Method and system for x-ray pulsar period estimation based on multiple criteria

Abstract

This application discloses a method and system for estimating the period of an X-ray pulsar based on multiple evaluation criteria. The method includes: pre-setting multiple different candidate periods; constructing a pulsar profile waterfall plot for each candidate period using a contour waterfall plot folding method; performing principal component analysis on the pulsar profile waterfall plot to calculate the contribution rate of the principal eigenvalues ​​and the projection variance of the principal components corresponding to the candidate period; identifying the peak trajectory in the pulsar profile waterfall plot; fitting the peak trajectory using a support vector regression model to obtain the slope of the regression line corresponding to the candidate period; and determining the estimated value of the X-ray pulsar period from the multiple pre-set different candidate periods based on the contribution rate of the principal eigenvalues, the projection variance of the principal components, and the slope of the regression line. This application can achieve accurate period prediction, thereby further improving the estimation accuracy of pulsar time delay measurement information.

Description

Technical Field

[0001] This application relates to the field of pulsar navigation technology, and in particular to an X-ray pulsar period estimation method and system based on multiple evaluation criteria. Background Technology

[0002] In recent years, with the continuous development of deep space exploration technology, research on autonomous astronomical navigation for deep space probes has become increasingly in-depth. As a navigation method well-suited for deep space exploration missions, astronomical navigation technology has been widely applied in this field. Astronomical navigation is a type of autonomous navigation method where spacecraft determine their attitude, position, and velocity by observing natural celestial bodies such as stars, planets, or pulsars and utilizing their spatial position, radiation characteristics, and periodic stability. Based on the different measurements, astronomical 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 often cannot be guaranteed. However, as an emerging astronomical distance measurement navigation method, X-ray pulsar navigation can provide spacecraft with a stable spatiotemporal reference and potentially ultra-high positioning accuracy, and is considered one of the most promising astronomical navigation technologies for autonomous exploration missions in multiple flight phases, including the cruise, approach, and orbit phases. In pulsar navigation systems, the spacecraft's orbital dynamics equations are typically used as the state model, while pulsar measurement information (such as the arrival time delay of pulsar signals) is used as the measurement model. Estimation algorithms such as Kalman filtering are employed to fuse the system state and measurement information to achieve spacecraft navigation and positioning. The acquisition and estimation of pulsar measurement information plays a crucial role in the entire navigation process, and its accuracy directly determines the positioning performance of the pulsar navigation system.

[0003] To address the problem of acquiring measurement information in pulsar navigation, existing research typically uses pulsar time delay as the system's measurement information. Pulsar time delay refers to the time difference between the arrival of the pulsar signal at the spacecraft and its arrival at the reference position at the solar system's center of mass. Due to the highly stable periodicity of pulsar radiation, pulsar time delay is usually estimated by comparing the phase shift between the signal received by the spacecraft and the standard pulsar signal at the solar system's center of mass. However, under actual observation conditions, the radiation intensity of pulsars in the X-ray band is weak, making it difficult for detectors to directly resolve signals within a single period. Therefore, it is usually necessary to estimate the pulsar period in real time and combine it with signal enhancement techniques such as epoch folding algorithms to reconstruct the pulsar period signal. In this process, the accuracy of the period estimation directly affects the quality of the folding profile, thus determining the accuracy of the phase delay and time delay estimates. Therefore, pulsar period estimation is a crucial step in the pulsar measurement information estimation process, and its accuracy has a decisive impact on the measurement information estimation results.

[0004] Existing methods for estimating cycles primarily rely on statistical tests. Early research focused on... Using the test as the objective function, the candidate period with the strongest folding contour significance was selected. Subsequent research further optimized this approach, proposing a method more sensitive to signal contours. Statistics. Based on this, relevant research... The statistical measures have been improved and simplified, and their application scope has been expanded to more general waveforms. Furthermore, researchers have proposed an improved Rayleigh entropy test statistic by incorporating contour peak-valley characteristics. These statistical test methods are computationally simple and widely applicable, but their estimation accuracy and computational efficiency are still limited under complex observation conditions. In recent years, to address the limitation of computational efficiency, researchers have proposed an improved fast folding algorithm, which significantly improves period search efficiency while maintaining high estimation accuracy. Meanwhile, with the deepening research on high-quality navigation pulsar sources, period estimation methods based on specific contour templates have also seen significant development. Some studies use compressed sensing algorithms for fast and high-precision pulsar period estimation. Other studies use pulsar period estimation methods based on variable encapsulation segments with equal photon distribution. Still other studies utilize Hilbert transform to convert pulsar contours into two-dimensional images, combine prior template information, and use convolutional neural networks to estimate the period. In addition, research on pulsar phase estimation using Transformer networks provides a similar approach to data-driven feature learning in period estimation. These methods offer high estimation accuracy but require incorporating prior information about the pulsar source. It is worth noting that, unlike the methods mentioned above that rely on a single significance criterion, this new research approach proposes a waterfall plot-principal component analysis method, which jointly discriminates candidate periods from the perspectives of signal significance and phase consistency. This method has significant potential for period estimation, but it still suffers from problems such as sensitivity to noise.

[0005] Secondly, regarding the simulation of pulsar navigation methods in multi-mission scenarios, existing research has extensively explored system modeling and performance verification of pulsar navigation across different flight phases and orbital environments. These studies primarily cover typical mission phases such as Earth orbit, Earth-Moon transfer, deep space cruise, and planetary approach and orbit. However, existing multi-scenario application simulation research still has shortcomings. While existing work covers multiple mission phases, most are focused on single mission contexts, lacking stability and easily affected by data changes. Summary of the Invention

[0006] The technical problem to be solved by this application is: to address the application simulation problem of pulsar navigation methods in multi-task scenarios and the problem of noise sensitivity, a pulsar period estimation method based on a waterfall plot multi-criteria framework is provided to achieve robust estimation of pulsar period, with advantages such as high accuracy and good stability, which can significantly improve the estimation performance of pulsar measurement information.

[0007] The objective of this application is achieved through the following technical solution:

[0008] According to the first aspect of this application, a method for estimating the period of an X-ray pulsar based on multiple evaluation criteria is provided, comprising: Step 1, pre-setting multiple different candidate periods, and constructing a pulsar profile waterfall plot for each candidate period using a profile waterfall plot folding method; Step 2, performing principal component analysis on the pulsar profile waterfall plot, calculating the contribution rate of principal eigenvalues ​​and the projection variance of principal components corresponding to the candidate period; Step 3, identifying the peak trajectory in the pulsar profile waterfall plot, fitting the peak trajectory using a support vector regression model, and obtaining the slope of the regression line corresponding to the candidate period; Step 4, determining the estimated value of the X-ray pulsar period from the multiple pre-set different candidate periods based on the contribution rate of principal eigenvalues, the projection variance of principal components, and the slope of the regression line.

[0009] Preferably, step 1 includes: presetting multiple different candidate periods, dividing the total observation time of the observed event into multiple equally spaced time periods, and performing the following operations for each candidate period: dividing each time period equally according to the candidate period, and further dividing the resulting candidate period equally into multiple phase grids; determining the photon information value corresponding to each phase grid based on the acquired pulsar photon sequence, wherein the photon information value includes the photon count within the phase grid; constructing a pulsar signal contour model corresponding to each time period by using each phase grid as the abscissa and the photon information value corresponding to each phase grid as the ordinate; normalizing the pulsar signal contour models corresponding to all time periods and sorting and encoding them in chronological order, and combining them to obtain a pulsar contour waterfall plot under the candidate period.

[0010] Preferably, step 2, performing principal component analysis on the pulsar contour waterfall plot, includes: performing principal component analysis on the pulsar contour waterfall plot to obtain the waterfall plot covariance matrix; performing eigenvalue decomposition on the waterfall plot covariance matrix to obtain multiple eigenvalues ​​and their corresponding eigenvectors; extracting the largest eigenvalue as the principal eigenvalue; and the eigenvector corresponding to the largest eigenvalue being the first principal direction.

[0011] Preferably, step 2, calculating the principal eigenvalue contribution rate and principal component projection variance corresponding to the candidate period, includes: calculating the principal eigenvalue contribution rate corresponding to the candidate period based on the principal eigenvalue and the plurality of eigenvalues; extracting the principal component projection score vector based on the pulsar contour waterfall plot and the first principal direction; and calculating the principal component projection variance corresponding to the candidate period based on the principal component projection score vector.

[0012] Preferably, step 3 includes: identifying peak points in the pulsar contour waterfall plot and obtaining the coordinates of each peak point, wherein the coordinates of the peak points include the position index of the folded contour and the position index of the peak point on the phase axis; using a support vector regression model to fit the peak trajectory based on the position index of the folded contour and the position index of the peak point on the phase axis; and obtaining the slope of the regression line corresponding to the candidate period based on the fitted peak trajectory model.

[0013] Preferably, step 4 includes: using the contribution rate of principal eigenvalues, the variance of principal component projections, and the slope of the regression line as evaluation indicators to construct a multi-criteria fusion framework, and determining the estimated value of the X-ray pulsar period based on the multi-criteria fusion framework.

[0014] Preferably, the contribution rate of principal eigenvalues, the variance of principal component projection, and the slope of the regression line are used as evaluation indicators to construct a multi-criteria fusion framework, and the estimated value of the X-ray pulsar period is determined based on the multi-criteria fusion framework, including: using the extreme value independent variable operator to construct structural significance criteria, principal projection significance criteria, and geometric consistency criteria according to the contribution rate of principal eigenvalues, the variance of principal component projection, and the slope of the regression line corresponding to the candidate period; and selecting the corresponding optimal candidate period from a set of multiple candidate periods according to formulas (15), (16), and (18) based on the structural significance criteria, principal projection significance criteria, and geometric consistency criteria.

[0015] (15)

[0016] (16)

[0017] (18)

[0018] in, For the maximum value independent variable operator, For the minimum value operator, The optimal candidate period selected based on the structural significance criterion. Indicates candidate period Contribution rate of principal eigenvalues; The optimal candidate period is selected based on the main projection significance criterion. Indicates candidate period Principal component projection variance; The optimal candidate period selected based on the geometric consistency criterion. Candidate period The slope of the lower regression line The absolute value of the period; the average of the three selected optimal candidate periods is used as an estimate of the X-ray pulsar period.

[0019] Preferably, the method further includes: based on the estimated value of the X-ray pulsar period, using the pulsar signal profile model to reconstruct the profile of the observed event to obtain the current observation profile; performing cross-correlation matching between the current observation profile and the standard profile at the center of the solar system to obtain the optimal phase offset of the current observation profile relative to the standard profile; and calculating the total time delay of the X-ray pulsar based on the optimal phase offset, combined with the integer number of cycles and the estimated value of the X-ray pulsar period; wherein the integer number of cycles represents the integer delay accumulated relative to the reference standard profile during the propagation of the pulsar signal.

[0020] According to a second aspect of this application, an X-ray pulsar period estimation system based on multiple evaluation criteria is provided, comprising: a waterfall plot construction module, a principal component analysis module, a slope extraction module, and a period estimation module. The waterfall plot construction module is configured to preset multiple different candidate periods and construct a pulsar contour waterfall plot for each candidate period using a contour waterfall plot folding method; the principal component analysis module is configured to perform principal component analysis on the pulsar contour waterfall plot, calculating the contribution rate of principal eigenvalues ​​and the projection variance of principal components corresponding to the candidate periods; the slope extraction module is configured to identify peak trajectories in the pulsar contour waterfall plot, fit the peak trajectories using a support vector regression model, and obtain the slope of the regression line corresponding to the candidate periods; the period estimation module is configured to determine an estimated value of the X-ray pulsar period from the preset multiple different candidate periods based on the contribution rate of principal eigenvalues, the projection variance of principal components, and the slope of the regression line.

[0021] According to a third aspect of this application, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of the first aspect of this application.

[0022] According to a fourth aspect of this application, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the method of the first aspect of this application.

[0023] Compared with the prior art, the main advantages of this application are:

[0024] (1) This application constructs a pulsar contour waterfall plot and extracts periodic structure features from the perspectives of principal eigenvalue intensity contribution, principal projection significance and peak trajectory geometric consistency to achieve accurate period prediction, thereby further improving the estimation accuracy of pulsar time delay measurement information.

[0025] (2) This application constructs a time delay information estimation method based on a waterfall plot multi-criteria framework according to different evaluation criteria. On the one hand, the contribution rate of principal eigenvalues ​​is used as the first evaluation criterion to characterize the overall significance of the candidate periodic structure; on the other hand, the variance of principal component projection is used as the second evaluation criterion to measure the prominence of the candidate periodic pattern in the principal subspace. At the same time, considering the geometric consistency characteristics of the candidate periodic stripes in the waterfall plot, the peak trajectory of the waterfall plot is extracted, and a support vector regression model is used to fit the peak trajectory. The slope of the regression line is used as the third evaluation criterion to characterize the geometric consistency and stability of the candidate periodic structure. On this basis, a multi-criteria fusion framework is constructed to comprehensively evaluate the candidate periodicity. Among them, the multi-criteria fusion strategy further improves the robustness of pulsar time delay estimation. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0027] Figure 1 This is a flowchart illustrating an X-ray pulsar period estimation method based on multiple evaluation criteria according to an embodiment of this application.

[0028] Figure 2 This is a flowchart illustrating a multi-criteria-based X-ray pulsar period estimation method according to another embodiment of this application.

[0029] Figure 3 This is a main projection profile view under different candidate periods according to an embodiment of this application;

[0030] Figure 4 This is a schematic diagram illustrating the periodic estimation error of six methods according to an embodiment of this application. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. Furthermore, the technical features involved in the various embodiments described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this application adopts the following technical solutions.

[0032] Figure 1 This is a flowchart illustrating an X-ray pulsar period estimation method based on multiple evaluation criteria according to an embodiment of this application. Figure 1 As shown, the method includes: Step S101, pre-setting multiple different candidate periods, and constructing a pulsar contour waterfall plot for each candidate period using the contour waterfall plot folding method. Step S102, performing principal component analysis on the pulsar contour waterfall plot, calculating the contribution rate of the principal eigenvalues ​​and the projection variance of the principal components corresponding to the candidate periods. Step S103, identifying the peak trajectory in the pulsar contour waterfall plot, fitting the peak trajectory using a support vector regression model, and obtaining the slope of the regression line corresponding to the candidate periods. Step S104, determining the estimated value of the X-ray pulsar period from the pre-set multiple different candidate periods based on the contribution rate of the principal eigenvalues, the projection variance of the principal components, and the slope of the regression line.

[0033] This application embodiment constructs a pulsar contour waterfall plot and performs principal component analysis and support vector regression fitting on the constructed pulsar contour waterfall plot. By combining the contribution rate of principal eigenvalues, the variance of principal component projections, and the slope of the regression line, it achieves accurate prediction of the period, thereby further improving the estimation accuracy of pulsar time delay measurement information.

[0034] Figure 2 This is a flowchart illustrating a multi-criteria-based X-ray pulsar period estimation method according to another embodiment of this application. The following will be combined with… Figure 1 and Figure 2 The embodiments of this application are described in detail.

[0035] Reference Figure 2 In some embodiments, step S101 may include:

[0036] First, several different candidate periods of X-ray pulsars (i.e., pulsar folding periods, hereinafter referred to as candidate periods) are preset. The candidate periods are predicted before this work, that is, by estimating the actual period within a certain interval and then selecting a series of candidate periods within this interval.

[0037] Then, based on the acquired pulsar photon sequence, a pulsar contour waterfall plot is constructed for each candidate period. This involves using a contour waterfall plot folding method to divide the observed event into several sub-events, and merging the X-ray pulsar signal contours obtained using the epoch folding method into a three-dimensional structure. Specifically, the total observation time of the observed event is divided into equally spaced intervals. There are three time periods (each time period corresponds to one sub-event). The observation duration for each time period is... Represented in seconds, i.e., total observation time For each candidate period (Unit: seconds), each time period is divided according to the candidate period. Average score Section, i.e. ; Divide each candidate period into equal parts Divide into equal parts Each phase bin, using This represents the duration (in seconds) of each phase division. These N bins are used as the abscissa (phase axis) of each pulsar signal profile model. The photon information value in each bin is determined based on the pulsar photon sequence, and this photon information value is used as the corresponding ordinate (i.e., profile signal intensity) to construct the pulsar signal profile model for each time period (hereinafter referred to as the profile model, also known as the folded profile). In some embodiments, the photon information value includes the photon count falling into the bin or the normalized relative photon intensity. During epoch folding, the observed photons are mapped to the corresponding bins according to their arrival time, and the photons in the bin are counted to obtain the original photon count, which directly reflects the instantaneous intensity of X-ray radiation in that bin. Because the total observation time of the observed event includes... A time period, therefore a candidate period correspond A contour model. (The rest is missing.) The contour models are combined to form a contour waterfall plot, which is the pulsar contour waterfall plot for that candidate period.

[0038] The contour model corresponding to each time period can be represented by formula (1):

[0039] (1)

[0040] in, Indicates the index of the contour model. ; Indicates the index of bin. ; express The Middle one bin, Indicates the first time period within that time period indivual of The photon information value in; express The Middle one bin, Indicates the first time period within that time period indivual of The photon information value in; Indicates the first The first contour model Each bin (which can be understood as the x-coordinate of the contour model) Indicates the first The contour signal intensity of a contour model (which can be understood as the ordinate of the contour model).

[0041] After normalizing the contour models corresponding to all time periods, they are encoded in chronological order to construct color scales and contour signal strength. The mapping relationship between them is used to obtain the candidate period. The outline waterfall plot is shown below. The model of the outline waterfall plot can be represented by formula (2):

[0042] (2)

[0043] Continue to refer to Figure 2 , set at the Candidate Cycles The outline waterfall diagram constructed below is In some embodiments, step S102 may include:

[0044] First, according to formula (3) Centralized processing:

[0045] (3)

[0046] in, This represents the mean vector for each bin. This represents a centered waterfall chart with a mean of 0. The constant coefficient, .

[0047] Secondly, principal component analysis was performed on the centered pulsar contour waterfall plot to obtain the waterfall plot covariance matrix. Specifically, let... Let be the projection vector in a certain direction, then Projection along this direction It can be expressed as in formula (4):

[0048] (4)

[0049] Principal component analysis seeks the direction that maximizes the variance of the waterfall plot projection, thereby preserving as much of the main change information in the original data as possible. The optimal projection direction can be expressed as a constrained optimization problem as shown in formula (5).

[0050] (5)

[0051] in, This is the transpose symbol.

[0052] Substituting formula (4) into formula (5), we get formula (6):

[0053] (6)

[0054] in, This is the covariance matrix of the waterfall plot.

[0055] Then, the covariance matrix of the waterfall plot is subjected to eigenvalue decomposition to obtain multiple eigenvalues ​​and their corresponding eigenvectors. The largest eigenvalue is extracted as the principal eigenvalue, and the eigenvector corresponding to the largest eigenvalue is the first principal direction. Specifically, the Lagrangian function is constructed as shown in formula (7):

[0056] (7)

[0057] Differentiating formula (7) and calculating the extreme points, we obtain formula (8):

[0058] (8)

[0059] set up for eigenvalues, The number of eigenvalues. The largest eigenvalue. The main feature value reflects the strength of the most important structural information in the contour waterfall plot.

[0060] Based on the principal eigenvalue and multiple eigenvalues ​​obtained from the eigenvalue decomposition of the waterfall plot covariance matrix, calculate according to formula (9). Contribution rate of principal eigenvalues :

[0061] (9)

[0062] Let the largest eigenvalue be The corresponding eigenvector is the first principal direction. From equation (4), we can see that... First main direction The projection onto the surface can be expressed as in formula (10):

[0063] (10)

[0064] in, for The centered contour waterfall plot below the first principal direction The projected score vector on.

[0065] Calculate according to formula (11) Principal component projection variance :

[0066] (11)

[0067] in, This indicates the projection variance operation.

[0068] In some embodiments, step S103 may include:

[0069] First of all, Extract There are several peak points, and their expressions are shown in formula (12):

[0070] (12)

[0071] in, For the first The position index corresponding to each folded contour For the first The index of the position of the peak point of the folded profile on the phase axis.

[0072] To better characterize the overall arrangement trend of the peak point set, a linear support vector regression (SVR) model is used to establish a peak trajectory model as shown in formula (13) based on the position index of the folded contour and the position index of the peak points on the phase axis. This peak trajectory model obtains a stable linear trend of the peak point set by suppressing the influence of outliers on the fitting results while ensuring the smoothness of the regression.

[0073] (13)

[0074] in, Let be the slope of the regression line. The intercept is... As the independent variable, This is a regression function.

[0075] Then, within the linear SVR framework, the... and The solution is transformed into a constrained optimization problem as shown in equation (14):

[0076] (14)

[0077] in, The penalty coefficient is... For insensitive loss functions, and These are slack variables.

[0078] Finally, according to formula (14), we get The slope of the lower regression line .

[0079] In some embodiments, step S104 may include constructing a multi-criteria fusion framework by using the contribution rate of principal eigenvalues, the variance of principal component projections, and the slope of the regression line as evaluation indicators, and determining the estimated value of the X-ray pulsar period based on the multi-criteria fusion framework.

[0080] Continue to refer to Figure 2 In some embodiments, the contribution rate of principal eigenvalues, the variance of principal component projections, and the slope of the regression line are used as evaluation indicators to construct a multi-criteria fusion framework. Determining the estimated period of an X-ray pulsar based on this multi-criteria fusion framework may include:

[0081] The structural significance index is defined as the contribution rate of principal eigenvalues. The structural significance criterion based on principal component analysis is shown in formula (15):

[0082] (15)

[0083] in, For the maxima operator, The optimal candidate period is selected based on the structural significance criterion.

[0084] Figure 3 This is a main projection profile view under different candidate periods according to an embodiment of this application. For example... Figure 3 As shown, the significance of the principal projection profile gradually weakens as the candidate period deviates from the true period. Therefore, the significance index of the principal projection is defined as the variance of the principal component projection, and the significance criterion of the principal projection based on principal component analysis is shown in formula (16):

[0085] (16)

[0086] in, The optimal candidate period is selected based on the main projection significance criterion.

[0087] From formula (14) in step S103, we can see that the slope of the regression line is... This directly reflects the inclination of the peak trajectory relative to the horizontal axis. When the candidate period is close to the true period, the corresponding regression line is closer to a horizontal line, and its absolute slope is smaller. Conversely, when the candidate period deviates from the true value, the peak point follows the contour position index. A significant drift occurs, increasing the slope of the regression line and correspondingly increasing the absolute value of the slope. Based on this, the geometric consistency index is defined as the absolute value of the slope of the regression line. As shown in formula (17):

[0088] (17)

[0089] The geometric consistency criterion based on support vector regression is shown in formula (18):

[0090] (18)

[0091] in, For the minimum value operator, The optimal candidate period is selected for the geometric consistency criterion.

[0092] To comprehensively utilize the characterization capabilities of different criteria for the true period, information fusion is performed on the aforementioned criteria to obtain a comprehensive estimate of the pulsar period. In some embodiments, the contribution rate of the principal eigenvalue, the variance of the principal component projection, and the slope of the regression line corresponding to each candidate period can be calculated. Using the structural significance criterion, the principal projection significance criterion, and the geometric consistency criterion, the corresponding optimal candidate period is selected from a preset number of candidate periods according to formulas (15), (16), and (18), respectively. Then, according to formula (19), the average value of the three selected optimal candidate periods is used as the estimated value of the X-ray pulsar period, i.e., the estimated period. .

[0093] (19)

[0094] Set the pulsar folding period to the obtained estimated period. The contour of the observed event is restored using the contour folding model in formula (1) to obtain the current observed contour. Furthermore, the folded profile is compared with the standard profile at the center of mass of the solar system. Perform cross-correlation matching and calculate its phase delay information according to formula (20).

[0095] (20)

[0096] in, For the first Phase index of each bin, This represents the phase shift variable of the currently observed profile relative to the standard profile. This represents the optimal phase offset of the current observed profile relative to the standard profile.

[0097] Since the phase shift obtained by cross-correlation matching only reflects the fractional delay within one period, the total time delay of the pulsar needs to be calculated according to formula (21). :

[0098] (twenty one)

[0099] in, It is an integer number of cycles, used to characterize the integer delay accumulated relative to a reference standard profile during the propagation of a pulsar signal.

[0100] Based on the same inventive concept, one embodiment of this application provides an X-ray pulsar period estimation system based on multiple evaluation criteria, including: a waterfall plot construction module, a principal component analysis module, a slope extraction module, and a period estimation module. The waterfall plot construction module is configured to preset multiple different candidate periods and construct a pulsar contour waterfall plot for each candidate period using a contour waterfall plot folding method. The principal component analysis module is configured to perform principal component analysis on the pulsar contour waterfall plot, calculating the contribution rate of principal eigenvalues ​​and the projection variance of principal components corresponding to the candidate periods. The slope extraction module is configured to identify the peak trajectory in the pulsar contour waterfall plot, fit the peak trajectory using a support vector regression model, and obtain the slope of the regression line corresponding to the candidate period. The period estimation module is configured to determine the estimated value of the X-ray pulsar period from the preset multiple different candidate periods based on the contribution rate of principal eigenvalues, the projection variance of principal components, and the slope of the regression line. Since the system embodiment is basically similar to the method embodiment, the details of the relevant technical features and the effects of implementation can be found in the corresponding descriptions of the method embodiment provided above.

[0101] This application embodiment constructs a pulsar contour waterfall plot and performs principal component analysis and support vector regression fitting on the constructed pulsar contour waterfall plot. By combining the contribution rate of principal eigenvalues, the variance of principal component projections, and the slope of the regression line, it achieves accurate prediction of the period, thereby further improving the estimation accuracy of pulsar time delay measurement information.

[0102] The experimental simulation of the embodiments of this application will be described below.

[0103] This application uses HXMT satellite observation data with observation numbers P030229002-P030229006 (observation period from September 13, 2020 to November 13, 2020). The data from the five observation event groups were cleaned and divided into 94 independent observation events.

[0104] The performance of pulsar period estimation was analyzed for nearly 100 observational events in the HXMT data. The results were analyzed using... Test methods The accuracy of period estimation is compared and analyzed using the following methods: the structural significance criterion based on principal component analysis (PCA-1), the principal projection significance criterion (PCA-2), the geometric consistency criterion based on support vector regression (SVR), and the period estimation method integrating the three criteria (PCA-SVR) as described in this application. Specifically, the number of bins is selected as 300, and the period search step size is set to 0.1 ns.

[0105] Figure 4 This is a schematic diagram illustrating the periodic estimation error of six methods according to one embodiment of this application. Figure 4 As shown, The mean estimation error of the test method is 16.9798 ns. The mean estimation error of the test methods is 11.5606 ns, the mean estimation error of the structural significance criterion method (PCA-1) is 6.7447 ns, the mean estimation error of the principal projection significance criterion method (PCA-2) is 7.1447 ns, the mean estimation error of the geometric consistency criterion method based on support vector regression (SVR) is 8.2543 ns, while the mean estimation error of the method integrating the three criteria (PCA-SVR) in the embodiments of this application is 5.4032 ns. Compared with the classic... Test methods Compared to other testing methods, the period estimation method in this application significantly demonstrates higher estimation accuracy and a more stable distribution range. Compared to the three individual criteria proposed in this application, the period estimation method integrating these three criteria exhibits a smaller interquartile range and a shorter long-tailed distribution. This indicates that the embodiments of this application not only effectively improve the period estimation accuracy but also significantly enhance the robustness of the estimation method.

[0106] Table 1 provides the following information: Test methods The test method and the period estimation method of the embodiment of this application are compared with the mean, standard deviation and 95% confidence interval of the time delay estimation error obtained by using nearly 100 sets of HXMT satellite observation data.

[0107] Table 1

[0108]

[0109] As shown in Table 1, relative to Test methods The verification method shows that the time delay estimation accuracy of the period estimation method proposed in this application is improved by 68.68% and 50.43%, respectively, and the estimation stability is improved by 65.69% and 59.11%, respectively. This indicates that the embodiments of this application can demonstrate higher estimation accuracy and stronger estimation stability in pulsar time delay estimation.

[0110] The embodiments provided in this application can also be computer program products. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this application.

[0111] Computer-readable storage media can be tangible devices that hold and store instructions for use by an instruction execution device. Computer-readable storage media can include, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof.

[0112] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system and modules described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0113] In the embodiments provided in this application, it should be understood that the division of modules (or units) is merely a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units may be combined or integrated into another system, or some features may be ignored or not executed. In addition, the coupling or direct coupling or communication connection between units may be through some interfaces, or indirect coupling or communication connection between units, or it may be an electrical, mechanical or other form of connection.

[0114] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The aforementioned units can be implemented in hardware or as software functions.

[0115] The various embodiments in this application are described in a progressive manner, with each embodiment focusing on the differences from other embodiments or implementation methods. Similar or identical parts between the various embodiments of this application can be referred to mutually. The implementation principles and technical effects of the inventive concept can be mutually referenced, and will not be repeated here. Where there is no conflict, the various embodiments or implementation methods in this application can be combined with each other.

[0116] It should be noted that although the steps are described in a specific order above, it does not mean that the steps must be executed in the above specific order. In fact, some of these steps can be executed concurrently, or even in a different order, as long as the required function can be achieved.

[0117] This application uses specific embodiments to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the solution and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for estimating the period of an X-ray pulsar based on multiple evaluation criteria, characterized in that, include: Step 1: Preset multiple different candidate periods, and use the contour waterfall plot folding method to construct the pulsar contour waterfall plot for each candidate period; Step 2: Perform principal component analysis on the pulsar contour waterfall plot to calculate the contribution rate of the principal eigenvalues ​​and the projection variance of the principal components corresponding to the candidate periods; Step 3: Identify the peak trajectory in the pulsar contour waterfall plot, and fit the peak trajectory using a support vector regression model to obtain the slope of the regression line corresponding to the candidate period; Step 4: Determine the estimated value of the X-ray pulsar period from a set of multiple candidate periods based on the contribution rate of the principal eigenvalues, the variance of the principal component projection, and the slope of the regression line.

2. The method according to claim 1, characterized in that, Step 1 includes: Multiple different candidate periods are preset, and the total observation time of the observed events is divided into multiple equally spaced time periods. The following operations are performed for each candidate period: Each time period is divided equally according to the candidate period, and the resulting candidate period is further divided equally into multiple phase grids. The photon information value corresponding to each phase cell is determined based on the obtained pulsar photon sequence, and the photon information value includes the photon count in the phase cell; Using each phase grid as the horizontal axis and the photon information value corresponding to each phase grid as the vertical axis, a pulsar signal profile model corresponding to each time period is constructed. The pulsar signal profile models corresponding to all time periods are normalized and sorted and encoded in chronological order, and then combined to obtain the pulsar profile waterfall plot under the candidate period.

3. The method according to claim 1, characterized in that, Step 2, performing principal component analysis on the pulsar contour waterfall plot, includes: Principal component analysis was performed on the waterfall plot of the pulsar profile to obtain the covariance matrix of the waterfall plot; The covariance matrix of the waterfall plot is subjected to eigenvalue decomposition to obtain multiple eigenvalues ​​and their corresponding eigenvectors. The largest eigenvalue is extracted as the principal eigenvalue, and the eigenvector corresponding to the largest eigenvalue is the first principal direction.

4. The method according to claim 3, characterized in that, Step 2, calculating the principal eigenvalue contribution rate and principal component projection variance corresponding to the candidate period, includes: Based on the principal feature value and the plurality of feature values, calculate the principal feature value contribution rate corresponding to the candidate period; Based on the pulsar contour waterfall plot and the first principal direction, extract the principal component projection score vector; The principal component projection variance corresponding to the candidate period is calculated based on the principal component projection score vector.

5. The method according to claim 1, characterized in that, Step 3 includes: Identify the peak points in the pulsar contour waterfall plot and obtain the coordinates of each peak point. The coordinates of the peak points include the position index of the folded contour and the position index of the peak point on the phase axis. Using a support vector regression model, the peak trajectory is fitted based on the position index of the folded contour and the position index of the peak point on the phase axis; The slope of the regression line corresponding to the candidate period is obtained based on the peak trajectory model obtained from the fitting.

6. The method according to claim 1, characterized in that, Step 4 includes: The contribution rate of principal eigenvalues, the variance of principal component projection, and the slope of the regression line are used as evaluation indicators to construct a multi-criteria fusion framework, and the estimated value of the X-ray pulsar period is determined based on the multi-criteria fusion framework.

7. The method according to claim 6, characterized in that, Using the contribution rate of principal eigenvalues, the projection variance of principal components, and the slope of the regression line as evaluation indicators, a multi-criteria fusion framework is constructed. Based on this multi-criteria fusion framework, the estimated value of the X-ray pulsar period is determined, including: Using the extreme value independent variable operator, structural significance criteria, principal projection significance criteria, and geometric consistency criteria are constructed based on the contribution rate of principal eigenvalues, the variance of principal component projections, and the slope of the regression line corresponding to the candidate period, respectively. Based on the structural significance criterion, the principal projection significance criterion, and the geometric consistency criterion, the corresponding optimal candidate period is selected from the preset multiple candidate periods according to formulas (15), (16), and (18): （15） （16） （18） in, For the maximum value independent variable operator, For the minimum value operator, The optimal candidate period selected based on the structural significance criterion. Indicates candidate period Contribution rate of principal eigenvalues; The optimal candidate period is selected based on the main projection significance criterion. Indicates candidate period Principal component projection variance; The optimal candidate period selected based on the geometric consistency criterion. Candidate period The slope of the lower regression line The absolute value; The average of the three selected optimal candidate periods is used as an estimate of the X-ray pulsar period.

8. The method according to claim 1, characterized in that, Also includes: Based on the estimated period of the X-ray pulsar, the observation event is reconstructed using the pulsar signal profile model to obtain the current observation profile; The current observation profile is cross-correlated and matched with the standard profile at the center of mass of the solar system to obtain the optimal phase offset of the current observation profile relative to the standard profile. Based on the optimal phase offset, the total time delay of the X-ray pulsar is calculated by combining the number of integer periods and the estimated value of the X-ray pulsar period. The integer number of cycles represents the integer delay accumulated relative to the reference standard profile during the propagation of the pulsar signal.

9. A multi-criteria-based X-ray pulsar period estimation system, characterized in that, include: The system includes a waterfall plot construction module, a principal component analysis module, a slope extraction module, and a period estimation module; among which, The waterfall plot construction module is configured to preset multiple different candidate periods, and uses the contour waterfall plot folding method to construct the pulsar contour waterfall plot for each candidate period; The principal component analysis module is configured to perform principal component analysis on the pulsar contour waterfall plot, and calculate the contribution rate of the principal eigenvalues ​​and the projection variance of the principal components corresponding to the candidate period. The slope extraction module is configured to identify the peak trajectory in the pulsar contour waterfall plot, fit the peak trajectory using a support vector regression model, and obtain the slope of the regression line corresponding to the candidate period. The period estimation module is configured to determine the estimated value of the X-ray pulsar period from a plurality of preset candidate periods based on the contribution rate of the principal eigenvalue, the variance of the principal component projection, and the slope of the regression line.

10. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the X-ray pulsar period estimation method based on multiple evaluation criteria as described in any one of claims 1-8.

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