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Authors: Alves da Silva, H.* 
Camargo, P.* 
Galera Monico, J. F.* 
Aquino, M.* 
Marques, H. A.* 
De Franceschi, G.* 
Dodson, A.* 
Title: Stochastic modelling considering ionospheric scintillation effects on GNSS relative and point positioning
Journal: Advances in Space Research 
Series/Report no.: 9/45 (2010)
Publisher: Elsevier
Issue Date: 3-May-2010
DOI: 10.1016/j.asr.2009.10.009
Keywords: GNSS
Ionospheric scintillation
Receiver tracking models
Stochastic model
Relative and point positioning
Subject Classification01. Atmosphere::01.02. Ionosphere::01.02.05. Wave propagation 
01. Atmosphere::01.02. Ionosphere::01.02.07. Scintillations 
04. Solid Earth::04.03. Geodesy::04.03.08. Theory and Models 
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.
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