ASYMPTOTIC ANALYSIS OF THE OPTIMAL FILTERING PROBLEM FOR ONE-DIMENSIONAL DIFFUSIONS MEASURED IN A LOW NOISE CHANNEL, PART II.

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Abstract

We consider the problem of filtering one-dimensional diffusions with nonlinear drift coefficients, transmitted through a nonlinear low noise channel. We construct an asymptotic solution to Zakai's equation for the unnormalized conditional probability density of the signal, given the noisy measurements. This expansion is used to find the asymptotic expansion of the minimum error variance filter and its mean square estimation error (MSEE).

Original languageEnglish
Pages (from-to)1176-1191
Number of pages16
JournalSIAM Journal on Applied Mathematics
Volume44
Issue number6
DOIs
StatePublished - 1984

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