A method and system for determining integrated pulsar time based on timing residuals

Abstract

The present invention relates to the field of pulsar time technology, and in particular to a method and system for determining a comprehensive pulsar time based on timing residuals, including: preprocessing and filtering the initial timing residuals of each selected optimal pulsar to obtain a corresponding smoothed timing residual; selecting a reference pulsar, and according to the number of observation points of the reference pulsar, equally spaced downsampling the smoothed timing residuals and initial errors of each optimal pulsar to obtain the corresponding downsampled timing residuals and downsampled initial errors, thereby obtaining the stability of the comprehensive pulsar time. The present invention obtains the stability of the comprehensive pulsar time through preprocessing, Vondrak filtering, downsampling and weighted average algorithm, which not only ensures that all points of the pulsar timing residuals are aligned, has strong interpretability, but also makes the stability of the comprehensive pulsar time more than one order of magnitude higher than the average level of the stability of a single pulsar, and has high credibility.

Description

Technical Field

[0001] The present invention relates to the field of pulsar time technology, and in particular to a method and system for determining integrated pulsar time based on timing residuals. Background Art

[0002] In the positioning, navigation and timing (PNT) system, timing determines whether positioning and navigation can be successful, and high-precision timing is based on high-precision and high-stability timekeeping, ensuring the smooth and safe operation of various industries such as communications and finance. Among them, pulsars are neutron stars, which have the characteristics of strong magnetic field, small size, high density and high rotation speed. Every time a pulsar rotates once, the ground station will receive high-energy rays emitted by the two poles of the pulsar. Compared with the traditional atomic clock timekeeping method, pulsar timekeeping technology has considerable advantages in long-term stability, especially for millisecond pulsars, some of which have a rotation period change rate of up to 10 -19 ~10 -21 , known as the most stable clock in nature, and the stability of pulsar timing residuals can be used to measure the stability of high-energy pulse signals emitted by pulsars.

[0003] At present, when evaluating the stability of integrated pulsar time, the traditional pulsar time generation method mainly uses Vondrak filter preprocessing and cubic spline interpolation method to analyze its pulsar timing stability. However, in the process of evaluating the integrated pulsar time using traditional methods, not only can it not ensure that all points of the pulsar timing residuals are aligned, making the total timing residual and total error difficult to trust, but also only uses Vondrak filtering for data processing, which has limited contribution to timing stability. Summary of the invention

[0004] The present invention provides a method and system for determining a comprehensive pulsar time based on timing residuals, and solves the technical problem that the traditional pulsar time generation method not only cannot ensure the alignment of all points of the pulsar timing residuals, making the total timing residual and total error difficult to trust, but also only uses Vondrak filtering for data processing, which has limited contribution to timing stability.

[0005] In order to solve the above technical problems, the present invention provides a method and system for determining integrated pulsar time based on timing residuals.

[0006] In a first aspect, the present invention provides a method for determining integrated pulsar time based on timing residuals, the method comprising the following steps:

[0007] Selecting at least two optimal pulsars according to a preset optimal screening condition, and obtaining an initial timing residual and an initial error of each of the optimal pulsars;

[0008] Preprocessing and filtering the initial timing residual of each optimal pulsar in turn to obtain a corresponding smoothed timing residual;

[0009] Selecting a reference pulsar, and downsampling the smoothed timing residual and initial error of each of the optimal pulsars at equal intervals according to the number of observation points of the reference pulsar, to obtain the corresponding downsampled timing residual and downsampled initial error;

[0010] Obtaining the stability of each optimal pulsar according to the timing residual after downsampling and the initial error after downsampling;

[0011] According to the stability of each optimal pulsar, the comprehensive weighted residual and comprehensive weighted error are obtained;

[0012] The comprehensive pulsar time stability is obtained according to the comprehensive weighted residual, the comprehensive weighted error and the Julian day of the reference pulsar.

[0013] In a further embodiment, the preset optimal screening conditions include:

[0014] The optimal pulsar is a millisecond pulsar, and the observation time span of the optimal pulsar must meet a preset observation time span threshold, and the number of observation points must meet a preset observation point number threshold.

[0015] In a further embodiment, the step of sequentially preprocessing and filtering the initial timing residual of each optimal pulsar to obtain the corresponding smoothed timing residual comprises:

[0016] The absolute median deviation method is used to extract the coarse error points of the initial timing residuals of each optimal pulsar;

[0017] The gross error points of each optimal pulsar are set to zero, and the gross error points are interpolated using a piecewise cubic Hermite interpolation method to obtain a preprocessed initial timing residual;

[0018] The Vondrak filter is used to filter and denoise the preprocessed initial timing residuals to obtain the smoothed timing residuals of each optimal pulsar.

[0019] In a further embodiment, the calculation formulas of the comprehensive weighted residual and the comprehensive weighted error are respectively:

[0020]

[0021]

[0022] in,

[0023]

[0024] In the formula, res 总 Represents the comprehensive weighted residual; res i ′ represents the timing residual after downsampling of the i-th optimal pulsar; err 总 Represents the comprehensive weighted error; err i ′ represents the initial error of the i-th optimal pulsar after downsampling; w i represents the weight of the i-th optimal pulsar; σ zi represents the stability of the i-th optimal pulsar.

[0025] In a further embodiment, the calculation formula of the integrated pulsar time stability is:

[0026]

[0027] In the formula, σ 总 (τ) represents the stability of the integrated pulsar; τ represents the time scale; c3 represents the cubic polynomial coefficient; res 总 represents the comprehensive weighted residual; X(MJD3) represents the cubic polynomial fitting function; MJD3 represents the Julian day of the benchmark pulsar; err 总 represents the comprehensive weighted error.

[0028] In a further embodiment, the step of selecting a benchmark pulsar includes: screening all the optimal pulsars according to preset benchmark screening conditions to obtain a benchmark pulsar, and using the Julian day observed by the benchmark pulsar as the benchmark Julian day.

[0029] In a further embodiment, the preset benchmark screening condition includes: selecting the best pulsar with the least number of observation points as the benchmark pulsar.

[0030] In a second aspect, the present invention provides a comprehensive pulsar time determination system based on timing residuals, the system comprising:

[0031] An optimal pulsar acquisition module, used to select at least two optimal pulsars according to a preset optimal screening condition, and obtain an initial timing residual and an initial error of each of the optimal pulsars;

[0032] A pulsar data processing module, used to pre-process and filter the initial timing residual of each optimal pulsar in turn to obtain a corresponding smoothed timing residual; and also used to select a reference pulsar, and according to the number of observation points of the reference pulsar, perform equally spaced downsampling on the smoothed timing residual and initial error of each optimal pulsar to obtain a corresponding downsampled timing residual and downsampled initial error; and obtain the stability of each optimal pulsar according to the downsampled timing residual and the downsampled initial error;

[0033] The timing residual weighting module is used to obtain the comprehensive weighted residual and comprehensive weighted error according to the stability of each optimal pulsar;

[0034] The integrated pulsar time determination module is used to obtain the integrated pulsar time stability according to the integrated weighted residual, the integrated weighted error and the Julian day of the reference pulsar.

[0035] In a third aspect, the present invention further provides a computer device, comprising a processor and a memory, wherein the processor is connected to the memory, the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory so that the computer device performs the steps of implementing the above method.

[0036] In a fourth aspect, the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program implements the steps of the above method when executed by a processor.

[0037] The present invention provides a method and system for determining a comprehensive pulsar time based on timing residuals. The method preprocesses, Vondrak filters, and downsamples the initial timing residuals of the selected optimal pulsars, and downsamples the errors at the same time, so as to obtain the stability of each optimal pulsar according to the downsampled timing residuals and errors, and obtain weighted timing residuals and weighted errors according to the stability of each optimal pulsar, thereby calculating the comprehensive pulsar time. Compared with the prior art, the method determines the comprehensive pulsar time based on the pulsar timing residual processing of preprocessing-Vondrak filtering-downsampling, and uses the weighted average pulsar time algorithm at the same time, so that the stability of the comprehensive pulsar time is improved by more than one order of magnitude compared with the average level of the stability of a single pulsar, thereby improving the accuracy and reliability of the comprehensive pulsar time, and having strong practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic flow chart of a method for determining integrated pulsar time based on timing residuals provided by an embodiment of the present invention;

[0039] Figure 2 is a schematic diagram of a comprehensive pulsar time calculation process provided by an embodiment of the present invention;

[0040] Figure 3 1 is a schematic diagram of the comparison of the timing residuals of the pulsar J0437-4715 before and after the gross error points are removed by the MAD method provided by an embodiment of the present invention;

[0041] Figure 4 is a schematic diagram of comparing the timing residuals of the pulsar J0437-4715 before and after preprocessing provided by an embodiment of the present invention;

[0042] Figure 5 is a schematic diagram comparing the timing residuals of pulsar J0437-4715 before and after Vondrak filtering provided by an embodiment of the present invention;

[0043] Figure 6 1. It is a schematic diagram comparing the stability of the integrated pulsar timing provided by an embodiment of the present invention and the stability of the optimal pulsar alone under timing;

[0044] Figure 7 It is a block diagram of a system for determining integrated pulsar time based on timing residuals provided by an embodiment of the present invention;

[0045] Figure 8 It is a schematic diagram of the structure of a computer device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The following specifically illustrates the implementation mode of the present invention in conjunction with the accompanying drawings. The embodiments are provided for illustrative purposes only and cannot be understood as limiting the present invention. The accompanying drawings are provided 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.

[0047] refer to Figure 1 , the embodiment of the present invention provides a method for determining the integrated pulsar time based on timing residuals, such as Figure 1 As shown, the method comprises the following steps:

[0048] S1. Select at least two optimal pulsars according to preset optimal screening conditions, and obtain the initial timing residual and initial error of each of the optimal pulsars.

[0049] Specifically, according to the preset optimal screening conditions, in IPTA2019-Release2, this embodiment selects several optimal pulsars from the 37 pulsars observed by NANOGrav, and uses Tempo2 software to calculate the ephemeris file and model parameters of each of the pulsars to obtain the initial timing residual and initial error of each optimal pulsar. In this embodiment, the preset optimal screening conditions include:

[0050] (1) The optimal pulsar is a millisecond pulsar. Since millisecond pulsars have high rotation stability and small timing residuals, they are one of the basic requirements for being the optimal pulsar.

[0051] (2) The observation time span of the optimal pulsar must meet a preset observation time span threshold, so as to facilitate the subsequent calculation of the long-term stability of the pulsar and the study of noise characteristics. In this embodiment, the preset observation time span threshold is preferably set to be more than 10 yr (i.e., 10 years);

[0052] (3) The number of observation points (ie, TOAs) of the optimal pulsar must meet a preset observation point threshold to improve the fitting accuracy of the timing model. In this embodiment, the preset observation point threshold is preferably set to be greater than 8000.

[0053] Based on the above optimal screening conditions, this embodiment screens out 8 pulsars as shown in Table 1 from the 37 pulsars observed by NANOGrav. Table 1 is as follows:

[0054] Table 1

[0055]

[0056] It should be noted that, although the observation years of the PSR J0437-4715 pulsar are relatively long, the TOAs in its original observation data are only 5302, which is far less than that of other pulsars. If it is selected together, it will have a certain adverse effect on the number of points after downsampling of other pulsars, which is not conducive to improving the stability of the integrated pulsar. Therefore, this embodiment excludes the PSR J0437-4715 pulsar.

[0057] S2. Preprocess and filter the initial timing residual of each optimal pulsar in turn to obtain the corresponding smoothed timing residual.

[0058] In one embodiment, the step of sequentially preprocessing and filtering the initial timing residual of each optimal pulsar to obtain the corresponding smoothed timing residual comprises:

[0059] The absolute median deviation method is used to extract the coarse error points of the initial timing residuals of each optimal pulsar;

[0060] The gross error points of each optimal pulsar are set to zero, and the gross error points are interpolated using a piecewise cubic Hermite interpolation method to obtain a preprocessed initial timing residual;

[0061] The Vondrak filter is used to filter and denoise the preprocessed initial timing residuals to obtain the smoothed timing residuals of each optimal pulsar.

[0062] like Figure 2 As shown, in this embodiment, the initial timing residuals of the eight best pulsars are preprocessed and Vondrak filtered respectively, wherein the preprocessing step uses the median absolute deviation method (MAD) to extract the gross error points of the pulsar timing residuals, specifically:

[0063]

[0064] In the formula, x j(j=1,2,...,n) represents the initial timing residual vector.

[0065] If x j If the above formula is satisfied, it means that the initial timing residual exceeds the gross error threshold. In this embodiment, the initial timing residual is regarded as a gross error point, and the gross error point is set to zero. Then, the gross error point is interpolated using the piecewise cubic Hermite interpolation method to obtain the preprocessed initial timing residual, so that the preprocessed initial timing residual is more reasonable and smooth, thereby avoiding the Runge phenomenon. After preprocessing the initial timing residual, this embodiment also performs filtering and noise reduction processing on the preprocessed initial timing residual by Vondrak filtering to filter out high-frequency noise.

[0066] It should be noted that although pulsar J0437-4715 is not included in the eight best pulsars, it can be used for demonstration experiments (the results of the other eight pulsars are similar). Figure 3 This is a schematic diagram of the comparison of the timing residuals of pulsar J0437-4715 before and after removing the gross error points using the MAD method; Figure 4 This is a schematic diagram of the comparison of the timing residuals before and after preprocessing of pulsar J0437-4715. Figure 4 In the figure, the preprocessed curve with Runge phenomenon is the curve generated by replacing cubic Hermite interpolation with cubic spline interpolation in preprocessing; Figure 5 Schematic diagram of the comparison of the timing residuals of pulsar J0437-4715 before and after Vondrak filtering.

[0067] S3. Select a reference pulsar, and according to the number of observation points of the reference pulsar, perform equal-interval downsampling on the smoothed timing residual and initial error of each of the optimal pulsars to obtain the corresponding downsampled timing residual and downsampled initial error.

[0068] Specifically, this embodiment first screens all the optimal pulsars according to a preset benchmark screening condition to obtain a benchmark pulsar, and uses the observed Julian day of the benchmark pulsar as the benchmark Julian day; wherein the preset benchmark screening condition includes: selecting the optimal pulsar with the least number of observation points (TOAs) as the benchmark pulsar, according to the optimal pulsars selected in Table 1, this embodiment screens the pulsar PSR J1643-1224 with the least TOAs as the benchmark pulsar, and the observed Julian day (modified Julian date, MJD) range of the benchmark pulsar, that is, MJD3, is used as the benchmark Julian day.

[0069] Then, in this embodiment, N i (i=1,2,…8) is the TOAs of the i-th optimal pulsar. In particular, let N=min{Ni}=N3, where N3 represents the TOAs of the third reference pulsar PSR J1643-1224 in Table 1. Meanwhile, this embodiment records res i and err i are the smoothed timing residual and initial error of the i-th optimal pulsar, respectively, expressed as:

[0070]

[0071]

[0072] According to the number of observation points of the reference pulsar, the smoothed timing residual and the initial error of each optimal pulsar are downsampled at equal intervals to obtain the corresponding downsampled timing residual and downsampled initial error. In this embodiment, the timing residual and the error points of each optimal pulsar are aligned by downsampling, and the Julian day of the reference pulsar is selected as the unified condition for data processing, thereby forming an interpretable (credible) comprehensive pulsar time, wherein the downsampled timing residual and the downsampled initial error are respectively:

[0073]

[0074]

[0075] Among them, res i ′ represents the timing residual after downsampling of the i-th optimal pulsar; err i ′ represents the initial error of the i-th optimal pulsar after downsampling; <x>Indicates that x is rounded.

[0076] S4. Obtain the stability of each optimal pulsar according to the timing residual after downsampling and the initial error after downsampling.

[0077] In order to eliminate the influence of linear frequency drift, the stability of pulsars is usually measured by σ z Variance (also known as Hadamard variance) assessment, different from statistics such as Allan variance, σ z The calculation method does not require the residuals to be distributed at equal intervals, which is particularly convenient for analyzing pulsar data. z The calculation method is to use a cubic polynomial function to fit the (fitted) timing residual with a time scale of τ, and use the cubic polynomial coefficient c3 to determine its value, specifically: let the total observation time of the data be T = t N -t1, and divided into subsequences with equal intervals τ, set t0 as the reference time, and perform least squares fitting on each subsequence using a cubic polynomial function X(t), that is:

[0078] X(t)=c0+c1(t-t0)+c2(t-t0) 2 +c3(t-t0) 3

[0079] Among them, the stability of each optimal pulsar σ zi The calculation formula of (τ) is as follows:

[0080]

[0081] In the formula, t i (i=1,2,…,n) represents the observation time of the i-th optimal pulsar (in Julian days). Since 8 optimal pulsars are selected according to the above method, n=8; x i represents the timing residual of the i-th optimal pulsar; σ i represents the error of the i-th optimal pulsar; angle brackets It means that a weighted average is taken over all subsequences using the inverse square of the uncertainty of c3 as the weight.

[0082] S5. According to the stability of each optimal pulsar, the comprehensive weighted residual and the comprehensive weighted error are obtained.

[0083] In one embodiment, the calculation formulas of the comprehensive weighted residual and the comprehensive weighted error are respectively:

[0084]

[0085]

[0086] in,

[0087]

[0088] In the formula, res 总 Represents the comprehensive weighted residual; res i ′ represents the timing residual after downsampling of the i-th optimal pulsar; err 总 Represents the comprehensive weighted error; err i ′ represents the initial error of the i-th optimal pulsar after downsampling; w i represents the weight of the i-th optimal pulsar; σ zi represents the stability of the i-th optimal pulsar.

[0089] S6. Obtaining the comprehensive pulsar time stability according to the comprehensive weighted residual, the comprehensive weighted error and the reference Julian day.

[0090] In one embodiment, the calculation formula of the integrated pulsar time stability is:

[0091]

[0092] In the formula, σ 总 (τ) represents the stability of the integrated pulsar; τ represents the time scale; c3 represents the error; res 总 represents the comprehensive weighted residual; X(MJD3) represents the cubic polynomial fitting function; MJD3 represents the Julian day of the benchmark pulsar; err 总 represents the comprehensive weighted error.

[0093] In this embodiment, the Julian day MJD3 of the benchmark pulsar and the comprehensive weighted residual res 总 And the comprehensive weighted error err 总 The time stability of the integrated pulsar composed of 8 optimal pulsars is calculated. Figure 6 This is a schematic diagram comparing the stability of the combined pulsar timing and the stability of the eight best pulsars when they are kept individually. Figure 6 In the equation, the horizontal axis represents the time scale of calculating stability, which is numerically equivalent to the length of each subsequence (for example, when the horizontal axis is 0, the logarithm of the time scale τ is 0, so τ is 1yr, then in σ z When calculating stability, the observed data should be grouped and fitted in units of 1 year); the vertical axis represents σ z The logarithm of the stability value is given by Figure 6 It can be seen that the comprehensive pulsar time stability σ based on the classical weighted average algorithm in this embodiment is 总 (τ) reaches 1e-15.9 on a time scale of 22yr. Table 2 shows the long-term and short-term stability calculated for each of the eight best pulsars. Table 2 is as follows:

[0094] Table 2

[0095]

[0096] The time scales of long-term and short-term stability in Table 2 correspond to Figure 6 The left and right endpoints of the individual timing curves of the eight best pulsars are not a specific value, but a range covering twice the span. This is because the observation time of each pulsar is different, and σ z The stability is calculated in the time domain using a logarithmic discrete distribution with base 2 as the base; Figure 6 In the above table, the single best pulsar PSR J1713+0747 with the highest stability at 22 years only reaches 1e-15.0 (PSR J1909-3744 has an observation time of only half of 22 years and is not taken into account). Figure 6 The 22-yr stability of the integrated pulsar time is 1e-15.9, from which it can be concluded that the stability of the integrated pulsar time obtained by the timing residual data processing algorithm provided in this embodiment is generally one order of magnitude higher than that of a single pulsar.

[0097] The embodiment of the present invention provides a method for determining a comprehensive pulsar time based on timing residuals, wherein the method sequentially preprocesses and filters the initial timing residuals of each selected optimal pulsar to obtain a corresponding smoothed timing residual, and equally spaced downsamples the smoothed timing residuals and initial errors of each optimal pulsar, so as to determine the stability of the comprehensive pulsar time according to the downsampled timing residuals, the downsampled initial errors, and the Julian day of the reference pulsar. Compared with the prior art, the present embodiment adopts a pulsar timing residual processing method based on preprocessing-Vondrak filtering-downsampling, and simultaneously uses a classical weighted average algorithm to establish a comprehensive pulsar time for the timing residuals after processing 8 optimal pulsars, achieving a technical effect of 0.9 orders of magnitude improvement in stability at 22yr compared to the single pulsar with the highest stability, and more than 1 order of magnitude improvement compared to the average level of stability of a single pulsar at this time scale, which has important practical significance for pulsar timekeeping.

[0098] It should be noted that the size of the serial numbers of the above-mentioned processes does not mean 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 the present application.

[0099] In one embodiment, Figure 7 As shown, an embodiment of the present invention provides a comprehensive pulsar time determination system based on timing residuals, the system comprising:

[0100] The optimal pulsar acquisition module 101 is used to select at least two optimal pulsars according to a preset optimal screening condition, and obtain the initial timing residual and initial error of each of the optimal pulsars;

[0101] The pulsar data processing module 102 is used to pre-process and filter the initial timing residual of each optimal pulsar in sequence to obtain a corresponding smoothed timing residual; down-sample the smoothed timing residual and initial error of each optimal pulsar at equal intervals according to a pre-selected reference Julian day to obtain a corresponding down-sampled timing residual and down-sampled initial error; and obtain the stability of each optimal pulsar according to the down-sampled timing residual and the down-sampled initial error;

[0102] The timing residual weighting module 103 is used to obtain a comprehensive weighted residual and a comprehensive weighted error according to the stability of each optimal pulsar;

[0103] The integrated pulsar time determination module 104 is used to obtain the integrated pulsar time stability according to the integrated weighted residual, the integrated weighted error and the reference Julian day.

[0104] For the specific definition of a comprehensive pulsar time determination system based on timing residuals, please refer to the above-mentioned definition of a comprehensive pulsar time determination method based on timing residuals, which will not be repeated here. A person of ordinary skill in the art will appreciate 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 performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of this application.

[0105] The embodiment of the present invention provides a comprehensive pulsar time determination system based on timing residuals. The pulsar data processing module of the system adopts a pulsar timing residual processing method based on preprocessing-Vondrak filtering-downsampling. The timing residual weighting module processes the timing residual and error after the optimal pulsar processing through a weighted average algorithm, thereby determining the comprehensive pulsar time stability. Compared with the prior art, the present application can effectively guide the subsequent positioning, navigation and timing, improve the reliability and interpretability of pulsar timing, and has the advantages of wide application range, strong practicality, high navigation efficiency, etc.

[0106] Figure 8 A computer device provided by an embodiment of the present invention includes a memory, a processor and a transceiver, which are connected 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, and the processor can execute the program instructions stored in the memory to perform the steps of the above method.

[0107] The memory may include a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories; 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 may be a complex programmable logic device, a field programmable gate array, a general purpose array logic, or any combination thereof.

[0108] Additionally, the memory may be a physically separate unit or may be integrated with the processor.

[0109] It can be understood by those skilled in the art that Figure 8 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have the same component arrangement.

[0110] In one embodiment, the present invention provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented.

[0111] An embodiment of the present invention provides a method and system for determining a comprehensive pulsar time based on timing residuals. The method and system implement a pulsar timing residual processing based on preprocessing-Vondrak filtering-downsampling, and simultaneously utilize a classical weighted average pulsar time algorithm to obtain a comprehensive pulsar time stability with high credibility, which can be used to provide data support for pulsar navigation.

[0112] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part 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, the process or function described in the embodiment of the present invention is generated in whole or in part. 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 computer-readable storage medium. For example, the computer instructions can be transmitted from a website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) mode. 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 includes one or more available media integrated. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., an SSD), etc.

[0113] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods.

[0114] The above-mentioned embodiments only express several preferred implementation modes of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in the technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be regarded as the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be based on the protection scope of the claims.< / x>

Claims

1. A method for determining integrated pulsar time based on timing residuals, characterized in that: The following steps are involved: Selecting at least two optimal pulsars according to a preset optimal screening condition, and obtaining an initial timing residual and an initial error of each of the optimal pulsars; Preprocessing and filtering the initial timing residual of each optimal pulsar in turn to obtain a corresponding smoothed timing residual; Selecting a reference pulsar, and downsampling the smoothed timing residual and initial error of each optimal pulsar at equal intervals according to the number of observation points of the reference pulsar, to obtain the corresponding downsampled timing residual and downsampled initial error; Obtaining the stability of each optimal pulsar according to the timing residual after downsampling and the initial error after downsampling; According to the stability of each optimal pulsar, the comprehensive weighted residual and comprehensive weighted error are obtained; Obtaining a comprehensive pulsar time stability according to the comprehensive weighted residual, the comprehensive weighted error and the Julian day of the reference pulsar; The calculation formulas of the comprehensive weighted residual and the comprehensive weighted error are respectively: in, In the formula, represents the comprehensive weighted residual; represents the timing residual after downsampling of the i-th optimal pulsar; represents the comprehensive weighted error; represents the initial error of the i-th optimal pulsar after downsampling; represents the weight of the i-th optimal pulsar; represents the stability of the i-th optimal pulsar; The calculation formula of the comprehensive pulsar time stability is: In the formula, represents the integrated pulsar time stability; Indicates the time scale; represents cubic polynomial coefficients; represents the comprehensive weighted residual; represents the cubic polynomial fitting function; MJD3 represents the Julian day of the benchmark pulsar; Indicates comprehensive weighted error; angle brackets Indicates that on all subsequences, The weighted average is made using the inverse of the square of the uncertainty.

2. A method for determining integrated pulsar time based on timing residuals as claimed in claim 1, characterized in that: The preset optimal screening conditions include: The optimal pulsar is a millisecond pulsar, and the observation time span of the optimal pulsar must meet a preset observation time span threshold, and the number of observation points must meet a preset observation point number threshold.

3. A method for determining integrated pulsar time based on timing residuals as claimed in claim 1, characterized in that: The step of sequentially preprocessing and filtering the initial timing residual of each optimal pulsar to obtain the corresponding smoothed timing residual comprises: The absolute median deviation method is used to extract the coarse error points of the initial timing residuals of each optimal pulsar; The gross error points of each optimal pulsar are set to zero, and the gross error points are interpolated using a piecewise cubic Hermite interpolation method to obtain a preprocessed initial timing residual; The Vondrak filter is used to filter and denoise the preprocessed initial timing residuals to obtain the smoothed timing residuals of each optimal pulsar.

4. A method for determining integrated pulsar time based on timing residuals as claimed in claim 1, characterized in that: The step of selecting a reference pulsar includes: screening all the optimal pulsars according to a preset reference screening condition to obtain a reference pulsar, and using the Julian day of the reference pulsar as the reference Julian day.

5. The method for determining integrated pulsar time based on timing residuals according to claim 1, characterized in that: The preset benchmark screening condition includes: selecting the best pulsar with the least number of observation points as the benchmark pulsar.

6. A comprehensive pulsar time determination system based on timing residuals, characterized in that: The system comprises: An optimal pulsar acquisition module, used to select at least two optimal pulsars according to a preset optimal screening condition, and obtain an initial timing residual and an initial error of each of the optimal pulsars; A pulsar data processing module, used to pre-process and filter the initial timing residual of each optimal pulsar in turn to obtain a corresponding smoothed timing residual; and also used to select a reference pulsar, and according to the number of observation points of the reference pulsar, perform equally spaced downsampling on the smoothed timing residual and initial error of each optimal pulsar to obtain a corresponding downsampled timing residual and downsampled initial error; and obtain the stability of each optimal pulsar according to the downsampled timing residual and the downsampled initial error; The timing residual weighting module is used to obtain the comprehensive weighted residual and comprehensive weighted error according to the stability of each optimal pulsar; A comprehensive pulsar time determination module, used for obtaining the comprehensive pulsar time stability according to the comprehensive weighted residual, the comprehensive weighted error and the Julian day of the reference pulsar; The calculation formulas of the comprehensive weighted residual and the comprehensive weighted error are respectively: in, In the formula, represents the comprehensive weighted residual; represents the timing residual after downsampling of the i-th optimal pulsar; represents the comprehensive weighted error; represents the initial error after downsampling of the i-th optimal pulsar; represents the weight of the i-th optimal pulsar; represents the stability of the i-th optimal pulsar; The calculation formula of the comprehensive pulsar time stability is: In the formula, represents the integrated pulsar time stability; Indicates the time scale; represents cubic polynomial coefficients; represents the comprehensive weighted residual; represents the cubic polynomial fitting function; MJD3 represents the Julian day of the benchmark pulsar; Indicates comprehensive weighted error; angle brackets Indicates that on all subsequences, The weighted average is made using the inverse of the square of the uncertainty.

7. A computer device, characterized in that: The computer device comprises a processor and a memory, wherein the processor is connected to the memory, the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the computer device executes the method according to 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, and when the computer program is executed, the method according to any one of claims 1 to 5 is implemented.

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