  This paper proposes a novel Gaussian process approach to fault removal in
time-series data. Fault removal does not delete the faulty signal data but,
instead, massages the fault from the data. We assume that only one fault occurs
at any one time and model the signal by two separate non-parametric Gaussian
process models for both the physical phenomenon and the fault. In order to
facilitate fault removal we introduce the Markov Region Link kernel for
handling non-stationary Gaussian processes. This kernel is piece-wise
stationary but guarantees that functions generated by it and their derivatives
(when required) are everywhere continuous. We apply this kernel to the removal
of drift and bias errors in faulty sensor data and also to the recovery of EOG
artifact corrupted EEG signals.
