A method for estimating the period of an X-ray pulsar based on a fast folding algorithm

Abstract

The application discloses a kind of X-ray pulsar period estimation methods based on fast folding algorithm, belong to pulsar navigation technical field, including: the PTOA sequence received by detector is divided according to time interval isochronous, and is converted into pulse intensity sequence, pulse intensity sequence is divided into group, each group contains sub-pulse intensity sequence;The half area division of each sub-pulse intensity sequence in each group is carried out, and the half area data in FFA is operated by the cyclic shift of butterfly-shaped summation algorithm, until the iteration of all layers is completed;The phase difference between the two parts of folding profile of interlayer output layer in butterfly-shaped summation process is utilized, combined with the quantization relationship of initial observation time difference and phase difference, the one-time fast estimation of optimal period is realized by period calculation formula.The application provides more efficient, more accurate time delay estimation information for X-ray pulsar navigation, and can improve X-ray pulsar navigation performance.

Description

Technical Field

[0001] This invention belongs to the field of pulsar navigation technology, specifically relating to an X-ray pulsar period estimation method based on a fast folding algorithm. Background Technology

[0002] Celestial navigation, as an effective method for truly autonomous navigation, has received widespread attention and in-depth research in missions such as near-Earth flight and deep space exploration. Celestial navigation uses celestial sensors to acquire the positional information of natural celestial bodies (such as stars, Earth, Moon, Sun, and other planets) and combines this information with ephemeris data to calculate the spacecraft's position, velocity, and attitude. Compared with other navigation technologies, celestial navigation has many advantages, such as passive measurement without external signals, high-precision navigation, strong anti-interference capabilities, good reliability, the ability to simultaneously provide position and attitude information, and the characteristic that navigation errors are not easily accumulated over time. X-ray pulsar navigation, in particular, measures the time delay of the pulse signal reaching the spacecraft and the Solar System Barycenter (SSB), and then converts this into the distance between the spacecraft and the SSB for positioning, possessing significant engineering application value and strategic research significance.

[0003] Pulsar frequency estimation is primarily achieved by contour folding and verification of PTOA sequences observed by the detector over a period of time. However, when the spacecraft's state changes rapidly, excessively long frequency estimation times can lead to delayed position updates, directly impacting navigation and positioning accuracy. Therefore, the speed of frequency estimation methods is crucial for moving vehicles with high dynamic characteristics. Currently, the Fast Folding Algorithm (FFA) and its variations are the most widely used fast folding methods for pulsar contours. The concept of FFA was initially proposed in radio astronomy and applied to find pulse signals of unknown frequencies in radio bands with noisy backgrounds. However, these methods have not yet undergone more targeted optimization and improvement to address the layered additive folding characteristics within FFA. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides an X-ray pulsar period estimation method based on a fast folding algorithm. This method offers a more efficient and accurate dynamic estimation of pulsar frequency, further enhancing X-ray pulsar navigation performance. It involves isochronously partitioning the received photon arrival time-of-arrival (PTOA) sequence and statistically analyzing photon intensities to construct a pulse intensity matrix and perform group partitioning, thus optimizing the originally complex signal. The pulse intensity matrix is ​​divided into front and rear halves, and a butterfly summation algorithm is used for cyclic shifting and contour folding, effectively improving the efficiency of contour folding. The interlayer output layer obtained from the butterfly summation is used as computational material, and the optimal period is estimated in a single step using the phase difference characteristics of the interlayer output layer and the period calculation formula, accelerating the period estimation speed.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for estimating the period of an X-ray pulsar based on a fast folding algorithm includes the following steps:

[0007] Step 1: Divide the PTOA sequence received by the detector into equal time intervals and convert it into a pulse intensity sequence. Divide the pulse intensity sequence into... Groups, each group contains Individual pulse intensity sequence;

[0008] Step 2: Divide each sub-pulse intensity sequence in each group into front and back halves. Use the butterfly summation algorithm in FFA to perform a cyclic shift operation on the data in the back half and the front half until the iteration of all layers is completed.

[0009] Step 3: Utilizing the phase difference between the two folded profiles of the interlayer output layer during the butterfly summation process, and combining the quantization relationship between the initial observation time difference and the phase difference, the optimal period is estimated quickly in one go through the period calculation formula.

[0010] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for estimating the period of an X-ray pulsar based on a fast folding algorithm.

[0011] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for estimating the period of an X-ray pulsar based on a fast folding algorithm.

[0012] The beneficial effects of this invention are as follows:

[0013] (1) The present invention can generate multiple candidate frequency folding profiles at a fixed resolution at one time through the FFA method folding operation, which greatly improves the folding efficiency of the profile within the trial frequency range and reduces the cumbersomeness of actual engineering applications.

[0014] (2) This invention proposes to use the phase relationship between the folded profiles output by FFA to establish a quantitative relationship between the phase difference of the folded profiles of the interlayer output layer and the initial observation time difference, thereby realizing a one-time rapid estimation of the optimal period, optimizing the subsequent large-scale folded profile inspection process, and significantly improving the speed of period estimation. Attached Figure Description

[0015] Figure 1 This is a schematic diagram outlining the principle of an X-ray pulsar period estimation method based on a fast folding algorithm according to the present invention.

[0016] Figure 2 This describes the implementation process of the fast folding algorithm.

[0017] Figure 3 For the FFA contour folding process;

[0018] Figure 4 The phase difference in the folded profile is caused by different initial folding times;

[0019] Figure 5 This describes the layer folding profile phenomenon in the interlayer output of FFA;

[0020] Figure 6 This explains the phase difference that occurs during the FFA folding process. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] like Figure 1 As shown, this invention proposes a method for estimating the period of an X-ray pulsar based on a fast folding algorithm. First, the received PTOA sequence is divided into isochronous segments and photon intensity statistics are performed to construct a pulse intensity sequence. Second, a butterfly summation is performed on the pulse intensity sequence. Finally, the interlayer output layer of the butterfly summation is used as the calculation material, and the estimated period is calculated using the phase difference characteristics of the interlayer output layer and the period calculation formula. Specifically, the method includes the following steps:

[0023] Step 1: First, process the PTOA sequence received by the detector according to the time interval. By performing isochronous partitioning and counting the number of photons within each time interval, the irregular discretized PTOA sequence is transformed into a corresponding ordered pulse intensity sequence. Next, the pulse intensity sequence is divided into... Groups, each group contains The sequence of sub-pulse intensity constitutes The pulse intensity matrix. And to ensure the smooth progress of subsequent butterfly summation and to prevent aliasing, the following must be satisfied. x is a natural number.

[0024] Step 2: Divide the intensity sequence of each sub-pulse within each group into front and back halves, such as... Figure 2 As shown, the butterfly summation algorithm in FFA is used to perform a cyclic shift operation on each group of pulse intensity sequences, and reorganize them into a new pulse intensity matrix until the iteration of all layers is completed.

[0025] Using the aforementioned rapid folding operation, the PTOA sequence received by the detector can be folded into profiles for multiple candidate frequencies through a single butterfly summation operation. Specifically, based on the FFA parameters from the previous section, multiple folded profiles at a fixed resolution can be calculated at once, and the most significant folded profile can be selected through waveform significance testing, thereby determining the corresponding optimal frequency, such as... Figure 3 As shown.

[0026] Each sub-pulse intensity sequence within each group is further split, dividing each group into a "front half" and a "back half". Through a cyclic shift operation, the back half is shifted by a specified step size and then added element-by-element to the front half, recombining them into a new pulse intensity matrix. As the number of butterfly layers increases, the step size increases layer by layer until all layers have been iterated.

[0027] The trial range of this method's period (frequency) is:

[0028] (1)

[0029] The candidate period (frequency) output in a single step during the FFA process satisfies:

[0030] (2)

[0031] The sampling precision for the trial period is:

[0032] (3)

[0033] Using FFA to conduct a single multi-cycle test folding to extend the observation duration of the probe mission. There are also certain restrictions that need to be met:

[0034] (4)

[0035] in, For the observation duration of the exploration mission, The sampling time interval, Number of groups The number of sampling points within a group, since each group includes Sub-pulse intensity sequence, here = , This is the optimal estimation period.

[0036] Step 3: Utilizing the phase difference between the two folded profiles of the interlayer output layer during the butterfly summation process, and combining the quantization relationship between the initial observation time difference and the phase difference, the optimal period is estimated quickly and in one go using the period calculation formula. The specific design process is as follows:

[0037] Pulsar frequency estimation mainly consists of two parts: contour folding and contour verification. The fast folding algorithm improves computational efficiency and reduces redundancy by performing "parallel" calculations on the contour folding of multiple candidate frequencies, thus optimizing the contour folding process for pulsar frequency estimation. In the subsequent contour verification process, a method of performing significance tests one by one is still used to select the optimal result.

[0038] To optimize the significance test process, the phase relationship between the folded profiles output by the FFA can be directly used to achieve faster pulsar frequency estimation. When using PTOA sequences for profile folding, the initial phase of the folded profile is often determined by the initial moment of the detector's observation mission. Specifically, when using the true frequency for pulsar profile folding, if the initial observation times of the detector are different, there will be differences in the initial phase between the reconstructed profiles, i.e., there is a phase difference between the folded profiles.

[0039] like Figure 4 As shown, for a PTOA sequence, if different starting points are used for contour folding, the folded contours will have a phase difference. Furthermore, the phase difference between contours can be quantized by the time difference between the starting points. Let the number of bins in the folded contour be... The bin number displacement between the folded contours is Then the phase difference between the two contours can be expressed as:

[0040] (5)

[0041] Let the observation time difference between the two folds be . The actual cycle is The initial observation time difference Phase difference with folded profile The relationship between them can be represented as:

[0042] (6)

[0043] The phase difference of the folded profile can be determined using the above formula. Time difference from initial observation The quantitative relationship between them.

[0044] Accordingly, during the rapid contour folding process, the final output of the FFA is the detector PTOA sequence with a fixed resolution within a certain frequency search range. The folded profiles of several candidate frequencies are shown below. It is worth noting that, combined with... Figure 2 As can be seen from the principle of the folding process, the output profile of FFA in the secondary output layer (i.e., the interlayer output layer) can be divided into two parts. Both parts are the folding profiles of candidate frequencies of the PTOA sequence at the same resolution within the same frequency search range, and both have the same resolution. In other words, FFA can obtain two folded profiles of candidate frequencies at the interlayer output layer, with the same search range as the final output layer but half the resolution, and the PTOA calculation processes of these two parts are completely independent and undependent. Specific phenomena include... Figure 5 As shown.

[0045] A thorough analysis of the contour folding process reveals that the phase difference between the two folded contours of the interlayer output layer is caused by the difference in their initial observation times, despite using the same PTOA sequence. This means there is an initial observation time difference between the two folded contours. Combining formulas (5) and (6), it can be seen that by establishing the phase difference of the folded contours of the interlayer output layer... Time difference from initial observation The optimal cycle can be achieved by quantifying the relationship between them. This allows for a rapid one-time estimation, thereby optimizing the subsequent large-scale folded contour inspection process.

[0046] Depend on Figure 6 It can be seen that during the FFA process, the initial observation time difference of the output layer between layers... It can be represented as:

[0047] (7)

[0048] Therefore, combining formulas (13) and (14), we can obtain:

[0049] (8)

[0050] Specifically,

[0051] (9)

[0052] In the formula, This is the initial testing period, i.e. .

[0053] At this point, the phase difference of the fold profile of the interlayer output layer can be expressed as:

[0054] (10)

[0055] The number of bins in the folded contour is The bin number displacement between the folded contours is , This is the initial testing period, i.e. That is, the optimal estimation period. It can be represented as:

[0056] (11)

[0057] Therefore, the optimal period A one-time fast estimation can be achieved by solving the phase difference between FFA layers, and the frequency estimate can be obtained based on the optimal estimation of the period.

[0058] This study primarily uses cross-correlation calculations of contour signals to solve for the phase difference between FFA layer outputs. Let the contour at the first part of the interlayer output layer be... The outline of the second part is The definition of the operation of cyclic cross-correlation is:

[0059] (12)

[0060] In the formula, Indicates phase shift The cross-correlation value between the folded profile and the standard profile.

[0061] Therefore, the output phase difference between FFA layers can be expressed as:

[0062] (13)

[0063] In summary, based on formula (9), this invention can achieve a one-time rapid initial estimation of frequency through the FFA interlayer output phase difference model, thereby initially locking the target frequency within a large search range and providing a more accurate search range for subsequent high-resolution frequency local refinement search.

[0064] Example

[0065] This invention uses the Crab pulsar for simulation and experimental verification. First, the Crab pulsar is one of the pulsar sources with the highest flux in the X-ray band. Especially in the 2-10 keV energy range, its high brightness ensures clear detection in low Earth orbit, medium Earth orbit, and deep space. Second, the X-ray pulse profile of the Crab pulsar is clear and stable. Its profile has a bimodal structure, with a stable time interval between the two pulse peaks, almost unaffected by external environmental factors, making it a relatively reliable time / position marker source. Simultaneously, the Crab pulsar has a stable period, allowing for precise timing and positioning. It possesses strong signal modulation capabilities and sub-millisecond timing accuracy, making it ideal for constructing X-ray-based autonomous navigation systems. Therefore, the simulation and analysis primarily focus on period estimation using the Crab pulsar. The specific parameters used in the simulation are shown in Table 1 below.

[0066] Table 1

[0067]

[0068] To demonstrate the superiority of this invention compared to other methods, the following are comparisons between the method using this invention and conventional methods not using this invention. A comparative analysis of the period estimation velocity of the verification method (the most widely used and generally effective) was conducted using quantitative simulation.

[0069] Specifically, in this section, the observation duration is set to 140 seconds, and the detector area is set to 10000 cm². 2 The search range is set to [0.0337000000s, 0.0337050000s], and the search step size is set to 10. -9 s. The number of discretization bins in the testing method is set to 256. The number of groups in the method of this invention is... Set it to 4096.

[0070] Comparison of the method using the present invention and the method not using the present invention The test method underwent hundreds of Monte Carlo experiments, and the statistical mean of the computation time for the two methods is shown in Table 2 below.

[0071] Table 2

[0072]

[0073] As shown in Table 2 above, the traditional The computation time of the verification method is 123.2332 s, while the computation time of the method using this invention is 8.5133 s. This represents a 93.09% improvement in computational efficiency, demonstrating the superiority of this invention in improving the computational efficiency of period estimation methods.

[0074] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for estimating the period of an X-ray pulsar based on a fast folding algorithm.

[0075] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for estimating the period of an X-ray pulsar based on a fast folding algorithm.

[0076] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for estimating the period of an X-ray pulsar based on a fast folding algorithm, characterized in that, Includes the following steps: Step 1: Divide the PTOA sequence received by the detector into equal time intervals and convert it into a pulse intensity sequence. Divide the pulse intensity sequence into... Groups, each group contains Individual pulse intensity sequence; Step 2: Divide each sub-pulse intensity sequence in each group into front and back halves. Use the butterfly summation algorithm in FFA to perform a cyclic shift operation on the data in the back half and the front half until the iteration of all layers is completed. Step 3: Utilize the phase difference between the two folded profiles of the interlayer output layer during the butterfly summation process, and combine the quantization relationship between the initial observation time difference and the phase difference, to achieve a one-time rapid estimation of the optimal period through the period calculation formula; Step 1 includes: The PTOA sequence received by the detector is divided into equal time intervals, and the number of photons in each time interval is counted, thereby converting the irregular discrete PTOA sequence into a corresponding ordered pulse intensity sequence. The pulse intensity sequence is divided into Groups, each group contains The sequence of sub-pulse intensity constitutes The pulse intensity matrix satisfies x is a natural number.

2. The X-ray pulsar period estimation method based on the fast folding algorithm according to claim 1, characterized in that, Step 2 involves performing a cyclic shift operation on the data in the second half and the first half of the data using the butterfly summation algorithm in FFA. This includes shifting the second half of the data by a specified step size and then adding it element by element to the first half of the data.

3. The X-ray pulsar period estimation method based on the fast folding algorithm according to claim 2, characterized in that, The step size of the cyclic shift operation increases layer by layer as the number of butterfly summation layers increases.

4. The X-ray pulsar period estimation method based on the fast folding algorithm according to claim 2, characterized in that, The periodic trial range of the butterfly summation algorithm in step 2 is: (1) In the formula, For the optimal estimation period, The number of sub-pulse intensity sequences in each group. The sampling time interval; The candidate cycle output during the FFA process satisfies: (2) In the formula Number of groups; The sampling precision for the trial period is: (3) Using FFA to conduct a single multi-cycle test folding to extend the observation duration of the probe mission. The following conditions must be met: (4) in, For the observation duration of the exploration mission, The number of sampling points within the group. = .

5. The X-ray pulsar period estimation method based on the fast folding algorithm according to claim 4, characterized in that, Step 3 includes: Extract the two fold profiles of the interlayer output layer during the butterfly summation process and calculate their phase difference; Based on the quantitative relationship between the initial observation time difference and the phase difference, a period calculation formula is established: The optimal phase difference is determined using cross-correlation calculations, and the optimal estimated period is calculated using the following formula: (11) In the formula, The bin number displacement is the distance between the contours obtained by folding.

6. The X-ray pulsar period estimation method based on the fast folding algorithm according to claim 5, characterized in that, The phase difference is determined by calculating the displacement corresponding to the maximum value of the cross-correlation function of the two folded contours.

7. The X-ray pulsar period estimation method based on the fast folding algorithm according to claim 5, characterized in that, The initial observation time difference of the interlayer output layer Represented as: (7) Let the observation time difference between the two folds be . The actual cycle is The initial observation time difference Phase difference with folded profile The relationship between them is represented as follows: (6)。 8. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the X-ray pulsar period estimation method based on the fast folding algorithm as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the X-ray pulsar period estimation method based on the fast folding algorithm as described in any one of claims 1-7.

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