A dynamic estimator on SE(3) using range-only measurements

Abstract

This paper addresses the problem of estimating the attitude and position of a rigid body when the available measurements consist only of the relative distances between a set of body fixed beacons and a set of Earth fixed landmarks. The proposed solution is given in terms of a dynamical system evolving on the Special Euclidean group SE(3), the trajectories of which are shown to locally converge to the actual attitude and position of the rigid body. Local asymptotic stability of the dynamical system is proven by using a suitable Lyapunov function, under the assumption that there is a set of noncoplanar landmarks and beacons. Simulation results are shown to illustrate the behaviour of the proposed estimator.

Accurate Localization of a Rigid Body Using Multiple Sensors and Landmarks

“…Alternatively, we consider the non-negative scalar weighting (7) which corresponds to the weighting matrix of the form . Let us denote the weighted average values By setting to zero the derivative of with respect to , we obtain the solution of as (8) We shall denote and . Putting (8) back to gives (9) where is a constant independent of .…”

“…Putting (10) back to (8) gives the solution for the translation vector. We shall denote the solution from step-1 as .…”

“…The results are generated using the algorithm given in Section V. The initial solution needed in step-1 is obtained using both the distance and Doppler measurements. In particular, we apply the method in Appendix D to obtain the sensor position estimates and then (8) and (10) to form . Figs.…”

“…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.…”

“…The estimator requires good initial guesses for convergence to the correct solution. Under the noise free assumption, [8] derived a solution by constructing a dynamic system that evolves on the special Euclidean group where local asymptotic stability can be maintained. This method requires many numerical integrations to determine the evolving state of the system and its performance under noisy measurements is not guaranteed.…”