A nonlinear filter for estimating a sinusoidal signal and its parameters in white noise: on the case of a single sinusoid

Author

Nishiyama, Kiyoshi

Author_Institution

Dept. of Inf. & Comput. Eng., Polytech. Univ., Kanagawa, Japan

Volume

45

Issue

4

fYear

1997

fDate

4/1/1997 12:00:00 AM

Firstpage

970

Lastpage

981

Abstract

A nonlinear filter is proposed for estimating a complex sinusoidal signal and its parameters (frequency, amplitude, and phase) from measurements corrupted by white noise. This filter is derived by applying an extended complex Kalman filter (ECKF) to a nonlinear stochastic system whose state variables are a function of its frequency and a sample of an original signal, and then, proof of the stability is given in the case of a single complex sinusoid. Simulations demonstrate that the proposed nonlinear filter is effective as a method for estimating a single complex sinusoid and its frequency under a low signal-to-noise ratio (SNR). In addition, the effect of the initial condition in the filter on frequency estimation is also discussed

Keywords

Kalman filters; amplitude estimation; filtering theory; frequency estimation; nonlinear filters; phase estimation; signal sampling; stochastic systems; white noise; SNR; amplitude estimation; complex sinusoidal signal; extended complex Kalman filter; frequency estimation; initial condition; low signal to noise ratio; measurements; nonlinear filter; nonlinear stochastic system; phase estimation; signal parameters; signal sample; simulations; single complex sinusoid; sinusoidal signal estimation; stability; state variables; white noise; Amplitude estimation; Frequency estimation; Frequency measurement; Noise measurement; Nonlinear filters; Phase estimation; Phase measurement; Stability; Stochastic systems; White noise;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.564185

Filename

564185