  Gaussian Process (GP) regressions have proven to be a valuable tool to
predict disturbances and model mismatches and incorporate this information into
a Model Predictive Control (MPC) prediction. Unfortunately, the computational
complexity of inference and learning on classical GPs scales cubically, which
is intractable for real-time applications. Thus GPs are commonly trained
offline, which is not suited for learning disturbances as their dynamics may
vary with time. Recently, state-space formulation of GPs has been introduced,
allowing inference and learning with linear computational complexity. This
paper presents a framework that enables online learning of disturbance dynamics
on quadcopters, which can be executed within milliseconds using a state-space
formulation of GPs. The obtained disturbance predictions are combined with MPC
leading to a significant performance increase in simulations with jMAVSim. The
computational burden is evaluated on a Raspberry Pi 4 B to prove the real-time
applicability.
