A New Estimation Algorithm for the GNSS-R Interference Pattern Technique: The Segmented Maximum-Likelihood
During the last years, Global Navigation Satellite Systems (GNSS) reflectometry (GNSS-R) receivers have proven in several field experiments that GNSS signals reflected and scattered from the Earth’s surface can be used in passive remote sensing applications. In ground based GNSS-R receivers, when the line-of-sight (LOS) signal coherently combines at then antenna with the reflected signal, the measured signal-to-noise ratio (SNR) will slowly fluctuate with the change of the GNSS satellite elevation. The Interference Pattern Technique (IPT) was proposed in order to use these SNR fluctuations to infer the distance between the antenna and the ground, as well as some of the geophysical properties of the nearby reflecting surface. The IPT implies little or no modification on the GNSS receiver, but it usually requires fairly long observation periods leading to a poor spatial resolution. Using the existing models, it is possible to express the reflected signal amplitude as a function of the height of the receiver antenna, the surface relative permittivity, and a surface roughness coefficient. Using the output of the receiver’s prompt correlators, we propose a new computationally efficient optimization algorithm, the segmented maximum likelihood (SML), that makes use of the particular properties of the likelihood/cost function under consideration to obtain the maximum likelihood estimator (MLE). We also show, by computing the estimator’s root-mean-square error and comparing it with the Cramér-Rao lower bound, how the obtained estimator can be efficient even for relatively short observation times.