State-Space Model and Kalman Filter Gain Identification by a Kalman Filter of a Kalman Filter

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Minh Q. Phan ◽  
Francesco Vicario ◽  
Richard W. Longman ◽  
Raimondo Betti
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
State Space ◽  
Kalman Filters ◽  
State Space Model ◽  
Model Structure ◽  
System State ◽  
Input Output ◽  
Output Data ◽  
Space Model

This paper describes an algorithm that identifies a state-space model and an associated steady-state Kalman filter gain from noise-corrupted input–output data. The model structure involves two Kalman filters where a second Kalman filter accounts for the error in the estimated residual of the first Kalman filter. Both Kalman filter gains and the system state-space model are identified simultaneously. Knowledge of the noise covariances is not required.

Improvement of Observer/Kalman Filter Identification (OKID) by Residual Whitening

1995 ◽  
Vol 117 (2) ◽  
pp. 232-239 ◽  
Author(s):  
M. Phan ◽  
L. G. Horta ◽  
J.-N. Juang ◽  
R. W. Longman
Keyword(s):  
Kalman Filter ◽  
Linear System ◽  
State Space ◽  
Moving Average ◽  
State Space Model ◽  
Input Output ◽  
Output Data ◽  
Space Model ◽  
Auto Regressive ◽  
Average Description

This paper presents a time-domain method to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data. The identified filter has the properties that its residual is minimized in the least squares sense, orthogonal to the time-shifted versions of itself, and to the given input-output data sequences. The connection between the state space model and a particular auto-regressive moving average description of a linear system is made in terms of the Kalman filter and a deadbeat gain matrix. The procedure first identifies the Markov parameters of an observer system, from which a state space model of the system and the filter gain are computed. The developed procedure is shown to improve results obtained by an existing observer/Kalman filter identification method, which is based on an auto-regressive model without the moving average terms. Numerical and experimental results are presented to illustrate the proposed method.

Improved State-Space Model Identification Using Input and Output Data with Steady State Values

2004 ◽  
Vol 37 (11) ◽  
pp. 215-220
Author(s):  
Manabu Kosaka ◽  
Hiroshi Uda ◽  
Eiichi Bamba ◽  
Hiroshi Shibata
Keyword(s):  
Steady State ◽  
State Space ◽  
State Space Model ◽  
Model Identification ◽  
Output Data ◽  
Space Model ◽  
Input And Output

State-space Model Identification Using Input and Output Data With Steady State Values Zeroing Multiple Integrals of Output Error

2005 ◽  
Vol 128 (3) ◽  
pp. 746-749
Author(s):  
Manabu Kosaka ◽  
Hiroshi Uda ◽  
Eiichi Bamba ◽  
Hiroshi Shibata
Keyword(s):  
Steady State ◽  
System Identification ◽  
State Space ◽  
State Space Model ◽  
Hankel Matrix ◽  
Output Data ◽  
Single Input Single Output ◽  
Space Model ◽  
Output Error ◽  
Input And Output

This study proposes a new deterministic off-line identification method that obtains a state-space model using input and output data with steady state values. This method comprises of two methods: Zeroing the 0∼N-tuple integral values of the output error of single-input single-output transfer function model (Kosaka et al., 2004) and Ho-Kalman’s method (Zeiger and McEwen, 1974). Herein, we present a new method to derive a matrix similar to the Hankel matrix using multi-input and multi-output data with steady state values. State space matrices A, B, C, and D are derived from the matrix by the method shown in Zeiger and McEwen, 1974 and Longman and Juang, 1989. This method’s utility is that the derived state-space model is emphasized in the low frequency range under certain conditions. Its salient feature is that this method can identify use of step responses; consequently, it is suitable for linear mechanical system identification in which noise and vibration are unacceptable. Numerical simulations of multi-input multi-output system identification are illustrated.

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