Least square algorithm based on bias compensated principle for parameter estimation of canonical state space model

Author:

Liu Longlong1,Long Zhen1,Azar Ahmad Taher23,Zhu Quanmin4,Ibraheem Ibraheem Kasim5ORCID,Humaidi Amjad J6ORCID

Affiliation:

1. School of Mathematical Sciences, Ocean University of China, Qingdao, China

2. College of Computer and Information Sciences, Prince Sultan University, Riyadh, Saudi Arabia

3. Faculty of Computers and Artificial Intelligence, Benha University, Benha, Egypt

4. Department of Engineering Design and Mathematics, University of the West of England, Bristol, UK

5. Department of Computer Techniques Engineering, Dijlah University College, Baghdad, Iraq

6. Control and Systems Engineering Department, University of Technology, Baghdad, Iraq

Abstract

Due to the existence of system noise and unknown state variables, it is difficult to realize unbiased estimation with minimum variance for the parameter estimation of canonical state space model. This paper presents a new least squares estimator based on bias compensation principle to solve this problem, transforms canonical state space into the form suitable for the least square algorithm, introduces an augmented parameter vector and an auxiliary variable, derives parameter estimation formula based on noise compensation, realizes the unbiased estimation, and gives the specific algorithm. A simulation example is provided to verify the effectiveness of the estimator.

Publisher

SAGE Publications

Subject

Applied Mathematics,Control and Optimization,Instrumentation

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