CN110986922B - Method for acquiring X-ray pulsar short-time observation high signal-to-noise ratio contour - Google Patents
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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) 11 Infinity) 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 processing astronomical data.
Description
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 in USA in 11 months in 2017, 4 milliseconds pulsars 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 T i 1,2,3, according to pulsar calendarsCalculating photon arrival time t by pulsar timing model i Corresponding phase phi (t) i );
1b) Choose from (2) 11 Infinity) bin blocks to the photon arrival time t i Performing periodic folding or folding on t i Corresponding 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 has small amplitude, the spectrum is cut off 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 selects (2) 11 Infinity) number of special bins and truncating through the frequency domainThe breakpoint effectively separates the signal and the noise, shortens the calculation time and improves the calculation efficiency under the condition of obtaining the profile with the same signal to noise ratio.
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:
1.1) selecting a photon arrival time T of a period of observation time T i :
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 t i ;i=1,2,3;
1.2) calculating the photon arrival time t i Corresponding 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 model i Corresponding phase phi (t) i ) The formula is as follows:
wherein: phi (t) 0 ) Is a reference time t 0 Corresponding 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 frequency, and takes the value of-3.73397e-10;f (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 photon i And (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 time t i Carrying 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 T s Divided into P portions, as shown in FIG. 2(a), T s A value of 0.0335654311027 seconds;
2.2) number of blocks per bin M is 2 23 The 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 (t i ) I is [1, M ]](ii) a j takes the value [1, P ]];
2.3) the number of photons c in the ith bin in the jth period j (t i ) 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 signalWave formAs shown in figure 2(d) of the drawings,is represented by the following formula:
in the formula (I), the compound is shown in the specification,M=2 23 is the number of bin blocks, T b =T s /M,T s Pulsar period, value 0.0335654311027 seconds; c. C j (t i ) Is the number of photons in the ith bin during the jth period.
The pair of photon arrival time t i Corresponding phase phi (t) i ) And performing epoch folding, wherein the steps are as follows:
first, the arrival time t of the photon i Corresponding phase phi (t) i ) Divided into Q portions by period, where phi (t) i ) The period value of (1);
second, the number of blocks per bin M is 2 23 Dividing each phase period equally, and calculating the photon number C in the ith bin of the jth integer phase j,i And i takes the value of [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 counted j,i Adding 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 waveformThe expression is as follows:
This example uses, but is not limited to, photon arrival time t i Corresponding phase phi (t) i ) And performing epoch folding.
And 3, carrying out Fourier transform on the time domain waveform.
According to Fourier transform formula, on time domain waveformFourier transformation is carried out to obtain a frequency spectrum, and the formula is as follows:
in the formula: m2 23 Is the bin block number;in order to observe the signal waveform in the time domain,the spectrum of the time domain observation signal waveform after Fourier transform.
And 4, calculating an interception point of the frequency spectrum, and separating signals and noise by using the interception 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:
in the formula,S k For crab cloud crab pulsar standard profile fourier transform,for the spectrum after fourier transformation of the time domain observed signal waveform,is the conjugate of the standard profile fourier transform of the pulsar,is the conjugate of the time domain observed signal waveform Fourier transform, q is the frequency domain truncation point,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 takenThe 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 is as follows:
in the formula: m2 23 Is the number of the bin blocks,is a time domain observed signal waveform, q is a frequency domain truncation point,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 contour comprises the following steps:
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 is subjected toThe direct current component is removed, that is, the value of the zero-order frequency component is removed, and the formula is as follows:
in the formula: m2 23 Is the bin block number;observing a signal waveform for a time domain; q is a frequency domain truncation point and takes the value of 22;in order for the spectrum to be intercepted by the truncation point,is a pair ofRemoving 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 an inverse Fourier transform formula, 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:
in the formula: m-2 23 Is the bin block number; n is the number of time-domain sampling points, and the value is 1024; q is a frequency domain truncation point and takes the value of 22;in order for the spectrum to be intercepted by the truncation point,is a pair ofThe frequency spectrum of the zero-order frequency components is removed,the time domain complex signal after Fourier inverse transformation is obtained;
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:
in the formula: n is the number of time-domain sampling points, and the value of N is 1024;is the time domain complex signal after the inverse fourier transform,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:
in the formula: m2 23 Is the number of the bin blocks,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:
in the formula:for a time-domain observation profile that does not contain a dc component,the time-domain observation profile is high in signal-to-noise ratio, the signal-to-noise ratio is 17.71dB, and the time-domain profileThe correlation coefficient with the standard profile is 0.9876.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
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 photon arrival time T of a period of observation time T i And 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 ephemeris i Corresponding phase phi (t) i );
1b) Choose (2) 11 Infinity) bin blocks to the photon arrival time t i Performing periodic folding or folding on t i Corresponding 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 an interception point of a 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 model i The corresponding phase is expressed as follows:
wherein: phi (t) 0 ) Is a reference time t 0 Corresponding initial phase, f denotes the rotation frequency, f (L) The expression is the partial derivative of the L order of the rotation frequency, and the value of L is 2.
3. The method of claim 1, wherein step 1b) employs (2) 11 Infinity) bin blocks to photon arrival time t i Periodic folding is performed, and the formula is as follows:
4. The method of claim 1, wherein step 1b) employs (2) 11 Infinity) bin blocks to photon arrival time t i Corresponding phase phi (t) i ) Performing epoch folding, wherein the formula is as follows:
5. The method of claim 1, wherein 2) time-domain waveformsFourier transformation is carried out to obtain a frequency spectrum, and the formula is as follows:
6. The method of claim 1, wherein the spectral cutoff point is calculated in 3a) by:
in the formula, S k For the fourier transform of the standard signal,for the fourier transformed spectrum of the time domain observed signal waveform,is the conjugate of the standard signal fourier transform,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,in order to obtain the value of the cost function,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:
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:
in the formula: m is the number of bin blocks, the value range (2) 11 An infinite); n is the number of time domain sampling points, q is the frequency domain truncation point,in order for the spectrum to be intercepted by the truncation point,is a pair ofThe frequency spectrum of the zero-order frequency component is removed,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:
11. The method of claim 1, wherein the high signal-to-noise ratio temporal observation profile obtained in 4d) is formulated as follows:
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