Haiyan Fang

Denoising of X-ray pulsar observed profile using biorthogonal lifting wavelet transform

In X-ray pulsar-based navigation, strong X-ray background noise leads to a low signal-to-noise ratio (SNR) of the observed profile, which consequently makes it very difficult to obtain an accurate pulse phase that directly determines the navigation precision. This signifies the necessity of denoising of the observed profile. Considering that the ultimate goal of denoising is to enhance the pulse phase estimation, a profile denoising algorithm is proposed by fusing the biorthogonal lifting wavelet transform of the linear phase characteristic with the thresholding technique. The statistical properties of X-ray background noise after epoch folding are studied. Then a wavelet-scale dependent threshold is introduced to overcome correlations between wavelet coefficients. Moreover, a modified hyperbola shrinking function is presented to remove the impulsive oscillations of the observed profile. The results of numerical simulations and real data experiments indicate that the proposed method can effectively improve SNR of the observed profile and pulse phase estimation accuracy, especially in short observation durations. And it also outperforms the Donoho thresholding strategy normally used in combination with the orthogonal discrete wavelet transform.

X-ray pulsar-based navigation using pulse phase and Doppler frequency measurements

In order to eliminate the impact of the Doppler effects caused by the motion of the spacecraft on the X-ray pulsar-based navigation, an innovative navigation method using the pulse phase and Doppler frequency measurements of the X-ray pulsars is proposed. Given the initial estimate of the spacecraft’s state, the real-time photon arrival model is established at the spacecraft with respect to the spacecraft’s position and velocity predicted by the orbit dynamic model and their estimation errors. On this basis, a maximum likelihood estimation algorithm directly using the observed photon event timestamps is developed to extract a single pair of pulse phase and Doppler frequency measurements caused by the spacecraft’s state estimation error. Since the phase estimation error increases as the observation time increases, we propose a new measurement updating scheme of referring the measurements to the middle time of an observation interval. By using the ground-based simulation system of X-ray pulsar signals, a series of photon-level simulations are performed. The results testify to the feasibility and real-timeliness of the proposed navigation method, and show that the incorporation of the Doppler measurement as well as the pulse phase into the navigation filter can improve the navigation accuracy.摘要创新点1.提出了一种新的基于脉冲相位和多普勒频率联合观测量的 X 射线脉冲星导航方法.2.分别建立了脉冲相位及多普勒频率观测量与航天器初始位置及速度误差的关系.3.将联合观测量的参考时刻取为观测时段的中间时刻, 有效地提高了导航精度.

A novel period estimation method for X-ray pulsars based on frequency subdivision

Period estimation of X-ray pulsars plays an important role in X-ray pulsar based navigation (XPNAV). The fast Lomb periodogram is suitable for period estimation of X-ray pulsars, but its performance in terms of frequency resolution is limited by data length and observation time. Longer observation time or oversampling can be employed to improve frequency analysis results, but with greatly increased computational complexity and large amounts of sampling data. This greatly restricts real-time autonomous navigation based on X-ray pulsars. To resolve this issue, a new method based on frequency subdivision and the continuous Lomb periodogram (CLP) is proposed to improve precision of period estimation using short-time observation data. In the proposed method, an initial frequency is first calculated using fast Lomb periodogram. Then frequency subdivision is performed near the initial frequency to obtain frequencies with higher precision. Finally, a refined period is achieved by calculating the CLP in the obtained frequencies. Real data experiments show that when observation time is shorter than 135 s, the proposed method improves period estimation precision by 1–3 orders of magnitude compared with the fast Lomb periodogram and fast Fourier transform (FFT) methods, with only a slight increase in computational complexity. Furthermore, the proposed method performs better than efsearch (a period estimation method of HEAsoft) with lower computational complexity. The proposed method is suitable for estimating periods of X-ray pulsars and obtaining the rotation period of variable stars and other celestial bodies.

The Research of X-Ray Pulsar Signals Simulation Method

X-ray can’t be directly observed at laboratory due to the absorption of atmosphere. Furthermore, observation at space consumes a great deal of financial and material resources and is highly risky. Therefore, simulation data of X-ray pulsar is of great importance, whereas the current simulation method can only generate X-ray signals of constant period at the Solar System Barycenter (SSB), without considering the slow varying property of pulsar period and the large scale space-time effects. This paper proposes a new simulation method for X-ray pulsar signal. First, the arrival phase of the next photon at the SSB is recursively calculated according to the phase of the previous photon. Next, seek the pulsar ephemeris to obtain the phase evolution model of the current time. Then, transform the arrival phase of the photon to its arrival time at the SSB using the obtained phase evolution model. Subsequently, utilizing the solar system ephemeris and orbital parameters of the spacecraft, the arrival time of the corresponding photon at the spacecraft can be acquired by an iterative algorithm. Simulation results show the validity of the proposed methods. The simulation data of the proposed method includes the slow varying property of pulsar period and the large scale space-time effects, also is very similar to the RXTE observation data. Thus the proposed method can be applied to the validation of all the algorithms needed in the practical navigation, such as profile integrating and large scale time transformation.

X-ray counting imaging based on spherical collimation

Aiming at the difficulty in X-ray focusing, small field of view and the low sensitivity for the X-ray imaging, a spherically collimated X-ray counting imaging method was proposed based on the concept of single-pixel camera. The spatial X-ray star maps that are sparse in the airspace were measured under the function of binary sparse observation matrix, and reconstructed rapidly by the use of TVAL3 algorithm. Finally, a series of simulations were designed to evaluate the performance of the reconstruction in Peak Signal to Noise Ratio (PSNR), Bhattacharyya Coefficient and Pearson Correlation Coefficient (PCC). The results demonstrate that the PSNR and PCC of the reconstructed image are respectively 27.1992 and 0.94273 for the sparse ratio 0.05.

Research on Pulse Profile Stability of the X-ray Pulsar PSR B1509-58

Pulse profiles of X-ray pulsars play an important role in X-ray pulsar-based navigation (XPNAV) and studying the rotation and emission characteristics of the pulsars. In this paper, we present an X-ray timing analysis of the young Crab-like pulsar PSR B1509-58 by using archival Rossi X-ray Timing Explorer (RXTE) data. We have investigated the stability of the PSR B1509-58 pulse profile in the energy band of 2–60 keV. The analysis results show that in the energy band of 2–30 keV, the flux is the largest than that of the 30–45, 45–60 keV, the 2–30 keV energy band possess the most photon series in 2–60 keV. As the energy range increases, the Pearson’s correlation, between the standard pulse profile and the integrated pulse profiles of 2–30, 30–45, 45–60 keV, varies small, all the Pearson’s correlations in different energy ranges are above 0.99, meanwhile, in the energy ranges of 2–30 keV, there is no obvious phase delay between the integrated pulse profile and the standard pulse profile, which means that the pulse profile is stable.