Full Newton method for inverse transmission line problems, utilising explicit second order derivatives

Abstract

The full Newton's method is considered as an optimisation approach to the inverse transmission line problem in the frequency-domain. For the sake of accuracy and computational efficiency, the gradient and the Hessian of the cost-functional, with respect to parameter functions in the L2-space, are derived explicitly by means of the adjoint transmission line problem and the first and second order Frechét differentials of the cost-functional. The numerical implementation, when reducing to a finite dimensional parameter space, and a regularisation technique for the resulting ill-conditioned Hessian matrix are presented. For the reconstruction of one or two parameters, the algorithm is tested on synthetic reflection data contaminated with gaussian noise. The algorithm is also tested on measured reflection data to reconstruct a piecewise constant shunt-capacitance. The generalisation to the three-dimensional inverse scattering problem for bianisotropic media is presented.