  Consider a sensor network consisting of both anchor and non-anchor nodes. We
address the following sensor network localization (SNL) problem: given the
physical locations of anchor nodes and relative measurements among all nodes,
determine the locations of all non-anchor nodes. The solution to the SNL
problem is challenging due to its inherent non-convexity. In this paper, the
problem takes on the form of a multi-player non-convex potential game in which
canonical duality theory is used to define a complementary dual potential
function. After showing the Nash equilibrium (NE) correspondent to the SNL
solution, we provide a necessary and sufficient condition for a stationary
point to coincide with the NE. An algorithm is proposed to reach the NE and
shown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim of
reducing the information exchange within a network, a distributed algorithm for
NE seeking is implemented and its global convergence analysis is provided.
Extensive simulations show the validity and effectiveness of the proposed
approach to solve the SNL problem.
