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

Abstract

The application discloses a kind of X-ray pulsar frequency estimation methods based on swarm optimization, belong to pulsar navigation technical field.The method includes: through waterfall chart folding to observation task, from the consistency of profile signal intensity and segmented phase two aspects to candidate frequency is jointly analyzed;According to the actual sample distribution characteristics reconstruction high-dimensional space sample distance model, nonlinear random neighborhood embedding dimension reduction is carried out to waterfall chart;Three-dimensional image information is converted into two-dimensional plane point group data, and the mean distance origin standard deviation of plane point group is used as the evaluation index of frequency estimation;Combined with the principle of local focusing, the search behavior of scout bees in the bee colony optimization algorithm is improved, and the optimal frequency is efficiently searched;Through simulation comparison with existing methods, the superiority of the method proposed in the application in the performance of pulsar frequency estimation is proved from the aspects of estimation accuracy and operation time.

Description

Technical Field

[0001] This invention belongs to the field of pulsar navigation technology, and particularly relates to an X-ray pulsar frequency estimation method based on bee colony optimization. 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 the field. Based on different measurement methods, 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 near-celestial bodies, and their navigation accuracy often cannot be guaranteed. However, as an emerging astronomical distance measurement navigation method, X-ray pulsar navigation has a highly stable time standard and extremely high positioning measurement accuracy, making it an ideal navigation method for deep space probes.

[0003] Pulsars are high-speed spinning neutron stars with stable spin periods, continuously radiating stable periodic signals into space. However, because the signals emitted by pulsars in the X-ray band are extremely weak, detectors cannot directly receive the complete periodic signal; instead, they only receive a sequence of time-series arrivals of pulsar photons. Therefore, accurately estimating the pulsar frequency and losslessly reconstructing its periodic signal is crucial for improving the accuracy of X-ray pulsar navigation.

[0004] The estimation of X-ray pulsar frequencies mainly relies on a method of traversing and searching all candidate frequencies. The test was first proposed as the objective function, and the contour folding was performed by iterating through the candidate frequencies one by one. The optimal frequency was selected through testing. This frequency is chosen for its stronger noise immunity and greater sensitivity to weak signals. The objective function was subsequently proposed as a test. Some researchers converted the one-dimensional contour signal obtained by folding candidate frequencies into a two-dimensional signal using space-filling curves, and then used image-based methods such as template matching and neural network discrimination to find the optimal frequency. To improve the efficiency of candidate frequency discrimination and reduce computational complexity, some researchers improved the fast folding algorithm by introducing a post-order traversal method based on binary trees, enhancing the estimation accuracy of X-ray pulsar frequencies under low signal-to-noise ratio conditions. These methods all perform a traversal search of candidate frequencies, achieving high estimation accuracy, but the computational cost increases with the observation duration. Meanwhile, to optimize the "traversal" process and further improve estimation efficiency, a pulsar frequency estimation method based on compressed sensing matrices was proposed. This method utilizes the frequency variation during the folding process to achieve a one-time, rapid frequency estimation. Although this method significantly reduces computation, it is highly dependent on low-frequency features, which may affect its estimation accuracy.

[0005] The methods described above are currently widely used in various X-ray pulsar frequency estimation tasks, such as space navigation and astronomical observations. However, different detector performances and limitations on observation duration during different flight phases directly lead to variations in the amount of photon data received during detection. For observation tasks with low data volumes, the ergonomic search method, which primarily relies on statistical tests, exhibits stronger detection capabilities and demonstrates significant 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 aforementioned methods have limited ability to improve estimation accuracy, and continuing to use an ergonomic search approach further increases computational costs. Summary of the Invention

[0006] The technical problem this invention aims to solve is that X-ray pulsar observation tasks with high data volume have high computational costs and slow traversal search speeds. This invention provides an X-ray pulsar frequency estimation method based on bee colony optimization to improve the accuracy and speed of pulsar frequency estimation.

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

[0008] A method for estimating the frequency of X-ray pulsars based on bee colony optimization, comprising:

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

[0010] Step 2: Based on the contour waterfall plot, introduce prior information on the peak shift of the folded contour, perform weighted correction on the Euclidean distance between samples, and construct a high-dimensional space sample pair distance calculation model.

[0011] Step 3: Using a distance calculation model, establish a low-dimensional spatial distribution. Use the KL divergence objective function to measure the similarity between the high-dimensional spatial distribution and the low-dimensional spatial distribution. Iterate continuously to find the low-dimensional spatial distribution that best matches the high-dimensional spatial distribution, thus reducing the dimensionality of the high-dimensional data.

[0012] Step 4: After dimensionality reduction, the folding effect of candidate frequencies is evaluated by calculating the standard distance of the points in the dimensionality reduction plane relative to the origin, i.e., the standard deviation of the mean distance from the origin.

[0013] Step 5: Improve the scout bee exploration behavior in the bee colony optimization algorithm by combining the principle of local focus. Repeat steps 1 to 4 for the candidate frequencies selected by the algorithm to obtain the corresponding standard deviation of the mean from the origin. Use the standard deviation of the mean from the origin to quantify and evaluate the folding effect of different candidate frequencies and search for the optimal frequency.

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

[0015] (1) Applicable to observation tasks with high data volume characteristics. Simulation experiments show that as the observation time gradually increases, the data volume of the observation task also increases, and the estimation accuracy of the WDBO method is significantly improved. Furthermore, it has a clear advantage over other methods with large data volumes. The WDBO method can further improve the estimation accuracy.

[0016] (2) High estimation accuracy and stable estimation performance. Compared to Inspection and The WDBO method demonstrates higher estimation accuracy and lower RMSE, indicating that it exhibits excellent and stable estimation performance.

[0017] (3) High computational efficiency and short computation time. Compared with the traditional detection method of traversing and searching for frequencies, the WDBO method uses an optimization algorithm to accelerate the frequency search process and has a faster search speed. Attached Figure Description

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

[0019] Figure 2 The computational process for dimensionality reduction of the improved method of nonlinear stochastic neighborhood embedding (SNE) based on high-dimensional sample distance reconstruction;

[0020] Figure 3 A diagram illustrating the effect of SNE dimensionality reduction on a waterfall plot;

[0021] Figure 4 A schematic diagram illustrating how to improve the scouting behavior of reconnaissance bees by focusing on specific areas;

[0022] Figure 5 The charts show bar graphs and box plots for the three estimation methods. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the 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 merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0024] like Figure 1 The flowchart of the X-ray pulsar frequency estimation method based on bee colony optimization of this invention is shown below. The following technical solution is adopted: Taking Crab pulsar as an example, the specific implementation steps of this invention are explained:

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

[0026] Contour waterfall plot analysis is a highly accurate frequency analysis method. It fully extracts signal frequency information from both the intensity and phase perspectives by breaking down observation data into multiple segments for joint analysis. Therefore, this method is typically suitable for tasks with long observation times or large amounts of data. The visualization steps for a contour waterfall plot are: dividing the total observation time into equal intervals... Segments, within each segment based on the same candidate frequency By folding the contours separately, you can obtain... A series of folded contour curves are then combined in chronological order to obtain a color image in which the color scale is correlated with the contour signal intensity. That is, the candidate frequency. The following is a waterfall plot of the contour. Let the number of bins in the folded contour be... Then the waterfall diagram can be represented as:

[0027] (1)

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

[0029] Step 2: In the contour intensity, the prior information of the peak shift of the folded contour is introduced, and the Euclidean distance between samples is weighted and corrected to construct a high-dimensional space sample pair distance calculation model.

[0030] The phase of the folded contour gradually shifts, and the peak value of a single folded contour exhibits a significant misalignment. Therefore, this invention introduces prior information about the peak shift of the folded contour to perform weighted correction on the Euclidean distance between samples, reconstructing a high-dimensional space sample pair distance calculation model, thus mitigating the instability of the Euclidean distance between samples caused by the deformation of the folded contour.

[0031] The high-dimensional spatial sample pair distance calculation model based on prior information of peak movement in folded contours can be expressed as:

[0032] (2)

[0033] In the formula, To recalculate the distance between the high-dimensional sample pairs, M represents the number of folded contour curves, x represents the high-dimensional sample data, i and j are the data numbers, q is the candidate frequency, and P is the number of high-dimensional sample data points. for The slope of the peak phase of the folded profile. This invention obtains the slope by fitting the number of time intervals in the waterfall plot to the peak phase of the profile.

[0034] Step 3: Using a distance calculation model, establish a low-dimensional spatial distribution. Use the KL divergence objective function to measure the similarity between the high-dimensional and low-dimensional spatial distributions. Iterate continuously to find the low-dimensional spatial distribution that best matches the high-dimensional spatial distribution, thus reducing the dimensionality of the high-dimensional data. The calculation process for dimensionality reduction using the SNE improvement method based on high-dimensional sample distance reconstruction is as follows: Figure 2 As shown, it includes the following steps:

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

[0036] (3)

[0037] (4)

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

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

[0040] (5)

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

[0042] Step 3.2 Calculate the joint probability of the low-dimensional samples. Using the t-distribution as the basic model for 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 based on the iteration results. :

[0043] (6)

[0044] In the formula, Let k and l be the data points of the high-dimensional sample data.

[0045] Step 3.3 Calculate the KL divergence between the high-dimensional and low-dimensional distributions. The KL divergence is used as the objective function to measure the similarity between the high-dimensional and low-dimensional distributions.

[0046] (7)

[0047] Step 3.4 Optimize the KL divergence of the objective function. Using the low-dimensional space distribution as the optimization variable, continuously optimize the KL divergence of the objective function using gradient descent until the dimensionality reduction result in the low-dimensional space that best matches the high-dimensional space distribution is obtained.

[0048] (8)

[0049] Step 4: After dimensionality reduction, the folding effect of candidate frequencies is evaluated by calculating the standard distance of the points in the dimensionality reduction plane relative to the origin, i.e., the standard deviation of the mean distance from the origin.

[0050] Figure 3 This is a planar scatter plot obtained by dimensionality reduction of the contour waterfall plot using an improved SNE method. The distribution of the dimensionality-reduced two-dimensional data points in the planar plane can well reflect the frequency variation of pulsars. In order to quantify such variations through evaluation metrics to determine the optimal candidate frequency, this invention uses the Standard Deviation from Origin (SDO), i.e., the root mean square distance of the data points from the origin, as an evaluation criterion to quantify the uniformity and compactness of the distribution of the two-dimensional data points in the plane.

[0051] SDO (Dispersion Dispersion) is a statistic used to measure the overall dispersion of data points in a planar space. SDO integrates the deviations of all data points from the origin, reflecting whether the dimensionality-reduced data clusters around the origin. A smaller SDO indicates a more compact distribution of data points, closer to the origin. Conversely, a larger SDO indicates a more dispersed distribution, farther from the origin. Using SDO to quantify planar point distribution is robust, less affected by outliers, and the results are easy to interpret, allowing for a direct comparison of the dispersion and concentration of different distributions. Specifically, SDO can be expressed as:

[0052] (9)

[0053] In the formula, L is the dimension of the data points distributed in space. denoted as x and y, respectively, are the standard deviations in the x and y directions.

[0054] Step 5: Improve the scout bee exploration behavior in the bee colony optimization algorithm by combining the principle of local focus, such as... Figure 4 As shown, for the candidate frequencies selected by the algorithm, steps 1 to 4 are repeated to obtain the corresponding standard deviation of the mean from the origin. The standard deviation of the mean from the origin is used to quantify and evaluate the folding effect of different candidate frequencies and search for the optimal frequency.

[0055] Worker bee stage: Each initial food source (candidate frequency SDO) is searched locally for potential better food sources. If a better food source is found, the initial food source is replaced. Otherwise, it remains unchanged.

[0056]

[0057] Observation phase: Based on the updated food source information from the local search, a probability calculation is performed to determine whether further observation peaks should be conducted. Based on the probability values, a more in-depth search is then conducted for the more favorable food sources.

[0058]

[0059] The reconnaissance bee stage based on local focus: In order to avoid getting trapped in local optima and to accelerate the search rate in a targeted manner, the food source information that cannot be found better in the long term during the iteration process is replaced near the "current optimal value" according to the principle of local focus, and the new area near the "current optimal value" is searched again to find better food source information as much as possible.

[0060]

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

[0062] The simulation parameters were set as follows: duration 1000 seconds, pulse period 33.7 ms, and effective photon flux 1.54 ph / cm². 2 / s, background photon flux 0.005ph / cm 2 / s, the effective area of ​​the detector is 1m² 2 The number of bins is 256.

[0063] Table 1. Mean error and RMSE of different estimation methods

[0064]

[0065] As shown in Table 1, under the simulation conditions, the method of the present invention has the highest estimation accuracy, and compared with the traditional method... The verification method of this invention improves the estimation accuracy by nearly double. This is because the cumulative number of photons is large over a longer observation period. The test method, due to its characteristic of calculating the statistical mean, can demonstrate a greater advantage, resulting in higher estimation accuracy compared to [other methods]. The verification method shows a significant improvement. Furthermore, the method proposed in this invention, after performing waterfall plot operations, can better sense subtle changes in the signal intensity and phase of the waterfall plot, making it more effective in long-term observations than... The testing method offers higher estimation accuracy.

[0066] At the same time, combined Figure 5 As can be seen from (a) and (b), the method proposed in this invention has a smaller RMSE, confidence interval, and interquartile range, which all indicate that among the three estimation methods, the method of this invention has more stable estimation performance and the highest reliability.

[0067] Table 2. Average computation time of the three estimation methods

[0068]

[0069] As can be seen from Table 2, due to Inspection and Both methods employ statistical tests to traverse and search the candidate periods, resulting in similar computational complexity and similar processing time. However, the proposed method uses an optimized search algorithm for estimation instead of a traversal search, thus achieving shorter processing time and higher computational efficiency.

[0070] The above embodiments are provided merely for the purpose of describing the present invention and are not intended to limit the scope of the invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the invention should be covered within the scope of the invention.

Claims

1. A method for estimating the frequency of X-ray pulsars based on bee colony optimization, characterized in that: Specifically, the following steps are included: Step 1: Segment and fold the feature observation task data of candidate frequencies to obtain a contour waterfall plot; Step 2: Based on the contour waterfall plot, introduce prior information on the movement of contour peaks, perform weighted correction on the Euclidean distance between samples, and construct a high-dimensional space sample pair distance calculation model. Step 3: Using a distance calculation model, establish a low-dimensional spatial distribution. Use the KL divergence objective function to measure the similarity between the high-dimensional spatial distribution and the low-dimensional spatial distribution. Iterate continuously to find the low-dimensional spatial distribution that best matches the high-dimensional spatial distribution, thus reducing the dimensionality of the high-dimensional data. Step 4: After dimensionality reduction, the folding effect of candidate frequencies is evaluated by calculating the standard distance of the points in the dimensionality reduction plane relative to the origin, i.e., the standard deviation of the mean distance from the origin. Step 5: Improve the scout bee exploration behavior in the bee colony optimization algorithm by combining the local focus principle. Repeat steps 1 to 4 for the candidate frequencies selected by the algorithm to obtain the corresponding standard deviation of the mean from the origin. Use the standard deviation of the mean from the origin to quantify the folding effect of different candidate frequencies and search for the optimal frequency. In step 1, the steps for obtaining the contour waterfall plot are as follows: divide the total observation time into equal intervals. Segments, within each segment based on the same candidate frequency Fold the contours separately to obtain These folded contours are combined in chronological order to obtain a color image in which the color scale is correlated with the contour signal intensity. That is, the candidate frequency. The following is a waterfall outline diagram; let the number of bins in the folded outline be... The outline waterfall diagram is then represented as: (1) In the formula, Let m be the matrix element, m be the time period number, and n be the frequency candidate value number.

2. The X-ray pulsar frequency estimation method based on bee colony optimization according to claim 1, characterized in that, The implementation method for step 2 is as follows: The high-dimensional spatial sample pair distance calculation model based on the prior information of contour peak movement is expressed as follows: (2) In the formula, To recalculate the distance between the high-dimensional sample pairs, for The slope of the peak phase of the profile. For the number of outlines, For high-dimensional sample data points, Number the data. For candidate frequencies, This represents the number of high-dimensional sample data points.

3. The X-ray pulsar frequency estimation method based on bee colony optimization according to claim 2, characterized in that, Step 3 includes: Step 3.1 Calculate the joint probability of high-dimensional sample pairs; First, using Euclidean distance as a measure of similarity between high-dimensional sample pairs, calculate the conditional probability of similarity between each pair of samples. and : (3) (4) In the formula, For high-dimensional sample data points, This represents the Euclidean distance between samples. First, we calculate the variance of the high-dimensional sample distribution; second, we calculate the joint probability between high-dimensional sample pairs: (5) In the formula, The number of high-dimensional sample data points; Step 3.2 Calculate the joint probability of low-dimensional sample pairs; using the t-distribution as the basic model for the low-dimensional distribution, 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 iteration results. : (6) In the formula, For high-dimensional sample data points, k and l are the 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: Optimize the KL divergence of the objective function by taking its derivative; using the low-dimensional space distribution as the optimization variable, continuously optimize the KL divergence of the objective function using gradient descent until the dimensionality reduction result in the low-dimensional space that best matches the high-dimensional space distribution is obtained. (8)。 4. The X-ray pulsar frequency estimation method based on bee colony optimization according to claim 3, characterized in that, The implementation method of step 4 is to use the root mean square distance from the origin to the standard deviation of the plane two-dimensional data points obtained after dimensionality reduction to quantify the uniformity and compactness of the distribution of the two-dimensional data points on the plane.

5. The X-ray pulsar frequency estimation method based on bee colony optimization according to claim 4, characterized in that, The standard deviation (SDO) of the mean distance from the origin is expressed as: (9) In the formula, L is the dimension of the data points distributed in space. These are the standard deviations in the x and y directions, respectively. These are sample data points.

6. The X-ray pulsar frequency estimation method based on bee colony optimization according to claim 5, characterized in that, Step 5 of the bee colony optimization algorithm includes: worker bee working phase, observation peak working phase, and reconnaissance peak working phase based on local focus; During the worker bee's working phase, it performs a local neighborhood search on the mean standard deviation (SDO) of the initial food source (i.e., candidate frequency) to find potential better food sources; if a better food source is found, the initial food source is replaced; otherwise, it remains unchanged. During the observation bee work phase, based on the updated food source information from the local search, a probability calculation is performed to determine whether further observation bee work should be carried out; based on the probability value, a more in-depth search is conducted again for the better food sources; In the reconnaissance bee phase based on local focus, in order to avoid getting trapped in local optima and to accelerate the search rate in a targeted manner, the food source information that cannot be found better in the long-term iteration process is replaced near the current optimal value according to the principle of local focus, and a new search is carried out in the new area near the current optimal value to find better food source information.

7. The X-ray pulsar frequency estimation method based on bee colony optimization according to claim 6, characterized in that, The algorithm for the worker bee's working phase is as follows: Input includes candidate frequencies , standard deviation from origin Cyclic critical value and the number of worker bees ; For each worker bee, perform the following operations: Randomly generate search scale factor And randomly select another worker bee According to worker bees Information, in worker bees Identify new candidate frequencies in the vicinity Calculate new candidate frequencies ; If the mean of the new candidate frequencies deviates from the standard deviation of the origin Better than the current best frequency Then update the current optimal candidate frequency. and Reset worker bees Cyclic critical value ; Otherwise, increase worker bees Cyclic critical value ; The output at this stage includes candidate frequencies. The mean deviation of candidate frequencies from the origin And the critical value of worker bee cycles. .

8. The X-ray pulsar frequency estimation method based on bee colony optimization according to claim 7, characterized in that, The algorithm for the observation peak working phase is as follows: the input includes candidate frequencies. The mean deviation of candidate frequencies from the origin Cyclic critical value worker bee count The process is as follows: Based on the mean deviation of candidate frequencies from the origin and standard deviation Calculate each observed peak Probability of being selected ; Perform the following operations on each worker bee: If the randomly generated screening factor satisfy Then the observation peak is allowed to perform the work of the worker bee stage and conduct exploration; The output at this stage includes candidate frequencies. The mean deviation of candidate frequencies from the origin And the critical value of worker bee cycles. .

9. The X-ray pulsar frequency estimation method based on bee colony optimization according to claim 7, characterized in that, The algorithm for the reconnaissance peak working stage based on local focusing is as follows: the input includes the cyclic critical value. worker bee count and maximum number of paused updates The process is as follows: For each worker bee, perform the following operations: If satisfied Generate new candidate frequencies near the current optimal frequency. , As a random search factor, To determine the search range near the optimal value, recalculate the mean standard deviation of the new candidate frequencies from the origin. Reset worker bees Cyclic critical value ; The output at this stage includes candidate frequencies. The mean deviation of candidate frequencies from the origin And the critical value of worker bee cycles. .

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