A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise | Zendy

V. Mandrekar | Zendy; Thilo MeyerBrandis | Zendy; Frank Proske | Zendy

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A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise

Author(s) -

V. Mandrekar,

Thilo MeyerBrandis,

Frank Proske

Publication year - 2011

Publication title -

journal of probability and statistics

Language(s) - English

Resource type - Journals

eISSN - 1687-9538

pISSN - 1687-952X

DOI - 10.1155/2011/259091

Subject(s) - mathematics , bayes' theorem , nonlinear filter , gaussian , gaussian noise , filter (signal processing) , filtering problem , conditional probability distribution , noise (video) , jump , nonlinear system , linear filter , statistical physics , algorithm , statistics , computer science , bayesian probability , artificial intelligence , kalman filter , filter design , physics , extended kalman filter , quantum mechanics , image (mathematics) , computer vision

A Bayes-type formula is derived for the nonlinear filter where the observation contains both general Gaussian noise as well as Cox noise whose jump intensity depends on the signal. This formula extends the well-known Kallianpur-Striebel formula in the classical non-linear filter setting. We also discuss Zakai-type equations for both the unnormalized conditional distribution as well as unnormalized conditional density in case the signal is a Markovian jump diffusion

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