Open AccessDesign and convergence analysis of stochastic frequency estimator using contraction theory
Author(s) -
Mohamed Majeed,
Kar Indra Narayan
Publication year - 2013
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2012.0251
Subject(s) - estimator , contraction (grammar) , convergence (economics) , computer science , symbolic convergence theory , mathematics , mathematical optimization , algorithm , statistics , economics , linguistics , construct (python library) , economic growth , philosophy , programming language
This study investigates the design and analysis of an estimator for unknown frequencies of a sinusoid in the presence of additive noise. A dynamic stochastic estimator is proposed to ensure simultaneous globally convergent estimation of the state and the frequencies of a sinusoid comprising multiple frequencies. Approach given in this study exploits the results of stochastic contraction theory and the observers. The concept of contraction theory related to semi‐contracting systems is used to show the asymptotic convergence of the proposed non‐linear estimator. The boundedness and convergence of the state and frequencies estimates for all initial conditions and frequency values has been shown analytically. The proposed estimator is generalised to estimate n ‐unknown frequencies of a given noisy sinusoid. Numerical simulations of estimator are presented for different combinations of frequencies to justify the claim.