Conditional mean and maximum likelihood approaches to multiharmonic frequency estimation

The performance of an extended Kalman filter (EKF) applied to the problem of estimating the (assumed constant) parameters (fundamental frequency, harmonic phases, and amplitudes) of a complex multiharmonic signal measured in noise is shown to be asymptotically (i.e., as the number of measurements tends to infinity) efficient. The Cramer-Rao (CR) bounds associated with the estimation problem are derived for the case where the measurements commence at an arbitrary time distinct from zero.>