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

Authors:
K. Nishiyama
Affiliations:
Dept. of Inf. & Comput. Eng., Polytech. Univ., Kanagawa
Venue:
IEEE Transactions on Signal Processing
Year:
1997

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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