This paper investigates the state estimation problem for a stochastic nonlinear differential systems, driven by standard Wiener processes. A novel algorithm is proposed, based on a mixed observer-filter approach, which can be resumed in three steps: the first step makes use of a state observer for nonlinear systems, applied to the system equations disregarding the noises. The observed state constitutes the trajectory around which a Carleman approximation of the stochastic differential system is achieved. This second step allows to define an approximate representation of the system by means of a bilinear system (i.e. linear drift and multiplicative noise), for which a filtering algorithm is available from the literature, third step.
Cacace, F., Germani, A., Palumbo, P. (2011). A new approach to nonlinear filtering via a mixed state observer and polynomial Kalman-Bucy scheme. In 18th IFAC World Congress on Automatic Control (IFAC2011) (pp.4477-4482). IFAC Secretariat [10.3182/20110828-6-IT-1002.02058].
A new approach to nonlinear filtering via a mixed state observer and polynomial Kalman-Bucy scheme
Palumbo, P
2011
Abstract
This paper investigates the state estimation problem for a stochastic nonlinear differential systems, driven by standard Wiener processes. A novel algorithm is proposed, based on a mixed observer-filter approach, which can be resumed in three steps: the first step makes use of a state observer for nonlinear systems, applied to the system equations disregarding the noises. The observed state constitutes the trajectory around which a Carleman approximation of the stochastic differential system is achieved. This second step allows to define an approximate representation of the system by means of a bilinear system (i.e. linear drift and multiplicative noise), for which a filtering algorithm is available from the literature, third step.File | Dimensione | Formato | |
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2011-08 IFAC-Milano - Nonlinear filtering via a mixed observer and polynomial scheme.pdf
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