Joint iterative state and parameter estimation for bilinear systems with autoregressive noises via the data filtering

This paper proposes a novel iterative algorithm for the joint state and parameter estimation of bilinear state–space systems disturbed by colored noise. Estimating the states and parameters of such systems is challenging due to their nonlinearity and greater number of parameters compared to linear systems. Our method is to modify the Kalman filtering appropriately to estimate the unknown states of bilinear systems. Once the unknown states are estimated, we develop the Kalman filtering-based multi-innovation gradient-based iterative (KF-MIGI) algorithm for parameter estimation. To further improve estimation accuracy and cope with colored noises, we introduce a data filtering-based KF-MIGI algorithm that uses an adaptive filter to filter input–output data. Additionally, we compare the gradient-based iterative algorithm and the stochastic gradient algorithm. The effectiveness of the proposed algorithm is demonstrated through numerical examples.