Generalised crosscorrelator with data-estimated weighting function: a simulation analysis

The distinctive feature of a generalised crosscorrelator (GCC) over a conventional one is the presence of a filtering section which enables it to enhance its performance according to some optimality criterion. This section provides a weighting action on the crosspower density spectrum of the input signals and, if properly designed, can improve the estimate of the time delay existing between waveforms generated by a single acoustic source and received at two spatially separate sensors. An assumption which is commonly made on the weighting window is that it is exactly matched to signal and noise spectral characteristics, that are supposedly known a priori. Unfortunately this does not happen in most practical situations, and the only means to acquire knowledge about the spectral characteristics of signal and noises is estimating them from the received waverforms. Since this operation is expected to degrade the GCC performance, an analysis of these degradations is called for. This work focuses on the analysis of the performance attainable with a particular window, namely the Hassab-Boucher-II (HBII) window, in the assumption that all necessary spectra are estimated from finite segments of the observed input signals. The selected window theoretically exhibits a good capability to combat the ambiguity effect produced by strong sinusoidal components affecting the signal. On the other hand, it has also been shown that this window performs reasonably well in the presence of broadband noise alone. For comparison purposes, the analysis has been carried out with simulated signals in three different crosscorrelator configurations: (i) GCC employing the Hassab-Boucher-II window calculated exactly on the basis of the a priori knowledge of signal and noise spectral characteristics, (ii) GCC employing the Hassab-Boucher-II window calculated on the basis of the spectral characteristics estimated from a finite record of signals, and (iii) conventional crosscorrelator. In each configur- ation the mean and the variance of the measured delay have been estimated; the results are discussed and compared with the Cramer-Rao lower bound (CRLB). The performance of the three configurations is also analysed in the presence of a sinusoidal component affecting both inputs, which simulates a strong narrowband signal.