A Strategy for Obtaining Explicit Estimators of Signal Delay

A new strategy for extracting the delay parameter τ from observed data of the form s(t - τ) + n(t), where s(t) is a deterministic signal and n(t) is a sample function from an arbitrary random process, is presented and analyzed. The strategy requires no a priori statistics of the delay parameter and only second-order statistics (the autocorrelation function) of the additive noise process. The strategy involves correlating the received data with the sum of the properly weighted signal derivatives or, alternately, passing the observed data into a linear filter matched to the sum of the properly weighted signal derivatives. The filter output is approximately given by the true signal delay plus a term due to the noise.