CN110986922A - Method for acquiring X-ray pulsar short-time observation high signal-to-noise ratio contour - Google Patents

Method for acquiring X-ray pulsar short-time observation high signal-to-noise ratio contour Download PDF

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CN110986922A
CN110986922A CN201911388880.3A CN201911388880A CN110986922A CN 110986922 A CN110986922 A CN 110986922A CN 201911388880 A CN201911388880 A CN 201911388880A CN 110986922 A CN110986922 A CN 110986922A
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CN110986922B (en
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方海燕
李连升
张力
苏剑宇
李小平
曹阳
陆鹏杰
李成
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations

Abstract

The invention discloses a method for acquiring a profile with a high signal-to-noise ratio by short-time observation of an X-ray pulsar, which mainly solves the problem that the pulsar needs to be observed for a long time in the conventional pulsar profile acquisition. The implementation scheme is as follows: 1) choose from (2)11Infinity) bin blocks fold photon arrival time sequences or phases to acquire time domain waveforms; 2) carrying out Fourier transform on the time domain waveform to obtain a frequency spectrum, intercepting a low-frequency spectrum of the frequency spectrum by determining a proper frequency domain interception point, and separating a signal from noise in a frequency domain; 3) respectively carrying out inverse Fourier transform on the zero-order frequency component frequency spectrum and the single-side frequency spectrum of other frequency components in the intercepted frequency spectrum to obtain a direct-current component and a time domain complex signal; and (3) taking twice the real part of the time domain complex signal and adding the direct current component to obtain the high signal-to-noise ratio time domain observation profile. The invention can acquire the high signal-to-noise ratio pulse profile by observing the pulsar for a short time, improves the pulsar navigation efficiency, and can be used for astronomical dataAnd (4) processing.

Description

Method for acquiring X-ray pulsar short-time observation high signal-to-noise ratio contour
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a method for acquiring a high signal-to-noise ratio pulse profile by short-time observation, which can be used for processing astronomical data.
Background
The X-ray pulsar navigation is the most potential deep space autonomous navigation in the future, is developing to engineering application at the present stage, and in an on-orbit experiment carried out by NASA (national aviation and space administration) in 2017 in 11 months, 4 milliseconds of pulsar are selected as beacons, each pulsar beacon is observed for about 5-15 min and then autonomously rotated to the next pulsar beacon, and experiments in 2 days show that the full-automatic navigation system realizes the first pulsar three-dimensional positioning verification in the world, realizes a predetermined target with the precision within 16km and the highest precision of about 4.8 km. High signal-to-noise ratio pulse profiles are one of the keys to implementing pulsar navigation applications. At present, the following two methods are used for acquiring the pulse profile from pulsar observation data:
the first method is a period folding method in which each photon arrival time is folded into bin blocks equally divided in one pulse period by time period, and the number of photons in each bin block is counted to obtain an accumulated pulse profile.
The second method is epoch folding, which is to calculate the phase of each photon arrival time relative to the reference epoch, and to classify the phase into each bin block in a phase period, and then count the number of photons in each bin block to obtain the cumulative pulse profile.
In the two methods, because photons received by the spacecraft contain pulsar signals and noise, the pulsar needs to be observed for a long time to obtain a high signal-to-noise ratio pulse profile, and the long observation time influences the real-time performance and accuracy of X-ray pulsar navigation XPNAV and increases the calculated amount, the navigation difficulty is increased, and the actual engineering requirements are difficult to meet.
Disclosure of Invention
The invention aims to provide a method for acquiring a high signal-to-noise ratio profile of short-time observation of an X-ray pulsar to reduce pulse observation time and acquire a high-precision pulse profile, aiming at overcoming the defects of the prior art.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
(1) folding the photon arrival time sequence to obtain a time domain waveform:
1a) selecting a photon arrival time T of an observation time TiAnd i is 1,2,3, calculating the arrival time t of the photons through a pulsar timing model according to the rotation frequency parameters of the pulsar ephemerisiCorresponding phase phi (t)i)；
1b) Choose from (2)11Infinity) bin blocks to photon arrival time tiPerforming periodic folding or folding on tiCorresponding phase phi (t)i) Performing epoch folding to obtain a time domain waveform;
(2) fourier transformation is carried out on the time domain waveform to obtain a frequency spectrum;
(3) separating the frequency spectrum from the noise:
3a) selecting a cost function and calculating the cut-off point of the frequency spectrum;
3b) according to different frequency domain characteristics that the frequency domain of the signal is mainly concentrated at low frequency, the noise is distributed in the whole frequency domain and the amplitude is small, the spectrum is cut by using a cut-off point, and the spectrum between 0 point and the cut-off point is selected to separate the signal from the noise;
(4) and (3) restoring the high signal-to-noise ratio time domain observation profile:
4a) removing direct current components from the intercepted frequency spectrum, namely removing the value of zero-order frequency components;
4b) carrying out inverse Fourier transform on the frequency spectrum with the zero-order frequency component removed to obtain a time domain complex signal without a direct current component, and taking a real part of the time domain complex signal without the direct current component to obtain a time domain observation contour without the direct current component;
4c) carrying out inverse Fourier transform on the value of the zero-order frequency component to obtain a direct-current component;
4d) and adding the direct current component to the time domain observation profile without the direct current component to obtain the high signal-to-noise ratio time domain observation profile.
Compared with the prior art, the invention has the following advantages:
1. according to the invention, according to different frequency domain characteristics that the frequency domain of the signal is mainly concentrated at low frequency, the noise is distributed in the whole frequency domain and the amplitude is small, the signal and the noise are effectively separated by selecting partial frequency spectrum, and the short-time observation is realized to obtain a high-precision observation profile;
2. the invention is due to the selection of (2)11Infinity) special bin block number, and effectively separating signals and noise thereof through a frequency domain truncation point, shortening the calculation time and improving the calculation efficiency under the condition of obtaining the same signal-to-noise ratio contour.
Drawings
FIG. 1 is a general flow chart of an implementation of the present invention;
FIG. 2 is a schematic diagram of the periodic folding of the present invention.
Detailed Description
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the implementation steps of this example are as follows:
step 1, selecting photon arrival time tiAnd calculates its corresponding phase phi (t)i)。
1.1) selecting a photon arrival time T of a period of observation time Ti：
The rochese RXTE satellite was in orbit for 16 years and provided a large amount of X-ray pulsar observation data that was archived in the data archive of the high energy physics research center of the NASA flight center of the national aerospace agency.
The crab cloud crab pulsar 90802_02_02_00 data packet is selected, the observation time of the data packet is 906 seconds, and the observation time of the data packet in the first 20 seconds is intercepted and used as the photon arrival time ti；i＝1,2,3；
1.2) calculating the photon arrival time tiCorresponding phase phi (t)i)
According to the autorotation frequency parameter of the pulsar ephemeris, the photon arrival time t is calculated through a pulsar timing modeliCorresponding phase phi (t)i) The formula is as follows:
Figure BDA0002344393690000031
wherein: phi (t)0) Is a reference time t0Corresponding initial phase, f(L)L-order partial derivatives of the rotation frequency are respectively, L is 2, f is the rotation frequency of the pulsar, and is 29.7925564233089 hz; f. of(1)Is the first derivative of the frequency, and takes the value of-3.73397 e-10; f. of(2)Is the second derivative of the frequency, and the value is 8.00 e-21.
Step 2. for the arrival time t of the photoniAnd (4) folding.
Folding includes periodic folding and epoch folding, wherein:
period folding, namely folding each photon arrival time into bin blocks equally divided in a pulse period according to the time period, and counting the number of photons in each bin block to obtain an accumulated pulse profile;
and the epoch folding is to calculate the phase of each photon arrival time relative to a reference epoch, classify the phase into each bin block in a phase period, and count the number of photons in each bin block to obtain an accumulated pulse profile.
Referring to fig. 2, the folding principle is as follows:
dividing photon arrival time or corresponding phases into P parts according to periods, equally dividing each period according to the number of bin blocks, calculating the number of photons in each bin block, accumulating the number of photons in each bin block to a first period, and performing normalization processing to obtain a time domain waveform;
the pair of photon arrival times tiCarrying out periodic folding, and comprising the following steps:
2.1) the arrival time of a photon with an observation time length T of 20 seconds is determined by the pulse period TsDivided into P portions, as shown in FIG. 2(a), TsValue 0.0335654311027 seconds;
Figure BDA0002344393690000035
2.2) number of blocks per bin M is 223The number of photons c in the ith bin in the jth cycle is calculated by dividing each cycle equally as shown in FIG. 2(b)j(ti) I is [1, M ]](ii) a j takes the value of [1, P]；
2.3) the number of photons c in the ith bin in the jth periodj(ti) Adding up to the first period to obtain an unnormalized time domain observation signal, as shown in fig. 2 (c);
2.4) normalizing the unnormalized time domain observation signal to obtain a time domain observation signal waveform
Figure BDA0002344393690000032
As shown in figure 2(d) of the drawings,
Figure BDA0002344393690000033
is represented by the following formula:
Figure BDA0002344393690000034
in the formula (I), the compound is shown in the specification,
Figure BDA0002344393690000036
M＝223is the number of bin blocks, Tb＝Ts/M，TsPulsar period, value 0.0335654311027 seconds; c. Cj(ti) Is the number of photons in the ith bin in the jth period.
The pair of photon arrival times tiCorresponding phase phi (t)i) And performing epoch folding, wherein the steps are as follows:
first, the arrival time t of the photoniCorresponding phase phi (t)i) Divided into Q portions by period, where phi (t)i) The period value of (1);
Figure BDA0002344393690000041
second, the number of blocks per bin M is 223Each phase period is divided equallyCalculating the number of photons C in the ith bin of the jth integer phasej,iI is [1, M ]](ii) a j takes the value of [1, Q]；
Thirdly, the number of photons C in the ith bin of the jth integer phase is countedj,iAdding the signals to the position between [0,1) to obtain an unnormalized time domain observation signal;
fourthly, normalizing the unnormalized time domain observation signal to obtain a time domain observation signal waveform
Figure BDA0002344393690000042
The expression is as follows:
Figure BDA0002344393690000043
in the formula:
Figure BDA0002344393690000044
Cj,iis the number of photons in the ith bin of the jth integer phase.
This example uses, but is not limited to, photon arrival time tiCorresponding phase phi (t)i) And performing epoch folding.
And 3, carrying out Fourier transform on the time domain waveform.
According to Fourier transform formula, for time domain waveform
Figure BDA0002344393690000045
Fourier transformation is carried out to obtain a frequency spectrum, and the formula is as follows:
Figure BDA0002344393690000046
in the formula: m223Is the bin block number;
Figure BDA0002344393690000047
in order to observe the signal waveform in the time domain,
Figure BDA0002344393690000048
for time-domain observation of signal waveform fourierThe leaf transformed spectrum.
And 4, calculating the cut-off point of the frequency spectrum, and separating the signal and the noise by using the cut-off point.
4.1) calculating the cut-off point of the frequency spectrum:
4.1.1) the following cost function is constructed by using the mean-integral mean-square error M.I.S.E:
Figure BDA0002344393690000049
in the formula, SkFor crab cloud crab pulsar standard profile fourier transform,
Figure BDA00023443936900000410
for the fourier transformed spectrum of the time domain observed signal waveform,
Figure BDA00023443936900000411
is the conjugate of the standard profile fourier transform of the pulsar,
Figure BDA00023443936900000412
is the conjugate of the Fourier transform of the time domain observed signal waveform, q is the frequency domain truncation point,
Figure BDA00023443936900000413
is a cost function value;
4.1.2) according to the property that the cost function value monotonically decreases to the minimum value along with the truncation point q and keeps monotonically increasing all the time, the q corresponding to the minimum value is taken as the optimal frequency truncation point of the frequency spectrum by the cost function, and the step is taken
Figure BDA0002344393690000051
The extreme point of the cost function is 22, namely the truncation point q is 22;
4.2) Signal to noise separation
According to the knowledge of signal processing, the frequency domain of the signal is mainly concentrated in low frequency, the noise is distributed in the whole frequency domain and has different frequency domain characteristics with smaller amplitude, the signal-to-noise ratio in the low frequency band is high, the influence of the noise on the signal is small, the signal-to-noise ratio in the high frequency band is low, the influence of the noise on the signal is large, the spectrum is cut by utilizing a cut-off point, the spectrum from a zero point to the cut-off point is selected, and the signal and the noise are separated, wherein the formula:
Figure BDA0002344393690000052
in the formula: m223Is the number of the bin blocks,
Figure BDA0002344393690000053
is a time domain observed signal waveform, q is a frequency domain truncation point,
Figure BDA0002344393690000054
is the spectrum intercepted by the truncation point.
And 5, restoring the high signal-to-noise ratio time domain observation profile.
The time domain observation contour comprises a direct current component and a non-direct current component, the non-direct current component is the time domain observation contour without the direct current component, when the high signal-to-noise ratio time domain observation contour is restored, the direct current component and the time domain observation contour without the direct current component need to be restored respectively, the frequency spectrum intercepted by the interception point comprises the frequency spectrum of the direct current component and the frequency spectrum of the non-direct current component, the direct current component needs to be removed from the frequency spectrum intercepted by the interception point, the frequency spectrum without the direct current component is subjected to Fourier inverse transformation to obtain the time domain observation contour without the direct current component, and the frequency spectrum of the direct current component is subjected to Fourier inverse transformation to obtain the direct current component, wherein the time domain observation:
5.1) for spectra intercepted by truncation points
Figure BDA0002344393690000055
And (3) processing:
because the direct current component of the time domain corresponds to the amplitude of the zero-order frequency component of the frequency domain, the intercepted frequency spectrum
Figure BDA0002344393690000056
The direct current component is removed, that is, the value of the zero-order frequency component is removed, and the formula is as follows:
Figure BDA0002344393690000057
in the formula: m223Is the bin block number;
Figure BDA0002344393690000058
observing a signal waveform for a time domain; q is a frequency domain truncation point and takes the value of 22;
Figure BDA0002344393690000059
in order for the spectrum to be intercepted by the truncation point,
Figure BDA00023443936900000510
is a pair of
Figure BDA00023443936900000511
Removing the frequency spectrum of the zero-order frequency component;
5.2) restoring a time-domain observation profile which does not contain a direct-current component:
5.2.1) according to the formula of inverse Fourier transform, carrying out inverse Fourier transform on the frequency spectrum without the zero-order frequency component to obtain a time domain complex signal without a direct current component, wherein the formula is as follows:
Figure BDA0002344393690000061
in the formula: m223Is the bin block number; n is the number of time-domain sampling points, and the value of N is 1024; q is a frequency domain truncation point and takes the value of 22;
Figure BDA0002344393690000062
in order for the spectrum to be intercepted by the truncation point,
Figure BDA0002344393690000063
is a pair of
Figure BDA0002344393690000064
The frequency spectrum of the zero-order frequency component is removed,
Figure BDA0002344393690000065
the time domain complex signal after Fourier inverse transformation;
5.2.2) taking the real part of the time domain complex signal to obtain a time domain observation profile without a direct current component, wherein the formula is as follows:
Figure BDA0002344393690000066
in the formula: n is the number of time-domain sampling points, and the value of N is 1024;
Figure BDA0002344393690000067
is the time domain complex signal after the inverse fourier transform,
Figure BDA0002344393690000068
a time domain observation profile which does not contain a direct current component;
5.3) acquiring a direct current component, and recovering a high signal-to-noise ratio time domain observation profile:
5.3.1) obtaining the direct current component, according to the inverse Fourier transform formula, the amplitude of the frequency domain zero-order frequency component corresponds to the direct current component of the time domain, and the formula is as follows:
Figure BDA0002344393690000069
in the formula: m223Is the number of the bin blocks,
Figure BDA00023443936900000610
the amplitude of the zero order frequency component;
5.3.2) restoring the high signal-to-noise ratio time domain observation profile, namely obtaining the high signal-to-noise ratio time domain observation profile according to the time domain observation profile containing the direct current component and the time domain observation profile not containing the direct current component, wherein the formula is as follows:
Figure BDA00023443936900000611
in the formula:
Figure BDA00023443936900000612
for a time-domain observation profile that does not contain a dc component,
Figure BDA00023443936900000613
the time domain observation profile is high in signal-to-noise ratio, the signal-to-noise ratio is 17.71dB, and the time domain profile
Figure BDA00023443936900000614
The correlation coefficient with the standard profile is 0.9876.
The foregoing description is only an example of the present invention and is not intended to limit the invention, so that it will be apparent to those skilled in the art that various modifications and variations can be made in the form and detail without departing from the spirit and structure of the invention, and the scope of the appended claims is to be accorded the full scope of the invention.

Claims (11)

1. An X-ray pulsar short-time observation high signal-to-noise ratio contour acquisition method is characterized by comprising the following steps:
(1) folding the photon arrival time sequence to obtain a time domain waveform:
1a) selecting a photon arrival time T of an observation time TiAnd i is 1,2,3, calculating the arrival time t of the photons through a pulsar timing model according to the rotation frequency parameters of the pulsar ephemerisiCorresponding phase phi (t)i)；
1b) Choose from (2)11Infinity) bin blocks to photon arrival time tiPerforming periodic folding or folding on tiCorresponding phase phi (t)i) Performing epoch folding to obtain a time domain waveform;
(2) fourier transformation is carried out on the time domain waveform to obtain a frequency spectrum;
(3) separating the frequency spectrum from the noise:
3a) selecting a cost function and calculating the cut-off point of the frequency spectrum;
3b) according to different frequency domain characteristics that the frequency domain of the signal is mainly concentrated at low frequency, the noise is distributed in the whole frequency domain and the amplitude is small, the spectrum is cut by using a cut-off point, and the spectrum between 0 point and the cut-off point is selected to separate the signal from the noise;
(4) and (3) restoring the high signal-to-noise ratio time domain observation profile:
4a) removing direct current components from the intercepted frequency spectrum, namely removing the value of zero-order frequency components;
4b) carrying out Fourier inversion on the frequency spectrum without the zero-order frequency component to obtain a time domain complex signal without a direct current component, and taking a real part of the time domain complex signal without the direct current component to obtain a time domain observation contour without the direct current component;
4c) carrying out inverse Fourier transform on the value of the zero-order frequency component to obtain a direct-current component;
4d) and adding the direct current component to the time domain observation profile without the direct current component to obtain the high signal-to-noise ratio time domain observation profile.
2. The method of claim 1, wherein the photon arrival time t in 1a) is calculated by a pulsar timing modeliThe corresponding phase is expressed as follows:
Figure FDA0002344393680000011
wherein: phi (t)0) Is a reference time t0Corresponding initial phase, f(L)Respectively, L-order partial derivatives of the rotation frequency, and the value of L is 2.
3. The method of claim 1, wherein step 1b) employs (2)11Infinity) bin blocks to photon arrival time tiPeriodic folding is performed, and the formula is as follows:
Figure FDA0002344393680000021
in the formula, TsIs pulsar period, P ═ T/TsM is the number of bin blocks, the value range (2)11，∞)，Tb＝Ts/M，cj(ti) Is the number of photons in the ith bin in the jth period,
Figure FDA0002344393680000022
the signal waveform is observed in the time domain.
4. The method of claim 1, wherein step 1b) employs (2)11Infinity) bin blocks to photon arrival time tiCorresponding phase phi (t)i) Performing epoch folding, wherein the formula is as follows:
Figure FDA0002344393680000023
in the formula: m is the number of bin blocks, the value range (2)11Infinity); f is the frequency of the pulsar, Q is the number of phase cycles of the pulsar, Cj,iIs the number of photons in the ith bin of the jth integer phase,
Figure FDA0002344393680000024
the signal waveform is observed in the time domain.
5. The method of claim 1, wherein 2) time-domain waveforms
Figure FDA0002344393680000025
Fourier transformation is carried out to obtain a frequency spectrum, and the formula is as follows:
Figure FDA0002344393680000026
in the formula: m is the number of bin blocks, the value range (2)11，∞)；
Figure FDA0002344393680000027
In order to observe the signal waveform in the time domain,
Figure FDA0002344393680000028
when isThe spectrum of the signal waveform after Fourier transform is observed in the domain.
6. The method of claim 1, wherein the spectral cutoff point is calculated in 3a) by:
Figure FDA0002344393680000029
in the formula, SkFor the fourier transform of the standard signal,
Figure FDA00023443936800000210
for the fourier transformed spectrum of the time domain observed signal waveform,
Figure FDA00023443936800000211
is the conjugate of the standard signal fourier transform,
Figure FDA00023443936800000212
is the conjugate of the frequency spectrum after the Fourier transform of the time domain observation signal waveform, q is a frequency domain truncation point,
Figure FDA00023443936800000213
in order to obtain the value of the cost function,
Figure FDA00023443936800000214
the method has the property of monotonically decreasing to the minimum value along with the truncation point q and then keeping monotonically increasing, and the q corresponding to the minimum value is taken as the optimal frequency truncation point of the frequency spectrum by the cost function.
7. The method of claim 1, wherein the signal in 3b) is separated from noise by the following equation:
Figure FDA0002344393680000031
in the formula: m is the number of bin blocks, the value range (2)11，∞)；
Figure FDA0002344393680000032
Is a time domain observed signal waveform, q is a frequency domain truncation point,
Figure FDA0002344393680000033
is the spectrum intercepted by the truncation point.
8. The method of claim 1, wherein the inverse fourier transform of the frequency spectrum with the zero-order frequency component removed in 4b) obtains a time-domain complex signal without a dc component, and the formula is as follows:
Figure FDA0002344393680000034
in the formula: m is the number of bin blocks, the value range (2)11Infinity); n is the number of time domain sampling points, q is the frequency domain truncation point,
Figure FDA0002344393680000035
in order for the spectrum to be intercepted by the truncation point,
Figure FDA0002344393680000036
is a pair of
Figure FDA0002344393680000037
The frequency spectrum of the zero-order frequency component is removed,
Figure FDA0002344393680000038
is a time domain complex signal containing no dc component.
9. The method of claim 1, wherein the time-domain observation profile obtained in 4b) without dc component is formulated as follows:
Figure FDA0002344393680000039
in the formula: n is the number of time-domain sampling points,
Figure FDA00023443936800000310
for time domain complex signals that do not contain a dc component,
Figure FDA00023443936800000311
is a time-domain observation profile that does not contain a dc component.
10. The method of claim 1, wherein the dc component obtained in 4c) is formulated as follows:
Figure FDA00023443936800000312
in the formula: m is the number of bin blocks, the value range (2)11，∞)；
Figure FDA00023443936800000313
Is the amplitude of the zero-order frequency component, s0Is a direct current component.
11. The method of claim 1, wherein the high signal-to-noise ratio time-domain observation profile obtained in 4d) is formulated as follows:
Figure FDA00023443936800000314
in the formula: n is the number of time-domain sampling points, s0In order to be a direct current component,
Figure FDA0002344393680000041
for a time-domain observation profile that does not contain a dc component,
Figure FDA0002344393680000042
the profile is observed for high signal-to-noise ratio time domain.
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