Estimation of Attitude and Position from Range-Only Measurements using Geometric Descent Optimization on the Special Euclidean Group

This paper addresses the problem of estimating the position and attitude of a rigid body when the available measurements consist only of distances (or ranges) between a set of body fixed beacons and a set of earth fixed landmarks. To this effect, a maximum likelihood (ML) estimator is derived by solving an optimization problem on the special Euclidean group SE(n);n = 2,3 using intrinsic gradient and Newton-like algorithms. The theoretical tools used borrow from optimization theory on Riemannian manifolds. Supported by recent results on performance bounds for estimators on Riemannian manifolds, the intrinsic variance lower bound (IVLB) is derived for the problem at hand. Simulation results are presented to illustrate the estimator performance and to validate the tightness of the IVLB in a wide range of signal to noise ratio scenarios