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Stochastic modelling considering ionospheric scintillation effects on GNSS relative and point positioning
Author(s)
Language
English
Obiettivo Specifico
3.9. Fisica della magnetosfera, ionosfera e meteorologia spaziale
5.4. Banche dati di geomagnetismo, aeronomia, clima e ambiente
Status
Published
JCR Journal
JCR Journal
Peer review journal
Yes
Title of the book
Issue/vol(year)
9/45 (2010)
Publisher
Elsevier
Pages (printed)
1113 - 1121
Issued date
May 3, 2010
Abstract
Global Navigation Satellite Systems (GNSS), in particular the Global Positioning System (GPS), have been widely used for high accuracy
geodetic positioning. The Least Squares functional models related to the GNSS observables have been more extensively studied than
the corresponding stochastic models, given that the development of the latter is significantly more complex. As a result, a simplified stochastic
model is often used in GNSS positioning, which assumes that all the GNSS observables are statistically independent and of the
same quality, i.e. a similar variance is assigned indiscriminately to all of the measurements. However, the definition of the stochastic model
may be approached from a more detailed perspective, considering specific effects affecting each observable individually, as for example the
effects of ionospheric scintillation. These effects relate to phase and amplitude fluctuations in the satellites signals that occur due to diffraction
on electron density irregularities in the ionosphere and are particularly relevant at equatorial and high latitude regions, especially
during periods of high solar activity. As a consequence, degraded measurement quality and poorer positioning accuracy may result.
This paper takes advantage of the availability of specially designed GNSS receivers that provide parameters indicating the level of phase
and amplitude scintillation on the signals, which therefore can be used to mitigate these effects through suitable improvements in the least
squares stochastic model. The stochastic model considering ionospheric scintillation effects has been implemented following the approach
described in Aquino et al. (2009), which is based on the computation of weights derived from the scintillation sensitive receiver tacking models
of Conker et al. (2003). The methodology and algorithms to account for these effects in the stochastic model are described and results of
experiments where GPS data were processed in both a relative and a point positioning mode are presented and discussed.
Two programs have been developed to enable the analyses: GPSeq (currently under development at the FCT/UNESP Sao Paulo State
University – Brazil) and PP_Sc (developed in a collaborative project between FCT/UNESP and Nottingham University – UK). The
point positioning approach is based on an epoch by epoch solution, whereas the relative positioning on an accumulated solution using
a Kalman Filter and the LAMBDA method to solve the Double Differences ambiguities. Additionally to the use of an improved stochastic
model, all data processing in this paper were performed using an option implemented in both programs, to estimate, for each
observable, an individual ionospheric parameter modelled as a stochastic process, using either the white noise or the random walk correlation
models. Data from a network of GPS Ionospheric Scintillation and TEC Monitor (GISTM) receivers set up in Northern Europe
as part of the ISACCO project (De Franceschi et al., 2006) were used in the experiments. The point positioning results have shown
improvements of the order of 45% in height accuracy when the proposed stochastic model is applied. In the static relative positioning,
improvements of the order of 50%, also in height accuracy, have been reached under moderate to strong scintillation conditions. These
and further results are discussed in this paper.
geodetic positioning. The Least Squares functional models related to the GNSS observables have been more extensively studied than
the corresponding stochastic models, given that the development of the latter is significantly more complex. As a result, a simplified stochastic
model is often used in GNSS positioning, which assumes that all the GNSS observables are statistically independent and of the
same quality, i.e. a similar variance is assigned indiscriminately to all of the measurements. However, the definition of the stochastic model
may be approached from a more detailed perspective, considering specific effects affecting each observable individually, as for example the
effects of ionospheric scintillation. These effects relate to phase and amplitude fluctuations in the satellites signals that occur due to diffraction
on electron density irregularities in the ionosphere and are particularly relevant at equatorial and high latitude regions, especially
during periods of high solar activity. As a consequence, degraded measurement quality and poorer positioning accuracy may result.
This paper takes advantage of the availability of specially designed GNSS receivers that provide parameters indicating the level of phase
and amplitude scintillation on the signals, which therefore can be used to mitigate these effects through suitable improvements in the least
squares stochastic model. The stochastic model considering ionospheric scintillation effects has been implemented following the approach
described in Aquino et al. (2009), which is based on the computation of weights derived from the scintillation sensitive receiver tacking models
of Conker et al. (2003). The methodology and algorithms to account for these effects in the stochastic model are described and results of
experiments where GPS data were processed in both a relative and a point positioning mode are presented and discussed.
Two programs have been developed to enable the analyses: GPSeq (currently under development at the FCT/UNESP Sao Paulo State
University – Brazil) and PP_Sc (developed in a collaborative project between FCT/UNESP and Nottingham University – UK). The
point positioning approach is based on an epoch by epoch solution, whereas the relative positioning on an accumulated solution using
a Kalman Filter and the LAMBDA method to solve the Double Differences ambiguities. Additionally to the use of an improved stochastic
model, all data processing in this paper were performed using an option implemented in both programs, to estimate, for each
observable, an individual ionospheric parameter modelled as a stochastic process, using either the white noise or the random walk correlation
models. Data from a network of GPS Ionospheric Scintillation and TEC Monitor (GISTM) receivers set up in Northern Europe
as part of the ISACCO project (De Franceschi et al., 2006) were used in the experiments. The point positioning results have shown
improvements of the order of 45% in height accuracy when the proposed stochastic model is applied. In the static relative positioning,
improvements of the order of 50%, also in height accuracy, have been reached under moderate to strong scintillation conditions. These
and further results are discussed in this paper.
References
Aquino, M., Monico, J.F.G., Dodson, A.H., Marques, H.A., De
Franceschi, G., Alfonsi, L., Romano, V., Andreotti, M. Improving
the GNSS positioning stochastic model in the presence of ionospheric
scintillation. Journal of Geodesy, in press. doi: 10.1007/s00190-009-
0313-6.
Bock, Y., Gourevitch, S.A., Counselman III, C.C., King, R.W., Abbot,
R.I. Interferometric analysis of GPS phase observations. Manuscripta
Geodaetica 11, 282–288, 1986.
Conker, R.S., El-Arini, M.B., Hegarty, C.J., Hsiao, T. Modeling the
effects of ionospheric scintillation on GPS/satellite-based augmentation
system availability. Radio Science 38 (1), 2003.
De Franceschi, G., Alfonsi, L., Romano, V. ISACCO: an Italian project
to monitor the high latitudes ionosphere by means of GPS receivers.
GPS Solutions 18, 263–267, doi:10.1007/s10291-006-0036-6, 2006.
Gelb, A., Kasper Jr., J.F., Nash Jr., R.A., Price, C.F., Sutherland Jr., A.A.
Applied Optimal Estimation. The M.I.T. Press, Cambridge, Massachusetts,
374p, 1974. Klobuchar, J.A. Ionospheric effects of GPS, in: Parkinson, B., Spilker, J.
(Eds.), Global Positioning System: Theory and Applications. 4th
Printing, vol. 2. The American Institute of Aeronautics and Astronautics
Inc. (Chapter 12), 1996.
Liu, G. C. Ionosphere Weighted Global Positioning System Carrier Phase
Ambiguity Resolution. M.Sc. Dissertation. Department of Geomatics
Engineering – The University of Calgary, Calgary, Alberta, Canada,
2001.
Odijk, D. Fast Precise GPS Positioning in the Presence of Ionospheric
Delays. Ph.D. Dissertation. Faculty of Civil Engineering and Geosciences,
Delft University of Technology, Delft, 2002.
Teunissen, P.J.G. GPS carrier ambiguity fixing concepts, in: Teunissen,
P.J.G., Kleusberg, A. (Eds.), GPS for Geodesy, 2nd ed Springer-
Verlag, Berlin, pp. 319–383, 1998.
Van Dierendonck, A.J. Measuring ionospheric scintillation effects from
GPS signals, in: Proceedings of 57th Annual Meeting of the Institute of
Navigation. Albuquerque, New Mexico, USA, pp. 391–396, 2001.
Van Dierendonck, A.J., Klobuchar, J., Hua, Q. Ionospheric scintillation
monitoring using commercial single frequency C/A code receivers, in:
Proceedings ION GPS-93: Sixth International Technical Meeting of
the Satellite Division of the Institute of Navigation. Salt Lake City,
Utah, pp. 1333–1342, 1993.
Franceschi, G., Alfonsi, L., Romano, V., Andreotti, M. Improving
the GNSS positioning stochastic model in the presence of ionospheric
scintillation. Journal of Geodesy, in press. doi: 10.1007/s00190-009-
0313-6.
Bock, Y., Gourevitch, S.A., Counselman III, C.C., King, R.W., Abbot,
R.I. Interferometric analysis of GPS phase observations. Manuscripta
Geodaetica 11, 282–288, 1986.
Conker, R.S., El-Arini, M.B., Hegarty, C.J., Hsiao, T. Modeling the
effects of ionospheric scintillation on GPS/satellite-based augmentation
system availability. Radio Science 38 (1), 2003.
De Franceschi, G., Alfonsi, L., Romano, V. ISACCO: an Italian project
to monitor the high latitudes ionosphere by means of GPS receivers.
GPS Solutions 18, 263–267, doi:10.1007/s10291-006-0036-6, 2006.
Gelb, A., Kasper Jr., J.F., Nash Jr., R.A., Price, C.F., Sutherland Jr., A.A.
Applied Optimal Estimation. The M.I.T. Press, Cambridge, Massachusetts,
374p, 1974. Klobuchar, J.A. Ionospheric effects of GPS, in: Parkinson, B., Spilker, J.
(Eds.), Global Positioning System: Theory and Applications. 4th
Printing, vol. 2. The American Institute of Aeronautics and Astronautics
Inc. (Chapter 12), 1996.
Liu, G. C. Ionosphere Weighted Global Positioning System Carrier Phase
Ambiguity Resolution. M.Sc. Dissertation. Department of Geomatics
Engineering – The University of Calgary, Calgary, Alberta, Canada,
2001.
Odijk, D. Fast Precise GPS Positioning in the Presence of Ionospheric
Delays. Ph.D. Dissertation. Faculty of Civil Engineering and Geosciences,
Delft University of Technology, Delft, 2002.
Teunissen, P.J.G. GPS carrier ambiguity fixing concepts, in: Teunissen,
P.J.G., Kleusberg, A. (Eds.), GPS for Geodesy, 2nd ed Springer-
Verlag, Berlin, pp. 319–383, 1998.
Van Dierendonck, A.J. Measuring ionospheric scintillation effects from
GPS signals, in: Proceedings of 57th Annual Meeting of the Institute of
Navigation. Albuquerque, New Mexico, USA, pp. 391–396, 2001.
Van Dierendonck, A.J., Klobuchar, J., Hua, Q. Ionospheric scintillation
monitoring using commercial single frequency C/A code receivers, in:
Proceedings ION GPS-93: Sixth International Technical Meeting of
the Satellite Division of the Institute of Navigation. Salt Lake City,
Utah, pp. 1333–1342, 1993.
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