The detection of the X-ray pulsar signal is important for the autonomous navigation system using X-ray pulsars. In the condition of short observation time and limited number of photons for detection, the noise does not obey the Gaussian distribution. This fact has been little considered extant. In this paper, the model of the X-ray pulsar signal is rebuilt as the nonhomogeneous Poisson distribution and, in the condition of a fixed false alarm rate, a fast detection algorithm based on maximizing the detection probability is proposed. Simulation results show the effectiveness of the proposed detection algorithm.
X-ray pulsars are rapidly rotating neutron stars which could emit X-ray signals periodically, stably, and uniquely [
The first widely used X-ray pulsar signal detection algorithm is based on the Fast Fourier Transform (FFT), which has been proved to be invalid when the signal’s profile is nonsinusoidal or the noise is nongaussian [
For XPNAV, the accurate prior knowledge about the X-ray pulsar signal is essential. The prior knowledge includes the X-ray background noise’s rate, the signal’s flux, period, and profile. By using the prior information, we may build the Probability Density Function (PDF) [
The rest of this paper is organized as follows. Section
Unlike the radio signal, the X-ray pulsar signal shows the particle property, which means the output of X-ray detector on the spacecraft is not an analog signal but a discrete arriving time sequence of individual photons. Assuming the observation time is
We divide the observation timeline into
The observation timeline.
Since the random variables in the different bins are independent, the Joint Probability Density Function (JPDF) could be expressed as
If the X-ray pulsar signal exists in the received photons,
If the X-ray pulsar signal does not exist in the received photons,
In the condition of a fixed probability of false alarm
If
Since
If
From ( The X-ray detector on-board receives the photons and notes each photons’ arriving time Convert the transferred arriving time Search the arriving rate Add up all
The prior knowledge before the detection process includes the XPNAV database about the arriving rate functions Set a fixed probability of false alarm Generate the arriving time of the photons based on the Poisson distribution with the arriving rate Calculate Repeat step (II) and step (III) for Rank each simulation result in descending order, and set a threshold
Besides the prior knowledge, how to convert the arriving time
Assuming
For the practical navigation application,
Three weak X-ray pulsars (B0540-69, B1744-24A, and B1823-13) are selected to simulate the proposed detection algorithm’s performance. The parameters of the X-ray pulsars are shown in Table
The parameters of X-ray pulsar sources.
ID | Name | RA(J2000) (hh:mm:ss) | DE(J2000) (dd:mm:ss) | Flux (photons/cm2/s) | Period (s) |
---|---|---|---|---|---|
1 | B0540-69 | 05:39:39 | −69:44:36 | | 0.0505 |
2 | B1744-24A | 17:48:02 | −24:46:38 | | 0.0116 |
3 | B1823-13 | 18:26:13 | −13:34:47 | | 0.1015 |
The normalization standard profile templates of three X-ray pulsars.
The initial phase
The MF algorithm calculates the correlation peak for the X-ray pulsar signal’s profile with the standard signal template [
We divide the simulation algorithm into three groups: (I) the optimal NP detection algorithm; (II) the suboptimal NP detection algorithm, and the number of segments for searching both
The detection probability for B0540-69.
The detection probability for B1744-24A.
The detection probability for B1823-13.
From Figures
Since the limited number of photons, the estimation for
The detection for the X-ray pulsar signal is important for XPNAV and some other navigation scenarios using X-ray pulsars. In this paper, we propose a fast detection algorithm for the X-ray pulsar signal based on NP criteria. Computer simulations show that, in the condition of short observation time and limited number of photons, the detection probability of the proposed algorithm is still high. Besides that, the fast detection algorithm may be extended to other detection issues when the signals obey the Poisson distribution.
The authors declare that they have no competing interests.
This work was supported by National Natural Science Foundation of China (61271265 and 61671263) and Tsinghua University Initiative Scientific Research Program (2013089244 and 20161080057).