Fine delay estimation with time integrating correlators

The bias and variance of the delay estimation from a time integrating acoustooptic correlator are considered. A parabolic interpolation of the sampled correlation output is included. General expressions for the bias and variance are derived that include the effect of finite detector element area. Quantitative data are provided for the case of an exponential autocorrelation signal model as functions of various system, signal, and noise parameters. These results show that the estimate is biased. They also provide guidelines on the delay estimation variance obtainable from a given system and on the design of a system to achieve a desired estimation accuracy.