Thermal layer atmospheric density calibration method and system
By combining measured density and empirical models, and using fitting methods and residual fusion recurrent neural networks for multi-layer calibration, the problem of poor accuracy in existing methods is solved, and high-precision calibration of thermospheric atmospheric density is achieved.
Patent Information
- Application Number
- CN202610176061.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-06
- Publication Date
- 2026-05-15
AI Technical Summary
Existing thermospheric atmospheric density calibration methods rely on a single technical approach, resulting in poor calibration accuracy and an inability to effectively adapt to high-frequency nonlinear disturbances and multi-scale error imbalances.
By combining measured real density and empirical models, daily factor data at the current moment is obtained through fitting methods, residuals are calculated, and an adaptive moment estimation optimizer is used to train a residual fusion recurrent neural network for multi-layer calibration, including the superposition calculation of prior model prediction and residual fusion recurrent neural network.
It improves the accuracy of thermospheric atmospheric density calibration, effectively captures systematic trend errors and nonlinear, high-frequency detail deviations of empirical models, forms a complementary synergy, avoids the limitations of single methods, and improves the accuracy of calibration results.
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Figure CN122045702A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of space physics technology, and in particular to a method and system for calibrating thermospheric atmospheric density. Background Technology
[0002] The density of the thermospheric atmosphere is a core parameter determining atmospheric drag during the operation of low-Earth orbit satellites. Its accuracy directly affects the precision of spacecraft orbit determination, the reliability of long-term orbit forecasts, and the effectiveness of collision warnings. Density errors can lead to deviations in atmospheric drag calculations, which in turn can cause errors in orbital deviation predictions and, in severe cases, may result in spacecraft collisions or mission failures.
[0003] The thermosphere is located in the outer layer of Earth's atmosphere and is affected by the nonlinear coupling of space environment factors such as solar radiation (such as solar flares and coronal mass ejections) and geomagnetic disturbances (such as geomagnetic storms). Its density distribution exhibits significant spatiotemporal dynamic changes, with both long-term periodic fluctuations and short-term sudden violent disturbances. This poses a natural challenge to accurately obtaining the density of the thermosphere.
[0004] To meet the needs of engineering applications, the industry currently widely uses empirical models (such as the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere 2.0 (NRLMSIS 2.0) and the Jacchia-Bowman 2008 model (JB2008)) to quickly calculate thermospheric atmospheric density. These models are built based on the statistical regularities of massive historical observation data and can preliminarily characterize the trend of density variation with time, space, and environmental parameters. However, due to limitations in the spatiotemporal resolution of the modeling data, the simplification of physical assumptions, and the difficulty in fully characterizing the complex coupling effect of solar activity and geomagnetic disturbances, the prediction error of empirical models is usually maintained between 15% and 30%, which can no longer meet the requirements of modern low-Earth orbit satellite high-precision missions (such as millimeter-level orbit determination and minute-level collision warning).
[0005] Against this backdrop, using measured density data obtained by inversion from spaceborne accelerometers (such as the high-precision accelerometer on the GravityRecovery and Climate Experiment-A (GRACE-A) satellite) to perform targeted calibration of empirical models has become a core technical approach to compensate for model defects and improve the accuracy of density calculations. It is also a current research focus in the field of aerospace environmental parameter optimization.
[0006] Most existing thermospheric atmospheric density calibration methods rely on a single technical approach (based on model parameter correction or pure neural network calibration). Methods relying solely on parameter correction are limited by the inherent analytical structure of empirical models, only able to selectively adjust predefined physical parameters to capture large-scale trend errors, and struggling to adapt to detailed deviations caused by high-frequency nonlinear perturbations. Methods relying solely on neural networks, lacking physical constraints, exhibit "black box characteristics" and are prone to multi-scale error imbalances during the fitting process. The inherent limitations of these two single technical approaches ultimately lead to poor accuracy in thermospheric atmospheric density calibration results. Summary of the Invention
[0007] This invention provides a method and system for calibrating thermospheric atmospheric density, which solves the technical problem that existing thermospheric atmospheric density calibration methods rely on a single technical path to carry out calibration work, resulting in poor accuracy of thermospheric atmospheric density calibration results.
[0008] The first aspect of this invention provides a method for calibrating the density of the thermosphere, comprising:
[0009] Acquire measured real density, spatial environment data, and empirical model, and use a fitting method to fit the measured real density to obtain the daily factor data corresponding to the empirical model at the current time.
[0010] The residuals are calculated based on the measured actual density, the daily factor data corresponding to the empirical model at the current moment, and the original calculated density at the current moment.
[0011] Based on the residual and the daily factor data corresponding to the current time of the empirical model, the prior model prediction value is calculated, the prior model prediction value is output, and the prior model prediction value is compared with the measured real density to obtain the residual after prior model calibration.
[0012] Based on the adaptive moment estimation optimizer, the residuals after the prior model calibration and the spatial environment data are used to train the residual fusion recurrent neural network to be trained, and the trained residual fusion recurrent neural network is determined.
[0013] The trained residual fusion recurrent neural network outputs the residual prediction value, and the prior model prediction value is superimposed with the residual prediction value to calculate the final calibrated density of the thermospheric atmosphere.
[0014] Optionally, the daily factor data at the current time includes the daily scale factor and the daily bias factor at the current time; the calculation of residuals based on the measured true density, the daily factor data at the current time corresponding to the empirical model, and the original calculated density at the current time includes:
[0015] Based on the current time daily scale factor, current time daily deviation factor and current time original computation density corresponding to the empirical model, output the simulated density;
[0016] The simulated density is compared with the measured actual density, and the residual is output.
[0017] Optionally, the step of calculating the prior model prediction value based on the residual and the daily factor data corresponding to the current time of the empirical model, and outputting the prior model prediction value, includes:
[0018] Perform a Fourier transform on the residual to output the dominant frequency and amplitude;
[0019] Based on the dominant frequency and the amplitude, a periodic term is constructed;
[0020] Based on the current time daily scale factor and the current time daily deviation factor, a prediction is made, and the future time daily scale factor and the future time daily deviation factor are output.
[0021] Based on the original computational density of future time, the daily scale factor of future time, the daily deviation factor of future time, and the periodic term corresponding to the empirical model, the predicted value of the prior model is calculated.
[0022] Optionally, the adaptive moment estimation optimizer, which uses the residuals after prior model calibration and the spatial environment data to train the residual fusion recurrent neural network to determine the trained residual fusion recurrent neural network, includes:
[0023] The space environment data is standardized to obtain dynamic covariates;
[0024] The residual fusion recurrent neural network to be trained outputs fusion features based on the dynamic covariates and the residuals after calibration of the prior model;
[0025] Based on the adaptive moment estimation optimizer, and using the mean absolute error as the loss function, the residual fusion recurrent neural network to be trained is iteratively trained according to the fusion features to obtain the trained residual fusion recurrent neural network.
[0026] Optionally, the residual fusion recurrent neural network to be trained includes a temporal feature extraction module, a normalized linear module, and a residual block; the step of using the residual fusion recurrent neural network to be trained to output fused features based on the dynamic covariates and the residuals calibrated by the prior model includes:
[0027] The time-series feature extraction module uses a segmented input and parallel multi-step prediction strategy to extract long-range low-frequency dependency features from the residuals after the prior model calibration, thereby obtaining low-frequency residual prediction components.
[0028] The residuals after prior model calibration are used as the input of the normalized linear module, and the high-frequency residual prediction components are output.
[0029] The residual block is used to sequentially perform linear encoding, ReLU activation and Dropout regularization on the dynamic covariate to obtain the feature vector of the dynamic covariate.
[0030] The low-frequency residual prediction component, the high-frequency residual prediction component, and the dynamic covariate feature vector are fused to obtain fused features.
[0031] Optionally, the step of using the residuals after prior model calibration as input to the normalized linear module and outputting high-frequency residual prediction components includes:
[0032] The residuals after calibration of the prior model are normalized to obtain the normalized residuals;
[0033] Perform a linear transformation on the normalized residuals to obtain the transformed residuals;
[0034] The transformed residuals are scaled back to output high-frequency residual prediction components.
[0035] A second aspect of the present invention provides a thermospheric atmospheric density calibration system, comprising:
[0036] The acquisition module is used to acquire measured real density, spatial environment data and empirical model, and to use a fitting method to fit the measured real density to obtain the daily factor data corresponding to the empirical model at the current time.
[0037] The calculation module is used to calculate the residual based on the measured true density, the daily factor data corresponding to the empirical model at the current time, and the original calculated density at the current time.
[0038] The comparison module is used to calculate the prior model prediction value based on the residual and the daily factor data corresponding to the current time of the empirical model, output the prior model prediction value, and compare the prior model prediction value with the measured real density to obtain the residual after prior model calibration.
[0039] The training module is used to train the residual fusion recurrent neural network to be trained based on the adaptive moment estimation optimizer, using the residuals after the prior model calibration and the spatial environment data, and to determine the trained residual fusion recurrent neural network.
[0040] The output module is used to output residual prediction values through the trained residual fusion recurrent neural network, and to calculate the final calibrated density of the thermospheric atmosphere by superimposing the prior model prediction values with the residual prediction values.
[0041] A third aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the thermospheric density calibration method described above.
[0042] The fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed, implements the thermospheric atmospheric density calibration method as described above.
[0043] The fifth aspect of the present invention provides a computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, wherein, when the program instructions are executed by a computer, the computer performs the steps of the thermospheric density calibration method described above.
[0044] As can be seen from the above technical solutions, the present invention has the following advantages:
[0045] The above-mentioned technical solution of the present invention provides a method for calibrating thermospheric atmospheric density. This method acquires measured real density, space environment data, and an empirical model. A fitting method is used to fit the measured real density to obtain the daily factor data corresponding to the empirical model at the current time. Based on the measured real density, the daily factor data corresponding to the empirical model at the current time, and the original calculated density at the current time, residuals are calculated. Based on the residuals and the daily factor data corresponding to the empirical model at the current time, a priori model prediction is calculated, and the priori model prediction is output. The priori model prediction is then compared with the measured real density to obtain the residuals after priori model calibration. Based on an adaptive moment estimation optimizer, the residuals after prior model calibration and the space environment data are used to train a residual fusion recurrent neural network to determine the trained residual fusion recurrent neural network. The invention employs a trained residual fusion recurrent neural network to output residual predictions, which are then superimposed with the prior model predictions to calculate the final calibrated thermospheric atmospheric density. Based on this foundation, the invention utilizes a prior model constructed from daily factor data and residuals fitted to measured real density. This model can specifically capture the systematic trend errors of empirical models, providing a stable physical scale basis for calibration results. Meanwhile, the residual fusion recurrent neural network, trained with the residuals and space environment data after prior model calibration, can accurately learn nonlinear and high-frequency detail deviations not covered by the prior model. The two complement each other, effectively avoiding the problems of single-parameter correction methods being unable to adapt to high-frequency nonlinear disturbances and single neural network methods being prone to multi-scale error imbalances, thereby improving the accuracy of thermospheric atmospheric density calibration results. Attached Figure Description
[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0047] Figure 1 This is a flowchart of the steps of a thermosphere atmospheric density calibration method provided in Embodiment 1 of the present invention;
[0048] Figure 2 This is a schematic diagram of the prior model construction and parameter prediction process provided in Embodiment 1 of the present invention;
[0049] Figure 3 This is a schematic diagram of the internal structure of the residual fusion recurrent neural network provided in Embodiment 1 of the present invention;
[0050] Figure 4 This is a schematic flowchart of a thermosphere atmospheric density calibration method provided in Embodiment 1 of the present invention;
[0051] Figure 5 This is an overall framework diagram of a thermosphere atmospheric density calibration method provided in Embodiment 1 of the present invention;
[0052] Figure 6 This is a structural block diagram of a thermosphere atmospheric density calibration system provided in Embodiment 2 of the present invention. Detailed Implementation
[0053] This invention provides a method and system for calibrating thermospheric atmospheric density, which solves the technical problem that existing thermospheric atmospheric density calibration methods rely on a single technical path to carry out calibration work, resulting in poor accuracy of thermospheric atmospheric density calibration results.
[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that in the optional embodiments of the present invention, the object information and other related data involved require the permission or consent of the object when the embodiments of the present invention are applied to specific products or technologies, and the collection, use, and processing of related data must comply with the relevant laws, regulations, and standards of the relevant countries and regions. That is to say, if the embodiments of the present invention involve data related to the object, it needs to be obtained with the authorization and consent of the object, the authorization and consent of the relevant departments, and in compliance with the relevant laws, regulations, and standards of the country and region. If personal information is involved in the embodiments, the acquisition of all personal information requires the consent of the individual. If sensitive information is involved, the separate consent of the information subject is required, and the embodiments also need to be implemented with the authorization and consent of the object.
[0055] Terminology Explanation:
[0056] Empirical model of thermospheric atmospheric density: A mathematical model constructed based on historical observation data to characterize the variation of thermospheric atmospheric density with time, space, and environmental parameters. This embodiment of the invention uses the NRLMSIS 2.0 model as the calibration object.
[0057] Prior Model: The first-level calibration model proposed in this invention specifically refers to a linear statistical model constructed based on the least squares method and Fourier transform, which is used to remove the main systematic error trends (scale, bias and periodic terms) in the empirical model.
[0058] ReFRNN (Residual Fusion Recurrent Neural Network): The second-level calibration model proposed in this invention, namely "residual fusion recurrent neural network", is used to perform nonlinear fitting on the residuals after the prior model is calibrated.
[0059] SegRNN (Segment Recurrent Neural Network): A core module of ReFRNN, it employs segmented input and parallel multi-step prediction strategies to extract long-range dependencies and low-frequency features of time series.
[0060] NLinear: Normalized Linear Model, one of the core modules in ReFRNN, used to handle high-frequency components in residual sequences and alleviate the data distribution shift problem.
[0061] Dynamic covariates refer to spatial environment indices (such as F10.7, F10.7a, ap) within the forecast period, which are used as external stimulus inputs to the neural network.
[0062] Please see Figure 1 , Figure 1 This is a flowchart illustrating the steps of a thermosphere atmospheric density calibration method provided in Embodiment 1 of the present invention.
[0063] This invention provides a method for calibrating the density of the thermosphere, comprising:
[0064] Step 101: Obtain the measured actual density, spatial environment data, and empirical model, and use a fitting method to fit the measured actual density to obtain the daily factor data corresponding to the empirical model at the current time.
[0065] The measured true density refers to the true density data of the thermospheric atmosphere obtained by inversion using the high-precision onboard accelerometer carried by the GRACE-A (Gravity Recovery and Climate Experiment-A) satellite. It is GRACE-A measured data and serves as the benchmark reference data for calibrating empirical models.
[0066] Space environment data includes solar radiation flux (F10.7, F10.7a) and geomagnetic activity index (ap).
[0067] Empirical models are mathematical models constructed based on historical observation data to characterize the variation of thermospheric atmospheric density with time, space, and environmental parameters.
[0068] It should be noted that the measured actual density, space environment data, and empirical model are obtained, and a fitting method is used to fit the measured actual density to obtain the daily factor data corresponding to the empirical model at the current time. The daily factor data at the current time specifically includes the daily scale factor and the daily deviation factor at the current time, which provides the basis for the subsequent calculation of the residual by combining the measured actual density with the original calculated density of the empirical model at the current time.
[0069] The fitting methods used are least squares or Kalman filtering for dynamic parameter estimation.
[0070] Specifically, it should be noted that in order to eliminate the main systematic errors in the empirical model (NRLMSIS 2.0), a prior model based on statistical regularities is first established. This invention uses the least squares method or Kalman filtering to fit the daily scale factor and bias factor of the empirical model using GRACE-A measured data (i.e., measured true density). These are the current-time daily scale factor and the current-time daily bias factor of the empirical model. The formulas are as follows:
[0071] ;
[0072] in, Calculate the density (i.e., simulated density) for the corrected empirical model. The daily scaling factor is an empirical model calibration parameter obtained by fitting the actual density measured by GRACE-A using the least squares method or Kalman filtering. Its function is to scale the original calculated density of the empirical model and correct the systematic scaling error of the model. This represents the original computational density of the empirical model (the original computational density at the current moment). The daily deviation factor is an empirical model calibration parameter obtained by fitting the measured real density of GRACE-A using the least squares method or Kalman filtering. Its function is to correct the offset of the original calculated density of the empirical model and correct the systematic fixed bias of the model.
[0073] Step 102: Calculate the residuals based on the measured actual density, the daily factor data corresponding to the empirical model at the current time, and the original calculated density at the current time.
[0074] The raw calculated density at the current moment refers to the thermospheric atmospheric density data at the current moment calculated directly by the empirical model without being corrected by the daily factor data at the current moment. It is the initial density data for the preliminary correction of the empirical model.
[0075] It should be noted that the original calculated density at the current time is corrected by using the daily factor data at the current time, and then the residual is obtained by calculating the difference between the measured actual density and the corrected density. This provides core error data support for the calculation of the predicted values of the subsequent prior model.
[0076] Furthermore, step 102 may include the following sub-steps:
[0077] S21. Based on the current time daily scale factor, current time daily deviation factor and current time original calculation density corresponding to the empirical model, output the simulation density;
[0078] S22. Compare the simulated density with the measured real density and output the residual.
[0079] It should be noted that, based on the daily scale factor, daily deviation factor, and original calculated density corresponding to the empirical model at the current time, the original calculated density is scaled proportionally by the scale factor, and offset correction is performed by combining the deviation factor to output the simulated density. The simulated density is compared with the measured real density, and the residual is output by calculating the difference between the two. This process initially eliminates the systematic proportional error and fixed deviation existing in the empirical model, providing core error data support for the subsequent construction of the prior model and training of the residual fusion recurrent neural network. It effectively avoids the defect that it cannot adapt to high-frequency disturbances when relying on only a single parameter for correction, and lays the foundation for improving the final calibration accuracy.
[0080] Step 103: Calculate the prior model prediction value based on the residuals and the daily factor data corresponding to the current time of the empirical model, output the prior model prediction value, and compare the prior model prediction value with the measured real density to obtain the residual after prior model calibration.
[0081] It should be noted that the prior model prediction is calculated based on the residuals and the daily factor data corresponding to the current time of the empirical model. By extracting the periodic features in the residuals and combining them with the temporal variation pattern of the daily factor data, the prior model prediction is output. The prior model prediction is then compared with the measured actual density to obtain the residual after prior model calibration, which provides accurate error input for the subsequent training of the residual fusion recurrent neural network.
[0082] Furthermore, step 103 may include the following sub-steps:
[0083] S31. Perform a Fourier transform on the residual and output the dominant frequency and amplitude;
[0084] S32. Construct a periodic term based on the dominant frequency and amplitude;
[0085] S33. Based on the current time daily scale factor and the current time daily deviation factor, make predictions and output the future time daily scale factor and the future time daily deviation factor.
[0086] S34. Calculate the prior model prediction value based on the original computational density of future time, the daily scale factor of future time, the daily deviation factor of future time, and the periodic term corresponding to the empirical model.
[0087] It should be noted that a Fourier transform is performed on the residuals to identify the dominant frequency and amplitude, and the period term is constructed using the least squares method.
[0088] ;
[0089] in, These are the least squares fitting coefficients. , Main frequency, They are used to characterize the amplitude of the cosine mode in the residual and the amplitude of the sinusoidal mode in the residual, respectively. The time variable represents the current time-series input and is used to characterize the dynamic changes of the periodic components over time.
[0090] Furthermore, the output of the prior model (i.e., the prediction of the prior model) can be expressed as:
[0091] ;
[0092] in, The prior model prediction (i.e., the output of the prior model) is the predicted value of the thermospheric atmospheric density at future times obtained by the empirical model after multi-dimensional correction of scale, bias and periodic terms, and is used to realize the prediction of thermospheric atmospheric density. The daily scale factor for future times is a calibration parameter predicted by methods such as autoregressive models (AR models), moving averages (MA), or linear extrapolation. It is used to scale the original computational density of the empirical model and correct the systematic scaling error of the model. The original calculated density of the empirical model is the calculated value of the thermospheric atmospheric density at future times directly output by the empirical model (such as NRLMSIS2.0) without any calibration. It is the initial input data for the correction of the a priori model. The daily deviation factor for future time moments is a calibration parameter predicted by methods such as AR model, MA or linear extrapolation. It is used to correct the fixed offset of the original computational density of the empirical model and correct the systematic fixed bias of the model. The periodic term is a periodic fluctuation component extracted from historical residuals (obtained by fitting after identifying the dominant frequency and amplitude through Fourier transform). It is used to correct the periodic error in the residuals of the empirical model and further optimize the prediction accuracy of the prior model.
[0093] It is worth mentioning that, in order to achieve the forecasting function, this invention uses an autoregressive model (AR model), moving average (MA), or simple linear extrapolation to predict the future scale and bias parameters (i.e., the daily scale factor and the daily bias factor at future time).
[0094] In this embodiment, as Figure 2 As shown, a Fourier transform is performed on the residuals, and the dominant frequency and amplitude in the residual sequence are identified through spectral analysis, outputting the dominant frequency and amplitude. Based on the dominant frequency and amplitude, a periodic function composed of cosine and sine is fitted using the least squares method to construct a periodic term. Based on the current daily scale factor and the current daily deviation factor, a time series prediction model is used for time series extrapolation, outputting the future daily scale factor and the future daily deviation factor. Based on the original computational density of the future time, the future daily scale factor, the future daily deviation factor, and the periodic term corresponding to the empirical model, the predicted value of the prior model is calculated through a combination of scaling, offset correction, and periodic fluctuation superposition. This invention compensates for the limitation of single parameter correction, which can only handle static errors, by integrating periodic features and time series prediction for multi-dimensional correction. At the same time, this stage removes the linear trend and periodic fluctuations in the error, so that the remaining residuals mainly contain high-frequency details and nonlinear changes, which are more suitable for neural network learning.
[0095] Step 104: Based on the adaptive moment estimation optimizer, the residuals after prior model calibration and the spatial environment data are used to train the residual fusion recurrent neural network to be trained, and the trained residual fusion recurrent neural network is determined.
[0096] It should be noted that, based on the adaptive moment estimation optimizer, the residuals after prior model calibration and spatial environment data are used to train the residual fusion recurrent neural network to be trained. The residuals after prior model calibration are used as training labels and the spatial environment data are used as input features. The network parameters are iteratively adjusted by the adaptive moment estimation optimizer to minimize the prediction error. After training is completed, the trained residual fusion recurrent neural network is determined, which provides model support for subsequent residual prediction.
[0097] Furthermore, step 104 may include the following sub-steps:
[0098] S41. Standardize the spatial environment data to obtain dynamic covariates;
[0099] It should be noted that standardizing spatial environment data eliminates the differences in the dimensions and numerical ranges of spatial environment data from different dimensions, bringing various spatial environment indices to the same order of magnitude and obtaining dynamic covariates.
[0100] S42. The residual fusion recurrent neural network to be trained outputs fusion features based on the residuals after calibration by the dynamic covariates and the prior model.
[0101] The residual fusion recurrent neural network to be trained includes a temporal feature extraction module, a normalized linear module, and a residual block.
[0102] It should be noted that, as Figure 3 As shown, for the residual data after prior model calibration, this invention designs a dedicated Residual Fusion RNN (ReFRNN) for secondary calibration. The ReFRNN comprises three specially designed modules:
[0103] 1. Temporal feature extraction module (specifically, a SegRNN module (Segment Recurrent Neural Network), Transformer (such as Informer), or TCN (Temporal Convolutional Network) used to process low-frequency residuals and extract sequence features):
[0104] 1) It adopts a segmented input and parallel multi-step prediction strategy to replace the point-by-point iteration of the traditional RNN (Recurrent Neural Network).
[0105] 2) Used to extract long-term low-frequency dependencies implicit in residuals that have not been completely eliminated by the prior model.
[0106] 2. Normalized Linear Module (i.e., NLinear module, used to handle high-frequency residuals):
[0107] 1) Normalize the input sequence (subtract the last value and add it back after prediction) to solve the data distribution offset problem.
[0108] 2) Used to capture rapid fluctuations and detailed features (high-frequency components) in atmospheric density.
[0109] 3. Residual Block (Dynamic Covariate Injection):
[0110] 1) The dynamic covariates (geomagnetic index ap, solar radiation flux F10.7 and its 81-day average F10.7a) for the forecast period are encoded and injected into the network.
[0111] 2) Enhance the model's ability to respond to sudden changes in future space weather.
[0112] Further, step S41 may include the following sub-steps:
[0113] S411. Through the time series feature extraction module, using a segmented input and parallel multi-step prediction strategy, long-range low-frequency dependency features in the residuals after prior model calibration are extracted to obtain low-frequency residual prediction components.
[0114] Parallel multi-step prediction strategy refers to a prediction method in which the time series feature extraction module, after receiving segmented time series segments, does not need to make predictions step by step, but instead outputs multi-step low-frequency residual prediction results simultaneously through model structure design. This can improve prediction efficiency and avoid error accumulation caused by step-by-step recursion.
[0115] It should be noted that the temporal feature extraction module employs a segmented input and parallel multi-step prediction strategy. The residual sequence after prior model calibration is divided into multiple continuous time segments, which are then input into the module one by one. Simultaneously, multi-step prediction results are output in parallel to accurately capture the slowly changing, long-term correlated error features in the residuals. This involves extracting long-range low-frequency dependency features from the residuals after prior model calibration, thus obtaining low-frequency residual prediction components. This strategy effectively overcomes the gradient vanishing or long-range feature forgetting problems that easily occur when using traditional single-model processing of long-term data. It comprehensively uncovers the easily overlooked low-frequency error patterns in the residuals, providing reliable support for subsequent fusion with high-frequency error components to form complete residual prediction results.
[0116] S412. Use the residuals after prior model calibration as the input of the normalized linear module and output the high-frequency residual prediction components.
[0117] Further, step S412 may include the following sub-steps:
[0118] S4121. Normalize the residuals after prior model calibration to obtain normalized residuals;
[0119] S4122. Perform a linear transformation on the normalized residuals to obtain the transformed residuals;
[0120] S4123. Scale the transformed residuals and output the high-frequency residual prediction components.
[0121] It should be noted that the residuals after prior model calibration are normalized using methods such as min-max normalization or Z-score normalization to eliminate numerical fluctuations and dimensional influences in the residual data, resulting in normalized residuals with more stable data distribution. Based on the normalized residuals, a linear mapping operation is performed using a preset linear transformation matrix to specifically extract high-frequency error features that change rapidly and fluctuate in the residuals, obtaining the transformed residuals. The transformed residuals are then subjected to a scale restoration operation (inverse scaling) to restore them to a numerical scale consistent with the original prior model calibration residuals, outputting the high-frequency residual prediction components. This step, through a complete link of normalization-linear transformation-scale restoration, achieves accurate extraction and effective preservation of high-frequency error features, overcoming the deficiency of easily ignoring short-term high-frequency errors under a single technical path. It complements the low-frequency residual prediction components, providing comprehensive support for the subsequent generation of complete residual prediction results.
[0122] S413. The dynamic covariates are sequentially processed by linear encoding, ReLU activation and Dropout regularization using residual blocks to obtain the feature vector of the dynamic covariates.
[0123] Dynamic covariates refer to the input features of the adaptive model training obtained after the space environment data has been standardized. They can dynamically reflect the changing state of the space environment and are one of the core inputs of residual fusion recurrent neural networks.
[0124] It should be noted that by using residual blocks to sequentially perform linear encoding (mapping the dynamic covariates to the appropriate feature dimension), ReLU activation (introducing nonlinearity to capture the complex correlation of environmental features), and Dropout regularization (suppressing model overfitting), dynamic covariate feature vectors that can accurately represent the dynamic features of the environment are obtained, providing appropriate environmental feature inputs for subsequent feature fusion.
[0125] S414. Perform feature fusion on the low-frequency residual prediction component, the high-frequency residual prediction component, and the dynamic covariate eigenvector to obtain fused features.
[0126] It should be noted that feature fusion is performed on low-frequency residual prediction components, high-frequency residual prediction components, and dynamic covariate eigenvectors. A fusion strategy combining feature splicing and weighted summation is adopted to deeply integrate the low-frequency components that characterize the long-term trend of residuals, the high-frequency components that reflect short-term fluctuations, and the covariate features that relate to the dynamic changes of the environment. This fully explores the intrinsic correlation information among the three and obtains a fused feature that can comprehensively cover the error characteristics and the correlation laws of the environment.
[0127] S43. Based on the adaptive moment estimation optimizer, and using the mean absolute error as the loss function, iteratively train the residual fusion recurrent neural network to be trained according to the fusion features to obtain the trained residual fusion recurrent neural network.
[0128] It should be noted that, based on the adaptive moment estimation optimizer and using the mean absolute error (MAE) as the loss function, the fused features are used as input to the residual fusion recurrent neural network to be trained. The network outputs residual prediction values, and the deviation between the residual prediction values and the residuals (training labels) after prior model calibration is accurately calculated using the MAE loss function. The adaptive moment estimation optimizer then backpropagates based on this deviation signal, iteratively adjusting the network's core parameters such as weights and biases to continuously reduce the prediction deviation until the model converges (the prediction deviation stabilizes within a preset threshold), resulting in a trained residual fusion recurrent neural network. This step leverages the comprehensive error features and environmental correlation information contained in the fused features, combined with the precise quantification capability of the MAE loss function and the stable convergence characteristics of the adaptive moment estimation optimizer. This allows the network to efficiently and accurately learn complex nonlinear and high-frequency detailed error patterns not covered by the prior model, overcoming the limitations of traditional single-technical approaches that make it difficult for models to comprehensively capture multi-dimensional error features. This effectively improves the model's generalization ability and prediction accuracy, providing a reliable model guarantee for subsequent output of accurate residual prediction results and further improving the accuracy of thermospheric atmospheric density calibration.
[0129] Step 105: Output the residual prediction value through the trained residual fusion recurrent neural network, and calculate the final calibrated density of the thermosphere by superimposing the prior model prediction value and the residual prediction value.
[0130] It should be noted that the trained residual fusion recurrent neural network performs precise calculations on the input dynamic covariates and other features, outputting residual prediction values that can compensate for the prediction bias of the prior model. Since the residual prediction values represent the nonlinear and high-frequency detail errors not covered by the prior model, the results of the two are superimposed to obtain the final calibration value: Final calibration density (i.e., final calibration density of thermospheric atmosphere) = Priormodel prediction value (i.e., prior model prediction value) + ReFRNN prediction value (i.e., residual prediction value). This invention constructs a dual calibration link of "preliminary correction of the prior model + precise residual compensation by the neural network", which comprehensively covers the systematic errors, periodic errors, and complex nonlinear high-frequency errors of the empirical model. It completely breaks through the limitations of incomplete error capture and insufficient calibration accuracy under the traditional single technical path, directly improving the accuracy and reliability of thermospheric atmospheric density calibration, and effectively solving the problem of poor calibration accuracy caused by the existing single technical path.
[0131] The trained residual fusion recurrent neural network first feeds the features fused with the input dynamic covariates and low-frequency and high-frequency residual prediction components into the network's temporal feature extraction module (SegRNN / Transformer / TCN). This module captures the long-range temporal dependencies and high-frequency fluctuation correlation patterns contained in the features. Then, the extracted temporal features are fed into the residual block for nonlinear mapping (linear encoding + ReLU activation) and Dropout regularization to enhance effective features and avoid overfitting risks. Finally, the NLinear linear prediction head maps the high-dimensional features into one-dimensional values and outputs residual prediction values that can compensate for the prediction bias of the prior model.
[0132] It is worth noting that, regarding the hardware and software environment and specific configuration parameters in this embodiment, the specific implementation plan of the present invention is built based on the following hardware and software environment, and the model training parameters have all been experimentally verified to ensure the convergence speed and calibration accuracy of the ReFRNN combined model when processing long-sequence thermospheric atmospheric density data.
[0133] 1. Hardware Environment
[0134] The computation and training process in this embodiment is completed on a high-performance computing server, and the core hardware configuration is as follows:
[0135] 1) Graphics Processing Unit (GPU): NVIDIA RTX3080 graphics card.
[0136] 2) Graphics memory capacity: 10GB.
[0137] The SegRNN module involves segmented parallel computation of long historical sequences (Sequence Length = 720). The high computing power of the RTX 3080 and 10GB of video memory can meet the needs of large-scale matrix operations and accelerate model training convergence.
[0138] 2. Software Framework
[0139] The algorithm logic of this invention is implemented based on mainstream deep learning frameworks:
[0140] 1) Deep learning framework: PyTorch.
[0141] This involves using PyTorch's automatic differentiation mechanism to construct complex network structures in ReFRNN (including SegRNN, NLinear, and Residual Block), and implementing the backpropagation algorithm.
[0142] 3. Model Training Strategy and Parameter Configuration
[0143] This embodiment uses the following specific configuration:
[0144] 1) Loss Function: Use Mean Absolute Error (MAE).
[0145] The calculation formula is as follows: ;in, This represents the loss value due to the mean absolute error (MAE). The total number of samples involved in the loss calculation; This represents the true label value of the i-th sample; This is the model prediction value for the i-th sample.
[0146] Compared to mean squared error, MAE is less sensitive to outliers in atmospheric density data and can more robustly guide the model to learn residual patterns.
[0147] 2) Optimizer: Select Adam optimizer.
[0148] Experiments show that Adam converges the fastest and has the highest accuracy in training SegRNN models (compared to NAdam and AdamW).
[0149] 3) Input sequence length: Set to 720 (corresponding to hourly data from the past 30 days or relevant time steps) to fully capture historical dependency information.
[0150] 4) Training Strategy:
[0151] The maximum number of training epochs is set to 30.
[0152] Early Stopping Mechanism: Set Patience = 6. That is, if the validation set error does not decrease for 6 consecutive rounds, training is stopped to prevent overfitting.
[0153] Learning Rate Scheduler: The initial learning rate remains constant for the first three rounds, and then decreases by 0.8 in each subsequent round. The initial learning rate is set between 0.0001 and 0.001, depending on the prediction duration.
[0154] 5) Network Hyperparameters:
[0155] For forecast tasks of different durations (1 hour to 24 hours), the batch size and model dimension (d_model) are dynamically adjusted. For example, in a 24-hour long-term forecast task, the batch size is set to 128 and the d_model is set to 2048 to enhance the model's feature extraction capabilities.
[0156] It is worth noting that the experiment was based on GRACE-A satellite data from 2006, a period encompassing both periods of calm and intense solar activity, demonstrating the robustness of the combined model. Furthermore, those skilled in the art will understand that the algorithm of this invention can be executed on various computing devices, including but not limited to computing devices equipped with GPUs (such as NVIDIA RTX series, Tesla series), TPUs, or FPGAs. The RTX3080 and PyTorch framework mentioned above are merely examples.
[0157] For comparison of technical effects, existing technologies can be used as a reference. Depending on the calibration object, existing empirical model calibration methods can be mainly divided into the following two categories:
[0158] Category 1: Parametric Calibration based on model intrinsic parameters:
[0159] We assume that the model error mainly stems from inaccuracies in internal physical parameters. We identify key parameters (such as exosphere temperature and inflection point temperature) through sensitivity analysis, and then use measured data and algorithms such as the least squares method to correct these physical parameters. Finally, we substitute the corrected parameters into the original model formula to recalculate the density.
[0160] The second category: calibration methods based on model output density (Density Correction / Non-parametric):
[0161] Without altering the internal physical structure of the empirical model, a mapping relationship is directly established between the measured density and the model's calculated density, thereby correcting the final density value output by the model.
[0162] Based on the above, the two existing categories of calibration methods each have significant shortcomings and are unable to meet the requirements for high-precision, high-resolution real-time calibration:
[0163] 1. Disadvantages of the first type of method (based on model parameters):
[0164] 1) This type of method relies on the analytical structure specific to the empirical model. Calibration is limited to adjusting predefined physical parameters (such as temperature), which makes it unable to correct errors caused by structural defects in the model itself.
[0165] 2) It can only capture large-scale trends and cannot capture high-frequency atmospheric variations beyond the model's parametric equations.
[0166] 2. Disadvantages of the second type of method (based on model density):
[0167] 1) Limitations of traditional mathematical fitting: such as the calibration factor method, which usually has low time resolution (e.g., the main correction daily average), the calibrated data lacks detailed features, and it is difficult to handle complex nonlinear errors.
[0168] 2) Limitations of pure neural network methods (the main problem addressed by this invention):
[0169] Multi-scale error mixtures are difficult to handle: Atmospheric density errors contain both low-frequency trend terms (caused by model system biases) and high-frequency random terms (caused by instantaneous environmental disturbances). Single neural networks often tend to fit the main trend while ignoring details, or lead to unstable predictions when learning high-frequency noise.
[0170] Poor physical consistency: Pure neural networks are black-box models, lacking physical constraints. In situations where data is scarce or solar activity is intense (out-of-distribution samples), they are prone to producing prediction results that do not conform to physical laws.
[0171] To address the shortcomings of the two main categories of methods mentioned above, such as... Figure 4 As shown, this invention proposes a thermospheric atmospheric density calibration method (ReFRNN Combined Model). The purpose of this invention is:
[0172] 1. Advantages of combining the two methods:
[0173] By using a prior model (similar to traditional mathematical fitting, based on least squares and Fourier transform), the main scale, bias and periodic trends (low-frequency errors) are first removed to ensure the correctness and stability of the calibration results in terms of physical quantities.
[0174] The ReFRNN neural network is used to specifically learn residuals (high-frequency / nonlinear errors) that cannot be handled by prior models. The residual trends and details in the residuals are extracted by SegRNN and NLinear modules, respectively.
[0175] 2. Achieve fine-grained frequency division processing of errors:
[0176] To address the issue that a single model cannot simultaneously capture both macro trends and micro details, a layered architecture (prior model layer + neural network layer) is used to gradually approximate the true density.
[0177] 3. Enhance responsiveness to dynamic environments:
[0178] To address the issue of lag in traditional parameter calibration methods, a rapid response to sudden space weather events (such as geomagnetic storms) is achieved by introducing dynamic covariates (F10.7, ap) for the forecast period into the neural network.
[0179] Specifically, such as Figure 5 As shown, this method employs a two-stage cascaded calibration framework combining "traditional methods + neural network methods," clearly dividing the calibration process into a prior model calibration stage and a ReFRNN residual calibration stage. First, a prior model (traditional mathematical model) is used to process the macroscopic trend error of thermospheric atmospheric density. The least squares method is used to fit the Scale and Bias parameters, and Fourier transform is used to extract the Period term. Simultaneously, an AR (autoregressive) model is used to perform time-series prediction on the fitted Scale and Bias parameter sequences, achieving prior calibration of future density and initially removing the main error trends. Next, ReFRNN (deep neural network) is used to perform residual calibration. This network includes parallel SegRNN branches, NLinear branches, and a Residual Block for fusing space environment indices. The SegRNN branch specifically handles microscopic low-frequency residual trends, while the NLinear branch focuses on detailed high-frequency residual fluctuations, accurately learning the remaining nonlinear residuals after prior calibration. Finally, the output of the prior model is superimposed with the ReFRNN residual prediction results to obtain the final calibrated density.
[0180] Compared with existing technologies, the combined calibration framework of this invention achieves significant breakthroughs in multiple dimensions: In terms of accuracy, the original NRLMSIS2.0 model has an error of 31.3%, which is reduced to 8.1% after calibration using only the prior model (traditional method), and further reduced to 2.6% after using the ReFRNN combined model. This achieves the lowest prediction error compared to using the traditional method or the neural network alone. Regarding the balance between physical rationality and data detail, the prior model ensures the correctness of the calibration results in terms of physical magnitude, avoiding the outrageous predictions that may occur with pure neural networks, while R... eFRNN supplements the complex details that traditional models cannot fit, achieving a deep fusion of physical laws and data features. In terms of anti-interference and dynamic response capabilities, by injecting dynamic covariates into the combined model, the model of this invention was able to quickly adapt to environmental changes during the December 2006 geomagnetic storm event (a period of intense solar activity), with a prediction error significantly lower than that of traditional models. In terms of long-sequence prediction capabilities, by utilizing the segmented parallel strategy of SegRNN, combined with the benchmark role of prior models, it effectively solves the problem of error accumulation in 24-hour long-sequence prediction by traditional LSTM, providing reliable support for long-term space environment forecasting.
[0181] In this embodiment of the invention, the above-mentioned technical solution provides a thermospheric atmospheric density calibration method. This method acquires measured real density, space environment data, and an empirical model. A fitting method is used to fit the measured real density to obtain the daily factor data corresponding to the empirical model at the current time. Based on the measured real density, the daily factor data corresponding to the empirical model at the current time, and the original calculated density at the current time, residuals are calculated. Based on the residuals and the daily factor data corresponding to the empirical model at the current time, a priori model prediction is calculated, and the priori model prediction is output. The priori model prediction is then compared with the measured real density to obtain the residuals after priori model calibration. Based on an adaptive moment estimation optimizer, the residuals after prior model calibration and space environment data are used to train a residual fusion recurrent neural network to determine the trained residual fusion recurrent neural network. The invention employs a recurrent neural network. A trained residual fusion recurrent neural network outputs residual predictions, which are then superimposed with the prior model predictions to calculate the final calibrated thermospheric atmospheric density. Based on this foundation, the invention utilizes a prior model constructed from daily factor data and residuals fitted to measured real density. This allows for targeted capture of systematic trend errors in empirical models, providing a stable physical scale basis for calibration results. The residual fusion recurrent neural network, trained with the residuals and space environment data after prior model calibration, can accurately learn nonlinear and high-frequency detail deviations not covered by the prior model. This complementary and synergistic approach effectively avoids the problems of single-parameter correction methods struggling to adapt to high-frequency nonlinear disturbances and single neural network methods prone to multi-scale error imbalances, thereby improving the accuracy of thermospheric atmospheric density calibration results.
[0182] Please see Figure 6 , Figure 6 This is a structural block diagram of a thermosphere atmospheric density calibration system provided in Embodiment 2 of the present invention.
[0183] This invention provides a thermospheric atmospheric density calibration system, comprising:
[0184] The acquisition module 601 is used to acquire the measured real density, spatial environment data and empirical model, and to use a fitting method to fit the measured real density to obtain the daily factor data corresponding to the empirical model at the current time.
[0185] Calculation module 602 is used to calculate the residual based on the measured real density, the daily factor data corresponding to the empirical model at the current time, and the original calculated density at the current time.
[0186] The comparison module 603 is used to calculate the prior model prediction value based on the residual and the daily factor data corresponding to the current time of the empirical model, output the prior model prediction value, and compare the prior model prediction value with the measured real density to obtain the residual after the prior model is calibrated.
[0187] Training module 604 is used to train the residual fusion recurrent neural network to be trained based on the adaptive moment estimation optimizer, using the residuals after prior model calibration and spatial environment data, and to determine the trained residual fusion recurrent neural network.
[0188] The output module 605 is used to output the residual prediction value through the trained residual fusion recurrent neural network, and to calculate the final calibrated density of the thermospheric atmosphere by superimposing the prior model prediction value and the residual prediction value.
[0189] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system and modules described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.
[0190] This invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program; when the computer program is executed by the processor, the processor performs the steps of the thermospheric density calibration method as described in the above embodiments.
[0191] This invention also provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the thermospheric atmospheric density calibration method as described in the above embodiments.
[0192] This invention also provides a computer program product, including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, wherein when the program instructions are executed by a computer, the computer performs the steps of the thermospheric atmospheric density calibration method as described in the above embodiments.
[0193] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.
[0194] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[0195] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.
[0196] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0197] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for calibrating the density of the thermosphere, characterized in that, include: Acquire measured real density, spatial environment data, and empirical model, and use a fitting method to fit the measured real density to obtain the daily factor data corresponding to the empirical model at the current time. The residuals are calculated based on the measured actual density, the daily factor data corresponding to the empirical model at the current moment, and the original calculated density at the current moment. Based on the residual and the daily factor data corresponding to the current time of the empirical model, the prior model prediction value is calculated, the prior model prediction value is output, and the prior model prediction value is compared with the measured real density to obtain the residual after prior model calibration. Based on the adaptive moment estimation optimizer, the residuals after the prior model calibration and the spatial environment data are used to train the residual fusion recurrent neural network to be trained, and the trained residual fusion recurrent neural network is determined. The trained residual fusion recurrent neural network outputs the residual prediction value, and the prior model prediction value is superimposed with the residual prediction value to calculate the final calibrated density of the thermospheric atmosphere.
2. The thermospheric atmospheric density calibration method according to claim 1, characterized in that, The current time daily factor data includes the current time daily scale factor and the current time daily deviation factor; The step of calculating the residual based on the measured true density, the daily factor data corresponding to the empirical model at the current time, and the original calculated density at the current time includes: Based on the current time daily scale factor, current time daily deviation factor and current time original computation density corresponding to the empirical model, output the simulated density; The simulated density is compared with the measured actual density, and the residual is output.
3. The thermospheric atmospheric density calibration method according to claim 2, characterized in that, The calculation of prior model predictions based on the residuals and the daily factor data corresponding to the current time of the empirical model, and the output of the prior model predictions, includes: Perform a Fourier transform on the residual to output the dominant frequency and amplitude; Based on the dominant frequency and the amplitude, a periodic term is constructed; Based on the current time daily scale factor and the current time daily deviation factor, a prediction is made, and the future time daily scale factor and the future time daily deviation factor are output. Based on the original computational density of future time, the daily scale factor of future time, the daily deviation factor of future time, and the periodic term corresponding to the empirical model, the predicted value of the prior model is calculated.
4. The thermospheric atmospheric density calibration method according to claim 1, characterized in that, The adaptive moment estimation optimizer uses the residuals after prior model calibration and the spatial environment data to train the residual fusion recurrent neural network to be trained, and determines the trained residual fusion recurrent neural network, including: The space environment data is standardized to obtain dynamic covariates; The residual fusion recurrent neural network to be trained outputs fusion features based on the dynamic covariates and the residuals after calibration of the prior model; Based on the adaptive moment estimation optimizer, and using the mean absolute error as the loss function, the residual fusion recurrent neural network to be trained is iteratively trained according to the fusion features to obtain the trained residual fusion recurrent neural network.
5. The thermospheric atmospheric density calibration method according to claim 4, characterized in that, The residual fusion recurrent neural network to be trained includes a temporal feature extraction module, a normalized linear module, and a residual block; The residual fusion recurrent neural network to be trained outputs fusion features based on the dynamic covariates and the residuals calibrated by the prior model, including: The time-series feature extraction module uses a segmented input and parallel multi-step prediction strategy to extract long-range low-frequency dependency features from the residuals after the prior model calibration, thereby obtaining low-frequency residual prediction components. The residuals after prior model calibration are used as the input of the normalized linear module, and the high-frequency residual prediction components are output. The residual block is used to sequentially perform linear encoding, ReLU activation and Dropout regularization on the dynamic covariate to obtain the feature vector of the dynamic covariate. The low-frequency residual prediction component, the high-frequency residual prediction component, and the dynamic covariate feature vector are fused to obtain fused features.
6. The thermospheric atmospheric density calibration method according to claim 5, characterized in that, The step of using the residuals after prior model calibration as input to the normalized linear module and outputting high-frequency residual prediction components includes: The residuals after calibration of the prior model are normalized to obtain the normalized residuals; Perform a linear transformation on the normalized residuals to obtain the transformed residuals; The transformed residuals are scaled back to output high-frequency residual prediction components.
7. A thermospheric atmospheric density calibration system, characterized in that, include: The acquisition module is used to acquire measured real density, spatial environment data and empirical model, and to use a fitting method to fit the measured real density to obtain the daily factor data corresponding to the empirical model at the current time. The calculation module is used to calculate the residual based on the measured true density, the daily factor data corresponding to the empirical model at the current time, and the original calculated density at the current time. The comparison module is used to calculate the prior model prediction value based on the residual and the daily factor data corresponding to the current time of the empirical model, output the prior model prediction value, and compare the prior model prediction value with the measured real density to obtain the residual after prior model calibration. The training module is used to train the residual fusion recurrent neural network to be trained based on the adaptive moment estimation optimizer, using the residuals after the prior model calibration and the spatial environment data, and to determine the trained residual fusion recurrent neural network. The output module is used to output residual prediction values through the trained residual fusion recurrent neural network, and to calculate the final calibrated density of the thermospheric atmosphere by superimposing the prior model prediction values with the residual prediction values.
8. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor causes the processor to perform the steps of the thermospheric atmospheric density calibration method as described in any one of claims 1-6.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the thermospheric atmospheric density calibration method as described in any one of claims 1-6.
10. A computer program product, characterized in that, The computer program product includes a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, wherein when the program instructions are executed by a computer, the computer performs the steps of the thermospheric atmospheric density calibration method as described in any one of claims 1-6.