Detecting time-varying seasonal signal in GPS position time series with different noise levels

Abstract

The coordinate time series determined with the Global Positioning System (GPS) contain annual and semi-annual periods that are routinely modeled by two periodic signals with constant amplitude and phase-lag. However, the amplitude and phaselag of the seasonal signals vary slightly over time. Various methods have been proposed to model these variations such as Wavelet Decomposition (WD), writing the amplitude of the seasonal signal as a Chebyshev polynomial that is a function of time (CP), Singular Spectrum Analysis (SSA), and using a Kalman Filter (KF). Using synthetic time series, we investigate the ability of each method to capture the time-varying seasonal signal in time series with different noise levels. We demonstrate that the precision by which the varying seasonal signal can be estimated depends on the ratio of the variations in the seasonal signal to the noise level. For most GPS time series, this ratio is between 0.05 and 0.1. Within this range, the WD and CP have the most trouble in separating the seasonal signal from the noise. The most precise estimates of the variations are given by the SSA and KF methods. For real GPS data, SSA and KF can model 49-84 and 77-90% of the variance of the true varying seasonal signal, respectively.

Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

“…Initially, the seasonal variation of GNSS position time series was modelled by harmonic model [19][20][21], which assumed that the amplitude of signal was constant. However, it can be seen from Figure 9 that the amplitude of nonlinear seasonal signals varies with epoch to epoch, which is also demonstrated by others [17,18]. Moreover, it has been verified that the WA can decompose the position time series into different scales ( Figure 6) and the reconstructed component of each layer has different frequencies ( Figure 7).…”

“…For daily GNSS position time series, its sampling frequency is one day. Considering that the annual and semi-annual signals are the two main periodic oscillations, with the periods of about 182 ∈ (2 7 , 2 8 ) days and 365 ∈ (2 8 , 2 9 ) days, respectively, the number of layers to be decomposed J is chosen as 8 and the reconstructed components of seventh and eighth level can be considered to be the annual and semi-annual signal, which is also confirmed by Klos et al [18].…”

“…From Figure 9, we can find that both two approaches can better describe the non-linear variation of the GNSS position time series and the extracted signals have slight difference, with mean absolute differences are 0.09 mm, 0.10 mm and 0.23 mm for north, east and up components, respectively. After the signals are removed from time series, the average error of residual time series can be calculated with Equation (17) for WA and Equation (18) for WWA as follows 2 ( ) (18) where ˆW A e and ˆW WA e are the residuals by WA and WWA, S denotes the epoch set of observations and M is the number of dataset. Since the total weights are same for WA and WWA, the average error can be used to characterize the quality of extracted signal [50].…”

“…Therefore, there has been an increasing interest in extracting signals from GNSS position time series, especially seasonal signals. Since a seasonal signal is irregular and its amplitude varies over time [17,18], it cannot be characterized by using a combination of annual and semi-annual harmonic functions with constant amplitudes that are solved by least squares estimation (LSE) [19][20][21]. Moreover, besides the annual and semi-annual signals, there still exist some other periodic signals with periods of 350 days and their fractions [22][23][24].…”

On the noise characteristics of time series recorded with nearby located GPS receivers and superconducting gravity meters

“…In superconducting gravity records, it can be caused by irregular instrumental drift from capacitance bridge, magnetic (instrumental) variations, gas adsorption on the levitating sphere, or helium gas pressure variations plus uncorrected small steps arising from local hydrosphere co-seismic event or instrumental disturbance as well as the tectonic movement (Van Camp and Francis 2006). In the following research, we estimated the non-linear trend in GPS and SG data using polynomials of 4th order as they perform better than any other method which may significantly bias the spectral content of the residuals (Klos et al 2018).…”