On the Impact and Mitigation of Signal Crosstalk in Ground-Based and Low Altitude Airborne GNSS-R
Abstract
:1. Introduction
- From an estimation point of view, we assess the impact that a possible crosstalk may have on the reflected signal time-delay estimation performance, if not correctly accounted for. This is done by comparing the single source conditional maximum likelihood estimator (CMLE) performance in a dual source context with the corresponding single source CRB.
- By resorting to dual source estimators, we show the optimal time-delay estimation performance in a dual source crosstalk context, as a function of path separation and the reflected-to-direct signal amplitude ratio (RDR), compared to the corresponding dual source CRBs.
- As a complementary analysis of practical importance, we assess the robustness of such dual source estimators under a misspecified number of sources, i.e., when two sources are estimated, but crosstalk is not present in the signal.
- The performance of the VE, proposed in [40] for crosstalk mitigation, is compared to the CRB and non-coherent dual source estimators, which to the best of the authors’ knowledge is an important missing estimation performance analysis in the literature.
2. Theoretical Background
2.1. Preliminaries: A Geometrical Analysis
2.2. Single and Dual Source GNSS Signal Model
2.3. Single and Dual Source CRBs
3. Single/Dual Source Delay/Doppler/Phase Estimators
3.1. Single and Dual Source CMLEs
3.2. CLEAN-RELAX Estimator
3.3. Non-Coherent and Variance Estimators
4. Results and Discussions on Coherent Estimation
4.1. Crosstalk Impact on GNSS-R Time-Delay Estimation
4.1.1. Analysis Setup
- Case (1): suboptimal single source estimation, that is two sources are present, but the corresponding estimator considers only one source.
- Case (2): optimal dual source estimation, that is it is known that two sources are present, and the corresponding estimator is matched to this.
4.1.2. Suboptimal Single Source Estimation
4.2. Optimal Dual Source Estimation
4.3. On the Dual Source Estimators’ Robustness: Misspecified Number of Sources
5. Results and Discussion on Non-Coherent Estimation
5.1. Analysis Setup
- Scenario #1: 20 PRNs, each one with a different random phase.
- Scenario #2: four blocks of five PRNs where (i) the first five PRNs have the same phase as the LOS signal and (ii) the other three blocks of five PRNs have three different random phases.
- Scenario #3: two blocks of 10 PRNs where (i) the first 10 PRNs have the same phase as the LOS signal and (ii) the other two blocks of five PRNs have two different random phases.
- Scenario #4: four blocks of five PRNs where (i) the first 15 PRNs have the same phase as the LOS signal and (ii) the remaining block of five PRNs has a random phase.
5.2. On the Estimation Performance of the Variance Estimator and Non-Coherent CRE
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Lubeigt, C.; Ortega, L.; Vilà-Valls, J.; Lestarquit, L.; Chaumette, E. On the Impact and Mitigation of Signal Crosstalk in Ground-Based and Low Altitude Airborne GNSS-R. Remote Sens. 2021, 13, 1085. https://doi.org/10.3390/rs13061085
Lubeigt C, Ortega L, Vilà-Valls J, Lestarquit L, Chaumette E. On the Impact and Mitigation of Signal Crosstalk in Ground-Based and Low Altitude Airborne GNSS-R. Remote Sensing. 2021; 13(6):1085. https://doi.org/10.3390/rs13061085
Chicago/Turabian StyleLubeigt, Corentin, Lorenzo Ortega, Jordi Vilà-Valls, Laurent Lestarquit, and Eric Chaumette. 2021. "On the Impact and Mitigation of Signal Crosstalk in Ground-Based and Low Altitude Airborne GNSS-R" Remote Sensing 13, no. 6: 1085. https://doi.org/10.3390/rs13061085
APA StyleLubeigt, C., Ortega, L., Vilà-Valls, J., Lestarquit, L., & Chaumette, E. (2021). On the Impact and Mitigation of Signal Crosstalk in Ground-Based and Low Altitude Airborne GNSS-R. Remote Sensing, 13(6), 1085. https://doi.org/10.3390/rs13061085