Kalman Filter for Linear Systems With Unknown Structural Parameters

This brief considers Kalman filter for linear systems with unknown structural parameters. We design a Bayesian parameter identification algorithm based on maximum likelihood (ML) criterion and expectation maximization (EM). Under the identification of structural parameter, we perform the Kalman filter to estimate the states. The Kalman filter and the parameter identification algorithm are interactive to estimate the states and the structural parameters. More specifically, first, we use EM algorithm together with Kalman smoother to estimate the structural parameters. Then, on the basis of results provided by the first step, we employ the classical Kalman filter to predict and update the states, which formulates the final proposed Kalman filter. Performance analysis and simulation results verify the presented filter.