CN111125885A - ASF correction table construction method based on improved kriging interpolation algorithm - Google Patents
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Abstract
An ASF correction table construction method based on an improved kriging interpolation algorithm comprises the following specific steps: step 1: collecting partial discrete ASF time delay values in a prediction region as experiment sample data; step 2: calculating an experimental variation function by using the collected sample data to obtain a lag distance and discrete points of the experimental variation function; and step 3: selecting a theoretical model and fitting an experimental variation function by using a moth fire suppression optimization algorithm to obtain parameters of a corresponding variation function fitting model; and 4, step 4: establishing a kriging interpolation equation set according to the fitted variation function, and solving the kriging interpolation equation weight lambdaK(ii) a Step 5, combining the values of the known sample points to calculate the time delay value ASF of the position point to be estimatedpre(ii) a Step 6, comparing interpolation prediction accuracies of different fitting models by using cross validation, selecting an optimal prediction model according to an evaluation index RMSE, and step 7, repeating the steps 4 and 5 by using the optimal prediction model to solve all the modelsAnd predicting the ASF information of the points, and drawing an ASF correction table of the area to be estimated.
Description
Technical Field
The invention belongs to the technical field of radio wave propagation theoretical calculation, and relates to an ASF correction table construction method based on an improved kriging interpolation algorithm.
Background
The correction of the time delay of the ground wave propagation plays a key role in improving the positioning accuracy of the Rowland-C system, the time delay of the long wave propagation mainly comprises three parts, namely a basic time delay PF, a secondary phase factor SF and an additional secondary phase factor ASF, the PF and the SF can be accurately obtained through calculation, but factors influencing the ASF time delay are complex and are difficult to obtain through theoretical calculation, and the factors are also main factors of long wave propagation errors. In practical engineering application, a large amount of manpower and material resources are consumed for ASF time delay measurement, so that the ASF time delay correction prediction method is improved and perfected to improve the positioning accuracy, and the Roland-C has the most important significance for being an effective backup of a satellite navigation system.
The current calculation method of the ASF is mainly divided into: three theoretical models of a uniform smooth path, a segmented uniform smooth path and an irregular path. The calculation method of the uniform smooth path model mainly comprises a Fock diffraction method, the calculation method of the segmented uniform smooth path model mainly comprises a Mirington empirical formula, a Wait integral method and a wave-mode conversion method, and the calculation method of the irregular path model mainly comprises an integral equation, a PE method and the like. Compared with experimental measurement, the theoretical calculation method is easier to implement, but the calculation accuracy mainly depends on geological parameters of a division path, and the current world geoelectrical conductivity map set cannot meet the accuracy requirement of time delay correction, so that the method cannot be used for generating an ASF correction table.
Disclosure of Invention
The invention provides an ASF correction table construction method based on an improved kriging interpolation algorithm, which solves the problems that the existing theoretical calculation method cannot be used for large-area ASF prediction and high-density actual measurement ASF consumes time and manpower, and the prediction precision of optimized kriging interpolation by using a Moth fire suppression algorithm (MFO) is improved to a certain extent compared with that of a common kriging interpolation algorithm.
The technical scheme adopted by the invention is as follows:
an ASF correction table construction method based on an improved kriging interpolation algorithm comprises the following specific steps:
step 1: collecting partial discrete ASF time delay values in a prediction region as experiment sample data;
step 2: calculating an experimental variation function by using the collected sample data, and setting a delay distance tolerance to group the variation functions to obtain a delay distance and discrete points of the experimental variation function;
and step 3: selecting a theoretical model and fitting an experimental variation function by using a moth fire suppression optimization algorithm (MFO) to obtain parameters of a corresponding variation function fitting model;
and 4, step 4: establishing a kriging interpolation equation set according to the fitted variation function, and solving the kriging interpolation equation weight lambdaK；
Step 6, comparing interpolation prediction accuracies of different fitting models by using cross validation, and selecting an optimal prediction model according to an evaluation index RMSE;
and 7, repeating the steps 4 and 5 by using the optimal prediction model to obtain the ASF information of all the prediction points, and drawing an ASF correction table of the area to be estimated.
Further, the method also comprises the step 1 of removing abnormal values of the sample data by adopting a Lauda criterion, and replacing the removed points with the data at the previous moment.
Furthermore, the sample points in step 1 use wavelet filtering to denoise and smooth the data, so that the influence of random noise on data analysis can be reduced.
Further, the experimental variation function in step 2 is shown in formula (1):
where N (h) is the number of point pairs corresponding to a lag of h, Z (x)i) At a lag distance of xiExperimental value of (A), Z (x)i+ h) is offset by hThe measured value.
Further, in step 3, a spherical model, a Gaussian model and an exponential model are respectively adopted to carry out variation function fitting, and the basic value C in various models is determined through fitting0A base value c and a range a, wherein
(1) Spherical model
(2) Index model
(3) Gauss model
Furthermore, an MFO algorithm is adopted to fit the variation function in the step 3, the MFO algorithm is a new group optimization algorithm, and is widely used for solving the problem of nonlinear programming, and the fitting problem of the variation function can be quickly solved by utilizing the MFO algorithm. The objective function is designed as follows (5), where k is the number of samples, N (h) is the logarithm of points with a lag distance of h, γ (h) is the experimental value,
is the fitting value with fitting parameter C0C, a, the influence of point logarithm on the variation function is fully considered in the formula, so that the spatial correlation information can be more effectively described;
further, the kriging interpolation equation in step 4 is as formula (6):
wherein x0Is the position point to be estimated, k isNumber of samples, xKIs the kth sample point, μ is the Lagrangian multiplier, the equation right inverse matrix variation function γ (x)i,xj) Can be calculated according to the sample information and the formula (1), gamma (x)k,x0) According to the fitted variation function model calculation, the weight coefficient lambda can be calculated by multiplying two matrixesK。
Further, the time delay value ASF of the position point to be estimated in step 5preIs given by the formula (7):
wherein ASFkIs the delay value of the kth sample point.
Further, leave-one-out cross-validation is used to verify the prediction results in step 6. The cross validation method is to remove a known sample point, perform Krigin interpolation on the deleted sampling point by using the rest sampling values, and finally obtain the true value and the estimated value of each sampling point to perform error analysis.
Further, the evaluation in step 6 uses the root mean square error RMSE as a check criterion, and the calculation formula is shown in (8):
wherein k is the total number, ziIs a measure of the amount of time that,
the prediction model is an estimated value, which belongs to an overall index for measuring interpolation precision, and the smaller the value is, the better the interpolation result is, so that the optimal prediction model can be selected.
The invention has the beneficial effects that: only a small amount of locally dispersed ASF measured data is used, an ASF correction table in the whole observation area can be generated, the problems that the ASF data period is long, manpower and material resources are consumed and the like in large-area measurement are effectively solved, and the traditional common Kriging interpolation is optimized by using an MFO algorithm, so that the prediction precision is obviously improved. The kriging interpolation utilizes various information provided by spatial sampling to the maximum extent, takes the time delay information of ground wave propagation as a regional variable, and not only considers the spatial distance between a point to be estimated and an adjacent known sampling point, but also considers the position relationship between the adjacent sampling points when estimating an unknown sampling point, thereby providing the best linear unbiased prediction for the predicted position. The ASF correction table is drawn by adopting the improved kriging interpolation without considering geological parameters, propagation environment and other related information, so that the ASF correction table is more universal in application scenes.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a data sample point distribution diagram.
FIG. 3 is a graph fitted with a Gaussian model experimental variogram.
FIG. 4 is a graph fitted with an exponential model experimental variogram.
Fig. 5 is a graph fitted with a spherical model experimental variation function.
Fig. 6 is an ASF correction table generated using an improved kriging interpolation sphere model.
Detailed Description
The present invention is further illustrated by the following examples, which are not intended to limit the invention to these embodiments. It will be appreciated by those skilled in the art that the present invention encompasses all alternatives, modifications and equivalents as may be included within the scope of the claims.
Referring to fig. 1, the embodiment provides an ASF correction table construction method based on an improved kriging interpolation algorithm, according to the following principle: the kriging interpolation is a space interpolation algorithm for performing linear optimal and unbiased estimation on a position to be estimated by utilizing the structural characteristics of sampling data and a variation function, takes an ASF time delay value as a regionalized variable, fits the variation function by utilizing an MFO algorithm, and improves the interpolation precision by fully considering the influence of point logarithm on the variation function. And finally, completing the construction of an ASF correction table in the observation area by using an improved kriging interpolation algorithm. The method comprises the following specific steps:
step 1, collecting partially discrete ASF information in a prediction area as experiment sample data, removing abnormal values of original data by adopting a Lauda criterion, replacing data of a removed point by data of a previous moment, wherein the Lauda criterion is one of the most commonly used abnormal value correction methods at present, and the specific method is that if the absolute value of the difference value of the average value of a measured value and the measured value is more than three times of a standard deviation, the value is considered to be removed, and the specific formula is as follows:
wherein z iskIn order to be able to take the value of the observation,
is the mean value, σdIs the standard deviation. In order to reduce the influence of random noise on data analysis, the wavelet filtering is used for denoising and smoothing the original data, and because the characteristics of noise expressed in a wavelet domain are different, a certain wavelet base signal is adopted for processing so as to achieve the purpose of smoothing the data.
Step 2, setting a lag distance tolerance according to a formula (1) to group the variation functions, calculating an experimental variation function of sample data to obtain a lag distance and discrete points of the experimental variation function, wherein N (h) is a point pair number corresponding to the lag distance h, and Z (x) isi) Is at a distance xiExperimental values of (a). Usually, the data cannot be exactly in a particular direction, and the distances between two points are calculated to be different, and then the scattered discrete points need to be grouped according to a certain distance tolerance, and then averaged, usually the distance tolerance can be half of the basic lag distance,
step 3, selecting a theoretical model, fitting the experimental variation function by using an MFO algorithm, and determining a basic value C in various models through fitting0Base station value c and variation a, the variation function fitting model used is given below:
(1) ball model
(2) Index model
(3) Gauss model
The moth fire-fighting optimization algorithm is an emerging group optimization algorithm and is widely used for solving the problem of nonlinear programming. The algorithm is generated by simulating the spotlight flight of moths, wherein the moths and fire are two important information carriers in the algorithm, the moths are used as candidate solutions of problems, the space positions of the moths are formed by the variables of the optimization problems, and the moths can change the positions of the moths to fly freely in the space. According to the principle of geostatistics, the optimal fitting to the theoretical model is to make the predicted value
The fitness function is designed according to the following formula (5) in the algorithm, so that the lower the error is, the smaller the fitness function value is, and the fitting problem of the variation function is converted into the optimization problem by utilizing the algorithm;
the point logarithm corresponding to different lag distances is different, the influence of the point logarithm on the variation function is fully considered in the formula, the more the point logarithm is, the more credible the variation function in the range is shown, and the variation function fitted by the fitness function can more accurately describe the change condition of the regionalized variable, so that the improvement of the accuracy of the Krigin interpolation is facilitated. It can be seen that as long as an appropriate mutation function model can be established based on the measurement data, the spatial correlation of the regionalized variables can be accurately described, and the ASF of the unknown point can be accurately predicted.
and 6, evaluating the interpolation result by using leave-one-out cross validation. The cross validation method is to remove a known sample point, perform Krigin interpolation on the deleted sampling point by using the rest sampling values, and finally obtain the true value and the estimated value of each sampling point to perform error analysis. Where Root Mean Square Error (RMSE) is used as the test criterion, the calculation formula is shown below,
wherein k is the total number, ziIs a measure of the amount of time that,
is an estimated value. The error belongs to an integral index for measuring interpolation precision, and the smaller the value of the error is, the better the interpolation result is, so that the optimal prediction fitting model can be selected.
And 7, repeating the steps 4 and 5 by using the optimal prediction model to finish the drawing of the ASF correction table of the area to be estimated.
FIG. 2 shows 10 sampling points of the experiment, for which the method of the present invention is appliedThe method performs ASF correction table construction. Firstly, calculating an experimental variation function according to a formula (2) for processed data, dividing the data into 10 groups according to a lag distance to obtain discrete points of the experimental variation function and the lag distance, and then respectively fitting a Gaussian model, an exponential model and a spherical model by adopting an MFO algorithm, wherein parameters are set as c ═ 0,0.01],a＝[0.30]，C0＝[0,0.005]The initial population of the algorithm is 30, the maximum iteration number is 100, and the number of the optimized parameters is 3. Fig. 3, 4 and 5 show the least squares fitting results for ordinary kriging in the graphs for comparison of the improved effect using gaussian, exponential and spherical models, respectively, for fitting curves. It can be seen from the figure that the fitted curve of the MFO algorithm has smaller fluctuation around the true value, and particularly, the backward part is closer to the true value, which is beneficial to improving the prediction precision of the kriging interpolation.
The results of the evaluation index RMSE obtained by establishing a kriging interpolation equation set according to different fitting models and comparing the results with the results of the common kriging interpolation by one-leave cross validation are shown in Table 1.
TABLE 1 Cross-validation error comparison of two methods for different fitting models
As can be seen from comparison in table 1, in this embodiment, the prediction accuracy of kriging interpolation improved by using the MFO algorithm is improved for different fitting models, wherein the gaussian model with the worst interpolation effect is improved most obviously by about 4.6%, the optimal prediction model of the experiment is a spherical model fitted by using MFO, the root mean square error is only 86ns, the interpolation effect is improved by 0.2% compared with that of the common kriging interpolation, and the ASF prediction value is best matched with the ASF experiment value. And finally, meshing the prediction region according to one prediction point with the step length of about 500m, repeating the steps 4 and 5 by using an optimal prediction model, interpolating the unknown region by adopting an improved Krigin algorithm, and finishing the drawing of an ASF correction table of the whole region, wherein the unit of a predicted value is mu s as shown in figure 6. It can be seen that the invention does not need to implement high-density ASF measurement in a specified area, and can obtain an ASF correction table with a larger range and without losing precision by only needing a small number of scattered sample points, which has important significance for improving the Roland c positioning precision.
Claims (9)
1. An ASF correction table construction method based on an improved kriging interpolation algorithm comprises the following specific steps:
step 1: collecting partial discrete ASF time delay values in a prediction region as experiment sample data;
step 2: calculating an experimental variation function by using the collected sample data, and setting a delay distance tolerance to group the variation functions to obtain a delay distance and discrete points of the experimental variation function;
and step 3: selecting a theoretical model and fitting an experimental variation function by using a moth fire suppression optimization algorithm to obtain parameters of a corresponding variation function fitting model;
and 4, step 4: establishing a kriging interpolation equation set according to the fitted variation function, and solving the kriging interpolation equation weight lambdaK；
Step 5, after the weight coefficient of the kriging interpolation is solved, the time delay value ASF of the position point to be estimated can be calculated by combining the values of the known sample pointspre；
Step 6, comparing interpolation prediction accuracies of different fitting models by using cross validation, and selecting an optimal prediction model according to an evaluation index RMSE;
and 7, repeating the steps 4 and 5 by using the optimal prediction model to obtain the ASF information of all the prediction points, and drawing an ASF correction table of the area to be estimated.
2. The ASF correction table construction method based on the improved kriging interpolation algorithm as claimed in claim 1, wherein: and (3) eliminating abnormal values of the sample points in the step (1) by adopting a Lauda criterion, and replacing the eliminated points with data at the previous moment.
3. The ASF correction table construction method based on the improved kriging interpolation algorithm as claimed in claim 2, wherein: and (3) denoising and smoothing the data by using wavelet filtering at the sample point in the step 1.
4. The ASF correction table construction method based on the improved kriging interpolation algorithm as claimed in claim 1, wherein: the experimental variation function in step 2 is shown in formula (1):
where N (h) is the number of point pairs corresponding to a lag of h, Z (x)i) At a lag distance of xiExperimental value of (A), Z (x)i+ h) is the actual value at offset h.
5. The method for constructing an ASF correction table based on the improved kriging interpolation algorithm as claimed in claim 4, wherein: step 3, respectively adopting a spherical model, a Gaussian model and an exponential model to carry out variation function fitting, and determining a base value C in various models through fitting0A base value c and a range a, wherein
(1) Spherical model
(2) Index model
(3) Gauss model
6. The method for constructing an ASF correction table based on the improved kriging interpolation algorithm as claimed in claim 4, wherein: and 3, fitting a variation function by adopting a moth fire suppression optimization algorithm, wherein the target function is shown as a formula (5):
where k is the number of samples, N (h) is the number of points corresponding to a lag of h,
is the fitting value of the variation function, and the fitting parameter is C0、C、a。
7. The method for constructing an ASF correction table based on the improved kriging interpolation algorithm as claimed in claim 6, wherein: the kriging interpolation equation in step 4 is as formula (6):
wherein x0Is the position point to be estimated, k is the number of samples, xKIs the kth sample point, μ is the Lagrangian multiplier, the equation right inverse matrix variation function γ (x)i,xj) Can be calculated according to the sample point information and the formula (1), gamma (x)k,x0) According to the fitted variation function model calculation, the weight coefficient lambda can be calculated by multiplying two matrixesK。
8. The ASF correction table construction method based on the improved kriging interpolation algorithm as claimed in claim 7, wherein: time delay value ASF of position point to be estimatedpreIs given by the formula (7):
wherein ASFkIs the delay value of the kth sample point.
9. The ASF correction table construction method based on the improved kriging interpolation algorithm as claimed in claim 1, wherein: the evaluation in step 6 uses the root mean square error RMSE as the test criterion, and the calculation formula is shown in (8):
wherein k is the total number, ziIs a measure of the amount of time that,
the error belongs to an integral index for measuring interpolation precision, and the smaller the value is, the better the interpolation result is.
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| CN117293826A (en) * | 2023-11-27 | 2023-12-26 | 山东大学 | Distributed photovoltaic missing power real-time prediction method, system, medium and equipment |
| CN117293826B (en) * | 2023-11-27 | 2024-04-05 | 山东大学 | Distributed photovoltaic missing power real-time prediction method, system, medium and equipment |
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