Minimum number of sensors to ensure observability of physiological systems: A case study

Physiological signals are often spatiotemporal dependent. Some of these signals include electroencephalogram (EEG), electromyogram (EMG) or electrocardiogram (ECG) signals, just to name a few. Coupled-fractional dynamical systems have shown to capture such properties, but methods to determine where to place sensors for these dynamical systems are still lacking. In this paper, we show that the problem of determining the minimum number of sensors such that the global dynamics can be recovered from the collected data is NP-hard. Subsequently, we propose a polynomial algorithm to obtain suboptimal solutions with optimality guarantees. Finally, as a case study, we illustrate the proposed selection mechanism in the context of determining a small subset of sensors to retrieve the overall dynamics in the context of EEG, EMG and ECG signals.