Expectation-maximization algorithm for bilinear state-space models with time-varying delays under non-Gaussian noise

In this paper, the parameter identification of bilinear state-space model (SSM) in the presence of random outliers and time-varying delays is investigated. Under the basis of the observable canonical form of the bilinear model, the system output can be written as a regressive form, and a bilinear state observer is applied to estimate the unknown states. To eliminate the influence of outliers and time-varying delays on parameter estimation, we employ the Student's t$$ t $$ distribution to deal with the measurement noise and use a first-order Markov chain to model the delays. In the framework of expectation-maximization (EM) algorithm, the unknown parameters, delays, noise variance, states and transition probability matrix can be estimated iteratively. A numerical simulation and a continuous stirred tank reactor (CSTR) process demonstrate that the proposed algorithm has good immunity against outliers and time-varying delays and offers good estimation accuracy for the bilinear SSM.