Entropy measure of stepwise component in GPS time series

A new method for estimating the stepwise component in the time series is suggested. The method is based on the application of a pseudo-derivative. The advantage of this method lies in the simplicity of its practical implementation compared to the more common methods for identifying the peculiarities in the time series against the noise. The need for automatic detection of the jumps in the noised signal and for introducing a quantitative measure of a stepwise behavior of the signal arises in the problems of the GPS time series analysis. The interest in the jumps in the mean level of the GPS signal is associated with the fact that they may reflect the typical earthquakes or the so-called silent earthquakes. In this paper, we offer the criteria for quantifying the degree of the stepwise behavior of the noised time series. These criteria are based on calculating the entropy for the auxiliary series of averaged stepwise approximations, which are constructed with the use of pseudo-derivatives.