Modified Kalman filtering based multi-step-length gradient iterative algorithm for ARX models with random missing outputs

Abstract This study presents a modified Kalman filtering-based multi-step-length gradient iterative algorithm to identify ARX models with missing outputs. The Kalman filtering method is modified to enhance the estimation of unmeasurable outputs, laying the foundation for enabling the multi-step-length gradient iterative algorithm to update effectively the ARX model parameter estimation through the estimated outputs. Compared to the classical gradient iterative algorithm, this study improves the estimation accuracy of the missing outputs by introducing a modified Kalman filter, and the parameter estimation convergence rate by deriving a new multi-step-length formulation. To validate the framework and the algorithm developed, a series of bench tests were conducted with computational experiments. The simulated numerical results are consistent with the analytically derived results in terms of the feasibility and effectiveness of the proposed procedure.

[1]  Yuanjin Zheng,et al.  Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms , 2014, Syst. Control. Lett..

[2]  Yongtan Liu,et al.  Spectrum optimization via FFT-based conjugate gradient method for unimodular sequence design , 2018, Signal Process..

[3]  Guang-Ren Duan,et al.  Gradient based iterative algorithm for solving coupled matrix equations , 2009, Syst. Control. Lett..

[4]  Rajamani Doraiswami,et al.  Robust Kalman filter-based least squares identification of a multivariable system , 2018 .

[5]  Farhad Farokhi,et al.  On reconstructability of quadratic utility functions from the iterations in gradient methods , 2015, Autom..

[6]  F. Ding,et al.  Modified stochastic gradient identification algorithms with fast convergence rates , 2011 .

[7]  Feng Ding,et al.  Gradient Based Iterative Algorithms for Solving a Class of Matrix Equations , 2005, IEEE Trans. Autom. Control..

[8]  Feng Ding,et al.  Multi-step-length gradient iterative algorithm for equation-error type models , 2018, Syst. Control. Lett..

[9]  Biao Huang,et al.  State estimation incorporating infrequent, delayed and integral measurements , 2015, Autom..

[10]  Biao Huang,et al.  Variational Bayesian approach for ARX systems with missing observations and varying time-delays , 2018, Autom..

[11]  Xiaoping Liu,et al.  Auxiliary model-based interval-varying multi-innovation least squares identification for multivariable OE-like systems with scarce measurements , 2015 .

[12]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[13]  Huamin Zhang,et al.  New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation , 2017, J. Frankl. Inst..

[14]  Changfeng Ma,et al.  Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations , 2018, Appl. Math. Comput..

[15]  Wei Xing Zheng,et al.  Recursive Identification of Hammerstein Systems: Convergence Rate and Asymptotic Normality , 2017, IEEE Transactions on Automatic Control.

[16]  Ai-Guo Wu,et al.  An iterative algorithm for discrete periodic Lyapunov matrix equations , 2018, Autom..

[17]  Roberto Sanchis,et al.  Estimation in multisensor networked systems with scarce measurements and time varying delays , 2012, Syst. Control. Lett..

[18]  J. Chu,et al.  Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle , 2013 .

[19]  Lincheng Zhou,et al.  Gradient based iterative parameter identification for Wiener nonlinear systems , 2013 .

[20]  Ahmed Alsaedi,et al.  Gradient estimation algorithms for the parameter identification of bilinear systems using the auxiliary model , 2020, J. Comput. Appl. Math..