A New Method for 2-D Moving Average Model Parameter Estimation

ABSTRACT

This paper presents a new method for the causal quarter-plane region of support two-dimensional (2-D) moving average (MA) model parameter estimation. The new approach is based on approximation of 2-D MA by the 2-D AR model. To achieve this aim, the corresponding relations are extended to a 2-D case and the related algorithm is presented. In this method, a 2-D series with the MA model has been approximated by a 2-D AR model with higher order and then the parameters of the AR model are estimated by the new method that is presented. Then the relation between the parameters of the 2-D AR and 2-D MA model is obtained and finally by using this relation, the parameters of the 2-D MA model are obtained. Since the proposed method does not involve complex and time consuming matrix computations, it is computationally efficient. The presented method also has good accuracy in standard deviation and mean value; a fact that has been shown by applying this method to a numerical example and presenting the results of simulation.

Keywords:

• Moving average model
• Parameter estimation
• Time series
• Two-dimensional

ACKNOWLEDGEMENT

We would like to thank Dr. Iman Zamani for a number of helpful suggestions and corrections of the manuscript in the preliminary version.

Additional information

Notes on contributors

Mahdi Zeinali

Mahdi Zeinali received the BS degree in control engineering from the Sahand University of Technology, Tabriz, Iran, in 2001 and his MSc degree in control engineering from Sharif University of Technology, Tehran, Iran, in 2004. He is currently working towards the PhD degree in the Control Systems Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran. He is the author of over seven research papers. His interests are in the area of multi-dimensional (M-D) systems, system identification, and digital signal processing.

E-mail: [email protected]

Masoud Shafiee

Masoud Shafiee received his BSc degree in mathematics in 1975, his MSc degree in mathematics and MSc degree in systems engineering from Wright State University, Dayton, Ohio, in 1980 and 1982, respectively, and his M.Sc. and Ph.D. degrees in electrical engineering from Louisiana State University, Baton Rouge, LA, in 1984 and 1987, respectively. Prof. M. Shafiee is currently a full professor in the Department of Electrical Engineering at Amirkabir University of Technology, Tehran, Iran. Also, he has joined the SIC Research Institute from 2014. He is the author of over 230 research papers and 13 books (as author) and 11 books (as translator). His research interests include multi-dimensional (M-D) system, singular systems, information and communications, robotics, and network stability.

E-mail: [email protected]