A modified observer/Kalman filter identification (OKID) algorithm employing output residuals

The observer/Kalman filter identification (OKID) is an algorithm widely used for the identification of state space models. The standard OKID algorithm involves the estimation of the Kalman filter and system Markov parameters, followed by the realization of a state space model of the system using the eigensystem realization algorithm (ERA). In this paper, a modified and conceptually simple version of the OKID algorithm, termed the residual-based observer/Kalman filter identification (ROKID), is proposed. The ROKID algorithm uses ordinary least square method twice to solve two linear regression problems yielding the Kalman filter residuals and the system Markov parameters, respectively. Finally, the ERA algorithm is used to obtain a state space model of the system. The efficacy of the proposed algorithm is examined and compared with the standard OKID algorithm and the recently proposed OKID with deterministic projection (OKID/DP) algorithm via a simulation example. The results show that the proposed algorithm outperforms the standard OKID algorithm. Although its performance is less than that of the OKID/DP algorithm, due to its simplicity, the proposed algorithm represents a useful tool for linear state space model identification.

[1]  Michel Verhaegen,et al.  Filtering and System Identification: Frontmatter , 2007 .

[2]  Richard W. Longman,et al.  Output‐only observer/Kalman filter identification (O3KID) , 2015 .

[3]  Richard W. Longman,et al.  Observer Kalman Filter Identification of Suspen-Dome , 2017 .

[4]  M. Chidambaram,et al.  Subspace Identification of Transfer Function Models for an Unstable Bioreactor , 2015 .

[5]  Esmaeil S. Nadimi,et al.  Observer Kalman filter identification and multiple-model adaptive estimation technique for classifying animal behaviour using wireless sensor networks , 2009 .

[6]  M. Phan,et al.  Identification of observer/Kalman filter Markov parameters: Theory and experiments , 1993 .

[7]  Wei Chen,et al.  Observer/Kalman Filter Identié cation for Online System Identié cation of Aircraft , 2003 .

[8]  S. Qin,et al.  Subspace identification with non-steady Kalman filter parameterization , 2014 .

[9]  Si-Zhao Joe Qin,et al.  An overview of subspace identification , 2006, Comput. Chem. Eng..

[10]  Leang-San Shieh,et al.  An improvement on the transient response of tracking for the sampled-data system based on an improved PD-type iterative learning control , 2014, J. Frankl. Inst..

[11]  Richard W. Longman,et al.  OKID via Output Residuals: A Converter from Stochastic to Deterministic System Identification , 2017 .

[12]  V. Verdult,et al.  Filtering and System Identification: A Least Squares Approach , 2007 .

[13]  Minh Q. Phan,et al.  Identification and Control of Mechanical Systems: Frontmatter , 2001 .

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

[15]  Minh Q. Phan,et al.  Identification and control of mechanical systems , 2001 .

[16]  Bart De Moor,et al.  Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .

[17]  Robert Sutton,et al.  Observer Kalman filter identification of an autonomous underwater vehicle , 2004 .

[18]  Paul M. J. Van den Hof,et al.  An indirect method for transfer function estimation from closed loop data , 1993, Autom..

[19]  Ajay Mahajan,et al.  Adaptive intelligent control of ionic polymer?metal composites , 2005 .

[20]  Richard W. Longman,et al.  Optimal bilinear observers for bilinear state-space models by interaction matrices , 2015, Int. J. Control.

[21]  Giorgio Picci,et al.  Subspace identification of closed loop systems by the orthogonal decomposition method , 2005, Autom..

[22]  Richard W. Longman,et al.  State-Space Model and Kalman Filter Gain Identification by a Kalman Filter of a Kalman Filter , 2018 .