn) And elevation anomaly calculation value
Figure BDA0002391804850000023
As an input, △ξnTaking the normalized value as output, training the wavelet neural network to obtain an elevation anomaly residual error model;
s5: for the plane coordinate in the target area as (x)t,yt) According to the quadratic polynomial model fitted in S2, calculating an elevation anomaly calculation value ξt(ii) a Will (x)t,yt) And ξtInputting the normalized residual error into an elevation abnormal residual error model trained by S4 to obtain a normalized residual error of a ground to be measured, and performing reverse normalization to obtain a residual error △ξtAnd then the elevation abnormal value of the to-be-measured land is as follows:
Figure BDA0002391804850000021
in the step S2, a least square method is used to determine the fitting coefficient a0,a1,…,a5。
The wavelet neural network established in the step S4 includes an input layer, a hidden layer, and an output layer that are connected in sequence;
the input layer comprises 3 input units, the hidden layer comprises 15 hidden units, and the output layer comprises 1 output unit;
the activation function of the hidden layer is a wavelet basis function, the weight of the hidden layer is a translation factor of the wavelet basis function, and the threshold of the hidden layer is a scaling factor of the wavelet basis function.
The wavelet basis function is Morlet wavelet, and the expression is as follows:
Figure BDA0002391804850000022
and S4, training the wavelet neural network by adopting a gradient descent method of error back propagation to obtain an elevation anomaly residual error model.
Has the advantages that: the elevation abnormal value calculation method disclosed by the invention adopts the wavelet neural network to establish a high-precision elevation abnormal residual error model, and can accurately calculate the residual error of the elevation abnormal value for the position points in the large-area measurement area, thereby obtaining more accurate elevation abnormal value and realizing accurate conversion between the geodetic height and the normal height of the GPS.
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FIG. 1 is a flow chart of a method for calculating an elevation anomaly according to the present disclosure;
FIG. 2 is a distribution diagram of leveling co-measurements in an embodiment;
FIG. 3 is a diagram showing error distributions of fitting results of two methods in the example.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described below with reference to the accompanying drawings.
As shown in fig. 1, the present invention discloses an elevation abnormal value calculation method, including:
s1: acquiring elevation abnormal values of a plurality of GPS level connection points in a target area, pre-fitting the acquired data by adopting a quadric surface method, taking an error in three times as a limit difference, and removing gross errors;
in this embodiment, taking a Jiangsu area as an example, 171 level-C GPS network level joint measurement points in Jiangsu province are adopted, and three leveling measurements are adopted to obtain an elevation abnormal value of each level joint measurement point. 171 point positions are uniformly distributed on 100000km in Jiangsu province2The average density of the leveling linkage points is about: every 1000km2The number of the leveling joint measuring points is equal to 1.7, Jiangsu provinces belong to plain areas, and the maximum and minimum values of elevation abnormity are ξmax＝12.5377m，ξmin＝-8.2549m。
Of the 171 data, 131 data were selected as modeling sample data, and the other 40 data were selected as verification samples, and the distribution is as shown in fig. 2. And (3) carrying out quadratic surface method pre-fitting on the elevation abnormal data of all 131 modeling samples to obtain a curve fitting model with the error of +/-43.3 cm, and taking the error of 3 times as a tolerance, wherein the tolerance is +/-129.9 cm. According to the result, fitting errors of 4 points are all larger than a limit difference, so that the 4 points are considered as gross errors and are removed;
s2: eliminating the height abnormal values of the N GPS level combined measuring points after the gross errors of the S1
Figure BDA0002391804850000033
Fitting by using a quadratic polynomial:
ξ(x,y)＝a0+a1x+a2y+a3x2+a4xy+a5y2
wherein ξ (x, y) is an elevation anomaly at planar coordinates (x, y); a0,a1,…,a5Is a fitting coefficient; n is 1,2, …, N;
and performing quadratic surface fitting on the remaining 127 pieces of elevation abnormal data. And the error in the overall fitting is +/-24.6 cm, and taking the error in the triple as the tolerance, all point positions meet the tolerance requirement, so that all gross errors are considered to be eliminated.
The present embodiment determines the fitting coefficient a by using the least square method0,a1,…,a5。
S3: using two times obtained in S2A polynomial model for calculating the abnormal elevation calculation values of N GPS level connection points
Figure BDA0002391804850000032
Calculating the fitting residual:
Figure BDA0002391804850000031
s4, constructing a wavelet neural network, wherein the input of the wavelet neural network is plane coordinates (X, Y) and an elevation anomaly calculation value ξ1The output is residual △ξ;
the wavelet neural network has two structures: the method is a loose structure, namely, wavelet analysis is carried out on data firstly, and a result is input into a neural network to be used as an input layer; and secondly, in a compact structure, a wavelet basis function is used for replacing an activation function in a hidden layer structure of the neural network, and translation and expansion factors of the wavelet basis function are used for replacing weight values and threshold values of the hidden layer, so that more compact fusion is realized on the structure. The invention adopts a compact wavelet neural network, which comprises an input layer, a hidden layer and an output layer which are connected in sequence; the input layer comprises 3 input units, the hidden layer comprises 15 hidden units, and the output layer comprises 1 output unit; the wavelet basis function is Morlet wavelet, and the expression is as follows:
Figure BDA0002391804850000041
connecting the plane coordinates (x) of N GPS level measuring pointsn,yn) And elevation anomaly calculation value
Figure BDA0002391804850000045
As an input, △ξnTaking the normalized value as output, training the wavelet neural network to obtain an elevation anomaly residual error model;
the normalization in this embodiment uses the following calculation formula:
Figure BDA0002391804850000042
wherein the content of the first and second substances,r is an initial value before normalization, Rmax,RminRespectively, the maximum value and the minimum value of the initial data, T is the normalized value, Tmax,TminRespectively the maximum and minimum values after the normalized transformation. In this example, TmaxA value of 0.9, TminThe value is 0.1.
The inverse normalization is calculated as follows:
Figure BDA0002391804850000043
and training the wavelet neural network by adopting a gradient descent method of error back propagation to obtain an elevation abnormal residual error model.
S5: for the plane coordinate in the target area as (x)t,yt) According to the quadratic polynomial model fitted in S2, calculating an elevation anomaly calculation value ξt(ii) a Will (x)t,yt) And ξtInputting the normalized residual error into an elevation abnormal residual error model trained by S4 to obtain a normalized residual error of a ground to be measured, and performing reverse normalization to obtain a residual error △ξtAnd then the elevation abnormal value of the to-be-measured land is as follows:
Figure BDA0002391804850000044
in order to compare the effects of the method disclosed by the invention, the elevation abnormal values of the 40 verification sample data are calculated by respectively adopting a quadric surface fitting method and the method disclosed by the invention and are compared with the elevation abnormal values measured at the 40 verification samples. The results of the two methods are shown in table 1.
As can be seen from Table 1, when elevation anomaly fitting modeling is performed in a large-area (provincial area), fitting is performed by a traditional quadric surface fitting method, and the obtained precision is +/-23.1 cm. The accuracy of the elevation abnormal value calculation method provided by the invention is +/-8.6 cm, and is improved by 62.8% compared with the accuracy of the traditional quadric surface model.
Fig. 3 shows the error distribution of the fitting results of the two methods in this embodiment. As can be seen from FIG. 3, the elevation abnormal value calculation method proposed by the present invention has a larger improvement at each inspection point compared to the quadric surface method specified in the engineering survey Specification
TABLE 1 comparison of the fitted residuals
Figure BDA0002391804850000051

Claims (5)

1. An elevation anomaly calculation method, comprising:
s1: acquiring elevation abnormal values of a plurality of GPS level connection points in a target area, pre-fitting the acquired data by adopting a quadric surface method, taking an error in three times as a limit difference, and removing gross errors;
s2: eliminating the height abnormal values of the N GPS level combined measuring points after the gross errors of the S1
Figure FDA0002391804840000014
Fitting by using a quadratic polynomial:
ξ(x，y)＝a0+a1x+a2y+a3x2+a4xy+a5y2
wherein ξ (x, y) is an elevation anomaly at planar coordinates (x, y); a0，a1，...，a5Is a fitting coefficient; n is 1,2, …, N;
s3: calculating the elevation abnormity calculation values of the N GPS level joint measurement points by utilizing the quadratic polynomial model obtained in the step S2
Figure FDA0002391804840000011
Calculating the fitting residual:
Figure FDA0002391804840000012
s4, constructing a wavelet neural network, wherein the input of the wavelet neural network is plane coordinates (X, Y) and an elevation anomaly calculation value ξ1The output is residual △ξ;
connecting the plane coordinates (x) of N GPS level measuring pointsn，yn) Height anomaly meterCalculation of value
Figure FDA0002391804840000015
As an input, △ξnTaking the normalized value as output, training the wavelet neural network to obtain an elevation anomaly residual error model;
s5: for the plane coordinate in the target area as (x)t，yt) According to the quadratic polynomial model fitted in S2, calculating an elevation anomaly calculation value ξt(ii) a Will (x)t，yt) And ξtInputting the normalized residual error into an elevation abnormal residual error model trained by S4 to obtain a normalized residual error of a ground to be measured, and performing reverse normalization to obtain a residual error △ξtAnd then the elevation abnormal value of the to-be-measured land is as follows:
Figure FDA0002391804840000013
2. the elevation abnormal value calculation method according to claim 1, wherein the fitting coefficient a is determined by a least square method in step S20，a1，...，a5。
3. The elevation outlier calculating method as claimed in claim 1, wherein said wavelet neural network established in step S4 comprises an input layer, a hidden layer and an output layer connected in sequence;
the input layer comprises 3 input units, the hidden layer comprises 15 hidden units, and the output layer comprises 1 output unit;
the activation function of the hidden layer is a wavelet basis function, the weight of the hidden layer is a translation factor of the wavelet basis function, and the threshold of the hidden layer is a scaling factor of the wavelet basis function.
4. The elevation outlier calculation method of claim 3, wherein the wavelet basis function is a Morlet wavelet, and the expression is:
Figure FDA0002391804840000021
5. the elevation outlier calculating method of claim 1, wherein in step S4, the wavelet neural network is trained by a gradient descent method of error back propagation to obtain an elevation outlier residual model.
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Cited By (5)

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Publication number Priority date Publication date Assignee Title
CN112731453A (en) * 2020-12-21 2021-04-30 自然资源部第一海洋研究所 Vertical reference detection method for tide station by utilizing GNSS buoy
CN112946691A (en) * 2021-02-06 2021-06-11 长江水利委员会水文局长江上游水文水资源勘测局 Zonal area coordinate conversion segmentation method considering elevation abnormal trend change
CN113111573A (en) * 2021-03-24 2021-07-13 桂林电子科技大学 Landslide displacement prediction method based on GRU
CN113358092A (en) * 2021-06-10 2021-09-07 国家基础地理信息中心 Big data numerical algorithm for determining vertical deviation of national elevation standard
CN113532397A (en) * 2021-07-07 2021-10-22 天津大学 Regional elevation anomaly fitting method based on extension algorithm

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Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112731453A (en) * 2020-12-21 2021-04-30 自然资源部第一海洋研究所 Vertical reference detection method for tide station by utilizing GNSS buoy
CN112731453B (en) * 2020-12-21 2022-03-01 自然资源部第一海洋研究所 Vertical reference detection method for tide station by utilizing GNSS buoy
CN112946691A (en) * 2021-02-06 2021-06-11 长江水利委员会水文局长江上游水文水资源勘测局 Zonal area coordinate conversion segmentation method considering elevation abnormal trend change
CN112946691B (en) * 2021-02-06 2024-03-12 长江水利委员会水文局长江上游水文水资源勘测局 Band-shaped region coordinate conversion segmentation method considering elevation anomaly trend change
CN113111573A (en) * 2021-03-24 2021-07-13 桂林电子科技大学 Landslide displacement prediction method based on GRU
CN113358092A (en) * 2021-06-10 2021-09-07 国家基础地理信息中心 Big data numerical algorithm for determining vertical deviation of national elevation standard
CN113358092B (en) * 2021-06-10 2023-01-13 国家基础地理信息中心 Big data numerical algorithm for determining vertical deviation of national elevation standard
CN113532397A (en) * 2021-07-07 2021-10-22 天津大学 Regional elevation anomaly fitting method based on extension algorithm
CN113532397B (en) * 2021-07-07 2022-07-15 天津大学 Regional elevation anomaly fitting method based on expansion algorithm

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