Simultaneous state and parameter estimation: the role of sensitivity analysis

TL;DR

This paper explores how sensitivity analysis can improve simultaneous state and parameter estimation in systems where the augmented model is not fully observable, proposing a new MHE approach and demonstrating its effectiveness through simulations.

Contribution

It introduces a novel method using sensitivity analysis for variable selection in non-observable augmented systems and integrates it into a moving horizon estimation framework.

Findings

Sensitivity analysis relates to system observability.

The proposed method enhances estimation accuracy.

Simulations confirm the approach's efficiency.

Abstract

State and parameter estimation is essential for process monitoring and control. Observability plays an important role in both state and parameter estimation. In simultaneous state and parameter estimation, the parameters are often augmented as extra states of the original system. When the augmented system is observable, various existing state estimation approaches may be used to estimate the states and parameters simultaneously. However, when the augmented system is not observable, how we should proceed to maximally extract the information contained in the measured outputs is not clear. This paper concerns about simultaneous state and parameter estimation when the augmented system is not fully observable. Specifically, we first show how sensitivity analysis is related to observability of a dynamical system, and then illustrate how it may be used to select variables for simultaneous estimation. We also propose a moving horizon state estimation (MHE) design that can use the variable selection results in a natural way. Extensive simulations are carried out to show the efficiency of the proposed approach.