A new hybrid method to improve the ultra-short-term prediction of LOD

On the improvement of heart rate prediction using the combination of singular spectrum analysis and copula-based analysis approach

In recent years, many people have been working from home due to the exceptional circumstances concerning the coronavirus disease 2019 (COVID-19) pandemic. It has also negatively influenced general health and quality of life. Therefore, physical activity has been gaining much attention in preventing the spread of Severe Acute Respiratory Syndrome Coronavirus. For planning an effective physical activity for different clients, physical activity intensity and load degree needs to be appropriately adjusted depending on the individual's physical/health conditions. Heart rate (HR) is one of the most critical health indicators for monitoring exercise intensity and load degree because it is closely related to the heart rate. Heart rate prediction estimates the heart rate at the next moment based on now and other influencing factors. Therefore, an accurate short-term HR prediction technique can deliver efficient early warning for human health and decrease the happening of harmful events. The work described in this article aims to introduce a novel hybrid approach to model and predict the heart rate dynamics for different exercises. The results indicate that the combination of singular spectrum analysis (SSA) and the Clayton Copula model can accurately predict HR for the short term.

The Short-Term Prediction of Length of Day Using 1D Convolutional Neural Networks (1D CNN)

Accurate Earth orientation parameter (EOP) predictions are needed for many applications, e.g., for the tracking and navigation of interplanetary spacecraft missions. One of the most difficult parameters to forecast is the length of day (LOD), which represents the variation in the Earth's rotation rate since it is primarily affected by the torques associated with changes in atmospheric circulation. In this study, a new-generation time-series prediction algorithm is developed. The one-dimensional convolutional neural network (1D CNN), which is one of the deep learning methods, is introduced to model and predict the LOD using the IERS EOP 14 C04 and axial Z component of the atmospheric angular momentum (AAM), which was taken from the German Research Centre for Geosciences (GFZ) since it is strongly correlated with the LOD changes. The prediction procedure operates as follows: first, we detrend the LOD and Z-component series using the LS method, then, we obtain the residual series of each one to be used in the 1D CNN prediction algorithm. Finally, we analyze the results before and after introducing the AAM function. The results prove the potential of the proposed method as an optimal algorithm to successfully reconstruct and predict the LOD for up to 7 days.

Middle- and Long-Term UT1-UTC Prediction Based on Constrained Polynomial Curve Fitting, Weighted Least Squares and Autoregressive Combination Model

Universal time (UT1-UTC) is a key component of Earth orientation parameters (EOP), which is important for the study of monitoring the changes in the Earth’s rotation rate, climatic variation, and the characteristics of the Earth. Many existing UT1-UTC prediction models are based on the combination of least squares (LS) and stochastic models such as the Autoregressive (AR) model. However, due to the complex periodic characteristics in the UT1-UTC series, LS fitting produces large residuals and edge distortion, affecting extrapolation accuracy and thus prediction accuracy. In this study, we propose a combined prediction model based on polynomial curve fitting (PCF), weighted least squares (WLS), and AR, namely, the PCF+WLS+AR model. The PCF algorithm is used to obtain accurate extrapolation values, and then the residuals of PCF are predicted by the WLS+AR model. To obtain more accurate extrapolation results, annual and interval constraints are introduced in this work to determine the optimal degree of PCF. Finally, the multiple sets prediction experiments based on the International Earth Rotation and Reference Systems Service (IERS) EOP 14C04 series are carried out. The comparison results indicate that the constrained PCF+WLS+AR model can efficiently and precisely predict the UT1-UTC in the mid and long term. Compared to Bulletin A, the proposed model can improve accuracy by up to 33.2% in mid- and long-term UT1-UTC prediction.

Improved Ultra-Rapid UT1-UTC Determination and Its Preliminary Impact on GNSS Satellite Ultra-Rapid Orbit Determination

Errors in ultra-rapid UT1-UTC primarily affect the overall rotation of spatial datum expressed by GNSS (Global Navigation Satellite System) satellite ultra-rapid orbit. In terms of existing errors of traditional strategy, e.g., piecewise linear functions, for ultra-rapid UT1-UTC determination, and the requirement to improve the accuracy and consistency of ultra-rapid UT1-UTC, the potential to improve the performance of ultra-rapid UT1-UTC determination based on an LS (Least Square) + AR (Autoregressive) combination model is explored. In this contribution, based on the LS+AR combination model and by making joint post-processing/rapid UT1-UTC observation data, we propose a new strategy for ultra-rapid UT1-UTC determination. The performance of the new strategy is subsequently evaluated using data provided by IGS (International GNSS Services), iGMAS (international GNSS Monitoring and Assessment System), and IERS (International Earth Rotation and Reference Systems Service). Compared to the traditional strategy, the numerical results over more than 1 month show that the new strategy improved ultra-rapid UT1-UTC determination by 29–43%. The new strategy can provide a reference for GNSS data processing to improve the performance of ultra-rapid products.

On Entropy of Probability Integral Transformed Time Series

The goal of this paper is to investigate the changes of entropy estimates when the amplitude distribution of the time series is equalized using the probability integral transformation. The data we analyzed were with known properties-pseudo-random signals with known distributions, mutually coupled using statistical or deterministic methods that include generators of statistically dependent distributions, linear and non-linear transforms, and deterministic chaos. The signal pairs were coupled using a correlation coefficient ranging from zero to one. The dependence of the signal samples is achieved by moving average filter and non-linear equations. The applied coupling methods are checked using statistical tests for correlation. The changes in signal regularity are checked by a multifractal spectrum. The probability integral transformation is then applied to cardiovascular time series-systolic blood pressure and pulse interval-acquired from the laboratory animals and represented the results of entropy estimations. We derived an expression for the reference value of entropy in the probability integral transformed signals. We also experimentally evaluated the reliability of entropy estimates concerning the matching probabilities.