X-ray pulsar period estimation method based on fast folding algorithm

Abstract

The invention discloses an X-ray pulsar period estimation method based on a fast folding algorithm, and belongs to the technical field of pulsar navigation, and the method comprises the steps: carrying out the isochronous division of a PTOA sequence received by a detector according to a time interval, converting the PTOA sequence into a pulse intensity sequence, dividing the pulse intensity sequence into # imgabs0 # groups, and enabling each group to comprise # imgabs1 # sub-pulse intensity sequences; dividing each sub-pulse intensity sequence in each group into a front half region and a rear half region, and performing cyclic shift operation on data of the rear half region and the front half region through a butterfly summation algorithm in FFA until iteration of all layers is completed; and realizing one-time rapid estimation of an optimal period through a period calculation formula by utilizing a phase difference between two folded contours of an inter-layer output layer in a butterfly-shaped summation process and combining a quantitative relationship between an initial observation time difference and the phase difference. According to the method, more efficient and more accurate time delay estimation information is provided for X-ray pulsar navigation, and the performance of the X-ray pulsar navigation can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of pulsar navigation, and particularly relates to an X-ray pulsar period estimation method based on a fast folding algorithm. Background Art

[0002] As an effective method that can truly achieve autonomous navigation, celestial navigation has received extensive attention and in-depth research in tasks such as near-Earth flight and deep space exploration. Celestial navigation calculates the position, velocity, and attitude of a spacecraft by using a celestial sensor to obtain the azimuth information of natural celestial bodies (such as stars, the Earth, the Moon, the Sun, and other planets, etc.) and combining ephemeris data. Compared with other navigation technologies, celestial navigation has many advantages, such as passive measurement without external signals, high-precision navigation, strong anti-interference ability, good reliability, the ability to provide position and attitude information simultaneously, and the navigation error is not easy to accumulate over time. Among them, X-ray pulsar navigation locates by measuring the time delay of the pulse signal arriving at the spacecraft and the Solar System Barycenter (SSB), and then converting it into the distance between the spacecraft and the Solar System Barycenter, which has important engineering application value and strategic research significance.

[0003] Pulsar frequency estimation is mainly achieved by performing profile folding and profile testing on the PTOA sequence observed by the detector over a period of time. However, when the spacecraft state changes rapidly, if the frequency estimation process takes too long, it will lead to a lag in the update of position information, thus directly affecting the navigation and positioning accuracy. Therefore, the rapidity of the frequency estimation method is crucial for a moving vehicle with high dynamic characteristics. For the fast folding method of pulsar profiles, currently, the fast folding algorithm (Fast Folding Algorithm, FFA) and its variant applications are the most widely used. The concept of FFA was initially proposed in the field of radio astronomy and applied to search for pulsed signals with unknown frequencies in the radio band with a noisy background. However, these methods have not been more specifically optimized and improved for the hierarchical additive folding characteristics inside FFA. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides an X-ray pulsar period estimation method based on a fast folding algorithm, which is a pulsar frequency dynamic estimation method that can provide more efficient and accurate time delay estimation information, further improving the performance of X-ray pulsar navigation; the received photon arrival PTOA (Photons Time of Arrival, PTOA) sequence is equally divided in time and the photon intensity is statistically analyzed, and then a pulse intensity matrix is constructed and grouped, optimizing the originally complex signal. The pulse intensity matrix is divided into the front and rear half regions, and circular shifting and profile folding are performed through the butterfly summation algorithm, effectively improving the efficiency of profile folding. The inter-layer output layer of the butterfly summation is taken as the calculation material, and the optimal period is estimated once through the phase difference characteristics of the inter-layer output layer and the period calculation formula, accelerating the speed of period estimation.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] An X-ray pulsar period estimation method based on a fast folding algorithm, comprising the following steps:

[0007] Step 1: The received PTOA sequence of the detector is equally divided in time according to the time interval and converted into a pulse intensity sequence, and the pulse intensity sequence is divided into groups, each group containing sub-pulse intensity sequences;

[0008] Step 2: Each sub-pulse intensity sequence within each group is divided into the front and rear half regions, and circular shifting operations are performed on the data of the rear half region and the front half region through the butterfly summation algorithm in the FFA until the iteration of all layers is completed;

[0009] Step 3: Using the phase difference between the two folded profiles of the inter-layer output layer during the butterfly summation process, combined with the quantization relationship between the initial observation time difference and the phase difference, a one-time fast estimation of the optimal period is realized through the period calculation formula.

[0010] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; 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 foregoing X-ray pulsar period estimation method based on a fast folding algorithm.

[0011] In a third aspect, the present invention provides a computer-readable storage medium, on which an executable instruction is stored, and when the instruction is executed by a processor, the processor can implement the foregoing X-ray pulsar period estimation method based on a fast folding algorithm.

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

[0013] (1) Through the folding operation of the FFA method, the present invention can generate multiple candidate frequency folding profiles at a fixed resolution at one time, greatly improving the profile folding efficiency within the trial frequency range and reducing the complexity of actual engineering applications.

[0014] (2) The present invention proposes to establish a quantitative relationship between the folding profile phase difference of the interlayer output layer and the initial observation time difference by using the phase relationship between the folding profiles output by the FFA, so as to achieve a one-time rapid estimation of the optimal period, optimize the subsequent large-range folding profile inspection process, and significantly improve the speed of period estimation. Brief Description of the Drawings

[0015] Figure 1 It is a schematic diagram of the principle of an X-ray pulsar period estimation method based on a fast folding algorithm of the present invention;

[0016] Figure 2 It is the implementation process of the fast folding algorithm;

[0017] Figure 3 It is the FFA profile folding process;

[0018] Figure 4 It is the phase difference of the folding profile caused by different initial folding times;

[0019] Figure 5 It is the phenomenon of the folding profile of the FFA interlayer output layer;

[0020] Figure 6 It is the reason for the phase difference generated in the FFA folding process. Detailed Embodiments

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

[0022] As Figure 1 shown, the present invention proposes an X-ray pulsar period estimation method based on a fast folding algorithm. First, the received PTOA sequence is equally divided in time and the photon intensity is statistically analyzed to construct a pulse intensity sequence; secondly, the pulse intensity sequence is subjected to butterfly summation; finally, the interlayer output layer of the butterfly summation is used as the calculation material, and the primary estimated period is calculated through the phase difference characteristics of the interlayer output layer and the period calculation formula. The specific steps are as follows:

[0023] Step 1. First, equally divide the PTOA sequence received by the detector according to the time interval and statistically analyze the number of photons in each time interval, so as to convert the irregular discrete PTOA sequence into a corresponding ordered pulse intensity sequence. Secondly, divide the pulse intensity sequence into groups, and each group contains The sub - pulse intensity sequences form the pulse intensity matrix. And to ensure the smooth progress of subsequent butterfly summation and avoid aliasing, it is necessary to satisfy , where x is a natural number.

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

[0025] Using the above - mentioned fast folding operation, the PTOA sequence received by the detector can achieve the profile folding of multiple candidate frequencies through a single butterfly summation operation. Specifically, based on the FFA parameters in the previous section, the folding profiles at multiple fixed resolutions can be calculated at one time, and the most significant folding profile can be selected through waveform significance testing to determine the corresponding optimal frequency, as shown in Figure 3 .

[0026] Further split each sub - pulse intensity sequence within each grouped group, dividing each group into a "front - half region" and a "back - half region". Through the cyclic shift operation, shift the back - half region by a specified step and add it element - by - element to the front - half region, and reorganize it into a new pulse intensity matrix. As the number of butterfly layers increases, the step size increases layer by layer until the iteration of all layers is completed.

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

[0028] (1)

[0029] The candidate periods (frequencies) output at one time during the FFA process satisfy:

[0030] (2)

[0031] The sampling accuracy of the trial period is:

[0032] (3)

[0033] Using the FFA for one - time multi - period trial folding also has certain limitations on the observation duration of the detection task that need to be satisfied:

[0034] (4)

[0035] Among them, is the observation duration of the detection task, is the sampling time interval, is the number of groups, is the number of sampling points within a group. Since each group includes sub - pulse intensity sequences, where = , is the optimal estimation period.

[0036] Step 3: Utilize the phase difference between the two folded profiles of the inter - layer output layer in the butterfly summation process, combine the quantization relationship between the initial observation time difference and the phase difference, and achieve a one - time fast estimation of the optimal period through the period calculation formula. The following is the specific design process:

[0037] The estimation of the pulsar frequency mainly includes two parts: profile folding and profile inspection. The fast folding algorithm optimizes the profile folding process of pulsar frequency estimation by performing "parallel" calculations on the profile folding of multiple candidate frequencies, improving the calculation efficiency and reducing redundancy. In the subsequent profile inspection process, the method of performing significance tests one by one is still used to screen the optimal results.

[0038] To optimize the significance test process, the phase relationship between the folded profiles output by the FFA can be directly utilized to achieve a faster estimation of the pulsar frequency. When using the PTOA sequence for profile folding, the initial phase of the folded profile is often determined by the initial moment of the detector's observation task. Specifically, when folding the pulsar profile using the true frequency, if the initial observation moments of the detector are different, there will be a difference in the initial phases between the restored profiles, that is, there is a phase difference between the folded profiles.

[0039] As Figure 4 shown, for a PTOA sequence, if different starting points are used for profile folding, there will be a phase difference between the folded profiles. And the phase difference between the profiles can be quantitatively represented by the time difference between the starting points. Let the number of bins in the folded profile be , and the bin number displacement between the folded profiles be , then the phase difference between the two profiles can be expressed as:

[0040] (5)

[0041] Let the observation time difference between two foldings be , and the true period be , then the relationship between the initial observation time difference and the phase difference of the folded profile can be expressed as:

[0042] (6)

[0043] Using the above formula, the phase difference of the folded profile and the initial observation time difference can be determined. The quantization relationship between

[0044] Accordingly, during the fast contour folding process, the FFA finally outputs the folded contours of several candidate frequencies at a fixed resolution within a certain frequency search range of the detector PTOA sequence. It should be noted that, combined with the principle of the folding process in Figure 2 it can be known that the output contour of the FFA in the secondary output layer (i.e., the inter-layer output layer) can be divided into two parts, both of which are the folded contours of the candidate frequencies at the same resolution within the same frequency search range of the PTOA sequence, and the resolution is , that is, the FFA can obtain the folded contours of two parts of candidate frequencies with the same search range as the final output layer and half the resolution in the inter-layer output layer, and the PTOA calculation processes of these two parts are completely independent and do not depend on each other. The specific phenomenon is as Figure 5 shown.

[0045] By deeply analyzing the contour folding process, it can be found that the reason for the phase difference between the two parts of the folded contours in the inter-layer output layer is that although the same PTOA sequence is used for the two parts, there is a difference in the starting observation time, that is, there is an initial observation time difference between the two parts of the folded contours. Combining formulas (5) - (6), it can be known that by establishing the quantization relationship between the phase difference of the folded contours in the inter-layer output layer and the initial observation time difference , the one-time fast estimation of the optimal period

[0046] can be realized from Figure 6 it can be seen that during the FFA process, the initial observation time difference of the inter-layer output layer can be expressed as:

[0047] (7)

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

[0049] (8)

[0050] Specifically,

[0051] (9)

[0052] In the formula, is the initial trial period, that is, .

[0053] At this time, the phase difference of the folded contours in the inter-layer output layer can be expressed as:

[0054] (10)

[0055] Among them, the number of bins in the folding profile is , and the bin number displacement between the folded profiles is , is the initial trial period, that is . That is, the optimal estimation period can be expressed as:

[0056] (11)

[0057] Therefore, the optimal period can be quickly estimated once by solving the inter-layer output phase difference of the FFA, and the estimated value of the frequency can be obtained based on the optimal estimation of the period.

[0058] For the solution of the inter-layer output phase difference of the FFA, this study is mainly realized through the cross-correlation calculation of the contour signals. Let the contour at the first part of the inter-layer output layer be , and the contour at the second part be . Then the definition of the cyclic cross-correlation operation is:

[0059] (12)

[0060] In the formula, represents the cross-correlation operation value between the folded contour and the standard contour when the phase shift is .

[0061] Therefore, the inter-layer output phase difference of the FFA can be expressed as:

[0062] (13)

[0063] In summary, combined with formula (9), it can be seen that the present invention can realize a one-time fast initial estimation of the frequency through the inter-layer output phase difference model of the FFA, thereby initially locking the target frequency within a large search range and providing a more accurate search interval for subsequent high-resolution frequency local refinement search.

[0064] Embodiment

[0065] The present invention selects the Crab pulsar for simulation and experimental verification. First of all, the Crab pulsar is one of the pulsar sources with the largest X-ray band flux at present. Especially in the 2-10 keV energy band, its high brightness ensures clear detection in low Earth orbit, medium Earth orbit, and deep space. Secondly, the X-ray band pulse profile of the Crab pulsar is clear and its characteristics are stable. Its profile has a double-peak structure, and the time interval between the two pulse peaks is stable and hardly affected by the external environment. It is a relatively reliable time / position marking source at present. At the same time, the Crab pulsar has a stable period and can be accurately timed and positioned. It has strong signal modulation ability and sub-millisecond timing accuracy, which is extremely ideal for constructing an X-ray-based autonomous navigation system. Therefore, the simulation and analysis of the period estimation of the Crab pulsar are mainly selected. The specific parameters used in the simulation are shown in Table 1 below.

[0066] Table 1

[0067] To demonstrate the superiority of the present invention compared with other methods, the following is a comparative analysis of the quantization simulation of the period estimation speed of the method applying the present invention and the traditional method that does not apply the present invention (the most widely used and generally effective) inspection method.

[0068] Specifically, in this section, the observation duration is set to 140 s, the detector area is set to 10000 cm 2 , the search range is set to [0.0337000000 s, 0.0337050000 s], and the search step size is set to 10 -9 s. The number of discretized bins for the inspection method is set to 256. The number of groups for the method of the present invention is set to 4096.

[0069] For the method applying the present invention and the inspection method that does not apply the present invention hundreds of Monte Carlo experiments are carried out, and the statistical mean values of the calculation times of the two methods are shown in Table 2 below.

[0070] Table 2

[0071] As shown in Table 2 above, the operation time of the traditional inspection method is 123.2332 s, while the operation time of the method applying the present invention is 8.5133 s. In comparison, its calculation efficiency is improved by 93.09%, which can prove the superiority of the present invention in improving the calculation efficiency of the period estimation method.

[0072] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; 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 are caused to implement the foregoing method for estimating the period of an X-ray pulsar based on a fast folding algorithm.

[0073] In a third aspect, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which when executed by a processor can cause the processor to implement the foregoing method for estimating the period of an X-ray pulsar based on a fast folding algorithm.

[0074] The specific embodiments described above further elaborate on the objectives, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall 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 It includes the following steps: Step 1: Divide the PTOA sequence received by the detector isochronously according to the time interval, and convert it into a pulse intensity sequence. Divide the pulse intensity sequence into groups, each group containing sub-pulse intensity sequences; Step 2: Divide each sub-pulse intensity sequence within each group into the front half and the back half, and perform cyclic shift operations on the data of the back half and the front half through the butterfly summation algorithm in the FFA until the iteration of all layers is completed; Step 3: Utilize the phase difference between the two folded profiles of the inter-layer output layer during the butterfly summation process, combine the quantization relationship between the initial observation time difference and the phase difference, and achieve a one-time rapid estimation of the optimal period through the period calculation formula.

2. The X-ray pulsar period estimation method based on a fast folding algorithm according to claim 1, wherein The said Step 1 includes: Equally divide the PTOA sequence received by the detector according to the time interval, and count the number of photons in each time interval, so as to convert the irregular discrete PTOA sequence into a corresponding ordered pulse intensity sequence; Divide the pulse intensity sequence into groups, each group contains sub-pulse intensity sequences, and form pulse intensity matrix, satisfying , where x is a natural number.

3. A method for estimating the period of an X-ray pulsar based on a fast folding algorithm according to claim 1, characterized in that, In the said Step 2, the cyclic shift operation on the data of the back half and the front half through the butterfly summation algorithm in the FFA includes adding each element of the back half to the front half element by element after misaligning the back half by a specified step through the cyclic shift operation.

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

5. A method for estimating the period of an X-ray pulsar based on a fast folding algorithm according to claim 3, characterized in that, The period trial range of the butterfly summation algorithm in the said Step 2 is: (1) In the formula, is the optimal estimation period, is the number of sub-pulse intensity sequences in each group, is the sampling time interval; The candidate periods output at one time during the FFA process satisfy: (2) where is the number of groups; The sampling accuracy of the trial period is: (3) Observation duration of the detection task for one-time multi-cycle exploratory folding using FFA It is necessary to satisfy: (4) Among them, is the observation duration of the detection task, is the number of sampling points within the group, = .

6. The X-ray pulsar period estimation method based on a fast folding algorithm according to claim 5, characterized in that, The said Step 3 includes: Extract the two folded profiles of the inter-layer output layer during the butterfly summation process, and calculate the phase difference between them; Based on the quantization relationship between the initial observation time difference and the phase difference, establish a period calculation formula: Determine the optimal phase difference using cross-correlation operation , and calculate the optimal period through the following formula: (11) In the formula, is the bin number displacement between the folded contours.

7. A method for estimating the period of an X-ray pulsar based on a fast folding algorithm according to claim 6, characterized in that, The said phase difference is determined by calculating the displacement corresponding to the maximum value of the cross-correlation function of the two folded profiles.

8. The X-ray pulsar period estimation method based on a fast folding algorithm according to claim 6, characterized in that The initial observation time difference of the inter-layer output layer is expressed as: (7) Let the observed time difference between two folds be , the true period be , then the initial observed time difference and the phase difference of the folding profile are related as follows: (6)。 9. An electronic device, characterized in that, It includes: One or more processors; 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 a method for estimating the period of an X-ray pulsar based on a fast folding algorithm according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, Stored thereon are executable instructions, which when executed by a processor can enable the processor to implement a method for estimating the period of an X-ray pulsar based on a fast folding algorithm according to any one of claims 1-8.

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