Short-term Prediction of Polar Motion Parameters Using Deep Neural Networks

There are many instabilities in the earth's rotation due to celestial bodies, gravitational forces, and earth internal dynamics which make the calculation of Earth Orientation Parameters (EOP) and Polar Motion (PM) parameters a challenging task. In today's world due to the increasing requests for predicting EOP and PM parameters in a wide range of fields such as Astronomy, Geodesy, Oceanography, and Hydrography various methods are used. These days it is possible to calculate accurate values of EOP and PM parameters by means of global positioning system (GPS), very-long baseline interferometry (VLBI) and satellite laser ranging (SLR). The core reason for the short-term prediction of these parameters is the impossibility of calculating these parameters in real-time due to heavy preprocessing procedures. Hence, researchers are seeking to employ different methods for accurate short-term prediction of EOP and PM parameters. In recent years, non-parametric methods such as least square (LS) with autoregressive moving average (ARMA) and also singular spectrum analysis (SSA) have been used to estimate these parameters. Another method for the prediction of the aforementioned parameters was conventional artificial neural network (ANN). Currently, Deep Learning has become a popular field that attracts many researchers. Deep learning is a subset of artificial intelligence (AI) and machine learning that uses multiple layers and parameters in order to extract complex features from the inputs. It is widely used in computer vision and time series prediction applications. In this paper, we used three deep learning methods namely LSTM, CNN, and MLP in order to predict PM parameters (x and y parameters). Furthermore, we have used Least square harmonic estimation (LSHE) method in order to compare the final results with different networks. LSTM equipped with a short-term recursive memory. This recursive mechanism prepares LSTM for handling time series data. CNN extracts important features of input data by convolution multiplication and each convolution layer within CNN architecture produces feature maps as output. These Feature maps contain recognized patterns which will be used as input of next layer. CNN networks, which were primarily designed for the computer vision, are being used more and more in timeseries prediction applications. MLP networks are similar to conventional back propagation feedforward networks, however, new activation functions and optimizers could be used in MLP networks. For sufficient training of different architectures, we used 35 years of daily PM parameters from 1st January 1980 to 31 December 2015 and we predicted 40 days periods ahead for the future 5 years. For comparison of predicted values by different networks, we used mean absolute error (MAE) as a criterion and illustrate results in two tables. Also, we depicted different figures to show how networks are working. In addition, we used two LSTM, four CNN, and two MLP Networks with ADAM optimizer, ReLU activation function, and learning rate of 0.001- 0.0001 in order to select the best network with the lowest errors.  Moreover, the figures of predicted values vs actual values and plots of MAE for 40 days are shown on four figures for better comprehension of ultimate results. In the end, it turned out that LSTM networks outperformed CNN and MLP networks and in this network the final results are better than the others in most days. For the x parameter in the first, twentieth and fortieth days, the best MAE values are 0.41 mas, 5.58 mas, and 12.45 mas and the best values for RMSE are 0.49 mas, 6.69 mas, 15.05 mas, respectively. For the y parameter in the first, twentieth and fortieth days, the best values of MAE are 0.54 mas, 3.24 mas and 7.56 mas and the best values for RMSE are 0.68 mas, 4.72 mas, 9.22 mas, respectively. The final results show that the neural networks outperformed LSHE method and the accuracies of the deep learning networks are satisfying and LSTM and CNN networks are capable to predict values accurately.