Non-informative Bayesian dispersion particle filter
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Abstract
In this research paper, we attempt to introduce a new algorithm for filtering a state-space model. The observations of this algorithm follow an exponential dispersion model. The paper focuses here on the inclusion of non-informative prior knowledge in parameter estimation on nonlinear state-space models using an improper uniform prior measure. Therefore, a new particle filter is introduced. A conventional particle filter (PF) produces an incorrect sample from a discrete approximation distribution. This new algorithm is a regularized continuous distribution method that is obtained with the exponential dispersion model. A necessary and sufficient condition for the existence and convergence of the non-informative Bayesian estimator of dispersion parameters is established. This methodology extends the classical PF implemented by this new estimation method for the exponential dispersion model framework using a non-informative Bayesian approach. In order to evaluate the performance of the proposed algorithm, a case study with simulations and microscopic image restoration is carried out. The results exhibit a great performance improvement from the proposed approach
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