A Comparison between NCF-EKF and EPLL for Parameter Estimation of Sinusoidal Signals

This paper compares the Nearly Constant Frequency model-based Extended Kalman Filter algorithm (NCF-EKF) and the Enhanced-Phase Locked-Loop (EPLL). Both algorithms estimate the amplitude, frequency, and phase angle of a sinusoidal signal corrupted by white noise. They are compared because they use the same state vector. The EPLL assumes that the amplitude estimation is decoupled from frequency and phase estimation. It is shown that the NCF-EKF considers the interrelationship between amplitude, and frequency and phase. Besides, if the covariance elements between amplitude and frequency and phase angle are set to zero in the state error covariance matrix, the NCF-EKF discrete-time recursive equations can be written in the form of the EPLL discrete-time recursive equations. Moreover, the parameters that determine the steady-state error and the transient behavior of the EPLL can be related to the Kalman gain vector of the NCF-EKF. Simulations are carried out to evaluate the algorithms.