  For dynamical systems that can be modelled as asymptotically stable linear
systems forced by Gaussian noise, this paper develops methods to infer or
estimate their modes from observations in real time. The modes can be real or
complex. For a real mode, we wish to infer its damping rate and mode shape. For
a complex mode, we wish to infer its frequency, damping rate and (complex) mode
shape. Their amplitudes and correlations are encoded in a mode covariance
matrix. 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.
