Inference of modes for linear stochastic processes

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer their modes from observations in real time. The modes can be real or complex. For a real mode, we infer its damping rate, mode shape and amplitude. For a complex mode, we infer its frequency, damping rate, (complex) mode shape and (complex) amplitude. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of other applications are given.