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

Abstract

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.