Published November 2017
| Version public
Book Section - Chapter
Time estimation for heat diffusion on graphs
Abstract
This paper studies the estimation of the starting time of a diffusion process from its noisy measurements when there is a single point source located on a known vertex of a graph with unknown starting time. The diffusion process is assumed to be governed by the heat equation. In particular, the Cramer-Rao lower bound (CRLB) for the problem is derived. It is shown that the problem has a larger CRLB for graphs with higher connectivity. Closed form expression of the bound is derived for some graphs. The ML estimator is numerically verified to be unbiased, and achieve the CRLB for some graphs.
Additional Information
© 2017 IEEE. This work was supported in parts by the ONR grants N00014-15-1-2118 and N00014-17-1-2732, the NSF grant CCF-1712633, and the Electrical Engineering Carver Mead Research Seed Fund of the California Institute of Technology.Additional details
Identifiers
- Eprint ID
- 85971
- Resolver ID
- CaltechAUTHORS:20180419-095409264
Funding
- Office of Naval Research (ONR)
- N00014-15-1-2118
- Office of Naval Research (ONR)
- N00014-17-1-2732
- NSF
- CCF-1712633
- Caltech
Dates
- Created
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2018-04-19Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field