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目的:针对现有脉冲星周期估计算法精度低的问题,研究一种利用短时观测数据进行高精度X射线脉冲星周期估计的算法,为促进实时高精度X射线脉冲星导航提供算法支撑。创新点:提出频率细分的方法,推导continuous Lomb periodogram(CLP),实现X射线脉冲星非等间隔到达光子序列在细分频率处的频域分析。该方法可以显著减少运算复杂度,同时提高频域分析的频率分辨率,进而提高脉冲星周期估计的精度。方法:首先,考虑到X射线脉冲星信号是非等间隔到达的光子序列,本文采用专门用于非等间隔数据处理的fast Lomb方法对一段短时观测的脉冲星实测数据进行频域分析,获得一个初始频率作为脉冲星旋转频率的初值。然后,在该初始频率附近以高的频率分辨率做频率细分,获取设定数量的高精度细分频率。最后,对该段短时观测的脉冲星数据在这些细分频率处做CLP分析。在CLP中,峰值位置所对应的频率即为估计出的具有较高精度的脉冲星旋转频率,由该频率就可以确定高精度的脉冲星旋转周期。实测数据分析表明:当观测数据小于135 s时,本文算法的周期估计精度比fast Lomb方法和FFT方法高1到3个数量级,且仅增加了一点计算复杂度。同时,相比于HEAsoft的周期估计方法(efsearch),本文算法具有精度高计算复杂度低的优势。结论:本文算法解决了fast Lomb方法在周期估计时精度受数据长度和观测时间限制的问题,显著提高了X射线脉冲星周期估计的精度并降低了计算复杂度。同时短时高精度的周期估计有助于提高TOA估计精度及X射线脉冲星导航中实时位置和速度的估计精度。本文算法还可以用于变星及其他天体的周期估计。
OBJECTIVE: To solve the problem of low accuracy of existing pulse period estimation algorithms, an algorithm for estimating the period of high-precision X-ray pulsars using short-time observation data is proposed and provides an algorithm support for the promotion of real-time high-precision X-ray pulsar navigation. Innovative point: Propose the method of frequency subdivision, derive the continuous Lomb periodogram (CLP), and realize the frequency domain analysis of the non-equidistant arrival photon sequence of X-ray pulsar at the subdivision frequency. This method can significantly reduce the computational complexity and improve the frequency resolution of the frequency domain analysis, so as to improve the accuracy of the pulsar period estimation. Firstly, considering the photon sequence that X-ray pulsar signal arrives at non-equidistant intervals, a fast Lomb method specially used for non-equidistant data processing is used to analyze the measured data of a short period of pulsars in frequency domain to obtain a Initial frequency as the initial value of the pulsar rotation frequency. Then, frequency subdivision is performed at a high frequency resolution near the initial frequency to obtain a set number of high-precision subdivision frequencies. Finally, the Pulsar data from this short-term observation are analyzed for CLP at these subdivided frequencies. In the CLP, the frequency corresponding to the peak position is the estimated pulsar rotation frequency with higher accuracy, from which the high-precision pulsar rotation period can be determined. The measured data analysis shows that the proposed algorithm has 1 to 3 orders of magnitude higher accuracy than the fast Lomb method and the FFT method when the observed data is less than 135 s, and only adds a little computational complexity. Meanwhile, compared with HEAsoft’s periodic efsearch, the proposed algorithm has the advantages of high precision and low computational complexity. Conclusion: The proposed algorithm solves the problem that the accuracy of fast Lomb method is limited by data length and observation time in period estimation, which improves the accuracy of X-ray pulsar periodic estimation and reduces the computational complexity significantly. At the same time, short-term and high-precision periodic estimation can help improve the TOA estimation accuracy and the estimation accuracy of real-time position and velocity in X-ray pulsar navigation. The algorithm in this paper can also be used to estimate the periodicity of variable stars and other celestial bodies.