CN106595672B - Pulsar arrival time estimation method and system based on the perception of anti-noise Fast Compression - Google Patents
Pulsar arrival time estimation method and system based on the perception of anti-noise Fast Compression Download PDFInfo
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Abstract
The present invention provides a kind of pulsar arrival time estimation method and system based on the perception of anti-noise Fast Compression, building including redundant dictionary, based on hadamard matrix, the observation energy for defining some row vector is the product variation range of the row vector and each column vector of dictionary, according to preset observation energy threshold, if the observation energy of some row vector is greater than thresholding, which is selected as a line of observing matrix；Match tracing is realized according to the correlation of measurement vector and each dictionary column vector.Compared with the compressed sensing based pulsar arrival time estimation method of tradition, technical solution of the present invention has stronger robustness to noise, and measurement vector number is less, and is convenient for hardware realization, has important application value.
Description
Technical field
The invention belongs to Spacecraft Autonomous Navigation field, in particular to a kind of compressed sensing based pulsar arrival time
Estimation method and system.
Background technique
X-ray pulsar navigation is a kind of emerging Spacecraft Autonomous Navigation method.X-ray pulsar navigation is to utilize arteries and veins
Star radiation signal is rushed to navigate.The external stable radiation of X-ray pulsar, periodically pulsing signal.These signals are pressed
It is accumulated according to the period, can get stable pulse profile.The profile is compared with calibration pulse profile, arteries and veins can be obtained
The fractional part of (TOA, time-of-arrival) is rushed arrival time, and its number of cycles part can then be predicted by spacecraft
It is estimated position.
Pulsar arrival time is the basis that pulsar navigation system can work normally.Currently, pulsar arrival time is estimated
Meter is the research hotspot in pulsar navigation field.In recent years, existing scholar starts compressed sensing being applied to pulsar signal
Processing.Such as: Su Zhe et al. delivered on " Chinese science: physics mechanics astronomy " " compressed sensing based in 2011
Pulsar profile developing algorithm "；Shen Lirong et al. has delivered " A robust compressed in 2016 on " Optik "
Sensing based method for X-ray Pulsar Profile construction, robust compression sensing method exist
Application in pulsar signal reconstruct ".Both methods focuses mainly on pulsar signal reconstruct.In fact, pulsar signal is gone
It makes an uproar, the final purpose of reconstruct is all to obtain high-precision pulse star arrival time.Li Shengliang et al. was sent out on " Optik " in 2014
Table " Fleet algorithm for X-ray pulsar profile construction and TOA solution
Based on compressed sensing, compressed sensing based pulsar profile and TOA fast algorithm "；Yu Hang et al. in
" A sparse representation- has been delivered on " aerospace science and technology " within 2015
based optimization algorithm for measuring the time delay of pulsar
Integrated pulse profile, using the pulsar accumulated pulse profile time delay measurement method of rarefaction representation ".This
Two articles estimate compressed sensing applied to pulsar arrival time, achieve preferable effect.But in measurement vector
All be in selection it is random, certain measurement vectors possibly can not play a role or act on very little.In this way, a large amount of useless observation arrows
Amount is selected, and useful measurement vector is then missed.
The application in other field is perceived compared to conventional compression, the compression in current PRF star arrival time estimation method
Perception has following feature:
(1) each element in dictionary is not orthogonal, redundancy.Element in dictionary possesses out of phase
Same pulse profile.
(2) pulsar contour signal is considered as 1 rank sparse signal.
For following condition need to be met convenient for the realization pulsar arrival time estimation method on spacecraft:
(1) amplitude and phase are two parameters of pulsar profile.Since pulsar radiation intensity is unstable, the arteries and veins of acquisition
It is also unknown for rushing star-wheel exterior feature amplitude.Pulsar TOA estimation emphasis is to obtain phase.Therefore, compressed sensing based pulsar
TOA algorithm for estimating should not be interfered by amplitude.
(2) for the ease of hardware realization, observing matrix coefficient need to be { 1, -1 }.
(3) in order to reduce calculation amount, measurement vector number should be reduced to the greatest extent.
But there has been no the appearance of suitable technical solution at present.
Summary of the invention
The invention proposes a kind of pulsar arrival time estimation technique schemes based on the perception of anti-noise Fast Compression, it is intended to
More accurate pulse arrival time estimation is rapidly provided for navigation system.
To achieve the above object of the invention, the technical scheme is that
A kind of pulsar arrival time estimation method based on the perception of anti-noise Fast Compression, includes the following steps,
Step 1, the building of redundant dictionary, realization is as follows,
If the redundant dictionary of pulsar accumulation profile is expressed as,
Wherein, n is serial number, and n={ 0,1,2 ... N-1 }, N are pulsion phase seat interval number, and redundant dictionary ψ is N × N's
Matrix；
It is the column vector of N × 1 for n-th of column vector in dictionary, expression formula is as follows,
Wherein, s is pulsar nominal contour, and i is variable, i={ 0,1,2 ... N-1 },ForI-th of element,
Mod () indicates modulus；
Step 2, observing matrix is set, realization is as follows,
If H is N rank hadamard matrix,
H=[h0；h1；h2；…hn；…hN-1]
Wherein, hnIt is the row vector in hadamard matrix, is 1*N, n={ 0,1,2 ... N-1 }；
Define some row vector hnObservation energy enFor the product variation range of the row vector and each column vector of dictionary, en
Expression formula is as follows,
en=max (hn·Ψ)-min(hn·Ψ)
Wherein, max (hnΨ) indicate row vector hnWith the maximum value of the product of each column vector of dictionary, min (hnΨ) then
Indicate row vector hnWith the minimum value of the product of each column vector of dictionary；
According to preset observation energy threshold T, if some row vector hnObservation energy enGreater than T, which is selected as
A line of observing matrix, otherwise gives up；
It is the matrix of m × N if observing matrix is expressed as Φ, m is the line number being selected in hadamard matrix H；
Step 3, the acquisition of measurement vector, realization is as follows,
Y=Φ x
Wherein, y is measurement vector, is the vector of m × 1；X is that pulsar accumulates profile, is 1 × N vector；
Step 4, match tracing, realization is as follows,
First find out measurement vector y and each dictionary column vectorCorrelation, be denoted asN=0,1,2 ... N-
1 }, subscript T indicates transposition；
Serial number n corresponding with the dictionary vector of observation correlation maximumτExpression formula it is as follows,
Pulsar arrival time estimated valueExpression formula is
Moreover, the expression formula that pulsar accumulates i-th of phason interval in profile x is as follows in step 3,
X (i)=Poisson (At λb/N+A·t·λs·s(mod(i-τ·N/p,N)))
Wherein, Poisson is Poisson distribution random signal generator, λbFor background noise photon flux density, λsFor pulse
Star radiated photons flux density, A are X-ray detector effective area, and t is pulsar radiation signal observation time, and τ prolongs for the time
Late, p is the pulsar radiation signal period.
It is including following the present invention also provides a kind of pulsar arrival time estimating system based on the perception of anti-noise Fast Compression
Module, the first module, for the building of redundant dictionary, realization is as follows,
If the redundant dictionary of pulsar accumulation profile is expressed as,
Wherein, n is serial number, and n={ 0,1,2 ... N-1 }, N are pulsion phase seat interval number, and redundant dictionary ψ is N × N's
Matrix；
It is the column vector of N × 1 for n-th of column vector in dictionary, expression formula is as follows,
Wherein, s is pulsar nominal contour, and i is variable, i={ 0,1,2 ... N-1 },ForI-th of element,
Mod () indicates modulus；
Second module, for setting observing matrix, realization is as follows,
If H is N rank hadamard matrix,
H=[h0；h1；h2；…hn；…hN-1]
Wherein, hnIt is the row vector in hadamard matrix, is 1*N, n={ 0,1,2 ... N-1 }；
Define some row vector hnObservation energy enFor the product variation range of the row vector and each column vector of dictionary, en
Expression formula is as follows,
en=max (hn·Ψ)-min(hn·Ψ)
Wherein, max (hnΨ) indicate row vector hnWith the maximum value of the product of each column vector of dictionary, min (hnΨ) then
Indicate row vector hnWith the minimum value of the product of each column vector of dictionary；
According to preset observation energy threshold T, if some row vector hnObservation energy enGreater than T, which is selected as
A line of observing matrix, otherwise gives up；
It is the matrix of m × N if observing matrix is expressed as Φ, m is the line number being selected in hadamard matrix H；
Third module, for the acquisition of measurement vector, realization is as follows,
Y=Φ x
Wherein, y is measurement vector, is the vector of m × 1；X is that pulsar accumulates profile, is 1 × N vector；
4th module is used for match tracing, and realization is as follows,
First find out measurement vector y and each dictionary column vectorCorrelation, be denoted asN=0,1,2 ... N-
1 }, subscript T indicates transposition；
Serial number n corresponding with the dictionary vector of observation correlation maximumτExpression formula it is as follows,
Pulsar arrival time estimated valueExpression formula is
Moreover, the expression formula that pulsar accumulates i-th of phason interval in profile x is as follows in third module,
X (i)=Poisson (At λb/N+A·t·λs·s(mod(i-τ·N/p,N)))
Wherein, Poisson is Poisson distribution random signal generator, λbFor background noise photon flux density, λsFor pulse
Star radiated photons flux density, A are X-ray detector effective area, and t is pulsar radiation signal observation time, and τ prolongs for the time
Late, p is the pulsar radiation signal period.
The present invention has studied under a kind of Low SNR, and the pulsar arrival time based on the perception of anti-noise Fast Compression is estimated
Technical solution is counted, in compressed sensing, the pulse profile of out of phase constitutes the sparse dictionary of redundancy；Using hadamard matrix as base
Plinth selects a small amount of Hadamard vectorial structure observing matrix to observe energy as criterion, and the observing matrix line number is less, anti-noise energy
Power is strong；Finally, estimating pulse arrival time using match tracing.Estimate with tradition compressed sensing based pulsar arrival time
Method is compared, which has stronger robustness to noise, and measurement vector number is less, and is convenient for hardware realization,
In first place in the world, there is important market value.
Detailed description of the invention
Fig. 1 is the flow chart of the embodiment of the present invention；
Fig. 2 is the PSR B1937+21 calibration pulse profile schematic diagram of the embodiment of the present invention；
Fig. 3 is the observation energy diagram of the embodiment of the present invention；
Fig. 4 is the dependency diagram of the embodiment of the present invention.
Specific embodiment
Technical solution of the present invention is specifically described below in conjunction with drawings and examples.
In the prior art, a large amount of useless measurement vectors are selected, and useful measurement vector is then missed.For this
Problem, invention defines observation energy, and useful measurement vector are selected according to this, and constitute observing matrix.
In embodiment, the invention will be further described by taking X-ray pulsar PSR B1937+21 as an example.Pulse profile number
According to can be downloaded from European pulsar website (The European Pulsar Network).It will be to mark after the data normalization
Quasi- pulse profile.Fig. 2 gives the calibration pulse profile of PSR B1937+21.
Embodiment provide process the following steps are included:
Step 1: the building of redundant dictionary.
The redundant dictionary of pulsar PSR B1937+21 accumulation profile may be expressed as:
Wherein, n is serial number, and n={ 0,1,2 ... N-1 }, N are pulsion phase seat interval number, in the present embodiment, N=
1024.Redundant dictionary ψ is the matrix of N × N.
It is the column vector of N × 1, expression formula for n-th of column vector in dictionary are as follows:
Wherein, s is pulsar nominal contour, and for waveform as shown in Fig. 2, waveform abscissa is phase, ordinate is photon
Density.I is variable, i={ 0,1,2 ... N-1 },ForI-th of element, i.e. the element of n-th the i-th row of column in dictionary ψ.
Mod () indicates modulus.
Step 2: the setting of observing matrix.
For the ease of hardware realization, observing matrix coefficient need to be { 1, -1 }.Hadamard (Hadamard) matrix be by+1 and-
The orthogonal square matrix that 1 element is constituted.The present invention proposes based on hadamard matrix, designs observing matrix.If H is N rank Hadamard
Matrix.In the present embodiment, H is 1024 rank hadamard matrixs.
H=[h0；h1；h2；…hn；…hN-1] (3)
Wherein, hnIt is the row vector in hadamard matrix, is 1*N, n={ 0,1,2 ... N-1 }.
Define some row vector hnObservation energy enFor the product variation range of the row vector and each column vector of dictionary, en
Expression formula is as follows:
en=max (hn·Ψ)-min(hn·Ψ) (4)
Row vector hnH is denoted as with each column vector product of dictionary ψnΨ specifically includes hnWith N number of column vector(n=0,
1,2 ... N-1 }) product is taken respectively, N number of element, max (h is obtainednIt Ψ) indicates the maximum value in these elements, swears at once
Measure hnWith the maximum value of the product of each column vector of dictionary；min(hnΨ) then indicate minimum value, i.e. expression row vector hnWith dictionary
The minimum value of the product of each column vector.The two difference embodies amplitude of variation.If the value does not change or amplitude of variation very little,
The element in dictionary cannot be distinguished according to the observation, i.e. the value restores without effect signal.Therefore, observation energy is bigger, hn
It can more play a role in signal recovery, it more can anti-noise.Corresponding observation energy such as Fig. 3 of each row vector in hadamard matrix
It is shown.
Definition observation energy threshold T extracts the Hadamard row vector of high observation energy according to thresholding.If observation energy is greater than
The thresholding, hnThe a line that may be selected as observing matrix, otherwise gives up.It is the matrix of m × N if observing matrix is represented by Φ, m is
The selected line number of hadamard matrix.In general, thresholding T is smaller, line number m is more, and precision is higher, but calculation amount increases；Instead
?.
In the present embodiment, if setting thresholding T as 1.9, m 6, that is, the 128th of hadamard matrix has been selected, 192,
256,320,384,448 rows；If setting thresholding T as 1.5, m 14；If setting thresholding T as 0.5, m 62；If setting door
It is limited to 0.2, then m is 116；If setting door T is limited to 0, m 1024.In the present embodiment, by emulation experiment, in calculation amount
It trades off between pulsar arrival time estimated accuracy, threshold sets 0.2.When it is implemented, those skilled in the art can be certainly
Row presets the value of observation energy threshold T as needed.
Step 3: the acquisition of measurement vector.
The calculating formula of measurement vector is as follows:
Y=Φ x (5)
Wherein, y is measurement vector, is the vector of m × 1.X is that pulsar accumulates profile, is 1 × N vector.
Since the arrival time of photon obeys Poisson distribution, the expression formula at i-th of phason interval is as follows in x:
X (i)=Poisson (At λb/N+A·t·λs·s(mod(i-τ·N/p,N))) (6)
Wherein, Poisson is Poisson distribution random signal generator, λbFor background noise photon flux density, λsFor pulse
Star radiated photons flux density, A are X-ray detector effective area, and t is pulsar radiation signal observation time, and τ prolongs for the time
Late, p is the pulsar radiation signal period.
In the present embodiment, λbFor 0.005ph/cm2/ s, λsFor 4.99*10-5ph/cm2/ s, A 384cm2, t is
1000s, p 1.5578ms, τ 0.38945ms.
Step 4: the realization of match tracing.
Since the sparse order of signal is 1, matching pursuit algorithm of the present invention is not necessarily to iteration.Measurement vector y and each can first be found out
Dictionary column vectorCorrelation, be denoted asN={ 0,1,2 ... N-1 }, subscript T indicate transposition.Different dictionary arrows
It measures as shown in Figure 4 with the correlation of observation.Serial number n corresponding with the dictionary vector of observation correlation maximumτIt is as required.It is comprehensive
On, nτExpression formula it is as follows:
Since matching process is unrelated with signal amplitude value, so, pulsar profile amplitude will not generate shadow to phase estimation
It rings.
Pulsar arrival time estimated valueExpression formula is as follows:
To sum up, this method meets three conditions applied to spacecraft, has preferable performance.
500 Monte Carlo simulations are carried out to technical solution of the embodiment of the present invention, error 1.4669us is corresponding
Position error is 440m.
When it is implemented, method provided by the present invention can realize automatic running process based on software technology, mould can also be used
Block mode realizes corresponding system.The embodiment of the present invention accordingly provides a kind of pulsar arrival based on the perception of anti-noise Fast Compression
Time Estimate system, comprises the following modules,
First module, for the building of redundant dictionary, realization is as follows,
If the redundant dictionary of pulsar accumulation profile is expressed as,
Wherein, n is serial number, and n={ 0,1,2 ... N-1 }, N are pulsion phase seat interval number, and redundant dictionary ψ is N × N's
Matrix；
It is the column vector of N × 1 for n-th of column vector in dictionary, expression formula is as follows,
Wherein, s is pulsar nominal contour, and i is variable, i={ 0,1,2 ... N-1 },ForI-th of element,
Mod () indicates modulus；
Second module, for setting observing matrix, realization is as follows,
If H is N rank hadamard matrix,
H=[h0；h1；h2；…hn；…hN-1]
Wherein, hnIt is the row vector in hadamard matrix, is 1*N, n={ 0,1,2 ... N-1 }；
Define some row vector hnObservation energy enFor the product variation range of the row vector and each column vector of dictionary, en
Expression formula is as follows,
en=max (hn·Ψ)-min(hn·Ψ)
Wherein, max (hnΨ) indicate row vector hnWith the maximum value of the product of each column vector of dictionary, min (hnΨ) then
Indicate row vector hnWith the minimum value of the product of each column vector of dictionary；
According to preset observation energy threshold T, if some row vector hnObservation energy enGreater than T, which is selected as
A line of observing matrix, otherwise gives up；
It is the matrix of m × N if observing matrix is expressed as Φ, m is the line number being selected in hadamard matrix H；
Third module, for the acquisition of measurement vector, realization is as follows,
Y=Φ x
Wherein, y is measurement vector, is the vector of m × 1；X is that pulsar accumulates profile, is 1 × N vector；
4th module is used for match tracing, and realization is as follows,
First find out measurement vector y and each dictionary column vectorCorrelation, be denoted asN=0,1,2 ... N-
1 }, subscript T indicates transposition；
Serial number n corresponding with the dictionary vector of observation correlation maximumτExpression formula it is as follows,
Pulsar arrival time estimated valueExpression formula is
Each module specific implementation can be found in corresponding steps, and it will not go into details by the present invention.
Specific embodiment described herein is only an example for the spirit of the invention.The neck of technology belonging to the present invention
The technical staff in domain can make various modifications or additions to the described embodiments or replace by a similar method
In generation, however, it does not deviate from the spirit of the invention or beyond the scope of the appended claims.
Claims (4)
1. a kind of pulsar arrival time estimation method based on the perception of anti-noise Fast Compression, it is characterised in that: including following step
Suddenly,
Step 1, the building of redundant dictionary, realization is as follows,
If the redundant dictionary of pulsar accumulation profile is expressed as,
Wherein, n is serial number, and n={ 0,1,2 ... N-1 }, N are pulsion phase seat interval number, and redundant dictionary ψ is the square of N × N
Battle array；
It is the column vector of N × 1 for n-th of column vector in dictionary, expression formula is as follows,
Wherein, s is pulsar nominal contour, and i is variable, i={ 0,1,2 ... N-1 },ForI-th of element, mod
() indicates modulus；
Step 2, observing matrix is set, realization is as follows,
If H is N rank hadamard matrix,
H=[h0；h1；h2；…hn；…hN-1]
Wherein, hnIt is the row vector in hadamard matrix, is 1*N, n={ 0,1,2 ... N-1 }；
Define some row vector hnObservation energy enFor the product variation range of the row vector and each column vector of dictionary, enExpression
Formula is as follows,
en=max (hn·Ψ)-min(hn·Ψ)
Wherein, max (hnΨ) indicate row vector hnWith the maximum value of the product of each column vector of dictionary, min (hnΨ) then indicate
Row vector hnWith the minimum value of the product of each column vector of dictionary；
According to preset observation energy threshold T, if some row vector hnObservation energy enGreater than T, which is selected as observing
A line of matrix, otherwise gives up；
It is the matrix of m × N if observing matrix is expressed as Φ, m is the line number being selected in hadamard matrix H；
Step 3, the acquisition of measurement vector, realization is as follows,
Y=Φ x
Wherein, y is measurement vector, is the vector of m × 1；X is that pulsar accumulates profile, is 1 × N vector；
Step 4, match tracing, realization is as follows,
First find out measurement vector y and each dictionary column vectorCorrelation, be denoted asN={ 0,1,2 ... N-1 }, on
Marking T indicates transposition；
Serial number n corresponding with the dictionary vector of observation correlation maximumτExpression formula it is as follows,
Pulsar arrival time estimated valueExpression formula isP is the pulsar radiation signal period.
2. the pulsar arrival time estimation method according to claim 1 based on the perception of anti-noise Fast Compression, feature exist
In: in step 3, the expression formula that pulsar accumulates i-th of phason interval in profile x is as follows,
X (i)=Poisson (At λb/N+A·t·λs·s(mod(i-τ·N/p,N)))
Wherein, Poisson is Poisson distribution random signal generator, λbFor background noise photon flux density, λsFor pulsar spoke
Photon flux density is penetrated, A is X-ray detector effective area, and t is pulsar radiation signal observation time, and τ is time delay, p
For the pulsar radiation signal period.
3. a kind of pulsar arrival time estimating system based on the perception of anti-noise Fast Compression, it is characterised in that: including with lower die
Block,
First module, for the building of redundant dictionary, realization is as follows,
If the redundant dictionary of pulsar accumulation profile is expressed as,
Wherein, n is serial number, and n={ 0,1,2 ... N-1 }, N are pulsion phase seat interval number, and redundant dictionary ψ is the square of N × N
Battle array；
It is the column vector of N × 1 for n-th of column vector in dictionary, expression formula is as follows,
Wherein, s is pulsar nominal contour, and i is variable, i={ 0,1,2 ... N-1 },ForI-th of element, mod
() indicates modulus；
Second module, for setting observing matrix, realization is as follows,
If H is N rank hadamard matrix,
H=[h0；h1；h2；…hn；…hN-1]
Wherein, hnIt is the row vector in hadamard matrix, is 1*N, n={ 0,1,2 ... N-1 }；
Define some row vector hnObservation energy enFor the product variation range of the row vector and each column vector of dictionary, enExpression
Formula is as follows,
en=max (hn·Ψ)-min(hn·Ψ)
Wherein, max (hnΨ) indicate row vector hnWith the maximum value of the product of each column vector of dictionary, min (hnΨ) then indicate
Row vector hnWith the minimum value of the product of each column vector of dictionary；
According to preset observation energy threshold T, if some row vector hnObservation energy enGreater than T, which is selected as observing
A line of matrix, otherwise gives up；
It is the matrix of m × N if observing matrix is expressed as Φ, m is the line number being selected in hadamard matrix H；
Third module, for the acquisition of measurement vector, realization is as follows,
Y=Φ x
Wherein, y is measurement vector, is the vector of m × 1；X is that pulsar accumulates profile, is 1 × N vector；
4th module is used for match tracing, and realization is as follows,
First find out measurement vector y and each dictionary column vectorCorrelation, be denoted asN={ 0,1,2 ... N-1 }, on
Marking T indicates transposition；
Serial number n corresponding with the dictionary vector of observation correlation maximumτExpression formula it is as follows,
Pulsar arrival time estimated valueExpression formula isP is the pulsar radiation signal period.
4. the pulsar arrival time estimating system according to claim 3 based on the perception of anti-noise Fast Compression, feature exist
In: in third module, the expression formula that pulsar accumulates i-th of phason interval in profile x is as follows,
X (i)=Poisson (At λb/N+A·t·λs·s(mod(i-τ·N/p,N)))
Wherein, Poisson is Poisson distribution random signal generator, λbFor background noise photon flux density, λsFor pulsar spoke
Photon flux density is penetrated, A is X-ray detector effective area, and t is pulsar radiation signal observation time, and τ is time delay, p
For the pulsar radiation signal period.
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| CN104296755A (en) * | 2014-10-23 | 2015-01-21 | 中国空间技术研究院 | Determination method of pulse TOA of X-ray pulsar-based navigation |
| CN104535067A (en) * | 2015-01-14 | 2015-04-22 | 中国人民解放军国防科学技术大学 | Method for quickly calculating arrival time of pulse signal based on sector search |
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| CN103674032A (en) * | 2012-09-04 | 2014-03-26 | 西安电子科技大学 | Satellite autonomous navigation system and method integrating pulsar radiation vector and timing observation |
| CN102997922A (en) * | 2012-11-30 | 2013-03-27 | 北京控制工程研究所 | Method for determining pulse arrival time difference by utilizing optical navigation information |
| CN103217162A (en) * | 2013-03-21 | 2013-07-24 | 西安电子科技大学 | Pulsar accumulated pulse profile time delay measurement method by sparse representation |
| CN103900577A (en) * | 2014-04-14 | 2014-07-02 | 武汉科技大学 | Formation-flying-oriented relative navigation speed measurement and combined navigation method |
| CN104296755A (en) * | 2014-10-23 | 2015-01-21 | 中国空间技术研究院 | Determination method of pulse TOA of X-ray pulsar-based navigation |
| CN104535067A (en) * | 2015-01-14 | 2015-04-22 | 中国人民解放军国防科学技术大学 | Method for quickly calculating arrival time of pulse signal based on sector search |
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