TY - GEN
T1 - Limited benefit of cooperation in distributed relative localization
AU - Rossi, Wilbert Samuel
AU - Frasca, Paolo
AU - Fagnani, Fabio
PY - 2013
Y1 - 2013
N2 - Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: A node-indexed vector has to be reconstructed from measurements of differences between neighbor nodes. In a recent note, we have studied the estimation error of a popular gradient descent algorithm showing that the mean square error has a minimum at a finite time, after which the performance worsens. This paper proposes a suitable modification of this algorithm incorporating more realistic a priori information on the position. The new algorithm presents a performance monotonically decreasing to the optimal one. Furthermore, we show that the optimal performance is approximated, up to a 1 + ε factor, within a time which is independent of the graph and of the number of nodes. This bounded convergence time is closely related to the minimum exhibited by the previous algorithm and both facts lead to the following conclusion: in the presence of noisy data, cooperation is only useful till a certain limit.
AB - Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: A node-indexed vector has to be reconstructed from measurements of differences between neighbor nodes. In a recent note, we have studied the estimation error of a popular gradient descent algorithm showing that the mean square error has a minimum at a finite time, after which the performance worsens. This paper proposes a suitable modification of this algorithm incorporating more realistic a priori information on the position. The new algorithm presents a performance monotonically decreasing to the optimal one. Furthermore, we show that the optimal performance is approximated, up to a 1 + ε factor, within a time which is independent of the graph and of the number of nodes. This bounded convergence time is closely related to the minimum exhibited by the previous algorithm and both facts lead to the following conclusion: in the presence of noisy data, cooperation is only useful till a certain limit.
UR - http://www.scopus.com/inward/record.url?scp=84902340845&partnerID=8YFLogxK
U2 - 10.1109/CDC.2013.6760743
DO - 10.1109/CDC.2013.6760743
M3 - Conference contribution
AN - SCOPUS:84902340845
SN - 978-1-4673-5714-2
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5427
EP - 5431
BT - 52nd IEEE Conference on Decision and Control
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 52nd IEEE Conference on Decision and Control, CDC 2013
Y2 - 10 December 2013 through 13 December 2013
ER -