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On frame and orientation localization for relative sensing networks

Date

2013

Authors

Piovan, Giulia
Shames, Iman
Fidan, Baris
Bullo, Francesco
Anderson, Brian

Journal Title

Journal ISSN

Volume Title

Publisher

Pergamon-Elsevier Ltd

Abstract

We develop a novel localization theory for networks of nodes that measure each other's bearing, i.e.; we assume that nodes do not have the ability to perform measurements expressed in a common reference frame. We begin with some basic definitions of frame localizability and orientation localizability. Based on some key kinematic relationships, we characterize orientation localizability for planar networks with angle-of-arrival sensing. We then address the orientation localization problem in the presence of noisy measurements. Our first algorithm computes a least-squares estimate of the unknown node orientations in a ring network given angle-of-arrival sensing. For arbitrary connected graphs, our second algorithm exploits kinematic relationships among the orientations of nodes in loops in order to reduce the effect of noise. We establish the convergence of the algorithm, and through some simulations we show that the algorithm reduces the mean-square error due to the noisy measurements in a way that is comparable to the amount of noise reduction obtained by the classic least-square estimator. We then consider networks in 3-dimensional space and we explore necessary and sufficient conditions for orientation localizability in the noiseless case.

Description

Keywords

Keywords: 3-dimensional; Angle-of-arrival; Connected graph; Decentralized system; Distributed control; Least Square; Least-square estimators; Localizability; Localization problems; Localization theory; Noisy measurements; Planar networks; Reference frame; Ring netw Decentralized systems; Distributed control; Sensor networks

Citation

Source

Automatica

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

DOI

10.1016/j.automatica.2012.09.014

Restricted until

2037-12-31