A common discrete implementation of the cross correlator uses a parabolic fit to the peak when the delay is not an integral multiple of the sampling period. This correspondence analyzes and assesses the pitfalls of this approach. It is shown that this yields a biased estimate of the time delay, with both the bias and variance of the estimate dependent on the location of the delay between samples, SNR, signal and noise bandwidths, and the prefilter or window used in the generalized correlator.
Ahtruct-Under consideration is the effectiveness of various windowing functions in the generalized correlator when a strong spectral peak, i.e., a sinusoid, is present in the signal. The windows W~I I ( W ) and WXOT(W) or &(w) avoid the ambiguity problem that is encountered by the other windows when sinusoids are present in the signal.
A structure is presented for passive estimation of range and bearing as well as velocity of a source from a linear array. It uses a quasi-optimal post processor of the time delays, which are obtained from a generalized correlator with finite observation time. The post processor ultimately maps the sequential time-delay observations onto invariant source trajectory parameters over which smoothing is performed to reduce, jointly, the variance and the bias in the estimate of the source kinematics. The present approach remains viable for moving sources at long ranges, off-broadside source directions and high time-delay variances. Analysis and simulation results are presented to justify its usefulness under the stated stringent conditions. Review of and comparison to existing approaches are made to highlight the viability of present approach in the estimation of source trajectory.
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