Free interpolation of GLONASS/GPS orbits: solving a two-point boundary-value problem without solving differential equations

Abstract: This talk will give a totally different view to the problem addressed in my previous talk

"Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters".

Using a sort of adaptive filtering we solve the problem of boundary attenuation effects of polynomial filters. The techniques we use may be classified as (elementary) machine learning.

Another facet of the GNSS (Global Navigation Satellite Systems) theory and practice exposed in this talk is the problem of interpolation of positions of GNSS satellites. Using 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 with an accuracy of a few millimeters. It is natural to call the described interpolation technique "free" since it is not related to polynomials, nor trigonometric and other functions commonly used in standard interpolation techniques.

The free interpolation technique also allows developing much more accurate (nevertheless very simple) models of media that are important in the operation of space navigation systems: the ionosphere, troposphere, etc.

The 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 following conclusion turned out to be paradoxical, but real: the main problem when working with big data is that there are too few of them...

This talk is a modified version of my Russian language talk given in 2018: www.mathnet.ru/php/presentation.phtml?&presentid=24129&option_lang=eng

Paper references:

1. Pustoshilov, A. S., & Tsarev, S. P. (2017). Universal coefficients for precise interpolation of GNSS orbits from final IGS SP3 data. In 2017 International Siberian Conference on Control and Communications (SIBCON) (pp. 1-6). IEEE. ieeexplore.ieee.org/abstract/document/7998463

2. Pustoshilov, A. S., & Tsarev, S. P. (2018). Two-point free nonlinear interpolation of coordinates and velocities of navigation satellites from SP3 data. (in Russian) Achievements of Modern Radioelectronics / №12 - 2018 www.radiotec.ru/article/22602#english

3. Tsarev, S. P., Denisenko, V. V., & Valikhanov, M. M. (2018). Multidimensional free interpolation framework for high-precision modeling of slant total electron contents in mid-latitude and equatorial regions. elib.sfu-kras.ru/handle/2311/109067?locale-attribute=en

Zoom link: us04web.zoom.us/j/2084211239?pwd=bzZoZFF0RFl6TzBBZ2hHa3pZS0prQT09

machine learningmathematical softwaresymbolic computationmathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemscomputational physicsdata analysis, statistics and probability

Audience: researchers in the topic

( slides | video )

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Mathematical models and integration methods

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