Trend detection in time series of measurement data in solving problems in space geodynamics and other research areas

Abstract

<p>This article discusses the problem of trend detection in time series generated by technical devices. The solution to this problem is closely related to the problem of detecting coarse measurements (outliers), which negatively impact the accuracy of estimates of various physical quantities. These are crucial in many applications in various scientific fields in which the input data are observations, such as space geodynamics, geodesy, and others. Previously, the author proposed a trend-detecting method based on the condition of maximizing the amount of data cleared of outliers and used in further processing. The reference values used for trend construction are determined as a result of a completely convergent iterative process, the core of which is the minimizing sets (MS) method developed earlier by the author. At each step of the iterative process, the trend is approximated by a function from a predefined functional class depending on the physical problem under consideration. The method was tested on trend-detection problems in the power polynomial class. In this article, the set of functions when searching for a trend by the MS method was extended into two additional functional classes: trigonometric functions with a given set of frequencies and harmonic functions with unknown frequencies, phases, and amplitudes. In the latter case, the trend-forming functions are nonlinearly dependent on the sought parameters; their search was carried out by the conjugate gradients method generalized to nonlinear problems. The article considered test tasks on trend search in data obtained by computer simulation.</p>