(A) potential game approach to sensor network planning problems

Abstract

The goal of a cooperative planning problem for a sensor network is to find out the sensing locations to minimize uncertainty in some variables of interest. In this thesis, a potential game approach is proposed for distributed cooperative selection of informative sensing locations. Firstly, a sensor network planning problem is formulated as a potential game. The mathematical formulation of the cooperative sensor planning is given by the optimization problem maximizing the mutual information between the measurements and the variables of interest. From a game-theoretic perspective, each sensing agent is considered as a player who tries to maximize its own utility. It is proved that a local utility defined by the conditional mutual information of a sensing agent conditioned on the other agents' decisions leads to a potential game, with the potential function being the original mutual information. This formulation enables many learning algorithms for Nash equilibrium to be applied for the optimization process. One of the learning dynamics, the joint strategy fictitious play(JSFP) method is then applied to obtain a distributed solution that provably converges to a pure strategy Nash equilibrium. To compute the utility function efficiently, two approximation methods are suggested: restricting the conditioning variables to the ones that have correlation with the sensing agent's decision and a sampling method for nonlinear and non-Gaussian cases. Two illustrative numerical examples are presented to demonstrate good convergence and performance properties of the proposed game-theoretic approach. Lastly, we present a non-myopic sensor management for a multi-target tracking problem. The planning objective is to select the sequence of sensing points over $K>1$ future time steps to minimize overall tracking error at $K$-th step. The problem is formulated as a potential game and JSFP-based learning algorithm is proposed so that the computation cost increases linearly with the size of the problem.