CN114114881A - Pulsar timing performance optimization method and system - Google Patents
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Abstract
The invention discloses a pulsar timing performance optimization method and a system, comprising the following steps: selecting N pulsar (N is more than or equal to 9) according to a preset star selection index; obtaining first timing residual error data of each pulsar through operation of an ephemeris file and model parameters of each pulsar; sequentially carrying out filtering noise reduction and gross error detection processing on the first timing residual data, and setting the detected gross error to zero to obtain corresponding second timing residual data; and carrying out interpolation processing on the second timing residual data by utilizing a segmented cubic Hermite interpolation method to obtain corresponding third timing residual data which is used as timing residual data of each pulsar after timing performance optimization. The invention carries out preprocessing of filtering noise reduction, gross error detection and elimination on the timing residual data of the pulsar, improves the smoothness and stability of the timing residual data, and analyzes the timing performance of the pulsar by comparing the stability of the pulsar.
Description
Technical Field
The invention relates to the field of data processing, in particular to a pulsar timing performance optimization method and system.
Background
The pulsar is a compact neutron star rotating at high speed, and the autorotation period of the pulsar is very stable. By adopting a proper analysis method, a plurality of pulsar is observed in a timing way, and a comprehensive pulsar time scale can be established.
The method has the advantages that the proper pulsar is selected for timing, the influence on timing precision and stability is great, however, at present, no systematic pulsar optimization method is available for research, only partial scattered empirical analysis is available, the theoretical basis is lacked, the conditions of insufficient sample capacity, too low TOA point number or too short observation time span are easy to occur, the fitting precision of a timing model is low, and the long-term stability of the selected pulsar is influenced. Meanwhile, the existing processing method for pulsar data mainly comprises Vondrak filtering and preprocessing (including gross error elimination, fitting interpolation and the like), but the magnitude order of the long-term stability of pulsar is not enough due to the lack of a complete processing flow of pulsar residual error data.
Disclosure of Invention
The invention provides a pulsar timing performance optimization method and system, and aims to solve the technical problems of insufficient stability of pulsar timing residual data and insufficient timing performance analysis.
In order to solve the above technical problem, an embodiment of the present invention provides a pulsar timing performance optimization method, including:
selecting N pulsar according to a preset satellite selection index; wherein N is more than or equal to 9;
obtaining first timing residual error data of each pulsar through operation of an ephemeris file and model parameters of each pulsar;
sequentially carrying out filtering noise reduction and gross error detection processing on the first timing residual data, and setting the detected gross error to zero to obtain second timing residual data corresponding to each pulsar;
and performing interpolation processing on the second timing residual data by utilizing a segmented cubic Hermite interpolation method, and completely replacing zero-set data in the second timing residual data with non-zero data to obtain third timing residual data corresponding to each pulsar, wherein the third timing residual data is used as the timing residual data of each pulsar after the timing performance is optimized.
Further, according to a preset satellite selection index, selecting N pulsar specifically:
and selecting N pulsar from the observation data set of the international pulsar timing array according to the satellite selection index that the observation time span is more than 8 years and the number of the TOAs is more than 6000.
Further, the performing filtering and noise reduction processing on the first timing residual data specifically includes:
removing repeated observed values in the first timing residual data on the same julian day;
and selecting a smoothing factor, and performing filtering and noise reduction processing on the first timing residual data after the repeated observation values are removed by using Vondrak filtering.
Further, the timing residual data of each pulsar after the timing performance optimization is processed by utilizing the Hadamard variance to obtain the stability of each pulsar after the timing performance optimization, and the stability is respectively subjected to transverse comparison and longitudinal comparison to obtain the stability comparison of different pulsars and the stability comparison of the same pulsar before and after the timing performance optimization.
In order to solve the same technical problem, the invention also provides a pulsar timing performance optimization system, which comprises:
the pulsar selecting module is used for selecting N pulsars according to a preset satellite selecting index, wherein N is more than or equal to 9;
the initial data acquisition module is used for obtaining first timing residual error data of each pulsar through calculation of an ephemeris file and model parameters of each pulsar;
and the data processing module is used for sequentially carrying out filtering and noise reduction processing, gross error detection and elimination preprocessing on the first timing residual data to obtain timing residual data of each pulsar with optimized timing performance.
Further, the pulsar selecting module is specifically configured to:
and selecting N pulsar from the observation data set of the international pulsar timing array according to the satellite selection index that the observation time span is more than 8 years and the number of the TOAs is more than 6000.
Further, the data processing module includes:
the filtering and noise reducing processing unit is used for eliminating the repeated observed value in the first timing residual data under the same julian day and performing filtering and noise reducing processing on the first timing residual data after the repeated observed value is eliminated by using Vondrak filtering;
and the data preprocessing unit is used for performing coarse difference detection processing on the first timing residual data on the basis of the filtering and noise reduction processing, setting the detected coarse difference to zero to obtain second timing residual data corresponding to each pulsar, then performing interpolation processing on the second timing residual data by using a segmented cubic Hermite interpolation method, and completely replacing the data set to zero in the second timing residual data with non-zero data to obtain third timing residual data corresponding to each pulsar, wherein the third timing residual data is used as the timing residual data of each pulsar after the timing performance is optimized.
Further, the pulsar timing performance optimization system further includes:
and the performance analysis module is used for processing the timing residual error data of each pulsar after the timing performance optimization by utilizing the Hadamard variance to obtain the stability of each pulsar after the timing performance optimization, and respectively performing transverse comparison and longitudinal comparison on the stability to obtain the stability comparison of different pulsars and the stability comparison of the same pulsar before and after the timing performance optimization.
Compared with the prior art, the embodiment of the invention has the following beneficial effects:
the invention provides a pulsar timing performance optimization method and system, which are used for carrying out preprocessing of filtering noise reduction processing, gross error detection and elimination on timing residual data of selected pulsars and further improving smoothness and stability of the timing residual data, wherein the gross error is set to zero, and the set zero data is completely replaced by non-zero data by utilizing a segmented cubic Hermite interpolation method so as to realize elimination of the gross error.
Furthermore, a pulsar selection index is provided, a basis is provided for pulsar selection, and the accuracy of subsequent data processing and stability analysis is improved. And simultaneously, respectively carrying out stability evaluation on timing residual data after Vondrak filtering and noise reduction processing and after preprocessing, respectively comparing the stability of different pulsar with the stability of each data processing node of the same pulsar before and after, and further evaluating the timing performance of the pulsar.
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FIG. 1: the invention provides a flow diagram of an embodiment of a pulsar timing performance optimization method;
FIG. 2: the invention provides a comparison graph of timing residual data of a J0437-4715 pulsar before and after filtering and noise reduction processing;
FIG. 3: the invention provides a data schematic diagram of timing residual data of a J0437-4715 pulsar after gross error detection and zero setting for the pulsar timing performance optimization method;
FIG. 4: the invention provides a data schematic diagram of timing residual data of a pulsar after interpolation processing, wherein the timing residual data of the pulsar is J0437-4715;
FIG. 5: the invention provides a flow diagram of another embodiment of a pulsar timing performance optimization method;
FIG. 6: the stability comparison graph of the timing residual data of the pulsar from J0437 to 4715 before and after filtering noise reduction processing and preprocessing is used for the pulsar timing performance optimization method provided by the invention;
fig. 7 to 14: the stability comparison graph of the timing residual data of other 8 pulsar samples before and after filtering noise reduction processing and preprocessing is used for the pulsar timing performance optimization method provided by the invention;
FIG. 15: the invention provides a structural schematic diagram of a pulsar timing performance optimization system;
FIG. 16: the invention provides a schematic structural diagram of a data processing module of a pulsar timing performance optimization system.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The first embodiment is as follows:
referring to fig. 1, a method for optimizing pulsar timing performance according to an embodiment of the present invention includes:
s101: selecting N pulsar according to a preset satellite selection index; wherein N is more than or equal to 9.
In this embodiment, further, the selecting N pulsar signals according to a preset satellite selection index specifically includes:
and selecting N pulsar from the observation data set of the international pulsar timing array according to the satellite selection index that the observation time span is more than 8 years and the number of the TOAs is more than 6000.
It should be noted that the number N of pulsar is not less than 9, so as to ensure sufficient sample capacity; and according to the preset satellite selection index, a proper pulsar is selected for timing, so that the precision of data processing and stability analysis is improved conveniently. Further, the pulsar selected in this embodiment is 8 sample stars selected from 37 millisecond pulsar observed by NANOGrav in the observation data set of the international pulsar timing matrix, plus J0437-4715 pulsar which is observed for a long time and is commonly used.
S102: and obtaining first timing residual error data of each pulsar through the operation of the ephemeris file and the model parameter of each pulsar.
It should be noted that, in this embodiment, the ephemeris file and the model parameters of each pulsar are downloaded from an international pulsar timing array network, and the ephemeris file and the model parameters of each pulsar are calculated by using Tempo2 software under a Linux system, so as to obtain first timing residual data of each pulsar.
S103: and sequentially carrying out filtering noise reduction and gross error detection processing on the first timing residual data, and setting the gross error obtained by detection to zero to obtain second timing residual data corresponding to each pulsar.
It should be noted that, in this embodiment, further, the performing, by filtering and denoising the first timing residual data, specifically includes:
inputting the first timing residual error data into matlab software;
removing repeated observed values in the first timing residual data on the same julian day;
selecting a smoothing factor, and performing filtering and noise reduction processing on the first timing residual data after the repeated observation values are removed by using Vondrak filtering, specifically:
let the observed data be x (t)i) (i ═ 1,2, …, N), the objective function of the von brak filtering is:
Q＝min{F+λ2S}
wherein the content of the first and second substances,
F＝∑pi[x′(ti)-x(ti)]2
ε＝1/λ2
where x' (t)i) Is the smoothed value, p, to be solved foriIs the weight for each set of data, F is the fitness, and S represents the overall smoothness.
According to engineering experience, different smoothing factors are selected according to the timing residual error of each pulsar, so that a better noise elimination effect is achieved. The value range referred to is (10)－7，10－3) Taking J0437-4715 pulsar as an example, an appropriate smoothing factor is selected to be 10－3And thus a compromise between smoothness and fitness is achieved, see fig. 2, which is a graph of the J0437-4715 pulsar timing residual data before and after the filtering and noise reduction process, wherein the horizontal axis is the simplified julian day (MJD); the vertical axis is the size of the timing residual (residual).
In this embodiment, taking version a of J0437-4715 pulsar as an example, the second timing residual data obtained by coarsely detecting and zeroing the timing residual data after filtering and denoising processing is referred to fig. 3.
S104: and performing interpolation processing on the second timing residual data by utilizing a segmented cubic Hermite interpolation method, and completely replacing zero-set data in the second timing residual data with non-zero data to obtain third timing residual data corresponding to each pulsar, wherein the third timing residual data is used as the timing residual data of each pulsar after the timing performance is optimized.
It should be noted that, taking J0437-4715 pulsar as an example, according to fig. 3, the number of points with zero value on the vertical axis is searched, and it is found that there are 129 points that are set to zero, the percentage is 2.46%, and the warning threshold value is less than the preset 10%, which meets the condition. Then, a method of segmented three-time Hermite interpolation in the interp1 function is called (the coordinates and the change rate of each node are specified and then interpolation is carried out, if a non-segmented high-order Hermite algorithm is directly used, the dragon lattice phenomenon is easily generated), all 129 zero-value points are replaced by non-zero points, interpolation processing is carried out on the zero-set points, and third timing residual data is obtained, and reference is made to FIG. 4.
Comparing fig. 3 and fig. 4, it can be seen that obviously abnormal data is removed, and random fluctuation of residual error is more consistent with a common principle.
As an example of this embodiment, the pulsar timing performance optimization method of the present invention further includes a timing performance analysis process, and refer to fig. 5 in detail. Fig. 5 is a schematic flowchart of a pulsar timing performance optimization method according to another embodiment of the present invention. Fig. 5 differs from fig. 1 in that step S105 is further included after step S104. The steps of this example are as follows:
s105: and processing the timing residual data of each pulsar after the timing performance optimization by utilizing a Hadamard variance to obtain the stability of each pulsar after the timing performance optimization, and respectively carrying out transverse comparison and longitudinal comparison on the stability to obtain the stability comparison of different pulsars and the stability comparison of the same pulsar before and after the timing performance optimization.
Note that the stability σzThe specific calculation of (A) can be summarized as the following steps:
sequentially recording observation time, residual error and error as ti，xi，σiI 1,2,3, …, N, the observation time span is TN-t1Equally spaced into subsequences of τ. Let t0For an arbitrary reference instant, the following cubic polynomial is used for each subsequence:
X(t)＝c0-c1(t-t0)+c2(t-t0)2+c3(t-t0)3
performing a least squares fit such that:
[(xi-X(ti))/σi]2
minimum, defined as:
wherein the content of the first and second substances,<>is shown on all subsequences to be3The square of the error is inversely proportional to the weight average. X (t) in units of time, σzAnd no dimension is required.
The coarse difference detection, the zero-setting processing and the interpolation processing are collectively referred to as preprocessing, and taking J0437-4715 pulsar as an example, a stability comparison chart before and after performing von rak filtering and preprocessing on timing residual data of pulsar is shown in fig. 6.
Further, stability maps before and after Vondrak filtering and preprocessing are performed on the timing residual data of pulsar J0613-0200, pulsar J1012+5307, pulsar J1643-1224, pulsar J1713+0747, pulsar J1744-1134, pulsar J1909-3744, pulsar J1918-0642 and pulsar J2145-0750, and refer to FIGS. 7 to 14, respectively.
Referring to fig. 15, in order to solve the same technical problem, the present invention further provides a system for optimizing pulsar timing performance, including:
the pulsar selecting module is used for selecting N pulsars according to a preset satellite selecting index, wherein N is more than or equal to 9;
the initial data acquisition module is used for obtaining first timing residual error data of each pulsar through calculation of an ephemeris file and model parameters of each pulsar;
and the data processing module is used for sequentially carrying out filtering and noise reduction processing, gross error detection and elimination preprocessing on the first timing residual data to obtain timing residual data of each pulsar with optimized timing performance.
In this embodiment, further, the pulsar timing performance optimization system further includes:
and the performance analysis module is used for processing the timing residual error data of each pulsar after the timing performance optimization by utilizing the Hadamard variance to obtain the stability of each pulsar after the timing performance optimization, and respectively performing transverse comparison and longitudinal comparison on the stability to obtain the stability comparison of different pulsars and the stability comparison of the same pulsar before and after the timing performance optimization.
In this embodiment, further, the pulsar selecting module is specifically configured to:
and selecting N pulsar from the observation data set of the international pulsar timing array according to the satellite selection index that the observation time span is more than 8 years and the number of the TOAs is more than 6000.
Referring to fig. 16, in the present embodiment, the data processing module further includes:
the filtering and noise reducing processing unit is used for eliminating the repeated observed value in the first timing residual data under the same julian day and performing filtering and noise reducing processing on the first timing residual data after the repeated observed value is eliminated by using Vondrak filtering;
and the data preprocessing unit is used for performing coarse difference detection processing on the first timing residual data on the basis of the filtering and noise reduction processing, setting the detected coarse difference to zero to obtain second timing residual data corresponding to each pulsar, then performing interpolation processing on the second timing residual data by using a segmented cubic Hermite interpolation method, and completely replacing the data set to zero in the second timing residual data with non-zero data to obtain third timing residual data corresponding to each pulsar, wherein the third timing residual data is used as the timing residual data of each pulsar after the timing performance is optimized.
Compared with the prior art, the embodiment of the invention has the following beneficial effects:
the invention provides a pulsar timing performance optimization method and system, which are used for carrying out preprocessing of filtering noise reduction processing, gross error detection and elimination on timing residual data of selected pulsars and further improving smoothness and stability of the timing residual data, wherein the gross error is set to zero, and the set zero data is completely replaced by non-zero data by utilizing a segmented cubic Hermite interpolation method so as to realize elimination of the gross error.
Furthermore, a pulsar selection index is provided, a basis is provided for pulsar selection, and the accuracy of subsequent data processing and stability analysis is improved. And simultaneously, respectively carrying out stability evaluation on timing residual data after Vondrak filtering and noise reduction processing and after preprocessing, respectively comparing the stability of different pulsar with the stability of each data processing node of the same pulsar before and after, and further evaluating the timing performance of the pulsar.
The above-mentioned embodiments are provided to further explain the objects, technical solutions and advantages of the present invention in detail, and it should be understood that the above-mentioned embodiments are only examples of the present invention and are not intended to limit the scope of the present invention. It should be understood that any modifications, equivalents, improvements and the like, which come within the spirit and principle of the invention, may occur to those skilled in the art and are intended to be included within the scope of the invention.
Claims (8)
1. A pulsar timing performance optimization method is characterized by comprising the following steps:
selecting N pulsar according to a preset satellite selection index; wherein N is more than or equal to 9;
obtaining first timing residual error data of each pulsar through operation of an ephemeris file and model parameters of each pulsar;
sequentially carrying out filtering noise reduction and gross error detection processing on the first timing residual data, and setting the detected gross error to zero to obtain second timing residual data corresponding to each pulsar;
and performing interpolation processing on the second timing residual data by utilizing a segmented cubic Hermite interpolation method, and completely replacing zero-set data in the second timing residual data with non-zero data to obtain third timing residual data corresponding to each pulsar, wherein the third timing residual data is used as the timing residual data of each pulsar after the timing performance is optimized.
2. The pulsar timing performance optimization method according to claim 1, wherein the selecting of N pulsar signals according to a preset satellite selection index specifically comprises:
and selecting N pulsar from the observation data set of the international pulsar timing array according to the satellite selection index that the observation time span is more than 8 years and the number of the TOAs is more than 6000.
3. The method for optimizing pulsar timing performance according to claim 1, wherein the filtering and denoising processing on the first timing residual data specifically comprises:
removing repeated observed values in the first timing residual data on the same julian day;
and selecting a smoothing factor, and performing filtering and noise reduction processing on the first timing residual data after the repeated observation values are removed by using Vondrak filtering.
4. The pulsar timing performance optimization method according to claim 1, further comprising analyzing the stability of each pulsar after timing performance optimization, specifically:
and processing the timing residual data of each pulsar after the timing performance optimization by utilizing a Hadamard variance to obtain the stability of each pulsar after the timing performance optimization, and respectively carrying out transverse comparison and longitudinal comparison on the stability to obtain the stability comparison of different pulsars and the stability comparison of the same pulsar before and after the timing performance optimization.
5. A pulsar timing performance optimization system, comprising:
the pulsar selecting module is used for selecting N pulsars according to a preset satellite selecting index, wherein N is more than or equal to 9;
the initial data acquisition module is used for obtaining first timing residual error data of each pulsar through calculation of an ephemeris file and model parameters of each pulsar;
and the data processing module is used for sequentially carrying out filtering and noise reduction processing, gross error detection and elimination preprocessing on the first timing residual data to obtain timing residual data of each pulsar with optimized timing performance.
6. The pulsar timing performance optimization system of claim 5, wherein the pulsar selection module is specifically configured to:
and selecting N pulsar from the observation data set of the international pulsar timing array according to the satellite selection index that the observation time span is more than 8 years and the number of the TOAs is more than 6000.
7. The pulsar timing performance optimization system of claim 5, wherein said data processing module comprises:
the filtering and noise reducing processing unit is used for eliminating the repeated observed value in the first timing residual data under the same julian day and performing filtering and noise reducing processing on the first timing residual data after the repeated observed value is eliminated by using Vondrak filtering;
and the data preprocessing unit is used for performing coarse difference detection processing on the first timing residual data on the basis of the filtering and noise reduction processing, setting the detected coarse difference to zero to obtain second timing residual data corresponding to each pulsar, then performing interpolation processing on the second timing residual data by using a segmented cubic Hermite interpolation method, and completely replacing the data set to zero in the second timing residual data with non-zero data to obtain third timing residual data corresponding to each pulsar, wherein the third timing residual data is used as the timing residual data of each pulsar after the timing performance is optimized.
8. The pulsar timing performance optimization system of claim 5, further comprising:
and the performance analysis module is used for processing the timing residual error data of each pulsar after the timing performance optimization by utilizing the Hadamard variance to obtain the stability of each pulsar after the timing performance optimization, and respectively performing transverse comparison and longitudinal comparison on the stability to obtain the stability comparison of different pulsars and the stability comparison of the same pulsar before and after the timing performance optimization.
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