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A new application of duality relations of stochastic processes isdemonstrated. Although conventional usages of the duality relations needanalytical solutions for the dual processes, we here employ numerical solutionsof the dual processes and investigate the usefulness. As a demonstration,estimation problems of hidden variables in stochastic differential equationsare discussed. Employing algebraic probability theory, a little complicatedbirth-death process is derived from the stochastic differential equations, andan estimation method based on the ensemble Kalman filter is proposed. As aresult, the possibility for making faster computational algorithms based on theduality concepts is shown.

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