A discrete time domain approach on time delay estimation

Jorma Kekalainen


A time delay estimation method based on the discrete time domain approach is introduced here. In this dual-channel time delay estimation model, the criterion function compares the time differences of time sequences between channels, not the magnitude values of time functions as in the conventional cross-correlation method. An estimation task is formulated as an extreme value problem in discrete index space. Using the index delay giving extreme value to the criterion function, it is possible to find the best estimate for time delay distribution in the meaning of that criterion. Using this method, the estimated delay distribution and criterion function are clearly separated. Thus, there are no theoretical problems in the determination of the average time delay or velocity in the non-constant or changing time delay case as long as a sufficient statistical similarity (correlation) exists between channel signals. 

The theoretical values of several criterion functions and the probability of occurrence of an anomalous estimate with the cross-covariance criterion function are derived. A basic performance analysis of the estimation method is presented. Some potential real-time supervision methods based on the use of criterion functions in the detection of the possible unreliability of the time delay estimate are outlined.

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DOI: http://dx.doi.org/10.21014/acta_imeko.v8i1.600