Refining Time Delay Estimate of Complex Signal Using Polynomial Interpolation in Time Domain
Oksana Guschina
Abstract
This paper deals with time delay estimation of a complex random signal carried out in the time domain where its discrete-time finite observation is being processed. The paper observes polynomial interpolation methods applied to a sampled cross-correlation function (CCF) in the neighborhood of its maximum. This kind of approximation compromises the fast computation of the delay with the high accuracy of resultant estimate. The second and third order polynomial approximation schemes are considered for three approaches based on absolute value of correlation samples or their complex originals. The latter is shown to be obligatory forced with the condition that time delay estimate has to be real-valued despite the fact that complex signals are processed. The numerical simulation performed for first-order autoregressive model random process allows estimating the dependency of the bias, variance and total error of the estimates on signal-to-noise ratio. The comparative analysis conducted for the methods shows that second-order approximation applied to absolute value of CCF produce the accuracy that can be treated as satisfactory for general purpose.