Smoothing algorithms for nonlinear finite-dimensional systems
作者:
Brian D. O. Anderson,
Ian B. Rhodes,
期刊:
Stochastics
(Taylor Available online 1983)
卷期:
Volume 9,
issue 1-2
页码: 139-165
ISSN:0090-9491
年代: 1983
DOI:10.1080/17442508308833251
出版商: Gordon and Breach Science Publishers Inc,
数据来源: Taylor
摘要:
Systems are considered where the state evolves either as a diffusion process or as a finitestate Markov process, and the measurement process consists either of a nonlinear function of the state with additive white noise or as a counting process with intensity dependent on the state. Fixed interval smooting is considered, and the first main result obtained expresses a smoothing probability or a probability density symmetrically in terms of forward filtered, reverse-time filterd and unfiltered quantities; an associated result replaces the unfiltered and reverse-time filtered qauantities by a likelihood function. Then stochastic differential equationsare obtained for the evolution of the reverse-time filtered probability or probability density and the reverse-time likelihood function. Lastly, a partial differential equation is obtained linking smoothed and forward filterd probabilities or probability densities; in all instances considered, this equation is not driven by any measurement process. The different approaches are also linked to known techniques applicable in the linear-Gaussian case.
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