Interpolation of TW time transfer from measured points onto standard MJD for UTC generation

We often need to determine the time transfer result for an epoch at which no direct measurement was made. For example, the time tag used in Circular T is 0 h UTC of the standard MJD, which is not generally a measuring epoch. Usual time transfer practice is to first smooth the raw data to filter out white measurement noise, and then interpolate the smoothed data to determine the time transfer value for the required epoch. However, up until the end of 2009, for two-way (TW) time transfer only simple linear interpolation (but any high-order interpolation method) was used. This was because, when TW was introduced into the computation of UTC in 1998, there were not enough measured points to allow a mathematically rigorous smoothing-interpolation process. Since the end of 2005 the number of measurements has increased to between 12 and 24 per day. To exploit the redundancy of this increased number of data points, in 2005 it was proposed that a higher order smoothing-interpolation method be used. It was concluded that: (1) a high-order smoothing interpolation is better than a simple linear interpolation; and (2) Vondrak smoothing is preferable to other high-order smoothing-interpolation techniques. This paper builds on the previous study, examining the Vondrak smoothing-interpolation method with the benefit of a new powerful tool: the GPS PPP time-transfer solution. This provides an objective measure of the performance of different smoothing-interpolation methods. We conclude that in most cases Vondrak smoothing to the power 10
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leads to the best interpolation results.