Variance Analysis of Unevenly Spaced Time Series Data

We have investigated the effect of uneven data spacing on the computation of delta (sub chi)(gamma). Evenly spaced simulated data sets were generated for noise processes ranging from white phase modulation (PM) to random walk frequency modulation (FM). Delta(sub chi)(gamma) was then calculated for each noise type. Data were subsequently removed from each simulated data set using typical two-way satellite time and frequency transfer (TWSTFT) data patterns to create two unevenly spaced sets with average intervals of 2.8 and 3.6 days. Delta(sub chi)(gamma) was then calculated for each sparse data set using two different approaches. First the missing data points were replaced by linear interpolation and delta (sub chi)(gamma) calculated from this now full data set. The second approach ignored the fact that the data were unevenly spaced and calculated delta(sub chi)(gamma) as if the data were equally spaced with average spacing of 2.8 or 3.6 days. Both approaches have advantages and disadvantages, and techniques are presented for correcting errors caused by uneven data spacing in typical TWSTFT data sets.