A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China
College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, China
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 356; https://doi.org/10.3390/math7040356
Received: 7 March 2019 / Revised: 31 March 2019 / Accepted: 8 April 2019 / Published: 17 April 2019
(This article belongs to the Section Engineering Mathematics)
This paper is concerned with the joint state and parameter estimation methods for a bilinear system in the state space form, which is disturbed by additive noise. In order to overcome the difficulty that the model contains the product term of the system input and states, we make use of the hierarchical identification principle to present new methods for estimating the system parameters and states interactively. The unknown states are first estimated via a bilinear state estimator on the basis of the Kalman filtering algorithm. Then, a state estimator-based recursive generalized least squares (RGLS) algorithm is formulated according to the least squares principle. To improve the parameter estimation accuracy, we introduce the data filtering technique to derive a data filtering-based two-stage RGLS algorithm. The simulation example indicates the efficiency of the proposed algorithms.