Position estimation from relative distance measurements in multi-agents formations

The problem of reconstructing the geometric position of nodes in a networked formation from inter-nodal distance measurements is a complex computational task that involves the minimization of a non-convex and highly multi-modal cost criterion. In this paper, we examine three numerical techniques for attacking this problem, namely an iterative Least-Squares (LS) approach, a Trust-Region (TR) approach, and a Global Continuation (GC) technique based on iterative smoothing. The implementation details of the three methods are discussed in the paper, and extensive numerical simulations are performed in order to highlight the complementary properties of these methods in terms of required computational effort and ability to achieve global convergence.