Satellite carrier-to-noise ratio prediction method suitable for carrier attitude change

By constructing the carrier motion feature data set and using a random forest regression model, combined with higher-order feature combinations, the problem that satellite carrier-noise ratio prediction in the prior art is difficult to adapt to carrier posture changes, and efficient and accurate carrier-noise ratio prediction is achieved.

CN119828183APending Publication Date: 2025-04-15BEIJING AUTOMATION CONTROL EQUIP INST
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Patent Information

Application Number
CN202411949861.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-27
Publication Date
2025-04-15

AI Technical Summary

Technical Problem

The prior art is difficult to adapt to carrier attitude changes when predicting satellite carrier-to-noise ratio, resulting in high computational complexity and poor dynamic adaptability.

Method used

By constructing the feature data set during the carrier motion, a random forest regression model is used to combine higher-order feature combinations to predict the satellite carrier-to-noise ratio and skip some complex geometric calculations.

Benefits of technology

It significantly reduces the computational complexity, improves the adaptability to dynamic scenarios, and reduces the error in carrier-to-noise ratio prediction.

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Abstract

The invention provides a satellite carrier-to-noise ratio prediction method suitable for carrier attitude change. The satellite carrier-to-noise ratio prediction method comprises the following steps: S10, constructing a feature data set in a carrier movement process; s20, obtaining a processed feature data set; s30, obtaining a feature data set after outliers are removed; s40, dividing into a training set and a test set; s50, establishing a random forest regression model; s60, obtaining a random forest regression model after current training; s70, drawing a learning curve and a residual image based on the random forest regression model after the current training; s80, judging whether over-fitting, under-fitting and systematic deviation do not occur at the same time, if so, completing training and turning to S90, otherwise, turning to S60; s90, obtaining a mean square error and a decision coefficient of the trained random forest regression model; s100, judging a mean square error, determining whether coefficients meet requirements at the same time or not, if yes, completing the test and turning to S110, and if not, turning to S60; s110, acquiring feature data in the movement process of the carrier; and S120, predicting the carrier-to-noise ratio of the satellite.
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Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation observation information prediction, and in particular to a satellite carrier-to-noise ratio prediction method applicable to carrier attitude changes. Background Art

[0002] With the construction and improvement of the new generation Beidou navigation system, the widespread application of satellite navigation receivers in military and civilian fields, and the vigorous development of emerging machine learning technologies, the field of intelligent prediction of satellite navigation observation information has become increasingly valuable for research.

[0003] Satellite carrier-to-noise ratio is an important indicator to describe the performance of satellite receivers. When the attitude of the carrier to which the satellite receiver is attached changes rapidly, the satellite carrier-to-noise ratio will fluctuate. When the satellite carrier-to-noise ratio drops below the satellite signal tracking threshold, the satellite receiver will lose tracking of the satellite signal and become unable to locate. Therefore, satellite carrier-to-noise ratio prediction based on carrier attitude changes is very important for assessing the risk of satellite receivers not being able to locate when moving with the carrier. At the same time, because the size of the satellite carrier-to-noise ratio is independent of the noise bandwidth used by the satellite receiver, the size of the satellite carrier-to-noise ratio is usually used as a universal performance evaluation scale between different satellite receivers, so its prediction method has high application value.

[0004] At present, in order to predict the satellite receiver carrier-to-noise ratio information, the traditional method needs to explicitly calculate the geometric relationship between the satellite receiver and the satellite position, obtain the satellite signal's arrival azimuth, elevation, relative distance, etc., and further obtain the satellite signal's arrival power, and finally calculate the predicted satellite carrier-to-noise ratio information. The shortcomings of the traditional method of explicitly calculating and predicting the satellite carrier-to-noise ratio mainly include: involving complex geometric calculations, the calculation complexity is relatively large; and the dynamic adaptability to the rapid movement of the carrier is poor. Summary of the invention

[0005] The present invention provides a satellite carrier-to-noise ratio prediction method applicable to carrier attitude changes, which can solve the above technical problems.

[0006] The present invention provides a satellite carrier-to-noise ratio prediction method applicable to carrier attitude changes, the method comprising:

[0007] S10, constructing a feature data set during the carrier motion process; wherein the feature data set is obtained by using a satellite receiving mechanism, and the feature data set includes satellite carrier-to-noise ratio information and satellite position information given by multiple satellite solution channels, and carrier position information and attitude information determined by a satellite receiver positioning solution;

[0008] S20, extracting, stacking and high-order combining the feature data sets according to different satellite channels to obtain a processed feature data set; wherein the processed feature data set includes satellite carrier-to-noise ratio, X, Y, and Z-axis satellite coordinates in the geodetic coordinate system, carrier positioning longitude, carrier positioning latitude, carrier positioning altitude, carrier pitch angle, carrier roll angle, carrier heading angle, relative distance from the satellite receiver to the satellite, satellite azimuth, and satellite elevation angle;

[0009] S30, performing outlier detection on the processed feature data set to obtain a feature data set after removing outliers;

[0010] S40, dividing the feature data set after removing outliers into a training set and a test set according to a preset ratio;

[0011] S50, establish a random forest regression model;

[0012] S60, inputting the training set into the random forest regression model for grid search and cross validation to obtain the random forest regression model after the current training;

[0013] S70, drawing a learning curve and a residual graph based on the random forest regression model after the current training; evaluating whether the random forest regression model after the current training has overfitting or underfitting based on the learning curve; and evaluating whether the random forest regression model after the current training has systematic deviations based on the residual graph;

[0014] S80, judging whether the random forest regression model after the current training satisfies the conditions of no overfitting, underfitting and systematic deviation at the same time, if so, completing the training and going to S90, otherwise, adjusting the parameters of the random forest regression model after the current training to obtain the adjusted random forest regression model, and going to S60;

[0015] S90, inputting the test set into the trained random forest regression model to obtain the mean square error and determination coefficient of the trained random forest regression model;

[0016] S100, determining whether the mean square error is less than a first preset threshold and the determination coefficient is greater than a second preset threshold at the same time, if so, completing the test and going to S110, otherwise, adjusting the parameters of the random forest regression model after the current training, obtaining an adjusted random forest regression model, and going to S60;

[0017] S110, using a satellite receiver to obtain characteristic data of the carrier during its motion; wherein the characteristic data includes satellite position information given by multiple satellite solution channels, and position information and attitude information of the carrier determined by the satellite receiver;

[0018] S120. Extract, stack and high-order combine the feature data according to different satellite channels to obtain processed feature data; input the processed feature data into a tested random forest regression model to predict the satellite carrier-to-noise ratio; wherein the processed feature data include X, Y, and Z-axis satellite coordinates in the geodetic coordinate system, carrier positioning longitude, carrier positioning latitude, carrier positioning altitude, carrier pitch angle, carrier roll angle, carrier heading angle, the relative distance from the satellite receiver to the satellite, satellite azimuth, and satellite elevation.

[0019] By applying the technical solution of the present invention, during the training process, by adding the carrier attitude information to a specific data set and extracting, stacking and combining high-order features, combined with a random forest regression model, the problem that the existing technology cannot adapt to the carrier attitude changes in the field of satellite carrier-to-noise ratio prediction is solved. In the prediction process, the position information solved by the satellite receiver, the satellite coordinate information and the attitude information of the carrier to which the satellite receiver is attached are used as input features, and the nonlinear relationship between the satellite carrier-to-noise ratio and the attitude information and position information of the carrier can be learned and fitted efficiently and with high quality. This method skips some complex geometric calculations through data fitting, significantly reducing the computational complexity; by combining multi-dimensional high-order features to fit the nonlinear relationship between the carrier attitude and the satellite carrier-to-noise ratio, the adaptability to dynamic scenes is improved; by optimizing the model parameters, the error of the carrier-to-noise ratio prediction can be significantly reduced. The implementation process of this method is relatively simple and has high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The included drawings are used to provide a further understanding of the embodiments of the present invention, which constitute a part of the specification, are used to illustrate the embodiments of the present invention, and together with the text description, explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0021] Figure 1 A flow chart of a satellite carrier-to-noise ratio prediction method applicable to carrier attitude changes provided in accordance with an embodiment of the present invention is shown;

[0022] Figure 2 A learning curve diagram of a random forest regression model provided according to an embodiment of the present invention is shown;

[0023] Figure 3 A residual graph of a random forest regression model provided according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0024] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0025] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0026] Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, numerical expressions and numerical values ​​do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be regarded as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0027] like Figure 1 As shown, the present invention provides a satellite carrier-to-noise ratio prediction method applicable to carrier attitude changes, the method comprising:

[0028] S10, constructing a feature data set during the carrier movement process; wherein the feature data set is obtained by using a satellite receiving mechanism, and the feature data set includes satellite carrier-to-noise ratio information and satellite position information (CSCG2000 geodetic coordinate system) given by multiple satellite solution channels, and carrier position information (longitude, latitude and altitude) and attitude information (pitch angle, roll angle and heading angle) determined by satellite receiver positioning;

[0029] S20, extracting, stacking and high-order combining the feature data sets according to different satellite channels to obtain a processed feature data set; wherein the processed feature data set includes satellite carrier-to-noise ratio, X, Y, and Z-axis satellite coordinates in the geodetic coordinate system, carrier positioning longitude, carrier positioning latitude, carrier positioning altitude, carrier pitch angle, carrier roll angle, carrier heading angle, relative distance from the satellite receiver to the satellite, satellite azimuth, and satellite elevation angle;

[0030] S30, performing outlier detection on the processed feature data set to obtain a feature data set after removing outliers;

[0031] S40, dividing the feature data set after removing outliers into a training set and a test set according to a preset ratio; wherein the absolute median function can be used to perform a sliding window scan on the data to complete outlier detection preprocessing;

[0032] S50, establish a random forest regression model;

[0033] S60, inputting the training set into the random forest regression model for grid search and cross validation to obtain the random forest regression model after the current training;

[0034] S70, drawing a learning curve and a residual graph based on the random forest regression model after the current training; evaluating whether the random forest regression model after the current training has overfitting or underfitting based on the learning curve; and evaluating whether the random forest regression model after the current training has systematic deviations based on the residual graph;

[0035] S80, judging whether the random forest regression model after the current training satisfies the conditions of no overfitting, underfitting and systematic deviation at the same time, if so, completing the training and going to S90, otherwise, adjusting the parameters of the random forest regression model after the current training to obtain the adjusted random forest regression model, and going to S60;

[0036] S90, inputting the test set into the trained random forest regression model to obtain the mean square error and determination coefficient of the trained random forest regression model;

[0037] S100, determining whether the mean square error is less than a first preset threshold and the determination coefficient is greater than a second preset threshold at the same time, if so, completing the test and going to S110, otherwise, adjusting the parameters of the random forest regression model after the current training, obtaining an adjusted random forest regression model, and going to S60;

[0038] S110, using a satellite receiver to obtain characteristic data of the carrier during its motion; wherein the characteristic data includes satellite position information given by multiple satellite solution channels, and position information and attitude information of the carrier determined by the satellite receiver;

[0039] S120. Extract, stack and high-order combine the feature data according to different satellite channels to obtain processed feature data; input the processed feature data into a tested random forest regression model to predict the satellite carrier-to-noise ratio; wherein the processed feature data include X, Y, and Z-axis satellite coordinates in the geodetic coordinate system, carrier positioning longitude, carrier positioning latitude, carrier positioning altitude, carrier pitch angle, carrier roll angle, carrier heading angle, the relative distance from the satellite receiver to the satellite, satellite azimuth, and satellite elevation.

[0040] By applying the technical solution of the present invention, during the training process, by adding the carrier attitude information to a specific data set and extracting, stacking and combining high-order features, combined with a random forest regression model, the problem that the existing technology cannot adapt to the carrier attitude changes in the field of satellite carrier-to-noise ratio prediction is solved. In the prediction process, the position information solved by the satellite receiver, the satellite coordinate information and the attitude information of the carrier to which the satellite receiver is attached are used as input features, and the nonlinear relationship between the satellite carrier-to-noise ratio and the attitude information and position information of the carrier can be learned and fitted efficiently and with high quality. This method skips some complex geometric calculations through data fitting, significantly reducing the computational complexity; by combining multi-dimensional high-order features to fit the nonlinear relationship between the carrier attitude and the satellite carrier-to-noise ratio, the adaptability to dynamic scenes is improved; by optimizing the model parameters, the error of the carrier-to-noise ratio prediction can be significantly reduced. The implementation process of this method is relatively simple and has high application value.

[0041] In order to further understand the present invention, the following Figure 1-Figure 3 The satellite carrier-to-noise ratio prediction method applicable to carrier attitude change of the present invention is described in detail, and specifically comprises the following steps:

[0042] Step 1: Collect relevant data of the existing satellite receiver during the movement of the carrier, including: the carrier-to-noise ratio information of the observed satellite, the coordinate information of the known satellite (x_stat, y_stat, z_stat), the position information of the satellite receiver positioning solution (longitude long, latitude lat and altitude h), and the attitude information of the satellite receiver moving with the carrier (pitch angle pitch, roll angle roll and heading angle yaw). If the data of m positioning solution cycles are collected and the i-th (i={1,2,…,m}) positioning solution cycle contains n i If the carrier-to-noise ratio information of satellites is obtained, the number of feature values ​​contained in the row data corresponding to the i-th positioning solution cycle is at most (4n i +6), so the total number of feature values ​​in m positioning solution cycles is at most ∑(4n i +6).

[0043] Furthermore, the n in the i-th row of data in step 1 iThe 10 features of the satellite's carrier-to-noise ratio, satellite coordinate information, position information, and attitude information are extracted and stacked according to different satellites: the i-th row of data is extracted to make its dimension from 1×(4n i +6) dimension becomes n i 1×(4+6)-dimensional row data, the row data feature names become: satellite carrier-to-noise ratio CN0, satellite coordinates x_stat, satellite coordinates y_stat, satellite coordinates z_stat, positioning longitude long, positioning latitude lat, positioning altitude h, carrier pitch angle pitch, carrier roll angle roll, carrier heading angle yaw; after stacking, we get a ∑n i ×10-dimensional data.

[0044] Furthermore, the satellite coordinates x_stat, y_stat, z_stat, longitude long, latitude lat, and altitude h are used to convert the coordinates of the satellite receiver in the normal measurement coordinate system (x_ms, y_ms, z_ms). Then, the following high-order combined features are calculated by the formula, so that the feature data row dimension becomes 1×13, and a ∑n is obtained. i ×13-dimensional data:

[0045] Relative distance R = sqrt(square(x_ms)+square(y_ms)+square(z_ms);

[0046] Satellite azimuth A = arctan(y_ms / x_ms);

[0047] Satellite elevation angle E = arctan(z_ms / sqrt(square(x_ms)+square(y_ms))).

[0048] Among them, sqrt is the square root function, square is the square function, and arctan is the inverse tangent function.

[0049] Finally, the absolute median function is used to perform a sliding window scan on each feature column data to complete the outlier detection preprocessing, and the obtained preprocessed data is used as the input of the learning system. The following table 1 is a summary of the sample preprocessed data information after feature engineering:

[0050] Table 1 Summary of sample preprocessing data information

[0051]

[0052]

[0053] Step 2: In the construction of the learning system, the "satellite carrier-to-noise ratio" feature column data of the example preprocessed data is first used as the dependent variable of the regression model, and the remaining feature column data is used as the independent variable of the regression model; then the independent variable data and the dependent variable data are divided into a training set and a test set in proportion; then a random forest regression model is constructed, and the training set data is used for grid search and cross-validation to complete model evaluation and parameter selection; finally, a learning curve is drawn for the selected regression model to evaluate whether the model learning is overfitting or underfitting; a residual graph is drawn for the selected regression model to evaluate whether the model learning has systematic deviations; and the test set data is used to perform MSE and R2 evaluation on the selected regression model.

[0054] Furthermore, the random forest regression model selected by the learning system in step 2 is a combination algorithm based on several classification trees. The prediction value of the random forest regression model is formed by finding the average value of multiple regression trees. Its mathematical model can be expressed as:

[0055] y=f(X,θ)

[0056] Among them, X is the independent variable, y is the dependent variable, f(·) is the regression model, and θ is the model parameter.

[0057] Furthermore, in step 2, the data set is divided into 80% for training set and 20% for test set, and the division method is:

[0058] X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2)

[0059] Among them, train_test_split represents the data partitioning function method, X_train, X_test, y_train, and y_test represent the independent variables of the training set, the independent variables of the test set, the dependent variables of the training set, and the dependent variables of the test set, respectively.

[0060] Furthermore, the random forest regression model initialization method in step 2 is:

[0061] model=RandomForestRegressor()

[0062] Among them, model represents the initialization model, and RandomForestRegressor represents the random forest regression model initialization function method.

[0063] Furthermore, the grid search and cross-validation method for model evaluation and parameter selection in step 2 is:

[0064] grid_search=GridSearchCV(model,param_grid,cv=k)

[0065] grid_search.fit(X_train,y_train)

[0066] Among them, GridSearchCV represents the parameter grid search function method, param_grid is the search range of the model configuration parameters, the setting value k of cv is k-fold cross validation, and the fit function is the training function.

[0067] Furthermore, the regression model after model evaluation and parameter selection in step 2 is:

[0068] best_params=grid_search.best_params_

[0069] best_model=grid_search.best_estimator_

[0070] Among them, best_params is the optimal model configuration parameters within the parameter search range, best_model is the regression model that has learned the optimal model parameters θ, and best_estimator is the optimal model.

[0071] Furthermore, in step 2, a learning curve is drawn for the selected regression model, such as Figure 2 As shown, it can be seen that the learning of the regression model does not appear overfitting or underfitting; the residual graph is drawn for the selected regression model, such as Figure 3 As shown, it can be seen that there is no systematic deviation in the learning of the regression model; the regression model selected in step 2 is scored using the test set data, with an MSE score of 0.356 and an R2 score of 0.998, which meets the preset conditions.

[0072] Step 3: Extract the random forest regression model from the storage, first perform feature engineering on the latest data, and then input the tested random forest regression model for prediction to obtain the prediction result (satellite carrier-to-noise ratio).

[0073] In summary, the present invention provides a satellite carrier-to-noise ratio prediction method suitable for carrier attitude changes. In the training process, by adding carrier attitude information to a specific data set and extracting, stacking and combining high-order features, combined with a random forest regression model, the problem that the existing technology cannot adapt to carrier attitude changes in the field of satellite carrier-to-noise ratio prediction is solved. In the prediction process, the position information solved by the satellite receiver, the satellite coordinate information and the attitude information of the carrier to which the satellite receiver is attached are used as input features, and the nonlinear relationship between the satellite carrier-to-noise ratio and the attitude information and position information of the carrier can be efficiently and high-quality learned and fitted. This method skips some complex geometric calculations through data fitting, significantly reducing the computational complexity; by combining multi-dimensional high-order features to fit the nonlinear relationship between the carrier attitude and the satellite carrier-to-noise ratio, the adaptability to dynamic scenes is improved; by optimizing model parameters, the error of carrier-to-noise ratio prediction can be significantly reduced. The implementation process of this method is relatively simple and has high application value.

[0074] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0075] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. If not otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0076] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A satellite carrier-to-noise ratio prediction method suitable for carrier attitude changes, characterized in that: The method comprises: S10, constructing a feature data set during the carrier motion process; wherein the feature data set is obtained by using a satellite receiver, and the feature data set includes satellite carrier-to-noise ratio information and satellite position information given by multiple satellite solution channels, and carrier position information and attitude information determined by the satellite receiver positioning solution; S20, extracting, stacking and high-order combining the feature data sets according to different satellite channels to obtain a processed feature data set; wherein the processed feature data set includes satellite carrier-to-noise ratio, X, Y, and Z-axis satellite coordinates in the geodetic coordinate system, carrier positioning longitude, carrier positioning latitude, carrier positioning altitude, carrier pitch angle, carrier roll angle, carrier heading angle, relative distance from the satellite receiver to the satellite, satellite azimuth, and satellite elevation angle; S30, performing outlier detection on the processed feature data set to obtain a feature data set after removing outliers; S40, dividing the feature data set after removing outliers into a training set and a test set according to a preset ratio; S50, establish a random forest regression model; S60, inputting the training set into the random forest regression model for grid search and cross validation to obtain the random forest regression model after the current training; S70, drawing a learning curve and a residual graph based on the random forest regression model after the current training; evaluating whether the random forest regression model after the current training has overfitting or underfitting based on the learning curve; and evaluating whether the random forest regression model after the current training has systematic deviations based on the residual graph; S80, judging whether the random forest regression model after the current training satisfies the conditions of no overfitting, underfitting and systematic deviation at the same time, if so, completing the training and going to S90, otherwise, adjusting the parameters of the random forest regression model after the current training to obtain the adjusted random forest regression model, and going to S60; S90, inputting the test set into the trained random forest regression model to obtain the mean square error and determination coefficient of the trained random forest regression model; S100, determining whether the mean square error is less than a first preset threshold and the determination coefficient is greater than a second preset threshold at the same time, if so, completing the test and going to S110, otherwise, adjusting the parameters of the random forest regression model after the current training, obtaining an adjusted random forest regression model, and going to S60; S110, using a satellite receiver to obtain characteristic data of the carrier during its motion; wherein the characteristic data includes satellite position information given by multiple satellite solution channels, and position information and attitude information of the carrier determined by the satellite receiver; S120, extract, stack and combine the feature data according to different satellite channels to obtain processed feature data; input the processed feature data into the tested random forest regression model to predict the satellite carrier-to-noise ratio. The processed feature data includes the X, Y, and Z-axis satellite coordinates in the geodetic coordinate system, the carrier positioning longitude, the carrier positioning latitude, the carrier positioning altitude, the carrier pitch angle, the carrier roll angle, the carrier heading angle, the relative distance from the satellite receiver to the satellite, the satellite azimuth, and the satellite elevation.