Continuous-discrete models refer to systems described by continuous ordinary or stochastic differential equations, with measurements acquired at discrete sampling instants. Here we investigate the state estimation problem in the stochastic framework, for a class of nonlinear systems characterized by a linear drift and a generic nonlinear diffusion term. Motivation stems from a large variety of applications, ranging from systems biology to finance. By using a Carleman linearization approach we show how the original system can be embedded into an infinite dimensional bilinear system, for which it is possible to write the equations of the optimal linear filter, in case of measurements provided by linear state transformations. A finite dimensional approximation of the optimal linear filter is finally derived. Results are applied to a case of interest in financial applications

Cacace, F., Cusimano, V., Germani, A., Palumbo, P., Papi, M. (2018). Optimal linear filter for a class of nonlinear stochastic differential systems with discrete measurements. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, VIC, Australia, 12-15 December 2017 (pp.2807-2812). IEEE Institute of Electrical and Electronics Engineers [10.1109/CDC.2017.8264067].

Optimal linear filter for a class of nonlinear stochastic differential systems with discrete measurements

Palumbo, P
Co-primo
;
2018

Abstract

Continuous-discrete models refer to systems described by continuous ordinary or stochastic differential equations, with measurements acquired at discrete sampling instants. Here we investigate the state estimation problem in the stochastic framework, for a class of nonlinear systems characterized by a linear drift and a generic nonlinear diffusion term. Motivation stems from a large variety of applications, ranging from systems biology to finance. By using a Carleman linearization approach we show how the original system can be embedded into an infinite dimensional bilinear system, for which it is possible to write the equations of the optimal linear filter, in case of measurements provided by linear state transformations. A finite dimensional approximation of the optimal linear filter is finally derived. Results are applied to a case of interest in financial applications
paper
Linear filtering; Continuous-discrete systems; Nonlinear differential stochastic systems
English
EEE 56th Annual Conference on Decision and Control (CDC) DEC 12-15
2017
2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, VIC, Australia, 12-15 December 2017
978-1-5090-2873-3
2018
2807
2812
open
Cacace, F., Cusimano, V., Germani, A., Palumbo, P., Papi, M. (2018). Optimal linear filter for a class of nonlinear stochastic differential systems with discrete measurements. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, VIC, Australia, 12-15 December 2017 (pp.2807-2812). IEEE Institute of Electrical and Electronics Engineers [10.1109/CDC.2017.8264067].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/246801
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