An iterative filtering based integrated pulsar timing analysis method and system

Abstract

This invention relates to the field of pulsar timing technology, and more particularly to a comprehensive pulsar timing analysis method and system based on iterative filtering. The method includes combining the timing residuals of pulsars in pairs according to combination rules to form multiple master-slave groups of pulsar timing residuals, and iteratively filtering them using the Vondrak-Cepek filtering algorithm to obtain the corresponding filtered timing residuals. After each round of iterative filtering, the filtered timing residuals output from the previous round of iterative filtering are combined in pairs according to combination rules to obtain updated master-slave groups of pulsar timing residuals, which are then used as input for the next round of iterative filtering, until the total number of filtering iterations is reached, thereby obtaining the comprehensive pulsar timing stability. Compared to a single pulsar, this invention, through multiple rounds of iterative Vondrak-Cepek filtering, establishes a comprehensive pulsar timing for selected millisecond pulsars, which can simultaneously improve both short-term and long-term stability.

Description

Technical Field

[0001] This invention relates to the field of pulsar timing technology, and in particular to a comprehensive pulsar timing analysis method and system based on iterative filtering. Background Technology

[0002] The definition of a second is determined by cesium atomic clocks, while pulsars have higher long-term timing stability than atomic clocks and have broad application prospects in the generation of long-term timescales. They can serve as an effective supplement to atomic time. By combining the timing residuals of multiple pulsars through a certain algorithm, the resulting composite pulsar time has much better timing stability than that of a single pulsar. Therefore, this algorithm is called the composite pulsar time algorithm. The evaluation index of timing stability is divided into short-term stability and long-term stability. The common observation period of pulsars is 7-14 days (d), and some pulsars with longer observation periods have reached more than 20 years (yr). Therefore, it is natural to refer to the evaluation period on the order of 30d-1yr as short-term stability, and the evaluation period on the order of 1yr-20yr as long-term stability.

[0003] Currently, pulsar time synthesis algorithms are mainly divided into three categories: generalized least squares fitting based on TEMPO2 software, Bayesian analysis methods based on TEMPO2 and TEMPONEST software, and Wiener filtering algorithms. However, although traditional pulsar time synthesis algorithms improve long-term stability by about two orders of magnitude compared to the original algorithms, the improvement is still not ideal. Among all the literature on pulsar time synthesis that can be found, only one paper records that by using simulated noise sources to remove simulation data (only white noise was added; if red noise is added, this order of magnitude cannot be achieved), a long-term stability of 1e-18 can be achieved. Moreover, the short-term stability of traditional pulsar time synthesis algorithms has not been improved. Summary of the Invention

[0004] This invention provides a comprehensive pulsar timing analysis method and system based on iterative filtering. The technical problem it solves is that the long-term stability improvement of traditional comprehensive pulsar timing algorithms is limited, and their short-term stability has not been improved.

[0005] To address the above technical problems, this invention provides a comprehensive pulsar time analysis method and system based on iterative filtering.

[0006] In a first aspect, the present invention provides a comprehensive pulsar time analysis method based on iterative filtering, the method comprising the following steps:

[0007] Select several pulsars, and combine the timing residuals of all the selected pulsars in pairs according to a preset combination rule to form multiple pulsar timing residual master-slave groups;

[0008] Each pulsar timing residual is sequentially grouped into master and slave groups and iteratively filtered using the Vondrak-Cepek filtering algorithm to obtain the corresponding filtered timing residual.

[0009] After each round of iterative filtering, the filtered timing residuals output by each of the pulsar timing residual master-slave groups in the previous round of iterative filtering are combined in pairs according to the combination rules to obtain the updated pulsar timing residual master-slave groups. The updated pulsar timing residual master-slave groups are then used as the input for the next round of iterative filtering until the preset total number of filtering iterations is reached.

[0010] Based on the filtered timing residuals output from the last round of iterative filtering, the stability of the master-slave group of pulsar timing residuals in the corresponding iterative filtering round is obtained, and it is used as the comprehensive pulsar timing stability.

[0011] In a further embodiment, the method further includes:

[0012] In any iteration filtering round, the optimal filtering parameters for the pulsar timing residual master-slave group in the corresponding iteration filtering round are determined using the grid method based on the short-term stability and long-term stability of the pulsar corresponding to each pulsar timing residual master-slave group.

[0013] In a further embodiment, the optimal filtering parameters include an optimal smoothing factor.

[0014] In a further implementation, the combination rule specifically includes:

[0015] Sort all pulsars used for pairwise combinations or pulsar timing residual master-slave groups in descending order of their corresponding pulsar long-term stability to generate the sorting results;

[0016] The pulsars or pulsar timing residual master-slave groups in the first half of the sorting results are used as master clocks to form a master clock set.

[0017] The pulsars or pulsar timing residual master-slave groups in the latter half of the sorting result are taken as slave clocks, and all the slave clocks are sorted in descending order according to the short-term stability of their corresponding pulsars to form a slave clock set.

[0018] One master clock is selected sequentially from the master clocks in the master clock set as the target master clock. Then, all slave clocks in the slave clock set are traversed sequentially according to their order. Based on preset long-term stability difference thresholds and short-term stability difference thresholds, the target master clock is paired with slave clocks in the slave clock set to form pulsar timing residual master-slave groups. This ensures that in all the pulsar timing residual master-slave groups formed, the long-term stability difference and short-term stability difference between the master clock and the slave clock are greater than the preset long-term stability difference thresholds and short-term stability difference thresholds, and the final output comprehensive pulsar timing stability is optimal.

[0019] In a further implementation, the step of selecting several pulsars includes: selecting millisecond pulsars whose observation time span is greater than a preset observation time span threshold and whose number of observation points is greater than a preset number of observation points threshold.

[0020] In a further implementation, the formula for calculating the preset total number of filtering iterations is:

[0021] M=2 n

[0022] In the formula, M represents the total number of pulsars selected; n represents the total number of filtering iterations.

[0023] Secondly, the present invention provides a comprehensive pulsar time analysis system based on iterative filtering, the system comprising:

[0024] The grouping construction module is used to select several pulsars and combine the timing residuals of all the selected pulsars in pairs according to a preset combination rule to form multiple pulsar timing residual master-slave groups;

[0025] The first filtering module is used to iteratively filter each of the pulsar timing residuals master-slave groups sequentially through the Vondrak-Cepek filtering algorithm to obtain the corresponding filtered timing residuals.

[0026] The second filtering module is used to combine the filtered timing residuals output by each pulsar timing residual master-slave group in the previous iteration filtering according to the combination rules after each iteration filtering to obtain the updated pulsar timing residual master-slave group, and use the updated pulsar timing residual master-slave group as the input for the next iteration filtering, until the preset total number of filtering iterations is reached.

[0027] The stability determination module is used to obtain the stability of the master-slave group of pulsar timing residuals in the corresponding iterative filtering round based on the filtering timing residuals output in the last round of iterative filtering, and use it as the comprehensive pulsar timing stability.

[0028] In a further embodiment, the system further includes a filter parameter determination module;

[0029] The filter parameter determination module is used to determine the optimal filter parameters of the pulsar timing residual master-slave group in the corresponding iterative filtering round by using the grid method, based on the short-term stability and long-term stability of the pulsar corresponding to each pulsar timing residual master-slave group.

[0030] Thirdly, the present invention also provides a computer device, including a processor and a memory, the processor being connected to the memory, the memory being used to store a computer program, and the processor being used to execute the computer program stored in the memory, so that the computer device performs the steps of implementing the above-described method.

[0031] Fourthly, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0032] This invention provides a comprehensive pulsar timing analysis method and system based on iterative filtering. The method iteratively filters the master-slave groups of pulsar timing residuals obtained by pairwise combinations using the Vondrak-Cepek filtering algorithm, obtaining the filtered timing residuals output in each iteration. After each iteration, the filtered timing residuals output in the previous iteration are combined pairwise according to a combination rule to obtain updated master-slave groups of pulsar timing residuals. These updated master-slave groups are then used as input for the next iteration until a preset total number of filtering iterations is reached, thereby obtaining the comprehensive pulsar timing stability. Compared with existing technologies, this method, by selecting Vondrak-Cepek filtering parameters for iterative filtering, not only improves the long-term stability of the final comprehensive pulsar timing by three orders of magnitude but also improves the short-term stability by one order of magnitude compared to a single pulsar. It has advantages such as simple principle, strong operability, easy promotion, and high reliability. Attached Figure Description

[0033] Figure 1 This is a schematic flowchart of a comprehensive pulsar time analysis method based on iterative filtering provided in an embodiment of the present invention;

[0034] Figure 2 This is a schematic diagram of the integrated pulsar timing process of three-iteration Vondrak-Cepek filtering provided in an embodiment of the present invention;

[0035] Figure 3This is a comparative diagram of the first pulsar timing residual master-slave grouping filtering before and after the first round of Vondrak-Cepek filtering provided in the embodiment of the present invention;

[0036] Figure 4 This is a comparative diagram of the master-slave grouping of the second pulsar timing residual in the first round of Vondrak-Cepek filtering provided in the embodiment of the present invention before and after filtering;

[0037] Figure 5 This is a comparative diagram of the master-slave grouping of the timing residual of the third pulsar in the first round of Vondrak-Cepek filtering provided in the embodiment of the present invention before and after filtering.

[0038] Figure 6 This is a comparative diagram of the master-slave grouping of the timing residual of the fourth pulsar in the first round of Vondrak-Cepek filtering provided in the embodiment of the present invention before and after filtering.

[0039] Figure 7 This is a comparative diagram of the first pulsar timing residual master-slave group filtering before and after the second round of Vondrak-Cepek filtering provided in the embodiment of the present invention;

[0040] Figure 8 This is a comparative diagram of the second pulsar timing residual master-slave grouping filtering before and after the second round of Vondrak-Cepek filtering provided in the embodiment of the present invention;

[0041] Figure 9 This is a comparative diagram of the pulsar timing residual master-slave grouping filtering before and after the third round of Vondrak-Cepek filtering provided in the embodiments of the present invention;

[0042] Figure 10 This is a schematic diagram of the stability curves of the timing residuals of eight pulsars after the first round of Vondrak-Cepek filtering, provided in an embodiment of the present invention.

[0043] Figure 11 This is a schematic diagram of the stability curves of the timing residuals of the eight pulsars provided in this embodiment of the invention after the second round of Vondrak-Cepek filtering;

[0044] Figure 12 This is a schematic diagram of the stability curves of the timing residuals of 8 pulsars provided in this embodiment of the invention after the third round of Vondrak-Cepek filtering;

[0045] Figure 13 This is a schematic diagram comparing the individual stability of eight pulsars and the combined pulsar time stability under two algorithms provided in this embodiment of the invention.

[0046] Figure 14This is a block diagram of a comprehensive pulsar time analysis system based on iterative filtering provided in an embodiment of the present invention;

[0047] Figure 15 This is a schematic diagram of the structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0048] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0049] refer to Figure 1 This invention provides a comprehensive pulsar time analysis method based on iterative filtering, such as... Figure 1 As shown, the method includes the following steps:

[0050] S1. Select several pulsars, and combine the timing residuals of all the selected pulsars in pairs according to a preset combination rule to form multiple pulsar timing residual master-slave groups.

[0051] In this embodiment, the step of selecting several pulsars includes: selecting millisecond pulsars whose observation time span is greater than a preset observation time span threshold and whose number of observation points is greater than a preset number of observation points threshold.

[0052] In one embodiment, the combination rules for pairwise combinations in this embodiment specifically include:

[0053] Sort all pulsars used for pairwise combinations or pulsar timing residual master-slave groups in descending order of their corresponding pulsar long-term stability to generate the sorting results;

[0054] The pulsars or pulsar timing residual master-slave groups in the first half of the sorting results are used as master clocks to form a master clock set.

[0055] The pulsars or pulsar timing residual master-slave groups in the latter half of the sorting result are taken as slave clocks, and all the slave clocks are sorted in descending order according to the short-term stability of their corresponding pulsars to form a slave clock set.

[0056] One master clock is selected sequentially from the master clocks in the master clock set as the target master clock. Then, all slave clocks in the slave clock set are traversed sequentially according to their order. Based on preset long-term stability difference thresholds and short-term stability difference thresholds, the target master clock is paired with slave clocks in the slave clock set to form pulsar timing residual master-slave groups. This ensures that in all the pulsar timing residual master-slave groups formed, the long-term stability difference and short-term stability difference between the master clock and the slave clock are greater than the preset long-term stability difference thresholds and short-term stability difference thresholds, and the final output comprehensive pulsar timing stability is optimal.

[0057] Specifically, such as Figure 2 As shown, this embodiment selects 8 pulsars according to the pulsar selection rules. Before the first filtering iteration, the timing residuals of the 8 pulsars are paired to obtain 4 sets of pulsar timing residual master-slave groups. Each pulsar timing residual master-slave group contains one master clock and one slave clock. The timing residuals represented by the master clock and the slave clock are used as the first observation sequence and the second observation sequence, respectively, and input into the Vondrak-Cepek filtering algorithm. Each pulsar timing residual master-slave group outputs a corresponding filtered timing residual. It should be noted that the timing residual of the master clock represents the first observation sequence input into the Vondrak-Cepek filtering algorithm, and the timing residual of the slave clock represents the second observation sequence input into the Vondrak-Cepek filtering algorithm. In this embodiment, the division between master and slave clocks is based on the comparison of the long-term and short-term stability of pulsars in the master-slave clock pair (pulsar timing residual master-slave grouping). Since the timing residual data of the master clock is directly input into the Vondrak-Cepek filtering algorithm, it can better characterize the long-term data variation characteristics, while the timing residual data of the slave clock needs to be input after first-order difference, which can better characterize the short-term data variation characteristics. In a master-slave clock pair (pulsar timing residual master-slave grouping), this embodiment considers the clock with better long-term stability as the master clock and the clock with better short-term stability as the slave clock. Table 1 shows the long-term and short-term stability tables of 8 pulsars. For ease of understanding, this embodiment uses the pulsar PSRs shown in Table 1. The master-slave clock pair formed by J0613-0200 and pulsar PSR J1012+5307 is briefly explained. The former has better short-term stability, while the latter has better long-term stability. Therefore, in this embodiment, pulsar PSR J0613-0200 is used as the slave clock and pulsar PSR J1012+5307 is used as the master clock. This behavior can also be called "using the master clock to control the slave clock". Table 1 is shown below:

[0058] Table 1

[0059]

[0060] Since the most prominent feature of pulsars is their good long-term stability, this embodiment considers grouping the 8 pulsars into master clocks with 4 pulsars that have good long-term stability and the rest into slave clocks. When pairing them, pulsars with large differences in long-term and short-term stability are paired to maximize the advantages of both master and slave clocks. This approach is applicable to both the first and second rounds of the Vondrak-Cepek filtering algorithm (there is only one master-slave clock pair in the third round).

[0061] Based on the long-term stability ranking of the eight pulsars shown in Table 1, pulsars PSR J1012+5307, PSR J1713+0747, PSR J1909-3744, and PSR J1918-0642 are designated as master clocks, while the others are designated as slave clocks. This explains why... Figure 2 Similarly, in the subsequent second round of filtering, ① and ② were grouped together because their long-term stability differs more significantly.

[0062] S2. The timing residuals of each pulsar are sequentially grouped and iteratively filtered using the Vondrak-Cepek filtering algorithm to obtain the corresponding filtered timing residuals.

[0063] S3. After each round of iterative filtering, the filtered timing residuals output by each of the pulsar timing residual master-slave groups in the previous round of iterative filtering are combined in pairs according to the combination rules to obtain updated pulsar timing residual master-slave groups. The updated pulsar timing residual master-slave groups are then used as inputs for the next round of iterative filtering until the preset total number of filtering iterations is reached. In this embodiment, the formula for calculating the preset total number of filtering iterations is:

[0064] M=2 n

[0065] In the formula, M represents the total number of pulsars selected; n represents the total number of filtering iterations.

[0066] In this field, the Vondrak-Cepek filtering algorithm considers two observation sequences as input, the first observation...

[0067] ′

[0068] The sequence is measured at a certain time with observation weight p j Observed y j The second observation sequence at a certain time is weighted by the observations. Observed The Vondrak-Cepek filtering algorithm combines two input sequences into a single output sequence, outputting the filtered value. As an existing filtering algorithm, the Vondrak-Cepek algorithm will not be elaborated upon here. It should be noted that although the Vondrak-Cepek filtering algorithm can fuse two different frequency sources to generate a new time base combining the advantages of both, offering a significant advantage over the Vondrak algorithm which can only filter a single frequency source, current research lacks application of the Vondrak-Cepek filtering algorithm to the joint timing of multiple pulsars. Furthermore, no one has used an iterative Vondrak-Cepek filtering algorithm to process pulsar timing residuals. This embodiment applies the Vondrak-Cepek filtering algorithm to process pulsar timing residuals, aiming to improve the short-term and long-term stability of pulsars through the Vondrak-Cepek filtering algorithm.

[0069] Since the Vondrak-Cepek filtering algorithm receives two input data points but outputs only one, this embodiment obtains four output sequences (filtered timing residuals) after the first round of Vondrak-Cepek filtering. These four filtered timing residuals are labeled ①②③④. Similarly, this embodiment can combine ① to ④ in pairs through the second round of Vondrak-Cepek filtering, obtaining two output sequences (filtered timing residuals) through the division of master and slave clocks. These two output sequences (filtered timing residuals) are labeled ⑤⑥. Finally, the output sequence after the third round of Vondrak-Cepek filtering is labeled ⑦, which is the filtered timing residual after merging the timing residuals of the eight pulsars. When calculating the composite pulsar based on the filtered timing residual represented by ⑦, Figure 2 In this context, Round1, Round2, and Round3 represent the first, second, and third rounds of Vondrak-Cepek filtering, respectively. It should be noted that in any iteration of the filtering process, this embodiment determines the optimal filtering parameters for each pulsar timing residual master-slave group in the corresponding iteration using a grid method, based on the short-term and long-term stability of the pulsar. The optimal filtering parameters include the optimal smoothing factor.

[0070] For ease of understanding, the three rounds of Vondrak-Cepek iterative filtering for the above eight pulsars will be explained in detail below:

[0071] (1) First round of Vondrak-Cepek filtering:

[0072] Based on the aforementioned master-slave clock allocation principle, the first pulsar combination uses pulsar PSRJ1012+5307 to drive pulsar PSR J0613-0200. The timing residuals of these two pulsars are combined as the first master-slave timing residual grouping. When the timing residuals of pulsars PSRJ1012+5307 and PSR J0613-0200 in the first pulsar combination are iteratively filtered using the Vondrak-Cepek filtering algorithm, the optimal filtering parameter ε is determined. 11 and The selection aimed to improve short-term stability (15-30 days) and long-term stability (11-22 years), within a pre-set range of 10... 3 -10 10 Within the range, the optimal parameter pair is selected logarithmically. ε is selected from the master-slave group of the pulsar timing residuals in this group. 11 =10 6 and As the optimal smoothing factor, such as Figure 3 As shown, round1-1 represents the master-slave grouping of the first pulsar timing residual in the first round of filtering.

[0073] Similarly, the second pulsar combination uses pulsar PSR J1713+0747 to drive pulsar PSR J1643-1224, and sets the corresponding optimal smoothing factor ε. 21 , 10 respectively 7 and 10 4 The third pulsar combination uses pulsar PSR J1918-0642 to drive pulsar PSR J1744-1134, and sets the corresponding optimal smoothing factor ε. 31 , 10 respectively 6 and 10 6 The fourth pulsar combination uses pulsar PSR J1909-3744 to drive pulsar PSR J2145-0750, and sets the corresponding optimal smoothing factor ε. 41 , 10 respectively 6 and 10 6 Those skilled in the art can adjust the specific value of the optimal smoothing factor according to the specific implementation, and are not limited to the embodiments of the present invention. Figure 4 A comparative diagram of the master-slave grouping of the second pulsar timing residual in the first round of Vondrak-Cepek filtering provided in an embodiment of the present invention; Figure 5 A comparative diagram of the master-slave grouping of the timing residual of the third pulsar in the first round of Vondrak-Cepek filtering provided in an embodiment of the present invention; Figure 6This is a comparative diagram of the master-slave grouping of the fourth pulsar timing residual in the first round of Vondrak-Cepek filtering provided in an embodiment of the present invention. Round 1-2 represents the master-slave grouping of the second pulsar timing residual in the first round of filtering, Round 1-3 represents the master-slave grouping of the third pulsar timing residual in the first round of filtering, and Round 1-4 represents the master-slave grouping of the fourth pulsar timing residual in the first round of filtering.

[0074] Since the stability trends of pulsars are generally similar, and their stability increases with observation time, the retention of long-term components of the first observation sequence and short-term components of the second observation sequence by the Vondrak-Cepek filter cannot be directly observed from the timing residual plot. However, the smoothing factor ε and the [missing information] can be seen from the residual amplitude. The impact on sequence smoothness.

[0075] (2) Second round of Vondrak-Cepek filtering:

[0076] The master-slave clock group allocation principle for the second round of Vondrak-Cepek filtering is the same as that for the first round of Vondrak-Cepek filtering, and will not be repeated below. This round of filtering is divided into two groups. The first group uses clock group ② to control clock group ①, and sets the corresponding optimal smoothing factor ε. 51 , 10 respectively 5 and 10 8 , Figure 7 This is a schematic diagram comparing the first pulsar timing residual before and after master-slave grouping filtering in the second round of Vondrak-Cepek filtering provided in this embodiment of the invention; the second group uses clock group ④ to control clock group ③, and sets the corresponding optimal smoothing factor ε. 61 , Take 10 respectively 3 and 10 7 , Figure 8 This is a comparative diagram of the master-slave grouping of the second pulsar timing residual in the second round of Vondrak-Cepek filtering provided in an embodiment of the present invention. round2-1 represents the first master-slave grouping of the pulsar timing residual in the second round of filtering, and round2-2 represents the second master-slave grouping of the pulsar timing residual in the second round of filtering.

[0077] (3) Third round of Vondrak-Cepek filtering:

[0078] This round combines clock group ⑤ and clock group ⑥ generated from the second round of Vondrak-Cepek filtering, using clock group ⑥ to control clock group ⑤, and sets the corresponding optimal smoothing factor ε. 71 , 10 respectively 4 and 107 , Figure 9 This is a comparative diagram of the pulsar timing residual master-slave grouping filtering before and after the third round of Vondrak-Cepek filtering provided in this embodiment of the invention. Round 3-1 represents the pulsar timing residual master-slave grouping in the third round of filtering. It should be noted that in this embodiment, ε and ε are set as optimal filtering parameters. Using a base-10 logarithmic scale in 10 3 -10 10 Within the range of experience, parameters can be flexibly adjusted, with the goal of achieving stability σ. z To evaluate the scale so that its long-term and short-term stability reach their minimum values ​​(i.e., its stability is at its highest).

[0079] In this embodiment, after each round of Vondrak-Cepek filtering, the stability of the master-slave grouping of pulsar timing residuals in the corresponding iterative filtering round is calculated based on the output filter timing residuals. Figure 10 , Figure 11 , Figure 12 It can be seen that with each iteration of the Vondrak-Cepek filter, the output composite pulsar time has improved to a certain extent in both short-term and long-term stability. After the third round of Vondrak-Cepek filtering, a qualitative leap was achieved, especially in long-term stability.

[0080] In this field, timing stability is a measure of a time series. For timing stability analysis of atomic clocks, Allan variance is generally used; however, timing residual data of pulsars exhibit linear frequency drift, therefore, σ is currently commonly used. z Variance is evaluated by dividing all observed data into subsequences with equal intervals of τ, and then performing a least-squares fit on all subsequences based on a reference time, denoted as:

[0081]

[0082] In the formula, σ z (τ) represents the pulsar stability; τ represents the time scale; t i x represents the observation time of the i-th pulsar; i X(t) represents the timing residual of the i-th pulsar; i ) represents a cubic polynomial function; σ i Indicates the error of the i-th pulsar; angle brackets This means that the weighted average is calculated over all subsequences using the reciprocal of the square of the uncertainty of c3 as the weight.

[0083] S4. Based on the filtered timing residuals output from the last round of iterative filtering, obtain the stability of the master-slave group of pulsar timing residuals in the corresponding iterative filtering round, and use it as the comprehensive pulsar timing stability.

[0084] like Figure 13 As shown, this embodiment compares the comprehensive pulsar time based on the classic weighted average algorithm and the iterative Vondrak-Cepek filtering algorithm proposed in this embodiment with the pulsar stability of each of the eight pulsars. Figure 13 It can be seen that the overall pulsar time stability under the Vondrak-Cepek filtering algorithm is superior to the classical weighted algorithm at all time scales from 30 days to 22 years. In terms of short-term stability, the overall pulsar time stability based on the Vondrak-Cepek filter outperforms the classical weighted algorithm at a 30-day time scale using σ... z The calculated value reaches 1e-13.4, which is 1.2 orders of magnitude better than the 1e-12.2 of the classical weighted average method. Regarding long-term stability, the comprehensive pulsar time based on the Vondrak-Cepek filter achieves σ0 on a timescale of 22 yr. z The stability reached 1e-18.1, which is 2.2 orders of magnitude higher than the 1e-15.9 of the classic weighted average algorithm. It is also 3.1 orders of magnitude higher than the highest stability achieved by a single pulsar at the corresponding time scale (1e-15.0, pulsar PSR J1713+0747). Among them, pulsar PSR J1909-3744 is not considered because the observation time is only 10.8 yr.

[0085] The Vondrak-Cepek filtering algorithm not only inherits the excellent characteristic of the Vondrak filtering algorithm's high tolerance to raw data, but also serves as an excellent pulsar timing residual fusion method to generate a comprehensive pulsar time with excellent long-term and short-term stability. In this embodiment, the Vondrak-Cepek filtering algorithm replaces the classic weighted average algorithm, performing three rounds of iterative data fusion on the timing residuals of eight pulsars that have only undergone preprocessing. The resulting comprehensive pulsar time has a σ value of 30 days. z Short-term stability and σ at 22yr z The long-term stability reached 1e-13.4 and 1e-18.1, respectively, which are 1.2 and 2.2 orders of magnitude higher than the classical weighted algorithm, especially at σ = 22 yr. zThe long-term stability is improved by 3.1 orders of magnitude compared to a single pulsar, and the long-term stability of 1e-18.1 is also the best stability in existing pulsar timekeeping methods. However, there is still room for improvement within the framework of the iterative Vondrak-Cepek filtering algorithm provided in this embodiment. It should be noted that, compared to traditional pulsar timekeeping methods, the core of this embodiment lies in improving the short-term stability of the original single pulsar by one order of magnitude and the long-term stability by three orders of magnitude by using the iterative Vondrak-Cepek filtering method, thus making up for the deficiencies of existing technologies. This has great potential for pulsar timekeeping.

[0086] This invention provides a comprehensive pulsar time analysis method based on iterative filtering. The method uses the Vondrak-Cepek filtering algorithm to iteratively filter the master-slave grouping of pairwise pulsar timing residuals, establishing a comprehensive pulsar time for selected millisecond pulsars. Compared with existing technologies, the comprehensive pulsar time analysis method based on iterative Vondrak-Cepek filtering provided in this embodiment can simultaneously improve the short-term and long-term stability of the original single pulsar. Specifically, regarding short-term stability, the comprehensive pulsar time based on Vondrak-Cepek filtering achieves better stability on a 30-day timescale using σ... z The calculation reaches 1e-13.4, which is more than an order of magnitude better than the original single pulsar; in terms of long-term stability, the σ of the synthesized pulsar based on the Vondrak-Cepek filter is higher at a timescale of 22 yr. z The stability reached 1e-18.1, which is 3.1 orders of magnitude higher than the highest stability achieved by a single pulsar at the corresponding timescale (1e-15.0, PSRJ1713+0747).

[0087] It should be noted that the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0088] In one embodiment, such as Figure 14 As shown, this embodiment of the invention provides a comprehensive pulsar time analysis system based on iterative filtering, the system comprising:

[0089] Grouping module 101 is used to select a number of pulsars and combine the timing residuals of all the selected pulsars in pairs according to a preset combination rule to form multiple pulsar timing residual master-slave groups;

[0090] The first filtering module 102 is used to iteratively filter each of the pulsar timing residuals master-slave groups sequentially through the Vondrak-Cepek filtering algorithm to obtain the corresponding filtered timing residuals.

[0091] The second filtering module 103 is used to combine the filtered timing residuals output by each of the pulsar timing residual master-slave groups in the previous iteration filtering according to the combination rules after each iteration filtering to obtain the updated pulsar timing residual master-slave group, and use the updated pulsar timing residual master-slave group as the input for the next iteration filtering, until the preset total number of filtering iterations is reached.

[0092] The stability determination module 104 is used to obtain the stability of the master-slave group of pulsar timing residuals in the corresponding iterative filtering round based on the filtering timing residuals output in the last round of iterative filtering, and use it as the comprehensive pulsar timing stability.

[0093] In one embodiment, the integrated pulsar time analysis system based on iterative filtering provided in this embodiment further includes a filter parameter determination module;

[0094] The filter parameter determination module is used to determine the optimal filter parameters of the pulsar timing residual master-slave group in the corresponding iterative filtering round by using the grid method, based on the short-term stability and long-term stability of the pulsar corresponding to each pulsar timing residual master-slave group.

[0095] For specific limitations regarding the integrated pulsar time analysis system based on iterative filtering, please refer to the above-described limitations regarding the integrated pulsar time analysis method based on iterative filtering, which will not be repeated here. Those skilled in the art will recognize that the various modules and steps described in conjunction with the embodiments disclosed in this application can be implemented in hardware, software, or a combination of both. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0096] This invention provides a comprehensive pulsar timing analysis system based on iterative filtering. The system uses a grouping construction module to combine selected pulsar timing residuals in pairs, forming multiple pulsar timing residual master-slave groups. Through a first filtering module, a second filtering module, and a stability determination module, it generates comprehensive pulsar timing stability superior to existing algorithms based on iterative Vondrak-Cepek filtering. Compared to existing technologies, this application, through multiple rounds of iterative Vondrak-Cepek filtering, can simultaneously improve the short-term and long-term stability of the original single pulsar when establishing a comprehensive pulsar from selected millisecond pulsars, providing data support for pulsar navigation.

[0097] Figure 15 This invention provides a computer device including a memory, a processor, and a transceiver, which are connected to each other via a bus. The memory is used to store a set of computer program instructions and data, and can transmit the stored data to the processor. The processor can execute the program instructions stored in the memory to perform the steps of the above method.

[0098] The memory may include volatile memory or non-volatile memory, or both; the processor may be a central processing unit, a microprocessor, an application-specific integrated circuit, a programmable logic device, or a combination thereof. By way of example, but not limitation, the programmable logic device described above may be a complex programmable logic device, a field-programmable gate array, a general-purpose array logic, or any combination thereof.

[0099] In addition, memory can be a physically independent unit or integrated with the processor.

[0100] Those skilled in the art will understand that Figure 15 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have the same component arrangement.

[0101] In one embodiment, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0102] The present invention provides a comprehensive pulsar time analysis method and system based on iterative filtering. The comprehensive pulsar time analysis method based on iterative filtering improves the short-term stability by more than one order of magnitude compared with the original single pulsar. At the same time, in terms of long-term stability, it is 3.1 orders of magnitude higher than the highest stability achieved by the original single pulsar at the corresponding time scale. This is of great significance for pulsar navigation.

[0103] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., SSD), etc.

[0104] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when the computer program is executed, it can include the processes of the embodiments of the above methods.

[0105] The embodiments described above are merely preferred embodiments of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various improvements and substitutions without departing from the technical principles of this invention, and these improvements and substitutions should also be considered within the scope of protection of this application. Therefore, the scope of protection of this patent application should be determined by the scope of the claims.

Claims

1. An iterative filter-based integrated pulsar timing analysis method, characterized in that, Includes the following steps: Select several pulsars, and combine the timing residuals of all the selected pulsars in pairs according to a preset combination rule to form multiple pulsar timing residual master-slave groups; Each pulsar timing residual is sequentially grouped into master and slave groups and iteratively filtered using the Vondrak-Cepek filtering algorithm to obtain the corresponding filtered timing residual. After each round of iterative filtering, the filtered timing residuals output by each of the pulsar timing residual master-slave groups in the previous round of iterative filtering are combined in pairs according to the combination rules to obtain the updated pulsar timing residual master-slave groups. The updated pulsar timing residual master-slave groups are used as the input for the next round of iterative filtering until the preset total number of filtering iterations is reached. Among them, the clock with better long-term stability is used as the master clock, and the clock with better short-term stability is used as the slave clock. Based on the filtered timing residuals output from the last round of iterative filtering, the stability of the master-slave group of pulsar timing residuals in the corresponding iterative filtering round is obtained, and it is used as the comprehensive pulsar timing stability. The method further includes: in any iterative filtering round, determining the optimal filtering parameters of the pulsar timing residual master-slave group in the corresponding iterative filtering round using a grid method based on the short-term stability and long-term stability of the pulsar corresponding to each pulsar timing residual master-slave group.

2. The comprehensive pulsar time analysis method based on iterative filtering as described in claim 1, characterized in that: The optimal filtering parameters include the optimal smoothing factor.

3. The comprehensive pulsar time analysis method based on iterative filtering as described in claim 1, characterized in that, The combination rules specifically include: Sort all pulsars used for pairwise combinations or pulsar timing residual master-slave groups in descending order of their corresponding pulsar long-term stability to generate the sorting results; The pulsars or pulsar timing residual master-slave groups in the first half of the sorting results are used as master clocks to form a master clock set. The pulsars or pulsar timing residual master-slave groups in the latter half of the sorting result are taken as slave clocks, and all the slave clocks are sorted in descending order according to the short-term stability of their corresponding pulsars to form a slave clock set. One master clock is selected sequentially from the master clocks in the master clock set as the target master clock. Then, all slave clocks in the slave clock set are traversed sequentially according to their order. Based on preset long-term stability difference thresholds and short-term stability difference thresholds, the target master clock is paired with slave clocks in the slave clock set to form pulsar timing residual master-slave groups. This ensures that in all the pulsar timing residual master-slave groups formed, the long-term stability difference and short-term stability difference between the master clock and the slave clock are greater than the preset long-term stability difference thresholds and short-term stability difference thresholds, and the final output comprehensive pulsar timing stability is optimal.

4. The comprehensive pulsar time analysis method based on iterative filtering as described in claim 1, characterized in that, The step of selecting several pulsars includes: selecting millisecond pulsars whose observation time span is greater than a preset observation time span threshold and whose number of observation points is greater than a preset number of observation points threshold.

5. A method of integrated pulsar timing analysis based on iterative filtering as recited in claim 1, wherein, The formula for calculating the preset total number of filtering iterations is as follows: In the formula, M represents the total number of pulsars selected; n represents the total number of filtering iterations.

6. A comprehensive pulsar time analysis system based on iterative filtering, characterized in that, The system includes: The grouping construction module is used to select several pulsars and combine the timing residuals of all the selected pulsars in pairs according to a preset combination rule to form multiple pulsar timing residual master-slave groups; The first filtering module is used to iteratively filter each of the pulsar timing residuals master-slave groups sequentially through the Vondrak-Cepek filtering algorithm to obtain the corresponding filtered timing residuals. The second filtering module is used to combine the filtered timing residuals output by each pulsar timing residual master-slave group in the previous iteration filtering according to the combination rules after each iteration filtering to obtain an updated pulsar timing residual master-slave group, and use the updated pulsar timing residual master-slave group as the input for the next iteration filtering, until the preset total number of filtering iterations is reached; wherein, the clock with better long-term stability is used as the master clock, and the clock with better short-term stability is used as the slave clock; The stability determination module is used to obtain the stability of the master-slave group of pulsar timing residuals in the corresponding iterative filtering round based on the filtered timing residuals output in the last round of iterative filtering, and use it as the comprehensive pulsar timing stability. The system also includes a filter parameter determination module; The filter parameter determination module is used to determine the optimal filter parameters of the pulsar timing residual master-slave group in the corresponding iterative filtering round by using the grid method, based on the short-term stability and long-term stability of the pulsar corresponding to each pulsar timing residual master-slave group.

7. A computer device, characterized by: The device includes a processor and a memory, the processor being connected to the memory for storing computer programs, and the processor for executing the computer programs stored in the memory to cause the computer device to perform the method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that, when executed, implements the method as described in any one of claims 1 to 5.

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