Gradient-Based Parameter Identification Algorithms for Observer Canonical State Space Systems Using State Estimates

Abstract

This paper considers the parameter identification problem of the state space observer canonical model for linear stochastic systems, and proposes a Kalman filterbased gradient iterative algorithm and an observer-based multi-innovation stochastic gradient algorithm. The fundamental idea is to replace the unmeasurable states in the information vector with the estimated states and to compute the states of the systems through the Kalman filter or the state observer using the previous parameter estimates. Examples are provided to confirm the effectiveness of the proposed algorithms.

Least square algorithm based on bias compensated principle for parameter estimation of canonical state space model

“…1 Therefore, the parameter estimation of the state space model has always been a research hotspot in control field. At present, the main methods to estimate the parameters of state space are subspace method, 2 Kalman filter method, 3,4 gradient search method, 5,6 least squares method, 7,8 etc.…”

A Multi-innovation Recursive Least Squares Algorithm with a Forgetting Factor for Hammerstein CAR Systems with Backlash

“…Since Ding et al introduced the multi-innovation identification idea into the parameter identification, the multi-innovation identification methods have been widely studied and used [8,30,33,51]. Recently, an auxiliary model-based multi-innovation extended stochastic gradient algorithm was proposed to identify output error systems with colored measurement noises [5]; an auxiliary model-based multi-innovation stochastic gradient algorithm was derived for the multi-input single-output systems [29]; and a multi-innovation stochastic gradient algorithm parameter estimation-based adaptive control scheme for discrete-time systems was presented [50].…”

Combined Parameter and State Estimation Algorithms for Multivariable Nonlinear Systems Using MIMO Wiener Models

“…Recently, much attention has been paid to blocksoriented state-space systems which have been successfully used for control algorithms, identification schemes, and signal filtering [30,31]. However, the parameter estimation has become more difficult because the blocks-oriented models not only include the unknown parameter of linear and nonlinear subsystems but also include the unmeasurable state variables [32][33][34][35]. In this framework, Wang and Ding proposed a recursive parameter and state estimation for Hammerstein state-space systems [36] and for Hammerstein-Wiener state-space systems [37], using the hierarchical principal; Wang et al [38] discussed an iterative identification algorithm Hammetstein state-space system, by combining the iterative least square and the hierarchical identification method.…”