BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sergey P. Tsarev (Siberian Federal University\, Krasnoyarsk\, Russ ia) DTSTART:20200617T110000Z DTEND:20200617T120000Z DTSTAMP:20260423T005839Z UID:mmandim/4 DESCRIPTION:Title: Free interpolation of GLONASS/GPS orbits: solving a two-point boundary-val ue problem without solving differential equations\nby Sergey P. Tsarev (Siberian Federal University\, Krasnoyarsk\, Russia) as part of Mathemati cal models and integration methods\n\n\nAbstract\nThis talk will give a to tally different view to the problem addressed in my previous talk\n\n"Disc rete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters". \n\nUsing a sort of adaptive filtering we solve t he problem of boundary attenuation effects of polynomial filters. The tech niques we use may be classified as (elementary) machine learning.\n\nAnoth er facet of the GNSS (Global Navigation Satellite Systems) theory and prac tice exposed in this talk is the problem of interpolation of positions of GNSS satellites.\nUsing the data from IGS (International GNSS Service) as an example\, we demonstrate a simple but unexpectedly effective technique that allows interpolation of the positions of GPS and GLONASS satellites w ith an accuracy of a few millimeters. It is natural to call the described interpolation technique "free" since it is not related to polynomials\, no r trigonometric and other functions commonly used in standard interpolatio n techniques.\n\nThe free interpolation technique also allows developing m uch more accurate (nevertheless very simple) models of media that are impo rtant in the operation of space navigation systems: the ionosphere\, tropo sphere\, etc.\n\nThe basis for the development of this method is Big Data\ , accumulated over many years of operation of satellite navigation systems . We will discuss some common problems of the Big Data we use. The followi ng conclusion turned out to be paradoxical\, but real: the main problem wh en working with big data is that there are too few of them...\n\nThis talk is a modified version of my Russian language talk given in 2018:\nhttp:// www.mathnet.ru/php/presentation.phtml?&presentid=24129&option_lang=eng\n\n Paper references:\n\n1. Pustoshilov\, A. S.\, & Tsarev\, S. P. (2017). Uni versal coefficients for precise interpolation of GNSS orbits from final IG S SP3 data. In 2017 International Siberian Conference on Control and Commu nications (SIBCON) (pp. 1-6). IEEE. https://ieeexplore.ieee.org/abstract/d ocument/7998463\n\n2. Pustoshilov\, A. S.\, & Tsarev\, S. P. (2018). Two-p oint free nonlinear interpolation of coordinates and velocities of navigat ion satellites from SP3 data. (in Russian) Achievements of Modern Radioele ctronics / №12 - 2018 http://www.radiotec.ru/article/22602#english\n\n3. Tsarev\, S. P.\, Denisenko\, V. V.\, & Valikhanov\, M. M. (2018). Multidi mensional free interpolation framework for high-precision modeling of slan t total electron contents in mid-latitude and equatorial regions. http://e lib.sfu-kras.ru/handle/2311/109067?locale-attribute=en\n\nZoom link: \nhtt ps://us04web.zoom.us/j/2084211239?pwd=bzZoZFF0RFl6TzBBZ2hHa3pZS0prQT09\n LOCATION:https://researchseminars.org/talk/mmandim/4/ END:VEVENT END:VCALENDAR