Experimental Evaluation of some Thresholding Methods for Estimating Time-Delays in Open-Loop
2003 (English)Report (Other academic)
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. The purpose with this work is to test and evaluate a certain class of methods for time-delay estimation, especially with automatic control applications in mind. Particularly interesting it is to determine the best method. Is one method best in all situations or should different methods be used for different situations? The tested class of methods consists essentially of thresholding the cross correlation between the output and input signals. This is a very common method for time-delay estimation. The methods are tested and evaluated experimentally with the aid of simulations and plots of RMS error, bias and confidence intervals. The results are: The methods often miss to detect because the threshold is too high. The threshold has nevertheless been selected to give the best result. All methods over-estimate the time-delay. Nearly the whole RMS error is due to the bias. None of the tested methods is always best. Which method is best depends on the system and what is done when missing detections. Some form of averaging of the cross correlation, e.g. integration to step response or CUSUM, is advantageous. Fast systems are easiest. White noise input signal is easiest and steps is hardest. The RMS-errors are high in average (approximately greater than 6 sampling intervals). The error is lower for fast system or for high SNR.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2003. , 28 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2525
Time-delay, Dead-time, Estimation, System identification, Linear dynamic systems, Cross correlation, ANOVA, Confidence intervals, Simulations
IdentifiersURN: urn:nbn:se:liu:diva-55946ISRN: LiTH-ISY-R-2525OAI: oai:DiVA.org:liu-55946DiVA: diva2:316791