A method for estimating X-ray pulsar period and pulse time delay

Abstract

The present invention discloses a method for estimating the period and pulse time delay of an X-ray pulsar, and belongs to the technical field of pulsar navigation. The method comprises: finding the optimal harmonic truncation order for each observation through the H test, that is, according to the principle of minimizing the average integrated square error between the Fourier series estimator and the true profile; realizing adaptive selection of the harmonic truncation order under different data qualities according to the prior information of the observed event; re-estimating the phase of the binned data according to the principle of equal photon intensity segmentation within the bin, so that the folded profile is closer to the true profile; combining simulation and measured data for quantitative analysis, selecting the optimal number of bins, and providing the folded profile with the best discrimination for statistical test. The present invention has the advantages of being suitable for navigating pulsar sources, high reliability, strong environmental adaptability, high estimation accuracy, strong estimation stability, etc., and can further improve the navigation performance of X-ray pulsars.

Description

Technical Field

[0001] The present invention belongs to the technical field of pulsar navigation, and in particular relates to a method for estimating the period and pulse time delay of an X-ray pulsar. Background Art

[0002] In recent years, with the continuous development of deep space exploration technology, the research on autonomous celestial navigation of deep space probes has become more and more in-depth. As a navigation method that is more suitable for deep space exploration missions, celestial navigation technology has been widely used in the field of deep space exploration. According to the different measurements, celestial navigation can be divided into angle measurement navigation, velocity measurement navigation and distance measurement navigation. Traditional astronomical angle measurement navigation methods (such as starlight angular distance navigation) are greatly affected by the distance between the spacecraft and the near celestial body, and their navigation accuracy is often not guaranteed. However, as an emerging astronomical distance measurement navigation method, X-ray pulsar navigation has a highly stable time standard and ultra-high positioning measurement accuracy, and is an ideal deep space probe navigation method.

[0003] A pulsar is a high-speed spinning neutron star with a stable spin period, which continuously radiates stable periodic signals into the universe. At present, there are about 300 pulsars that can be used for navigation, and pulsars that can be used for navigation need to meet many conditions, such as X-ray photon flux, pulse duty cycle, X-ray background radiation flux, duty cycle, pulse profile width, etc., which are all important factors to measure whether a pulsar can be used for navigation. It can be seen that the profile of a pulsar signal is crucial to whether it can be used for navigation. At present, PSR B0531+21 is widely used as a navigation pulsar. It is located in the center of the Crab Nebula and is a relatively young neutron star. Because it is very bright, the flux density and spectrum are constant, and it can provide strong periodic signals, it is often used as a calibration source for X-ray astronomy.

[0004] X-ray pulsar navigation used in deep space exploration missions mainly uses the time delay between the pulse profile signal reaching the spacecraft and the center of mass of the solar system as a measurement for navigation filtering. Therefore, the estimation of time delay directly determines the accuracy of pulsar navigation. However, since the pulsar signal in the X-ray band is relatively weak, the detector can only receive a series of photon arrival times. Therefore, accurately recovering the pulsar profile by estimating the pulsar period is crucial for time delay estimation.

[0005] At present, the estimation methods for pulsar period and time delay can be mainly divided into two categories: estimation based on profile prior information and estimation based on unknown profile prior information. For the estimation method with known profile prior information, in 2007, the maximum likelihood estimation method was used to estimate pulsar period and time delay. This method takes the known pulsar profile as prior information and the photon arrival time series as the independent variable to construct the likelihood function. With the maximum likelihood function as the goal, the pulsar period and time delay are estimated; the image matching method is used to estimate pulsar period and time delay. This method uses the inverse space filling curve to convert the pulsar profile into a two-dimensional image, and matches the image with the standard pulsar template to achieve period and time delay estimation. This type of estimation method based on profile prior information has a relatively stable estimation effect and high accuracy, but the amount of calculation is large.

[0006] The estimation method of prior information of unknown contours is mainly based on statistical test methods. The pulsar period estimation method based on the test function performs epoch folding on the candidate periods and compares the folded contours. The optimal period is determined by statistics. However, although this method has a small amount of calculation, it is greatly affected by noise interference, especially in actual detection tasks with large background noise. The estimation accuracy is low. 2 The period estimation method of the test function can effectively improve the problem of reduced estimation accuracy due to excessive noise, but in this method, all photon events are involved in the calculation, and the calculation speed is slow. 2 The selection of the harmonic truncation order in the test function will also have a certain impact on the accuracy of period estimation. 2 Based on the test function, the harmonic truncation order is determined by the Hart principle. In 2019, scholars 2 The test function is applied to the binned data, which greatly improves the operation speed and will be Z in 2021. 2 The application of statistics is extended to more general waveforms. 2 The use conditions of the test function period estimation method are relatively limited, and the estimation effect is good only for pulsars with relatively flat profiles. For pulsars with more complex profiles, using only traditional methods often cannot obtain good estimation results. Summary of the invention

[0007] In order to solve the above technical problems, the present invention proposes a method for estimating the period and pulse time delay of an X-ray pulsar based on an improved Z 2 The function expansion is verified and can be applied to the estimation of pulsar period and time delay with complex profiles.

[0008] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0009] A method for estimating X-ray pulsar period and pulse time delay comprises the following steps:

[0010] Step 1: Determine the optimal harmonic truncation order under the photon number task based on the Hart test, and find the quantitative relationship between the prior information of the spacecraft detector on the number of photons and the optimal harmonic truncation order;

[0011] Step 2: Re-estimate the optimal phase of the boxed data by the principle of “equal area division” within the box;

[0012] Step 3: Establish a quantitative relationship between the number of boxes of packed data and the estimation accuracy and calculation cost, and select the optimal number of boxes;

[0013] Step 4: Perform steps 1 to 3 in all candidate cycles to improve Z 2 The highest statistic is used as the discrimination criterion to select the optimal X-ray pulsar period estimate, and the time delay estimate of the X-ray pulsar is obtained through cross-correlation calculation based on the profile folded from the optimal X-ray pulsar period estimate.

[0014] The beneficial effects of the present invention are:

[0015] (1) Z 2 The statistics are applied to navigation pulsar sources with more complex profiles to provide more accurate period and time delay estimates for X-ray pulsar navigation.

[0016] (2) Compared with traditional methods, the method proposed in the present invention can provide more accurate estimation results under observation conditions with poor data quality, such as short observation time, small detector area, and large noise interference. This makes the method more suitable for the complex and changeable X-ray pulsar navigation mission in actual deep space exploration.

[0017] (3) By processing the measured data of XPNAV-1, the proposed method improves the period estimation accuracy by 58.86% and the profile phase accuracy by 50.71% compared with the traditional method. At the same time, the stability of the period and profile phase estimation of this method is also greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A schematic diagram of a process flow of an X-ray pulsar period and pulse time delay estimation method according to the present invention;

[0019] Figure 2 The number of observed photons under the satellite's on-orbit observation mission and the result of searching for the optimal harmonic truncation order using the H test;

[0020] Figure 3 It is a schematic diagram of the binning phase partitioning process;

[0021] Figure 4 Schematic diagram of the division of equal photon numbers;

[0022] Figure 5 The processing results of simulation data and measured data are shown in Figure 1, where (a) is the relationship curve between the estimation accuracy of simulation data and the operation time, and (b) is the relationship curve between the estimation accuracy of measured data and the operation time;

[0023] Figure 6 Schematic diagram of folding contours under different bin numbers, where (a) is 64 bins, (b) is 256 bins, and (c) is 4096 bins;

[0024] Figure 7 For the present invention and tradition The statistical error mean of the estimated pulsar period and time delay is shown in Figure 1, where (a) is the relationship between the period estimation error and the detector area, (b) is the relationship between the profile phase error and the detector area, and (c) is the relationship between the period estimation error and the background noise flow.

[0025] Figure 8 For the present invention and tradition The period estimation accuracy and contour folding effect of the test method under different background flow rates, where (a) is the folding contour when the background flow rate is 0.01ph / cm² / s, and (b) is the folding contour when the background flow rate is 3ph / cm² / s. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the exemplary embodiments of the present invention will be further described in detail below. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0027] like Figure 1 As shown in the figure, the present invention proposes a method for estimating the period and pulse time delay of an X-ray pulsar based on the improved Z 2The test can be applied to the estimation of pulsar period and pulse time delay of complex profiles. First, the PTOA data is obtained by X-ray pulsar detectors. In the first candidate period, the quantitative relationship between photon prior information and the optimal harmonic truncation order is established according to the H test principle. The photon prior information is used to adaptively determine the optimal harmonic truncation order under a certain observation task, so as to weaken the influence of noise on the folded profile waveform. Secondly, the phase of the binned data is re-estimated according to the principle of "equal photon intensity in the box" to reduce the profile deviation caused by phase inaccuracy. Finally, the optimal number of bins for the binned data is determined based on the experimental results of simulation and measured data to improve the discrimination of the statistical test and further improve the estimation accuracy. The above three steps are used to perform Z 2 Statistics improvement, and traverse all candidate cycles in turn to improve Z 2 The highest statistic is used as the criterion to select the optimal estimation period. At the same time, the time delay estimation is realized by using the cross-correlation operation. The specific implementation steps are as follows:

[0028] Step 1: Determine the optimal harmonic truncation order under the photon number task based on the Hart test, and find the quantitative relationship between the prior information of the spacecraft detector on the number of photons and the optimal harmonic truncation order, so as to achieve the adaptive value of the optimal harmonic truncation order and provide a folding profile with less noise for subsequent statistical tests;

[0029] Step 2: Re-estimate the optimal phase of the boxed data by the principle of “equal area segmentation” in the box to reduce the folding contour deviation caused by inaccurate phase value, so that the folding contour is closer to the real contour;

[0030] Step 3: Combine the simulation data with the actual observation data to establish a quantitative relationship between the number of boxes of the packed data and the estimation accuracy and computational cost, and select the optimal number of boxes to provide a folding profile with the best discrimination for statistical testing.

[0031] Step 4: Use the above three steps to perform Z 2 Statistics improvement, and traverse all candidate cycles in turn to improve Z 2 The highest statistic is used as the criterion to select the optimal X-ray pulsar period estimate. At the same time, the time delay of the X-ray pulsar is estimated through cross-correlation calculation based on the outline folded from the optimal X-ray pulsar period estimate.

[0032] Furthermore, in step 1, the number of photons observed by the satellite in an actual on-orbit observation mission is taken as an example to illustrate the implementation method of this step. The specific technical solution is as follows:

[0033] First, the optimal harmonic truncation order is found under each observation state according to the H test, so that the average integrated square error between the Fourier series estimator and the true profile is minimized. The H test can be simplified as:

[0034] (1)

[0035] In the formula, is the upper limit of the search order. is the optimal harmonic cutoff order, is Z under the optimal harmonic stage order 2 Statistics.

[0036] Secondly, based on the prior information of the observed events, the optimal harmonic truncation order is adaptively selected under different data qualities: Since the photons in the X-ray band are weak, only the photon arrival time series can be received. Therefore, when recovering the pulsar profile signal, the number of observed events plays a decisive role in the restoration effect. In the actual deep space exploration navigation mission, the number of photon events received by the spacecraft each time is different. Figure 2 It is the result of the number of observed photons under the satellite's on-orbit observation mission and the search for the optimal harmonic cutoff order using the H test.

[0037] according to Figure 2 It can be found that the optimal harmonic truncation order is different under different data qualities. This may be because if the number of photons in an observation task is large, that is, the data quality is good, the restored profile is more stable and the effect is better. At this time, using a larger harmonic truncation order can not only better describe the shape characteristics of the complex profile, but also will not be disturbed by too much high-frequency noise. However, if the number of observed photons is small, the restoration effect is poor and is more affected by noise. At this time, selecting a larger harmonic truncation order may introduce greater high-frequency noise interference. Therefore, if the same harmonic truncation order is used to describe the pulsar profile under different data qualities, a continuous optimal estimate will often not be obtained.

[0038] At the same time, by Figure 2 It can be seen that the information of data quality can provide a certain basis for the selection of the optimal harmonic truncation order. Therefore, the prior information of known observation events, that is, the number of photons received in each observation task, can be used to determine the more reasonable harmonic truncation order under different data qualities, so as to achieve the optimal harmonic truncation order for Z. 2 Test the estimated harmonic truncation order and select it adaptively. 2 The test function can be expressed as:

[0039] (2)

[0040] In the formula, is the Z with the optimal harmonic cutoff order after the specific binning operation 2 Statistics, is the number of photons received in this observation mission, is the specific correspondence between data quality and the optimal harmonic cutoff order, is the packing quantity, For the The number of photons in a box, For the The representative phase selected for each bin.

[0041] Regarding the specific correspondence between data quality and the optimal harmonic truncation order, the present invention is based on Figure 2 The experimental results in , choose a relatively simple linear relationship to describe, namely:

[0042] (3)

[0043] In the formula, the parameters It is an empirical value artificially set based on the actual observation task and the results of the H test. It is worth noting that due to the existence of different detection accuracy and detection environment, the specific quantitative relationship can be selected more accurately according to different conditions.

[0044] Furthermore, in step 2, the optimal phase of the boxed data is re-estimated by the principle of "equal area division" in the box to reduce the folding contour deviation caused by inaccurate phase value. Figure 3 As shown, for the pulsar signal profile with complex shape characteristics, when the number of bins is selected to be small, it means that the phase interval length of each bin is long, and the change of the profile signal in the bin may no longer be smooth, but a sharp rise or fall occurs near the peak of the signal. At this time, if the midpoint of the phase interval of the bin is still used as the representative value of the binned phase, it will cause a large deviation to the profile recovery. In order to solve the problem of large deviation, the optimal phase estimation method for binned data of the present invention is: using the method of "dividing the phase by equal photon intensity in the bin" to optimize the phase estimation for the sudden change of the photon flow in the bin. Specifically, for the division of the binned phase, the midpoint of the bin interval is no longer used as the representative value of the binned phase, but the phase value corresponding to the midpoint of the photon flow in the bin is used as a better estimate of the binned phase, that is, from the perspective of the mathematical formula, the bin is divided into "equal areas" to determine a better phase estimate.

[0045] For the specific method of equal photon intensity segmentation within a bin, under the condition of selecting an appropriate number of bins, the present invention uses a first-order function relationship to describe the variation trend of the photon intensity within a bin. Figure 4 As shown, suppose The left and right boundary phases of a bin are , the photon intensity of the left and right boundary phases in the real profile corresponds to , that is, by and The optimal estimated phase of the bin can be determined by the specific photon intensity change relationship and the "equal area division" principle. The optimal estimated phase can be specifically expressed as:

[0046] (4)

[0047] Among them, the intermediate parameters A, B, and C are expressed as:

[0048] (5)

[0049] (6)

[0050] (7)

[0051] For the The phase value obtained by re-estimating the bins is Indicates the total number of boxes.

[0052] Furthermore, in step 3, the simulation data and the actual observation data are combined to establish a quantitative relationship between the number of boxes of the boxed data and the estimation accuracy and computational cost, and the optimal number of boxes is selected. The appropriate number of boxes can not only ensure the resolution of the folded contour, but also ensure a good contour folding and restoration effect, while ensuring the operation speed, reducing the impact of interference noise, and solving the problem that when the number of boxes is small, the resolution of the folded contour is not enough, resulting in poor contour folding and restoration effect, and when the number of boxes is large, the operation speed is low and the data in the box is more sensitive to large interference noise. The specific implementation method is: set the number of boxes to 64, 128, 256, 512, 1024, 2048, 4096, and use Z suitable for complex contours. 2 The test function estimates the period of the PSR B0531+21 pulsar, which has the best navigation effect. The number of bins will be analyzed from the following two aspects to obtain the optimal number of bins:

[0053] (1) Estimation accuracy: Figure 5As shown in the figure, (a) is the curve of the relationship between the estimation accuracy of the simulation data and the operation time, and (b) is the curve of the relationship between the estimation accuracy of the measured data and the operation time. As the number of bins increases, the cycle estimation accuracy gradually increases. When the number of bins is 2048, the cycle estimation accuracy of the measured data decreases. As the number of bins increases, the cycle estimation accuracy shows an increasing trend. However, as the number of bins increases, the amount of calculation will also increase, which will lead to a decrease in the calculation speed.

[0054] (2) Contour folding effect: Figure 6 As shown in the figure, it is a schematic diagram of the folded contour under different bin numbers, where (a) is 64 bins, (b) is 256 bins, and (c) is 4096 bins. When the bin number is too small, such as setting the bin number to 64, the resolution of the contour is poor, and the characteristic information of the pulsar signal contour cannot be accurately restored through the folding operation. When the bin number is too large, such as setting the bin number to 2048, the signal contour is too affected by uncertainty factors, so that the contour features are gradually submerged in the noise, which also does not make use of the subsequent pulse time delay estimation and solution.

[0055] In combination with the above two factors, in order to improve the accuracy and operation speed of period estimation without affecting the subsequent navigation accuracy due to poor contour restoration, the present invention proposes that setting the number of bins to 256 is the optimal number of bins. 2 The test function can be expressed as:

[0056] (8)

[0057] In the formula, The appropriate number of bins selected for navigation pulsar sources with different shape characteristics, For the The phase value obtained by re-estimating each box.

[0058] The experimental simulation of the present invention is as follows:

[0059] The simulation experiment parameters are set as pulse period of 33.7ms and effective photon flux of 1.54ph / cm 2 / s, background photon flux 0.005ph / cm 2 / s, the number of bins is 256.

[0060] The observation time was set to 200s, 400s, 600s, 800s, 1000s, and 1200s respectively, and the effect of the present invention on improving Z was studied under different observation time. 2 Inspection and tradition The accuracy of the period and pulse time delay estimation of the test method is tested. The simulation process estimates the period and time delay through hundreds of Monte Carlo experiments, and the detector area is set to 500cm 2 .

[0061] Some errors estimated using the traditional period estimation method and the method of the present invention are shown in Table 1.

[0062] Table 1

[0063]

[0064] It can be seen that in the case of poor photon data quality due to short observation time, the method of the present invention can provide better estimation performance than the traditional method.

[0065] The effective receiving area of ​​the X-ray detector is also an important factor affecting the estimation of period and time delay. The detector area is set to 50cm 2 , 100cm 2 , 500cm 2 , 1000cm 2 、5000cm 2 , 10000cm 2 , explore the specific impact of different detector areas on estimation accuracy. The simulation process estimates the cycle and time delay through hundreds of Monte Carlo experiments, and the simulation duration is set to 400s. 2 Inspection and tradition The statistical error mean of the estimated pulsar period and profile phase is as follows: Figure 7 As shown, (a) is the relationship curve of period estimation error with detector area, (b) is the relationship curve of profile phase error with detector area, and (c) is the relationship curve of period estimation error with background noise flow.

[0066] It can be seen that when the detector area is small, improving Z 2 The estimation accuracy of the inspection method is significantly better than that of the traditional method. When the detector area is large, the estimation accuracy of the traditional method will show a greater advantage. In the actual navigation mission of deep space exploration, the detector area is usually limited, and the larger photon receiving area is often not well utilized. Therefore, under the condition of limited detector area, it is necessary to improve Z 2 The verification method has greater potential in the estimation of pulsar period and pulse time delay.

[0067] In the actual deep space exploration navigation mission, the impact of noise interference on navigation accuracy cannot be ignored. Therefore, how to achieve more accurate pulsar period and pulse time delay estimation under the condition of greater noise interference is crucial to improving navigation accuracy. In order to better explore the resistance of the method proposed in the present invention to noise interference, the background flow is set to 0.1 ph / cm 2 / s、0.5ph / cm 2 / s、1ph / cm 2 / s、1.5ph / cm 2 / s, 2ph / cm 2 / s, 2.5ph / cm 2 / s、3ph / cm 2 / s, specifically quantitatively studying the impact of the two estimation methods on the accuracy under different background flows. The simulation process estimates the period and time delay through hundreds of Monte Carlo experiments. The observation time is set to 200s and the detector area is 200cm 2 The cycle estimation accuracy of the two methods under different background flows and the contour folding effects of the two methods under different background flows are shown in Figure 8 As shown, (a) is the folding profile when the background flow rate is 0.01 ph / cm² / s, and (b) is the folding profile when the background flow rate is 3 ph / cm² / s.

[0068] It can be seen that in the case of large noise, the estimation accuracy of the traditional inspection method will drop rapidly. 2 The statistic’s resistance to interference noise will limit the impact of noise interference on the folding contour to a certain extent, improving Z 2 The verified method indeed has better performance in estimating pulsar period and pulse time delay.

[0069] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating X-ray pulsar period and pulse time delay, characterized in that: The following steps are involved: Step 1: Determine the optimal harmonic truncation order under the photon number task based on the Hart test, and find the quantitative relationship between the prior information of the spacecraft detector on the number of photons and the optimal harmonic truncation order; Step 2: Re-estimate the optimal phase of the boxed data by the principle of "equal area division" within the box; Set up The left and right boundary phases of each bin are , left and right boundary phase The photon intensities in the real profile are , then the re-estimation of the optimal phase is expressed as: (4) Among them, the intermediate parameters A, B, and C are expressed as: (5) (6) (7) For the The phase value obtained by re-estimating the bins is Indicates the total number of boxes; Step 3: Establish a quantitative relationship between the number of boxes of packed data and the estimation accuracy and calculation cost, and select the optimal number of boxes; Step 4: Perform steps 1 to 3 in all candidate cycles to improve Z 2 The highest statistic is used as the discrimination criterion to select the optimal X-ray pulsar period estimate, and the time delay estimate of the X-ray pulsar is obtained through cross-correlation calculation based on the profile folded from the optimal X-ray pulsar period estimate.

2. The method for estimating X-ray pulsar period and pulse time delay according to claim 1, characterized in that: The step 1 comprises: According to the H test, the optimal harmonic truncation order is found for each observation task, so that the average integrated square error between the Fourier series estimator and the true profile is minimized; Using the prior information of known observation events, that is, the number of photons received in each observation task, the optimal harmonic truncation order under different data qualities is determined to achieve Test the adaptive selection of the estimated optimal harmonic cutoff order.

3. The method for estimating X-ray pulsar period and pulse time delay according to claim 1, characterized in that: The step 3 comprises: The number of bins of different sizes is set respectively, and the contour folding operation is performed on the photon arrival time series. The simulation data and the measured data of pulsar are compared using the improved statistical test function to determine the optimal number of bins.

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