CN116976393A - Neural network forecasting method for navigation satellite clock error data - Google Patents
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Abstract
The invention provides a neural network forecasting method of navigation satellite clock error data, which establishes a short-term clock error forecasting model of combined SSA (Sparrow Search Algorithm ) and BiLSTM (bidirectional long-short-term memory neural network, two-way long-short-term memory neural network), reversely expands a neural network layer of LSTM (long-short-term memory neural network, long-short-term memory neural network model), establishes BiLSTM, and then combines SSA to effectively solve the problem that the neural network super parameters obtained by artificial experience adjustment in LSTM can reduce the accuracy of the model, obtain a long-short-term memory neural network forecasting model SSA-BiLSTM which is more in line with the actual situation of clock error data and more fully utilizes the BDS-3 precise satellite clock error data provided by GFZ to conduct single-day forecasting example and multi-day calculating example analysis, and can improve the accuracy and stability of the long-short-term memory neural network model in satellite clock error forecasting.
Description
Technical Field
The invention relates to the field of satellite clocks, in particular to a neural network forecasting method for navigation satellite clock error data.
Background
The satellite navigation positioning system needs to have high accuracy and high stability of system time as a basis, wherein the influence of time errors is not neglected, for example, the distance error corresponding to the time error of 1ns is about 3dm, and the centimeter-level positioning requirement of a user is seriously influenced. The short-term forecast of the satellite clock error can provide important priori information for real-time dynamic positioning, and the accuracy of the real-time positioning is improved. Therefore, the short-term prediction accuracy of satellite clock error is improved, the satellite autonomous navigation performance can be improved, and the positioning accuracy is improved. In recent years, scholars have proposed a number of models based on mathematical theory, such as polynomial models, gray models, spectral analysis models, kalman filter models, semi-parametric models, etc. The model improves the quality of clock error forecast, but the satellite-borne atomic clock has complex time-frequency characteristics and is extremely easily influenced by external environment, satellite clock error data generally has the characteristics of nonlinearity and randomness change, and the nonlinearity are difficult to parameterize and represent, so that accurate forecast cannot be carried out by means of a single mathematical model.
In order to solve the problem that the data cannot be parameterized and accurately represented, researchers begin to explore short-term satellite clock error prediction methods based on machine learning and neural networks, such as machine learning methods like support vector machines and extreme learning machines, and neural network methods like radial basis, back propagation and wavelet.
In recent years, long-short-term memory neural networks (LSTMs) have been widely used in the field related to time series prediction due to their advantages in capturing time dependence and nonlinear characteristics, which also make LSTMs have great application value in satellite clock error prediction. The research in the prior art shows that the LSTM model has a good forecasting function in the aspect of clock error forecasting, improves the precision of clock error forecasting, and still has two problems: first, it is difficult to determine neural network hyper-parameters such as initial learning rate of the model and the number of hidden layer neurons. The magnitude of the neural network learning rate directly influences the training effect of the model, while the number of hidden layer neurons determines the fitting capacity of the model, and the parameters are obtained by artificial experience adjustment, so that the accuracy of the model is generally reduced. Secondly, although LSTM can handle time series dependency, it can only handle input sequences in order, and as the data length increases, LSTM cannot effectively capture nonlinear dependency relationships far apart, resulting in performance degradation, in the face of predicting short-term large-capacity data.
Disclosure of Invention
Aiming at the technical problems existing in the prior art, the invention provides a neural network forecasting method for navigation satellite clock error data, and provides a two-way long and short memory neural network (BiLSTM) of a sparrow super-parameter optimization algorithm. The sparrow optimization algorithm solves the problem of super-parameter optimization of LSTM so as to improve the accuracy of short-term prediction of clock error data. The BiLSTM expands the LSTM network hidden layer, so that the neural network can conduct forward and backward bidirectional feature extraction on clock difference data, and the long-term dependence problem existing in the traditional LSTM is effectively solved.
According to a first aspect of the present invention, there is provided a neural network forecasting method of navigation satellite clock difference data, comprising:
step 1, processing original clock difference data into a primary difference clock difference data sequence;
step 2, constructing a BiLSTM model for short-term clock error prediction, wherein the input of the BiLSTM model is a current clock error data sequence, and after a front-back mapping relation between clock error data is learned, a predicted value of the clock error data sequence is output;
step 3, training the BiLSTM model, and performing optimization search on the super parameters of the BiLSTM model by using a sparrow optimization algorithm to find a global optimal super parameter set of the BiLSTM model, wherein the super parameters comprise: the number of neurons, the learning rate, the loss layer range and the regularization coefficient;
and 4, carrying out short-term clock error forecast by using the trained BiLSTM model.
According to the neural network forecasting method for the navigation satellite clock error data, in satellite clock error forecasting, the forecasting performance and generalization capability of a neural network model can be effectively improved; compared with the traditional LSTM, the BiLSTM model of the sparrow optimization algorithm has more comprehensive modeling capability on the clock difference sequence, shows better forecasting accuracy, and obviously improves the forecasting average precision of BDS-3 full-series satellites compared with the traditional quadratic polynomial model, wavelet neural network, long-short-term memory neural network, two-way long-short memory neural network and other models.
Drawings
FIG. 1 is a flowchart of an embodiment of a neural network forecasting method for navigation satellite clock error data provided by the present invention;
FIG. 2 is a block diagram of an embodiment of a BiLSTM provided by the present invention;
FIG. 3 (a) is a graph of the prediction residual error of each model full-series satellite 1h provided by the embodiment of the invention;
FIG. 3 (b) is a graph of the 3h forecast residuals for each model full-series satellite provided by an embodiment of the present invention;
FIG. 3 (c) is a graph of the model-wide series of satellite 6h prediction residuals provided by an embodiment of the present invention;
FIG. 3 (d) is a graph of the model-wide series of satellite 12h prediction residuals provided by an embodiment of the present invention;
FIG. 3 (e) is a chart of 24h forecast residuals for each model full-series satellite provided by an embodiment of the present invention;
fig. 3 (f) is a diagram of a model full-range satellite 48h prediction residual provided by an embodiment of the present invention.
Detailed Description
The principles and features of the present invention are described below with reference to the drawings, the examples are illustrated for the purpose of illustrating the invention and are not to be construed as limiting the scope of the invention.
Fig. 1 is a flowchart of a neural network forecasting method for clock error data of a navigation satellite, provided by the invention, as shown in fig. 1, and the method comprises the following steps:
and step 1, processing the original clock difference data into a primary clock difference data sequence.
And carrying out primary difference on the original clock difference data to obtain clock difference change rate value data of the characteristic and error item of the highlighted clock difference data.
And 2, constructing a BiLSTM model for short-term clock error prediction, wherein the input of the BiLSTM model is a current clock error data sequence, and after a front-back mapping relation between clock error data is learned, outputting a predicted value of the clock error data sequence.
And 3, optimizing and searching the super-parameters of the BiLSTM model by utilizing a sparrow optimization algorithm to find the global optimal super-parameters of the BiLSTM model, training the BiLSTM model, wherein the super-parameters comprise: neuron number, learning rate, loss layer range, regularization coefficient, etc.
And 4, carrying out short-term clock error forecast by using the trained BiLSTM model.
The BiLSTM model is used for short-term clock error forecasting and comprises two steps of training and forecasting. In the training stage, the clock difference sequence is used as training input and expected output of the network, and the BiLSTM model learns the front-back mapping relation between clock difference data. In the forecasting stage, the BiLSTM model utilizes the learned mapping relation and topological structure to input the current clock difference data into the network, and then the current clock difference data are extrapolated step by step to obtain a forecasting result. The BiLSTM model performs short-term clock error forecast according to the topological structure by learning the mapping relation between clock error data.
The invention provides a neural network forecasting method of navigation satellite clock error data, and provides a two-way long and short memory neural network (BiLSTM) of a sparrow super-parameter optimization algorithm. The sparrow optimization algorithm solves the problem of super-parameter optimization of LSTM so as to improve the accuracy of short-term prediction of clock error data. The BiLSTM expands the LSTM network hidden layer, so that the neural network can conduct forward and backward bidirectional feature extraction on clock difference data, and the long-term dependence problem existing in the traditional LSTM is effectively solved.
Example 1
An embodiment 1 of the present invention provides an embodiment of a neural network forecasting method for clock error data of a navigation satellite, and as can be known from fig. 1, the embodiment of the forecasting method includes:
and step 1, processing the original clock difference data into a primary clock difference data sequence.
And carrying out primary difference on the original clock difference data to obtain clock difference change rate value data of the characteristic and error item of the highlighted clock difference data.
In one possible embodiment, step 1 further comprises:
abnormal data in the clock difference data is detected by using a median method, and the abnormal data is replaced by using a piecewise linear interpolation method.
In particular, the clock-difference sequence l= [ L ] 1 ，l 2 ，…，l i ]I=1, 2, …, n, its primary difference data sequence is Δl= [ Δl ] 1 ，Δl 2 ，…，Δl j ]J=1, 2, …, m, where m=n-1, Δl j ＝Δl i+1 -Δl i 。
Will Deltal j Substituting the following formula:
|Δl j |>n MAD (1)
MAD＝Median{|Δl j -K|/0.6745} (2)
wherein: n is a constant and is set according to the abnormal value proportion of the actual result; k is the intermediate number of the sequence delta L, the intermediate number m is added with a plurality of times of the median, and each frequency data is compared with the added value to exceed the abnormal value; and (3) processing the abnormal value positioned by the median method by adopting a linear function interpolation method.
And 2, constructing a BiLSTM model for short-term clock error prediction, wherein the input of the BiLSTM model is a current clock error data sequence, and after a front-back mapping relation between clock error data is learned, outputting a predicted value of the clock error data sequence.
When the time series data of the clock difference is processed, if the prediction can be performed by using the previous information and the reverse verification can be performed by the future information, the fitting accuracy can be further improved. To meet this demand, biLSTM has been developed. As shown in fig. 2, which is a block diagram of an embodiment of a BiLSTM provided by the present invention, it can be seen from fig. 2 that the BiLSTM is formed by stacking a forward LSTM and a backward LSTM, and state parameters of the two directions of LSTM are independent. Such a design enables the network to analyze the time series data in both forward and backward directions simultaneously, thereby taking full advantage of all the information in the clock-biased time series data. By the method, the characteristics of the clock error data can be comprehensively mastered, and the data utilization rate and the prediction accuracy rate are improved.
In fig. 2, X1, X2 … Xt represents clock difference data at consecutive t times, and Y1, Y2 … Yt are predicted clock difference data output at corresponding times, and in given consecutive t times of clock difference data, two LSTM layers are used to calculate the hidden layer state at each time. The forward LSTM layer and the reverse LSTM layer are used to capture the sequence information and the reverse sequence information, the forward LSTM layer calculates the sequence information at the current time, and the reverse LSTM layer calculates the reverse sequence information at the same time. And fusing the hidden layers obtained by the calculation of the forward LSTM layer and the reverse LSTM layer according to a certain weight to obtain a hidden layer state at the final moment t, and generating the predicted clock difference data Yt at the corresponding moment by using the hidden layer state on the basis.
Accordingly, biLSTM builds the following formula:
wherein ,indicating the forward hidden layer state at time t, < >>The state of a backward hidden layer at the moment t is represented; w (W) t 、v t Respectively representAnd->The corresponding weight; b t Indicating the bias of the hidden layer at time t.
And 3, optimizing and searching the super-parameters of the BiLSTM model by utilizing a sparrow optimization algorithm to find the global optimal super-parameters of the BiLSTM model, training the BiLSTM model, wherein the super-parameters comprise: neuron number, learning rate, loss layer range, regularization coefficient, etc.
The reasonable selection of the model hyper-parameters has important influence in data fitting and forecasting, in order to improve the forecasting effect of the BiLSTM model, the optimization of the hyper-parameters in the neural network model by using a group intelligent optimization algorithm is a feasible method, and SSA is an optimization algorithm based on group intelligent, and has good capacity of exploring a global optimal potential area.
When the sparrow optimization search algorithm is used for carrying out the super-parameter optimization of the model, each individual is expressed as a sparrow, the position of the sparrow represents a super-parameter combination, the position of each individual is expressed as a D-dimensional vector, and each dimension represents a super-parameter. Assuming that the population size is N, the current iteration number is t, and each sparrow i maintains own position and speed information x= [ x ] i,1 ，x i,2 ，…，x i,D] and v＝[vi,1 ，v i,2 ，…，v i,D ]. In the searching process, each sparrow can continuously update its own position and speed information, and the current position and speed optimal value and the global optimal value need to be considered during each update to guide the sparrow to approach to the global optimal solution.
The super parameters of the BiLSTM model are adaptively matched through a sparrow optimization algorithm, and the search parameter setting of the sparrow algorithm is shown in table 1.
Table 1: sparrow algorithm search parameter value table
In the searching process, the sparrow optimization algorithm considers various possible factors of group behaviors, can quickly converge near the optimal solution, and effectively avoids the situation of sinking into the local optimal solution.
And 4, carrying out short-term clock error forecast by using the trained BiLSTM model.
Example 2
In order to verify the effectiveness and feasibility of the optimization model, the embodiment 2 provided by the invention is an embodiment of a specific application of the neural network forecasting method for the navigation satellite clock difference data, and in order to better evaluate the forecasting precision of satellite clock differences of different models, the invention regards the clock difference data as systematic deviation, correspondingly eliminates the clock difference data and regards the GFZ post-precision satellite clock difference as true value. SSA-BiLSTM model and four comparison models (QP, WNN, LSTM, biLSTM) are established, in order to comprehensively evaluate the forecasting capability of each model in terms of model universality, precision clock difference data of 29 satellites in a full series from 1 month 1 day to 1 month 3 days in 2022 are selected, five models such as QP, WNN, LSTM, biLSTM, SSA-BiLSTM are used for forecasting satellite clock differences of 29 BDS-3 satellites in six total time periods of 1h, 3h, 6h, 12h, 24h and 48h, and clock difference data sampling intervals are five minutes. Fig. 3 (a) -3 (f) show graphs of prediction residuals for each model full-series satellite 1h, 3h, 6h, 12h, 24h, and 48h, respectively, where the red line is QP model prediction, the yellow line is WNN prediction, the green line is LSTM prediction, the purple line is BiLSTM prediction, and the blue line is SSA-BiLSTM prediction, where each line represents the prediction for one satellite.
As can be seen from fig. 3 (a) -3 (f), the prediction errors of QP, LSTM, etc. methods are generally more scattered, and theyThe prediction error distribution of the other methods is relatively concentrated. With the increase of the duration, the prediction error of different methods is larger, LSTM and WNN are obviously diverged at 24h and 48h forecast, while the divergence effect of SSA-BiLSTM and BiLSTM methods is smaller, and certain stability is shown. From quantitative analysis, the SSA-BiLSTM neural network model has good stability and universality in multi-day forecasting, and for further explanation of forecasting effects, table 7 gives a comprehensive of 29 satellite clock error forecasting resultsAnd->The calculation methods are given by formulas (15) - (17).
TABLE 2 prediction accuracy analysis of full series satellites
As can be calculated from Table 2, in 29 satellites used in the experiment, the prediction accuracy of the SSA-BiLSTM model is greatly improved compared with that of the QP model, the WNN model and the LSTM model. Experimental results show that compared with a polynomial model (QP), a Wavelet Neural Network (WNN), a long and short memory neural network (LSTM) model and a two-way long and short memory neural network (BiLSTM) model, the algorithm provided by the invention has the advantages that the accuracy can be obviously improved, and the long-term prediction accuracy and stability are higher.
In order to establish a long-short-period memory neural network prediction model which is more in line with the actual situation of clock error data and more fully utilizes the clock error data information, the invention provides a two-way long-short-period memory neural network model and a sparrow super-parameter optimization method matched with the two-way long-period memory neural network model, and the following conclusion is obtained through experiments:
1) In satellite clock error prediction, the super-parameter optimization algorithm can effectively improve the prediction performance and generalization capability of the neural network model.
2) Compared with the traditional LSTM, the BiLSTM model of the sparrow optimization algorithm has more comprehensive modeling capability on the clock difference sequence, shows better forecasting accuracy, and obviously improves the forecasting average precision of BDS-3 full-series satellites compared with the traditional quadratic polynomial model, wavelet neural network, long-term memory neural network, two-way long-term memory neural network and other models.
In the foregoing embodiments, the descriptions of the embodiments are focused on, and for those portions of one embodiment that are not described in detail, reference may be made to the related descriptions of other embodiments.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (10)
1. A neural network forecasting method for navigation satellite clock error data, the forecasting method comprising:
step 1, processing original clock difference data into a primary difference clock difference data sequence;
step 2, constructing a BiLSTM model for short-term clock error prediction, wherein the input of the BiLSTM model is a current clock error data sequence, and after a front-back mapping relation between clock error data is learned, a predicted value of the clock error data sequence is output;
step 3, training the BiLSTM model, and performing optimization search on the super parameters of the BiLSTM model by using a sparrow optimization algorithm to find a global optimal super parameter set of the BiLSTM model, wherein the super parameters comprise: the number of neurons, the learning rate, the loss layer range and the regularization coefficient;
and 4, carrying out short-term clock error forecast by using the trained BiLSTM model.
2. A forecasting method according to claim 1, characterized in that said step 1 further comprises:
abnormal data in the clock difference data is detected by using a median method, and the abnormal data is replaced by using a piecewise linear interpolation method.
3. A forecasting method as claimed in claim 2, characterized in that the process of detecting abnormal data in the clock-difference data using a median method comprises:
clock difference sequence l= [ L ] 1 ，l 2 ，…，l i ]I=1, 2, …, n, whose primary difference data sequence is Δl= [ Δl 1 ，Δl 2 ，…，Δl j ]J=1, 2, …, m, where m=n-1, Δl j ＝Δl i+1 -Δl i ；
Will Deltal j Substituting the following formula:
|Δl j |>n MAD；
MAD＝Median{|Δl j -K|/0.6745}；
wherein: n is a constant set according to the abnormal value proportion of the actual result; k is the intermediate number of the sequence DeltaL;
and adding the intermediate number and the set multiple of the median to obtain an added value, and determining the clock difference data exceeding the added value as abnormal data.
4. The forecasting method of claim 1, wherein the BiLSTM model is formed by superposition of forward LSTM and backward LSTM with independent state parameters;
capturing sequence information and reverse sequence information by using a forward LSTM layer and a reverse LSTM layer, wherein the forward LSTM layer calculates sequence information at the current moment, and the reverse LSTM layer calculates reverse sequence information at the same moment;
and fusing the hidden layers obtained by calculation of the forward LSTM layer and the reverse LSTM layer according to the set weights to obtain hidden layer states, and generating a clock difference data sequence predicted value at a corresponding moment by using the hidden layer states.
5. The forecasting method of claim 4, wherein,
using the hidden layer state of the time t to generate predicted clock difference data Yt of the corresponding time, the state of the BiLSTM model is expressed as:
wherein ,indicating the forward hidden layer state at time t, < >>The state of a backward hidden layer at the moment t is represented; w (W) t 、v t Respectively indicate->And (3) withThe corresponding weight; b t Indicating the bias of the hidden layer at time t.
6. A forecasting method according to claim 1, characterized in that said step 3 comprises:
step 301, determining the number of neurons, the number of hidden layers, the learning rate, the loss layer and the super-parameter domain space E of regularization parameters of the BiLSTM model, setting the maximum iteration number N, setting a gradient descent optimizer as Adam, and taking the root mean square error as a target loss function of the BiLSTM model.
7. A forecasting method according to claim 6, characterized in that said step 3 comprises:
step 302, using the position of each sparrow to represent a superparameter combination, obtaining data from the training data set as an input layer x= { xt|t=1, 2, …, n } of the bistm through SSA principle, randomly sampling from the superparameter space, and searching for a possible optimal superparameter combination;
step 303, performing network training on the BiLSTM model, in the training process, continuously searching and selecting the next group of evaluation points with the highest potential by using SSA, inputting each evaluation point as training data into the BiLSTM model for training, and then obtaining and outputting a group of new super-parameter combinations; in each iteration, the performance of the current BiLSTM model is evaluated by calculating the loss value of the objective function, the next evaluation point is selected by using the SSA rule, and each group of obtained super-parameters are combined and output and stored in a sample set F.
8. A forecasting method according to claim 7, characterized in that said step 303 is followed by:
step 304, repeatedly executing steps 302 and 303, calculating the prediction error of the BiLSTM model by using a cross-validation method, and selectively adding new super-parameter combinations into the set F according to a selected strategy;
and 305, if the model loss value of the newly selected evaluation point meets the requirement of the cross verification precision or the maximum iteration number N is reached, terminating the super-parameter optimization algorithm and outputting the current optimal super-parameter combination.
9. A forecasting method according to claim 8, characterized in that in step 304, in the process of evaluating the performance of the super-parametric optimization algorithm using cross-validation, the dataset is normalized and divided into several subsets that do not overlap each other, in each iteration of the neural network, one subset is selected as the theoretical dataset validation set, the remaining subsets are selected as training sets, and the validation set selection process is repeated several times to train respectively to find the average performance of the model.
10. A forecasting method according to claim 1, characterized in that said step 4 comprises: and (3) after the global optimal superparameter set found in the step (3) is used as the superparameter of the BiLSTM model, the BiLSTM model is used for carrying out primary difference data forecasting on the clock difference, and inverse normalization and contrast division operation are carried out on the forecasting data to obtain a clock difference forecasting value.
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