Exploiting geometric translations in TLS based robot localization from landmark bearings

In a previous study we showed that the total least squares (TLS) estimation performance for bearings-only localization is dependent on coordinate shifts. In this paper we extend this study to TLS-based robot localization from landmark bearings. We show that unlike nonlinear least squares estimators the TLS estimation performance is sensitive to where the local Cartesian coordinates are placed in the two-dimensional plane. Thus for a given set of landmark bearing measurements collected by a robot, the TLS performance is influenced by where the local coordinates are placed. The dependence of the TLS estimation bias on local coordinate translations is due to the dependence of TLS perturbations on local coordinate translations. We observe that the TLS estimate performs almost as well as the maximum likelihood estimate as the origin of the local coordinates is placed sufficiently away from the landmarks.