Delay estimation by expected value

The estimation of time delay between narrowband signals is discussed. A minimum mean square error (MMSE) estimator is used that utilizes the maximum likelihood (ML) window derived by Knapp and Carter in obtaining the required conditional probability density function from which the delay estimate is calculated. The results of simulations using a narrowband signal are presented which evaluate and compare the mean square error of the MMSE and ML processors. The MMSE estimator shows improvement over the ML estimator, particularly in regions below the threshold signal-to-noise ratio. Conditions for application of the MMSE processor are discussed as well as some important considerations for its implementation.