On the Cramér-Rao Bound of Multi-Subband Based High Accuracy Time Delay Estimation

The accuracy of time delay estimation (TDE) is primarily determined by the bandwidth of the received signal. For a passive system, however, the emitting signal is non-cooperative so the bandwidth is not controllable. Since a source may radiate or reflect multiple subband signals with different center frequencies but the time delay of each subband is the same, using the subbands together perhaps improves the TDE accuracy. This paper investigates the Cramer-Rao bound (CRB) derivation of multi-subband signals (MSS)-based TDE problem. The new CRB indicates that using multiple subbands should result in a better performance than the classical model. We formulate the MSS-based time delay estimating as a maximizing optimization problem under the least-squares criteria. Simulations illustrate the proposed method of reaching the CRB. And the MSS-based TDE shows notable superiority on the accuracy of both theoretical bound and numerical results.