- freely available
Remote Sens. 2019, 11(16), 1858; https://doi.org/10.3390/rs11161858
- Section 2 gives general background on the history of GNSS-R remote sensing and details the reasons why a custom GNSS-R open loop tracking algorithm is required. Additionally, this section also includes an outline of the presented GNSS-R open loop algorithm and how they are organized within the paper.
- Section 3 presents the algorithm for estimating the geographic location of the point of surface reflection, or specular point (SP), which represents the center of the surface scattering glistening zone. This point provides the center coordinated from which the GNSS-R open loop tracking delay and Doppler estimates are derived.
- Section 6 then performs a statistical analysis, using a much larger set of CYGNSS data, which demonstrates the open loop algorithms performance globally. This section also includes discussion of the algorithms convergence speed and how this was optimized for the case of CYGNSS low Earth orbit GNSS-R reflections.
- Section 7 provides a discussion of additional algorithm modifications which would potentially further improve the performance (both in terms of accuracy and speed of convergence).
2. Background and Algorithm Overview
2.1. Brief History of GNSS-R Remote Sensing
2.2. GNSS-R Signal Tracking Overview
- The delay and Doppler characteristics of a reflected signal vary significantly from surface to surface, causing significant variations in how the signal spreads in the delay and Doppler dimensions.
- The surface reflected signals are often very weak and can fluctuate wildly in magnitude (especially over land) due to the surface scattering conditions, often requiring extended non-coherent integration intervals for detection.
- Diffusely scattered signals often contain no information on the transmitted carrier phase, making traditional carrier phase tracking loops unreliable.
- This manuscript presents the first concise and self contained GNSS-R open loop tracking algorithm intended for general public use by the larger GNSS-R community world wide.
- The real time performance of this algorithm has been validated with a large set of on-orbit data and analyzed with respect to its feasibility for real-time implementation (i.e., speed of convergence and spacecraft processing resources).
- A land height correction technique is presented which will enable this algorithm to be run over low-lying land surfaces in addition to near ellipsoid ocean surfaces.
2.3. Applicability of Presented Open Loop Tracking Algorithm
2.4. Overview of GNSS-R Open Loop Tracker Algorithm
2.4.1. Defining Reflection Geometry
2.4.2. Estimating Open Loop Delay and Doppler
3. Method, Part 1: Specular Reflection Point Calculation
- The total path between the transmitter, surface specular point and the receiver will be the minimum of all possible paths across the Earth’s surface.
- The specular point must lie on the surface of the Earth. For reflections from the ocean the specular reflection point will lie close to the WGS84 ellipsoid. For reflections over land, local land height variations should be added to the local reference ellipsoid.
- The specular reflection will satisfy Snell’s Law, where the angle between the incoming wave and reflected waves with respect to the local surface ellipsoid normal are equal.
- For a real-time application, the specular reflection points need to be calculated slightly early and propagated forward, so that the open loop tracker predictions are available in real-time to the instrument observation processing hardware. Errors due to propagation inaccuracies are described in detail in .
- Determine an initial guess for the surface specular point location, . This could be either (a) an estimate based on previous, propagated or modeled initial specular point positions or (b) using the estimate of the receiver position , normalized to the Earth surface, calculated as,
- Solve for the correction derivative using Equation (6). Path magnitudes are calculated using best estimates of receiver and transmitter positions from GPS navigation solution, propagated ahead slightly to account for the non-zero computational time with respect to the application of the values in real-time on the instrument.
- Update estimated position of specular point from to using Equation (7).
- Calculate estimated Earth surface using Equation (8). Adjust WGS84 ellipsoid height (h) to account for height of surface topography over land or ocean height variations as needed.
- Project new corrected specular point estimate to the Earth’s surface using Equation (9).
- Start next iteration (step 2) with updated value for specular point calculated in Equation (9) until convergence criteria is met.
3.1. Successful Specular Reflection Point Convergence Criteria
4. Method, Part 2: Open Loop GNSS-R Delay and Doppler Tracking Algorithms
4.1. Instrument Hardware Considerations
4.2. Estimating the Reflected Signal Code Phase Delay
4.3. Estimating the Reflected Signal Doppler Frequency
5. Results: Algorithm Verification Using On-Orbit Data
5.1. Geolocation of the Example Reflection Tracks
5.2. Open Loop Tracker Code Phase Predictions
6. Results: Statistical Geographic Performance Validation and Analysis of Resource Requirements
6.1. On-Board Surface Reflection Prioritization
- Determine the surface specular points for a set of GNSS transmitters as described in Section 3. Generate a set of vectors from the GNSS-R satellite to the estimated specular reflection points.
- Map the vectors from the satellite receiver to the surface specular point into the satellite body frame, using a transformation derived using the satellite attitude matrix.
- Map the specular point direction in the body frame to an on board map of the GNSS-R instrument science antenna patterns figure of merit. The figure of merit can be simply the antenna gain, or a range corrected antenna gain .
- Rank the measurement points for all the GPS transmitters from highest to lowest figure of merit. Thus, sorting the surface reflections with high antenna gain to the highest ranking.
- Prioritize the reflections based on the highest figure of merit estimates and the available processing resources available within the GNSS-R receiver digital signal processing channels.
6.2. Performance Evaluation Using On-Orbit CYGNSS Data
7. Discussion and Algorithm Variations
7.1. Inclusion of Ancillary Maps for Improved Specular Point Accuracy Over Ocean and Land
7.2. Propagated Specular Point Search Initialization
7.3. Interpolated Prediction of Specular Point Parameters
- Depending on available computer resources, propagating forward the receiver satellite and transmitting satellite location using an existing orbit propagator, at 10 s intervals over a minute into the future for example.
- Estimate the surface specular points at each predicted future step.
- Use a standard polynomial fitting function to generate a function to forward predict the specular location, from which the delay and Doppler information can be quickly calculated. Or alternatively, perform a polynomial fit on the predicted delay and Doppler values directly.
- Use the generated polynomial function to calculate the open loop delay and Doppler over the entire measurement reflection track, while the reflection quality indicator indicates a viable measurement is possible.
7.4. Look Up Table Predictions
Conflicts of Interest
- Misra, P.; Enge, P. Global Positioning System: Signals, Measurements, and Performance; Ganga Jamuna Press: Lincoln, MA, USA, 2001; ISBN 0-9709544-0-9. [Google Scholar]
- Sokolovskiy, S.V. Tracking tropospheric radio occultation signals from low Earth orbit. Radio Sci. 2001, 36, 483–498. [Google Scholar] [CrossRef]
- Hall, C.; Cordy, R. Multistatic Scatterometry. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Edinburgh, UK, 12–16 September 1988. [Google Scholar]
- Martin-Neira, M. A passive reflectometry and interferometry system (PARIS): Application to ocean altimetry. ESA J. 1993, 17, 331–355. [Google Scholar]
- Garrison, J.L.; Katzberg, S.J.; Hill, M.I. Effect of Sea Roughness on Bistatically Scattered Range Coded Signals from the Global Positioning System. Geophys. Res. Lett. 1998, 25, 2257–2260. [Google Scholar] [CrossRef]
- Soulat, F. Sea Surface Remote Sensing with GNSS and Sunlight Reflections. Ph.D. Thesis, Universitat Politecnica de Catalunya, Barcelona, Spain, 2004. [Google Scholar]
- Germain, O.; Ruffini, G.; Soulat, F.; Caparrini, M.; Silvestrin, P. The Eddy Experiment II: GNSS-R Speculometry for Directional Sea Roughness Retrieval from Low Aircraft. Geophys. Res. Lett. 2003, 31. [Google Scholar] [CrossRef]
- Cardellach, E.; Ruffini, G.; Pino, D.; Rius, A.; Komjathy, A.; Garrison, J. Mediterranean Balloon Experiment: Ocean Wind Speed Sensing from the Stratosphere Using GPS Reflections. Remote Sens. Environ. 2003, 88, 351–362. [Google Scholar] [CrossRef]
- Armatys, M. Estimation of Sea Surface Winds Using Reflected GPS Signals. Ph.D. Thesis, University of Colorado at Boulder, Boulder, CO, USA, 2001. [Google Scholar]
- Komjathy, A.; Zavorotny, V.U.; Axelrad, P.; Born, G.H.; Garrison, J.L. GPS Signal Scattering from Sea Surface: Wind Speed Retrieval Using Experimental Data and Theoretical Model. Remote Sens. Environ. 2000, 73, 162–174. [Google Scholar] [CrossRef]
- Katzberg, S.J.; Dunion, J. Comparison of reflected GPS wind speed retrievals with dropsondes in tropical cyclones. Geophys. Res. Lett. 2009, 36, L17602. [Google Scholar] [CrossRef]
- Lowe, S.; LaBrecque, J.L.; Zuffada, C.; Romans, L.J.; Young, L.E.; Hajj, G.A. First Spaceborne Observation of an Earth-Reflected GPS Signal. Radio Sci. 2002, 37. [Google Scholar] [CrossRef]
- Gleason, S.; Hodgart, S.; Yiping, S.; Gommenginger, C.; Mackin, S.; Adjrad, M.; Unwin, M. Detection and Processing of Bistatically Reflected GPS Signals from Low Earth Orbit for the Purpose of Ocean Remote Sensing. IEEE Trans. Geosci. Remote Sens. 2005, 43, 1229–1241. [Google Scholar] [CrossRef]
- Clarizia, M.P.; Gommenginger, C.P.; Gleason, S.T.; Srokosz, M.A.; Galdi, C.; Di Bisceglie, M. Analysis of GNSS-R Delay-Doppler Maps From the UK-DMC Satellite Over the Ocean. Geophys. Res. Lett. 2009, 36, L02608. [Google Scholar] [CrossRef]
- Gleason, S. Space-Based GNSS Scatterometry: Ocean Wind Sensing Using an Empirically Calibrated Model. IEEE Trans. Geosci. Remote Sens. 2013, 51, 4853–4863. [Google Scholar] [CrossRef]
- Unwin, M.; Duncan, S.; Jales, P.; Blunt, P.; Brenchley, M. Implementing GNSS Reflectometry in Space on the TechDemoSat-1 Mission. Proc. Inst. Navigat. 2014, 2014, 1222–1235. [Google Scholar]
- Ruf, C.S.; Atlas, R.; Chang, P.S.; Clarizia, M.P.; Garrison, J.L.; Gleason, S.; Katzberg, S.J.; Jelenak, Z.; Johnson, J.T.; Majumdar, S.J.; et al. New Ocean Winds Satellite Mission to Probe Hurricanes and Tropical Convection. Bull. Am Meteorol. Soc. 2015. [Google Scholar] [CrossRef]
- Gleason, S.; Lowe, S.; Zavorotny, V. Remote Sensing Using Bistatic GNSS Reflections. In GNSS Applications and Methods; Gleason, S., Gebre-Egziabher, D., Eds.; Artech House: Norwood, MA, USA, 2009. [Google Scholar]
- Zavorotny, V.; Gleason, S.; Cardellach, E.; Camps, A. Tutorial on Remote Sensing Using GNSS Bistatic Radar of Opportunity. IEEE Geosci. Remote Sens. Mag. 2014. [Google Scholar] [CrossRef]
- Gleason, S. Remote Sensing of Ocean, Ice and Land Surfaces Using Bistatically Scattered GNSS Signals from Low Earth Orbit. Ph.D. Thesis, University of Surrey, Guildford, UK, 2006. [Google Scholar]
- Gleason, S.; Gebre-Egziabher, D. (Eds.) GNSS Applications and Methods; Artech House: Norwood, MA, USA, 2009. [Google Scholar]
- Jales, P. Spaceborne Receiver Design for Scatterometric GNSS Reflectometry. Ph.D. Thesis, University of Surrey, Guildford, UK, 2012. [Google Scholar]
- Jales, P. MERRByS Product Manual—GNSS Reflectomety on TDS-1 with the SGR-ReSI; Tech. Manual 0248366 (Rev. 001); Surrey Satellite Technology Limited: Guildford, UK, 2015. [Google Scholar]
- O’Brien. CYGNSS End-To-End Simulator Specular Reflection Point Solver Technical Note; The Ohio State University: Columbus, OH, USA, 2016. [Google Scholar]
- Gleason, S. Towards Sea Ice Remote Sensing with Space Detected GPS Signals: Demonstration of Technical Feasibility and Initial Consistency Check Using Low Resolution Sea Ice Information. Remote Sens. 2010, 2, 2017–2039. [Google Scholar] [CrossRef]
- Bate, R.R.; Mueller, D.D.; White, J.E. Fundamentals of Astrodynamics; Dover Publications Inc.: New York, NY, USA, 1971. [Google Scholar]
- Halliday, D.; Resnick, R. Fundamentals of Physics, 3rd ed.; Wiley and Sons: New York, NY, USA, 1988. [Google Scholar]
- Gleason, S.; Ruf, C.; Clarizia, M.P.; O’Brien, A.J. Calibration and Unwrapping of the Normalized Scattering Cross Section for the Cyclone Global Navigation Satellite System. IEEE Trans. Geosci. Remote Sens. 2016, 54, 2495–2509. [Google Scholar] [CrossRef]
- CYGNSS Science Team. CYGNSS Handbook. Cyclone Global Navigation Satellite System, Deriving Surface Wind Speeds in Tropical Cyclones. 2016. Available online: https://clasp-research.engin.umich.edu/missions/cygnss/reference/cygnss-mission/CYGNSS_Handbook_April2016.pdf (accessed on 6 August 2019).
- Global Mean Sea Surface; DTU Space, National Space Institute: Kongens Lyngby, Denmark, 2018.
- Gleason, S.; Ruf, C.; O’Brien, A.; McKague, D. The CYGNSS Level 1 Calibration Algorithm and Error Analysis Based On On-Orbit Measurements. IEEE JSTARS 2018. [Google Scholar] [CrossRef]
- NASA Shuttle Radar Topography Mission (SRTM). Available online: https://earthdata.nasa.gov/ and https://www2.jpl.nasa.gov/srtm/; (accessed on 6 August 2019).
- Hoots, F.R.; Roehrich, R.L. Models for Propagation of NORAD Element Sets. 1980. SPACETRACK REPORT NO. 3. Available online: https://celestrak.com/NORAD/documentation/spacetrk.pdf (accessed on 6 August 2019).
- Bussy-Virat, C.; Getchius, J.; Ridley, A. The Spacecraft Orbital Characterization Kit and its Applications to the CYGNSS Mission. Space Flight Mech. Meet. 2018, 1973. [Google Scholar] [CrossRef]
Sample Availability: CYGNSS data products are available though the NASA PO-DAAC.
|K||Snell Angle Tolerance||Mean Delay Error||Max Delay Error||Mean Iter.||Max Iter.|
|1.0 ×||0.1 degrees||0.13 chips||0.56 chips||8.6||29|
© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).