Abstract
A fast method of Newton-Raphson-based algorithm is presented for maximum likelihood estimation of the time-delay as well as the attenuation parameter of received signals in observation data corrupted by white Gaussian noise. Based on the mathematical method described by an Ito stochastic differential equation for the noisy observation data, the likelihood-ratio function is derived instead of the usual likelihood function, and the Cramér-Rao lower bounds for the time-delay and attenuation estimates are evaluated in a modified form using the likelihood-ratio function to show the uncertainty relation between these two estimates. Unbiasedness of these two estimates are theoretically demonstrated. Simulation results that confirm the effectiveness of the proposed method are given.
