A 4D tomographic ionospheric model to support PPP-RTK

Abstract

Successful implementation of integer ambiguity resolution enabled precise point positioning (aka PPP-RTK) algorithms is inextricably linked to the ability of a user to perform near real-time positioning by quickly and reliably resolving the integer carrier-phase ambiguities. In the PPP-RTK technique, a major barrier to successful ambiguity resolution is the unmodelled impact of the ionosphere. We present a 4D ionospheric tomographic model that computes in real time the ionospheric electron density as a linear combination of basis functions, namely B-splines. The results show that when the ionospheric estimates are provided as atmospheric corrections for a PPP-RTK end-user, the time to fix its horizontal position below 10 cm is around 20 epochs (the sample rate is 30 s) at the 90% of the cumulative distribution function (CDF), as opposed to the time it takes when no external corrections are provided, which is around 80 epochs at 90% of the CDF.

A Review of Voxel-Based Computerized Ionospheric Tomography with GNSS Ground Receivers

“…The estimation errors in SBAS can be reduced by 30-50% compared to a planar fit on the thin shell [92]. The convergence time in PPP-RTK can be reduced from 80 epochs to 20 epochs with a sample rate of 30 s compared to the time without external corrections provided [93]. Voxel-based CIT may be applied to these fields if the resolution and precision meet requirements.…”

A mean-squared-error condition for weighting ionospheric delays in GNSS baselines

“…It is a form of regularized least-squares (Gunst and Mason 1980;Toutenburg 1982;Tarantola 2005), of which Tikhonov regularization (Tihonov 1963), ridge-regression (Hoerl andKennard 1970), and principal component estimation (Jolliffe 2002) are prime examples. The ionosphere-weighted formulation is used in combination with external ionospheric models, see, e.g., (Schaer 1999;Memarzadeh 2009;Jee et al 2010;Feltens et al 2011;Olivares-Pulido et al 2019), and to incorporate ionospheric corrections from reference networks, for instance for PPP or PPP-RTK, see, e.g., (Odijk 2000(Odijk , 2002Collins et al 2012;Paziewski 2016;Odijk et al 2016;Wang et al 2018;Psychas and Verhagen 2020;Tomaszewski et al 2020;Teunissen 2021). As the ionosphere is known to decorrelate as a function of baseline length, the ionosphere-weighted formulation is also used for strengthening medium to long baseline models, see, e.g., (Schaffrin and Bock 1988;Goad and Yang 1994;Bock 1998;Teunissen 1998;Odijk 2002;Teunissen 2017, 2019;Brack et al 2021).…”

Analysis of different propagation models for the estimation of the topside ionosphere and plasmasphere with an ensemble Kalman filter

“…In this study, we apply the NeQuick model (version 2.0.2). The NeQuick model was developed at the International Centre for Theoretical Physics (ICTP) in Trieste, Italy, and at the University of Graz, Austria (see Hochegger et al, 2000;Radicella and Leitinger, 2001;Nava et al, 2008). The daily solar flux index of F10.7 is used to drive the NeQuick model.…”

“…These authors reconstruct the 3D ionosphere by algebraic iterative methods. An alternative is to estimate the electron density as a linear combination of smooth and continuous basis functions, like, for example, spherical harmonics (SPHs; Schaer, 1999), B-splines (Schmidt et al, 2008;Zeilhofer, 2008;Zeilhofer et al, 2009;Olivares-Pulido et al, 2019), B-splines and trigonometric B-splines (Schmidt et al, 2015), B-splines and Chapman functions (Liang et al, 2015(Liang et al, , 2016, and empirical orthogonal functions and SPHs .…”

“…Besides the algebraic methods, other techniques benefitting from information on spatial and temporal covariance information, such as optimal interpolation, the Kalman filter, 3D and 4D variational techniques and kriging, are applied to update the modelled electron density distributions (see Angling et al, 2008;Minkwitz et al, 2015 andNikoukar et al, 2015;Olivares-Pulido et al, 2019).…”