Extended Kalman filtering applied to high-rate GNSS-R sea level measurements

Coastal water monitoring is of increasing importance for applications such as sea level monitoring and urban planning. Currently, traditional tide gauge by radar measurement remains the most widely used method, but it involves placing a sensor close to the water surface, which can lead to its destruction, particularly in hostile maritime environments.

Sea level measurement by GNSS-R offers a promising alternative to traditional tide gauge methods by enabling continuous and global sea level measurements (e.g., Larson et al., 2013). It has the significant advantage of limiting the constraints linked to the installation of sensors physically close to the water surface, as a GNSS antenna can be placed away from the coast or on a high structure. Furthermore, this technique takes advantage of the high availability of existing GNSS installations around the globe, which would make it possible to considerably extend the scope of tide gauge measurements on a global scale.

Most of the methods used in GNSS-R are based on the analysis of the signal/noise ratio (SNR). They generally use a spectral analysis based on a Lomb-Scargle periodogram and are effective for monitoring mean sea level at the centimeter level (e.g., Larson et al., 2013; Santamaría-Gómez and Watson, 2017; Peng et al., 2021). However, they require a relatively long portion of the SNR series to obtain a precise estimate of the oscillation frequency of the SNR signal. This has the effect of limiting the sampling rate of the measurement series and limits spectral methods to the observation of slow variations in sea level such as the tide. Other approaches use Kalman filtering and show that it is possible to achieve an accuracy of less than 5cm in near real time (e.g., Strandberg, Hobiger and Haas, 2019; Liu et al., 2023). Furthermore, these methods show that it is possible to considerably increase the data sampling rate and thus monitor rapid variations in sea level. This extends the scope of GNSS-R techniques to all applications requiring real-time sea level measurement.

We present a novel approach for measuring sea level by analyzing SNR signals with Kalman filtering. This approach relies on the estimation of the oscillation frequency and amplitude of SNR signals using an extended Kalman filter. It has the advantage of providing sea level height estimates at a sampling rate as high as the SNR measurements. The major constraint linked to the method lies essentially in the estimation of the initial phase of the SNR signals, which particularly affects the fit of the SNR signals from setting satellites.

GNSS-R measurements were carried out with a sampling frequency of 1 second and compared to those of a tide gauge colocated on the Aix Island ILDX site (France). By combining data from different existing GNSS systems (GPS, GLONASS, Galileo, BDS) and considering all available carriers, we estimate that it is possible to obtain an RMS error of less than 5cm on sites with high tidal ranges (± 6m).