Alternating Minimization Based First-Order Method for the Wireless Sensor Network Localization Problem

We propose an algorithm for the Wireless Sensor Network localization problem, which is based on the well-known algorithmic framework of Alternating Minimization. We start with a non-smooth and non-convex minimization, and transform it into an equivalent smooth and non-convex problem, which stands at the heart of our study. This paves the way to a new method which is globally convergent: not only does the sequence of objective function values converge, but the sequence of the location estimates also converges to a unique location that is a critical point of the corresponding (original) objective function. The proposed algorithm has a range of fully distributed to fully centralized implementations, which all have the property of global convergence. The algorithm is tested over several network configurations, and it is shown to produce more accurate solutions within a shorter time relative to existing methods.