Efficient sensor network planning method using approximate potential game

This paper addresses information-based sensing point selection from a set of possible sensing locations, which determines a set of measurement points maximizing the mutual information between the sensor measurements and the variables of interest. A potential game approach has been applied to addressing distributed implementation of decision making for cooperative sensor planning. When a sensor network involves a large number of sensing agents, the local utility function for a sensing agent is hard to compute, because the local utility function depends on the other agents' decisions while each sensing agent is inherently faced with limitations in both its communication and computational capabilities. Accordingly, a local utility function for each agent should be approximated to accommodate limitations in information gathering and processing. We propose an approximation method for a local utility function using only a portion of the decisions of other agents. The part of the decisions that each agent considers is called the neighboring set for the agent. The error induced by the approximation is also analyzed, and to keep the error small we propose a neighbor selection algorithm that chooses the neighbor set for each agent in a greedy way. The selection algorithm is based on the correlation information between one agent's measurement selection and the other agents' selections. Futhermore, we show that a game with an approximate local utility function has an $\epsilon$-equilibrium and the set of the equilibria include the Nash equilibrium of the original potential game. We demonstrate the validity of our approximation method through two numerical examples on simplified weather forecasting and multi-target tracking.