Performance analysis of time delay estimation of a signal with arbitrary spectrum

The fundamental limitations of passive time delay estimation (TDE) are well understood for the case of a Gaussian, stationary single source of known, flat spectrum. The authors present results concerning the sensitivity of the achievable estimation performance of the signal source spectra. By applying the Barankin bound to the multi-dimensional parameter estimation problem, they derive an expression for a lower bound on the time delay estimation error of a broadband source with unknown spectral levels. They show that, when large estimation errors are assumed (below the threshold), the estimation performance is no longer insensitive to prior knowledge of the source spectra. However, in most practical situations the degradation in the performance of the TDE due to the lack of prior knowledge of the source spectral parameters is small. Nevertheless, the achievable estimation performance at a given signal-to-noise ratio depends strongly on the shape of the source spectrum.<>