A method for improving height measurement accuracy based on weighted average fusion feature extraction based on machine learning

Abstract

The present invention discloses a method for improving the accuracy of height measurement based on machine learning weighted average fusion feature extraction. The method uses a global navigation satellite system reflectometer to measure the sea surface height, and can improve the observation and inversion of ocean mesoscale processes by increasing the spatial coverage of ocean surface observations. In order to make up for the shortcomings of traditional inversion methods, the present invention constructs a new machine learning weighted average fusion feature extraction method based on a machine learning fusion model combined with the principle of feature extraction, which takes airborne time-delay waveform data as input and sea surface height as output. At the same time, two features HALF and DER that are sensitive to changes in sea surface height are constructed based on the time-delay waveform data set, and the influence of feature sets with different information details on the inversion accuracy of sea surface height is analyzed. The use of a new machine learning weighted average fusion feature extraction method can effectively improve the inversion accuracy of sea surface height, and the accuracy is improved by about 61%.

Description

Technical Field

[0001] The present invention belongs to the cross-technical fields of satellite altimetry, oceanographic mapping, etc., and in particular relates to a method for improving altimetry accuracy based on weighted average fusion feature extraction based on machine learning. Background Art

[0002] As an important ocean parameter, sea surface height plays an important role in the establishment of global tidal models, observation of large-scale ocean circulation, and monitoring of global sea level changes. Traditional satellite-borne radar altimeters obtain ocean physical parameter information by continuously transmitting radar pulses to the earth and receiving sea surface echoes, which has the disadvantages of low coverage, long repetition period, and high satellite cost. GNSS-R technology is an emerging remote sensing technology in sea surface altimetry in recent years. It inverts sea surface height by measuring the time delay between the reflected signal and the direct signal through the sea surface. In 1993, Martin-Neira first proposed the concept of PARIS (Passive reflectometry and interferometry system) and pointed out the possibility of using GPS reflected signals for altimetry. Compared with traditional remote sensing technology, GNSS-R ocean remote sensing technology has made up for the defects of existing ocean remote sensing technology to a large extent with its advantages of rich signal sources, low cost, low power consumption, all-weather and high real-time performance. At present, this technology has been used to detect parameters such as sea surface height, sea breeze, sea ice, and soil moisture.

[0003] In recent years, the successful launch of the British TDS-1, the American CYGNSS and the Chinese Fenghuo A / B dual satellites have marked that GNSS-R technology has entered a new stage of detecting global surface parameters. As a passive remote sensing technology, satellite-borne GNSS-R technology has the advantages of low cost and global monitoring, and has great development prospects in the field of sea surface height inversion. However, the main purpose of the satellite-borne GNSS-R receiving satellites launched in the world is not sea surface height inversion, and the satellite receivers have not optimized the height inversion, which limits the research on high-precision satellite-borne GNSS-R sea surface height inversion. Airborne altimetry technology is regarded as a pre-research technology for satellite-borne altimetry technology and is being widely studied. According to different antenna devices, GNSS-R altimetry can be divided into a single-antenna autocorrelation mode and a dual-antenna cross-correlation interference mode. Compared with the single-antenna mode, the dual-antenna mode has no strict requirements on the height of the observation platform, and has a wider range of application scenarios and scope. By analyzing the GNSS-R airborne experimental data of CSIC-IEEC in the Baltic Sea, Finland in 2011, both theoretical and experimental results show that the height measurement accuracy of the cross-correlation interference mode is higher than that of the CA code autocorrelation mode. Using the airborne experimental data of Monterey Bay, California, the measurement accuracy of the three re-tracking methods HALF, DER and PARA3 was analyzed, and various error models involved in the airborne GNSS-R height inversion process were established. The results show that the HALF method produces the most accurate measurement results, with an error of 1-4m compared to the DTU average sea surface height. By analyzing the GNSS-R airborne experimental data of CSIC-IEEC in the Baltic Sea, Finland on November 11, 2011, the experimental data at different elevation angles were inverted, and it was concluded that the elevation angle will have a greater impact on the accuracy of the height measurement results. The sea surface height inversion was carried out using the airborne data collected by CSIC-IEEC in the Baltic Sea on December 3, 2015. In view of the high complexity of the ZV model fitting method for delay estimation, the 7-β model and the corresponding delay estimation method were proposed. In previous studies, HALF, DER, FIT and other re-tracking methods were usually used for GNSS-R sea surface height inversion, and the various errors involved in the inversion model were analyzed to establish the corresponding error model to improve the height inversion accuracy. HALF, DER, FIT and other re-tracking methods are mostly empirical models, which often rely on limited scalar delay-Doppler map (DDM) observations. Only partial information of DDM can be used to invert the sea surface height, which affects the accuracy of height estimation. At the same time, the establishment of various error models makes the inversion model more complex and difficult to implement.

[0004] Compared with the previous inversion models, the machine learning algorithm is simple, can establish the relationship between multiple observations and sea level, can make full use of the physical quantities related to the inversion of sea level and is easy to operate, which makes up for the shortcomings of the traditional inversion method to a certain extent. Machine learning (ML) is one of the fastest growing technical fields today, integrating multiple disciplines such as computer science and statistics, and is used to solve the problem of how to automatically establish a computational model through experience. At present, machine learning algorithms have also been gradually integrated into the GNSS-R field and have achieved excellent results. The tree model algorithm in machine learning was used to establish a mapping model from TDS-1 (TechDemoSat-1) observation data to the European Center for Medium-Term Weather Forecasts (ECMWF) analysis field data, and the results obtained were significantly better than the traditional GNSS-R wind speed inversion method. The multi-hidden layer neural network was used for wind speed inversion, and the influence of the characteristics such as the DDM average value (DDMA), the leading edge slope (LES) of the delay waveform, and the incident angle on the inversion accuracy were analyzed using simulated data and real data. The XGBoost algorithm and GNSS-R technology were used to invert soil moisture characteristics, and the importance of input characteristics such as altitude angle, signal-to-noise ratio, and receiver gain to the soil moisture inversion model was evaluated.

[0005] However, machine learning models require a large number of labeled observations to train and build models. Spaceborne GNSS-R receivers can provide a large amount of observation data, but the corresponding high-precision sea surface height is difficult to obtain. At the same time, due to the weak GNSS-R signal, how to construct features that are sensitive to SSH changes is another major factor in the SSH inversion of machine learning fusion models. Summary of the invention

[0006] The technology of the present invention solves the problem: overcomes the shortcomings of the prior art and provides a method for improving the accuracy of height measurement based on machine learning weighted average fusion feature extraction, aiming to improve the accuracy of sea surface height measurement.

[0007] In order to solve the above technical problems, the present invention discloses a method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction, comprising:

[0008] Obtain airborne time delay waveform data through sea-surface airborne experiments;

[0009] According to the airborne time delay waveform data, a fusion feature input sample set is constructed, and a fusion feature output sample corresponding to each fusion feature input sample in the fusion feature input sample set is determined;

[0010] According to the fusion feature input sample set and the fusion feature output samples corresponding to each fusion feature input sample in the fusion feature input sample set, the hyperparameters of each regression model are optimized, and the optimal output of each regression model is obtained;

[0011] According to the comparison results of the optimal output of each regression model and the corresponding fusion feature output sample, N optimal regression models are screened out;

[0012] According to N optimal regression models, R 2 -Ranking fusion model;

[0013] The acquired airborne delay waveform data of the test area is used as R 2 -Ranking fusion model input, through R 2 -Ranking fusion model inverts the sea surface height and outputs the corresponding sea surface height value.

[0014] In the above-mentioned method for improving the height measurement accuracy based on machine learning weighted average fusion feature extraction, a fusion feature input sample set is constructed according to the airborne delay waveform data, and a fusion feature output sample corresponding to each fusion feature input sample in the fusion feature input sample set is determined, including:

[0015] The airborne time-delay waveform data and the tidal-corrected DTU global average sea surface data are temporally and spatially matched by time, longitude and latitude to obtain the original sample set; wherein the original sample set includes: original input samples, original output samples, and the corresponding relationship between the original input samples and the original output samples; the DTU global average sea surface data is provided by the DTU model;

[0016] The Pearson correlation coefficient method was used to screen the airborne time delay waveform data, and the features with a correlation coefficient of less than 0.1 with the DTU global average sea surface data were eliminated to obtain a first screening input sample;

[0017] Using principal component analysis, samples with a cumulative contribution rate of no less than 98% are extracted from the first screening input samples as the second screening input samples;

[0018] HALF features and DER features are introduced, and several secondary screening input samples, HALF features and DER features are used as fusion feature input samples to construct a fusion feature input sample set;

[0019] According to the correspondence between the original input samples and the original output samples in the original sample set, the fused feature output samples corresponding to each fused feature input sample are determined.

[0020] In the above method for improving the height measurement accuracy based on machine learning weighted average fusion feature extraction, the HALF feature refers to the normalized delay waveform peak value τ spec The time delay position corresponding to the point at 70% energy value of the front edge; where the normalized time delay waveform peak value τ spec The definition is as follows:

[0021]

[0022] Wherein, τ represents the reflected signal delay, and W(τ) represents the reflected signal related power delay waveform.

[0023] In the above method of improving the height measurement accuracy based on machine learning weighted average fusion feature extraction, the DER feature refers to the peak value τ of the differential waveform at the leading edge of the delay waveform. der The time delay position corresponding to the point at which the delay waveform is located; where the peak value of the leading edge differential waveform of the time delay waveform is τ der The definition is as follows:

[0024]

[0025] Wherein, τ represents the reflected signal delay, and W(τ) represents the reflected signal related power delay waveform.

[0026] In the above method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction, the regression model includes: a single regression model and an integrated tree regression model;

[0027] Single regression models include: linear regression model, ElasticNet regression model and support vector machine SVR regression model; among them, linear regression models include: Lasso regression model and Ridge regression model;

[0028] Ensemble tree regression models include: gradient boosting decision tree GBDT regression model based on Boost ensemble idea, extreme gradient boosting decision tree XGBoost regression model, light gradient boosting machine ensemble tree LightGBM regression model and random forest ensemble tree RF regression model based on Bagging ensemble idea.

[0029] In the above-mentioned method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction, grid search and K-fold cross validation methods are used to optimize the hyperparameters of each regression model.

[0030] In the above method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction, according to the comparison result between the optimal output of each regression model and the corresponding fusion feature output sample, N optimal regression models are screened and obtained, including:

[0031] According to the comparison results of the optimal output of each regression model and the corresponding fusion feature output sample, the determination coefficient of each regression model is determined;

[0032] According to the determined coefficient of determination of each regression model, N optimal regression models of different categories with the best inversion effect are screened out.

[0033] In the above method based on machine learning weighted average fusion feature extraction to improve the height measurement accuracy, according to N optimal regression models, R 2 -Ranking fusion model, including:

[0034] Determine the coefficient of determination of each optimal regression model on the fusion feature input sample set;

[0035] Determine the weight of each optimal regression model according to the determination coefficient corresponding to each optimal regression model;

[0036] According to the weights of the determined optimal regression models, we construct the R 2 -Ranking fusion model.

[0037] In the above method based on machine learning weighted average fusion feature extraction to improve height measurement accuracy, R 2 -Ranking fusion model expression is as follows:

[0038]

[0039] Where H(x) represents R 2 -Ranking fusion model output, ML_model i represents the output result sequence of the i-th optimal regression model, Feateure_set represents the fusion feature input sample, W i Represents the weight corresponding to the i-th optimal regression model.

[0040] In the above method for improving the height measurement accuracy based on machine learning weighted average fusion feature extraction,

[0041]

[0042] in, represents the determination coefficient corresponding to the i-th optimal regression model;

[0043]

[0044] Among them, ML_model i,mean represents the mean of the output result sequence of the i-th optimal regression model, and A represents the SSH value verification sequence provided by the DTU model.

[0045] The present invention has the following advantages:

[0046] (1) The present invention discloses a method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction. Compared with previous inversion models, the present invention performs sea surface height inversion based on a machine learning weighted average fusion model. The model algorithm is simple and there is no need to establish multiple error models.

[0047] (2) The present invention discloses a method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction, which can establish the relationship between multiple observation quantities and sea surface height, and can make full use of physical quantities related to sea surface height inversion to improve inversion accuracy.

[0048] (3) The present invention discloses a method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction. Compared with the traditional inversion method, the machine learning weighted average fusion model adopted in the present invention has better inversion effect and higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flowchart of the steps of a method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction in an embodiment of the present invention;

[0050] Figure 2 is a schematic diagram of a flight trajectory and the corresponding sea level height in an embodiment of the present invention;

[0051] Figure 3 is a schematic diagram of an error curve of prediction results of different regression models in an embodiment of the present invention;

[0052] Figure 4 It is a schematic diagram of the prediction results and correlation scatter points of an XGBoost regression model, an RF regression model and a Ridge regression model in an embodiment of the present invention;

[0053] Figure 5 It is a schematic diagram of scatter points of prediction results and correlation of a fusion model in an embodiment of the present invention;

[0054] Figure 6 It is a schematic diagram of experimental results of an Averaging fusion model in different data sets according to an embodiment of the present invention;

[0055] Figure 7 is an R in the embodiment of the present invention 2 -Schematic diagram of experimental results of ranking fusion model on different data sets;

[0056] Figure 8 It is a schematic diagram of experimental results of a Stacking fusion model in different data sets according to an embodiment of the present invention;

[0057] Fig. 9 is a polar coordinate diagram of the prediction performance of a fusion model in an embodiment of the present invention;

[0058] Fig.10 is an R in the embodiment of the present invention 2Schematic diagram of the experimental results of the -Ranking fusion model and the HALF and DER single-point tracking methods. DETAILED DESCRIPTION

[0059] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments disclosed in the present invention will be further described in detail below with reference to the accompanying drawings.

[0060] One of the core ideas of the present invention is to introduce a fusion model in machine learning to assist GNSS-R in delay re-tracking and sea level inversion, and to improve the accuracy of height measurement by increasing the available information of DDM. The inversion of sea level based on machine learning is essentially a nonlinear regression problem of supervised learning. The present invention first analyzes the height inversion accuracy of commonly used regression models in machine learning, such as single regression models (such as linear regression models, ElasticNet regression models, and support vector machine SVR regression models, etc.) and ensemble tree regression models (such as GBDT regression models, XGBoost regression models, LightGBM regression models, RF regression models). On this basis, regression models with better height inversion effects and lower correlation (such as RandomForests, XGBoost, and Ridge models) are selected for fusion to improve the height inversion accuracy of the fusion model. Furthermore, the fusion method adopts R 2 -Ranking method is used for weighted fusion, and the weights are allocated by the coefficient of determination of each regression model cross-validated on the fused feature input sample set. In addition, in order to obtain a fused feature input sample set that is more suitable for the sea surface height inversion model, a fused feature input sample set containing two features, HALF and DER, which are sensitive to sea surface height changes, is constructed using the feature construction method, and the influence of the fused feature input sample set with features of different information details on the sea surface height inversion accuracy is analyzed.

[0061] The use of machine learning algorithms to establish a sea level height prediction model is essentially a supervised learning regression problem, that is, using a labeled altimetry dataset as a training set to train the model, observing the performance of the trained model on the test set to optimize the model, and finally realizing the prediction of unknown data.

[0062] like Figure 1 In this embodiment, the method for improving the height measurement accuracy based on machine learning weighted average fusion feature extraction mainly consists of three parts: feature optimization, model fusion and model application. The specific implementation process is as follows:

[0063] Step 101, obtaining airborne delay waveform data through sea surface airborne experiments.

[0064] For example, in a specific example, the data obtained from the sea surface airborne experiment conducted by the Spanish IEEC in the Baltic Sea on December 3, 2015 can be selected as the airborne delay waveform data, DW data.

[0065] Step 102: construct a fused feature input sample set based on the airborne time delay waveform data, and determine a fused feature output sample corresponding to each fused feature input sample in the fused feature input sample set.

[0066] In this embodiment, feature optimization refers to selecting and constructing features related to sea level height by using the method in feature engineering, and then constructing a fusion feature input sample set. Specifically:

[0067] a) Data Matching

[0068] The airborne time-delay waveform data and the tidal-corrected DTU global average sea surface data can be matched in time and space by longitude and latitude to obtain the original sample set. The original sample set can specifically include: original input samples, original output samples, and the corresponding relationship between the original input samples and the original output samples. The DTU global average sea surface data is provided by the DTU model.

[0069] b) Feature Optimization

[0070] Since the airborne time delay waveform data has the problems of large feature dimension, high redundancy, strong correlation between adjacent features, and poor correlation between a large number of features and the DTU model, it is necessary to optimize the airborne time delay waveform data: the Pearson correlation coefficient method is used to screen the airborne time delay waveform data, and the features with a correlation coefficient of less than 0.1 with the DTU global average sea level data are eliminated to obtain the first screening input samples; the principal component analysis method is used to extract samples with a cumulative contribution rate of not less than 98% from the first screening input samples as the second screening input samples; further, in order to extract features containing sufficient information, two features HALF and DER that are sensitive to sea level changes are constructed on the basis of DW data to improve the accuracy of the fusion model, that is, the HALF feature and DER feature are introduced, and the obtained several second screening input samples, HALF features and DER features are used as fusion feature input samples to construct a fusion feature input sample set.

[0071] The HALF feature refers to the normalized delay waveform peak value τ spec The time delay position corresponding to the point at which the front edge has 70% energy value. Normalized time delay waveform peak value τ spec The definition is as follows:

[0072]

[0073] DER characteristic refers to the peak value τ of the differential waveform at the leading edge of the delay waveformder The time delay position corresponding to the point at . The peak value of the leading edge differential waveform of the time delay waveform τ der The definition is as follows:

[0074]

[0075] Wherein, τ represents the reflected signal delay, and W(τ) represents the reflected signal related power delay waveform.

[0076] c) Finally, according to the correspondence between the original input samples and the original output samples in the original sample set, the fused feature output samples corresponding to each fused feature input sample are determined.

[0077] Step 103 , based on the fused feature input sample set and the fused feature output samples corresponding to each fused feature input sample in the fused feature input sample set, optimize the hyperparameters of each regression model and obtain the optimal output of each regression model.

[0078] In this embodiment, considering that the sea level inversion mainly uses the regression method of supervised learning in machine learning, regression models such as linear regression model and ensemble tree regression model are selected for subsequent model fusion. Among them, the regression model can specifically include: a single regression model and an ensemble tree regression model. The single regression model can specifically include: a linear regression model (such as a Lasso regression model and a Ridge regression model), an ElasticNet regression model and a support vector machine SVR (Support Vector Regression, SVR) regression model. The ensemble tree regression model can specifically include: a gradient boosting decision tree GBDT (Gradient Boosting Decision Tree, GBDT) regression model based on the Boost integration idea, an extreme gradient boosting decision tree XGBoost (Extreme Gradient Boosting, XGBoost) regression model, a light gradient boosting machine ensemble tree LightGBM (Light Gradient Boosting Machine, LightGBM) regression model and a random forest ensemble tree RF (Random Forests, RF) regression model based on the Bagging integration idea.

[0079] Step 104, based on the comparison results of the optimal output of each regression model and the corresponding fusion feature output sample, N optimal regression models are screened and obtained.

[0080] In this embodiment, grid search and K-fold cross validation methods can be used to optimize the hyperparameters of each regression model. Further, the coefficient of determination of each regression model is determined based on the comparison results of the optimal output of each regression model and the corresponding fusion feature output sample; based on the determined coefficient of determination of each regression model, N optimal regression models of different categories with the best inversion effect are screened.

[0081] Step 105: construct R according to N optimal regression models 2 -Ranking fusion model.

[0082] In this embodiment, R 2 -Ranking fusion model is a weighted average fusion model based on the cross-validation error of the regression model (learner) on the fusion feature input sample set. This model uses a single regression model with higher accuracy and lower correlation for fusion to improve the model's measurement accuracy.

[0083] Preferably, R 2 The specific process of the -Ranking fusion model is as follows:

[0084] a) Determine the coefficient of determination of each optimal regression model on the fusion feature input sample set. The coefficient of determination is a commonly used performance evaluation indicator in machine learning regression models, which reflects the degree of fit of the machine learning regression model to the input data. The closer the coefficient of determination is to 1, the better the fit of the machine learning regression model to the input data.

[0085] b) Determine the weight of each optimal regression model according to the coefficient of determination corresponding to each optimal regression model. The method of determining the weight according to the coefficient of determination can be understood as follows: under the premise that overfitting does not occur, the larger the coefficient of determination, the better the effect of the fusion model and the higher the measurement accuracy.

[0086] c) According to the weights of the determined optimal regression models, construct and obtain R 2 -Ranking fusion model.

[0087] Preferably, R 2 -Ranking fusion model can be expressed as follows:

[0088]

[0089] Where H(x) represents R 2 -Ranking fusion model output, ML_model i represents the output result sequence of the i-th optimal regression model, Feateure_set represents the fusion feature input sample, W i Represents the weight corresponding to the i-th optimal regression model.

[0090] Furthermore,

[0091]

[0092] in, It represents the determination coefficient corresponding to the i-th optimal regression model:

[0093]

[0094] Among them, ML_model i,mean represents the mean of the output result sequence of the i-th optimal regression model, and A represents the SSH value verification sequence provided by the DTU model.

[0095] Step 106: Use the acquired airborne delay waveform data of the area to be measured as R 2 -Ranking fusion model input, through R 2 -Ranking fusion model inverts the sea surface height and outputs the corresponding sea surface height value.

[0096] Based on the above embodiments, the following is an example of R 2 -Ranking The accuracy evaluation of the fusion model is explained.

[0097] In this embodiment, the R 2 The output results (predicted values) obtained by the -Ranking fusion model are compared with the SSH value verification sequence (true value) provided by the DTU model, and the mean absolute error (MAD), root mean square error (RMSE) and Pearson correlation coefficient (CC) are used to compare R 2 -Ranking fusion model accuracy. The smaller the MAD and RMSE values ​​are, the better the fit between the predicted value and the true value is, and the smaller the error between the two is; the closer CC is to 1, the R 2 -Ranking The better the correlation between the fusion model and the DTU model.

[0098] in:

[0099]

[0100]

[0101]

[0102] Where T represents R 2 -The output result (prediction value) obtained by the Ranking fusion model; T j Represents R 2-Ranking fusion model’s j-th predicted value, A j Indicates that T j The jth true value of the corresponding DTU model; the number of predicted values ​​and true values ​​is the same, both n; Cov(T,A) represents the covariance of the predicted value and the verified value; σ T represents the variance of the prediction, σ A Represents the variance of the true value.

[0103] Based on the above embodiments, the verification and application of the method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction are described below.

[0104] verify

[0105] 1. Dataset

[0106] (1.1) Airborne delay waveform data

[0107] The airborne delay waveform data comes from an airborne experiment conducted by the Spanish IEEC in the Baltic Sea on December 3, 2015. During the experiment, the flight altitude was about 3km and the speed was about 50m / s. The direct and reflected GNSS signals were received by the 8-element antennas of the RHCP (Right Handed Circular Polarization) installed on the top of the aircraft and the LHCP (Left Handed Circular Polarization) installed on the belly of the aircraft, and down-converted to 19.42MHz intermediate frequency signals through the RF module, and then quantized and stored by 1bit. The one-dimensional delay waveform was obtained by cross-correlation interference method to cross-correlate the GPS direct and sea surface reflected signals.

[0108] The present invention uses GPS PRN1 satellite from 10:52:42 to 11:21:41 on December 3, 2015. In order to avoid the influence caused by the aircraft turning, the data of the aircraft turning are removed, and only the data when the aircraft flies in a straight line are selected for this experimental analysis. Figure 2 The flight trajectory of the aircraft in two time periods is given. The flight data of two time periods are analyzed. The first experimental data time period is GPS time 384702s-385121s ( Figure 2 The second experimental data period is GPS time 385542s-386501s ( Figure 2 AD segment in ).

[0109] (2) DTU model

[0110] When performing airborne GNSSS-R sea level inversion, it is necessary to compare and verify with the measured sea level data to determine the accuracy of airborne sea level inversion. Due to the lack of measured data, a verification model is used to verify the accuracy of sea level inversion. The present invention uses the DTU15 model composed of the global average sea level model DTU15 developed by the Technical University of Denmark and the TPXO8 global tide model provided by Oregon State University (OSU) as a verification model. The sea level (SSH) obtained by the verification model can be expressed as:

[0111] SSH=DTU15+TPXO tide

[0112] Among them, TPXO tide represents the tidal corrections calculated by the TPXO8 global ocean tide model.

[0113] (3) Dataset matching and division

[0114] The airborne delay waveform data is a continuous time-varying data set, while the DTU15 mean sea surface model is a grid data with longitude and latitude of 1′. Therefore, it is necessary to first match the airborne delay waveform data with the DTU15 mean sea surface model in time and space (longitude and latitude), extract the DTU15 mean sea surface value corresponding to the airborne delay waveform data, and then use the TPXO8 global ocean tide model to calculate the tidal correction of the same time and longitude and latitude as the airborne delay waveform, and superimpose it on the DTU15 mean sea level to obtain the sea surface height value SSH of the DTU15 verification model. The airborne delay waveform data and the corresponding sea surface height value SSH constitute the original sample set. The original sample set is divided into three parts: training set, verification set and test set. 80% of the data in the experimental data of the second time period (GPST: 385542s-386501s) is used as training data for model training; the remaining 20% ​​of the data is used as verification data for the optimization of model hyperparameters and preliminary evaluation of model performance. The experimental data of the first time period (GPST: 384702s-385121s) is used as the test data to evaluate the generalization ability of the final model.

[0115] 2. Analysis of Height Measurement Accuracy of Different Machine Learning Regression Models

[0116] (2.1) Analysis of training results of different machine learning regression models

[0117] The present invention uses a variety of machine learning regression models (such as linear regression models and ensemble tree regression models, etc.) to establish a mapping relationship between airborne delay waveform data and DTU15 verification models, and optimizes hyperparameters and preliminarily evaluates the performance of the model through the coefficient of determination of each machine learning regression model on the verification set. After 5-fold cross-validation training, the training summary of the above machine learning regression models is obtained, and it can be seen that the goodness of fit of the ensemble tree regression model is significantly higher than that of the linear regression model.

[0118] In the specific example of this embodiment, the XGBoost regression model obtains the highest goodness of fit of 0.95, indicating that after the XGBoost regression model training, the model can discover explanatory information from the input factors that explains 95% of the changes in the target factor. In the linear regression model, the Ridge regression model obtains the highest model goodness of fit of 0.78, indicating that after the linear regression training, the model can discover explanatory information from the input factors that explains 78% of the changes in the target factor.

[0119] (2.2) Generalization ability analysis of different machine learning regression models

[0120] The data in the test set is used to evaluate the generalization ability of the trained machine learning regression model to verify the final effect of each machine learning regression model. The height inversion results of each machine learning regression model are curve-fitted and then subtracted from the sea surface height value provided by the corresponding DTU15 model to obtain the following: Figure 3 The error curve is shown in Figure 2. Figure 3 It can be seen that the prediction error of the ensemble tree regression model is relatively small overall, among which the prediction result of the XGBoost regression model is the best; in the linear regression model, the inversion result of the Ridge regression model is the best. At the same time, it can be seen that the inversion errors of different types of regression models are quite different. The prediction error of the ensemble tree regression model has a significant downward bulge between the time axis 360-410s, while the error of the linear regression model has a significant upward bulge. This is mainly due to the missing of a section of data in the training data, which leads to the generation of data steps. At the same time, the different algorithmic rules of the ensemble tree regression model and the linear regression model will also lead to different focuses of the two regression models on data information mining.

[0121] 3. Height measurement accuracy analysis of machine learning fusion model

[0122] (3.1) Comparative analysis of the accuracy of single model and fusion model

[0123] The fusion model uses the XGBoost regression model with higher accuracy and lower correlation, the RF regression model and the Ridge regression model to further improve the model effect. The three model fusion methods Averaging, Stacking and R2 -Ranking; Averaging and R 2 -Ranking only fuses multiple model results, while Stacking requires multiple model results to be learned using sub-learners, and sub-learners need to be specified. The base learner of the Stacking fusion model of the present invention uses the XGBoost regression model and the RF regression model learner, and the sub-learner uses the Ridge regression model learner.

[0124] like Figure 4 and Figure 5 , gives the forecast results comparison chart of three regression models, XGBoost regression model, RF regression model and Ridge regression model and their fusion model (left picture), and the correlation scatter plot of the forecast results and the sea surface height value of the DTU15 model (right picture). Figure 4 and Figure 5 It can be seen that the three regression models all show good prediction effects compared with the single regression model. 2 -Ranking and Stacking prediction results are closer to the DTU15 model, with smaller inversion errors and R 2 -Ranking and Averaging model inversion results and DTU15 model have good correlations of 0.74 and 0.75 respectively. 2 -Ranking fusion model has the best inversion effect.

[0125] In order to verify the robustness of the fusion model, the five-fold cross-validation seed number was changed three times and the experiment was repeated. Changing the random seed number is equivalent to re-splitting the original data set and retraining the base learner on the new data set. Finally, the effects of the three fusion methods were compared through the inversion results still on the test set. The performance indicators of the three prediction results of different models were calculated, and it can be seen that the robustness of the three fusion models is good. The MAD, RMSE and PCC of each model in the three experiments did not change significantly, and the results of the three experiments were basically consistent. Averaging, R 2 -The inversion effect of the fusion model of Ranking and Stacking is almost always better than that of a single model, indicating that the fusion further improves the model effect.

[0126] 4. Impact of different features on model accuracy

[0127] In the field of data mining and machine learning, it is generally believed that data and features determine the upper limit of machine learning, and the model can only approach this upper limit infinitely. Therefore, in order to select features that are highly sensitive to the sea surface, six sets of feature sets with different information details were used for model training, and their accuracy was verified on the test set. As shown in Figure 6, Figure 7 and Figure 8 , respectively Averaging, R 2 -Comparison of the prediction results (after curve fitting) of the Ranking and Stacking fusion models in six different feature sets. It can be seen from the figure that the three fusion models did not achieve the best inversion effect on feature set 6 containing the most feature information, but showed the best inversion effect on feature set 5 consisting of DW data, HALF and DER features. This shows that the machine learning fusion model with feature set 5 can better learn the complex relationship between the original input features, thereby accurately inverting the height.

[0128] By calculating the performance indicators of the three fusion models on the six data sets, it can be seen that the MAD and RMSE of feature set 5 are the smallest among all data sets, that is, the inversion results of the three fusion models on data set 5 are the most accurate. At the same time, the correlation between the inversion results of data set 5 and the DTU15 model is also the best among the six data sets. In order to more intuitively compare the inversion accuracy of the three models on each data set, the experimental results are visualized using the polar coordinate system, as shown in the figure below. Fig. 9 shown.

[0129] application

[0130] The new GNSS-R sea surface height inversion model based on machine learning fusion model and feature optimization uses the information of the entire delay waveform for height inversion. The traditional single-point tracking rule estimates the delay by determining the position of the reflected waveform feature point within the delay window. The waveform feature points that have been used for sea surface height measurement include the differential waveform peak (DER) and the 0.7 percentile (HALF). In order to verify the superiority of the new machine learning weighted average fusion feature extraction method over the traditional sea surface inversion method, the present invention compares the inversion accuracy of the new machine learning weighted average fusion feature extraction method and the traditional single-point re-tracking method. The traditional single-point tracking method estimates the delay difference of the reflected signal relative to the direct signal using the DER and HALF feature points, respectively, and uses the sea surface height inversion method to correct the tropospheric delay in the measured delay and the distance error between antennas. Figure 10 shows the HALF, DER re-tracking method and the machine learning R 2 -Ranking fusion model inversion of sea surface height. Fig.10 It can be seen that the inversion results of the machine learning fusion model are significantly better than those of the HALF and DER single-point re-tracking methods. At the same time, the machine learning fusion model does not need to consider various error corrections in the time delay, which simplifies the complexity of height inversion to a certain extent. The machine learning fusion model is significantly better than the HALF and DER single-point re-tracking methods in terms of MAD, RMSE and CC. The application of the new machine learning weighted average fusion feature extraction method effectively improves the accuracy of sea surface height inversion, with MAD and RMSE increased by about 61%; CC increased by about 44%.

[0131] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0132] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction, characterized in that: include: Obtain airborne time delay waveform data through sea-surface airborne experiments; According to the airborne time delay waveform data, a fusion feature input sample set is constructed, and a fusion feature output sample corresponding to each fusion feature input sample in the fusion feature input sample set is determined; According to the fusion feature input sample set and the fusion feature output samples corresponding to each fusion feature input sample in the fusion feature input sample set, the hyperparameters of each regression model are optimized, and the optimal output of each regression model is obtained; According to the comparison results of the optimal output of each regression model and the corresponding fusion feature output sample, N optimal regression models are screened out; According to N optimal regression models, R 2 -Ranking fusion model; The acquired airborne delay waveform data of the test area is used as R 2 -Ranking fusion model input, through R 2 -Ranking fusion model inverts the sea surface height and outputs the corresponding sea surface height value; According to the airborne delay waveform data, a fusion feature input sample set is constructed, and the fusion feature output samples corresponding to each fusion feature input sample in the fusion feature input sample set are determined, including: The airborne time-delay waveform data and the tidal-corrected DTU global average sea surface data are temporally and spatially matched by time, longitude and latitude to obtain the original sample set; wherein the original sample set includes: original input samples, original output samples, and the corresponding relationship between the original input samples and the original output samples; the DTU global average sea surface data is provided by the DTU model; The Pearson correlation coefficient method was used to screen the airborne time delay waveform data, and the features with a correlation coefficient of less than 0.1 with the DTU global average sea surface data were eliminated to obtain a first screening input sample; Using principal component analysis, samples with a cumulative contribution rate of no less than 98% are extracted from the first screening input samples as the second screening input samples; HALF features and DER features are introduced, and several secondary screening input samples, HALF features and DER features are used as fusion feature input samples to construct a fusion feature input sample set; According to the correspondence between the original input samples and the original output samples in the original sample set, the fused feature output samples corresponding to each fused feature input sample are determined; The characteristic is that the HALF feature refers to the normalized delay waveform peak value τ spec The time delay position corresponding to the point at 70% energy value of the front edge; where the normalized time delay waveform peak value τ spec The definition is as follows: Wherein, τ represents the reflected signal delay, and W(τ) represents the reflected signal related power delay waveform; It is characterized by constructing R according to N optimal regression models. 2 -Ranking fusion model, including: Determine the coefficient of determination of each optimal regression model on the fusion feature input sample set; Determine the weight of each optimal regression model according to the determination coefficient corresponding to each optimal regression model; According to the weights of each optimal regression model, R 2 -Ranking fusion model; It is characterized in that R 2 -Ranking fusion model expression is as follows: Where H(x) represents R 2 -Ranking fusion model output, ML_model i represents the output result sequence of the i-th optimal regression model, Feateure_set represents the fusion feature input sample, W i Represents the weight corresponding to the i-th optimal regression model; It is characterized in that Among them, R i 2 represents the determination coefficient corresponding to the i-th optimal regression model; Among them, ML_model i,mean represents the mean of the output result sequence of the i-th optimal regression model, and A represents the SSH value verification sequence provided by the DTU model.

2. The method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction according to claim 1 is characterized in that: DER characteristic refers to the peak value τ of the differential waveform at the leading edge of the delay waveform der The time delay position corresponding to the point at which the delay waveform is located; where the peak value of the leading edge differential waveform of the time delay waveform is τ der The definition is as follows: Wherein, τ represents the reflected signal delay, and W(τ) represents the reflected signal related power delay waveform.

3. The method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction according to claim 1 is characterized in that: Regression models, including: single regression model and ensemble tree regression model; Single regression models include: linear regression model, ElasticNet regression model and support vector machine SVR regression model; among them, linear regression models include: Lasso regression model and Ridge regression model; Ensemble tree regression models include: gradient boosting decision tree GBDT regression model based on Boost ensemble idea, extreme gradient boosting decision tree XGBoost regression model, light gradient boosting machine ensemble tree LightGBM regression model and random forest ensemble tree RF regression model based on Bagging ensemble idea.

4. The method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction according to claim 1 is characterized in that: Grid search and K-fold cross validation methods are used to optimize the hyperparameters of each regression model.

5. The method for improving height measurement accuracy based on machine learning weighted average fusion feature extraction according to claim 1 is characterized in that: According to the comparison results of the optimal output of each regression model and the corresponding fusion feature output sample, N optimal regression models are screened out, including: According to the comparison results of the optimal output of each regression model and the corresponding fusion feature output sample, the determination coefficient of each regression model is determined; According to the determined coefficient of determination of each regression model, N optimal regression models of different categories with the best inversion effect are screened out.

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