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

• Published in: International journal of adaptive control and signal processing Vol. 37; no. 10; pp. 2706 - 2724
• Main Authors: Wang, Xinyue, Ma, Junxia, Xiong, Weili
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.10.2023
• Subjects: Algorithms; Canonical forms; Continuously stirred tank reactors; Markov chains; Mathematical models; Maximization; Noise measurement; Optimization; Outliers (statistics); Parameter estimation; Parameter identification; Random noise; State observers; Transition probabilities
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3657

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 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.