X-ray pulsar frequency estimation method based on bee colony optimization

Abstract

The invention discloses an X-ray pulsar frequency estimation method based on bee colony optimization, and belongs to the technical field of pulsar navigation. The method comprises the following steps: carrying out waterfall plot folding on an observation task, and carrying out conjoint analysis on candidate frequencies from two aspects of contour signal intensity and segmented phase consistency; reconstructing a high-dimensional space sample distance model according to actual sample distribution characteristics, and performing nonlinear random neighborhood embedding dimensionality reduction on the waterfall plot; the three-dimensional image information is converted into two-dimensional plane point group data, and the average distance original point standard deviation of a plane point group is adopted as an evaluation index of frequency estimation; the reconnaissance bee exploration behavior in the bee colony optimization algorithm is improved in combination with the local focusing principle, and the optimal frequency is efficiently searched; compared with an existing method, the method provided by the invention is proved to have superiority in the aspect of pulsar frequency estimation performance from the aspects of estimation precision, operation duration and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of pulsar navigation, and particularly relates to an X-ray pulsar frequency estimation method based on swarm optimization. Background Technique

[0002] In recent years, with the continuous development of deep space exploration technology, the research on autonomous astronomical navigation of deep space detectors has become more and more in-depth. As a navigation means more suitable for deep space exploration missions, astronomical navigation technology has been widely applied in the field of deep space exploration. Astronomical navigation can be divided into angle measurement navigation, velocity measurement navigation and range measurement navigation according to different measured quantities. Traditional astronomical angle measurement navigation methods (such as starlight angle 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 a new astronomical range measurement navigation method, X-ray pulsar navigation has a highly stable time standard and ultra-high positioning measurement accuracy, and is an ideal navigation method for deep space detectors.

[0003] A pulsar is a high-speed spinning neutron star with a stable spin period, continuously radiating stable periodic signals into the cosmic space. However, since the signals emitted by pulsars in the X-ray band are very weak, the detector cannot directly receive the complete periodic signal, but can only receive a time series of the arrival times of a series of pulsed star photons at the detector. Therefore, accurately estimating the pulsar frequency to restore its periodic signal losslessly is crucial for improving the X-ray pulsar navigation accuracy. Restoring the signal losslessly is crucial for improving the X-ray pulsar navigation accuracy.

[0004] The estimation of the X-ray pulsar frequency mainly relies on the method of traversing all candidate frequencies. Taking the chi-square test as the objective function was first proposed, and the profile folding was performed by traversing the candidate frequencies one by one to perform the chi-square test to select the optimal frequency. With stronger anti-noise ability and more sensitive to weak signals Testing is then proposed as the objective function. Some scholars have converted the one-dimensional profile signal obtained by using candidate frequency folding into a two-dimensional signal through a space-filling curve, and used image-based methods such as template matching and neural network discrimination to find the optimal frequency. In order to improve the discrimination efficiency of candidate frequencies and reduce the computational complexity, some scholars have improved the fast folding algorithm by introducing the post-order traversal method based on a binary tree, enhancing the estimation accuracy of X-ray pulsar frequencies under low signal-to-noise ratio conditions. These methods all perform traversal searches for candidate frequencies and have relatively high estimation accuracy, but the computational cost will increase with the increase in the observation duration. At the same time, in order to optimize the "traversal" process and further improve the estimation efficiency, a pulsar frequency estimation method based on a compressed sensing matrix has been proposed. This method utilizes the variation law of pulsar frequencies during the folding process to achieve a one-time fast frequency estimation. Although the computational amount of this method is greatly reduced, it has a large dependence on low-frequency features, which may affect its estimation accuracy.

[0005] The above methods have currently been widely applied to various X-ray pulsar frequency estimation tasks such as space navigation and astronomical observations. However, different detector performances and the limitations on the observation duration in different flight stages will directly lead to differences in the amount of photon data received during the detection process. For observation tasks with low data volume characteristics, the above traversal search methods mainly based on statistical tests have stronger detection capabilities and show greater advantages in suppressing noise interference and improving detection efficiency. However, the amount of photon data directly determines the accuracy of frequency estimation. When the amount of photon data is large, the above methods have limited ability to improve the estimation accuracy, and still adopting the traversal search method will further increase the computational cost. Summary of the Invention

[0006] The technical problem to be solved by the present invention is: for X-ray pulsar observation tasks with high data volume characteristics, the computational cost is high and the traversal search speed is too slow. A method for estimating X-ray pulsar frequencies based on swarm optimization is provided to improve the accuracy and search speed of pulsar frequency estimation.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A method for estimating X-ray pulsar frequencies based on swarm optimization, comprising:

[0009] Step 1: Segment and fold the data of the characteristic observation task of candidate frequencies to obtain a contour waterfall diagram;

[0010] Step 2: According to the contour waterfall diagram, introduce the prior information of the peak movement of the folded contour, weight and correct the Euclidean distance between samples, and construct a distance calculation model for high-dimensional space sample pairs;

[0011] Step 3: Use the distance calculation model to establish a low-dimensional space distribution. Use the KL divergence objective function to measure the similarity between the high-dimensional space distribution and the low-dimensional space distribution, and continuously iterate to find the low-dimensional space distribution that best matches the high-dimensional space distribution, and reduce the dimension of the high-dimensional data;

[0012] Step 4: After dimensionality reduction, evaluate the folding effect of the candidate frequency by calculating the standard distance of the points on the dimensionality reduction plane relative to the coordinate origin, that is, the standard deviation of the mean distance from the origin;

[0013] Step 5: Combine the local focusing principle to improve the exploration behavior of the scout bees in the bee colony optimization algorithm. For the candidate frequencies selected by the algorithm, repeat Steps 1 to 4 to obtain the corresponding standard deviation of the mean distance from the origin. Use the standard deviation of the mean distance from the origin to quantitatively evaluate the folding effect of different candidate frequencies, and search for the optimal frequency.

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

[0015] (1) It is applicable to the observation tasks with high data volume features. Through simulation experiments, it can be found that when the observation time gradually increases, the data volume of the observation task increases accordingly, and the estimation accuracy of the WDBO method improves significantly. And compared with the testing method, which has obvious advantages under large data volume, the WDBO method can further improve the estimation accuracy.

[0016] (2) High estimation accuracy and stable estimation performance. Compared with testing and testing, the WDBO method shows higher estimation accuracy and smaller RMSE. This shows that the WDBO method has excellent and stable estimation performance.

[0017] (3) High operation efficiency and short operation time. Compared with the traditional detection method that traverses and searches for frequencies, the WDBO method uses an optimization algorithm to accelerate the frequency search process and has a faster search speed. Description of the Drawings

[0018] Figure 1 is the overall flowchart of the X-ray pulsar frequency estimation method based on bee colony optimization proposed by the present invention;

[0019] Figure 2 is the calculation process of dimensionality reduction by the improved method of non-linear stochastic neighbor embedding (Stochastic Neighbor Embedding, SNE) based on high-dimensional sample distance reconstruction;

[0020] Figure 3 is the effect schematic diagram after SNE dimensionality reduction of the waterfall plot;

[0021] Figure 4 is the schematic diagram of improving the exploration behavior of scout bees by local focusing;

[0022] Figure 5 Bar charts and box plots for three estimation methods. Detailed implementation manners

[0023] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used 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. To achieve the above objectives, the present invention adopts the following technical solutions.

[0024] As Figure 1 shown, the flowchart of the X-ray pulsar frequency estimation method based on swarm optimization of the present invention adopts the following technical solutions: Taking the Crab pulsar as an example, the specific implementation steps of the present invention are described as follows:

[0025] Step 1: Segment and fold the characteristic observation task data of the candidate frequency to obtain a contour waterfall plot;

[0026] Contour waterfall plot analysis is a very accurate frequency analysis method. This method can fully explore the signal frequency information from the two angles of folded signal intensity and phase by splitting the observation data into multiple segments for joint analysis. Therefore, this method is usually applicable to tasks with longer observation time or larger amount of observation data. The visualization steps of the contour waterfall plot are as follows: Divide the total observation time into segments at equal intervals, and perform contour folding respectively within each segment according to the same candidate frequency to obtain folded contour curves. And merge these contours together in chronological order to obtain a color image with the color scale associated with the contour signal intensity , which is the contour waterfall plot at this candidate frequency . Let the number of bins of the folded contour be

[0027] (1)

[0028] In the formula, is the matrix element, m is the number of the time period, and n is the number of the frequency candidate value.

[0029] Step 2: Introduce the prior information of the peak movement of the folded contour in the contour intensity, weight and correct the Euclidean distance between samples, and construct a distance calculation model for sample pairs in the high-dimensional space;

[0030] The phase of the folded profile gradually moves, and the peaks of the single-folded profile show obvious misalignment. Therefore, the present invention introduces the prior information of the peak movement of the folded profile, weights and corrects the Euclidean distance between samples, reconstructs the distance calculation model for high-dimensional space sample pairs, and weakens the problem of unstable Euclidean distance between samples caused by the deformation of the folded profile.

[0031] The distance calculation model for high-dimensional space sample pairs based on the prior information of the peak movement of the folded profile can be expressed as:

[0032] (2)

[0033] In the formula, is the recalculated distance of the high-dimensional sample pair, M is the number of folded profile curves, x is the high-dimensional sample data, i and j are data numbers, q is the candidate frequency, P is the number of high-dimensional sample data points, is the slope of the peak phases of the folded profiles. The present invention obtains this slope by performing a single fitting on the number of time intervals and the peak phases of the folded profiles in the waterfall plot.

[0034] Step 3: Use the distance calculation model to establish a low-dimensional space distribution, use the KL divergence objective function to measure the similarity between the high-dimensional space distribution and the low-dimensional space distribution, and continuously iterate to find the low-dimensional space distribution that best matches the high-dimensional space distribution to reduce the dimension of the high-dimensional data. The calculation process of dimensionality reduction using the improved SNE method based on the reconstruction of high-dimensional sample distances is as Figure 2 shown, including the following steps:

[0035] Step 3.1 Calculate the joint probability of high-dimensional samples. First, use the Euclidean distance as the measure of the similarity between high-dimensional sample pairs, and calculate the conditional probability of similarity and between two samples:

[0036] (3)

[0037] (4)

[0038] In the formula, is the high-dimensional sample data point, represents the Euclidean distance between samples, is the variance of the high-dimensional sample distribution, which is mainly determined by the hyperparameter perplexity.

[0039] Secondly, to reduce the influence of outliers on the iterative process, calculate the joint probability between high-dimensional samples:

[0040] (5)

[0041] In the formula, is the number of high-dimensional sample data points.

[0042] Step 3.2 Calculate the joint probability of low-dimensional samples. Using the t-distribution as the basic model of the low-dimensional distribution, update and calculate the joint probability in the low-dimensional space corresponding to the joint probability between two points in the high-dimensional space according to the iterative results :

[0043] (6)

[0044] In the formula, is the high-dimensional sample data point, and k, l are the data point numbers.

[0045] Step 3.3 Calculate the KL divergence between the high-dimensional distribution and the low-dimensional distribution. Using the KL divergence as the objective function to measure the similarity between the high-dimensional distribution and the low-dimensional distribution:

[0046] (7)

[0047] Step 3.4 Perform derivative optimization on the objective function KL divergence. Taking the low-dimensional space distribution as the optimization variable, continuously perform derivative optimization on the objective function KL divergence using the gradient descent method until the dimensionality reduction result of the low-dimensional space that best matches the high-dimensional space distribution is obtained:

[0048] (8)

[0049] Step 4. After dimensionality reduction, evaluate the folding effect of the candidate frequencies by calculating the standard distance of the dimensionality reduction plane points relative to the coordinate origin, that is, the standard deviation from the origin of the mean distance;

[0050] Figure 3 is the result of the planar scatter plot obtained by reducing the dimensionality of the contour waterfall plot using the improved SNE method. The distribution pattern of the planar two-dimensional data points after dimensionality reduction can well reflect the change of the pulsar frequency. In order to specifically quantify such changes through evaluation indicators to determine the optimal candidate frequencies, the present invention uses the standard deviation from the origin of the mean distance (SDO), that is, the root mean square distance of the data points to the origin, as an evaluation criterion to quantify the uniformity and compactness of the distribution of the two-dimensional data points on the plane.

[0051] SDO is a statistic used to measure the overall spread of data points in a two-dimensional space. SDO synthesizes the deviation of all data points from the origin and can reflect whether the data after dimensionality reduction is concentrated around the origin. If SDO is small, it indicates that the distribution of data points is relatively compact and close to the origin. Conversely, it means that the distribution of data points is relatively dispersed and far from the origin. Using SDO to quantify the distribution of planar points has strong robustness, is relatively less affected by outliers, and the quantification results are easy to interpret, enabling an intuitive comparison of the dispersion and concentration of different distributions. SDO can be specifically expressed as:

[0052] (9)

[0053] In the formula, L is the number of dimensions of the data point distribution in space, are the standard deviations in the x and y directions respectively.

[0054] Step 5: Improve the exploration behavior of scout bees in the bee colony optimization algorithm by combining the local focusing principle. As Figure 4 shown, for the candidate frequencies selected by the algorithm, repeat Steps 1 to 4 to obtain the corresponding standard deviations from the origin. Use the standard deviations from the origin to quantitatively evaluate the folding effects of different candidate frequencies and search for the optimal frequency;

[0055] Worker bee stage: Conduct a local neighborhood search for the information of the initial food sources (candidate frequency SDO) one by one to find potential better food sources. If a better food source appears, replace the initial food source. Otherwise, keep it unchanged.

[0056]

[0057] Observer bee stage: Calculate the probability of whether to carry out further observer bee work based on the information of the food sources updated by local search. Conduct an in-depth search for the better food sources again according to the probability values.

[0058]

[0059] Scout bee stage based on local focusing: To avoid falling into local optima and accelerate the search rate purposefully, replace the food source information that has not been able to find a better one for a long time during the iteration process near the "current optimal value" according to the local focusing principle, and re-search the new area near the "current optimal value" to find better food source information as much as possible.

[0060]

[0061] The experimental simulation of the present invention is as follows:

[0062] The simulation experiment parameters are set as follows: the duration is 1000 seconds, the pulse period is 33.7 ms, the effective photon flux is 1.54 ph / cm 2 / s, and the background photon flux is 0.005 ph / cm 2 / s. The effective area of the detector is 1 m 2 , and the number of bins is 256.

[0063] Table 1 Mean Error and RMSE of Different Estimation Methods

[0064] As can be seen from Table 1, under these simulation conditions, the method of the present invention has the highest estimation accuracy. Compared with the traditional test method, the estimation accuracy of the method of the present invention is nearly doubled. This is because at a relatively long observation time, the cumulative number of photons is large. At this time, the test method can show greater advantages due to its characteristic of calculating the statistical mean, resulting in a significant improvement in its estimation accuracy compared to the test method. And the method proposed by the present invention can better sense the subtle changes in the signal intensity and phase of the waterfall plot after performing the waterfall plot operation, making it have a higher estimation accuracy than the test method in long-term observations.

[0065] At the same time, by combining Figure 5 's (a) and (b), it can be found that the method proposed by the present invention has a smaller RMSE, confidence interval, and interquartile range, which all indicate that among the three estimation methods, the method of the present invention has more stable estimation performance and the highest reliability.

[0066] Table 2 Mean Operation Duration of Three Estimation Methods

[0067] As can be seen from Table 2, since the test and the test both use the statistical test to traverse and search for the candidate period, the computational complexity of these two methods is the same, which is reflected in having basically the same operation duration. And the method proposed in this paper uses an optimized search algorithm for estimation instead of traversing search, so it has a shorter operation duration and higher operation efficiency.

[0068] The above embodiments are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the present invention is defined by the appended claims. All equivalent substitutions and modifications made without departing from the spirit and principles of the present invention shall be covered within the scope of the present invention.

Claims

1. A method for estimating the frequency of X-ray pulsars based on swarm optimization, characterized in that: Specifically, it includes the following steps: Step 1: Segment and fold the feature observation task data of the candidate frequencies to obtain a contour waterfall plot; Step 2: According to the contour waterfall plot, introduce the prior information of contour peak movement, weight-correct the Euclidean distance between samples, and construct a distance calculation model for sample pairs in the high-dimensional space; Step 3: Use the distance calculation model to establish a low-dimensional space distribution. Use the KL divergence objective function to measure the similarity between the high-dimensional space distribution and the low-dimensional space distribution, and continuously iterate to find the low-dimensional space distribution that best matches the high-dimensional space distribution, and reduce the dimension of the high-dimensional data; Step 4: After dimension reduction, evaluate the folding effect of the candidate frequencies by calculating the standard distance of the points on the reduced-dimensional plane relative to the coordinate origin, that is, the standard deviation of the mean distance from the origin; Step 5: Combine the local focusing principle to improve the exploration behavior of the scout bees in the bee colony optimization algorithm. For the candidate frequencies selected by the algorithm, repeat Steps 1 to 4 to obtain the corresponding standard deviation of the mean distance from the origin. Use the standard deviation of the mean distance from the origin to quantitatively evaluate the folding effects of different candidate frequencies, and search for the optimal frequency.

2. The X-ray pulsar frequency estimation method based on swarm optimization according to claim 1, wherein In Step 1, the steps for obtaining the contour waterfall plot are as follows: The total observation time is equally divided into segments. Within each segment, contour folding is performed respectively according to the same candidate frequency to obtain folded contours. These folded contours are merged together in chronological order to obtain a color image with the color scale associated with the contour signal intensity , which is the contour waterfall plot at this candidate frequency . Assuming the number of bins of the folded contour is , the contour waterfall plot is expressed as: (1) In the formula, is a matrix element, m is the number of the time period, and n is the number of the frequency candidate value.

3. The method for estimating the X-ray pulsar frequency based on swarm optimization according to claim 2, wherein The implementation method of Step 2 is: The distance calculation model for sample pairs in the high-dimensional space based on the prior information of contour peak movement is expressed as: (2) In the formula, is the distance of the high-dimensional space sample pair obtained by recalculation, is the slope of the peak phases of contour numbers, is the high-dimensional sample data point, is the data number, is the candidate frequency, is the number of high-dimensional sample data points.

4. A method for estimating the frequency of X-ray pulsars based on swarm optimization according to claim 3, characterized in that, Step 3 includes: Step 3.1 Calculate the joint probability of high-dimensional sample pairs; first, use the Euclidean distance as a measure of the similarity between high-dimensional sample pairs, and calculate the conditional probability of similarity between pairwise samples and : (3) (4) In the formula, is the high-dimensional sample data point, represents the Euclidean distance between samples, is the variance of the high-dimensional sample distribution; secondly, calculate the joint probability between high-dimensional sample pairs: (5) Wherein, is the number of high-dimensional sample data points; Step 3.2 Calculate the joint probability of low-dimensional sample pairs; use the t-distribution as the basic model for the low-dimensional distribution, and update and calculate the joint probability in the low-dimensional space corresponding to the joint probability between two samples in the high-dimensional space based on the iterative results : (6) In the formula, is a high-dimensional sample data point, and k and l are data point numbers; Step 3.3 Calculate the KL divergence between the high-dimensional distribution and the low-dimensional distribution; use the KL divergence as the objective function to measure the similarity between the high-dimensional distribution and the low-dimensional distribution: (7) Step 3.4 Derive and optimize the objective function KL divergence; use the low-dimensional space distribution as the optimization variable, and continuously derive and optimize the objective function KL divergence using the gradient descent method until the low-dimensional space dimension reduction result that best matches the high-dimensional space distribution is obtained: (8)。 5. The method for estimating the frequency of X-ray pulsars based on swarm optimization according to claim 4, wherein The implementation method of Step 4 is to use the standard deviation of the mean distance from the origin, that is, the root mean square distance from the data point to the origin, to quantify the uniformity and compactness of the distribution of the two-dimensional data points on the plane for the two-dimensional data points obtained after dimension reduction.

6. The method for estimating the frequency of X-ray pulsars based on swarm optimization according to claim 5, wherein The standard deviation of the mean distance from the origin SDO is expressed as: (9) where L is the number of dimensions in which the data points are distributed in space, are the standard deviations in the x and y directions respectively, are the sample data points.

7. A method for estimating the frequency of X-ray pulsars based on swarm optimization according to claim 6, characterized in that The bee colony optimization algorithm in Step Five includes: the working stage of worker bees, the working stage of observing bees, and the working stage of scout bees based on local focusing; In the working stage of worker bees, perform a local neighborhood search on the standard deviation of the mean distance from the origin SDO of the initial food source, that is, the candidate frequency, to find potential better food sources; if a better food source appears, replace the initial food source; otherwise, keep it unchanged; In the working stage of observing bees, calculate the probability of whether to carry out further observing bee work based on the food source information updated by local search; conduct in-depth search again for the better food sources according to the probability values; In the stage of scout bees based on local focusing, to avoid falling into local optima and to speed up the search rate targeted, replace the food source information that has not been able to find a better one for a long time during the iteration process near the current optimal value according to the local focusing principle, and re-search the new area near the current optimal value to find better food source information.

8. A method for estimating the frequency of X-ray pulsars based on swarm optimization according to claim 7, characterized in that, The algorithm in the working stage of worker bees is: The input includes candidate frequencies , the standard deviation of the average distance from the origin , the cyclic critical value and the number of worker bees ; For each worker bee, perform the following operations: Randomly generate a search scale factor , and randomly select another worker bee . Based on the information of the worker bee , determine a new candidate frequency near the worker bee , and calculate the of the new candidate frequency ; If the standard deviation of the average distance from the origin of the new candidate frequency is better than that of the current optimal frequency and its update the current optimal candidate frequency and reset the loop critical value of the employed bee ; Otherwise, increase the worker bees of the cyclic critical value ; The output of this stage includes candidate frequencies , the standard deviation of the mean distance from the origin of the candidate frequencies , and the cyclic critical value of the worker bees .

9. A method for estimating the frequency of X-ray pulsars based on swarm optimization according to claim 7, wherein, The algorithm for the observation peak working stage is as follows: The input includes candidate frequencies , the standard deviation of the average distance from the origin of the candidate frequencies , the loop critical value , the number of worker bees ; The process is as follows: According to the standard deviation of the mean distance from the origin of the candidate frequencies , calculate the probability that each observed peak is selected; For each worker bee, perform the following operations: If the randomly generated screening factor satisfies , then let the observed peak perform the work in the worker bee stage and conduct exploration; The output of this stage includes candidate frequencies , the standard deviation of the average distance from the origin of the candidate frequencies , and the cyclic critical value of the worker bees .

10. A method for estimating the frequency of X-ray pulsars based on swarm optimization according to claim 7, characterized in that, The algorithm for the scouting peak working stage based on local focusing is as follows: The input includes the loop critical value , the number of worker bees , and the maximum stagnant update times ; The process is as follows: For each worker bee, perform the following operations: If the following conditions are met , generate new candidate frequencies near the current optimal frequency , where is the random search factor is the search range near the optimal value, and recalculate the standard deviation of the mean distance of the new candidate frequencies from the origin , and reset the loop critical value of the employed bee ; ; The output of this stage includes candidate frequencies , the standard deviation of the mean distance from the origin of the candidate frequencies , and the cyclic critical value of the worker bees .

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