Space target observation data error correction method based on machine learning

By constructing an error correction model using machine learning methods, the problem of multi-source composite errors in space target observation was solved, achieving high-precision error correction and improved data processing efficiency, adapting to different observation conditions.

CN120994969APending Publication Date: 2025-11-21ZHONGKE XINGTU MEASUREMENT & CONTROL TECH CO LTD
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Patent Information

Application Number
CN202511173612.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-08-21
Publication Date
2025-11-21

AI Technical Summary

Technical Problem

Traditional error correction methods are difficult to effectively handle multi-source composite errors in space target observation and cannot meet the requirements of high-precision observation.

Method used

Machine learning methods are employed to collect and preprocess spatial target observation data to construct a high-precision training dataset. Models such as gradient boosting decision trees, random forests, support vector machines, and neural networks are used for error correction. By combining features such as observation station location, environmental parameters, and time information, comprehensive analysis and processing of multi-source errors are achieved.

Benefits of technology

It significantly improves the accuracy and processing efficiency of space target observation data, can effectively correct errors under different observation conditions, adapts to complex environments, and expands the scope of applications.

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Abstract

The invention discloses a space target observation data error correction method based on machine learning, and the method comprises the steps: collecting space target observation data, building a high-precision training data set after preprocessing, building an error correction model, and carrying out the training optimization of the error correction model based on the training data set. And deploying the error correction model after training optimization, and performing error correction on the space target observation data. According to the method, inherent errors, environment disturbance errors and errors generated in the data processing process are comprehensively analyzed and processed through the powerful nonlinear modeling capacity and the self-adaptive characteristic of a machine learning model, the problem of multi-source composite errors in space target observation is effectively solved, systematic deviation of observation data is greatly reduced, and the method is suitable for large-scale popularization and application. And high-precision data support is provided for key tasks such as orbit determination and orbit forecasting.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of space target observation data error correction, and particularly relates to a space target observation data error correction method based on machine learning. BACKGROUND

[0002] In the field of space target observation, accurately obtaining relevant data of the target is the basis for carrying out key tasks such as orbit determination, orbit prediction and space target anomaly detection.

[0003] However, the measurement accuracy of observation data is often disturbed by various factors, mainly including device inherent errors such as optical distortion of optical equipment, nonlinear characteristics of sensors and the like; environmental disturbance errors such as atmospheric turbulence which will affect optical observation, ionospheric interference which will interfere with radar observation and the like; and errors generated in the data processing process, for example, deviations in coordinate system conversion, errors caused by different observation times and the like.

[0004] Traditional error correction methods include least squares method and Kalman filtering and the like, and in the face of complex situations of mutual coupling of multiple error sources, the traditional methods are difficult to fully play a role, have obvious limitations and cannot meet the needs of high-precision observation.

[0005] For example, the application number 202311824826.5 discloses a space target observation data matching and association method and system, which solves the problem of fuzzy matching and association, but the scheme has the limitations of traditional correction methods and does not fully utilize machine learning technology.

[0006] With the rapid development of artificial intelligence technology, machine learning provides a new way to solve the problem of multiple source compound errors in space target observation by virtue of its powerful nonlinear modeling capability and adaptive characteristics.

[0007] Therefore, a space target observation data error correction scheme based on machine learning which can effectively improve the accuracy of observation data is needed. SUMMARY

[0008] In view of the above problems, the present application aims to provide a space target observation data error correction method based on machine learning to solve the problem that multiple source compound errors in space target observation are difficult to correct effectively.

[0009] The present application provides a space target observation data error correction method based on machine learning.

[0010] The first aspect is a space target observation data error correction method based on machine learning, comprising:

[0011] S1, collect space target observation data, and construct a high-precision training data set after preprocessing;

[0012] S2, construct an error correction model, and train and optimize the error correction model based on the training data set;

[0013] S3, deploy the trained and optimized error correction model, and correct errors of the space target observation data.

[0014] In an embodiment of the present application, the space target observation data includes measured observation data of the space target and corresponding theoretical reference observation values.

[0015] In an embodiment of the present application, the measured observation data includes angle measurement data, speed measurement data and distance measurement data.

[0016] In an embodiment of the present application, the theoretical reference observation values include:

[0017] Based on high-precision orbit data of the space target, corresponding theoretical observation values are calculated and generated; or

[0018] Based on homologous station measurement data of the space target, corresponding theoretical observation values are calculated and generated.

[0019] In an embodiment of the present application, the space target observation data further includes observation station position information, environmental parameters at the observation time and time information.

[0020] In an embodiment of the present application, the preprocessing includes time alignment, outlier rejection, format standardization and normalization processing.

[0021] In an embodiment of the present application, the error correction model includes gradient boosting decision tree, random forest, support vector machine and neural network.

[0022] In an embodiment of the present application, the evaluation index of the trained and optimized error correction model is mean absolute error (MAE) and root mean square error (RMSE).

[0023] Second aspect: an electronic device, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the method provided in the first aspect when executing the program.

[0024] Third aspect: a non-transitory computer readable storage medium having a computer program stored thereon, wherein the computer program is executable on a processor to implement the steps of the method provided in the first aspect.

[0025] The present application has the following beneficial effects:

[0026] 1、The method has the powerful nonlinear modeling capability and the self-adaptive characteristics of the machine learning model, comprehensively analyzes and processes inherent errors, environmental disturbance errors and errors generated in the data processing process, effectively solves the multi-source compound error problem in space target observation, greatly reduces the systematic deviation of observation data, and provides high-precision data support for key tasks such as orbit determination and orbit prediction.

[0027] 2、The method is based on a high-precision training data set, and the systematic error correction model trained can process original measured observation data and associated features in real time and automatically, and output corrected observation values. The whole process does not need manual intervention, and can adapt to different types of observation data, significantly improving the efficiency and convenience of space target observation data processing.

[0028] 3、The method of the present application is aimed at cooperative targets, non-cooperative targets with public high-precision ephemeris and non-cooperative targets without high-precision ephemeris, and constructs a training set through two high-precision theoretical reference value generation methods to ensure that multiple errors can be effectively considered under different data availability scenarios. At the same time, the model integrates environmental parameters, observation station positions and other associated features to enhance the adaptability to complex observation conditions and expand the application range in the field of space target observation. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a flowchart of the space target observation data error correction method of the present application;

[0030] Figure 2 is a structural schematic diagram of the electronic device of the present application. DETAILED DESCRIPTION

[0031] The embodiments of the present application will be described in detail below, and examples of the embodiments are shown in the drawings, wherein the same or similar symbols represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present application, and cannot be understood as a limitation of the present application.

[0032] The existing space target observation data correction methods, such as least square method or Kalman filter method, have obvious limitations in processing these multi-error source coupling problems, and have low precision.

[0033] Embodiment:

[0034] To solve the above problems, the present embodiment provides a space target observation data error correction method based on machine learning. Figure 1 is a flowchart of the space target observation data error correction method of the present application, which comprises:

[0035] S1, collect space target observation data, and construct high-precision training data set after preprocessing.

[0036] Firstly, space target observation data collection is carried out. The collected space target observation data includes synchronous acquisition of measured observation data of space targets and corresponding theoretical reference observation values.

[0037] The measured observation data focuses on the core physical quantities of space targets. The collection types mainly include angle measurement data, speed measurement data and distance measurement data, which can ensure the coverage of key parameters in different observation scenarios. Among them:

[0038] The angle measurement data is to accurately record the azimuth angle and elevation angle in the horizontal coordinate system, or the right ascension and declination in the equatorial coordinate system according to the coordinate system used for observation. These data directly reflect the angular position of the target in the celestial coordinate system or the ground coordinate system.

[0039] The speed measurement data includes the radial velocity of the target relative to the observation station, as well as the velocity components decomposed in a specific coordinate system (such as the horizontal coordinate system or the equatorial coordinate system), which is used to capture the motion rate characteristics of the target.

[0040] The distance measurement data is to measure and record the straight-line distance between the target and the observation station by radar and other devices, which is an important parameter for representing the spatial position of the target.

[0041] The theoretical reference observation values need to maintain strict physical dimension and meaning consistent with the measured data, which serve as the benchmark for model training. The generation method is divided into two categories according to data availability:

[0042] One is to calculate the corresponding theoretical observation values based on the high-precision orbit of space targets, mainly including cooperative space targets (high-precision GNSS positioning data can be obtained through telemetry means) and non-cooperative space targets with high-precision ephemeris published by the owner (such as precise orbit parameters announced by satellite operators).

[0043] When calculating, the high-precision orbit data of space targets is used as the basis, combined with verified orbit mechanics model (considering celestial mechanics factors such as earth gravity and lunar perturbation) and observation geometry model (based on the geometric relationship between observation station coordinates and target position), through strict formula derivation and calculation, the theoretical observation values corresponding to the measured data are generated, ensuring that their precision matches the original orbit data.

[0044] Based on the measurement data of the same source station of space targets, the improved acquisition is carried out, which is suitable for non-cooperative targets (such as space debris and satellites without public high-precision orbit roots) that cannot obtain high-precision ephemeris.

[0045] The applicable prerequisite is that the same source station has accumulated continuous and high-density observation data (such as continuous observation records for several months) of the space target and other non-orbit-changing targets.

[0046] During the calculation, the orbit of the space target is precisely solved and improved using the above-mentioned homologous station orbit data, and the orbit after improvement that meets the specific precision index (for example: the orbit improvement residual RMS of the continuous 7-day orbit is less than the threshold, and the daily variation of the orbit semi-major axis is less than 1E-6) is used as the basis. The corresponding theoretical observation value is inverted as the training reference.

[0047] Further, in addition to the core measured observation value and the corresponding theoretical reference value, the space target observation data also includes related features that may affect the observation accuracy, including observation station location information, observation time environmental parameters, time information and other related parameters, wherein:

[0048] The observation station location information includes longitude, latitude and elevation information, etc. The geographical position information of the observation station is one of the key factors affecting the accuracy of the space target observation data, which specifically includes:

[0049] Longitude: the east or west coordinate accurate to several decimal places, which determines the position of the observation station in the east-west direction of the earth and directly affects the calculation reference of the azimuth angle of the observed target. Latitude: the north or south coordinate accurate to several decimal places, which reflects the position of the observation station in the north-south direction of the earth and is closely related to the calculation of the elevation angle. Elevation: the vertical height of the observation station relative to the average sea level (usually in meters, accurate to centimeters), which will affect the reference of the ranging data.

[0050] The differences in longitude, latitude and elevation will cause different geometric relationships between the observation station and the space target, and thus affect the accuracy of the angle measurement data. These position information is obtained through high-precision GNSS (Global Navigation Satellite System) measurement or geodetic measurement, ensuring that the error is within millimeters to centimeters, providing a reliable basis for the geometric model calculation of the observation data.

[0051] The environmental parameters at the observation time include temperature, relative humidity and atmospheric pressure, etc. Environmental factors will produce non-negligible errors on the observation data by affecting the electromagnetic wave propagation path and the performance of the observation equipment. The specific parameters include:

[0052] Temperature: The air temperature of the environment around the observation station at the observation time. Changes in temperature will cause changes in the refractive index of the atmosphere, affecting the propagation speed and path curvature of optical signals and radar waves, especially the accuracy of optical angle measurement and radar range measurement data. Relative humidity: The percentage of water vapor content in the air relative to the saturated water vapor content at the same temperature. High humidity environment may cause the optical equipment lens to fog and the radar antenna gain to decrease. At the same time, water vapor is one of the key factors affecting the refractive index of the atmosphere. Atmospheric pressure: The atmospheric pressure at the observation time, reflecting the weight of the air column per unit area. Changes in atmospheric pressure will change the atmospheric density distribution, and then affect the propagation path of electromagnetic waves in the atmosphere. Especially in radar range and speed data, it may introduce additional range delay and speed bias.

[0053] These environmental parameters are usually collected in real time by meteorological sensors deployed around the observation station, and in some cases, meteorological satellite or sounding data are also used to obtain the vertical profile of environmental parameters to more accurately model the influence of the environment on the observation.

[0054] Time information includes observation date and time, etc. Time parameters are important associated features of space target observation data, affecting the spatial position calculation of targets and the timeliness of error correction models, including:

[0055] Observation date: accurate to the day, used to distinguish the differences in the position of the earth's rotation and revolution in different seasons and different time periods, as well as the periodic changes of the space environment (such as solar activity and geomagnetic activity). Observation time: millisecond-level time information (usually UTC time), used to align the time of measured data and theoretical reference values, and to model the real-time changes in the azimuth and elevation angles of targets caused by the earth's rotation.

[0056] Time information is obtained through high-precision atomic clocks or GNSS time systems to ensure the accuracy of the observation time and provide an accurate time reference for the calculation of orbit mechanics models and observation geometry models.

[0057] Other parameters such as signal-to-noise ratio (SNR) and equipment status identification also affect error characteristics.

[0058] Signal-to-noise ratio (SNR): the ratio of the power of the effective signal to the power of the noise in the observed signal, reflecting the quality of the observed data. Low signal-to-noise ratio means that the noise interference in the data is strong, which may lead to an increase in the random error of the angle, speed, and distance measurement data. High signal-to-noise ratio means that the data is more stable and the error characteristics are more systematic, which is an important basis for distinguishing the reliability of the data. Device state identifier: used to record the running state of the observation device, including but not limited to: device model, calibration time, device working mode, hardware fault code. Changes in the state of the device will change its inherent error characteristics, for example, an optical device that has not been calibrated for a long time may have greater optical distortion, which will affect the systematic bias of the angle measurement data.

[0059] Further, the collected measured data and theoretical reference values are systematically processed to eliminate noise and inconsistencies, including:

[0060] Time alignment: due to the small differences in time records between the measured data and the theoretical reference values, the two are accurately aligned based on a unified time reference, ensuring that each set of measured data can be matched to the corresponding theoretical reference value.

[0061] Outlier rejection: through statistical analysis, physical reasonableness testing, and other methods, abnormal values caused by sudden device failure, extreme weather interference, data transmission errors, and other factors are identified and removed to avoid misleading the model training.

[0062] Format standardization: measured data and theoretical reference values from different devices and different data formats are converted to a unified structured format, with uniform field names and data units.

[0063] Normalization: linear or nonlinear normalization (such as mapping to the [0, 1] interval) is performed on numerical data to eliminate the impact of different physical quantities due to the difference in magnitude on model training, improving the convergence speed and stability of the model.

[0064] Through the above steps, the training data set constructed has high precision and high consistency, providing solid data support for the training of the subsequent error correction model.

[0065] S2, build an error correction model, train and optimize the error correction model based on the training data set;

[0066] First, the input feature vector of the error correction model is constructed, including: measured observation values, as the object to be corrected, which contain angle data, speed data and distance data, etc.; corresponding theoretical reference values, which have the same physical dimension and meaning as the measured data, and the theoretical reference values are used as high-precision training benchmarks for machine learning models; and related features that may affect observation accuracy, including observation station location information, observation time environmental parameters, time information and other related parameters (such as signal-to-noise ratio (SNR), equipment state identifier, etc.).

[0067] Then, the error correction model selection and training are performed. The optional error correction model types include gradient boosting decision tree, random forest, support vector machine and neural network, etc. During training, machine learning or automatic machine learning techniques are used to train models that can learn the complex nonlinear mapping relationship between measured observation values and theoretical reference values. The training goal is to minimize the difference between the model prediction value and the theoretical reference value.

[0068] Then, the model performance evaluation and verification are performed, and the mean absolute error (MAE) and root mean square error (RMSE) can be used as core quantitative indicators to evaluate the correction effect of the model on various types of observation data (angle, speed, distance) on the test set.

[0069] Then, the ablation experiment is performed to verify the influence of different data lengths (such as using 3 days, 7 days, 1 month of data for training) on the model performance, to determine the optimal training data size and ensure the robustness and practicality of the model.

[0070] By constructing and training the error correction model, the accuracy and reliability of the space target observation data can be significantly improved.

[0071] Further, in order to ensure the effectiveness of the error correction model, a continuous monitoring and updating mechanism is established, new observation data is collected regularly, and the model is retrained and fine-tuned to adapt to the influence of changes in the space environment, changes in observation equipment performance and other factors. It can also be combined with other advanced technologies such as big data analysis, cloud computing, etc., to further improve the efficiency and quality of error correction.

[0072] S3, deploy the trained and optimized error correction model to correct the error of the space target observation data.

[0073] First, the model is solidified and deployed. The optimal error correction model that has been trained and strictly verified is solidified to convert it into a standardized execution module that can be directly run. This module needs to be adapted through an interface to seamlessly integrate with the homologous station data processing system. During deployment, compatibility testing (including hardware environment adaptation, operating system version matching) and stress testing (high-concurrency data processing for 72 consecutive hours without exception) need to be completed to ensure that the model can be stably connected to the main process of station observation data processing and provide high-availability foundation support for subsequent real-time error correction.

[0074] Second, real-time or quasi-real-time error correction is implemented. When the station starts a space target observation task, the system automatically triggers the data collection and input process:

[0075] The data collection link synchronously acquires two types of core data: one is the original measured observation data (including angle measurement data, speed measurement data, and range measurement data), and the other is the associated feature data (including observation station location information, observation time environmental parameters, and time information). The data input mechanism realizes low-delay transmission through a dedicated data bus, and after format verification, the data is input into the deployed error correction model in real time.

[0076] Next, systematic bias compensation is performed. The error correction model calls the multi-source error coupling pattern library learned during the training phase to perform multi-layer correction operations on the input data, such as:

[0077] Based on feature matching to locate error sources (such as identifying the contribution of atmospheric refraction error through humidity parameters); using nonlinear mapping algorithms to calculate directional correction (distinguishing independent correction coefficients for angle / speed / range parameters); outputting dual-track results, separate results of original data and correction, and directly generated corrected fusion results, thereby achieving coordinated compensation of device inherent errors, environmental disturbance errors, and data processing errors.

[0078] Finally, precision improvement output is performed. The corrected data is subjected to quality verification, including correction reasonableness verification and consistency comparison with historical data trends, to generate high-precision observation results with metadata identification.

[0079] Verification and effect:

[0080] Select the observation station as the verification scene, the observation station is equipped with optical equipment and radar equipment in line with the space target observation standard, can stably collect observation data such as angle (azimuth angle, elevation angle, etc.), and has a perfect data storage and processing system, which can meet the basic needs of data collection, transmission and analysis of the experiment. At the same time, the space target observation data error correction model based on machine learning optimized by training is deployed to the data analysis platform of the observation station, the adaptation of the model and the observation station data interface is completed, and it is ensured that the model can normally read the observation data and output the correction result.

[0081] The observation station continuously observes a specific space target, synchronously collects original measured observation data, and covers key angle data such as azimuth angle and elevation angle in the horizontal coordinate system. The collected original data is preprocessed, including time alignment, outlier elimination and other operations, to remove abnormal values and interference information in the data and ensure that the data quality of the input model meets the requirements.

[0082] The preprocessed original measured data is input into the deployed error correction model, the model corrects the original data in real time based on the learned systematic error mode, and outputs the corrected observation data. During the experiment, the average errors of the elevation angle and the azimuth angle in the original measured data are recorded, and the average errors of the elevation angle and the azimuth angle after the model correction are recorded.

[0083] According to the recorded error data, the error reduction amplitude and the relative improvement ratio are calculated. According to the statistics:

[0084] The average error of the elevation angle is reduced from 0.13 degrees before correction to 0.017 degrees after correction, and the relative improvement is about 87%;

[0085] The average error of the azimuth angle is reduced from 0.044 degrees before correction to 0.024 degrees after correction, and the relative improvement is about 45% by calculation.

[0086] The above experimental results show that the error correction model of the present application can effectively reduce the systematic deviation of the space target observation data, and fully proves that the method of the present application has significant effect and accuracy in identifying and compensating systematic errors and improving observation accuracy.

[0087] The present application also provides an electronic device, Figure 2 The structure diagram of the electronic device provided by the embodiment of the present application is shown in Figure 2 As shown, the electronic device can include a processor, a communications interface, a memory and a communications bus, wherein the processor, the communications interface and the memory complete mutual communication through the communications bus. The processor can call the logical instructions in the memory, for example, to execute the following method:

[0088] S1, collect space target observation data, and construct a high-precision training data set after preprocessing;

[0089] S2, construct an error correction model, and train and optimize the error correction model based on the training data set;

[0090] S3, deploy the error correction model after training and optimization, and correct errors of the space target observation data.

[0091] In addition, the logical instructions in the memory described above can be implemented in the form of a software function unit and sold or used as an independent product, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts that contribute to the prior art or parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0092] The embodiments of the present application also provide a non-transitory computer readable storage medium having a computer program stored thereon, which is executed by a processor to implement the method provided by the above-mentioned embodiments, for example, including:

[0093] S1, collect space target observation data, and construct a high-precision training data set after preprocessing;

[0094] S2, construct an error correction model, and train and optimize the error correction model based on the training data set;

[0095] S3, deploy the error correction model after training and optimization, and correct errors of the space target observation data.

[0096] The system embodiments described above are only illustrative, wherein the units illustrated as separate components can or can not be physically separated, and the components illustrated as units can or can not be physical units, that is, they can be located in one place, or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the present embodiment according to actual needs. Those skilled in the art can understand and implement without creative labor.

[0097] Those skilled in the art can clearly understand the technical solutions of the various embodiments from the above description of the embodiments, and the various embodiments can be implemented by means of software with the necessary general hardware platforms, and of course, can also be implemented by hardware. Based on such understanding, the above technical solutions, essentially or in other words, the part of the prior art that makes a contribution, can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, and the like, and includes a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0098] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for some technical features therein; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for correcting observation data errors of space objects based on machine learning, characterized in that, The method comprises the following steps: S1, collecting space target observation data, and constructing a high-precision training data set after preprocessing; S2, constructing an error correction model, and training and optimizing the error correction model based on the training data set; S3, deploying the trained and optimized error correction model to correct errors of the space target observation data.

2. The method of claim 1, wherein, The space target observation data comprises measured observation data of space targets and corresponding theoretical reference observation values.

3. The method of claim 2, wherein, The measured observation data comprises angle measurement data, speed measurement data, and distance measurement data.

4. The method of claim 2, wherein, The theoretical reference observation values comprise: corresponding theoretical observation values calculated based on high-precision orbit data of the space targets; or corresponding theoretical observation values calculated based on homologous station measurement data of the space targets.

5. The method of claim 2, wherein, The space target observation data further comprises observation station position information, environmental parameters at the observation time, and time information.

6. The method of claim 1, wherein, The preprocessing comprises time alignment, outlier elimination, format standardization, and normalization processing.

7. The method of claim 1, wherein, The error correction model comprises gradient boosting decision trees, random forests, support vector machines, and neural networks.

8. The method of claim 1, wherein, After the training and optimization of the error correction model, the evaluation indexes are mean absolute error (MAE) and root mean square error (RMSE).

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the steps of the method according to any one of claims 1 to 8. 10.A non-transitory computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the method according to any one of claims 1 to 8.

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