Experimental Evaluation of some Cross Correlation Methods for Time-Delay Estimation in Linear Systems

In this report we study estimation of time-delays in linear dynamical systems with additive noise. Estimating time-delays is a common engineering problem, e.g. in automatic control, system identification and signal processing.We have experimentally studied cross correlation methods for time-delay estimation in order to find the "best" method or if none is best which method to use in different situations. We have simulated systems with time-delay and studied internal quantities of the methods, the time-delay estimates, RMS-errors of estimates, percentage of failed estimates, Analysis of Variance (ANOVA) and confidence intervals for different cases. Our result is that no method is always best but one method is clearly inferior to the other. The methods can be divided in two groups with similar properties: thresholding methods and area and moment methods. The thresholding methods work better for fast systems than slow systems whereas the area and moment methods works better for slow systems than fast. The thresholding methods work better with random binary input signals than steps as input whereas the area and moment methods works better with steps as input than random binary input