A Survey and Comparison of Time-Delay Estimation Methods in Linear Systems

Abstract: In this thesis the problem of time-delay estimation (TDE) in linear dynamic systems is treated. The TDE is studied for signal-to-noise ratios, input signals, and systems that are common in process industry. This also implies that both open-loop and closed-loop cases are of interest. The true time-delay is estimated, which may be different from the time-delay giving the best model approximation of the true system. Time-delays which are not a multiple of the sampling interval are also of interest to estimate.In this thesis, a review and a classification according to underlying principles of TDE methods in the literature are made. The main classes are: 1) Time-Delay Approximation Methods: The time-delay is estimated from a relation (a model) between the input and output signals expressed in a certain basis. The time-delay is not an explicit parameter in the model. 2) Explicit Time-Delay Parameter Methods: The time-delay is an explicit parameter in the model. 3) Area and Moment Methods: The time-delay is estimated from certain integrals of the impulse and step responses. 4) Higher Order Statistics Methods.Some new methods and variants of old ones are suggested and evaluated, some of which have good estimation performance and some poor performance. Properties of TDE methods are analyzed, both theoretically and experimentally. Recommendations are given on how to choose estimation method and input signal. Generally, prediction error methods where the time-delay parameter is explicit and is optimized simultaneously with the other model parameters give good estimation quality.Most evaluations have been conducted with factorial experiments using Monte Carlo simulations in open and closed loop. Some statistical analysis methods have been utilized: The RMS error of the time-delay estimates gives an absolute measure of the performance. ANOVA (ANalysis Of VAriance) and confidence intervals give conclusions with a certain level of confidence.