Estimating the Statistics of Non-Uniform and Time-Varying Distributed Parameter Fluctuations in a Transmission Line

摘要: The problem of estimating the statistics of the distributed parameters of a transmission line which are random functions of time and spatial location is addressed in this paper. The main idea is to transform the spatial–temporal PDE (partial differential equation) problem into a purely temporal problem using spatial test functions and then apply first-order perturbation theory to express the random components of the line voltage and current as linear functional of the random distributed parameters. We then evaluate the line voltage and current statistical correlations in terms of the distributed parameters correlations. Simulation studies are carried out for variance estimation of the resistance per unit length, and appropriate results are obtained.