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• Automatic selection of embedding dimension in Singular spectrum analysis is achieved. • Singular spectrum analysis yields the most stable and accurate sea level heights among the methods. • Singular spectrum analysis provides a better concentration of spectral power in the periodogram. In order to obtain reliable GNSS-R derived sea level heights (SLHs), it is crucial to extract accurate reflected signals from signal-to-noise ratio (SNR) data. In this study, Quadratic Fitting, Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), and Singular Spectrum Analysis (SSA) are adopted for extracting the reflected signals from SNR data, which are then analyzed with Lomb Scargle Periodogram (LSP) assisted with tidal harmonic analysis for GNSS-R SLHs. Three continuous GNSS stations including Onsala in Sweden, Friday Harbor in the United States, and Brest in France with tidal ranges of approximately 1 m, 3 m, and 7 m, respectively, were used in the study. The derived SLHs were evaluated against the nearby or co-located tide gauge records. The results reveal that the three proposed algorithms effectively cope with the multi-peaks spectrum problems when using the conventional Quadratic Fitting without a priori reflected height constraint, and SSA can provide the solutions with fewer outliers among the proposed methods with the RMSEs of 6.7 cm, 13.4 cm and 39.6 cm at Onsala, Friday Harbor, and Brest stations, respectively. Without implementing tidal harmonic analysis, SSA is the method capable of acquiring reliable SLHs among the stations, as evidenced by comparing with co-located gauge records, particularly at the Brest station. In summary, SSA not only distinguishes signals across different frequencies, but also orders the signal components according to their eigenvalues, demonstrating the potential to extract the reflected signals from SNR and enhance the stability and accuracy of GNSS-R applications. [ABSTRACT FROM AUTHOR]