TY - GEN
T1 - Unique Maximum Likelihood Localization of Nuclear Sources
AU - Anderson, B. D.O.
AU - Dasgupta, S.
AU - Baidoo-Williams, H. E.
AU - Anjum, M. F.
AU - Mudumbai, R.
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - In an earlier paper, [1], we have considered the Maximum Likelihood (ML) localization of a stationary nuclear source using the time of arrival of particles modeled as a Poisson process at a sensing vehicle moving with a constant velocity. In this paper we consider whether the ML location estimate characterized in [1] is unique. Using Morse theory we show that not only is the likelihood function unimodal on either side of the line the sensor moves on (note the source can only be localized uniquely if one knows on which side it resides), but that in fact it has only one critical point in each side and this critical point is the global maximum. These results strongly indicate that gradient ascent maximization will always work. We verify these results with real field data.
AB - In an earlier paper, [1], we have considered the Maximum Likelihood (ML) localization of a stationary nuclear source using the time of arrival of particles modeled as a Poisson process at a sensing vehicle moving with a constant velocity. In this paper we consider whether the ML location estimate characterized in [1] is unique. Using Morse theory we show that not only is the likelihood function unimodal on either side of the line the sensor moves on (note the source can only be localized uniquely if one knows on which side it resides), but that in fact it has only one critical point in each side and this critical point is the global maximum. These results strongly indicate that gradient ascent maximization will always work. We verify these results with real field data.
UR - http://www.scopus.com/inward/record.url?scp=85082479500&partnerID=8YFLogxK
U2 - 10.1109/CDC40024.2019.9028941
DO - 10.1109/CDC40024.2019.9028941
M3 - Conference contribution
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4127
EP - 4132
BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 58th IEEE Conference on Decision and Control, CDC 2019
Y2 - 11 December 2019 through 13 December 2019
ER -