4 papers · 1 filter
Bayesian Filters via the Stochastic Category
Kenichi Bannai, Masahiro Kurisaki
We extend the categorical treatment of Bayesian filters to models with feedback, whose transitions and observations may depend on the past observations. We work in the stochastic c…
Finite Cumulant Towers for Small-System-Noise Expansions in Nonlinear Filtering
Masahiro Kurisaki
We study asymptotic expansions for nonlinear filtering in the small-system-noise regime. Our main result is that the expansion coefficients of conditional cumulants satisfy a close…
Finite-Dimensional Recursions for Small-Noise Expansions in Nonlinear Filtering
Masahiro Kurisaki
This paper provides a recursive formula for computing the coefficients in a small-system-noise asymptotic expansion for nonlinear filtering. The expansion, obtained from the Kallia…
Asymptotic Expansion of the Kallianpur-Striebel Formula under Perturbations of Linear Models
Masahiro Kurisaki
In this paper, we study a nonlinear state-space model represented as a perturbation of a linear model and investigate an asymptotic expansion of the nonlinear filter with respect t…