Abstract
The sensor localization problem can be formalized using distance and orientation constraints, typically in 3D. Local methods can be used to refine an initial location estimation, but in many cases such estimation is not available and a method able to determine all the feasible solutions from scratch is necessary. Unfortunately, existing methods able to find all the solutions in distance space can not take into account orientations, or they can only deal with one- or two-dimensional problems and their extension to 3D is troublesome. This paper presents a method that addresses these issues. The proposed approach iteratively projects the problem to decrease its dimension, then reduces the ranges of the variable distances, and back-projects the result to the original dimension, to obtain a tighter approximation of the feasible sensor locations. This paper extends previous works introducing accurate range reduction procedures which effectively integrate the orientation constraints. The mutual localization of a fleet of robots carrying sensors and the position analysis of a sensor moved by a parallel manipulator are used to validate the approach.
Highlights
The accurate localization of a sensor is fundamental in many applications
Distance Geometry studies problems characterized by distance and orientation constraints between a given set of points [5]
The main issue of existing Distance Geometry techniques is that they can not deal with orientation constraints, which are fundamental in many applications [12,13]
Summary
The accurate localization of a sensor is fundamental in many applications. For instance, one of the main problems to address in sensor networks is the location of the nodes since most of the objectives of such networks rely on the correct association between the sensor readings and the location information [1]. It provides a formulation invariant to the reference frame and, it gives geometric insights on different problems that remain concealed when using Cartesian geometry These insights allow deriving solutions common to problems that otherwise have to be treated on a case-by-case basis [6]. This paper proposes novel Distance Geometry tools for the sensor localization problem. The main issue of existing Distance Geometry techniques is that they can not deal with orientation constraints, which are fundamental in many applications [12,13]. The proposed procedure is geometric, avoiding the use of Cayley-Menger determinants, the dominant tool in Distance Geometry [16,17,18], which generates formulations that rapidly get involved with the number of points and their dimension [19,20].
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