Ionosphere Modelling using Spherical harmonics with in-equality constraints over IRNSS service area

The ionosphere is a part of the atmosphere composed of free electrons and ions. Due to its ionized character, it affects the propagation of the radio signals passing through it. Therefore, for a satellite navigation system, ionosphere error corrections are required to accurately determine the user's position. The Indian Regional Navigation Satellite System (IRNSS) is an independent, regional navigation system meant to provide user position for single frequency as well as dual frequency users. In order to reduce errors in the user position, IRNSS provides two types of ionospheric corrections: Grid based as well as ionosphere coefficient based on L5 frequency. Users are advised to use grid based correction as compared to the coefficient based correction since grid based corrections are more accurate than coefficient based. In IRNSS, kriging method is applied to generate an ionosphere grid at IRNSS service area. However, spherical harmonics based ionosphere grid data is also frequently used by researchers worldwide. These geo-statistical methods (kriging and spherical harmonics) are equally good for the reconstruction of the global ionosphere data. However, the superiority of any of the geo-statistical methods over the other geo-statistical methods for the reconstruction of regional ionosphere data has not been explored enough. Therefore, in this paper, we reconstructed the ionosphere map over the IRNSS service area using a spherical harmonics method. Since the IRNSS service area lies in the ionosphere equatorial anomaly region, we directly implement non-negative physical constraints of the ionosphere in our algorithm. Mathematically, an inequality-constrained least squares method is proposed by imposing non-negative inequality constraints in the areas to avoid negative vertical Total Electron Content (TEC) values. The proposed technique utilizes a priori information from the Global Ionosphere Maps (GIM) of the Center for Orbit Determination in Europe (CODE). The GIM map has been degraded randomly to compare our techniques for reconstruction of TEC maps.