Multi-Innovation Stochastic Gradient Parameter and State Estimation Algorithm for Dual-Rate State-Space Systems with d-Step Time Delay

Ya Gu,Jicheng Liu,Quanmin Zhu,Peiyi Zhu,Yongxin Chou

doi:10.1155/2020/6128697

Abstract

This paper presents a multi-innovation stochastic gradient parameter estimation algorithm for dual-rate sampled state-space systems with d-step time delay by the multi-innovation identification theory. Considering the stochastic disturbance in industrial process and using the gradient search, a multi-innovation stochastic gradient algorithm is proposed through expanding the scalar innovation into an innovation vector in order to obtain more accurate parameter estimates. The difficulty of identification is that the information vector in the identification model contains the unknown states. The proposed algorithm uses the state estimates of the observer instead of the state variables to realize the parameter estimation. The simulation results indicate that the proposed algorithm works well.

Highlights

Is paper studies identification problems of a dual-rate state-space model with d-step time delay. e main contributions of this paper are as follows. e input-output representation is derived from a canonical state-space model of the state-delay system for the identification through eliminating the state variables in the systems, to derive a joint parameter and state estimation algorithm by means of the multi-innovation identification theory and the state observer for reducing the computational burden and improving the parameter estimation accuracy and the convergence speed
For the system in (1) and (2), if the state vector x(k) is known, the system matrix/vector (A, b) is easy to identify. is paper considers the case that the state x(k) is completely unavailable. e objective is to propose new methods for jointly estimating the unknown states and parameters from the measurement data 􏼈u(k), y(k): k 1, 2, . . .􏼉 and to study the performance of the proposed methods
In order to improve the accuracy of the SG algorithm, we extend the SG algorithm and derive a multi-innovation stochastic gradient algorithm by expanding the innovation length

Summary

Introduction

Is paper studies identification problems of a dual-rate state-space model with d-step time delay. e main contributions of this paper are as follows. e input-output representation is derived from a canonical state-space model of the state-delay system for the identification through eliminating the state variables in the systems, to derive a joint parameter and state estimation algorithm by means of the multi-innovation identification theory and the state observer for reducing the computational burden and improving the parameter estimation accuracy and the convergence speed. Is paper studies identification problems of a dual-rate state-space model with d-step time delay.

Results

Conclusion