Joint State and Parameter Estimation for the Fractional‐Order Wiener State Space System Based on the Kalman Filtering

ABSTRACT This paper mainly investigates the joint estimation of the parameters and states for the fractional‐order Wiener state space model. Based on the Kalman filter principle, a generalized recursive least squares algorithm with a forgetting factor is proposed. In addition, the filtering‐based generalized recursive least squares algorithm is presented, which reduces the influence of colored noise on the parameter estimation. A gradient identification algorithm is introduced to estimate the order of the fractional‐order. Under the persistent excitation conditions, the analysis indicates that the proposed parameter estimation algorithm can estimate the fractional‐order Wiener state space system. A simulation example is given to confirm that the proposed algorithms are effective.