  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.
