A comparative study of the LMS adaptive filter versus generalized correlation method for time delay estimation

This paper provides a comparison of the LMS adaptive filter versus conventional Generalized Correlation (GC) methods of time delay estimation in terms of their mean-square-error performance. The treatment is restricted to broadband stationary inputs with finite observation time without a priori knowledge of the processor input statistics. The time delay estimator probability distribution, variance, and error probability are derived for the LMS adaptive filter approach. Further, a performance index is given which is optimized with respect to choice of step size. The simulation results presented indicate that without a priori knowledge of the input statistics, both approaches yield similar sub-optimal results. On the other hand, optimal processing of the adaptive filter weights can yield an estimator with variance similar to that of the minimum variance GC method which approaches the Cramer-Rao Lower Bound.