Error Reduction of Parametric Auto Regressive Moving Average Estimation Algorithm to Reach Optimal Point
Keywords:
Estimation error, Cumulative noise, Optimum error point
Abstract
In the linear and nonlinear multi-input and multi-output systems, there are several methods for identifying and estimating system parameters. The method of detecting system parameters in a simulated autocorrelated system with a minimized error between the target data and output results is affected by noise. After adding the summed noise to the input data, the system coefficients are determined in the least-squares algorithm. The trend of system error changes decreases with increasing number of input samples. However, it does not mean that the estimation error decreases by increasing iteration during an increasing trend; where, the number of samples given to the system in order to obtain a specific error does not decrease with increasing number of replications. In addition, reducing the estimation error of the system is dependent on the input data more than the data replication.
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[7] L. Xiang, L. Xie, Y. Liao, and R. Ding, "Hierarchical least squares algorithms for single-input multiple-output systems based on the auxiliary model," Mathematical and Computer Modelling, vol. 52, no. 5, pp. 918-924, 2010/09/01/ 2010.
[8] F. Ding, P. X. Liu, and G. Liu, "Gradient based and least-squares based iterative identification methods for OE and OEMA systems," Digital Signal Processing, vol. 20, no. 3, pp. 664-677, 2010/05/01/ 2010.
[9] X. Liu and J. Lu, "Least squares based iterative identification for a class of multirate systems," Automatica, vol. 46, no. 3, pp. 549-554, 2010/03/01/ 2010.
[10] Y. Liu, D. Wang, and F. Ding, "Least squares based iterative algorithms for identifying Box–Jenkins models with finite measurement data," Digital Signal Processing, vol. 20, no. 5, pp. 1458-1467, 2010/09/01/ 2010.
[11] D. Wang, G. Yang, and R. Ding, "Gradient-based iterative parameter estimation for Box–Jenkins systems," Computers & Mathematics with Applications, vol. 60, no. 5, pp. 1200-1208, 2010/09/01/ 2010.
[12] A.-G. Wu, X. Zeng, G.-R. Duan, and W.-J. Wu, "Iterative solutions to the extended Sylvester-conjugate matrix equations," Applied Mathematics and Computation, vol. 217, no. 1, pp. 130-142, 2010/09/01/ 2010.
[13] M. S. Aslam, "Comments on “Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems”," Signal Processing, vol. 117, pp. 279-280, 2015/12/01/ 2015.
[14] B. Huang and C. Ma, "An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations," Applied Mathematics and Computation, vol. 328, pp. 58-74, 2018/07/01/ 2018.
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[16] X. Sheng and W. Sun, "The relaxed gradient based iterative algorithm for solving matrix equations AiXBi=Fi," Computers & Mathematics with Applications, vol. 74, no. 3, pp. 597-604, 2017/08/01/ 2017.
Published
2020-03-01
How to Cite
Mozafari, A. H., & Yousefi, N. (2020). Error Reduction of Parametric Auto Regressive Moving Average Estimation Algorithm to Reach Optimal Point. Majlesi Journal of Mechatronic Systems, 9(1), 11-15. Retrieved from https://ms.majlesi.info/index.php/ms/article/view/421
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