TY - JOUR
T1 - Geometric interpretation of theoretical bounds for RSS-based source localization with uncertain anchor positions
AU - Denkovski, Daniel
AU - Angjelichinoski, Marko
AU - Atanasovski, Vladimir
AU - Gavrilovska, Liljana
PY - 2017/9/1
Y1 - 2017/9/1
N2 - 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. It exploits the properties of semi-definiteness and symmetry of the Fisher Information Matrix and the Cramèr–Rao Lower Bound to derive 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.
AB - 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. It exploits the properties of semi-definiteness and symmetry of the Fisher Information Matrix and the Cramèr–Rao Lower Bound to derive 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.
KW - Cramèr–Rao lower bound
KW - Error ellipse
KW - Fisher information matrix
KW - Information ellipse
KW - Joint localization framework
KW - Received Signal Strength
UR - http://www.scopus.com/inward/record.url?scp=85020869857&partnerID=8YFLogxK
U2 - 10.1016/j.dsp.2017.06.003
DO - 10.1016/j.dsp.2017.06.003
M3 - Journal article
AN - SCOPUS:85020869857
SN - 1051-2004
VL - 68
SP - 167
EP - 181
JO - Digital Signal Processing: A Review Journal
JF - Digital Signal Processing: A Review Journal
ER -