CN103217161A - Combined estimation method of pulsar navigation position and speed - Google Patents

Combined estimation method of pulsar navigation position and speed Download PDF

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CN103217161A
CN103217161A CN2013100625342A CN201310062534A CN103217161A CN 103217161 A CN103217161 A CN 103217161A CN 2013100625342 A CN2013100625342 A CN 2013100625342A CN 201310062534 A CN201310062534 A CN 201310062534A CN 103217161 A CN103217161 A CN 103217161A
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刘劲
吴谨
孙永明
熊凌
李娟�
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Wuhan University of Science and Engineering WUSE
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Abstract

The invention relates to a combined estimation method of pulsar navigation position and speed. The invention belongs to the field of spacecraft autonomous navigation. According to the method, an observation interval is divided into a plurality of sub-intervals; in each observation sub-interval, pulse signals are superimposed according to a pulsar radiation period, such that a pulse accumulation sub-contour is obtained; the pulse accumulation sub-contour is processed with a quasi-maximum likelihood estimation method, such that a pulse arrival time of each sub-interval is obtained; and according to the pulse arrival times, spacecraft position and speed are estimated with a least square estimation method. The method provided by the invention provides high-precision positioning and speed determination, which are close to those of Cramer-Rao lower bound. Also, a computation amount is low. Therefore, the method provided by the invention has important practical significance upon spacecraft autonomous navigation based on pulsar.

Description

A kind of pulsar navigation position and velocity joint method of estimation
Technical field
The invention belongs to the spacecraft navigation field, particularly a kind of pulsar navigation position and velocity joint method of estimation.
Background technology
In the last few years, in order to fight for space resources, spacefaring nation was carried out the survey of deep space activity one after another, and accurate navigator fix is the prerequisite and the basis of all survey of deep space activities.At present, the spacecraft navigational system mainly comprises following several: land station's navigational system, GPS (Global Position System, GPS), gravity navigational system, earth-magnetic navigation system and celestial navigation system (CelestialNavigation System, CNS) etc.But these technology all are not suitable for survey of deep space, and subject matter is as follows: land station's navigational system, GPS, gravity navigational system and earth-magnetic navigation system can only provide navigation information for the aircraft of earth surface and the spacecraft of terrestrial space; CNS installs the optical sensitive device on spacecraft, realize the location by the relative position of measuring fixed star and nearly celestial body, and its bearing accuracy is subjected to the distance affects between spacecraft and the nearly celestial body, can't satisfy the requirement of interplanetary mission hi-Fix.
The X ray pulsar navigation is a kind of emerging spacecraft independent navigation mode, and navigation informations such as long-time, high-precision location and constant speed can be in whole space be provided for spacecraft.The X ray pulsar is a kind of magnetic neutron star of high speed rotation, can constantly external X ray signal stable radiation, foreseeable, unique.Spaceborne X-ray detector receives the pulse signal of a period of time (5 ~ 10 minutes), can obtain to arrive the time t of spacecraft by accumulation of pulse cycle and processing to it SCAnd this pulse arrives solar system barycenter (solar system barycenter, SSB) time t bThen can obtain by the pulse timing model prediction.Time delay t b-t SCIt then is the basic observed quantity of pulsar navigation system.From many pulsar direction of visual lines, can obtain a plurality of observed quantities, utilize Navigation Filter can estimate the spacecraft position again.
Obtaining of pulse arrival time needs by long-time (5 ~ 10 minutes) pile-up pulse star radiation signal.But, owing to spacecraft moves, and can't obtain long-time, high-accuracy speed information, the pulse signal that X-ray detector receives will inevitably be subjected to the influence of Doppler effect, and this effect can't effectively be eliminated.In the pulse signal accumulation, if accumulate by the pulsar radiation signal natural period, " passivation " can appear in pulse accumulation profile, and bearing accuracy also can descend significantly, when serious even can cause the pulsar navigation system can't operate as normal.Go up in " On pulse phase estimation and tracking of variable celestial X-ray sources (estimating and tracking) " literary composition of announcing at Institute of Navigation 63rd Annual Meeting (the 63rd annual meeting of association of navigating) about the impulse phase of variable celestial X-ray source, Golshan utilizes maximum Likelihood to determine position and speed according to the distortion of pulse profile.The precision of this method has approached a carat U.S. labor lower bound.But because the maximal value that this technology is searched for likelihood function by gridding method obtains the velocity estimation value, the calculating of each net point all relates to whole impulse radiation signal raw data.Under the prior art condition, detector resolution is in the microsecond magnitude, and accumulated time is 5～10 minutes, and then original data volume is 10 8～10 9Magnitude, very huge.This causes calculated amount, and very big (only the calculating of a net point just comprises 10 8～10 9Magnitude additive operation and 10 8～10 9The magnitude multiplying), so this algorithm can't requirement of real time.At periodical " Science China:Physics, Mechanics ﹠ Astronomy (Chinese science: physics mechanics uranology) " in " Modeling and Doppler measurement of X-ray pulsar (modeling of X ray pulsar and Doppler measurement) " literary composition of the 6th phase in 2011, pulsar signal is decomposed into a plurality of Gaussian functions, the notion of pulse accumulation profile entropy has been proposed, with the error between full sized pules profile and the accumulation profile is objective function, by adjusting time delay and Doppler speed, make the objective function minimum, thereby obtain the velocity estimation value of degree of precision.These two kinds of methods also need repeatedly be calculated the raw data of impulse radiation signal, and calculated amount is very big.
Summary of the invention
The present invention is directed to big this defective of existing pulsar navigation location and constant speed method calculated amount, a kind of position of pulsar navigation fast and velocity joint method of estimation are provided, calculate in real time to be implemented in rail.
Technical scheme of the present invention is a kind of pulsar navigation position and velocity joint method of estimation, may further comprise the steps:
Step 1, total observation time is (t at interval 0, t f) be divided into m observation that equates at interval, (t 0+ (i-1) T Obs/ m, t 0+ iT Obs/ m), i=1,2 ... m, wherein, observation time is T Obs=t f-t 0
Step 2 in each observation interval, is pressed pulsar cycle superimposed pulse signal, obtains pulse and accumulates sub-profile, utilizes accurate maximum Likelihood to estimate the impulse phase estimated value then According to gained impulse phase estimated value
Figure BDA00002865880300022
Conversion obtains pulse arrival time t i
Step 3 is with Least Square in Processing step 2 gained pulse arrival time t i, obtain spacecraft position and speed.
And, in the step 2, describedly utilize accurate maximum Likelihood to estimate the impulse phase estimated value
Figure BDA00002865880300023
As shown in the formula,
Figure BDA00002865880300024
Wherein, function h () is a normalization full sized pules profile,
Figure BDA00002865880300025
Be i observation son pile-up pulse profile at interval, θ and
Figure BDA00002865880300026
The expression phase place.
And, in the step 2, with gained impulse phase estimated value
Figure BDA00002865880300027
Conversion obtains pulse arrival time t iImplementation be, with the impulse phase estimated value As i observation impulse phase at interval
Figure BDA00002865880300029
Adopt following formula to change,
Figure BDA000028658803000210
Wherein, n iBe the pulse number of cycles between spacecraft and the solar system barycenter,
Figure BDA00002865880300031
It is solar system barycenter
Figure BDA00002865880300032
Corresponding constantly phase place, P 0Be the recurrence interval.
And, in the step 3, press the estimated value that following formula obtains spacecraft position and speed
r ^ = c · Σ i = 1 m t i m - v ⩓ · T obs 2
v ^ = 6 · T obs - 1 · c · Σ i = 1 m ( 2 i - m - 1 ) t i m 2 - 1
Wherein, c is the light velocity.
The present invention's advantage compared with prior art is:
(1) the present invention is not that distortion according to pulse accumulation profile comes estimating Doppler speed, but utilizes the variation of pulse arrival time to come estimating speed.Therefore, calculate and need not to relate to a large amount of impulse radiation photons, calculated amount has greatly reduced.
(2) estimated accuracy provided by the invention approaches a carat U.S. labor lower bound, location and constant speed precision height.
Description of drawings
Fig. 1 is the embodiments of the invention process flow diagrams.
Embodiment
Describe technical solution of the present invention in detail below in conjunction with drawings and Examples.The technical program can adopt the automatic operational scheme of computer software technology.
As the navigation pulsar, referring to Fig. 1, the flow process of embodiment may further comprise the steps embodiment with Crab pulsar:
Step 1: embodiment utilizes X-ray detector to collect the pulsar x-ray photon, the observation time segmentation in such a way at interval of the pulsed light subsequence correspondence that detector is obtained.Total observation time is (t at interval 0, t f) be divided into observation that m equates (t at interval 0+ (i-1) T Obs/ m, t 0+ iT Obs/ m), i=1,2 ... m, wherein, t 0Be observation zero-time, t fBe the observation concluding time, observation time is T Obs=t ft 0Set t among the embodiment 0=0s, t f=300s, m=30.
The value of m need satisfy
Figure BDA00002865880300036
Wherein, c is the light velocity, and v is a spacecraft speed, and δ is a pulse signal resolution, and its value equals the X-ray detector temporal resolution.δ=1ms among the embodiment, v=10km/s.
Step 2: in each observation interval, press pulsar radiation period superimposed pulse signal, obtain pulse and accumulate sub-profile, utilize quick accurate maximum Likelihood to estimate impulse phase then, with the impulse phase estimated value that obtains
Figure BDA00002865880300037
Be converted into pulse arrival time t iAs shown in fig. 1, the sub-profile 1 of accumulation, the sub-profile 2 of accumulation are arranged ... accumulate sub-profile m, handle respectively.
Because accurate maximum Likelihood of the prior art is only estimated impulse phase, its calculated amount is only relevant with profile length, rather than the pulse signal photon numbers, so calculated amount is less.Can be referring to document: Rinauro S, Colonnese S, Scarano G.Fast near-maximum likelihood phase estimation of X-ray pulsars (quick accurate maximum likelihood pulsar phase estimation) .Signal Processing (signal Processing), 2013,93 (1): 326-331. the present invention utilizes accurate maximum Likelihood can improve arithmetic speed.
The present invention utilizes accurate maximum Likelihood to estimate phase place as shown in Equation 1:
Wherein, function h () is a normalization full sized pules profile,
Figure BDA00002865880300042
It is i observation pulse accumulation profile at interval.In Fig. 1, the 1st, 2 ... m observation pulse accumulation profile at interval is designated as the sub-profile 1,2 of accumulation respectively ... m.θ and
Figure BDA00002865880300043
The expression phase place is variable, and wherein θ is an integration variable,
Figure BDA00002865880300044
Be independent variable.During concrete enforcement, the full sized pules profile can be observed acquisition for a long time by land station, and to make the profile integration be 1 in normalization then, can obtain normalization full sized pules profile.EPN database (The European Pulsar Network Data Archive, European pulsar observational network database) has been announced the full sized pules profile and the correlation parameter of pulsar, and China technician can obtain the full sized pules profile by this database.
Because the motion of spacecraft, i observation of acquisition be (t at interval 0+ (i-1) T Obs/ m, t 0+ iT Obs/ m) the corresponding initial time of phase value is not t 0Below, the present invention investigates i the observation corresponding initial time of phase value at interval of acquisition.The present invention supposes that the recurrence interval is P 0, the speed of spacecraft on the pulsar direction of visual lines is v, i observation first impulse phase at interval is
Figure BDA00002865880300045
Wherein,
Figure BDA00002865880300046
Therefore, i observation k impulse phase at interval is
Figure BDA00002865880300047
θ k i = θ k - 1 i + 2 π · v c = θ 0 i + 2 π · v · k c - - - ( 2 )
Wherein, c is the light velocity.
The present invention supposes during observation is at interval K pulse arranged, and the span of k is 0,1 ... K-1.When adopting approximate right method of estimation, the impulse phase at i observation interval of acquisition For
Figure BDA000028658803000410
Average, can calculate by formula 3:
Figure BDA000028658803000411
This impulse phase equals the phase place of (K-1)/2 pulse, i the observation phase value at interval that promptly obtains Corresponding to i the observation middle moment at interval,
Figure BDA000028658803000413
With i observation impulse phase at interval
Figure BDA000028658803000414
Be converted into pulse arrival time t i, as shown in Equation 4:
Figure BDA00002865880300051
Wherein, n iBe the pulse number of cycles between spacecraft and the solar system barycenter,
Figure BDA00002865880300052
Be at solar system barycenter
Figure BDA00002865880300053
Corresponding constantly impulse phase.P 0Be the recurrence interval.
Among the embodiment, utilize nearly maximum Likelihood to estimate that phase place obtains the impulse phase estimated value as the formula (1)
Figure BDA00002865880300054
Then as the formula (4) with the impulse phase estimated value that obtains
Figure BDA00002865880300055
As i observation impulse phase at interval
Figure BDA00002865880300056
Be converted into pulse arrival time t iGet final product.In the present embodiment, the recurrence interval P of Crab pulsar 0Be 0.0334s.
Step 3: with Least Square in Processing step 2 gained pulse arrival time t i, can obtain spacecraft position and speed.
According to step 2, it is right that the present invention obtains a series of data,
Figure BDA00002865880300057
I=1,2 ... m.
Figure BDA00002865880300058
With pulse arrival time t iBetween relation as follows:
c · t i = r ^ + v ^ · ( i - 1 2 ) T obs m - - - ( 5 )
Wherein, With
Figure BDA000028658803000511
For spacecraft at t 0Position and speed constantly, c is the light velocity.
Therefore, position and velocity estimation value is as follows:
r ^ = c · Σ i = 1 m t i m - v ^ Σ i = 1 m ( i - 1 2 ) T obs m m = c · Σ i = 1 m t i m - v ^ · T obs 2 - - - ( 6 )
v ^ = m · Σ i = 1 m [ ( i - 1 2 ) · T obs m · t i · c ] - Σ i = 1 m [ ( i - 1 2 ) · T obs m ] · Σ i = 1 m [ t i · c ] m · Σ i = 1 m [ ( i - 1 2 ) · T obs m ] 2 - { Σ i = 1 m [ ( i - 1 2 ) · T obs m ] } 2 = 6 · T obs - 1 · c · Σ i = 1 m ( 2 i - m - 1 ) t i m 2 - 1 - - - ( 7 )
Specific embodiment described herein only is that the present invention's spirit is illustrated.The technician of the technical field of the invention can make various modifications or replenishes or adopt similar mode to substitute described specific embodiment, but can't depart from spirit of the present invention or surmount the defined scope of appended claims.

Claims (4)

1. pulsar navigation position and velocity joint method of estimation is characterized in that: may further comprise the steps,
Step 1, total observation time is (t at interval 0, t f) be divided into m observation that equates at interval, (t 0+ (i-1) T Obs/ m, t 0+ iT Obs/ m), i=1,2 ... m, wherein, observation time is T Obs=t f-t 0
Step 2 in each observation interval, is pressed pulsar cycle superimposed pulse signal, obtains pulse and accumulates sub-profile, utilizes accurate maximum Likelihood to estimate the impulse phase estimated value then
Figure FDA00002865880200011
According to gained impulse phase estimated value
Figure FDA00002865880200012
Conversion obtains pulse arrival time t i
Step 3 is with Least Square in Processing step 2 gained pulse arrival time t i, obtain spacecraft position and speed.
2. according to claim 1 described pulsar navigation position and velocity joint method of estimation, it is characterized in that: in the step 2, describedly utilize accurate maximum Likelihood to estimate the impulse phase estimated value
Figure FDA00002865880200013
As shown in the formula,
Figure FDA00002865880200014
Wherein, function h () is a normalization full sized pules profile,
Figure FDA00002865880200015
Be i observation son pile-up pulse profile at interval, θ and
Figure FDA00002865880200016
The expression phase place.
3. according to claim 2 described pulsar navigation position and velocity joint method of estimation, it is characterized in that: in the step 2, gained impulse phase estimated value Conversion obtains pulse arrival time t iImplementation be, with the impulse phase estimated value
Figure FDA00002865880200018
As i observation impulse phase at interval
Figure FDA00002865880200019
Adopt following formula to change,
Figure FDA000028658802000110
Wherein, n iBe the pulse number of cycles between spacecraft and the solar system barycenter,
Figure FDA000028658802000111
It is solar system barycenter
Figure FDA000028658802000112
Corresponding constantly phase place, P 0Be the recurrence interval.
4. according to claim 3 described pulsar navigation position and velocity joint method of estimation, it is characterized in that: in the step 3, press the estimated value that following formula obtains spacecraft position and speed
Figure FDA000028658802000113
r ^ = c · Σ i = 1 m t i m - v ^ · T obs 2
v ^ = 6 · T obs - 1 · c · Σ i = 1 m ( 2 i - m - 1 ) t i m 2 - 1
Wherein, c is the light velocity.
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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103776454A (en) * 2014-01-21 2014-05-07 西安电子科技大学 Maximum likelihood phase estimation method based on X-ray pulsar
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
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
CN104567937A (en) * 2015-01-27 2015-04-29 中国空间技术研究院 High-precision X-ray pulsar signal simulation method
CN103954279B (en) * 2014-05-19 2016-08-17 武汉科技大学 Doppler's differential speed measuring model and the method with X-ray pulsar integrated navigation
CN109186612A (en) * 2018-09-06 2019-01-11 武汉科技大学 Fast-pulse star phase estimate method based on compressed sensing and carat Mei Lao circle
CN111649735A (en) * 2020-06-12 2020-09-11 中国空间技术研究院 Pulsar signal noise reduction method based on photon probability
CN113375697A (en) * 2021-06-23 2021-09-10 西安电子科技大学 X-ray pulsar signal time delay estimation method based on maximum posterior estimation

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101038169A (en) * 2007-02-13 2007-09-19 北京空间飞行器总体设计部 Navigation satellite autonomous navigation system and method based on X-ray pulsar
CN102175246A (en) * 2010-12-31 2011-09-07 北京航空航天大学 Spacecraft navigation system for equivalent device of X pulsar detector

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101038169A (en) * 2007-02-13 2007-09-19 北京空间飞行器总体设计部 Navigation satellite autonomous navigation system and method based on X-ray pulsar
CN102175246A (en) * 2010-12-31 2011-09-07 北京航空航天大学 Spacecraft navigation system for equivalent device of X pulsar detector

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
李建勋等: "基于泊松模型的X射线脉冲星信号的最大似然TOA估计", 《天文学报》, vol. 51, no. 3, 31 July 2010 (2010-07-31), pages 264 - 269 *
李建勋等: "基于脉冲星定时模型的自主导航定位方法", 《中国科学 G辑：物理学 力学 天文学》, vol. 39, no. 2, 31 December 2009 (2009-12-31), pages 311 - 316 *
李建勋等: "基于非齐次Poisson过程的脉冲星到达信号的最大似然相位估计", 《信号处理》, vol. 26, no. 8, 31 August 2010 (2010-08-31) *
费保俊等: "X射线脉冲星自主导航的光子到达时间转换", 《空间科学学报》, vol. 30, no. 1, 31 December 2010 (2010-12-31), pages 85 - 90 *

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* Cited by examiner, † Cited by third party
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CN103776454A (en) * 2014-01-21 2014-05-07 西安电子科技大学 Maximum likelihood phase estimation method based on X-ray pulsar
CN103776454B (en) * 2014-01-21 2016-08-17 西安电子科技大学 Maximum likelihood phase estimation method based on X-ray pulsar
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
CN103900577B (en) * 2014-04-14 2016-08-17 武汉科技大学 A kind of Relative Navigation towards formation flight tests the speed and Combinated navigation method
CN103954279B (en) * 2014-05-19 2016-08-17 武汉科技大学 Doppler's differential speed measuring model and the method with X-ray pulsar integrated navigation
CN104535067B (en) * 2015-01-14 2017-05-24 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
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
CN104567937A (en) * 2015-01-27 2015-04-29 中国空间技术研究院 High-precision X-ray pulsar signal simulation method
CN104567937B (en) * 2015-01-27 2017-08-29 中国空间技术研究院 A kind of high-precision X-ray pulsar signal imitation method
CN109186612A (en) * 2018-09-06 2019-01-11 武汉科技大学 Fast-pulse star phase estimate method based on compressed sensing and carat Mei Lao circle
CN109186612B (en) * 2018-09-06 2021-09-24 武汉科技大学 Rapid pulsar period estimation method based on compressed sensing and Clamei bound
CN111649735A (en) * 2020-06-12 2020-09-11 中国空间技术研究院 Pulsar signal noise reduction method based on photon probability
CN111649735B (en) * 2020-06-12 2021-11-16 中国空间技术研究院 Pulsar signal noise reduction method based on photon probability
CN113375697A (en) * 2021-06-23 2021-09-10 西安电子科技大学 X-ray pulsar signal time delay estimation method based on maximum posterior estimation
CN113375697B (en) * 2021-06-23 2022-09-23 西安电子科技大学 X-ray pulsar signal time delay estimation method based on maximum posterior estimation

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