Coherent superposition of multi-GNSS wavelet analysis periodogram for sea-level retrieval in GNSS multipath reflectometry

Abstract

The multipath signals of GNSS can act as a tide gauge via a technology called Global Navigation Satellite Systems multipath reflectometry (GNSS-MR), which is based on the relationship between multipath frequency and height to sea surface. In addition to the traditional frequency extraction method of Lomb–Scargle periodogram (LSP), wavelet analysis can be applied to extract instantaneous multipath frequencies of GPS L1, thus improving data utilization. However, because of the sensitivity of instantaneous frequency to noise and the introduction of more signals, multi-constellation retrievals exhibit many outliers and errors. The aim of this study is to apply wavelet analysis to multi-constellation multi-frequency signals and most importantly to find a method to avoid noise. We used coherent superposition to overlap the intra-track inter-signal instantaneous frequency spectrograms to enhance effective information and to weaken noise. This coherent superposition method can achieve intra-track inter-signal combination. The multi-GNSS data from two Multi-GNSS Experiment (MGEX) stations were used. The results showed that the coherent superposition spectrogram has a clear energy concentration, and the frequencies calculated from it depict sea-level changes. To compare the method with the LSP method and to combine inter-track retrievals, a robust regression method was used to combine retrievals and to produce equally spaced retrieval series. The results show that the combined retrievals from the coherent superposition method have a slightly higher accuracy than those from the classical LSP method. Because this method can be used to retrieve sea-level data from instantaneous frequency, it increases data utilization and provides a way to obtain details of SNR arcs, which is a potential method to benefit GNSS-MR, especially for sites with narrow reflecting sensing zones in a small sea azimuth range.