Nonstationary Smoothing and Prediction Using Network Theory Concepts

Nonstationary signal and noise statistics are assumed, such that ensembles with the same covariances can be generated by passing white noise through finite networks of linear, time-variable, positive elements. Linear least-squares smoothing and prediction operations are to be found. This paper may be regarded as an extension, to nonstationary systems, of methods applied to stationary systems by Bode and Shannon, using primarily circuit theory concepts. Analogous results are obtained by examining analogous operations in frequency domain, and differential equations terms.