Rigid Body Localization Using Sensor Networks

Abstract

Abstract-A framework for joint position and orientation estimation of a rigid body using range measurements is proposed. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the rigid body is not known. However, we know how the sensors are mounted on the rigid body, i.e., the sensor topology is known. The rigid body is localized using noisy range measurements between the sensors and a few anchors (nodes with known absolute positions), and without using any inertial measurements. We propose a least-squares (LS), and a number of constrained LS estimators, where the constrained estimators solve an optimization problem on the Stiefel manifold. As a benchmark, we derive a unitarily constrained Cramér-Rao bound. Finally, the known topology of the sensors can be perturbed during fabrication or if the body is not entirely rigid. To take these perturbations into account, constrained total-least-squares estimators are also proposed.

Towards multi-rigid body localization

“…Recently, it was shown in [5] and [6], that a rigid platform can be localized and tracked using distance measurements. That is, the position and orientation of a rigid body can be estimated using a few sensors installed on the platform and some anchors.…”

“…That is, the position and orientation of a rigid body can be estimated using a few sensors installed on the platform and some anchors. Here, we propose an extension of [5] to an anchorless network, where for the sake of exposition we assume only two rigid bodies. More specifically, we estimate the relative angles and translation between them rather than the absolute angles and translation as in [5].…”

“…Here, we propose an extension of [5] to an anchorless network, where for the sake of exposition we assume only two rigid bodies. More specifically, we estimate the relative angles and translation between them rather than the absolute angles and translation as in [5]. In order to solve the anchorless problem, we adopt a multi-dimensional scaling (MDS)-like approach by making use of only the noisy range measurements among the sensors on the rigid bodies.…”

Accurate Localization of a Rigid Body Using Multiple Sensors and Landmarks

“…It may suffer from long-term performance deviation and requires accurate calibration by additional devices [5]. Using GPS for the positioning problem could be costly as it requires complicated receivers [6] and it operates in outdoor environments only.…”

“…An alternative approach is to place a few sensors in the rigid body and uses some measurements [6]- [8] with respect to a few landmarks (simply called anchors in this paper) to identify its orientation and position. Different from the traditional sensor node localization in a network using a number of anchors [9]- [14], the relative positions of the sensors are known.…”