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On the two-filter approximations of marginal smoothing distributions in general state-space models

  • Thi Ngoc Minh Nguyen (a1), Sylvain Le Corff (a2) and Eric Moulines (a3)


A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state, given future observations.


Corresponding author

* Postal address: LTCI, Télécom ParisTech, 46, rue Barrault, 75013 Paris, France.
** Postal address: Laboratoire de Mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France. Email address:
*** Postal address: Centre de Mathématiques Appliquées, École Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France.


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