Noisy Range Network Localization Based on Distributed Multidimensional Scaling

This paper considers the noisy range-only network localization problem in which measurements of relative distances between agents are used to estimate their positions in networked systems. When distance information is noisy, existence and uniqueness of location solution are usually not guaranteed. It is well known that in presence of distance measurement noise, a node may have discontinuous deformations (e.g., flip ambiguities and discontinuous flex ambiguities). Thus, there are two issues that we consider in the noisy localization problem. The first one is the location estimate error propagated from distance measurement noise. We compare two kinds of analytical location error computation methods by assuming that each distance is corrupted with independent Gaussian random noise. These analytical results help us to understand effects of the measurement noises on the position estimation accuracy. After that, based on multidimensional scaling theory, we propose a distributed localization algorithm to solve the noisy range network localization problem. Our approach is robust to distance measurement noise, and it can be implemented in any random case without considering the network setup constraints. Moreover, a refined version of distributed noisy range localization method is developed, which achieves a good tradeoff between computational effort and global convergence especially in large-scale networks.