Analysis and Comparisons of Four Kinds of Ensemble Pulsar Time Algorithm

Details Analysis and Comparisons of Four Kinds of Ensemble Pulsar Time Algorithm Analysis and Comparisons of Four Kinds of Ensemble Pulsar Time Algorithm

Oct 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009acasn..50..425z&link_type=abstract

Acta Astronomica Sinica, vol. 50, no. 4, p.425-437

Astronomy and Astrophysics

Astronomy

3

Time, Pulsars: General, Methods: Miscellaneous

Scientific paper

Pulsars, rapidly rotating neutron stars, have extremely stable rotating periods. The pulsar time defined by a single pulsar is influenced by several noise resources. To weaken these influences, the ensemble analysis method is used to obtain the ensemble pulsar time so that the long-term stability of the ensemble pulsar time can be improved. In this paper, four algorithms -- the classical weighted average algorithm, the wavelet analysis algorithm, the Wiener filtration analysis algorithm and the Wiener filtration analysis in wavelet domain -- are applied to synthetically make an ensemble pulsar time. The data used are the residuals of the two millisecond pulsars (PSR B1855+09 and PSR B1937+21) observed by Arecibo Observatory. First, the classical weighted average algorithm is developed by Petit, in which only one weight can be chosen within the whole interval of the observation on each single pulsar time, and the criterion for weight is the stability σ2z(T) of each single pulsar time. Second, an ensemble pulsar time algorithm is developed based on the wavelet multi-resolution analysis and the wavelet packet analysis, which can be obtained by decomposing the observation residuals of pulsars, extracting the components of different frequency domain and then choosing the weight according to the stability of different component denoted with wavelet variance. Third, the pulsar timing residuals are caused by reference atomic clock and pulsar itself, which are uncorrelated. Considering this uncorrelation and the peculiarity of Wiener filtration, we put forward an ensemble pulsar time algorithm of Wiener filtration. Using this algorithm, the error can be separated from an atomic clock and the pulsar itself in the post-fit pulsar timing residuals. The atomic scale component can be filtered from the pulsar phase variations and the remains can be integrated to the ensemble pulsar time. Weights are chosen according to the mean square root. Forth, the wavelet analysis and the Wiener filtration algorithm are combined and a new ensemble pulsar time algorithm called the Wiener filtration analysis in wavelet domain is presented in this paper, which can remove the influence of noise more effectively. The pulsar timing residuals are decomposed to different components by wavelet. The influences of the atomic clock of different components are removed by Wiener filtration and then the ensemble pulsar time can be obtained by inverting the wavelet transform acting on these remains. The computed result indicates that the latter three algorithms are far better than the first one and the Wiener filtration analysis in wavelet domain could be the best one among all algorithms.

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