# Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Fundamentals of the GNSS-R Altimetry Using the Multipath Effect

_{d}and A

_{m}are the amplitudes of the direct and reflected signals, respectively, and δφ(t) is the phase caused by the excess range of the reflected signal compared with the direct one. The factors A and $\tilde{\psi}(t)$ represent the amplitude and phase of the composite signals received by the antenna, and ψ(t) represents the phase of the direct signal. The factor β(t) is the composite excess phase with respect to the direct phase, h is the vertical height between the antenna and the sea surface, θ is the satellite elevation angle and λ is the electromagnetic wave length of the GNSS signal.

#### 2.2. Sea Level Based on SNR Data

_{noise}is the noise power. In order to solve for reflector height (h), it is necessary to isolate the last item from Equation (6) by removing the first two items using a fifth-order polynomial detrending. The detrending of the SNR becomes

#### 2.3. Sea Level Based on Carrier Phase-Combination Measurements

_{i}represents ionospheric delays. T represents tropospheric delays, and Δ accounts for all other carrier-independent effects. To isolate the multipath, the L1–L2 combination of carrier phase measurements, shown in Equation (12), is used. For simplicity, this combination is referred to as L4 in this paper.

_{m}$\ll $A

_{d}, after substituting Equations (4) and (5) into Equation (14), Equation (14) can be further simplified as follows:

_{i}= 2h/λ

_{i}. Similar to the SNR method, a spectral analysis, such as LSP, is used to deal with the dL4 data because of the irregular sampling intervals of sinθ. As dL4 is the linear combination of L1 and L2, shown as a linear combination of two quasi-sinusoidal functions in Equation (15), there will be two peaks in its spectrogram (Figure 3b,d). The peak at the lower frequency is caused by L2, and the peak at the higher frequency is caused by L1. Their different frequencies depend on the carrier wavelengths, and L2 peaks are usually used because they show clearer spectral peaks than L1.

#### 2.4. Theoretical Model for Calculating Reflector Height

## 3. Experiment and Analysis of Results

#### 3.1. Brief Introduction to Station SC02

^{®}NETR9 receiver and TRM29659.00 choke-ring antenna (Trimble Inc., Sunnyvale, CA, USA) with a hemispherical radome. However, it only provides GPS measurements which contain a pseudo-random code with a single frequency (C/A1), a precise code (P2), a carrier phase with two frequencies (L1 and L2) and the SNR data at two frequencies (S1 and S2).

^{®}air acoustic sensor (Aquatrak Corp., Sanford, FL, USA) in a protective well. Sea level data at this TG are recorded at 6-min sampling intervals and were obtained from National Oceanic and Atmospheric Administration (NOAA) for comparison.

#### 3.2. Data Processing Strategies

#### 3.3. Results Analysis

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Cohen, J.E.; Small, C.; Mellinger, A.; Gallup, J.; Sachs, J.; Vitousek, P.M.; Mooney, H.A. Estimates of coastal populations. Science
**1997**, 278, 1211–1212. [Google Scholar] [CrossRef] - Feng, G.P.; Jin, S.G.; Zhang, T.Y. Coastal sea level changes in the Europe from GPS, tide gauge, satellite altimetry and GRACE, 1993–2011. Adv. Space Res.
**2013**, 51, 1019–1028. [Google Scholar] [CrossRef] - Ablain, M.; Cazenave, A.; Valladeau, G.; Guinehut, S. A new assessment of the error budget of global mean sea level rate estimated by satellite altimetry over 1993–2008. Ocean Sci.
**2009**, 5, 193–201. [Google Scholar] [CrossRef] - Traon, P.Y.L.; Morrow, R. Chapter 3 ocean currents and eddies. Int. Geophys.
**2001**, 69, 171–215. [Google Scholar] - Roussel, N.; Ramillien, G.; Frappart, F.; Darrozes, J.; Gay, A.; Biancale, R.; Striebig, N.; Hanquiez, V.; Bertin, X.; Allain, D. Sea level monitoring and sea state estimate using a single geodetic receiver. Remote Sens. Environ.
**2015**, 171, 261–277. [Google Scholar] [CrossRef] - Bouffard, J.; Roblou, L.; Birol, F.; Pascual, A.; Fenoglio-Marc, L.; Cancet, M. Introduction and assessment of improved coastal altimetry strategies: Case study over the Northwestern Mediterranean Sea. In Coastal Altimetry; Springer: Berlin/Heidelberg, Germany, 2011; pp. 297–330. ISBN 978-3-642-12795-3. [Google Scholar]
- Martin-Neira, M.; Caparrini, M.; Font-Rossello, J.; Lannelongue, S.; Vallmitjana, C.S. The paris concept: An experimental demonstration of sea surface altimetry using GPS reflected signals. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 142–150. [Google Scholar] [CrossRef] - Martin-Neira, M. A passive reflectometry and interferometry system (PARIS): Application to ocean altimetry. ESA J.
**1993**, 17, 331–355. [Google Scholar] - Lowe, S.T.; Zuffada, C.; Chao, Y.; Kroger, P.; Young, L.E.; Labrecque, J.L. 5-cm-Precision aircraft ocean altimetry using GPS reflections. Geophys. Res. Lett.
**2002**, 29, 1375. [Google Scholar] [CrossRef] - Ruffini, G.; Soulat, F.; Caparrini, M.; Germain, O.; Martin-Neira, M. The Eddy Experiment: Accurate GNSS-R ocean altimetry from low altitude aircraft. Geophys. Res. Lett.
**2004**, 31, L12306. [Google Scholar] [CrossRef] - Löfgren, J.S.; Haas, R.; Johansson, J.M. Monitoring coastal sea level using reflected GNSS signals. Adv. Space Res.
**2011**, 47, 213–220. [Google Scholar] [CrossRef] - Semmling, A.M.; Beyerle, G.; Stosius, R.; Dick, G.; Wickert, J.; Fabra, F.; Cardellach, E.; Ribó, S.; Rius, A.; Helm, A. Detection of Arctic Ocean tides using interferometric GNSS-R signals. Geophys. Res. Lett.
**2011**, 38, 155–170. [Google Scholar] [CrossRef] - Rius, A.; Aparicio, J.M.; Cardellach, E.; Martín-Neira, M.; Chapron, B. Sea surface state measured using GPS reflected signals. Geophys. Res. Lett.
**2002**, 29, 37-1–37-4. [Google Scholar] [CrossRef] - Bao, L.F.; Wang, N.Z.; Gao, F. Improvement of Data Precision and Spatial Resolution of cGNSS-R Altimetry Using Improved Device With External Atomic Clock. IEEE Geosci. Remote Sens.
**2016**, 13, 207–211. [Google Scholar] [CrossRef] - Clarizia, M.P.; Ruf, C.; Cipollini, P.; Zuffada, C. First spaceborne observation of sea surface height using GPS-Reflectometry. Geophys. Res. Lett.
**2016**, 43, 767–774. [Google Scholar] [CrossRef] [Green Version] - Rodriguez-Alvarez, N.; Camps, A.; Vall-Llossera, M.; Bosch-Lluis, X. Land Geophysical Parameters Retrieval Using the Interference Pattern GNSS-R Technique. IEEE Trans. Geosci. Remote Sens.
**2010**, 49, 71–84. [Google Scholar] [CrossRef] - Anderson, K.D. Determination of water level and tides using interferometric observations of GPS signals. J. Atmos. Ocean. Technol.
**1999**, 17, 1118–1127. [Google Scholar] [CrossRef] - Larson, K.M.; Small, E.E.; Gutmann, E. Using GPS multipath to measure soil moisture fluctuations: Initial results. GPS Solut.
**2008**, 12, 173–177. [Google Scholar] [CrossRef] - Larson, K.M.; Small, E.E.; Gutmann, E.D.; Bilich, A.L.; Braun, J.J.; Zavorotny, V.U. Use of GPS receivers as a soil moisture network for water cycle studies. Geophys. Res. Lett.
**2008**, 35, L24405. [Google Scholar] [CrossRef] - Larson, K.M.; Gutmann, E.D.; Zavorotny, V.U.; Braun, J.J.; Williams, M.W.; Nievinski, F.G. Can we measure snow depth with GPS receivers? Geophys. Res. Lett.
**2009**, 36, L17502. [Google Scholar] [CrossRef] - Small, E.E.; Larson, K.M.; Braun, J.J. Sensing vegetation growth with reflected GPS signals. Geophys. Res. Lett.
**2010**, 37, L12401. [Google Scholar] [CrossRef] - Chen, Q.; Won, D.; Akos, D.M. Snow depth sensing using the GPS L2C signal with a dipole antenna. EURASIP J. Adv. Signal Process.
**2014**, 2014, 106. [Google Scholar] [CrossRef] - Jin, S.; Qian, X.; Kutoglu, H. Snow depth variations estimated from GPS-Reflectometry: A case study in Alaska from L2P SNR data. Remote Sens.
**2016**, 8, 63. [Google Scholar] [CrossRef] - Tabibi, S.; Nievinski, F.G.; van Dam, T.; Monico, J.F. Assessment of modernized GPS L5 SNR for ground-based multipath reflectometry applications. Adv. Space Res.
**2015**, 55, 1104–1116. [Google Scholar] [CrossRef] - Ozeki, M.; Heki, K. GPS snow depth meter with geometry-free linear combinations of carrier phases. J. Geodesy
**2012**, 86, 209–219. [Google Scholar] [CrossRef] - Qian, X.; Jin, S. Estimation of snow depth from GLONASS SNR and phase-based multipath reflectometry. IEEE J.-STAR
**2016**, 9, 4817–4823. [Google Scholar] [CrossRef] - Yu, K.G.; Ban, W.; Zhang, X.; Yu, X. Snow Depth Estimation Based on Multipath Phase Combination of GPS Triple-Frequency Signals. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 5100–5109. [Google Scholar] [CrossRef] - Santamaría-Gómez, A.; Watson, C.; Gravelle, M.; King, M.; Wöppelmann, G. Levelling co-located GNSS and tide gauge stations using GNSS reflectometry. J. Geodesy
**2015**, 89, 241–258. [Google Scholar] [CrossRef] - Jin, S.; Qian, X.; Wu, X. Sea level change from BeiDou Navigation Satellite System-Reflectometry (BDS-R): First results and evaluation. Glob. Planet Chang.
**2017**, 149, 20–25. [Google Scholar] [CrossRef] - Strandberg, J.; Hobiger, T.; Haas, R. Inverse modelling of GNSS multipath for sea level measurements—Initial results. In Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China, 10–15 July 2016; pp. 1867–1869. [Google Scholar]
- Larson, K.M.; Johan, S.; Löfgren, J.S.; Haaset, R. Coastal sea level measurements using a single geodetic GPS receiver. Adv. Space Res.
**2013**, 51, 1303–1310. [Google Scholar] [CrossRef] - Löfgren, J.S.; Haas, R.; Scherneck, H.G. Sea-level analysis using 100 days of reflected GNSS signals. J. Geodyn.
**2014**, 80, 66–80. [Google Scholar] [CrossRef] - Larson, K.M.; Ray, R.D.; Williams, S.D.P. A ten-year comparison of water levels measured with a geodetic GPS receiver versus a conventional tide gauge. J. Atmos. Ocean. Technol.
**2017**, 34, 295–307. [Google Scholar] [CrossRef] - Wang, X.; Zhang, Q.; Zhang, S. Azimuth selection for sea level measurements using geodetic GPS receivers. Adv. Space Res.
**2018**, 61, 1546–1557. [Google Scholar] [CrossRef] - Benton, C.J.; Mitchell, C.N. Isolating the multipath component in GNSS signal-to-noise data and locating reflecting objects. Radio Sci.
**2016**, 46, RS6002. [Google Scholar] [CrossRef] - Elósegui, P.; Davis, J.L.; Jaldehag, R.T.K.; Johansson, J.M.; Niell, A.E.; Shapiro, I.I. Geodesy using the global positioning system: The effects of signal scattering on estimates of site position. J. Geophys. Res. Sol. Earth
**1995**, 100, 9921–9934. [Google Scholar] [CrossRef] - Kedar, S.; Hajj, G.A.; Wilson, B.D.; Heflin, M.B. The effect of the second order GPS ionospheric correction on receiver positions. Geophys. Res. Lett.
**2003**, 30, 341–345. [Google Scholar] [CrossRef] - Hofmann-Wellenhof, B.; Lichtenegger, H.; Wasle, E. GNSS—Global Navigation Satellite Systems; Springer: Vienna, Austria, 2008; pp. 647–651. ISBN 978-3-211-73017-1. [Google Scholar]
- Nievinski, F.G.; Larson, K.M. An open source GPS multipath simulator in Matlab/Octave. GPS Solut.
**2014**, 18, 473–481. [Google Scholar] [CrossRef] - Hall, C.D.; Cordey, R.A. Multistatic Scatterometry. In Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS’88), Edinburgh, UK, 12–16 September 1988; pp. 561–562. [Google Scholar]
- Larson, K.M.; Ray, R.D.; Nievinski, F.G.; Freymueller, J.T. The accidental tide gauge: A GPS refection case study from Kachemak Bay, Alaska. IEEE Geosci. Remote Sens. Lett.
**2013**, 10, 1200–1204. [Google Scholar] [CrossRef]

**Figure 1.**Simplified schematic diagram of the ground-based global navigation satellite system reflectometry (GNSS-R) altimetry system with one antenna and the multi-path effect of direct and reflected signals. Definitions: ARP, antenna reference point; GPS, global positioning system. TGZ: tide gauge zero.

**Figure 2.**(

**a**) GPS signal-to-noise ratio (SNR)1 observation at the SC02 GPS station; (

**b**) multipath pattern after detrending; (

**c**) Lomb–Scargle Periodogram for the PRN27 GPS satellite on 6 and 8 January 2015.

**Figure 3.**(

**a**) Multipath error of double-frequency phase combination; (

**b**) Lomb–Scargle Periodogram from satellite PRN30 recorded on 2 and 3 January 2015; (

**c**) Simulated double-frequency phase multipath using the software developed by [39]; (

**d**) Lomb–Scargle Periodogram of the simulated L4 multipath.

**Figure 4.**Graphical illustration of the linear relationship between peak frequencies and antenna height from the model for the elevation range 5–12°.

**Figure 5.**Photograph showing GPS station SC02 and the surrounding environment at Friday Harbor Port in Washington State, USA (image from http://www.sonel.org/spip.php?page=gps&idStation=2689).

**Figure 6.**Sea level changes over a 31-day period, as determined from GPS L1 and L2 SNR via double-frequency combination calculated from Equation (8) and the linear model for elevation range 5–15°. Tide gauge (TG) data are also shown (black curves) for the same 31-day period, for comparison.

**Figure 7.**Correlation of GPS dual-frequency phase combination and SNR estimations for the elevation range 5–15° using a linear regression model with tide gauge (TG) observations.

**Figure 8.**Correlation of GPS dual-frequency phase combination and SNR estimations for the elevation range 5–15°, using Equation (8) with tide gauge (TG) observations.

**Figure 9.**Residuals of sea surface height differences compared between SNR and geometry-free phase estimations for the elevation range 5–15° and tide gauge (TG) observations.

**Table 1.**Statistical analysis of residual data between sea level changes derived from the GPS multipath effect and tide gauge (TG) observations over the one month period of 1–31 January 2015 with different elevations ranges.

SNR1 | SNR2 | L4d | L4-Model | S2-Model | ||
---|---|---|---|---|---|---|

5°–12° | RMSE(cm) | 19.32 | 14.01 | 14.68 | 18.30 | 17.63 |

Corr-coeff^{@} | 0.9753 | 0.9822 | 0.9822 | 0.9701 | 0.9696 | |

5°–15° | RMSE(cm) | 14.69 | 12.36 | 13.81 | 13.67 | 13.17 |

Corr-coeff^{@} | 0.9778 | 0.9831 | 0.9810 | 0.9810 | 0.9831 |

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**MDPI and ACS Style**

Wang, N.; Xu, T.; Gao, F.; Xu, G.
Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR. *Remote Sens.* **2018**, *10*, 470.
https://doi.org/10.3390/rs10030470

**AMA Style**

Wang N, Xu T, Gao F, Xu G.
Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR. *Remote Sensing*. 2018; 10(3):470.
https://doi.org/10.3390/rs10030470

**Chicago/Turabian Style**

Wang, Nazi, Tianhe Xu, Fan Gao, and Guochang Xu.
2018. "Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR" *Remote Sensing* 10, no. 3: 470.
https://doi.org/10.3390/rs10030470