Method for eliminating or mitigating the effect of ionospheric scintillation on GNSS positioning at local, regional and global scale

Abstract

The present invention concerns a method for eliminating or mitigating the effect of ionospheric scintillation on GNSS enabled positioning over local, regional and global scale, in areas where static GNSS network providing streaming of S4 and σΦ scintillation indices are available. Depending on the application and on the update rate of the S4 and σΦ streaming by the static GNSS network, they can be used "as is" or can be used as input for the Short-Term Forecasting model (patent application number WO2016185500A1) which forecast the expected S4 and σΦ with a time horizon from seconds up to minutes in advance. Moreover, in the case of very harsh ionospheric conditions which prevent the algorithm from being successful in mitigation approach an alerting is provided to the user.

Description

[0001]Method for eliminating or mitigating the effect of ionospheric scintillation on GNSS positioning at local, regional and global scale ------ Applicant: SPACEARTH NAV S.R.L. Inventors: Marco Fermi, Pietro Vermicelli, Maurizio Vasta, Giorgiana De Franceschi ------ The present invention concerns a method for eliminating or mitigating the effect of ionospheric scintillation on GNSS positioning at local, regional and global scale, thus by improving the position accuracy. Background The occurrence, spatial distribution, characteristics, and dynamics of ionospheric irregularities are among the most widely studied features of ionospheric phenomenology. Despite the progress achieved in the last decades, the physics of ionospheric irregularities is far from being completely understood. Despite their ruling mechanisms and related plasma structuring being generally known, their behavior still challenges the modeling and predicting capabilities. This poses serious limitations in getting rid of the disruptive effects on GNSS-based navigation and positioning, such as scintillation. It is reasonable to say that effective and operative modeling able to predict the appearance and evolution of the ionospheric irregularities that cause signal scintillations is the last significant unsolved problem in ionospheric science Jacobacci & Partners / ANP applied to communications, positioning and navigation. Small / medium-scale irregularities (order of a few hundred meters or more) cause scintillation effects on GNSS signals, jeopardizing the rover receiver performance in terms of positioning accuracy degradation (through range errors) or even leading to a complete loss of signal tracking. Scintillation can degrade the performance of navigation systems and generate errors in received messages and measurements. The required levels of accuracy, integrity, functional consistency, and availability of GNSS signals are sometimes not satisfied, compromising commercial operations like offshore navigation, digital farming, and station keeping, including safety-critical applications. Systems and methods for mitigating the effect of ionospheric scintillation have been attempted for many years as for example in US2019 / 056505 A1. However, this approach proves problematic. In fact, US2019 / 056505 A1 is based on the mapping of Scintillation Bubbles, by identifying their spatial contour in the sky on some thin layer. This approach has two main drawbacks. The first drawback concerns the fact that Scintillation Bubble do not have, in general, a regular geometry. On the contrary, they show a very complex shape varying in time and small-scale dimension of the embedded ionospheric irregularities of the order of hundreds of meters. The referenced literature gives some method for scintillation mapping namely: a. L. F. C. de Rezende, E. R. de Paula, P. M. Kintner and I. J. Kantor, “Mapping and Survey of Jacobacci & Partners / ANP Plasma Bubbles over Brazilian Territory” THE JOURNAL OF NAVIGATION (2007), 60, 69–81. f The Royal Institute of Navigation doi:10.1017 / S0373463307004006 Printed in the United Kingdom (mentioned in US2019 / 056505 A1); b. DARYA ABDOLLAH MASOUD ET AL: "Mapping of 1,2 S4 Over the Arabian Peninsula During Solar Minimum", IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, IEEE, USA, vol. 19, 26 August 2022 (2022- 08-26), pages 1-5, XP011919738, ISSN: 1545-598X, DOI: 10.1109 / LGRS.2022.3202245 [retrieved on 2022- 08-26] section II. Data and methodology. Such references refer to the mapping respectively over Brazil (8.510.000 Km2) and over part of the Arabian Peninsula (~ 1680 Km2). In both the cases the pixels of the ground maps are of the order of tens of kms which, when projected at the Ionospheric Pierce Point, IPP, are even larger. This means that the Phase scintillation map claimed in US2019 / 056505 A1 has a qualitative significance only and the contour of the Scintillation Bubble could show an error higher than ten times the expected dimension of the bubble itself. The second drawback concerns the fact that Scintillation Bubble is a phenomenon typical of low latitude. At high latitude, different mechanism raises the ionospheric irregularities and then Scintillation; instead of Bubbles, in that case, the scientific communities refer to “Patches”, “Blobs”, and “Arcs” which show different mechanisms causing them and different physical dimensions. Consequently, Jacobacci & Partners / ANP scintillation indices may be expected to show different intensity and evolution in time and space (see the references in the bibliography section below). Another drawback of US2019 / 056505 A1 is that such mapping methods, when implemented, typically need: ^ Projecting onto the vertical the slant scintillation indices, so as to minimize the effect of the geometry of the GNSS network (Mannucci et al. 1993); ^ setting an IPP altitude for the determination of the vertical scintillation indices. This implies a significant lack of accuracy in the de-weighting of the GNSS signal. Patent document WO 2016 / 185500 A1 also cited below refers to the article of Conker et al., RADIO SCIENCE, VOL. 38, NO. 1, 1001, doi:10.1029 / 2000RS002604, 2003, for the calculation of corrected weights for one single GPS frequency, which however uses a specific analytical model for observables de-weighting, which is not applicable in many field cases and in particular for other constellation different from GPS. Moreover, scintillation parameters are taken as is without further elaboration or forecasting, and therefore they lack accuracy in the corrections both because it is tied to only the GPS satellites and because the corresponding measurement data are not expanded. In addition, the approach is not valid for S4 values higher than 0.7. A need is felt to devise a general quantitative and accurate method able to properly manage mitigation of scintillation impact on GNSS positioning independently Jacobacci & Partners / ANP from both the geographic area and the mechanism triggering the Scintillation phenomenon, from any analytical model of the scintillation phenomena, and possibly from a specific altitude of the single-layer ionosphere. Object and subject-matter of the invention It is an object of the present invention to provide a method for eliminating or mitigating the effect of ionospheric scintillation on GNSS positioning which solves the problems of the prior art, in particular by removing the contour mapping of the scintillation caused by the occurrence of ionospheric bubbles, thus supporting the mitigation capability on a global scale and not only at the low latitude where bubbles are more likely to form. Moreover, optionally short-term forecasting of the scintillation indices is sought to make up for longer acquisition intervals of scintillation parameters. It is a subject matter of the present invention a method and a system according to the attached claims. Detailed description of invention embodiments List of figures The invention will now be described by way of illustration but not by way of limitation, with particular reference to the drawings of the attached figures, in which: ^ Figure 1 shows a block diagram of the invention Jacobacci & Partners / ANP system; ^ Figure 2 shows a geometry of a satellite-ground station line-of-sight depicting the Ionospheric Pierce Point (IPP) that is the intersection between the GNSS ray-path and the single layer ionosphere; ^ Figure 3 shows, within a RoI, the line-of-sights between: a) the GNSS satellites and the static GNSS ground stations, and b) the GNSS satellites and the GNSS rovers. It is specified here that elements of different embodiments can be combined together to provide further embodiments without limits while respecting the technical concept of the invention, as the skilled person understands without problems from what has been described. The present description also refers to the known art for its implementation, with regard to the detailed characteristics not described, such as for example elements of minor importance usually used in the known art in solutions of the same type. When introducing an element, it always means that it can be “at least one” or “one or more”. When a list of elements or features is given in this description, it is meant that the invention according to the invention “includes” or alternatively “is composed of” such elements. When features are listed within the same sentence or bullet list, one or more of the individual features may be included in the invention without connection to the other features in the list. Jacobacci & Partners / ANP Two or more of the parts (elements, devices, systems) described above can be freely associated and considered as kits of parts according to the invention. Embodiments The present invention eliminates or mitigates the impact of scintillation on GNSS-based real-time positioning and navigation, by exploiting the streaming of the scintillation indices S4 and σΦprovided by a local, regional or global network of static GNSS receivers. S4 and σΦ are used to generate a weighing matrix for modifying the a-priori observables variance matrix of the GNSS rover receivers, the signal being corrupted by scintillation, thus updating the (stochastic) model of the PVT (Position, Velocity and Time) estimator of the rover receivers. Depending on the application and on the update rate of S4 and σΦstreaming by the static GNSS network, they can be used “as is” or can be used as input for a Short- Term Forecasting model (e.g. patent application number WO2016185500A1), which forecasts S4 and σΦ with a time horizon from seconds up to minutes (e.g. 10 minutes) in advance. It is here to specify that the static GNSS receivers are different from the rover receivers, in that the former are used to obtain S4 and σΦ and the latter are moving receivers that are to be tracked and / or guided on the ground, air or water. Jacobacci & Partners / ANP The effectiveness of the method is guaranteed locally in a Region of Interest (ROI) bound by the static GNSS stations. Moreover, the effectiveness of the method is guaranteed also on a larger scale in respect to the local one (i.e. regional and global) by partitioning the larger scale area into a subset of different adjacent ROIs each characterized by own static GNSS receivers’ network. Good performances in eliminating or mitigating the impact of Scintillation can be achieved always over the Global Scale providing a proper network of static GNSS receivers and selecting the appropriate ROI where the rover is moving. The innovation is applicable at local, regional and global scale with particular impact at low latitudes around the equator and at high latitudes as well, where the ionospheric scintillation is expected to pose the harshest conditions to positioning. At low latitudes, very harsh ionospheric conditions can happen sometimes and, in those cases, the invention method, if and when could not guarantee the effectiveness of the scintillation mitigation strategy, shall raise an Alert warning to the user about the potential lack of effectiveness of the invention method mitigation. An embodiment of the invention method is described in the following with reference to Fig. 1. Block 1 S4 and σΦ are streamed from a network of static GNSS receivers associated with a specific ROI with an update Jacobacci & Partners / ANP rate that could be variable from 1 s up to (e.g. 10) minutes. The S4 and σΦare defined as: (1a) (1b) wherein SI is the detrended signal intensity and Φ is the detrended phase and < … > denotes an ensemble running average on a time window of 1 minute or less (Fremouw et al. 1978). S4 and σΦcan optionally provide the proper inputs to the “Scintillation parameters forecasting” module (Block 4, which is described in patent application WO2016185500A1) in those cases in which forecasting is necessary, depending on the application requirements and on the update rate of the S4 and σΦstreaming. Whenever the updates are too distant from each other, forecasting can be used. Block 2 One or more rover receivers providing their position (according to National Marine Electronic Association, NMEA, or other protocols) to be used for the computation of the estimated S4 and σΦ of the rover receiver- satellite links (Block 5) and for the ROI selection (Block 3) . Jacobacci & Partners / ANP Block 3 It selects the appropriate ROI with reference to the rover position provided by Block 2. The following conditions must be satisfied: Latmin (ROI) < Latrov(t) <Latmax (ROI) Longmin (ROI)< Longrov(t) < Longmax (ROI) (3) Where Latrov(t) and Longrov(t) are the coordinates of the rover at time t and Latmin (ROI), Latmax (ROI), Longmin (ROI), Longmax (ROI) define the vertices of the given ROI. The vertices’ coordinates of the given ROI will be determined by the network of the static GNSS receivers within the ROI itself: Latmin (ROI)= minimum latitude among the static GNSS receivers within the ROI Latmax (ROI)= maximum latitude among the static GNSS receivers within the ROI Longmin (ROI)= minimum longitude among the static GNSS receivers within the ROI Longmax(ROI)= maximum longitude among the static GNSS receivers within the ROI When the condition (2) or (3) or both are no more satisfied, Block 3 selects an adjacent ROI served by a different network of GNSS receivers. The new ROI could have some stations in common with the previous ROI. Then the network of static GNSS receivers falling in the new Jacobacci & Partners / ANP ROI is updated and such information is sent to Block 1 in order to provide the updated set of S4 andσφvalues to be used for the calculation of the weights in the new ROI (Block 4,5,6). Ideally, Block 3 allows the method to be applied to the entire global GNSS network by partitioning the global surface in multiple subsets of ROI serving every rover within it. Figure 3 exemplifies the situation of the receivers and rovers. GNSS satellites 10 send their GNSS signals to static base receivers 20, through corresponding Ionospheric Pierce Points 50 in the Ionosphere layer 100, whereas rover 40 moving in the ROI area 210 has ionospheric Pierce Points 60. This holds for Fig. 2 as well, wherein only a GNSS satellite 10 is shown with a pierce point 15 whose elevation 30 is also shown with respect to Earth’s surface 200 and Earth center 250. Block 4 Forecasting of S4 and σΦaccording to e.g. the patented scintillation empirical short-term forecasting method (patent WO2016185500A1 “Method for forecasting ionosphere total electron content and / or scintillation parameters”), is optionally envisaged, depending on the application requirements and on the update rate of the S4 and σΦstreaming from the static GNSS network. The forecasted S4 and σΦ are then used to feed the interpolation module (Block 5), instead of S4 and σΦ“as is” (Block 1). Jacobacci & Partners / ANP Block 5 In block 5, the estimation of S4 and σΦ for any rover receiver-satellite links is performed using solely a regression model. For example, starting from S4=S4(elevation, azimuth) and σΦ=σΦ(elevation, azimuth) samples of the static GNSS receivers (“as is”-Block 1, or forecasted-Block 4) and applying the Gaussian Process Regression (GPR), (Rasmussen, C. E., & Williams, C. ,2006) with a specific set of pre-processing options, a regression model is obtained. Given latitude and longitude of the IPP (Fig. 2) of the rover receiver-satellite links, one estimates S4 and σΦfor each link. Any other method to estimate S4 and σΦ by regression, including interpolation functions, can be used without limiting the validity of the block as can be understood by those skilled in the art. Theestimated S4 and σΦare input to the module related to the satellite-receiver observables weight computation (Block 6). The application of a regression model approach to estimate the scintillation indices for each satellite- rover receiver link is different from the Phase Scintillation mapping proposed in US2019056505. While the latter focuses on the mapping of scintillation bubbles, here a completely different approach is proposed that allows to overcome the uncertainty in locating the bubbles irregularities causing scintillation and in following their spatial and Jacobacci & Partners / ANP temporal evolution. Moreover, the formation of scintillation bubbles occurs at low latitude whereas at high latitude the formation of patches, arcs, and blobs are expected to have strong negative impact on GNSS navigation and positioning (Crowley et al., 2000; Zernov et al., 2009; Spogli et al., 2013; De Franceschi et al., 2019). So, the application of a regression model approach makes the present invention fully independent from the geographical area where scintillation occurs and makes it applicable on a global basis. Block 5 is therefore performed without identifying scintillation regions in the ionosphere by any means. Furthermore, Block 6 is performed without using any analytical model of S4 and σΦ such as that of Conker et al., see above. Block 6 Block 6 deals with computing weights for GNSS observables (Pseudorange and Carrier phase) associated with each satellite-rover receiver link. This is typically to update the stochastic model in the Kalman filter included in the rover receiver PVT engine. This module can be performed as discussed below in a specific embodiment. Based on the state of the art (see, e.g., Chendong Li et al. ,2020), if both S4 and σφassume high values, this suggests the potential corruption of the observables along the link due to scintillation. Otherwise, if only S4 is high (particularly at low latitude), it could be Jacobacci & Partners / ANP due to multipath corruption, especially at low elevation. In the first case the weight calculation for the rover receiver observables is performed, otherwise the “a priori” weight is not updated. The weight calculation is done by a parametrized mitigation function applicated to the estimated S4 and σΦ(Block 5).According to the basic theory (Kevin P. Murphy, 2012), a mitigation function is based on a risk function (e.g. the risk that the data are corrupted by scintillation). The risk function is derived from a loss function. In this case the loss function is related to the loss of geometrical significance of the pseudorange and phase range measurements given by an error due to scintillation not modelled. For example, the 0-1 loss function can be defined for each k-th satellite-rover link as l(z;z_th)= {0,if z < z_th 1,otherwise (4) Where z is the measurable feature of interest (S4) and z_th a given threshold. Then the risk r(zth) can be defined as the probability that z exceeds z_th: r(z_th )= π ( z ≥ z_th ) (5) According to the present invention, the loss and risk functions can very advantageously coincide. In fact, in this case the probability that the S4 and σφ is lower or higher than a specific threshold is 1. Jacobacci & Partners / ANP According to the present invention, the risk function, used to generate weights for the satellite- rover receiver link, can be designed in a configurable and parametrizable way. It could be a very simple risk function, or it could consider the more complex classification of scintillation in weak, moderate, and strong. Moreover, it can be given by empirical fixed values associated with specific range of S4 and σφ. In general, for each k-th satellite-rover link, a risk function that considers the complex scintillation behavior looks as follows: Where: ^^^^Wherein the threshold is a configurable vector T=[^^1,^^2, …,^^^^] of scintillation indices and the vector r=[^^1,^^2, …,^^^^+1] is a configurable vector of empirical values associated to the specific ranges of S4 or σφ given by T. N is a configurable parameter depending on the geographic area and the related ionospheric dynamics. For example, in the case of a test of the invention method over Southern America, N has been empirically fixed at a value of 12 (see below). The general formulation of ^^^^is: Jacobacci & Partners / ANP and g is a generic increasing monotonic function over (0,1) with range (0,1). The weights for each satellite-rover receiver link are then given by: Where M is a given threshold for σΦ In a preferred embodiment, for I=S4 and N=2, the risk function is: 0^^^^ ^^4 < 0.5^^(^^4, ^^) = { ^^ (0.5) ^^^^ 0.5 ≤ ^^4 ≤1 1^^^^ ^^4 > 1Where T = [0.5, 1] for each respective satellite-rover receiver link and the specific function g is defined below: Wherein: Jacobacci & Partners / ANP^^ℎ^^ = 1α = 2.8γ = 0.4Having assumed that σΦ > ^^ where M is higher than 0.2radians. An example of risk table obtained by the method above is the following (for N=11): Range of S4 value Risk value 0-0.5 0 0.5-0.55 0.11 0.55-0.6 0.14 0.6-0.65 0.17 0.65-0.7 0.21 0.7-0.75 0.25 0.75-0.8 0.3 0.8-0.85 0.35 0.85-0.9 0.4 0.9-0.95 0.46 0.95-1 0.52 >1 1 In an application in South America, an ensuing mitigation has been obtained that is exemplified in the following table for some epochs: Epoch Solution 2D RMS Z RMS m M 13 / 01 / 202521:00 Mitig. 0.05 0.09 14 / 01 / 202504:00 Jacobacci & Partners / ANP Non Mitig. 0.07 0.11 18 / 01 / 202521:00 Mitig. 0.04 0.09 19 / 01 / 202504:00 Non Mitig. 0.15 0.16 26 / 01 / 202521:00 Mitig. 0.06 0.08 27 / 01 / 202504:00 Non Mitig. 0.14 0.33 In case of high latitude a preferred embodiment, for I=σΦand N=2 is given below. In this case the different thresholds are expressed in radians. The risk function can be expressed as in the following: <0.2≤ σφ ≤0.7 > 0.7Where T’ = [0.2, 0.7] for each respective satellite- rover receiver link and the specific function g is defined below: ^^ℎ^^ = 0.7k = 2An example of risk table obtained by the method above is the following (for N=11): Range of σΦ valueRisk value0-0.2 0 0.2-0.25 0.27 0.25-0.3 0.29 Jacobacci & Partners / ANP 0.3-0.35 0.31 0.35-0.4 0.33 0.4-0.45 0.35 0.45-0.5 0.38 0.5-0.55 0.40 0.55-0.6 0.43 0.6-0.65 0.45 0.65-0.7 0.48 >0.7 1 Finally, the module makes available the calculated weights directly to the rover receiver or to Service Providers who broadcast them through standard Network Transport RTCM via Internet Protocol, NTRIP, or other protocols, to update the a priori observables variance matrix, thus mitigating the impact on positioning of the observables corrupted by scintillation. Moreover: ^ An advantage of this approach is that the mitigation method is independent from the rover receiver characteristics. ^ The present method is valid on the global scale (low-middle-high latitude). ^ The present method is a (accurate) quantitative approach, since for any rover receiver-satellite link S4 and σΦvalues are estimated, not in area around the point or in a pixel of some grid in the sky but for that specific rover-receiver satellite link. ^ Estimated S4 and σΦvalues are used as input for Jacobacci & Partners / ANP the calculation of the weight matrix of the GNSS observables to properly de weight them in the PVT (Position, Velocity and Time) engine. ^ S4 and σΦare used properly both at low latitude and at high latitude. References WO 2016 / 185500 A1 (SPACEARTH TECH S R L [IT]) 24 November 2016 (2016-11-24), “Method for forecasting ionosphere total electron content and / or scintillation parameters” US 2019 / 056505 A1 (Morley Thomas [CA]) 21 February 2019 (2019-02-21) “System and method for generating a phase scintillation map utilized for de-weighting observations from GNSS satellites” Mannucci, A. J., B. D. Wilson, and C. D. Edwards (1993), A new method for monitoring the Earth ionosphere total electron content using the GPS global network paper presented at ION GPS 93, Inst. Of Navig., Salt Lake City, Utah Conker et al., RADIO SCIENCE, VOL. 38, NO. 1, 1001, doi:10.1029 / 2000RS002604, 2003 Chendong Li, Craig M. Hancock, Nicholas A.S. Hamm, Sreeja V. Veettil and Chong You (2012). Analysis of the relationship between Scintillation Parameters, Multipath and ROTI. Sensors 2020,20,2877;doi:10.3390 / s20102877 Crowley et al. (2000), Transformation of high- latitude ionospheric F region patches into blobs during the March 21, 1990, storm, JGR Space Physics, https: / / doi.org / 10.1029 / 1999JA900357 Jacobacci & Partners / ANP De Franceschi, G., et al. The ionospheric irregularities climatology over Svalbard from solar cycle 23. Sci Rep 9, 9232 (2019). https: / / doi.org / 10.1038 / s41598-019-44829-5 Fremouw, E. J., Leadabrand, R. L., Livingston, R. C., Cousins, M. D., Rino, C. L., Fair, B. C., & Long, R. A. (1978). Early results from the DNA Wideband satellite experiment—Complex-signal scintillation. Radio Science, 13(1), 167-187. Murphy Kevin P., “Machine Learning” MIT Press Ltd,2012 Rasmussen, C. E., & Williams, C. (2006). Gaussian processes for machine learning, the MIT press. Cambridge, MA, 32, 68. Spogli L. et al., GPS scintillations and total electron content climatology in the southern low, middle and high latitude regions, ANNALS OF GEOPHYSICS, 56, 2, 2013, R0220; doi:10.4401 / ag-6240 Zernov, N. N. et al. (2009), On the effects of scintillation of low-latitude bubbles on trans ionospheric paths of propagation, Radio Sci., 44, RS0A14, doi:10.1029 / 2008RS004074 List of abbreviations GNSS: Global Navigation Satellite System GPR: Gaussian Process Regression IPP: Ionospheric Pierce Point NMEA: National Marine Electronic Association PVT: Position, Velocity and Time ROI: Region of Interest Jacobacci & Partners / ANP In the foregoing, the preferred embodiments have been recognized, and variations of the present invention have been suggested, but it is to be understood that those skilled in the art will be able to make modifications and changes without thereby departing from the relevant scope of protection, as defined by the attached claims. Jacobacci & Partners / ANP

Claims

CLAIMS 1. Method for eliminating or mitigating the effect of ionospheric irregularities on GNSS positioning, comprising the execution of the following steps: A. obtaining (1) real-time scintillation parameters S4 and σΦ from a network of static GNSS receivers (20) linked to GNSS satellites (10) which provide GNSS signal; B. obtaining (2) a position from each of a plurality of rover receivers (40) linked to the GNSS satellites (10), the rover receivers (40) moving in a ROI (210) covered by the network of static GNSS receivers (10); C. estimating (5) S4 and σΦat a respective Ionospheric Pierce Point elevation and azimuth of each rover receiver-GNSS satellite link; D. computing (6) respective weights to be used to downweigh the GNSS signal in the respective satellite-rover receiver link, to eliminate or mitigate the impact of scintillation on the GNSS signal; E. sending the respective weights to the corresponding rover receivers (40); The method being characterized in that: - in step C the estimation is performed solely through a regression model based on data from Step A; - in step C the estimation is performed without identifying scintillation regions in the ionosphere. Jacobacci & Partners / ANP2. Method according to claim 1, wherein the regression model in step C is obtained based on S4 and σΦ as a function of Ionospheric Pierce Point latitude and longitude for a pre-defined single-layer ionosphere altitude for every satellite-static GNSS receiver link in the ROI, as obtained in step A.

3. Method according to claim 1 or 2, wherein the regression model in step C is obtained based on Gaussian Process Regression.

4. Method according to any one claim 1 to 3, wherein in step D the weights are calculated through a parametrized mitigation function based on a risk function which is derived from a loss function for the respective GNSS satellite-rover receiver link.

5. Method according to claim 4, wherein the loss and risk functions are coincident.

6. Method according to claim 5, wherein the risk function is: ^^2^^^^Wherein: ^^ = ^^4 or ^^ = σΦJacobacci & Partners / ANPT=[^^1,^^2, …,^^^^] is a N-dimensional vector of thresholds for I, and wherein ^^^^is: ^^and g is an increasing monotonic function over range (0,1), wherein the weights for each GNSS satellite-rover receiver link are given by: ^^Wherein M is a pre-defined threshold for σΦwhere M is higher than 0.2 radians.

7. Method according to claim 6, wherein, for I=S4 and N=2, the risk function is: 0^^^^ ^^4 < 0.5^^(^^4, ^^) = { ^^ (0.5) ^^^^ 0.5 ≤ ^^4 ≤1 1^^^^ ^^4 > 1Wherein T = [0.5, 1] for each respective satellite-rover receiver link and: Jacobacci & Partners / ANPWherein: ^^ℎ^^ = 1α = 2.8γ = 0.

48. Method according to claim 6 or 7, wherein, for I=σΦexpressed in radians, and N=2, the risk function is: ^^^^ σΦ < 0.2^^^^ 0.2 ≤ σΦ ≤0.7^^^^ σΦ > 0.7Wherein T’ = [0.2, 0.7] for each respective satellite- rover receiver link and the specific function g is defined as:^^ℎ^^ = 0.7<sub>k = 29. Method according to any one claim 1 to 7, wherein in step E the calculated weights are made available directly to the rover receiver (40) or to a Service Provider which broadcasts them through standard NTRIP or other protocols, to update an a-priori observables variance matrix mitigating the impact on positioning of the observables corrupted by scintillation. Jacobacci & Partners / ANP10. Method according to any one claim 1 to 9, wherein in step B the ROI is first selected and then the following sub-steps are performed: ^ defining the coordinates of vertices of the selected ROI; ^ checking the rover position within the ROI area vertices’ coordinates: ^ if the checking is not satisfied, selecting an adjacent ROI served by a different network of static GNSS receivers; ^ updating the static GNSS receiver network with said different network of static GNSS receivers in step A, and the ROI in step B.

11. Method according to any one claim 1 to 10, wherein in step A real-time S4 and σΦ are obtained from the network of static GNSS receivers with an update rate ranging between 1 s up to 10 minutes.

12. Method according to claim 11, wherein in a time interval between two consecutive updates, S4 and σΦ are obtained through the following step: F. forecasting (4) scintillation parameters S4 and σΦ based on scintillation parameters of step A.

13. System for eliminating or mitigating the effect of ionospheric irregularities on GNSS positioning, comprising: ^ a network of static GNSS receivers (20) linked Jacobacci & Partners / ANPto GNSS satellites (10) configured to provide GNSS signal, wherein the static GNSS receivers are configured to provide real-time scintillation parameters S4 and σΦ; ^ a plurality of rover receivers (40) linked to the GNSS satellites (10), the rover receivers (40) being configured to move in a ROI (210) covered by the network of static GNSS receivers (10); ^ a server configured to obtain a position from each of the rovers in the plurality of rover receivers (40) and the real-time scintillation parameters S4 and σΦ from the network of static GNSS receivers (20), the server being further configured to: ^ estimate (5) S4 and σΦat a respective Ionospheric Pierce Point latitude and longitude of each rover receiver-GNSS satellite link; ^ compute (6) respective weights to be used to downweigh the GNSS signal in the respective satellite-rover receiver link, to eliminate or mitigate the impact of scintillation on the GNSS signal; ^ Send the respective weights to the corresponding rover receivers (40); The system being characterized in that the server is further configured to: - estimate S4 and σΦsolely through a regression model based on the real-time scintillation parameters S4 and σΦ; Jacobacci & Partners / ANP- estimate S4 and σΦwithout identifying scintillation regions in the ionosphere. Jacobacci & Partners / ANP

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