A Novel Method of Ionospheric Inversion Based on Horizontal Constraint and Empirical Orthogonal Function

Abstract

Tomographic inversion of the ionosphere is a rank-deficient problem. To overcome the above problem, an algebraic reconstruction technique (ART) based on adaptive horizontal constraint and empirical orthogonal function (ARTHCEOF) is proposed. The new algorithm avoids the difficulty of vertically constrained matrix construction and resolves the description of the ionospheric vertical structure by using EOF. To confirm the feasibility and validate the ascendancy of the ARTHCEOF, three algorithms are first tested by using the emulated scheme. The test results show that the ARTHCEOF surpasses the ART and the ART based on the horizontal constraint (ARTHC) in both the inversion accuracy and computational efficiency. Finally, the ARTHCEOF method is applied to invert electron density values using the GNSS measurements during different geomagnetic activities. The tomographic images validate that the ARTHCEOF can reflect ionospheric daily changes in the European region. The altitudinal profiles in a fixed location are illustrated according to the inversion results of ARTHCEOF. Compared with the profiles recorded by the ionosonde station, the altitudinal profiles of ARTHCEOF have a good consistency. In the meantime, the VTEC values are inverted using the CIT results. The differential VTEC values are calculated by means of the inverted VTEC values and ionospheric products of CODE. The differential results further identify the dependability of ARTHCEOF.