Global Navigation Satellite Systems (GNSS) Advances in Marine Navigation – Marine Navigation and Safety of Sea Transportation – Weintrit (ed.)

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1 INTRODUCTION

Modern technological and socio-economic systems increasingly rely upon the operation and performance of satellite navigation systems (Thomas et al, 2011, Filjar & Huljenić, 2012). The GNSS vulnerabilities and risks assessment has become a major subject of numerous field studies in various positioning environments (Filjar & Huljenić, 2012). The GNSS performance response to space weather and ionospheric disturbances is one of the cornerstones of such an assessment (Hapgood & Thomson, 2010, American Meteorological Society, 2011, Filjar, 2008).

Here we report the results of an assessment of single-frequency horizontal GPS positioning error response to a moderate ionospheric storm on 7 March, 2012, based on the analysis of the single-frequency GPS positioning estimates' time series taken in the Northern Adriatic region (Hughes & Hase, 2010). Different sources of relevant data were used in the assessment, including GPS positioning samples and lower ionosphere screenings taken at GNSS Space Weather Laboratory, Faculty of Maritime Studies, University of Rijeka, Croatia. As the result, the time series of horizontal GPS positioning errors observed on both sides of the Northern Adriatic were compared both mutually and with the time series of the observed parameters of

local ionospheric disturbances during the moderate ionospheric storm.

The paper is organised as follows. After the presentation of problem description and previous research (Chapter 2), an outline of the applied methodology is given (Chapter 3). The presentation of the results of the experimental data analysis (Chapter 4) are followed by discussion of the results of the analysis (Chapter 5). The paper concludes (Chapter 6) with the assessment’s substance and proposals for future research.

2 PROBLEM DESCRIPTION AND PREVIOUS RESEARCH

The quality of service and robustness of the GNSS-based technological and socio-economic systems rely heavily on sustained and robust GNSS positioning, navigation and timing (PNT) services (Filjar and Huljenić, 2012, Thomas et al, 2011). Those are affected by various natural and artificial sources of errors and disruptions, with the space weather and the ionospheric effects as the major single source of GNSS PNT performance degradations and operation disruptions (Parkinson & Spilker, Jr, 1996).

The GNSS PNT performance degradation results from the satellite signals' propagation effects in the ionosphere, which increase the satellite signals'

Single-frequency Horizontal GPS Positioning Error Response to a Moderate Ionospheric Storm Over Northern Adriatic

R. Filjar, D. Brčić & S. Kos Faculty of Maritime Studies, University of Rijeka, Croatia

ABSTRACT: Assessment of the real ionospheric impact on GNSS Positioning, Navigation and Timing (PNT) services is essential for identification of vulnerabilities and risks to GNSS performance and operation, as well as to performance and operation of the GNSS-reliant technological and socio-economic systems. Here we present the assessment of the impact of a moderate ionospheric storm on the horizontal component of the single-frequency GPS positioning error in Northern Adriatic. While clearly identifying the effects of a moderate ionospheric storm on northing, easting and horizontal components of GPS positioning error, the results of our analysis show the inexpensive monitoring of the lower ionosphere may provide a feasible means for fast identification of approaching ionospheric-originated GNSS positioning performance disturbances.

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travelling time thus introducing the ionospheric GNSS PNT error (Davis, 1990, Helliwell, 2006, Parkinson & Spilker, Jr, 1996). The Maxwell Equations (Davis, 1990, Helliwell, 2006):

Jo

BtB

E

(1)

give the following definition of frequency-dependent refractive index n (Davis, 1990, Helliwell, 2006):

2

14

4

12

2

1

12

LY

jZXT

Y

jZXT

YjZ

Xn

(2)

with:

2

2N BX Y

vL TY Y ZL T

(3)

where ωN = angular plasma frequency; ωB = electron gyrofrequency; ωL = longitudinal component of ωB of direction of propagation; ωT = transversal component of ωB of direction of propagation; v = electron collision frequency; ω = angular wave frequency.

By definition, the GNSS ionospheric delay can be expressed as (Parkinson & Spilker, Jr, 1996):

dhnc

t )1(1

(4)

Using the approximation:

21

Xn (5)

the GNSS ionospheric delay can be expressed as (Parkinson & Spilker, Jr, 1996):

dhhNfc

t )(23.40

(6)

N(h) represents the so-called vertical ionospheric profile, an ionospheric parameter highly affected by space weather and geomagnetic conditions. Using the definition of the Total Electron Content (Parkinson & Spilker, Jr, 1996):

dhhNTEC )( (7)

the expressions (6) and (7) yields:

TECfc

t23.40

(8)

The ionospheric-related GNSS PNT performance deteriorations can be mitigated using differential satellite navigation techniques (DGNSS) or a GNSS ionospheric correction model (for instance, Klobuchar model for GPS, or NeQuick model for Galileo) (Davis, 1990, Parkinson & Spilker, Jr, 1996). However, due to usually global nature of the GNSS ionospheric correction models, single-frequency GNSS receivers often cannot compensate the ionospheric impact in full, or, even worse, increase the amount of GNSS ionospheric error by utilising the corrections inappropriate for local ionospheric status (Davis, 1990, American Meteorological Society, 2011, Filjar, 2008, Filjar, Kos & Kos, 2009).

3 METHODOLOGY

Various sources of observations were used in the assessment of the moderate ionospheric storm on 7 March, 2012 in the Northern Adriatic region, as follows: IGS RINEX-organised data taken at Medicina,

Italy reference station (IGS, 2012), US NOAA space weather indices (NOAA, 2012), single-frequency GPS position estimates and SID

monitor-based (Stanford Solar Center, 2010, Filjar, Kos & Kos, 2010) lower ionosphere data collected at GNSS Space Weather Laboratory, Faculty of Maritime Studies, University of Rijeka, Croatia. The GPS RINEX observed pseudo-ranges

collected at a 12 channel-GPS reference station in Medicina, Italy were used for reconstruction of the single-frequency horizontal GPS positioning performance (dynamics of GPS-based positioning estimates). The GPS RINEX data allowed for reconstruction of the positioning estimates time series with the 30 s-sampling period. The standard (Klobuchar) GPS ionospheric delay correction model was applied with the transmitted Klobuchar model coefficients. The true position of the Medicina reference station was noted in the GPS RINEX file, thus allowing for definition of the horizontal GPS positioning error components with the reference to true position (Parkinson & Spilker, Jr, 1996), as follows:

180

)( RTMm

E

(9)

180

)180

cos()(

MR

TMm

E (10)

where φE = northing error; φM = measured latitude; φT = true latitude; λE = easting error; λM = measured longitude; λT = true longitude; R = 6378137 m; π =

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3.1415927; latitudes and longitudes expressed in [º] units.

An R-based (R Development Core Team, 2010) software was developed for RINEX data processing and positioning estimates time series analysis.

Reconstruction of the space weather environment for satellite positioning was conducted using the NOAA SPIDR data, as shown in Figure 1.

Figure 1. Space weather environment, 6 - 9 March, 2012 (SPIDR-NOAA, 2012).

The parallel time series of GPS positioning

estimates were collected with the 2 s-sampling period using a single-frequency maritime GPS receiver at the GNSS Space Weather Laboratory, Faculty of Maritime Studies, University of Rijeka, Croatia, with the Klobuchar correction model applied. Again, a dedicated R-based software was developed for processing the GPS data in NMEA-0183 format and positioning estimates time series analysis. An advantage of a commercial Garmin GPS receiver's ability to provide the northing, easting and horizontal positioning error observables through a proprietary NMEA protocol extension has been exploited.

The local low-ionospheric status was reconstructed from time series of the Sudden Ionospheric Disturbance (SID) monitors' observations of two signals: 23.4 kHz signal broadcast from Rhauderfehn,

Germany 20.9 kHz signal broadcast from Rosnay, France.

The analysis of daily dynamics of received VLF radio signal strength samples contributes to the understanding of near-real time local ionospheric status, especially of lower ionospheric layers (Rice et al, 2009). A characteristic observed daily dynamics of received Rosnay VLF radio signal strength, as seen at the GNSS Space Weather Laboratory, Faculty of Maritime Studies, University of Rijeka, Croatia (in the rest of the paper: Rijeka, Croatia monitoring station) during the undisturbed ionospheric conditions, is presented on Figure 2.

Figure 2. A characteristic daily dynamics of Rosnay VLF radio signal strength during the period of quiet ionospheric condition, as observed at Rijeka, Croatia monitoring station.

Two dedicated SID monitors are deployed along

with the stationary reference single-frequency GPS receiver at Rijeka, Croatia monitoring station for continuous monitoring of two VLF signals from Rhauderfehn, Germany and Rosnay, France.

4 EXPERIMENTAL DATA ANALYSIS

The assessment's results generally fall into two categories: ionospheric dynamics, resulting from the

geomagnetic storm in effect GPS positioning error dynamics, resulting from

the ionospheric disturbances.

4.1 Ionospheric dynamics

Although announced as a potentially significant event, the geomagnetic storm of 7 March, 2012 turned to be a moderate storm. Caused by substantial Coronal Mass Ejection (CME) from the Sun, the geomagnetic storm followed a usual pattern, reaching the moderate activity level and dying out by the end of the day. Although its activities grew the following days, the storm remained at the moderate levels. Considering that the storm was preceded by a time interval of a low solar and ionospheric activity, the case of the geomagnetic storm on 7 March, 2012 provided a good environment for studying the GPS positioning performance during the moderately disturbed ionospheric and geomagnetic conditions, without the presence of remaining effects of previous ionospheric events.

General space weather conditions are summarised in Figure 1, provided by NOAA. It is evident from the figure that the space weather disturbance hit the Earth's environment in the early hours of 7 March, 2012, imminently causing geomagnetic disturbance with two slightly emphasised local maxima (around

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0900 and 1500, both times UTC). The geomagnetic storm died out towards the dusk and the end of the day.

The effects of the global geomagnetic storm were conveyed to the ionosphere, as evident from SID observations of VLF signals shown in Figures 3 (Rhauderfehn station signal) and 4 (Rosnay station signal), respectively. Compared with the common daily variations of received signal strengths (Figure 2), observations of the received VLF signal strengths can indirectly point to the status of the low ionospheric dynamics. The comparison of Rhauderfehn signal observations on 7 March, 2012 (Figure 3) with a common daily variations of VLF signal strengths reveals intensive low-ionosphere activities around 0900, 1500, 1800 and 2100 (all times UTC). The analysis of Rosnay signal observations on 7 March, 2012 clearly shows increased low-ionosphere dynamics around 0600, 0900 and 1500 (all times UTC), while the increased night-time signal levels cannot be clearly related to the effects of the ionospheric storm.

Figure 3. VLF Rhauderfehn, Germany 23.4 kHz signal received by SID monitor at Rijeka, Croatia monitoring station on 7 March, 2012.

Figure 4. VLF Rosnay, France 20.9 kHz signal received by SID monitor at Rijeka, Croatia monitoring station on 7 March, 2012.

4.2 GPS positioning error dynamics

Two independent sets of single-frequency GPS positioning estimates time series were used in research: RINEX observables taken at IGS Medicina, Italy

GNSS reference station, and NMEA observables collected by stationary

reference single-frequency GPS receiver at GNSS laboratory, Faculty of Maritime Studies, University of Rijeka, Croatia The selection of the sources of experimental

observables was carried out with the aim to provide the coverage of the Northern Adriatic area, with intensive commercial, recreational and military maritime traffic. Corrective measures were in operation at both sites to minimise the effects of multipath, and space and control segment.

The Medicina RINEX observables at 30 s sampling rate, taken from the IGS internet archive, was used for simulated single-frequency GPS positioning estimates, from which the GPS positioning error response to disturbed ionospheric conditions was derived (Figure 5). Medicina GPS error components time series dynamics on 7 March, 2012 are summarised in Table 1.

Figure 5. Time series of components of the single-frequency GPS position estimate errors, taken at Medicina, Italy GNSS reference station on 7 March, 2012 (30 s-sampling rate).

Table 1. Medicina (RINEX) GPS positioning error dynamics on 7 March, 2012. __________________________________________________ Error Dynamics description component (all times UTC) __________________________________________________ Northing Error dynamics noticeable, local maxima around 1200, 1400, 1730, 2100, plateau be- tween 0700 and 0900 Easting Negligible effects of the ionospheric storm, values slightly increased after 1600 Height Daily variation pattern slightly disturbed, with local maxima around 1600 and 1800 __________________________________________________

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The Rijeka NMEA observables at 2 s sampling rate were used as a source of receiver-based estimates of components of the GPS positioning error (Figure 6). The effects of the stochastic component were removed by utilisation of a simple Moving Average filter of the order of 120 (s).

Figure 6. Time series of components of the single-frequency GPS position estimate errors, taken at Rijeka, Croatia monitoring station on 7 March, 2012 (2 s-sampling rate, simple moving average filter of order 120 s applied).

Table 2. Rijeka (NMEA) GPS positioning error dynamics on 7 March, 2012. __________________________________________________ Error Dynamics description component (all times UTC) __________________________________________________ Northing Noticeable effects of the ionospheric storm, local maxima around 0600, 0900, 1500, 1800 Easting Negligible effects of the ionospheric storm, northing error consisting of DC bias and a mi- nor stochastic component Horizontal Daily variation governed by easting position- ing error dynamics, local maxima around 0600, 0900, 1500, 1800, 2100 __________________________________________________

5 DISCUSSION

The analysis of Medicina (RINEX) and Rijeka (NMEA) data sets revealed the impact of the minor ionospheric storm on 7 March, 2012 on GPS horizontal positioning error. Prominent effects were observed on the northing positioning error component both at Medicina, Italy, and Rijeka, Croatia. In both cases, the amounts of error exceed the common values at the times of local maxima. Prominent ionospheric storm effects on northing positioning error component, with the easting positioning error component experiencing only negligible effects, were observed in other case-studies in the region (Filjar, 2008, Filjar, Kos & Kos, 2007, Filjar, Kos & Kos, 2006).

Local maxima of horizontal GPS positioning errors at both Medicina, Italy and Rijeka, Croatia were well correlated with the local maxima of received VLF signals from both Rhauderfehn,

Germany and Rosnay, France, with the only exception of 1200 UTC maximum of GPS positioning error not correlated with VLF signal strength observables. This leads to the conclusion that the minor ionospheric storm on 7 March, 2012 created a regional ionospheric event that affected in the same manner the areas of both Medicina, Italy and Rijeka, Croatia. In due course, low ionosphere observations taken in Rijeka can be applied regionally for description of local low ionosphere dynamics, at least for the case in consideration.

The additional analysis of Rijeka GPS positioning errors dynamics was performed, with the outcome as follows. Histogram of Rijeka horizontal GPS positioning error estimates (Figure 7) shows a very good fit with the Gaussian (normal) distribution. This allows for establishment of simple statistical model of the process of the horizontal GPS positioning error generation during the ionospheric storm on 7 March, 2012.

Figure 7. Histogram of GPS positioning horizontal errors observed on 7 March, 2012 (curved-orange line represents the equivalent normal distribution).

Finally, a simple non-linear analysis (Hilborn,

2000, Ott, 2002) applied to GPS positioning time series did not reveal any embedded complex dynamics of horizontal GPS positioning error time series, as seen in two-dimensional state space diagrams of northing and easting GPS positioning errors (Figures 8 and 9, respectively).

Figure 8. Two-dimensional phase space diagram of northing GPS positioning errors.

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Figure 9. Two-dimensional phase space diagram of easting GPS positioning errors.

6 CONCLUSION

The results of the assessment of a minor ionospheric storm effects on a single-frequency GPS positioning performance are presented in this paper, with an emphasis given on the effects of the low-ionosphere dynamics. Time series of the actual GPS positioning error observables taken at Medicina, Italy and Rijeka, Croatia were correlated with common space weather indices, as well as with the indirect observables of low-ionosphere dynamics, taken at Rijeka, Croatia.

Our analysis show that the minor ionospheric storm of 7 March, 2012 created noticeable effects to GPS horizontal positioning error, but without embedded complexity. The effects of the ionospheric storm created similar satellite positioning conditions on both sides of the Adriatic Sea, suggesting an opportunity for a co-ordinated approach to identification and mitigation of the approaching ionospheric effects on GNSS PNT performance and operation.

The local maxima of horizontal GPS ionospheric errors were well correlated with VLF signal strengths recorded at Rijeka, Croatia, suggesting that the low-cost low-ionosphere activity monitoring may provide a valuable means for regional identification of approaching GPS positioning performance disturbances.

This paper reports the outcome of a case-study analysis which is to be explored and verified further in analysis of similar events taking place in the region in the future.

ACKNOWLEDGEMENTS

Research activities presented in this paper were conducted under the research project Research into the correlation of maritime-transport elements in marine traffic, supported by the Ministry of Science, Education and Sports, Republic of Croatia.

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