GNSS-SNR water level estimation using global optimization based on interval analysis

The signal-to-noise ratio (SNR) from GNSS receivers allows computing the height of a reflecting surface by analyzing the interference pattern. In classical interference pattern technique the distance between the antenna and the reflector is derived from the multipath pattern using a one-dimensional Lomb-Scargle periodogram (LSP) which permits the estimation of constant or quasi static reflector heights only. Inwaters with tidal influence some authors used one-dimensional LSP to iteratively estimate an approximate time-dependent correction term for the variable reflector height. Other authors applied nonlinear least squares adjustment that requires choosing initial parameters what might become crucial due to the multimodality of the problem. We suggest and apply an alternative approach that allows finding the global optimum of a multi-dimensional cost function of a common least squares adjustment based on interval analysis. This method reduces the computational efforts compared to LSP. The technique is demonstrated using a simulated data set derived fromreal measurements on the Weser river, Germany. Additionally, real data from a gauge in the North Sea is analyzed.