A Combined Smoothing Method of Ensemble Pulsar Timescale and Application for Pulsar Atomic Clock Combined Timescale

Clock difference between the ensemble pulsar timescale (PT) and the International Atomic Time (TAI) PT-TAI derived from the International Pulsar Timing Array (IPTA) data set indicates a very similar variation trend with the Terrestrial Time TT(BIPMXXXX)-TAI but PT has larger measurement error. In this paper, we discuss the smoothing method of PT using a combined smoothing filter and compare the results with that from other filters. The clock difference sequence between PT-TAI and the first time derivative series of the TT(BIPMXXXX)-TAI can be combined by a combined smoothing filter to yield two smooth curves tied by the constraints assuring that the latter is the derivative of the former. The ensemble pulsar time IPTA2016 with respect to TAI published by G. Hobbs et al. and first time derivative series of the TT(BIPM2017)-TAI with quadratic polynomial terms removed are processed by combined smoothing filter in order to demonstrate the properties of the smoothed results. How to correctly estimate two smoothing coefficients is described and the output results of the combined smoothing filter are analyzed. The results show that the combined smoothing method efficiently removes high frequency noises of two input data series and the smoothed data of the PT-TAI combine long term fractional frequency stability of the pulsar time and frequency accuracy of the terrestrial time. Fractional frequency stability analysis indicates that both short and medium time interval stability of the smoothed PT-TAI is improved while keeping its original long term frequency stability level. The combined smoothing filter is more suitable for smoothing observational pulsar timescale data than any filter that only performs smoothing of a single pulsar time series. The smoothed pulsar time by combined smoothing filter is a pulsar atomic time combined timescale. This kind of combined timescale can also be used as terrestrial time.