Water levels measured with SNR using wavelet decomposition and Lomb–Scargle periodogram

Abstract

The expansion of research and applications involving global navigation satellite systems, e.g., the Global Positioning System (GPS), has revealed multipath errors. Discrete wavelet decomposition can reduce the noise of a signal-to-noise ratio (SNR) series, and the detailed coefficient of the wavelet decomposition at a specific level can be fitted to the SNR series. Therefore, we present a method to extract the multipath frequency of SNR data by implementing Lomb–Scargle periodogram (LSP) analysis after wavelet decomposition. This characteristic frequency can be used first to deduce the distance between the GPS antenna and the sea and then to estimate the sea level. This study analyzed data from two test sites: the Friday Harbor GPS site SC02 in the San Juan Islands (WA, USA) and the Kachemak Bay GPS site PBAY (AK, USA). The performance of applying wavelet decomposition before using the LSP is discussed for different length data series, i.e., a long data length and a short data length. The sea levels at the two GPS sites, retrieved by LSP and by LSP after wavelet decomposition using the two different data length series, all convincingly reproduced the overall behavior of the National Oceanographic and Atmospheric Administration tide gauge data. Furthermore, the performance of the improved method for shorter SNR data is much better than for the longer SNR data.