Derivation of the Cramér-Rao Bound in the GNSS-Reflectometry Context for Static, Ground-Based Receivers in Scenarios with Coherent Reflection

Abstract

The use of the reflected Global Navigation Satellite Systems’ (GNSS) signals in Earth observation applications, referred to as GNSS reflectometry (GNSS-R), has been already studied for more than two decades. However, the estimation precision that can be achieved by GNSS-R sensors in some particular scenarios is still not fully understood yet. In an effort to partially fill this gap, in this paper, we compute the Cramér–Rao bound (CRB) for the specific case of static ground-based GNSS-R receivers and scenarios where the coherent component of the reflected signal is dominant. We compute the CRB for GNSS signals with different modulations, GPS L1 C/A and GPS L5 I/Q, which use binary phase-shift keying, and Galileo E1 B/C and E5, using the binary offset carrier. The CRB for these signals is evaluated as a function of the receiver bandwidth and different scenario parameters, such as the height of the receiver or the properties of the reflection surface. The CRB computation presented considers observation times of up to several tens of seconds, in which the satellite elevation angle observed changes significantly. Finally, the results obtained show the theoretical benefit of using modern GNSS signals with GNSS-R techniques using long observation times, such as the interference pattern technique.

Joint Delay-Doppler Estimation Performance in a Dual Source Context

“…A compact Fisher Information Matrix (FIM) for the general dual source narrowband CSM (i.e., where the Doppler effect on the band-limited baseband signal is not considered and amounts to a frequency shift) is provided in Section 3. This extends the work of [17,18] dealing with the single source narrowband CSM and completes the work of [28] in which the FIM is given for the specific case of a static, ground-based receiver, leading yo an identical Doppler effect for the two paths;…”

“…In order to study the dual source problem we consider a receiver with a single antenna able to collect both a LOS signal (signal labelled 0) and a single NLOS reflection (signal labelled 1), which may be reflected for instance in a ground, sea or building surface (see Figure 1). Here we assume a purely specular reflection with no scattering effect as considered in [28,41]. Note that this model is also related to the multipath model used in the GNSS literature ((6.42) [42]).…”

“…As previously mentioned, a formulation of the CRBs in the dual source context was proposed in [28]. In this reference, authors tackled the study of the best achievable performance in the estimation of a receiver altitude using GNSS-R.…”

“…When considering a multiple source signal model the CRB derivation complexity increases significantly. Examples of those CRB expressions were derived for the case of extended targets [25] and in GNSS-R for altimetry purposes [26][27][28]. Despite these contributions, a dual source delay-Doppler estimation compact closed-form CRB expression for generic band-limited signals is not available in the literature, being an important missing point and a result of broad interest.…”

A Novel Method for Ocean Wind Speed Detection Based on Energy Distribution of Beidou Reflections

“…During the initial period, scientists mainly focused on GNSS-R based ocean remote sensing, such as sea altimetry and scattermetry [1,2,3,4,5,6,7,8]. During the last two decades, the applications of the GNSS-R technique have expanded to various fields, such as monitoring of sea-ice, sea salinity, snow depth, oil spilling and soil moisture [9,10,11,12,13]. Meanwhile, various experimental activities have been performed to demonstrate the performance of this technique.…”