Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

“…8 Hizir et al identified the bilinear systems through equivalent linear models. [17][18][19] The Kalman filter (KF) is considered as one of the most common state filtering methods for the linear state-space systems with Gaussian noise since the 1960s. 10 Parameter estimation methods and state filtering can be applied to many areas, 11,12 such as information fusion and fault diagnosis, 13,14 system modelling, 15,16 and signal processing.…”

Highly computationally efficient state filter based on the delta operator

“…Although the state estimation algorithm in (10)- (12) can be directly derived based on the Kalman filtering principle, the most remarkable problem is its heavy computational burden, especially for large-scale systems. Although the state estimation algorithm in (10)- (12) can be directly derived based on the Kalman filtering principle, the most remarkable problem is its heavy computational burden, especially for large-scale systems.…”

“…Time delays often exist in signal transmission and signal modeling [12][13][14][15][16] and control systems. [17][18][19] For example, in communication, the measurements are often obtained with time delay because of the transmission congestion; the communication networks between subsystems are often unreliable, which will introduce the communication delays.…”

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

“…10 Recently, Meng derived a least squares algorithm and a multi-innovation stochastic gradient (MISG) algorithm for bilinear systems based on the multi-innovation identification theory 11 ; based on the hierarchical identification principle, a hierarchical auxiliary model-based least squares iterative algorithm, a three-stage gradient-based iterative algorithm, and a three-stage least squares-based iterative algorithm are derived for identifying the parameters of bilinear systems 12,13 ; Li et al proposed an iterative algorithm for bilinear systems using the fixed point theory 14 ; for bilinear state space systems, Zhang et al studied a bilinear state observer-based multi-innovation extended stochastic gradient (BSO-MI-ESG) algorithm and a filtering-based BSO-MI-ESG algorithm for improving the identification accuracy 15 and developed a bilinear state observer (BSO)-based recursive least squares algorithm and a BSO-based hierarchical least squares algorithm for reducing the computation burden. [22][23][24] Based on the decomposition technique, the hierarchical identification principle can reduce the computational burden of the identification algorithm for large scale systems. 17 They have been applied to many areas.…”