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 h as small relative bandwidth. Then, for signal to noise ratios below a certain threshold, the commonly used Cramer-Rao lower bound is not rea lizable. The study concentrates on the region of intermediate SNR valu es, where the Cramer-Rao bound is no longer achievable, but useful inf ormation on time delays can still be obtained from the measurement. Re alizable bounds for the single and two echo cases are obtained by deri ving a new form of the Barankin bound for active time delay estimation . This form maintains the realizability property of the most general f orm, but is of reasonable complexity. New bounds are derived for the m ultiple echo case. Examples are presented to illustrate the dependence of the bound on parameters such as SNR, relative bandwidth, and echo separation.