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 st...

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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0890-6327
1099-1115
DOI:10.1002/acs.3657