Frequency estimation of narrow band signals in Gaussian noise via Unscented Kalman Filter

In this paper the problem of frequency estimation of a harmonic signal embedded in noise is studied. We consider three frequency trackers, two in an input/output description and one in state space form, namely: the Notch Filter (NF), the Funnel Filter (FF) and the Cartesian Filter (CF). With the first two models, the estimation is carried on with prediction error minimization technique, whereas the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) are used in the third model. The estimation methods are compared each other by introducing two standard step profiles and evaluating the quality of estimation by means of two indices based on the achieved quality in the tracking of such profiles. From this analysis, it turns out that the CF with UKF outperforms the other techniques from all considered viewpoints: steady-state variance, convergence time and robustness to large frequency variations.