Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes

Jun Ohkubo
Phys. Rev. E 92, 043302 – Published 6 October 2015

Abstract

An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown.

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  • Received 14 May 2015
  • Revised 4 August 2015

DOI:https://doi.org/10.1103/PhysRevE.92.043302

©2015 American Physical Society

Authors & Affiliations

Jun Ohkubo

  • Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura, Saitama, 338-8570, Japan

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Vol. 92, Iss. 4 — October 2015

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