三种综合脉冲星时算法的研究和比较

Study and comparisons of three ensemble pulsar time algorithm

建立在小波分析基础上的综合脉冲星时算法,能把脉冲星的观测计时残差在小波域分解,提取出不同频率范围的分量,然后用小波方差表征脉冲星在不同频率范围的稳定度来对单脉冲星时进行加权平均,得到综合脉冲星时;脉冲星的计时残差包括了计时参考的原子钟的误差和与脉冲星本身有关的计时误差2部分,用维纳滤波的方法可以将两者进行一定区分,并消除估计的参考钟误差,将剩余部分作为计时残差实现对脉冲星计时的综合.实验证明,小波分析和维纳滤波方法比经典的加权算法更好,得到的综合脉冲星时的长期稳定度有了较大提高.

Pulsar time defined by single pulsar is influenced by several noise resources, to weaken these influences for gaining a more stable time scale, one can take ensemble analysis method to obtain ensemble pulsar time. Three algorithms of ensemble pulsar time are presented： classical weighted average algorithm, to gain the best long-term stability of ensemble pulsar time, one can choose the weight according to the long-term stability of each pulsar; the residuals of single pulsar can be decomposed by wavelet analysis in wavelet domain, and the component of different frequency range can be obtained. Then we can apply wavelet analysis algorithm to integrate the pulsar time;the weights are chosen according to reciprocal of wavelet average square error. The pulsar timing residuals are caused by reference atomic clock and pulsar itself. Wiener filtration analysis algorithm allows the separation of the contributions of an atomic clock and a pulsar itself to the post-fit pulsar timing residuals. The method allows to filter the atomic scale component from the pulsar phase variations. These three algorithms have been applied to the timing data of the millisecond pulsars PSR B1855 ＋ 09 and PSR B1937 ＋ 21. The result has indicated that the ensemble pulsar time obtained after the ensemble algorithm to pulsar time defined by several pulsar time weakens the influence of noise on a great extent, and consequently improves the stability. Furthermore the stability of the ensemble pulsar time obtained by wavelet analysis algorithm and Wiener filtration are better than the stability of the ensemble pulsar time obtained by sample weighted average algorithm. Obviously, wavelet analysis algorithm and Wiener filtration are more feasible approach to deal with time-frequency signals.