"Fast maximum likelihood joint estimation of frequency and frequency rate"

A Fast Maximum Likelihood Algorithm for the Joint estimation of the Frequency and Frequency rate of a sinusoid in Gaussian white noise is presented here. The novelty of this algorithm is the use of Newton's method for finding the zero of a function to determine the maximum of the log-likelihood function. The rate of convergence of Newton's method is extremely fast. Simulation of the algorithm shows that the RMSEs for frequency and frequency-rate are practically equal to the Cramer-Rao bound for all
SNR \geq 15
dB.