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.

Normalized GNSS Interference Pattern Technique for Altimetry

Mohammed Benjelloun, Cyril Botteron, Pierre-André Farine, Jérôme Leclère, Miguel Angel Ribot Sanfelix

It is well known that reflected signals from Global Navigation Satellite Systems (GNSS) can be used for altimetry applications, such as monitoring of water levels and determining snow height. Due to the interference of these reflected signals and the motion of satellites in space, the signal-to-noise ratio (SNR) measured at the receiver slowly oscillates. The oscillation rate is proportional to the change in the propagation path difference between the direct and reflected signals, which depends on the satellite elevation angle. Assuming a known receiver position, it is possible to compute the distance between the antenna and the surface of reflection from the measured oscillation rate. This technique is usually known as the interference pattern technique (IPT). In this paper, we propose to normalize the measurements in order to derive an alternative model of the SNR variations. From this model, we define a maximum likelihood estimate of the antenna height that reduces the estimation time to a fraction of one period of the SNR variation. We also derive the Cramér–Rao lower bound for the IPT and use it to assess the sensitivity of different parameters to the estimation of the antenna height. Finally, we propose an experimental framework, and we use it to assess our approach with real GPS L1 C/A signals.

Mdpi Ag2014

Parameter Estimation with GNSS-Reflectometry and GNSS Synthetic Aperture Techniques

Miguel Angel Ribot Sanfelix

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.

EPFL2018

Calibration of the GNSS Signal Amplitudes in the Interference Pattern Technique for Altimetry

Mohammed Benjelloun, Cyril Botteron, Pierre-André Farine, Miguel Angel Ribot Sanfelix

Global Navigation Satellite Systems signals can be used in bi-static radar systems in order to get altimetric measurements. With a single classic GNSS ground-based receiver processing the combination of the signals coming directly and after one reflection to the receiving antennas, the Interference Pattern Technique allows the computation of the height of the reflecting surface. In this case, the observed parameter is the Signal to Noise Ratio of the received composite signal, which oscillates at a frequency proportional to this height. However, the signal recordings are generally very long since the accuracy of the SNR frequency estimation is proportional to the variation of the satellite elevation during the observation interval. In this article, we propose a calibration technique that allows reducing the observation duration while keeping a centimeter accuracy performance. The proposed technique is tested on both synthetic and real data.

2014

Parameter Estimation with GNSS-Reflectometry and GNSS Synthetic Aperture Techniques

Miguel Angel Ribot Sanfelix

EPFL2018