Non-linear estimation is easy

TL;DR

This paper introduces a novel numerical differentiation-based methodology within differential algebra for non-linear state estimation, enabling efficient online estimation and addressing related problems like fault diagnosis.

Contribution

It presents a new approach using differential algebra for non-linear estimation, allowing handling of derivatives of any order and improving online estimation capabilities.

Findings

Effective in academic examples with online estimation

Handles derivatives of any order

Demonstrates practical simulation results

Abstract

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.