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Extracting parameter estimates from noisy observations of an underlying signal is a common problem in many fields. Time delay estimation (TDE) is essential for many areas, such as localization, array processing, and radar. The performance of any estimator is often evaluated via the mean square error (MSE) that can then be compared to analytical MSE lower bounds. In this paper, we first analyze a maximum likelihood (ML) estimator based on the knowledge of noisy second order statistics of thedoi:10.1186/s13638-018-1306-z fatcat:bq5wmtwr4vgtvdog36nijderee