A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise

Xiao Zhang,Ahmed Alsaedi,Tasawar Hayat,Ling Xu,Feng Ding

doi:10.3390/math7040356

Xiao Zhang, Ahmed Alsaedi + Show 3 more

Open Access

https://doi.org/10.3390/math7040356

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Abstract

This paper is concerned with the joint state and parameter estimation methods for a bilinear system in the state space form, which is disturbed by additive noise. In order to overcome the difficulty that the model contains the product term of the system input and states, we make use of the hierarchical identification principle to present new methods for estimating the system parameters and states interactively. The unknown states are first estimated via a bilinear state estimator on the basis of the Kalman filtering algorithm. Then, a state estimator-based recursive generalized least squares (RGLS) algorithm is formulated according to the least squares principle. To improve the parameter estimation accuracy, we introduce the data filtering technique to derive a data filtering-based two-stage RGLS algorithm. The simulation example indicates the efficiency of the proposed algorithms.

Highlights

Nonlinear systems widely exist in practical industrial processes
In order to improve the recursive generalized least squares (RGLS) parameter estimation accuracy, the section will construct a linear filter to filter the experimental data for estimating the system parameters
This paper presents a recursive parameter and state estimation algorithm on the basis of the hierarchical identification principle for bilinear systems

Summary

Introduction

Nonlinear systems widely exist in practical industrial processes. Employing mathematical models of these processes becomes increasingly significant in system analysis [1,2,3], system control [4,5,6] and signal processing [7,8,9,10], so it is necessary to find efficient methods for system modeling [11,12,13]. Stroud et al proposed a Bayesian method for the joint state and parameter estimation of state space models with additive Gaussian noise using the ensemble Kalman filter [47]. Li and Liu derived the input-output representation of the bilinear system through eliminating the state variables and proposed the filtering-based least squares iterative algorithm [51]. This paper presents a bilinear state estimator based on the Kalman filtering algorithm for computing the unknown states. We derive a state estimator-based RGLS algorithm for joint state and parameter estimation of bilinear state space models on the basis of the hierarchical identification principle.

System Description

The RGLS Algorithm Using the Bilinear State Estimates

The F-TS-RGLS Algorithm Using the Bilinear State Estimator

Numerical Example

Conclusions

Methods