Realizable lower bounds for time delay estimation

The accuracy of time delay estimates obtainable in active localization systems is studied, focusing on the effect of ambiguities in the time delay estimates. Such ambiguities occur when the transmitted signal has small relative bandwidth. Then, for signal to noise ratios below a certain threshold, the commonly used Cramer-Rao lower bound is not realizable. The study concentrates on the region of intermediate SNR values, where the Cramer-Rao bound is no longer achievable, but useful information on time delays can still be obtained from the measurement. Realizable bounds for the single and two echo cases are obtained by deriving a new form of the Barankin (1949) bound for active time delay estimation. This form maintains the realizability property of the most general form, but is of reasonable complexity. New bounds are derived for the multiple echo case. Examples are presented to illustrate the dependence of the bound on parameters such as SNR, relative bandwidth, and echo separation