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• W1627332787 abstract "This paper presents the results achieved within the project “Ionospheric Delay Corrections in GNSS Signals for High Precision Applications (IONODeCo)”. The goal was to design an optimal strategy to remove high order signal delays induced by ionospheric refraction from GNSS measurements. It was motivated by the fact that the higher order ionospheric effects (I2+) are one of the main limiting factors in very precise GNSS processing when millimeter precision is required. A comprehensive study of the I2+ effects in range and in GNSS products(such as receiver position, clock and tropospheric delay, GNSS satellite position, clocks, geocenter offset) is summarized, where all the relevant effects are considered (second and third order, geometric and dSTEC bending). Both effects and mitigation errors are characterized, after showing that the combination of multifrequency L-band observations is not a useful way to cancel the second order term. The different effects in terms of pseudo-observations have been generated with TOMION software from the actual GPS-constellation to ground-network geometry, using the International Reference Ionosphere (IRI2012). Then they have been analysed independently with BERNESE and GIPSY-OASIS softwares (network solutions), as far as with the ATOMIUM software (user PPP solution). The main conclusion is the confirmation that the I2 impact represents most of the overall I2+ one (more than 80%), and is the predominant source of mismodelling in GNSS network solution excepting for the tropospheric estimation (which is mostly due to both geometric and dSTEC bending influences). As a consequence I2 (and both dSTEC and geometric bending in a much smaller extent), should be corrected at both network solution (providing satellite orbits and clock products) and user level in a consistent way, by using as well an algorithm with direct estimation of STEC (with pseudorange or VTEC-map alignment estimation of the ionospheric phase ambiguity), avoiding the significant mapping function errors. In this way a nuisance residual error is found (sub-mm signature in network solution positioning). 1. GENERAL SPECIFICATIONS A large number of scientific applications demand high precision positioning and time transfer: seismic ground deformations, sea level monitoring or land survey applications require sub-centimetre precision in precise position; monitoring of stable atomic frequency standards requires an increasing sub-nanosecond precision. Differential GNSS is presently the best tool to reach these precisions, as it removes the majority of the errors affecting the signals. However, the associated need for dense GNSS observation networks is not fulfilled for many locations (e.g. Pacific, Africa). An alternative is to use Precise Point Positioning, but this technique requires correcting signal delays at the highest level of precision. The design of the GPS signals with two frequencies (f1 and f2) for each transmitted carrier phase was intended to minimize the effects of the ionosphere by allowing the possibility to work with signal combinations. Combining the two carrier phases in the ‘ionospherefree’ linear combination, it is possible to cancel out the first term in a series expansion of the refractive index of the ionosphere. However errors remain due to the higher order terms in this series expansion. There are also systematic errors due to bending of the signals, caused by the signals passing at an angle through gradients in the refractive index. The bending also affects f1 and f2 frequencies differently so they take slightly different paths, meaning that the ‘ionosphere-free’ linear combination may no longer completely cancel the first refractive index term. In order to properly cancel out the second and higher order terms (I2+ terms), or at least mitigate them, it has to be taken into account that the more preeminent one, at mid and high elevation, is the second order term (I2), which is proportional to the geomagnetic field projection along the ray, and to the number density of free electrons, both terms multiplied and integrated along the transmitter-receiver ray. For the I2 terms cancellation/mitigation, two main different approaches are possible: a) Combining independent and simultaneous measurements of the same transmitter-receiver pair at three different frequencies. It is theoretically possible to cancel out both I1 and I2 similarly as it is done typically in precise dual-frequency GNSS measurements for I1. b) Modeling (and removing from the GNSS measurements) the I2 term, in function of accurate values of electron content and geomagnetic field. This approach is applicable to the remaining higher order terms as well. Taking into account that the impact of second and higher order signal delays induced by ionospheric refraction constitute one of the main error sources on GNSS measurements, the goal of the project IONODeCo has been twofold. First, to assess a realistic evaluation of the impact of all the high order ionospheric terms in both range and geodetic domains. And, second, to identify optimal strategies to mitigate them. In this regard, the correction modelling from electron density and geomagnetic models have been the main options investigated. The first approach related to the combination of three Galileo or GPS modernized L-band measurements signals (for cancelling the I2 term) has been disregarded after showing, theoretically and experimentally, the impossibility to discriminate between the augmented noise and I2+ effect on the observables. However, our theoretical study has shown that an ionosphere-free combination of two L-band frequencies and one C-band frequency would remove the second-order terms with no significant noise amplification; the noise combination is 1.3 times the noise of the L-band signals. Furthermore, adding a Ku-band signal rather than a Cband signal would provide a combination noise similar as the noise of the L-band signal. As current GNSS only provide L-band signals, we have only concentrated our study on the I2+ correction modelling from electron density and geomagnetic models. 2. HIGHER ORDER IONOSPHERIC TERMS: BASIC INTRODUCTION AND MODELING OPTIONS The first order ionospheric refraction (I1) takes more than 99.9% of the total ionospheric delay. We will show that the correction of the I2 order term is necessary when requiring a precision better than one centimetre level in range for all the elevations (dSTEC and geometric bending effects should also be considered for low elevation). For precisions of more than one millimetre level, the correction of the I3 order term (and bending terms) may be also considered. The final implemented expressions for every I2+ terms used to assess their impact at range and geodetic domains are presented below. They have been taken from previous works, involving some of the co-authors of the IONO-DeCo project (Hernandez-Pajares et al (2007), IERS (2010), Petrie et al. (2010), Pireaux et al. (2010)) trying to assess their impact from different points of view.. The GNSS measurements with higher precision at a given frequency f , the carrier phase Lf, can be expressed in terms of a non-dispersive term ρ* (including the geometric distance, receiver and transmitter clock errors and tropospheric delay), its ambiguity Bf (the unknown initial pseudorange at phase locking time), the wind-up or phase rotation term φ and the first, second and third order terms in the straight line propagation approximation (If,1 , If,2 and If,3 respectively), among the geometric and STEC differential (dSTEC) bending terms (If,gb and If,dSb respectively): Lf = ρ* + Bf + (c/f)φ + If,1 + If,2 + If,3+ If,gb + If,dSb (1) where all the ionospheric terms, including the third order term which can be described in terms a main (If,3,M) and a small (If,3,s) term (If,3= If,3,M + If,3,s), are summarized in Table 1. 3. REPRESENTATIVE STUDY FOR ALL THE HIGHER ORDER IONOSPHERIC TERMS, AND ITS MITIGATION ERRORS, IN NOMINAL SOLAR MAXIMUM CONDITIONS Two aspects have been considered to assess the importance of the different higher order ionospheric corrections and their approximations: a) At range level, looking at the values of slant delays of the different high order terms. b) At geodetic domain level, provided by the impact of such values in the different geodetic parameters estimated consistently (i.e. simultaneously) from a global GNSS network. For that, a sub-network of 44 stations has been selected from the 232 stations of the IGS08 network (Rebischung, 2011) Iono Term ( If ) k ) / ( f k f f I    Considered Approximations f  (S.I. units) ) /( / k f c f I I  f c I P I / ) (" @default.
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• W1627332787 date "2013-01-01" @default.
• W1627332787 modified "2023-09-26" @default.
• W1627332787 title "Impact of higher order ionospheric delay on precise GNSS computation" @default.
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