Clock error prediction method based on multi-scale feature extraction and dynamic attention fusion

Abstract

The invention discloses a clock correction prediction method based on multi-scale feature extraction and dynamic attention fusion. The used prediction model comprises a multi-scale feature extraction layer, a double-branch time sequence modeling layer and a dynamic attention fusion layer; the multi-scale feature extraction layer extracts low-frequency features, transition features and high-frequency features of the input sequence, further generates three different features, and splices all the different features with the low-frequency features, the transition features and the high-frequency features in a channel dimension to obtain multi-scale fusion features; the multi-scale fusion features sequentially pass through channel attention and space attention, then pass through an adaptive gating network to generate two dynamic weight coefficients, and are subjected to weighted fusion to obtain input features of a high-frequency branch and a low-frequency branch; the double-branch time sequence modeling layer generates short-term fluctuation features and long-term trend features, and the dynamic attention fusion layer generates long and short-term fusion features. According to the method, the analysis capability of the model on the complex sudden change mode in the clock error data is remarkably improved, and the prediction precision is further remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of satellite clock error prediction, and particularly relates to a clock error prediction method based on multi-scale feature extraction and dynamic attention fusion. BACKGROUND

[0002] The clock error is a core parameter for a satellite navigation system to realize high-precision positioning, navigation and timing, and the precision thereof directly affects the service performance of the system. In order to realize the high-precision use requirement of the satellite navigation system, the clock error prediction research has become one of the important tasks at present. In actual application, the satellite clock is interfered by various complex factors, resulting in severe challenges for high-precision prediction. The satellite-borne atomic clock itself has the characteristics of drift and aging, and is superimposed with external environmental disturbances such as space radiation and temperature fluctuation, and observation condition restrictions such as signal shielding and instrument noise, so that the clock error data generally has abnormal components such as jump, discontinuity, periodic fluctuation and random noise, further increasing the difficulty of high-precision prediction. Therefore, it is of great significance to study a satellite clock error prediction method with high precision and high robustness for improving the positioning precision of the satellite navigation system.

[0003] At present, the satellite clock error prediction methods mainly include two types of traditional models and deep learning models. The traditional models include a quadratic polynomial model, a grey model and a Kalman filter. Although the quadratic polynomial model has simple structure and good timeliness, the long-term prediction error accumulates significantly. The grey model has poor stability and is sensitive to noise, and the prediction result has large variance, so it is difficult to adapt to complex disturbance scenes. The Kalman filter model is affected by the physical characteristics of the satellite-borne atomic clock, and cannot be compatible with satellites of different atomic clock types, so the long-time prediction performance is limited.

[0004] With the development and application of deep learning technology, the long short-term memory network (LSTM) can capture the long-term and short-term dependence relationship of time series data, and has higher precision than the traditional model. However, the LSTM still has the problem of insufficient local feature extraction capability, and it is difficult to accurately analyze the details in the data. On this basis, the attention mechanism is introduced to enhance the attention to key time sequence segments, but it still lacks effective mining of local spatial features. In the scene of complex noise interference or mixed multi-component features, it is difficult to separate and focus on the core information, so the prediction precision is limited. SUMMARY

[0005] In view of the deficiencies of the prior art, the technical problem to be solved by the application is to provide a clock error prediction method based on multi-scale feature extraction and dynamic attention fusion.

[0006] The application solves the technical problem by adopting the following technical scheme:

[0007] A clock error prediction method based on multi-scale feature extraction and dynamic attention fusion, characterized by comprising the following steps:

[0008] First step: obtain a plurality of original clock difference sequences, first difference the original clock difference sequences to obtain clock difference first difference sequences, preprocess the clock difference first difference sequences, slice the preprocessed clock difference first difference sequences by using a sliding window to obtain a plurality of clock difference first difference sequence segments, and form a clock difference data set;

[0009] Second step: constructing a prediction model, including a multi-scale feature extraction layer, a double-branch time series modeling layer and a dynamic attention fusion layer;

[0010] The multi-scale feature extraction layer extracts low-frequency features, transition features and high-frequency features of the input sequence, generates high-frequency-transition difference features, transition-low-frequency difference features and high-frequency-low-frequency difference features by using element-wise absolute value subtraction, concatenates all difference features with low-frequency features, transition features and high-frequency features in the channel dimension to obtain multi-scale fusion features, and the multi-scale fusion features sequentially pass through channel attention and spatial attention to obtain multi-scale fusion features enhanced by double attention; the multi-scale fusion features enhanced by double attention pass through an adaptive gating network to generate two dynamic weight coefficients, and the input features of the high-frequency branch and the low-frequency branch of the double-branch time series modeling layer are obtained by the following formula:

[0011] F h =δ1·F att +(1-δ1)·F high (1)

[0012] F l =δ2·F att +(1-δ2)·F low (2)

[0013] Wherein, F h , F l are the input features of the high-frequency branch and the low-frequency branch respectively, δ1, δ2 are two dynamic weight coefficients output by the adaptive gating network, F att is the multi-scale fusion features enhanced by double attention, F high , F low are high-frequency features and low-frequency features;

[0014] The double-branch time series modeling layer generates short-term fluctuation features by using the high-frequency branch, and generates long-term trend features by using the low-frequency branch;

[0015] In the dynamic attention fusion layer, the long-term trend features and the short-term fluctuation features are concatenated in the channel dimension to generate long-short-term joint features; the long-short-term joint features pass through the self-attention mechanism to generate an attention weight distribution, a fusion weight coefficient is intercepted from the attention weight distribution, and the long-term trend features and the short-term fluctuation features are weighted and fused by the following formula to obtain long-short-term fusion features:

[0016] H = ε · h l + (1 - ε) · h s (3)

[0017] where H is the long-short term fusion feature, ε is the fusion weight coefficient, h l , h s is the long-term trend feature and the short-term fluctuation feature;

[0018] The long-short term fusion feature sequentially passes through the fully connected layer and the activation function to obtain the normalized clock difference first-order difference prediction sequence; the normalized clock difference first-order difference prediction sequence is processed through the inverse normalization and the inverse first-order difference to obtain the clock difference prediction sequence;

[0019] Step 3: Use the clock difference dataset to train the prediction model, and use the trained prediction model for satellite clock difference prediction. Further, in the model training process, the loss is calculated by the following multi-order physical constraint loss function;

[0020] L loss = L MSE + α (L phy1 + βL phy2 ) + γL spec (4)

[0021]

[0022] where L MSE is the basic constraint loss, L phy1 , L phy2 is the first-order and second-order physical constraint loss, L spec is the spectrum constraint loss, α, β and γ are hyperparameters, y i , is the clock difference first-order difference real value and the prediction value of the i-th sample, N b is the number of samples in a single training batch, is the last value of the i-th sample, Δ(·) is the first-order difference operation, is the short-term fluctuation feature of the i-th sample, ||·||2 is the two-norm.

[0023] Further, in the adaptive gating network, the multi-scale fusion feature enhanced by the double attention passes through the global average pooling, the fully connected layer, the ReLU activation function, the fully connected layer and the Sigmoid activation function in sequence to generate the dynamic weight coefficient.

[0024] Further, in the double-branch time series modeling layer, the input feature of the high-frequency branch sequentially passes through the convolution, the batch normalization, the activation function, the global pooling and the fully connected layer to generate the short-term fluctuation feature; the input feature of the low-frequency branch passes through the long-short term memory network to generate the long-term trend feature.

[0025] Further, the multi-scale feature extraction layer generates high-frequency features by using a deep separable dilated convolution with a kernel size of 3 and an inflation rate of 1, generates transition features by using a deep separable dilated convolution with a kernel size of 7 and an inflation rate of 2, and generates low-frequency features by using a deep separable dilated convolution with a kernel size of 15 and an inflation rate of 3.

[0026] Further, the preprocessing includes abnormal point detection and filling, and normalization processing.

[0027] Compared with the prior art, the present application has the following beneficial effects:

[0028] First, the multi-scale feature extraction layer extracts features of different time spans, including high-frequency, transition and low-frequency features, by using deep separable dilated convolutions of different scales, and then extracts high-frequency-transition difference features, transition-low-frequency difference features and high-frequency-low-frequency difference features by using a multi-scale subtraction aggregation mechanism, explicitly models the transition mutation and trend turning point between different scale features, and then combines the channel and spatial double attention mechanisms to solve the problem that single feature fusion is not sensitive to cross-scale changes, significantly improves the model's ability to analyze complex mutation patterns in clock difference data, and further significantly improves the prediction accuracy. The channel and spatial double attention mechanism improves the utilization efficiency of multi-scale features, dynamically adjusts the importance weight of different feature channels through the channel attention mechanism, and strengthens effective features and suppresses redundant information; combined with the spatial attention mechanism, the feature response of the key time node is focused, so that the model can adaptively allocate attention according to the local fluctuation and global trend characteristics of the clock difference data, overcome the defects of the previous prediction model in adaptability to complex clock difference patterns, and improve the feature utilization efficiency and pattern recognition accuracy.

[0029] Second, the dual-branch time series modeling layer adopts a differentiated processing path, extracts short-term fluctuation features through the high-frequency branch, and extracts long-term trend features through the low-frequency branch, so that the model can capture both the local fluctuation details and the long-term time series dependence of the clock difference sequence, and further improve the prediction accuracy.

[0030] Third, the multi-order physical constraint loss function ensures the physical consistency of the prediction results, integrates the first-order smoothness constraint (controls the change amount at adjacent time points) and the second-order stability constraint (controls the stability of the change rate) of the clock difference change in the loss function, and suppresses unreasonable high-frequency fluctuations through the short-term fluctuation feature energy constraint, so that the prediction results not only fit the clock difference data distribution, but also conform to the physical characteristics of the clock difference change, and at the same time, the robustness and reliability of the model in complex disturbance scenarios are enhanced.

[0031] Fourth, the data preprocessing mechanism has robustness and adaptability, and provides a high-quality input sequence for the model. The fluctuation characteristics of the sequence are highlighted through first-order difference, and the accurate detection of abnormal values is realized by combining ridge regression and dynamic MAD, solving the problem that the traditional static detection method cannot adapt to the non-stationary characteristics of clock difference data; according to the effective data amount, the interpolation method is dynamically selected, while ensuring the continuity of the sequence, the original characteristics are maximally retained, and higher quality input data are provided for subsequent model training. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is the overall flowchart of the present application. DETAILED DESCRIPTION

[0033] The specific embodiments are described below in conjunction with the drawings, which are only used to specifically introduce the technical schemes of the present application, and do not limit the protection scope of the present application.

[0034] The present application provides a clock difference prediction method based on multi-scale feature extraction and dynamic attention fusion, comprising the following steps:

[0035] First step: obtain a plurality of original clock difference sequences, and perform first-order difference processing on the original clock difference sequences in chronological order to obtain clock difference first-order difference sequences, which can effectively eliminate the long-term trend in the original clock difference sequence and focus on the local jump feature; the clock difference first-order difference sequence is preprocessed, and the preprocessed clock difference first-order difference sequence is sliced by using a sliding window to obtain a plurality of clock difference first-order difference sequence segments, forming a clock difference data set, each clock difference first-order difference sequence including a plurality of continuous epoch clock difference first-order differences;

[0036] The preprocessing includes abnormal point detection and filling, and normalization processing; the dynamic MAD method is used for abnormal point detection, first, the trend item of the clock difference first-order difference sequence is fitted by using the ridge regression method, and the trend component and residual component in the sequence can be separated by fitting the trend item; then, the difference between the clock difference first-order difference sequence and the trend item is calculated to obtain a residual sequence; finally, the MAD value is calculated based on the residual sequence and the median, and the corrected Z-score of each data point is calculated based on the residual sequence and the MAD value, when the corrected Z-score is greater than the set threshold, the corresponding data point is an abnormal point, and the first-order difference of the abnormal point is marked as a missing value;

[0037] The first-order difference sequence of the clock error is traversed, and the data points not marked are regarded as valid data points; when the number of valid data points in the whole sequence is not less than a set number (4 in this embodiment), the abnormal values are filled by using cubic spline interpolation; when the number of valid data points in the whole sequence is less than the set number, the abnormal values are filled by using linear interpolation, so as to ensure the integrity of the sequence and obtain the first-order difference sequence of the clock error after filling of the abnormal values; and the first-order difference sequence of the clock error after filling of the abnormal values is normalized to obtain the first-order difference sequence of the clock error after preprocessing.

[0038] The second step is to construct a prediction model, including a multi-scale feature extraction layer, a double-branch time series modeling layer, and a dynamic attention fusion layer.

[0039] The multi-scale feature extraction layer extracts high-frequency features, transition features, and low-frequency features of the input sequence segment by using a heterogeneous three-pathway. The first pathway uses small-scale deep separable dilated convolution with a convolution kernel size of 3 and an expansion rate of 1 to perform channel-by-channel convolution operation on the input sequence, focusing on extracting high-frequency features of adjacent epochs. The second pathway uses medium-scale deep separable dilated convolution with a convolution kernel size of 7 and an expansion rate of 2 to capture transition features of medium time span by expanding the receptive field. The third pathway uses large-scale deep separable dilated convolution with a convolution kernel size of 15 and an expansion rate of 3 to further expand the receptive field to capture low-frequency features spanning multiple epochs. A multi-scale subtraction aggregation mechanism is used to calculate the difference features between low-frequency features, transition features, and high-frequency features by element-wise absolute value subtraction, obtaining high-frequency-transition difference features, transition-low-frequency difference features, and high-frequency-low-frequency difference features. The three difference features are concatenated with low-frequency features, transition features, and high-frequency features in the channel dimension to obtain multi-scale fusion features containing original scale information and scale relationship information. On this basis, a channel and spatial double attention mechanism is introduced to further enhance the multi-scale fusion features. The channel attention module first performs global average pooling on the multi-scale fusion features to aggregate spatial dimension information and obtain channel statistical features. The channel statistical features are then reduced in dimension by a fully connected layer, nonlinearly transformed by a ReLU activation function, and then increased in dimension by another fully connected layer to generate channel attention weights by a Sigmoid activation function. The channel attention weights are multiplied with the multi-scale fusion features along the channel dimension to dynamically adjust the importance of different channel features, obtaining channel attention enhanced multi-scale fusion features. The spatial attention module compresses the channel attention enhanced multi-scale fusion features in the channel dimension by 1x1 convolution to compress multi-channel features into single-channel features, and generates spatial attention weights by a Sigmoid activation function. The spatial attention weights are multiplied with the channel attention enhanced multi-scale fusion features along the spatial dimension to focus on key time point features, obtaining double attention enhanced multi-scale fusion features.

[0040] Based on the multi-scale fusion feature enhanced by the dual attention, two dynamic weight coefficients of different sizes are generated through an adaptive gating network, which are used to construct the input features of the low-frequency branch and the high-frequency branch; the adaptive gating network performs a global average pooling operation on the multi-scale fusion feature enhanced by the dual attention to aggregate the time dimension information and obtain statistical features in the channel dimension; the statistical features in the channel dimension are reduced in dimension through a fully connected layer, and are subjected to nonlinear transformation through a ReLU activation function, and then the features are output in dimension through a fully connected layer; the feature values are mapped to the interval [0, 1] through a Sigmoid activation function to generate a dynamic weight coefficient; similarly, another dynamic weight coefficient is generated through the same operation; the dynamic weight coefficients are fused with the multi-scale fusion feature enhanced by the dual attention and the high-frequency feature and the low-frequency feature through the following formula to obtain the input features of the high-frequency branch and the low-frequency branch;

[0041] F h = δ1·F att + (1-δ1)·F high (1)

[0042] F l = δ2·F att + (1-δ2)·F low (2)

[0043] wherein, F h , F l are the input features of the high-frequency branch and the low-frequency branch respectively, δ1, δ2 are two dynamic weight coefficients output by the adaptive gating network, F att is the multi-scale fusion feature enhanced by the dual attention, F high , F low are the high-frequency feature and the low-frequency feature.

[0044] The dual-branch time series modeling layer adopts a differentiated processing path, including a high-frequency branch and a low-frequency branch. The input features of the high-frequency branch are sequentially subjected to convolution, batch normalization, an activation function, a global pooling operation and a fully connected layer to generate short-term fluctuation features; the convolution operation is used to further extract local fluctuation features, the batch normalization operation is used to accelerate training convergence and enhance stability, the activation function introduces nonlinear transformation, and the global pooling operation compresses the feature dimension while preserving key fluctuation details. The low-frequency branch adopts a long short-term memory network, which effectively captures and preserves long-term time series dependencies in the sequence through two stacked LSTM layers to generate long-term trend features.

[0045] The dynamic attention fusion layer splices the long-term trend feature and the short-term fluctuation feature output by the double-branch time series modeling layer in the channel dimension to form a long-short-term joint feature; maps the long-short-term joint feature into a query vector, a key vector and a value vector, and the query vector, the key vector and the value vector pass through a self-attention mechanism to generate an attention weight distribution; adopts a weight clipping strategy, clips the first half (length of the hidden layer dimension) of the column dimension in the attention weight distribution as the fusion weight coefficient of the long-term trend feature based on the symmetry of the double-branch feature dimension, and the fusion weight coefficient of the short-term fluctuation feature is 1 minus the fusion weight coefficient of the long-term trend feature; the long-term trend feature and the short-term fluctuation feature are weighted and fused to realize dynamic fusion of the double-branch output feature, and a long-short-term fusion feature is obtained, which is represented as:

[0046] H = ε · h l + (1 - ε) · h s (3)

[0047] Wherein, H is the long-short-term fusion feature, ε is the fusion weight coefficient, h l and h s are the long-term trend feature and the short-term fluctuation feature.

[0048] Finally, the long-short-term fusion feature is converted into a single value prediction result through a fully connected layer, and then mapped to the [-1, 1] interval through an activation function to obtain a normalized clock difference first-order difference prediction sequence consistent with the input sequence range; the normalized clock difference first-order difference prediction sequence is processed through inverse normalization and inverse first-order difference to obtain a clock difference prediction sequence.

[0049] Third step: using the clock difference data set to train the prediction model, and using the trained prediction model for satellite clock difference prediction;

[0050] In the model training process, based on the physical characteristics of the clock difference data, a multi-order physical constraint loss function is designed to realize the fusion optimization of data driving and physical law. The physical characteristics of the clock difference data mainly reflect in three aspects: first, the time continuity, the clock difference change (increment) of adjacent ephemeris has smooth transition characteristics, and there is no abrupt change without physical basis; second, the change rate stability, the change rate (second-order characteristics) of the clock difference increment is limited by the physical characteristics of the satellite clock internal oscillator, and needs to be kept smooth and avoid violent fluctuations; third, the noise characteristics, the high frequency components in the data are mainly from observation noise or short-term electromagnetic interference and other non-physical factors, which will destroy the long-term prediction stability and need to be strictly suppressed. The loss function adopts multi-order physical constraint loss based on the characteristics of the clock difference data, including basic constraint loss, first-order physical constraint loss, second-order physical constraint loss and spectrum constraint loss, and the multi-order physical constraint loss function is represented as:

[0051] L loss = L MSE + α (Lphy1 + βL phy2 )+ γL spec (4)

[0052]

[0053] wherein, L MSE is the basic constraint loss, L phy1 , L phy2 is the first and second order physical constraint loss, L spec is the spectrum constraint loss; α, β and γ are hyperparameters, in the embodiment, α = 0.2, β = 0.1, γ = 0.01; y i , is the first order difference real value and predicted value of the clock error of the i th sample, N b is the number of samples in a single training batch, is the last value of the i th sample, Δ(·) is a first order difference operation, is the short-term fluctuation feature of the i th sample, ||·|| 2 is the two norm.

[0054] The first order physical constraint loss is designed for the time continuity characteristic of the clock error. Since the value of the clock error sequence at any time in the time dimension and the previous time both have physical continuity, the increment needs to present smooth transition. Therefore, by calculating the square mean of the predicted increment (i.e. the difference between the predicted value and the last value of the input sequence) as the first order physical constraint loss, the model is forced to learn the continuous change trend conforming to the physical law, avoiding the jump of the prediction result that violates the time continuity. The second order physical constraint loss is designed based on the stability characteristic of the clock error rate. The change rate (i.e. the second order characteristic) of the clock error increment is limited by the physical performance of the satellite clock oscillator. By performing a first order difference operation (calculating the difference between adjacent predicted increments) on the predicted increment and taking the square mean, the fluctuation amplitude of the clock error rate can be effectively limited, ensuring the second order stability of the clock error change. The spectrum constraint loss is designed for the noise characteristic of the clock error data. The high frequency component of the clock error is mostly non-physical interference, and the high frequency branch of the model focuses on capturing short-term detail features. If the output energy of the high frequency branch is too high, it means that too much high frequency noise is introduced. Therefore, by calculating the energy (square mean) of the output feature of the high frequency branch and limiting its upper limit as a constraint, the high frequency noise interference can be effectively suppressed.

[0055] To verify the effectiveness of the method, the precise satellite clock error data provided by the International GNSS Service (IGS) is used. The clock error data of Beidou satellites C22, C27 and C45 is selected, the time range is from February 7, 2024 to February 8, 2024 (the training set is the data of February 7, 2024, and the test set is part of the data of February 8, 2024), the sampling interval is 30 seconds, there are 120 data points per hour, and the total sample size is about 5760 (about 2880 for the training set, and the test set is dynamically selected according to the prediction length). The clock error data set is divided into training set and validation set according to the proportion of 8:2, which is used for model training and parameter optimization. The clock error of the future 0.1h, 0.3h, 0.5h, 1h and 3h is predicted, the input sequence length is 12 (corresponding to 6 minutes of historical data), in order to capture the short-term dynamics. Select the commonly used gray prediction model (GM [1] ) based on first-order difference in satellite clock error prediction field, quadratic polynomial model (QP [2] ), long short-term memory network (LSTM [3] ), long short-term memory network-self attention model (LSTM-Attention [4] ) as the comparison model. The GM model is suitable for non-stationary satellite clock error sequence, and the cumulative generation sequence is constructed by the difference sequence of the clock error to fit the trend, which is suitable for small sample data, but cannot capture the nonlinear fluctuations and multiscale characteristics of the clock error. QP model is a classical fitting method designed for Beidou satellite rubidium clock drift characteristics, which assumes that the clock error change conforms to a quadratic curve, and estimates the model parameters by least squares. The calculation is efficient, but ignores high-frequency noise and long-term time dependence, and the long-term prediction error is significant. LSTM is a benchmark model for deep learning time series prediction, which can effectively process nonlinear sequences through the gating mechanism (forget gate, input gate, output gate) to capture long-term dependencies, but it lacks the ability to separate multiscale features (such as high-frequency mutations and low-frequency trends). The LSTM-Attention model introduces a self-attention mechanism based on LSTM, which dynamically focuses on key time steps in the sequence. This model improves the ability to capture key information, but still relies on a single scale input and cannot explicitly model the differences in cross-scale features.

[0056] All models are trained under the same conditions, and the root mean square error (RMSE, unit: ns) is used to quantify the prediction accuracy, and the average of 5 experimental results is taken. The data preprocessing uniformly adopts first-order difference, dynamic MAD anomaly detection (threshold 3.5, ridge regression regularization parameter 0.1) and dynamic interpolation, and is normalized to the interval [-1, 1] to highlight the clock error fluctuation characteristics and remove the influence of outliers.

[0057] Table 1 shows the clock error prediction results of different models for Beidou satellite C22

[0058] GM QP LSTM LSTM_Attention The invention 0.1h 0.740 0.618 0.576 0.612 0.502 0.3h 0.725 0.642 0.608 0.637 0.541 0.5h 0.749 0.643 0.606 0.637 0.558 1h 0.795 0.667 0.626 0.679 0.616 3h 1.058 0.734 0.703 0.750 0.622

[0059] Table 2 Clock error prediction results of different models for Beidou satellite C27

[0060] GM QP LSTM LSTM_Attention The invention 0.1h 0.381 0.341 0.193 0.198 0.171 0.3h 0.395 0.353 0.189 0.211 0.145 0.5h 0.399 0.357 0.176 0.226 0.120 1h 0.414 0.369 0.163 0.257 0.096 3h 0.469 0.412 0.176 0.321 0.404

[0061] Table 3 Clock error prediction results of different models for Beidou satellite C45

[0062] GM QP LSTM LSTM_Attention The invention 0.1h 0.176 0.065 0.071 0.059 0.063 0.3h 0.146 0.093 0.123 0.109 0.089 0.5h 0.142 0.098 0.133 0.112 0.092 1h 0.143 0.108 0.145 0.099 0.098 3h 0.322 0.100 0.113 0.097 0.094

[0063] The above experimental results show that the model of the present application has significant superiority on Beidou satellites C22, C27 and C45. Taking 1-hour prediction as an example, the specific analysis is as follows:

[0064] Beidou satellite C22: The RMSE of the model of the present application is only 0.616 ns, which is reduced by 22.5% compared with GM (0.795 ns), reduced by 7.7% compared with QP (0.668 ns), reduced by 9.3% compared with LSTM (0.679 ns), and slightly better than LSTM+Attention (0.626 ns).

[0065] Beidou satellite C27: The RMSE of the model of the present application is 0.096 ns, which is reduced by 76.8% compared with GM (0.414 ns), reduced by 73.9% compared with QP (0.369 ns), reduced by 62.6% compared with LSTM (0.257 ns), and reduced by 41.1% compared with LSTM+Attention (0.163 ns), which is the most significant improvement.

[0066] Beidou satellite C45: The RMSE of the model of the present application is 0.098 ns, which is reduced by 31.9% compared with GM (0.144 ns), reduced by 9.3% compared with QP (0.108 ns), basically the same as LSTM (0.099 ns) (slightly better by 0.9%), and better than LSTM+Attention (0.145 ns).

[0067] It can be seen that the model can effectively suppress errors under different satellites and prediction lengths. This is because high-frequency features (reflecting detailed information), transition features and low-frequency features (reflecting change trends) are extracted by small / middle / large scale deep separable dilated convolution, and the difference features between modeling scales are displayed by a multi-scale subtraction aggregation mechanism, which significantly enhances the analysis ability of sudden abnormalities and cross-scale changes in clock error data. The channel and spatial double attention ensures the focus on key time points and important features, and the adaptive gating network generates different dynamic weight coefficients, which can flexibly adjust the input of high-frequency / low-frequency branches in different scenarios, ensuring balanced modeling of short-term fluctuations and long-term trends. High-frequency branches capture instantaneous details, and low-frequency branches extract long-term dependencies. The two are fused through dynamic attention, effectively improving prediction accuracy and generalization ability. The multi-order physical constraint loss function ensures the continuity and stability of the predicted curve through first-order smoothness and second-order stability constraints, and suppresses overfitting high-frequency noise through high-frequency energy constraints, so that the model prediction is more in line with the physical characteristics of the clock error, so the prediction accuracy of the present application is higher.

[0068] The source of the above comparative model is as follows:

[0069] [1] Liang, Y. J., et al. (2015). Grey model based on first difference in the application of the satellite clock bias prediction. Acta Astronomica Sinica, 56(3), 264-277.

[0070] [2] Huang, G. W., et al. (2018). An improved predicted model for BDS ultra-rapid satellite clock offsets. Remote Sensing, 10(1), 60.

[0071] [3] He, S., et al. (2023). Research on modeling and predicting of BDS-3 satellite clock bias using the LSTM neural network model. GPS Solutions, 27(3), 108.

[0072] [4] Cai, C. L., et al. (2024). Enhancing satellite clock bias prediction in BDS with LSTM-attention model. GPS Solutions, 28(92), 1-16.

[0073] The unmentioned parts of the invention apply to the prior art.

Claims

1. A clock error prediction method based on multi-scale feature extraction and dynamic attention fusion, characterized in that, Includes the following steps: Step 1: Obtain several original clock difference sequences, perform first-order differencing on the original clock difference sequences to obtain first-order differencing sequences of clock differences; preprocess the first-order differencing sequences of clock differences, and use a sliding window to slice the preprocessed first-order differencing sequences of clock differences to obtain several first-order differencing sequence fragments of clock differences, forming a clock difference dataset. The second step is to build a prediction model, including a multi-scale feature extraction layer, a two-branch temporal modeling layer, and a dynamic attention fusion layer. The multi-scale feature extraction layer extracts low-frequency features, transition features, and high-frequency features from the input sequence. It generates high-frequency-transition difference features, transition-low-frequency difference features, and high-frequency-low-frequency difference features by element-wise absolute value subtraction. All difference features are concatenated with low-frequency features, transition features, and high-frequency features in the channel dimension to obtain multi-scale fusion features. The multi-scale fusion features are then passed through channel attention and spatial attention to obtain multi-scale fusion features enhanced with dual attention. The multi-scale fusion features enhanced by dual attention are passed through an adaptive gating network to generate two dynamic weight coefficients, and the input features of the high-frequency branch and low-frequency branch of the dual-branch temporal modeling layer are obtained by the following formula; F h =δ1·F att +(1-δ1) F high (1) F l =δ2·F att +(1-δ2)·F low (2) Among them, F h F l These are the input features of the high-frequency branch and the low-frequency branch, respectively. δ1 and δ2 are two dynamic weight coefficients of the adaptive gating network output. F att It is a multi-scale fusion feature enhanced by dual attention, F high F low These are high-frequency and low-frequency features; The dual-branch time series modeling layer uses high-frequency branches to generate short-term fluctuation features and low-frequency branches to generate long-term trend features. In the dynamic attention fusion layer, long-term trend features and short-term fluctuation features are concatenated at the channel dimension to generate long-short joint features. The long-short joint features are then processed through a self-attention mechanism to generate an attention weight distribution. The fusion weight coefficients are extracted from the attention weight distribution and the long-term trend features and short-term fluctuation features are weighted and fused using the following formula to obtain the long-short fusion features. H=ε·h l +(1-e)·h s (3) Where H is the long-term and short-term fusion features, ε is the fusion weight coefficient, and h l h s It features both long-term trend characteristics and short-term fluctuation characteristics; The long-term and short-term fusion features are sequentially passed through a fully connected layer and an activation function to obtain a normalized clock error first-order difference prediction sequence; the normalized clock error first-order difference prediction sequence is then processed by inverse normalization and inverse first-order difference to obtain a clock error prediction sequence. Step 3: Train the prediction model using the clock bias dataset, and then use the trained prediction model for satellite clock bias prediction.

2. The clock error prediction method based on multi-scale feature extraction and dynamic attention fusion according to claim 1, characterized in that, During model training, the loss is calculated using the following multi-order physical constraint loss function; L loss =L MSE +α(L phy1 +βL phy2 )+γL spec (4) Among them, L MSE It is the basic constraint loss, L phy1 L phy2 It is the first-order and second-order physical constraint loss, L spec It is a spectral constraint loss, where α, β, and γ are hyperparameters, and y i , N represents the true and predicted values ​​of the first-order difference of the clock error for the i-th sample. b This refers to the number of samples in a single training batch. It is the last value of the i-th sample, and Δ(·) is the first-order difference operation. Let ||·||2 be the short-term fluctuation characteristic of the i-th sample, and ||·||2 be the L2 norm.

3. The clock error prediction method based on multi-scale feature extraction and dynamic attention fusion according to claim 1, characterized in that, In the adaptive gating network, the multi-scale fusion features enhanced by dual attention are sequentially processed through global average pooling, fully connected layers, ReLU activation function, fully connected layers, and Sigmoid activation function to generate dynamic weight coefficients.

4. The clock error prediction method based on multi-scale feature extraction and dynamic attention fusion according to claim 1, characterized in that, In the dual-branch temporal modeling layer, the input features of the high-frequency branch pass through convolution, batch normalization, activation function, global pooling and fully connected layer in sequence to generate short-term fluctuation features; The input features of the low-frequency branch are processed by a long short-term memory network to generate long-term trend features.

5. The clock error prediction method based on multi-scale feature extraction and dynamic attention fusion according to claim 1, characterized in that, The multi-scale feature extraction layer uses a depthwise separable dilated convolution with a kernel size of 3 and a dilation rate of 1 to generate high-frequency features, a depthwise separable dilated convolution with a kernel size of 7 and a dilation rate of 2 to generate transitional features, and a depthwise separable dilated convolution with a kernel size of 15 and a dilation rate of 3 to generate low-frequency features.

6. The clock error prediction method based on multi-scale feature extraction and dynamic attention fusion according to any one of claims 1 to 5, characterized in that, The preprocessing includes outlier detection and filling, and normalization.

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