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Sensors 2016, 16(12), 2063; doi:10.3390/s16122063

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

Electronics and Signal Processing Laboratory (ESPLAB), École Polythecnique Fédérale de Lausanne (EPFL), Maladière 71B (Microcity), Neuchâtel CH-2002, Switzerland
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Academic Editor: Mehrez Zribi
Received: 17 October 2016 / Revised: 24 November 2016 / Accepted: 30 November 2016 / Published: 5 December 2016
(This article belongs to the Section Remote Sensors)
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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. View Full-Text
Keywords: GNSS-R; Cramér–Rao bound; CRB; coherent reflection; L-band; soil moisture estimation; altimetry; interference pattern technique; IPT GNSS-R; Cramér–Rao bound; CRB; coherent reflection; L-band; soil moisture estimation; altimetry; interference pattern technique; IPT
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ribot, M.A.; Botteron, C.; Farine, P.-A. Derivation of the Cramér-Rao Bound in the GNSS-Reflectometry Context for Static, Ground-Based Receivers in Scenarios with Coherent Reflection. Sensors 2016, 16, 2063.

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