Parameter Estimation with GNSS-Reflectometry and GNSS Synthetic Aperture Techniques

Aside from intentional interference, multipath is the most significant error source for Global Navigation Satellite Systems (GNSS) receivers in many operational scenarios. In this thesis, we study the multipath estimation from two different perspectives: to retrieve useful information from it using GNSS-Reflectometry (GNSS-R) techniques; and to mitigate its effects or to estimate its direction-of-arrival (DOA) as well as the line-of-sight (LOS) signal¿s using synthetic aperture (SA) processing.

The first part of the thesis focuses on precision bounds for GNSS-R techniques for ground-based receivers, in scenarios where a single antenna simultaneously receives the LOS signal and a specular reflection. First, we derive the Cramér-Rao bound (CRB) of the receiver¿s height and the reflection coefficient, with the latter depending on the surface¿s electrical properties. More specifically, we propose a CRB derivation applicable to GNSS-R techniques that make use of the phase information and long observation times, such as the interference pattern technique (IPT). The derivation is based on the parameter transformation of the Fisher information matrix. We study the dependence of the computed CRB on the scenario and the receiver bandwidth. The CRB results for the simulated scenarios are consistent with the precision reported for many GNSS-R techniques used in these scenarios. The proposed CRB is meant to benchmark and compare new and existing techniques.

Besides the derived CRB, we propose an algorithm to obtain the maximum-likelihood (ML) estimator of the parameters of interest with the IPT: the segmented ML estimator (SML). The SML transforms a complex multivariate optimization problem into multiple simpler ones by dividing the parameter search space taking advantage of the cost function¿s particular structure. The SML is validated with simulated signal and asymptotically cross-validates the CRB results.

The second part of the thesis is devoted to the study of the SA processing of GNSS signals. The goal is to estimate the DOA of the signals received, and mitigate errors in the navigation solution caused by interfering signals, such as multipath. We start by deriving the CRB for the SA context, as a function of the antenna trajectory. This CRB considers the effect of the antenna complex gain, and we show in simulations that it is possible to achieve meaningful DOA estimation only by changing the antenna¿s orientation. We continue by proposing a development framework built upon a signal tracking architecture integrating SA processing. Before any SA processing, it is necessary to estimate and compensate any carrier phase contribution not related to the antenna motion. To do so, we propose two new sequential techniques based on the extended Kalman filter (EKF): EKF1 and EKF2. Also, we develop an open-loop version of the proposed SA tracking architecture, more robust than its closed-loop counterpart. Finally, we validate the proposed architecture and SA-based techniques with synthetic GPS signals at first, and then with real signals, recorded using an antenna mounted on a mechanical rotating arm. The obtained results validate the implemented techniques and show how the proposed SA architecture can ultimately mitigate the position bias error observed in environments with severe multipath interference.