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Proceedings Paper

Quasi-Monte Carlo particle filters: the JV filter
Author(s): Fred Daum
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Paper Abstract

We describe a new particle filter that uses quasi-Monte Carlo (QMC) sampling with product measures rather than boring old Monte Carlo sampling or QMC with or without randomization. The product measures for QMC were recently invented by M. Junk and G. Venkiteswaran, and therefore we call this new nonlinear filter the "JV filter". Standard particle filters use boring old Monte Carlo sampling and suffer from the curse of dimensionality, and they converge at the sluggish rate of c(d)/√N in which N is the number of particles, and c(d) depends strongly on dimension of the state vector (d). Oh's theory and numerical experiments (by us) show that for good proposal densities, c(d) grows as d3, whereas for poor proposal densities c(d) grows exponentially with d. In contrast, for certain problems, QMC converges much faster than MC with N. In particular, QMC converges as k(d)/N, in which k(d) is logarithmic in N and its dependence on d is an interesting story.

Paper Details

Date Published: 19 May 2006
PDF: 11 pages
Proc. SPIE 6236, Signal and Data Processing of Small Targets 2006, 62360J (19 May 2006); doi: 10.1117/12.663914
Show Author Affiliations
Fred Daum, Raytheon Co. (United States)


Published in SPIE Proceedings Vol. 6236:
Signal and Data Processing of Small Targets 2006
Oliver E. Drummond, Editor(s)

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