Challenges of Real-Time Monitoring of Ionospheric Perturbations and TEC Fluctuations with GPS Single Station

Ionosphere has a big influence on degradation of accuracy and reliability of the positioning with trans-ionospheric radio signals. Its influence is very critical. In the post processing mode, ionospheric characteristics can be determined very easily, but in nearand real-time it is a very challenging task. Determination of ionospheric characteristics requires permanent monitoring in real time, and nowcasting and forecasting of ionospheric indices. For now, we are familiar with the well known ionospheric indices:


Introduction
Ionosphere has a big influence on degradation of accuracy and reliability of the positioning with trans-ionospheric radio signals. Its influence is very critical. In the post processing mode, ionospheric characteristics can be determined very easily, but in near-and real-time it is a very challenging task. Determination of ionospheric characteristics requires permanent monitoring in real time, and nowcasting and forecasting of ionospheric indices. For now, we are familiar with the well known ionospheric indices: • number of electrons along the signal propagation path: Total Electron Content (TEC); • rapid and fast fluctuation of Radio Frequency (RF) signals' amplitude and phase (S4 and σ ϕ ) and • rate of change of TEC (ROT ).
In order to obtain information about the state of the ionosphere using single station GPS observations, we are developing and constantly upgrading our iono-tools module that is a part of the in-house academic software TUB-NavSolutions.
Previously, we presented some of the possibilities and methods to monitor ionospheric amplitude scintillation [1] and now we are dealing with TEC calculations, smoothing and levelling methods. As our algorithms and software are being tested, TEC estimation performance has been analysed in a simulated real-time mode. The achieved results are described here.
TEC values can be calculated from code-or carrier phase measurements. Usage of the carrier phases requires challenging ambiguity fixing, while TEC derived from code-phases are noisy.
Thus, for monitoring of the TEC in real-time the decision has been met to smooth code TEC using the carrier TEC. An approach, the so called levelling of TEC derived from the carrier phases using the code-phases, has been applied to overcome challenging fixing of carrier-phase ambiguity terms to integer numbers. Selected methods of smoothing of code TECs (levelling of carrier-phases) are described and compared with TEC available online at the Center for Orbit Determination in Europe (CODE) in the IONosphere Map Exchange Format (IONEX). In this paper some results of the analysis of applicability and performance of the algorithms, using GPS observations from two selected days have been presented: Data that has been taken into analysis has been collected at the Kiruna station in the polar area.
To track intensity of Earth's geomagnetic activity and to detect geomagnetic storms, two indices have been chosen: Ap and Kp. It is worth to mention that even though geomagnetic and ionospheric storms are related, geomagnetic storms refer to disturbance of Earth's magnetic field, and ionospheric storm is a disturbance of the ionosphere [8].

Total Electron Content estimation from GNSS single station measurements
Slant TEC has been estimated directly from GNSS dual frequency carrier-and code-phase insitu measurements using the following equations: Where • ϕ 1 and ϕ 2 are carrier-phase observations m , • P 1 and P 2 are code-phase observations m , • f 1 and f 2 are frequencies of L 1 and L 2 signals Hz , • T gd is transmitter's Estimated Group Delay between P 1 and P 2 measurements s , • c is velocity of the m / s .
TEC derived from the carrier-phases are ambiguous and those ones derived from codephases are very noisy. To take advantage that the ambiguous carrier-phases measurements have low noise and that the noisy code-phase measurements are not ambiguous, some smoothing and levelling methods have been applied.

TEC smoothing and levelling methods
TEC is calculated from both carrier-and code-phases using equations 1 and 2. After the both are calculated, levelling offset has been added according to the following formula: Where value of the offset depends on the method has been applied.

Method I
Calculation of the levelling offset between code-and carrier-phases derived TEC along the whole arc according to [7].
Where t i indicates time period in which TEC has been observed and N is number of calculated TEC in the whole arc of satellite visibility.

Method II
Levelling approach suggested by Jakowski [5]. Here the offset is defined by the following formulas:

Method III
Smoothing and filtering of code-with carrier-phases according to Hatch algorithm [3]. TEC derived from code-phases are being smoothed by previous TEC derived from carrier-phases observations. For real-time usage, when method III will be applied (Hatch filter), length of the filter must be reinitialized whenever cycle slip is detected. Detection of the cycle slips must be performed in all smoothing approaches.

Amplitude scintillation
For calculation of the amplitude scintillation, the S4 index was derived from signal power calculated from the I (in-phase) and Q (quadrature) components of bandpass signal (eq. 8): Power of the signal is now derived as: The scintillation index has been calculated using following formula: where and

Rate of change of Total Electron Content
In order to trace ionospheric irregularities [11] and to provide spatial variation of electron density [9], the rate of change of TEC (ROT ) is introduced. The equation below (eq.13) describes estimation of the ROT parameter: In our case we are calculating between epochs changes of TEC every one second. That gives us simplified equation of ROT without denominator because it is always equal to 1 sec (assuming there are no gaps).

Case study
Data processed for this analysis were collected at the Kiruna station in Sweden (67.5026°N , 20.2437°E ) with approximate position depicted in the Figure 1. In Kiruna there is a GNSS continuously operating station of the German Aerospace Center (DLR), division in Neustrelitz. The station is working for the Space Weather Application Center-Ionosphere (SWACI). It is configured for ionospheric scintillation monitoring and the observables (code-and carrier phases, and the I -and Q-amplitudes) are recorded with 50 Hz sampling rate.
Taken from Yahoo maps.  In the Figure 4 interesting are two deviations both detected roughly between 9:00 h and 11:00 h UTC (marked with green circles). This is approximately the same time when Ap and Kp indices reached values that indicate a strong geomagnetic storm. ROT values calculated from observations indicate disturbed ionospheric conditions for both days. In the both Figures, 6 and 7, we can notice sudden peaks and variations which confirm that at that time ionospheric perturbations took place.
If we compare TEC from the left panel of the Figure 4 with ROT from the left panel of the Figure 6 it is seen that larger oscillations appear in both time series at the same time. Special warning (based on strong ROT variations) comes a little bit before 11:00 h . • in the left panels of the Figures 5 and 7 with big peaks a little bit before 9:00 h , around 9:30 h and before 11:00 h , • in the right panels of the Figures 5 and 7 with sudden and big oscillation a little bit after 9:00 h and constant oscillations between 10:00 h and 11:00 h .
In the Figure 8 ionospheric amplitude scintillation parameter (S4) has been depicted. S4 values are displayed for each day and for all satellites in view. Even though ionosphere amplitude scintillation is less intense in polar regions, a few higher values (above 0.6) may be observed indicating ionospheric perturbations. Some TEC smoothing and levelling methods have been tested here in order to select the most appropriate one for our real -and near-real time applications. All three tested methods give very similar results of the final TEC values. It has been found that the method II and III fulfil requirements for usage in real-time. In the Fig. 4 and 5 results from the two methods, II (green line) and III (blue line) are displayed. Both curves are overlapping. That is why we can have impression that blue curve does not exist, but looking for numerical values it is seen that they differ between each other on second place after decimal point only.
There are easy seen biases between TEC derived from our obervations and interpolated using CODE. A source of the biases is not identified yet because not enough data was available up to now. Investigation of it will be continued.
The above described draft results of investigations allow to assume that TEC and ROT variability can be used for detection of perturbed ionospheric conditions and probably for issue of warnings for real-time users.
Investigation of applicability of TECand ROT for real-time warnings on ionospheric perturbations will be continued using GPS data collected at stations located in equatorial, midlatitude and polar areas.