Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

Abstract

Summary The combined iterative parameter and state estimation problem is considered for bilinear state‐space systems with moving average noise in this paper. There are the product terms of state variables and control variables in bilinear systems, which makes it difficult for the parameter and state estimation. By designing a bilinear state estimator based on the Kalman filtering, the states are estimated using the input‐output data. Furthermore, a moving data window (MDW) is introduced, which can update the dynamical data by removing the oldest data and adding the newest measurement data. A state estimator‐based MDW gradient‐based iterative (MDW‐GI) algorithm is proposed to estimate the unknown states and parameters jointly. Moreover, given the extended gradient‐based iterative (EGI) algorithm as a comparison, the MDW‐GI algorithm can reduce the impact of noise to parameter estimation and improve the parameter estimation accuracy. The numerical simulation examples validate the effectiveness of the proposed algorithm.

Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

“…As the number of iterations increases, the parameter estimates are updated. 29 Based on the hierarchical principle, the identification model is decomposed into three sub-models with smaller dimensions and fewer variables. The 3S-LSI algorithm is presented to estimate the system parameters.…”

“…The iterative method can process a batch of sampled data at each iteration. As the number of iterations increases, the parameter estimates are updated 29 . Based on the hierarchical principle, the identification model is decomposed into three sub‐models with smaller dimensions and fewer variables.…”

Variational Bayesian identification for bilinear state space models with Markov‐switching time delays

“…Combining (8) and (9), the regressive identification model of the bilinear state space system can be represented as…”

“…For example, Liu et al derived the moving data window gradient-based iterative algorithm of combined parameter and state estimation for bilinear system. 9 Verdult et al combined the subspace technique and separable least square optimization method to realize the identification for the bilinear state space system with multiple inputs and multiple outputs. 10 Zhang et al derived a state filtering-based forgetting factor recursive least square algorithm for bilinear system.…”

“…Many research studies have been studied in the parameter estimation of bilinear state space systems. For example, Liu et al derived the moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear system 9 . Verdult et al combined the subspace technique and separable least square optimization method to realize the identification for the bilinear state space system with multiple inputs and multiple outputs 10 .…”