State-space modal representations for decomposition of multivariate non-stationary signals

Abstract

Abstract This work introduces a parametric modal decomposition method for multivariate non-stationary signals based on a block-diagonal time-dependent state space representation and Kalman filtering/smoothing. Each second-order block is constructed with the real and imaginary parts of each mode instantaneous eigenvalues, and thus represents a single non-stationary oscillatory component. The identification of the state/parameter trajectories and the hyperparameters, constituted by the mode mixing matrix, the state, parameter and noise covariances, and initial conditions, is accomplished with a tailored Expectation-Maximization algorithm. The methodology is evaluated in a numerical example, concerning a multivariate signal with three modal components, featuring mode crossings and vanishing amplitudes. Codes and examples are available on https://github.com/ldavendanov/NS-modal-decomposition .