Abstract
Motivated by reduction of computational complexity,this work develops sign-error adaptive filtering algorithms for estimatingrandomly time-varyingsystemparameters.Different from the existing work on sign-error algorithms,the parameters are time-varying and their dynamics are modeled by a discrete-timeMarkov chain.Another distinctive feature of the algorithms is themulti-time-scale framework for characterizing parameter variations and algorithm updating speeds.This is realized by considering the stepsize of the estimation algorithms anda scaling parameter that defines the transition rate of the Markovjump process. Depending on the relative time scales of these two processes, suitably scaled sequencesof the estimatesare shown to converge to either anordinary differential equation, or a set of ordinary differential equations modulated by random switching, or a stochastic differential equation,or stochastic differential equations with random switching. Using weak convergence methods, convergence and rates of convergence of the algorithmsare obtained for all these cases. Simulation results are provided for demonstration.
Highlights
Recent rapid advancement in science and technology has introduced many emerging applications in which adaptive filtering is of substantial utility, including consensus controls, networked systems, and wireless communications; see [1, 2, 4, 5, 8, 7, 12, 13, 14, 16, 17, 18, 19, 20, 23, 24, 27]
Signal processing, algorithm implementation are subject to resource limitations, it is highly desirable to reduce data complexity. This is especially important when data shuffling involves communication networks. This understanding has motivated the main theme of this paper by using sign-error updating schemes, which carry much reduced data complexity, in adaptive filtering algorithms, without detrimental effects on parameter estimation accuracy and convergence rates
Depending on the relative time scales of these two processes, 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 equations with random switching
Summary
Adaptive filtering algorithms have been studied extensively, thanks to their simple recursive forms and wide applicability for diversified practical problems arising in estimation, identification, adaptive control, and signal processing [26]. Signal processing, algorithm implementation are subject to resource limitations, it is highly desirable to reduce data complexity This is especially important when data shuffling involves communication networks. This understanding has motivated the main theme of this paper by using sign-error updating schemes, which carry much reduced data complexity, in adaptive filtering algorithms, without detrimental effects on parameter estimation accuracy and convergence rates. A distinctive feature of the algorithms introduced in this paper is the multi-time-scale framework for characterizing parameter variations 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.
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