[G06-3] Ionosphere and space weather I

[G06-3-04] The optimal regularization (alpha-weighted BLE via A-optimal design) and its application in GNSS-based ionospheric tomography

^○Jianqing Cai¹, Kun Qian¹, Nico Sneeuw¹, Cheng Wang², Jiexian Wang³ (1.University of Stuttgart, Stuttgart, Germany, 2.Wuhan University, Wuhan, China, 3.Tongji University, Shanghai, China)

In this talk the optimal uniform Tykhonov-Phillips regularization (alpha-weighted BLE) by A-optimal design (minimizing the trace of the Mean Square Error matrix MSE) is reviewed. The determination of optimal regularization parameter via A-optimal design is introduced and its comparison with the results derived by numerical heuristic methods, such as by means of L-Curve, GCV and ridge trace is also performed. In which the A-optimal design regularization parameter has been shown to have minimum trace of MSE and its calculation has better efficiency.

In the reconstruction of ionospheric tomography based on the GNSS observations, geometrical limitations (no horizontal ray path, incomplete viewing angles, a limited number of receiving stations, etc.) of the data acquisition system cause the available data insufficient for ideal reconstruction tomography, which makes ionospheric tomographic reconstruction an ill-posed problem. In order to overcome the non-uniqueness of ionospheric tomographic reconstruction, many algorithms have been developed. For example, several kind of regularization algorithms have been applied in solving this kind of ill-posed problem. In these applications how to determinate an optimal regularization parameter is remaining an open problem. As a case study here the A-optimal design regularization will be implemented in solving the ill-posed problem of GNSS-based ionospheric tomographic reconstruction. The reconstruction results will be also analyzed and discussed in the sense of optimal and efficient aspects.