On the parametrization and design of an extended Kalman filter frequency tracker

The problem of estimating the frequency of a harmonic signal embedded in broad-band noise is considered. The paper focuses on the extended Kalman filter frequency tracker, which is the application of the extended Kalman filter (EKF) framework to the frequency estimation problem. The EKF frequency tracker recently proposed in the literature is characterized by a vector of three design parameters {q,r,ε}, whose role and tuning is still a controversial and unclear issue. In this paper it is shown that a wise parametrization of the extended Kalman frequency tracker is characterized by just one parameter: the ε must be set to zero to achieve the basic property of unbiasedness in a noise-free setting; the performances of the tracker are not influenced independently by q and r; and what really matters is the ratio λ=r/q only. The proposed simplification of the extended Kalman filter frequency tracker allows an easier and more transparent tuning of its tracking behavior