Evaluation of GNSS reflectometry method for sea level estimation in Indonesia

Over the last decade, GNSS-R (Global Navigation Satellite System reflectometry) has emerged as a technique for observing sea level height using data from GNSS observations. GNSS-R estimates sea level height from the phase center antenna using the reflection of the extracted GNSS signal at sea level. With a large number of tidal stations equipped with GNSS antennas, GNSS-R has the potential to be implemented in Indonesia. GNSS-R observations can also cover sea surface areas tens to hundreds of kilometres away from where the antenna is located over the coast. Furthermore, the installation of a GNSS antenna at a safe height on land allows for the observation of sea levels under extreme conditions such as during storms and cyclones. To employ GNSS-R effectively, several factors must be considered, including signal-to-noise ratio (SNR) data analysis, data processing, filtering control variables, and increased frequency extraction. This study will focus on trying to use GNSS-R method by identifying the best control variables for each study area and evaluating the results. This study used three months of GPS and GLONASS satellite SNR data from two stations, Barus and Morotai. The separated multipath data was then analyzed using the Lomb-Scargle Periodogram (LSP) based on its frequency. The results of GNSS-R sea surface height observations were validated using tide gauge data at both stations. Based on the test results, the RMSE values were 8.7 cm and 8.4 cm at Barus and Morotai stations, respectively. GNSS-R results strongly correlate with tide gauge data, with correlation coefficients of 95% and 98% at Barus and Morotai stations, respectively. Based on these findings, the GNSS-R method can be used to complement tidal sensor data by applying proper quality control.


Introduction
Multipath or reflected signals are one of the major error sources in high-accuracy GNSS (Global Navigation Satellite System) positioning, and there are numerous studies to mitigate the effects [1], [2], [3].In contrast, [4] introduced a method for environmental sensing using GNSS reflected signals.[5] utilized signal-to-noise ratio (SNR) to investigate interference patterns of reflected GNSS signals and measure the distance between the antenna phase center and seawater as a reflected surface.Since then, 1245 (2023) 012045 IOP Publishing doi:10.1088/1755-1315/1245/1/012045 2 research related to the use of reflected signals, also known as GNSS reflectometry (GNSS-R), has been carried out to measure sea level from the processing of the SNR that was acquired by a geodetic GNSS receiver [6], [7], [8].
The advantages of using GNSS-R include allowing sea level observations refer to a geocentric frame [9]; reaching a large area (with a radius of up to hundreds of kilometers) rather than a single point [10], [11]; and being installed at a safe height on land to avoid extreme weather in coastal areas [12].In Indonesia, there are 139 tidal stations managed by Geospatial Information Agency (BIG) until 2018 and some of them completed with GNSS installation [13].The GNSS installation above tidal station has potential and more advantage to complete the measurement from tide gauges.The GNSS-R measurements showed high correlations with tide gauges (exceeding 0.9) and delivered centimeter-level accuracy [8], [14], [15].The comparison between tidal constituents from GNSS-R results and tide gauges data also has a good agreement [16], [17] to get astronomical tide models.[12] used GNSS-R for detecting storm surges in Hong Kong by comparing GNSS-R results and the astronomical tides model.
To improve temporal resolution, however, several factors must be considered: (1) analysis of Signalto-Noise Ratio (SNR) data [18]; (2) processing control variables and data filtering [19]; (3) increased frequency extraction [20]; and (4) data with a longer observation time [21].This study will focus on the application of the GNSS-R method by investigating the control variables for optimal multipath signal separation based on GNSS data from Barus and Morotai stations in Indonesia.

Method
The GNSS-R method estimates sea level height using reflected signals (multipath) originating from the sea surface [22].Due to the distance between the receiver and the satellite as well as the antenna gain pattern, SNR data is dominated by long-period wave variations.Low-order polynomials eliminate longperiod variations at low elevations (30°), taking multipath effects [9].Multipath can be simply modelled for planar and horizontal reflectors.As explained by [1] ,the path delay  is dependent on two variables: the distance between the antenna and the plane of reflection; the satellite's elevation angle.The additional distance traveled by the multipath signal relative to the direct signal is written as (see Equation 1): where ℎ is the distance between the antenna and the reflecting surface and  is the satellite's elevation angle to the horizontal plane (see Figure 1).The composite SNR resulting from the direct signal and one multipath signal can be determined using the law of cosines.SNR is a function of the amplitude of the direct signal   , the amplitude of the multipath signal   , and the relative phase of the multipath θ, which can be written as [9], [14], [18], [22]: In this study, the polynomial used for the detrended process is a 4th order polynomial.To produce a dSNR (detrended SNR) arc, a lower order polynomial is fitted with each satellite arc and then removed.dSNR is a cosine function that represents the effect of the reflected signal on the SNR observation data [19], [23]: where  is the amplitude,   is the reflector height, the satellite elevation angle is , and ϕ is the phase.
The LSP, also known as least square spectral analysis, can be used to determine the reflector height over time.The dominant frequency of the multipath can be determined based on the spectral analysis of the dSNR as a function of the sin() of elevation angle.Assuming a constant reflector height in one satellite arc and a horizontal reflector, it is possible to convert the dominant frequency to a high reflector [24].
The reflector height determined from the LSP analysis is the distance between the reflecting plane, which is the sea surface, and the phase center of the antenna.To derive sea level height, the reflector height must be adjusted to correspond with the zero-tide palm on the tide sensor.This height difference is determined by the Geospatial Information Agency using a precise levelling measurement technique.Table 2 displays the height differences (offsets) for each station used in this study.

Results and discussions
The observation area is chosen based on the area of signal reflection, which is determined by the satellite's azimuth and elevation angle.At both stations, the First Fresnel Zone (FFZ) describes the signal reflection.The FFZ results are dependent on the satellite's elevation above the reflecting plane.The satellite's elevation decreases the size of the FFZ.When the satellite's elevation increases, the multipath effect decreases.CBRS uses various reflected signals from the satellite elevation angle of 5°-20° at azimuths of 30°-160° and 208°-350°, as depicted in Figure 2. At CMOR, the signal used to analyze multipath signal data arises from an azimuth of 180° to 360°.In this azimuth, as depicted in Figure 2, the FFZ of the satellite, with an elevation angle of 5°-25°, is located above the sea surface reflection plane.

Figure 2. The location of two stations and the reflected signal showed by FFZ. The ellipses represent the reflected GPS L1 signals for elevation angles 5° (yellow), 10° (blue), 15° (red), 20° (green), and 25° (cyan).
As described in the methods subsection (see subsection 2.2), multipath separation is obtained by removing the direct signal.In this research, the trend of direct signals can be obtained by detrending for processing using a 4 th -order fitting polynomial.The results from spectral analysis of the satellite arc showed no differences in reflector height for polynomials of degree 0-8 [15].So, using 4 th -order polynomial with not affect the SNR-analysis results.The multipath separation results are then processed with an LSP to determine the reflector height.LSP is utilized to estimate the normalized spectral strength or periodogram from a collection of successive SNR data, for each predetermined time interval.
Several obstacles, such as double peaks and excessive noise, are found during LSP spectral analysis.It is necessary to implement a minimum frequency amplitude strength value and a peak-to-noise ratio value in order to prevent visible noise in the presence of low frequency peaks that cause the reflector height to be zero.The average amplitude of all multipath SNR data from the LSP analysis can be used to calculate this value.Additionally, the range of approximated SNR data frequency values can be applied.This frequency range can be determined from the SNR analysis results by evaluating the noise frequency oscillations that exist before and after the dominant frequency in one spectrum of the SNR data series.
Figures 3 and 4 depict the sea level height results at CBRS and CMOR following an LSP analysis and quality control.The quality control is applied to the data from both stations during the LSP process by adjusting the peak-to-noise ratio (>2.1 for both stations), minimum amplitude (>4 for both stations), and reflector height (4-10 for both stations) to get valid reflector height.The red dots represent the sea level from GNSS-R using GPS and GLONASS observation data.The resulting sea level heights at both stations show a medium level of temporal variation over a given time interval.
Figure 3 shows that the temporal variation of GNSS-R sea level results at CBRS is not equally distributed.The number of sea level data using GNSS-R derived from three month's observational data was 933.The majority of these data were collected during periods of low tide, for example on doy 009 and 017 and doy 065 and 080.The quality of the resulting data will be evaluated by comparing the GNSS-R sea level height measurements from the two stations with the tide gauge measurements.It is possible to determine the high quality of the GNSS-R sea level results by examining the accuracy and correlation between the GNSS-R result data and the tidal sensors.The accuracy is represented by the Root Mean Square error (RMSe) value, whereas the correlation between the two data is indicated by the R-square ( 2 ).Table 3 summarizes the RMSe calculation results and correlation at each station.The RMSe values for CBRS and CMOR were 8.7 cm and 8.4 cm, respectively.While the correlation between GNSS-R and tide gauge data at both stations is 95.5% at CBRS and 98.8% at CMOR.At both stations, high correlation values indicate an agreement between the tidal sensor data and GNSS-R data.According to the number of data produced, CMOR data have greater temporal variations.
The difference between the correlation values at the two observation stations indicates the influence of local sea conditions and characteristics.The tides in the observation location impact the temporal resolution of the GNSS-R-derived sea level height data.It can be concluded from the distribution of data at the two stations that a large tidal range reduces the quantity of data collected.Consequently, this temporal resolution can influence the RMSe values and the obtained correlations.
The activities in nearby locations also influence the GNSS-R sea level results.The large number of ships that rely on the port and are close to the antenna receiver introduces more noise to the data.This noise is caused by multipath reflected not only from the sea surface but also from nearby buildings and objects capable of reflecting satellite signals.
The application of quality control affects the quantity of observational data collected as well.The quantity of parameters applied during LSP processing causes a significant amount of wasted data.The implementation of quality control parameters, on the other hand, can generate data with high reliability and accuracy.

Conclusion
The aim of this study was to evaluate the results of the GNSS-R at two sites, CBRS and CMOR.By using three months of L1 GPS and GLONASS data from CBRS and CMOR, it is possible to determine sea level height data with a strong correlation to data from the tide gauges.Using a low-order (order 4) polynomial fit, GNSS-R sea level observation data can be derived from multipath separation results with direct signals.At both stations, the quality of GNSS-R sea level height measurements relative to tidal sensors from the calculations of RMSe is 8 cm.The correlation coefficients for CBRS and CMOR are 95% and 98%, respectively.These results indicate that the GNSS-R method can be used to measure sea level height over Indonesian coasts.To achieve optimal results, however, optimal quality control is required by analysing the value for every parameter at study area.It will help to make strategy when analysing the result.In addition, the use of multiple satellites and multiple frequencies will result in enhanced temporal variations.

Figure 1 .
Figure 1.The scheme when GNSS signal reflected above the sea surface.The h is the different height between the sea surface and the antenna phase center.The e is the satellite elevation angle.

Figure 3 .
Figure 3.The result from GNSS-R method at CBRS.The red dots are the sea level data from GNSS-R.

Figure 4 .
Figure 4.The result from GNSS-R method at CMOR.The red dots are the sea level data from GNSS-R.

Table 2 .
The height difference between zero-palm and GNSS antenna.

Table 3 .
RMSE, correlation with tide gauge, and the number of observations from at CBRS and CMOR.