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Sign-Error Adaptive Filtering Algorithms for Markovian Parameters
- Publication Year :
- 2012
-
Abstract
- Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are time-varying and their dynamics are modeled by a discrete-time Markov chain. A distinctive feature of the algorithms is the multi-time-scale framework for characterizing parameter varia- tions and algorithm updating speeds. This is realized by considering the stepsize of the estimation algorithms and a scaling parameter that defines the transition rates of the Markov jump process. Depending on the relative time scales of these two pro- cesses, suitably scaled sequences of the estimates are shown to converge to either an ordinary differential equation, or a set of ordinary differential equations modulated by random switching, or a stochastic differential equation, or stochastic differential equa- tions with random switching. Using weak convergence methods, convergence and rates of convergence of the algorithms are obtained for all these cases.<br />Comment: Preprint, submitted to IEEE Transactions on Signal Processing, 26 pages, 5 figures
- Subjects :
- Mathematics - Optimization and Control
Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1212.5185
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3934/mcrf.2015.5.781