On the Accuracy Limit of Time-delay Estimation with a Band-limited Signal
Priyanka Sarkar Das, Jordi Vilà‐Valls, Éric Chaumette, François Vincent, Loïc Davain, Silvère Bonnabel · 2019
The derivation of tight estimation lower bounds is a key player to design and assess the performance of new estimators. Considering a generic band-limited signal formulation and constant transmitter to receiver propagation delay, we propose a novel compact closed-form expression of the Cramér-Rao bound for time-delay estimation. This new formulation, especially easy to use, allows to derive the best (lowest) Cramér-Rao bound for a band-limited signal of given length and energy, which provides an estimation performance loss metric. These results are illustrated with two representative band-limited signals.