Geometric Interpretation of Theoretical Bounds for RSS-based Source Localization with Uncertain Anchor Positions
Date Issued
2016-08-23
Author(s)
Daniel Denkovski
Marko Angjelichinoski
Vladimir Atanasovski
Liljana Gavrilovska
Abstract
The Received Signal Strength based source localization can encounter severe
problems originating from uncertain information about the anchor positions in
practice. The anchor positions, although commonly assumed to be precisely known
prior to the source localization, are usually obtained using previous
estimation algorithm such as GPS. This previous estimation procedure produces
anchor positions with limited accuracy that result in degradations of the
source localization algorithm and topology uncertainty. We have recently
addressed the problem with a joint estimation framework that jointly estimates
the unknown source and uncertain anchors positions and derived the theoretical
limits of the framework. This paper extends the authors previous work on the
theoretical performance bounds of the joint localization framework with
appropriate geometric interpretation of the overall problem exploiting the
properties of semi-definiteness and symmetry of the Fisher Information Matrix
and the Cram{\`e}r-Rao Lower Bound and using Information and Error Ellipses,
respectively. The numerical results aim to illustrate and discuss the
usefulness of the geometric interpretation. They provide in-depth insight into
the geometrical properties of the joint localization problem underlining the
various possibilities for practical design of efficient localization
algorithms.
problems originating from uncertain information about the anchor positions in
practice. The anchor positions, although commonly assumed to be precisely known
prior to the source localization, are usually obtained using previous
estimation algorithm such as GPS. This previous estimation procedure produces
anchor positions with limited accuracy that result in degradations of the
source localization algorithm and topology uncertainty. We have recently
addressed the problem with a joint estimation framework that jointly estimates
the unknown source and uncertain anchors positions and derived the theoretical
limits of the framework. This paper extends the authors previous work on the
theoretical performance bounds of the joint localization framework with
appropriate geometric interpretation of the overall problem exploiting the
properties of semi-definiteness and symmetry of the Fisher Information Matrix
and the Cram{\`e}r-Rao Lower Bound and using Information and Error Ellipses,
respectively. The numerical results aim to illustrate and discuss the
usefulness of the geometric interpretation. They provide in-depth insight into
the geometrical properties of the joint localization problem underlining the
various possibilities for practical design of efficient localization
algorithms.