Expectation-maximization Estimation Algorithm for Bilinear State-space Systems with Missing Outputs Using Kalman Smoother

In this paper, the parameter estimation of bilinear state-space systems with missing outputs is studied. The bilinear model is transformed into a linear time-varying state-space model, and Kalman smoother with a time-varying gain is adopted to estimate missing outputs and unmeasurable states. Under the expectation-maximization (EM) algorithm scheme, an iterative estimation algorithm based on Kalman smoother is derived, in which the unknown parameters, missing outputs, and unmeasurable states can be estimated simultaneously. Two simulation examples, including a numerical example and a three-tank system experiment, are adopted to verify the effectiveness of the proposed algorithm.