Explorability of noisy scalar fields

We consider mobile sensing agents taking measurements along their trajectories and navigating in a noisy scalar field. Not knowing the field value at its location, each agent decides its motion based on sensor measurements. When an agent changes its position, both the sensor measurement and the field value at its location change. If the change of the field value is not consistent with the change of the measurement, we say the agent performs a false-walk. We establish the notion of local explorability for the noisy scalar field to analyze the tendency that such field will induce false-walks for a sensing agent. We show that, a field being locally explorable is the sufficient and necessary condition for the probability of inducing a false-walk to be less than a certain threshold. We then connect explorability with the noise reduction capability using multiple sensing agents, and compute the minimum number of agents necessary to ensure explorability.