access icon free Design and convergence analysis of stochastic frequency estimator using contraction theory

© The Institution of Engineering and Technology
Received 11/12/2011, Accepted 28/03/2013, Revised 19/03/2013, Published

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.

Inspec keywords: signal processing; nonlinear estimation; convergence; numerical analysis; observers; frequency estimation

Other keywords: nonlinear estimator; contraction theory; dynamic stochastic estimator; multiple frequencies; asymptotic convergence; numerical simulations; frequency values; stochastic frequency estimator; semicontracting systems; additive noise; observers; sinusoidal signals

Subjects: Other topics in statistics; Signal processing and detection; Signal processing theory; Other numerical methods; Other topics in statistics; Other numerical methods; Simulation, modelling and identification

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