System Identification for Linear Dynamics with Bilinear Observation Models: An Expectation–Maximization Approach

In this paper, we study the system identification problem for linear time-invariant dynamics with bilinear observation models. Accordingly, we consider a suitable parametric description for the system model and formulate the identification problem as estimating the parameters characterizing the mathematical representation of the system through input-output measurement data. To this end, we employ a probabilistic framework aiming to obtain the maximum likelihood estimates of the parameters. Accordingly, we propose utilizing the expectation-maximization approach to improve the tractability of the identification procedure. Through the numerical experiments, we verify the efficacy of the proposed scheme and demonstrate its performance.