An infinite expansion for nonlinear filtering
A filtering equation is obtained for a partially observed system in terms of the innovation process. This equation was obtained by \textit{Th. Kailath} and others in a different way under different conditions [see IEEE Trans. Automatic Control AC-13, No. 6, 646-660 (1968); AC-16, No. 6, 720-727 (1971); AC-18, No. 5, 435-453 (1973; Zbl 0263.93048); AC-18, No. 6, 588-607 (1973)]. An infinite series expansion of nonlinear filters as sums of multiple stochastic Itô integrals with respect to the innovation process is obtained. This expansion is used to calculate the conditional expectation as well as the innovation process.
sums of multiple stochastic Ito integrals
infinite series expansion of nonlinear filters
scientific article; zbMATH DE number 672054
scientific article