Dealing with State Estimation in Fractional-Order Systems under Artifacts

TL;DR

This paper addresses the challenge of accurately estimating states in fractional-order systems affected by artifacts, proposing conditions and algorithms validated with real EEG data.

Contribution

It introduces necessary and sufficient conditions for state estimation in fractional-order systems with artifacts and provides a practical estimation algorithm.

Findings

Conditions for successful state recovery are established.

An algorithm for state estimation under artifacts is developed.

Validation with real EEG data demonstrates effectiveness.

Abstract

Fractional-order dynamical systems are used to describe processes that exhibit long-term memory with power-law dependence. Notable examples include complex neurophysiological signals such as electroencephalogram (EEG) and blood-oxygen-level dependent (BOLD) signals. When analyzing different neurophysiological signals and other signals with different origin (for example, biological systems), we often find the presence of artifacts, that is, recorded activity that is due to external causes and does not have its origins in the system of interest. In this paper, we consider the problem of estimating the states of a discrete-time fractional-order dynamical system when there are artifacts present in some of the sensor measurements. Specifically, we provide necessary and sufficient conditions that ensure we can retrieve the system states even in the presence of artifacts. We provide a state estimation algorithm that can estimate the states of the system in the presence of artifacts. Finally, we present illustrative examples of our main results using real EEG data.