Adaptive Particle Filter for Stable Distribution
Particle filters are considered as the most robust method in the estimation theory. However, all techniques presented in the literature consider only cases where the data can be described by a probability distribution function (PDF) with all statistical moments well defined. The present chapter a novel particle filter is introduced for estimating a posteriori PDF using a Bayesian scheme. The key issue is to consider an adaptive likelihood function. The scheme generalizes the traditonal particle filter approaches. The scheme can be applied to inverse problem, control theory, image and signal processing, and data assimilation.
KeywordsInverse Problem Probability Density Function Central Limit Theorem Data Assimilation Probability Density Function
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- [JaSo05]Jaipio, K., Somersalo, E.: Statistical and Computational Inverse Problems, Springer Verlag (2005). Google Scholar
- [GoSaSm93]Gordon, N., Salmond, D., Smith, A.D.: Novel approach to nonlinear/non-Gaussian Bayes ian state estimation. IEE Proc., 140, 107 (1993). Google Scholar
- [Do98]Doucet, A.: On Sequential Simulation-Based Methods for Bayesian Filtering, Tech. Report: Departament of Engineering, University of Cambridge (CB21PZ Cambridge UK), 1998. Google Scholar
- [No05]Nolan, J.P.: Stable Distributions: Models for Heavy Tailed Data, Birkhäuser, Boston, MA (2005). Google Scholar
- [Sc06]Schön, T.B.: Estimation of Nonlinear Dynamic Systems: Theory and Applications, Dissertations no. 998 (Linköping Studies in Sciense and Tecnology), 2006. Google Scholar
- [Pa89]Papoulis, A.: Probability and Statistics, Pearson Higher Education (1989). Google Scholar
- [TsQu07]Tsallis, C., Queiros, S.M.D.: Nonextensive statistical mechanics and central limit theorems I – Convolution of independent random variables and q-product, in Complexity, Metastability and Nonextensivity (CTNEXT 07) (Editors: S. Abe, H. Herrmann, P. Quarati, A. Rapisarda, and C. Tsallis), American Institute of Physics (2007). Google Scholar