CN118915102A - Satellite clock error forecasting method and system - Google Patents

Abstract

The present invention discloses a satellite clock error prediction method and system, the method comprising: performing a first difference processing on the clock error data of the same satellite to obtain phase data, and converting the phase data into frequency data; removing abnormal epochs from the frequency data by the median method to obtain frequency incomplete data, completing the frequency incomplete data by the Lagrange interpolation method based on the abnormal epochs to obtain a first difference minute difference data sequence; inputting the first difference minute difference data sequence into an IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock error prediction data, the IBOA-CNN-GRU prediction model is a model obtained by performing hyperparameter optimization on the CNN-GRU combination model by the improved BOA algorithm. The present invention uses an improved Bayesian algorithm to optimize the hyperparameters of the combination model, and provides reliable algorithm support for improving the performance of satellite clock error prediction.

Description

Satellite clock error prediction method and system

Technical Field

The present invention relates to the technical field of clock error data prediction, and in particular to a satellite clock error prediction method and system.

Background Art

The accuracy of the onboard atomic clock directly determines the quality of navigation, positioning and timing of the satellite navigation system. Since the physical characteristics of the onboard atomic clock are relatively complex and are greatly affected by external factors, the clock error data cannot be accurately predicted using a single prediction model in most cases, making it difficult to establish a high-precision clock error prediction model. Therefore, it is an important research direction for future clock error prediction to explore prediction models with stronger adaptability, higher stability and better prediction effect by combining the advantages and characteristics of each model.

Through research, it is found that clock error data has continuity, periodicity, randomness and nonlinearity in time series. The randomness and nonlinear characteristics of data have a greater impact on accuracy. For this reason, many scholars have introduced neural networks suitable for nonlinear processing into clock error prediction, such as EMD-SVM, wavelet neural network (WNN), BP neural network optimized by evolutionary algorithm (MEA-BP), radial basis function (RBF) neural network, recurrent neural network optimized long short-term memory model (RNN-LSTM), etc. These models have achieved good prediction accuracy. Although these models can capture the nonlinear relationship of clock error data, it is difficult to effectively extract the long-term dependence of clock error data, and the computational complexity is high. Therefore, how to improve the performance of satellite clock error prediction has become an urgent problem to be solved.

The above contents are only used to assist in understanding the technical solution of the present invention and do not constitute an admission that the above contents are prior art.

Summary of the invention

The main purpose of the present invention is to provide a satellite clock error prediction method and system, aiming to solve the technical problem of how to improve the satellite clock error prediction performance.

To achieve the above object, the present invention provides a satellite clock error prediction method, the satellite clock error prediction method comprising:

Performing a difference process on the clock error data of the same satellite to obtain phase data, and converting the phase data into frequency data;

Abnormal epochs are eliminated from the frequency data by the median method to obtain incomplete frequency data, and the incomplete frequency data are supplemented by the Lagrange interpolation method based on the abnormal epochs to obtain a first-order minute difference data sequence;

The first-order minute difference data sequence is input into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock difference prediction data. The IBOA-CNN-GRU prediction model is a model obtained by optimizing the hyperparameters of the CNN-GRU combination model through the improved BOA algorithm.

Optionally, before the step of inputting the first-order minute difference data sequence into the IBOA-CNN-GRU prediction model for inverse normalization and inverse difference processing to obtain satellite clock difference prediction data, the step includes:

Determine multiple groups of dominant populations corresponding to the hyperparameters in the CNN-GRU combination model based on the upper and lower bounds of the parameters, and determine local hyperparameters through the fitness function based on the multiple groups of dominant populations;

The CNN-GRU combined model is trained based on a one-time difference minute difference data training set and the local hyperparameters to obtain an IBOA-CNN-GRU combined model;

Determine the root mean square error corresponding to the output result of the IBOA-CNN-GRU combination model through a loss function;

If the root mean square error is less than or equal to a preset error threshold, and the local hyperparameter is a global optimal parameter, the IBOA-CNN-GRU combined model is used as the IBOA-CNN-GRU prediction model.

Optionally, the step of determining multiple groups of dominant populations corresponding to hyperparameters in the CNN-GRU combination model based on the parameter upper bound and the parameter lower bound includes:

Determine multiple groups of populations corresponding to hyperparameters in the CNN-GRU combination model based on the upper and lower bounds of the parameters, wherein the hyperparameters include the number of hidden units, the initial learning rate, and the L2 regularization parameter;

Multiple groups of dominant populations are selected from multiple groups of populations through fitness functions.

Optionally, the step of selecting multiple groups of dominant populations from multiple groups of populations by using a fitness function includes:

The fitness value corresponding to each group of populations is determined through the fitness function;

The fitness function is:

In the formula, _xm is the population, f( _xm ) is the fitness value corresponding to _xm , m is the predicted population size, is the predicted value of the ith data in the _xm population, and _Li is the true value of the ith data in the _xm population;

Selecting from the multiple groups of populations a plurality of groups of populations to be optimized corresponding to the fitness values being less than a preset fitness threshold;

By using a local search algorithm, multiple groups of populations to be optimized are adjusted respectively to obtain multiple groups of adjusted populations, and the fitness value corresponding to each group of adjusted populations is determined;

Multiple groups of dominant populations are determined according to the fitness values corresponding to each group of adjusted populations and the fitness values corresponding to each group of populations to be optimized.

Optionally, after the step of determining the root mean square error corresponding to the output result of the IBOA-CNN-GRU combined model by using a loss function, the following steps are included:

If the root mean square error is less than or equal to the preset error threshold, and the local hyperparameter is not the global optimal parameter, the multiple groups of populations are iteratively updated through the minimum hill climbing method and the pattern ant colony algorithm according to the iteration rule, and the step of selecting multiple groups of dominant populations from the multiple groups of populations through the fitness function is returned.

Optionally, the step of iteratively updating multiple groups of populations by using a minimum hill climbing method and a pattern ant colony algorithm according to an iterative rule includes:

Construct a Bayesian network structure based on multiple groups of dominant populations according to the scoring formula;

Selecting multiple groups of candidate populations from multiple groups of dominant populations by using a minimum hill climbing method and a pattern ant colony algorithm according to the Bayesian network structure;

Iteratively update multiple groups of populations based on multiple groups of candidate populations according to iterative rules.

Optionally, the step of constructing a Bayesian network structure based on multiple groups of dominant populations according to a scoring formula includes:

Determine multiple parent nodes based on multiple groups of dominant populations;

Determine a parent node set based on multiple parent nodes through a scoring formula;

The scoring formula is:

Where, _xi is the dominant population, _xj is the parent node, θ is the parameter in the score, N is the number of individuals in the topological network structure, _Πi is the parent node set, P is the likelihood function of _xi under _Πi , and D is the hyperparameter in _xi ;

A Bayesian network structure is constructed based on the parent node set.

Optionally, the step of selecting multiple groups of candidate populations from multiple groups of dominant populations by using a minimum hill climbing method and a pattern ant colony algorithm according to the Bayesian network structure includes:

The Bayesian network structure is adjusted, and based on the adjusted Bayesian network structure, a plurality of excellent solutions are determined according to a plurality of groups of dominant populations by using a minimum hill climbing method;

Constructing a pheromone matrix based on multiple excellent solutions, and adjusting the pheromone matrix through a pattern ant colony algorithm;

Multiple groups of candidate populations are determined according to the adjusted pheromone matrix.

In addition, to achieve the above object, the present invention also proposes a satellite clock error prediction system, the satellite clock error prediction system comprising:

A data processing module is used to perform a primary difference processing on the clock error data of the same satellite to obtain phase data, and convert the phase data into frequency data;

The data processing module is further used to remove abnormal epochs from the frequency data by the median method to obtain incomplete frequency data, and to complete the incomplete frequency data by the Lagrange interpolation method based on the abnormal epochs to obtain a first-order difference minute difference data sequence;

The model running module is used to input the first-order difference minute difference data sequence into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock difference prediction data. The IBOA-CNN-GRU prediction model is a model obtained by optimizing the hyperparameters of the CNN-GRU combination model through the improved BOA algorithm.

In addition, to achieve the above-mentioned purpose, the present invention also proposes a device based on satellite clock difference prediction, which includes: a memory, a processor, and a satellite clock difference prediction program stored in the memory and executable on the processor, and the satellite clock difference prediction program is configured to implement the steps of the satellite clock difference prediction method as described above.

In addition, to achieve the above-mentioned purpose, the present invention also proposes a storage medium, on which a satellite clock error prediction program is stored. When the satellite clock error prediction program is executed by a processor, the steps of the satellite clock error prediction method described above are implemented.

The present invention first performs a difference processing on the clock error data of the same satellite to obtain phase data, and converts the phase data into frequency data, then eliminates abnormal epochs from the frequency data by the median method to obtain frequency incomplete data, and completes the frequency incomplete data by the Lagrange interpolation method based on the abnormal epochs to obtain a first-difference minute difference data sequence, and then inputs the first-difference minute difference data sequence into an IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock error prediction data. The IBOA-CNN-GRU prediction model is a model obtained by performing hyperparameter optimization on the CNN-GRU combination model by the improved BOA algorithm. The present invention combines a convolutional neural network with a strong ability to extract sequence features with a GRU with a long-term memory structure, uses the convolution and pooling operations of CNN to automatically extract the spatial vectors of clock error data, mines the time series features in the data, and solves the problem of prediction error accumulation of the model by performing accuracy judgment on the prediction results. Then, the GRU is used to extract the time features of the clock error data, and the model performance is improved with very little calculation. The data mining ability of the model is brought into play, and the advantages of the two models are combined to establish a CNN-GRU combined model. The Bayesian algorithm is used to optimize the hyperparameters of the combined model, effectively jumping out of the local extreme value problem of difficult hyperparameter selection, and ensuring the global convergence of the algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the structure of a satellite clock error prediction device in a hardware operating environment according to an embodiment of the present invention;

FIG2 is a schematic diagram of a flow chart of a first embodiment of a satellite clock error prediction method according to the present invention;

FIG3 is a structural diagram of an IBOA-CNN-GRU combined model of a first embodiment of a satellite clock error prediction method according to the present invention;

FIG4 is a model processing flow chart of the first embodiment of the satellite clock error prediction method of the present invention;

FIG5 is a structural block diagram of the first embodiment of the satellite clock error prediction system of the present invention.

The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings.

DETAILED DESCRIPTION

It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

Refer to Figure 1, which is a schematic diagram of the structure of a satellite clock error prediction device based on the hardware operating environment involved in an embodiment of the present invention.

As shown in Figure 1, the satellite clock error prediction device may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. Among them, the communication bus 1002 is used to realize the connection and communication between these components. The user interface 1003 may include a display screen (Display), an input unit such as a keyboard (Keyboard), and the optional user interface 1003 may also include a standard wired interface and a wireless interface. The network interface 1004 may optionally include a standard wired interface and a wireless interface (such as a wireless fidelity (Wireless-Fidelity, Wi-Fi) interface). The memory 1005 may be a high-speed random access memory (Random Access Memory, RAM), or a stable non-volatile memory (Non-Volatile Memory, NVM), such as a disk storage. The memory 1005 may also be a storage system independent of the aforementioned processor 1001.

Those skilled in the art will appreciate that the structure shown in FIG. 1 does not constitute a limitation on the satellite clock error prediction device, and may include more or fewer components than shown in the figure, or a combination of certain components, or a different arrangement of components.

As shown in FIG. 1 , the memory 1005 as a storage medium may include an operating system, a network communication module, a user interface module, and a satellite clock error prediction program.

In the satellite clock difference prediction device shown in Figure 1, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and the memory 1005 in the satellite clock difference prediction device of the present invention can be set in the satellite clock difference prediction device, and the satellite clock difference prediction device calls the satellite clock difference prediction program stored in the memory 1005 through the processor 1001, and executes the satellite clock difference prediction method provided by the embodiment of the present invention.

An embodiment of the present invention provides a satellite clock error prediction method. Referring to FIG. 2 , FIG. 2 is a flow chart of a first embodiment of the satellite clock error prediction method of the present invention.

In this embodiment, the satellite clock error prediction method includes the following steps:

Step S10: Perform a difference process on the clock error data of the same satellite to obtain phase data, and convert the phase data into frequency data.

It is easy to understand that the executor of this embodiment can be a satellite clock error prediction system with functions such as data processing, network communication and program running, or other computer equipment with similar functions, etc., and this embodiment is not limited.

It should be noted that in order to increase the nonlinear influence of the original clock error data and reduce the influence of the trend term in the data, the clock error data of the same satellite needs to be subjected to a difference processing. The processed difference data is phase data, and the phase data also needs to be converted into frequency data.

Step S20: Abnormal epochs are eliminated from the frequency data by the median method to obtain incomplete frequency data, and the incomplete frequency data are completed by the Lagrange interpolation method based on the abnormal epochs to obtain a differential minute difference data sequence.

It should be understood that the use of the median method to detect gross errors in the frequency data of the first difference follows the principle that the number of outliers does not exceed 5% of the modeled data, which not only avoids the impact of abnormal data on model forecasts, but also avoids the elimination of effective information. For the eliminated epochs, the Lagrange interpolation method is used to complete them, and the data sequence after the first difference clock difference preprocessing (i.e., the first difference minute difference data sequence) is obtained.

Step S30: Input the first-order differential minute difference data sequence into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock difference prediction data. The IBOA-CNN-GRU prediction model is a model obtained by optimizing the hyperparameters of the CNN-GRU combination model through the improved BOA algorithm.

In this embodiment, the CNN model is mainly composed of convolutional layers, pooling layers, and fully connected layers. This structure simplifies the complexity of the network model. The convolutional layer is composed of one or more convolutional kernels. The convolutional kernel is a learnable parameter matrix. By moving the convolutional kernel on the data and performing dot product with the data, local features of different scales and directions are extracted and the depth of the features is increased. Since the clock error data is a one-dimensional sequence data, a one-dimensional convolutional neural network is selected, and the calculation formula is as follows:

In the formula, is the kth convolutional mapping of layer l, f is the activation function, is the weight of layer l, is the bias of the kth convolution kernel corresponding to layer l.

The pooling layer processes the feature matrix of the convolution layer through pooling operations, reducing the dimension of the clock error data features, reducing the parameters of the network, and preventing overfitting. While simplifying the data, it enhances the robustness of the features and obtains the local optimal features of the clock error data in the spatial structure.

Finally, the fully connected layer is connected to all neurons in the previous layer, all features of the neurons in the previous layer are extracted, and the feature vectors output by the pooling layer are integrated to achieve the final regression task.

CNN models often have multiple convolution and pooling layers. These network layers automatically generate feature vectors of the data by acquiring effective information, reducing the difficulty of feature extraction and data reconstruction, and improving the quality of spatial features.

The CNN model can extract key information from complex sample features and amplify these features, thereby finding implicit relationships between more abstract and deep features, reducing the computational load of the training process, and accelerating the convergence of the model; however, when processing time series data, the model lacks the ability to perceive the fluctuations of sample data before and after.

In the specific implementation, refer to Figure 3, which is a CNN-GRU combined model structure diagram of the first embodiment of the satellite clock error prediction method of the present invention. The present invention combines CNN with GRU, which not only makes up for the problem that the CNN network cannot adapt to time dependence, but also uses the GRU network to extract the nonlinear characteristics of the clock error data to achieve high-precision prediction of the clock error data. First, the CNN convolution layer is used to extract the spatial features of the input satellite clock error; then, it is passed to the GRU module to process the nonlinear characteristics of the clock error; finally, the forecast data of the clock error is output through the fully connected layer.

It should also be noted that in order to improve the computational efficiency, the BOA algorithm needs to be improved. In order to ensure the global convergence of the algorithm, by establishing a fitness function, in each operation of the algorithm, the minimum hill climbing method is combined to make local adjustments to each stage of the algorithm so that it tends to the optimal solution. The fitness inheritance of the generated solution can effectively save the fitness evaluation time, and the search for individual local substructures can effectively jump out of the local extreme value. In order to avoid useless search during the search process, the pattern ant colony algorithm is introduced for structural learning, nodes are selected according to the probability transfer rule, and the evolution direction is guided by the optimization pattern.

In the specific implementation, refer to Figure 4, which is a model processing flow chart of the first embodiment of the satellite clock error prediction method of the present invention. (1) Each time the data of a single satellite is used for processing, a differential processing is performed on the original clock error data to obtain the first differential data of the clock error. (2) The median gross error detection method is used to detect and remove the clock error anomaly of the first differential, and then the piecewise linear interpolation method is used to fill the abnormal values to obtain relatively complete clock error data. (3) Initialize the network model structure, normalize the data set, and divide the data set into a training set and a test set. Each time, a subset is selected as the test set, and the others are used as training sets to train the model. Set hyperparameters such as the input dimension, the number of convolution kernels of the CNN-GRU combination model, the convolution kernel size, the pooling size, the number of neurons, the number of hidden layers, the learning rate, and the regularization coefficient. (4) Input the clock error data from steps (1)-(3) into the CNN-GRU combined model for network training. In the process of training the CNN-GRU combined model, the minimum hill climbing method is used to determine the search path, and the pattern ant colony algorithm is used to continuously search and select the next group of most potential dominant populations. The loss function value is calculated in each iteration to evaluate the performance of the current model and generate candidate populations. These candidate populations will be used to update the model and perform the next round of new iterations. (5) Repeat step 4. If the dominant population of the new iteration meets the requirements or reaches the maximum number of iterations, the iteration is stopped and the super-optimal hyperparameter combination is output. Otherwise, return to step 4. (6) The optimal hyperparameters output from step 5 are used as the hidden layer, learning rate and L2 regularization coefficient of the IBOA-CNN-GRU combined model. Then, the model is used to predict the first difference data of the clock error, and the predicted data is denormalized and de-differentiated to finally obtain the clock error prediction value.

In this embodiment, it is necessary to determine the global optimal parameters of the CNN-GRU combination model through the improved BOA algorithm. Therefore, it is necessary to determine multiple groups of dominant populations corresponding to the hyperparameters in the CNN-GRU combination model based on the upper and lower bounds of the parameters, and determine the local hyperparameters through the fitness function according to the multiple groups of dominant populations; the CNN-GRU combination model is trained based on the one-time difference minute difference data training set and the local hyperparameters to obtain the IBOA-CNN-GRU combination model; the root mean square error corresponding to the output result of the IBOA-CNN-GRU combination model is determined through the loss function; if the root mean square error is less than or equal to the preset error threshold, and the local hyperparameter is the global optimal parameter, the IBOA-CNN-GRU combination model is used as the IBOA-CNN-GRU prediction model.

Furthermore, a processing method for determining multiple groups of dominant populations corresponding to hyperparameters in the CNN-GRU combination model based on parameter upper bounds and parameter lower bounds is as follows: determining multiple groups of populations corresponding to hyperparameters in the CNN-GRU combination model based on parameter upper bounds and parameter lower bounds, the hyperparameters including the number of hidden units, the initial learning rate and the L2 regularization parameter; and selecting multiple groups of dominant populations from the multiple groups of populations through a fitness function.

It should also be noted that the CNN-GRU combination model needs to be initialized at the beginning. At this time, multiple groups of initial populations x _m corresponding to the hyperparameters in the CNN-GRU combination model can be randomly generated based on the upper and lower bounds of the parameters. P(0) is the matrix corresponding to the multiple groups of initial populations.

It should also be understood that P(0) refers to the starting point of the algorithm, and then the size of its population M and the maximum number of iterations N will be set. At the same time, the CNN-GRU combination model has three parameters that need to be optimized: the number of hidden units (NumOfUnits), the initial learning rate (InitialLearnRate) and the L2 regularization parameter (L2Regularization). These parameters will set a lower bound and an upper bound. Assume that the lower bound is set to lb = [10, 0.0005, 1e-6]; the upper bound is set to ub = [50, 0.001, 1e-3], then P(0) is an M*3 matrix, where each row represents an initial population, and an initial population contains the three parameter values given above.

Assuming that the initial population size is 20, then P(0) is a 20*3 matrix.

The values in this matrix are all within this range. Random generation ensures the diversity of the population, covers the entire search space, and provides a basis for subsequent iterative optimization.

The formula can be expressed as:

P(0)＝[ _x1 ； _x2 … _xm ]

x _m =[x _m1 ,x _m2 …x _m3 ]

Furthermore, the processing method for selecting multiple groups of dominant populations from multiple groups of populations through the fitness function is to determine the fitness value corresponding to each group of populations through the fitness function; select multiple groups of populations to be optimized corresponding to fitness values less than a preset fitness threshold from the multiple groups of populations; adjust the multiple groups of populations to be optimized through a local search algorithm to obtain multiple groups of adjusted populations, and determine the fitness value corresponding to each group of adjusted populations; determine the multiple groups of dominant populations according to the fitness values corresponding to each group of adjusted populations and the fitness values corresponding to each group of populations to be optimized.

The fitness function is:

In the formula, _xm is the population, f( _xm ) is the fitness value corresponding to _xm , m is the predicted population size, is the predicted value of the i-th data in the _xm population, and _Li is the true value of the i-th data in the _xm population.

It should also be noted that the P(0) generated at the beginning is random, but each subsequent generation of P(t) is generated based on the previous generation through selection, local search, etc. For example, when t is 1, it is generated based on P(0) through selection and local search.

It should be understood that the fitness function is then used to evaluate the initial population _xm . Here, the fitness function f( _xm ) selects RMSE. Multiple groups of populations to be optimized are found by comparing the fitness values, and then the local search algorithm is used to adjust the multiple groups of populations to be optimized. Here, the main purpose is to adjust the fitness of the above-mentioned multiple groups of populations to be optimized to a better level, so as to obtain the best dominant population.

In the local search, the parameters of the current population to be optimized _xi are slightly adjusted in order to find a better population.

Assume that we select a population to be optimized _xi and adjust it. The new population to be optimized _x'i can be expressed as:

x' _i = _xi +δ

Where δ is a floating value used to adjust _xi , and its formula is:

δ _j = random × (ub _j - lb _j )

Among them, ub _j and lb _j are the upper and lower bounds of the j-th parameter, and random is a random number between [0,1].

It should be noted that the new population to be optimized _x'i and the previous population to be optimized _xi are brought into the fitness function to calculate the fitness value. By comparing the size of the fitness value, it is determined whether it needs to be updated. If the fitness of the dominant population _x'i is smaller than the fitness of the previous dominant population _xi , that is, f( _x'i )<f( _xi ), then the value of _x'i replaces the value of _xi , so that the local individual is optimally adjusted.

Furthermore, after the step of determining the root mean square error corresponding to the output result of the IBOA-CNN-GRU combination model through the loss function, if the root mean square error is less than or equal to the preset error threshold and the local hyperparameter is not the global optimal parameter, the multiple groups of populations are iteratively updated through the minimum hill climbing method and the pattern ant colony algorithm according to the iteration rule, and the step of selecting multiple groups of dominant populations from the multiple groups of populations through the fitness function is returned.

The processing method for iteratively updating multiple groups of populations through the minimum hill climbing method and the pattern ant colony algorithm according to the iteration rules is to construct a Bayesian network structure based on multiple groups of dominant populations according to the scoring formula; select multiple groups of candidate populations from the multiple groups of dominant populations through the minimum hill climbing method and the pattern ant colony algorithm according to the Bayesian network structure; and iteratively update the multiple groups of populations according to the multiple groups of candidate populations according to the iteration rules.

Furthermore, a processing method for constructing a Bayesian network structure based on multiple groups of dominant populations according to a scoring formula is to determine multiple parent nodes according to the multiple groups of dominant populations; determine a parent node set according to the multiple parent nodes through a scoring formula; and construct a Bayesian network structure based on the parent node set.

The scoring formula is:

Where _xi is the dominant population, _xj is the parent node, θ is the parameter in the score, N is the number of individuals in the topological network structure, _Πi is the set of parent nodes, P is the likelihood function of _xi under _Πi , and D is the hyperparameter within _xi .

In this embodiment, the dominant population matrix reports multiple groups of dominant populations x _i . In the dominant population matrix S(t), topological sorting of n variables is randomly generated. These sortings determine the order of population individuals, and these sortings provide the order of population individuals for the subsequent scoring algorithm.

According to the topological ordering of a given individual, parent nodes are gradually added to maximize the scoring function of the network.

Among them, the detailed steps of constructing the Bayesian network structure are:

1. Input the dominant population matrix S(t) and initialize the maximum number of parent nodes λ.

2. For x _i in the dominant population matrix S(t), initialize its parent node set At the same time, the structure matrix of the Bayesian network is set to a 0 matrix.

3. Process each dominant population xi _one by one in the order of topological sorting.

4. Add a parent node:

For the currently processed dominant population, initialize the optimal score Score (x _i , Π _i ), whose formula is:

Score(x _i ,Π _i )=logP(x _i ∣Π _i )

Where P is the likelihood function of _xi under _Πi , and logP( _xi | _Πi ) represents the log-likelihood value of _xi under _Πi .

Then try to use {x ₁ ,x ₂ ,…,xi _-1 } as the parent node of xi _one by one. For each parent node x _j (j<i), calculate the score after adding x _j . If x _j can improve the score, add it. The new score formula is:

Where θ is the specific parameter in the scoring (i.e., the parameter in the scoring), and N is the number of individuals in the topological network structure.

Continue trying to add parent nodes until the maximum number of parent nodes is reached or the score cannot be improved further.

Finally, the finalized Π _i is added to the Bayesian network.

Furthermore, a processing method for selecting multiple groups of candidate populations from multiple groups of dominant populations through the minimum hill climbing method and the pattern ant colony algorithm according to the Bayesian network structure is to adjust the Bayesian network structure, and determine multiple excellent solutions based on the multiple groups of dominant populations through the minimum hill climbing method based on the adjusted Bayesian network structure; construct a pheromone matrix based on the multiple excellent solutions, and adjust the pheromone matrix through the pattern ant colony algorithm; and determine multiple groups of candidate populations based on the adjusted pheromone matrix.

In this embodiment, the minimum hill climbing method and the pattern ant colony algorithm are used to search and obtain the highest evaluation structure diagram, and a candidate population matrix O(t) is generated based on the constructed Bayesian network. There are multiple groups of candidate populations in the candidate population matrix. The detailed steps of generating the candidate population matrix O(t) based on the constructed Bayesian network are as follows:

Hill climbing method: ensure the quality of the solution.

Starting from the Bayesian network structure, a better solution (i.e., one with low individual fitness) is searched in the neighborhood of the current constructed individual by adding, deleting, or reversing edges, and then calculating the function score of the new solution. If there is a solution with a better score in the neighborhood, the current solution is updated to that solution; otherwise, the search is stopped. The above process is repeated until there is no better solution.

Pattern ant colony algorithm: ensure the diversity of search space.

First, set the parameters such as the number of ants, number of iterations, pheromone importance factor, heuristic information importance factor, pheromone volatility rate, and pheromone increase intensity.

Then the ants construct solutions based on the pheromone matrix and heuristic information, and evaluate the quality of the solutions based on the scoring function. At the same time, the pheromone matrix is updated according to the solutions found by the ants, including global and local pheromone updates.

Pheromone matrix: Assuming there are n solutions, the pheromone matrix is an n*n matrix used to record the connections and strengths between solutions.

The role of the pheromone matrix: When constructing a solution, ants will choose a path based on the pheromone concentration. The higher the concentration, the greater the probability of choosing that path.

Pheromone update mechanism: Assuming there are y ants, the solution found by each ant is x _i , and its fitness is f(x _i ), then the formula for pheromone update is as follows:

Volatile:

τ _ij =(1-ρ)τ _ij

Where _τij represents the pheromone concentration from the ith solution to the jth solution, indicating the strength of the connection between two solutions, and ρ is the pheromone volatility coefficient, which ranges from 0 to 1.

Increase:

In the formula, It represents the information enhancement amount of ant k on path i to path j, and Q is a constant.

In this way, the pheromone matrix is dynamically adjusted through the volatilization and addition process, guiding the ants to find a better solution and improving the overall performance of the algorithm.

In summary, the candidate population matrix O(t) is generated using the hill climbing algorithm and the pattern ant colony algorithm.

It should also be noted that multiple groups of candidate populations in the newly generated candidate population matrix O(t) are used to replace the populations in the t-th generation population matrix P(t) to generate the next generation population matrix P(t+1), thereby improving the overall quality of the population.

It should be understood that when the maximum number of iterations N set at the beginning is reached or the fitness value no longer improves, the algorithm is stopped and the current optimal solution, that is, the optimal hyperparameters of the CNN-GRU combination model, is output, and the model is predicted using this hyperparameter.

Since the BOA algorithm may have useless searches during local optimization, it may fall into the local optimal extreme value. The optimized BOA algorithm enhances the global optimization ability of the BOA algorithm and improves the prediction accuracy of the model. The improved IBOA algorithm can not only improve the training and prediction time of the model, but also has high stability, which shows the feasibility of the IBOA-CNN-GRU model in short-term clock error prediction.

It should also be noted that the present invention constructs a CNN-GRU combination model, and optimizes the selection of hyperparameters on this basis. The CNN-GRU model can effectively improve the problem that the CNN model is difficult to adapt to long sequence time dependence, improve its stability and prediction accuracy, and is higher than the BP and LSTM models. The BOA model after adding the optimized Bayesian algorithm avoids the problem of difficult selection of hyperparameters, reduces the operation time, and has better prediction accuracy than CNN and CNN-GRU. The proposed IBOA-CNN-GRU model avoids the problem of error accumulation of a single model over time, and improves the useless search and local optimal solution in the selection of hyperparameters. Compared with several other neural network models, it has a significant improvement, reflecting the feasibility of clock error prediction.

In this embodiment, the clock error data of the same satellite are firstly subjected to a difference processing to obtain phase data, and the phase data is converted into frequency data. Then, the abnormal epochs are eliminated from the frequency data by the median method to obtain incomplete frequency data. The incomplete frequency data are completed by the Lagrange interpolation method based on the abnormal epochs to obtain a first-difference minute difference data sequence. Then, the first-difference minute difference data sequence is input into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock error prediction data. The IBOA-CNN-GRU prediction model is a model obtained by performing hyperparameter optimization on the CNN-GRU combination model through the improved BOA algorithm. This embodiment combines a convolutional neural network with a strong ability to extract sequence features with a GRU with a long-term memory structure, and uses the convolution and pooling operations of CNN to automatically extract the spatial vectors of the clock difference data, mine the time series features in the data, and solve the problem of prediction error accumulation of the model by performing accuracy judgment on the prediction results. Then, GRU is used to extract the time features of the clock difference data, and the model performance is improved with very little calculation. The data mining ability of the model is brought into play, and the advantages of the two models are combined to establish a CNN-GRU combined model. The Bayesian algorithm is used to optimize the hyperparameters of the combined model, effectively jumping out of the local extreme value problem of difficult hyperparameter selection, and ensuring the global convergence of the algorithm.

Refer to Figure 5, which is a structural block diagram of the first embodiment of the satellite clock error prediction system of the present invention.

As shown in FIG5 , the satellite clock error prediction system proposed in the embodiment of the present invention includes:

The data processing module 5001 is used to perform a difference process on the clock error data of the same satellite to obtain phase data, and convert the phase data into frequency data;

The data processing module 5001 is further used to remove abnormal epochs from the frequency data by the median method to obtain incomplete frequency data, and to complete the incomplete frequency data by the Lagrange interpolation method based on the abnormal epochs to obtain a first-order difference minute difference data sequence;

The model operation module 5002 is used to input the first-order difference minute difference data sequence into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock difference prediction data. The IBOA-CNN-GRU prediction model is a model obtained by optimizing the hyperparameters of the CNN-GRU combination model through the improved BOA algorithm.

In this embodiment, the clock error data of the same satellite are firstly subjected to a difference processing to obtain phase data, and the phase data is converted into frequency data. Then, the abnormal epochs are eliminated from the frequency data by the median method to obtain incomplete frequency data. The incomplete frequency data are completed by the Lagrange interpolation method based on the abnormal epochs to obtain a first-difference minute difference data sequence. Then, the first-difference minute difference data sequence is input into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock error prediction data. The IBOA-CNN-GRU prediction model is a model obtained by performing hyperparameter optimization on the CNN-GRU combination model through the improved BOA algorithm. This embodiment combines a convolutional neural network with a strong ability to extract sequence features with a GRU with a long-term memory structure, and uses the convolution and pooling operations of CNN to automatically extract the spatial vectors of the clock difference data, mine the time series features in the data, and solve the problem of prediction error accumulation of the model by performing accuracy judgment on the prediction results. Then, GRU is used to extract the time features of the clock difference data, and the model performance is improved with very little calculation. The data mining ability of the model is brought into play, and the advantages of the two models are combined to establish a CNN-GRU combined model. The Bayesian algorithm is used to optimize the hyperparameters of the combined model, effectively jumping out of the local extreme value problem of difficult hyperparameter selection, and ensuring the global convergence of the algorithm.

Other embodiments or specific implementations of the satellite clock error prediction system of the present invention can refer to the above-mentioned method embodiments and will not be described in detail here.

It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as a read-only memory/random access memory, a magnetic disk, or an optical disk), and includes a number of instructions for a terminal device (which can be a mobile phone, a computer, a server, or a network device, etc.) to execute the methods described in each embodiment of the present invention.

The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims (9)

1. A satellite clock error prediction method, characterized in that the satellite clock error prediction method comprises the following steps: Performing a difference process on the clock error data of the same satellite to obtain phase data, and converting the phase data into frequency data; Abnormal epochs are eliminated from the frequency data by the median method to obtain incomplete frequency data, and the incomplete frequency data are supplemented by the Lagrange interpolation method based on the abnormal epochs to obtain a first-order minute difference data sequence; The first-order minute difference data sequence is input into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock difference prediction data. The IBOA-CNN-GRU prediction model is a model obtained by optimizing the hyperparameters of the CNN-GRU combination model through the improved BOA algorithm. 2. The method according to claim 1, characterized in that before the step of inputting the first-order difference minute difference data sequence into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock difference prediction data, the method comprises: Determine multiple groups of dominant populations corresponding to the hyperparameters in the CNN-GRU combination model based on the upper and lower bounds of the parameters, and determine local hyperparameters through the fitness function based on the multiple groups of dominant populations; The CNN-GRU combined model is trained based on a one-time difference minute difference data training set and the local hyperparameters to obtain an IBOA-CNN-GRU combined model; Determine the root mean square error corresponding to the output result of the IBOA-CNN-GRU combination model through a loss function; If the root mean square error is less than or equal to a preset error threshold, and the local hyperparameter is a global optimal parameter, the IBOA-CNN-GRU combined model is used as the IBOA-CNN-GRU prediction model. 3. The method according to claim 2, characterized in that the step of determining multiple groups of dominant populations corresponding to the hyperparameters in the CNN-GRU combination model based on the upper limit value of the parameter and the lower limit value of the parameter comprises: Determine multiple groups of populations corresponding to hyperparameters in the CNN-GRU combination model based on the upper and lower bounds of the parameters, wherein the hyperparameters include the number of hidden units, the initial learning rate, and the L2 regularization parameter; Multiple groups of dominant populations are selected from multiple groups of populations through fitness functions. 4. The method according to claim 3, characterized in that the step of selecting multiple groups of dominant populations from multiple groups of populations by using a fitness function comprises: The fitness value corresponding to each group of populations is determined through the fitness function; The fitness function is: In the formula, _xm is the population, f( _xm ) is the fitness value corresponding to _xm , m is the predicted population size, is the predicted value of the ith data in the _xm population, and _Li is the true value of the ith data in the _xm population; Selecting from the multiple groups of populations a plurality of groups of populations to be optimized corresponding to the fitness values being less than a preset fitness threshold; By using a local search algorithm, multiple groups of populations to be optimized are adjusted respectively to obtain multiple groups of adjusted populations, and the fitness value corresponding to each group of adjusted populations is determined; Multiple groups of dominant populations are determined according to the fitness values corresponding to each group of adjusted populations and the fitness values corresponding to each group of populations to be optimized. 5. The method according to claim 3, characterized in that after the step of determining the root mean square error corresponding to the output result of the IBOA-CNN-GRU combination model through the loss function, it includes: If the root mean square error is less than or equal to the preset error threshold, and the local hyperparameter is not the global optimal parameter, the multiple groups of populations are iteratively updated through the minimum hill climbing method and the pattern ant colony algorithm according to the iteration rule, and the step of selecting multiple groups of dominant populations from the multiple groups of populations through the fitness function is returned. 6. The method of claim 5, characterized in that the step of iteratively updating the multiple populations by using the minimum hill climbing method and the pattern ant colony algorithm according to the iterative rule comprises: Construct a Bayesian network structure based on multiple groups of dominant populations according to the scoring formula; Selecting multiple groups of candidate populations from multiple groups of dominant populations by using a minimum hill climbing method and a pattern ant colony algorithm according to the Bayesian network structure; Iteratively update multiple groups of populations based on multiple groups of candidate populations according to iterative rules. 7. The method according to claim 6, characterized in that the step of constructing a Bayesian network structure based on multiple groups of dominant populations according to a scoring formula comprises: Determine multiple parent nodes based on multiple groups of dominant populations; Determine a parent node set based on multiple parent nodes through a scoring formula; The scoring formula is: Where, _xi is the dominant population, _xj is the parent node, θ is the parameter in the score, N is the number of individuals in the topological network structure, _Πi is the parent node set, P is the likelihood function of _xi under _Πi , and D is the hyperparameter in _xi ; A Bayesian network structure is constructed based on the parent node set. 8. The method according to claim 7, characterized in that the step of selecting multiple groups of candidate populations from multiple groups of dominant populations by using the minimum hill climbing method and the pattern ant colony algorithm according to the Bayesian network structure comprises: The Bayesian network structure is adjusted, and based on the adjusted Bayesian network structure, a plurality of excellent solutions are determined according to a plurality of groups of dominant populations by using a minimum hill climbing method; Constructing a pheromone matrix based on multiple excellent solutions, and adjusting the pheromone matrix through a pattern ant colony algorithm; Multiple groups of candidate populations are determined according to the adjusted pheromone matrix. 9. A satellite clock error prediction system, characterized in that the satellite clock error prediction system comprises: A data processing module is used to perform a primary difference processing on the clock error data of the same satellite to obtain phase data, and convert the phase data into frequency data; The data processing module is further used to remove abnormal epochs from the frequency data by the median method to obtain incomplete frequency data, and to complete the incomplete frequency data by the Lagrange interpolation method based on the abnormal epochs to obtain a first-order difference minute difference data sequence; The model running module is used to input the first-order difference minute difference data sequence into the IBOA-CNN-GRU prediction model for denormalization and dedifferentiation processing to obtain satellite clock difference prediction data. The IBOA-CNN-GRU prediction model is a model obtained by optimizing the hyperparameters of the CNN-GRU combination model through the improved BOA algorithm.