Iterative learning of DFT-domain dynamical models subject to parameter variations

We present a DFT-domain expectation-maximization framework for maximum-likelihood learning of linear dynamical models. The expectation step takes the form of a diagonalized DFT-domain Kalman filter coupled with a fixed-lag smoother, which effectively traces the evolution of the hidden state for a given underlying dynamical model defined via its covariance parameters. The maximization step learns the covariance parameters of the dynamical model and specifically discerns itself from a conventional algorithm by yielding distinct outputs for each block within the lag interval. Hence, in our approach the reliance on a fixed-lag for expressing the complete data likelihood does not necessarily entail the traditional conjecture of stationarity for the system within the duration of the lag interval. The capability to account for possible non-stationarity further helps the devised algorithm to carry out optimal and mutually synergetic state estimation and model inference, which we comprehensively substantiate with the help of simulation results.