CN104316048A - Method for building universal pulsar-based autonomous navigation measurement model - Google Patents

Abstract

The invention provides a method for building a universal pulsar-based autonomous navigation measurement model. The method comprises calculating the geometric delay of a pulsar pulse signal, the physical delay of the signal, time coordinate transformation correction and double-star orbital motion delay, respectively, and then building the universal pulsar-based autonomous navigation measurement model and a pulsar-based autonomous navigation observation equation. According to the method for building the universal pulsar-based autonomous navigation measurement model, a brand-new pulsar-based navigation measurement model is provided, which is capable of theoretically reaching the calculation accuracy of 1ns; and meanwhile, the space motion velocity of the pulsar and the time delay effect of the impulsion double-star orbital motion are taken into account.

Description

A kind of pulsar independent navigation measurement model construction method of universality

Technical field

The present invention relates to a kind of pulsar independent navigation measurement model, be applicable to all kinds of spacecraft independent navigation fields based on pulsar.

Background technology

The pulsar rotation period is highly stable, and its Spin parameters and uranometry parameter can high-precision measurings.One component is distributed in space all directions, and its locus coordinate and rotation model form inertia space-time frame of reference through the pulsar accurately measured, and can be used for all kinds of aircraft independent navigation.The basis of pulsar independent navigation builds high-precision pulsar navigation measurement model and observations of pulsar equation.At present, in the associated pulsation star independent navigation document delivered, about the measurement model of pulsar navigation, substantially the model of doctor Sheikh has all been continued to use (see Sheikh S I.the Use of Variable Celestial X Ray Sources for Spacecraft Navigation [D], Ph.D Dissertation.Dept.of Aerospace Engineering, University of Marylan, UMI, 2005).This model provides, and pulsar pulse arrives aircraft moment and the difference expression formula arriving the solar system barycenter moment, and this expression formula strictly can not describe the relation between pulsar pulse arrival aircraft moment and pulsar impulse ejection moment.Based on the pulsar navigation observation equation that Sheikh model is set up, introduce solar system barycenter inadequately relative to heliocentric position vector, do not eliminate solar system Shapiro delayed impact completely, do not comprise the single order Doppler delay that the relative solar system centroid velocity of pulsar causes, the orbital motion not relating to binary pulsar postpones correct problems.In addition, Sheikh model observes the Pulsar timing model adopted inconsistent with the radio timing of setting up pulsar ephemeris (rotation model parameter and uranometry parameter), when actual navigation application, and meeting drawing-in system error artificially.Application number be 200710191527.7 Chinese patent document disclose a kind of Combinated navigation method of Multi-information acquisition.Application number be 200910063267.4 Chinese patent document disclose a kind of pulsar/CNS Combinated navigation method.These documents, discuss the filtering algorithm problem of pulsar navigation, in principle, still based on measurement model and the observation equation of Sheikh.

Summary of the invention

In order to overcome the deficiencies in the prior art, the invention provides a kind of strict pulsar navigation measurement model of universality, this model strictly describes the theory relation between pulsar pulse arrival aircraft moment and pulsar impulse ejection moment, and is consistent with Pulsar timing observation model.Meanwhile, the navigation model provided take into account the impact of pulsar spatial movement speed and the impact of binary pulsar orbital motion, is a kind of more applicable pulsar navigation model.

The technical solution adopted for the present invention to solve the technical problems comprises the following steps:

1. build pulsar navigation measurement model

(1) geometric delay of pulsar pulse signal is calculated

${\mathrm{\Δ}}_g=\frac{1}{c}[(\hat{n}\·\stackrel{\→}{V})\mathrm{\Δt}-(\hat{n}\·\stackrel{\→}{r})]+\frac{1}{2c{R}_0}[r^2-{(\hat{n}\·\stackrel{\→}{r})}^2]-\frac{1}{c{R}_0}[\stackrel{\→}{V}\·\stackrel{\→}{r}-(\hat{n}\·\stackrel{\→}{V})(\hat{n}\·\stackrel{\→}{r})]\mathrm{\Δt}+\frac{1}{2c{R}_0}[V^2-{(\hat{n}\·\stackrel{\→}{V})}^2]{\left(\mathrm{\Δt}\right)}^2$

Wherein, at ephemeris with reference in epoch, solar system center-of-mass system, pulsar unit vector is relative solar system centroid distance is R ₀, spatial movement speed is observation moment satellite relative solar system barycenter vector is observation moment and ephemeris are Δ t with reference to difference epoch, and the light velocity is c;

(2) physical delay of signal is calculated

${\mathrm{\Δ}}_{\mathrm{Sh}}=-\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{{2\mathrm{GM}}_k}{c^3}\ln |\hat{n}\·{\stackrel{\→}{r}}_k+r_k|+\frac{4G^2{m}_{\mathrm{\Θ}}^2}{c^5{r}_{\mathrm{\Θ}}\tan \mathrm{\ψ}\sin \mathrm{\ψ}}$

Wherein, PB _sSbe the main celestial body number of the solar system, G is Newtonian gravitational constant, M _ka kth celestial body in solar system quality, the vector of the relative kth of a satellite celestial body in solar system, r _kbe mould, m _Θsolar mass, r _Θbe satellite to sun distance, ψ is the subtended angle of the sun and pulsar relative satellite;

(3) computing time, coordinate conversion corrected Δ t _c

${\mathrm{\Δt}}_C=L_G(t_{\mathrm{TCG}}-t_0)+\frac{1}{c^2}{\stackrel{\→}{r}}_S\·{\stackrel{\→}{v}}_E+{\∫}_{t_0}^{t_{\mathrm{TCB}}}[\frac{1}{c^2}(U_E+\frac{v_E^2}{2})+\mathrm{\Δ}{L}_C^{\left(\mathrm{PN}\right)}+\mathrm{\Δ}{L}_C^{\left(A\right)}]{\mathrm{dt}}_{\mathrm{TCB}}+\frac{V^2}{2c^2}(t_{\mathrm{BB}}-t_{\mathrm{pos}})$

Wherein t ₀corresponding JD=2443144.5003725, t _tCGthe TCG moment, w ₀terrestrial gravitation gesture and the rotation gesture sum at Geoid place, the position vector of observation moment satellite relative to the earth's core, be the earth's core relative to solar system velocity vector of enter of mass, t _tCBbe the TCB moment, celestial body in solar system is in the gravitational potential at the earth's core place m _jthe quality removing extratellurian J celestial body in solar system, r _eJthe distance that the earth arrives this celestial body, the impact of relativity higher order term, represent all asteroid impacts of the solar system, t _bBarrive the double star barycenter moment, t with the pulsar pulse that double star barycentric coordinate time represents _posthat pulsar ephemeris is with reference to epoch;

(4) calculate double star orbital motion and postpone Δ t _ob, Δ t _obcomprise Roemer delay, Einstein postpones, Shapiro postpones and aberration postpones;

(5) the pulsar independent navigation measurement model of universality

The clock correction supposing satellite clock is δ t, and it is t that the X-ray detector be arranged on satellite observes the pulsar pulse obtained arrive the satellite moment within integral time _obs, the impulse ejection moment of pulsar rotation model prediction is expressed as t _p, closing therebetween is t _p-t _obs=-Δ _g-Δ _sh+ Δ t _c-Δ t _ob+ δ t, obtains the pulsar navigation measurement model of universality:

$\begin{array}{c}{t}_p-t_{\mathrm{obs}}=\mathrm{\Δ}\widetilde{t_C}-\frac{1}{c}[(\hat{n}\·\stackrel{\→}{V})\mathrm{\Δt}-(\hat{n}\·\widetilde{\stackrel{\→}{r}})]-\frac{1}{2c{R}_0}[{\tilde{r}}^2-{(\hat{n}\·\widetilde{\stackrel{\→}{r}})}^2]+\frac{1}{c{R}_0}[\stackrel{\→}{V}\·\widetilde{\stackrel{\→}{r}}-(\hat{n}\·\stackrel{\→}{V})(\hat{n}\·\widetilde{\stackrel{\→}{r}})]\mathrm{\Δt}\\ -\frac{1}{2c{R}_0}[V^2-{(\hat{n}\·\stackrel{\→}{V})}^2]{\left(\mathrm{\Δt}\right)}^2+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{{2\mathrm{GM}}_k}{c^3}\ln |\hat{n}\·\widetilde{\stackrel{\→}{r_k}}+\widetilde{r_k}|-\frac{4G^2{m}_{\mathrm{\Θ}}^2}{c^5\widetilde{r_{\mathrm{\Θ}}}\tan \widetilde{\mathrm{\ψ}}\sin \widetilde{\mathrm{\ψ}}}-\mathrm{\Δ}\widetilde{t_{\mathrm{ob}}}\\ +\frac{1}{c}[\hat{n}-\frac{1}{R_0}\widetilde{\stackrel{\→}{r}}+\frac{1}{R_0}(\hat{n}\·\widetilde{\stackrel{\→}{r}})\hat{n}+\frac{1}{R_0}\stackrel{\→}{V}\mathrm{\Δt}-\frac{1}{R_0}(\hat{n}\·\stackrel{\→}{V}\mathrm{\Δt})\hat{n}+\frac{1}{c}{\stackrel{\→}{v}}_E+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}(\frac{{2\mathrm{GM}}_k}{c^2}\·\frac{\hat{n}+\frac{\widetilde{\stackrel{\→}{r_k}}}{\widetilde{r_k}}}{\hat{n}\·\widetilde{\stackrel{\→}{r_k}}+\widetilde{r_k}}){]}^T\mathrm{\δ}\stackrel{\→}{r}+\mathrm{\δt}\end{array};$

2. build pulsar independent navigation observation equation

$\begin{array}{c}{t}_p-t_{\mathrm{pobs}}=\\ \frac{1}{c}{[\hat{n}-\frac{1}{R_0}\widetilde{\stackrel{\→}{r}}+\frac{1}{R_0}(\hat{n}\·\widetilde{\stackrel{\→}{r}})\hat{n}+\frac{1}{R_0}\stackrel{\→}{V}\mathrm{\Δt}-\frac{1}{R_0}(\hat{n}\·\stackrel{\→}{V}\mathrm{\Δt})\hat{n}+\frac{1}{c}{\stackrel{\→}{v}}_E+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}(\frac{{2\mathrm{GM}}_k}{c^2}\·\frac{\hat{n}+\frac{\widetilde{\stackrel{\→}{r_k}}}{\widetilde{r_k}}}{\hat{n}\·\widetilde{\stackrel{\→}{r_k}}+\widetilde{r_k}})]}^T\mathrm{\δ}\stackrel{\→}{r}+\mathrm{\δt}\end{array}.$

The invention has the beneficial effects as follows: give brand-new pulsar navigation measurement model, model comprises pulsar pulse geometric delay, physical delay and time coordinate conversion and calculates, and in theory, model can reach 1ns computational accuracy.Meanwhile, model take into account pulsar spatial movement speed and binary pulsar orbital motion time delay effect, is a kind of more applicable pulsar navigation model.

Embodiment

Below in conjunction with embodiment, the present invention is further described, the present invention includes but be not limited only to following embodiment.

The pulsar independent navigation measurement model of universality, refers to the measurement model of all kinds of spacecraft independent navigations based on X-ray pulse Solo and bi-orbiters.Pulsar navigation measurement model describes to measure the pulsar pulse that obtains and arrive the spacecraft moment (TOA) and the theoretical model of relation between the pulsar impulse ejection moment.When building pulsar navigation measurement model, we are decomposed into the vacuum geometric delay (for X ray wave band, Dispersion of Media postpone can ignore) of pulsar pulse signal, physical delay and reference frame conversion it and calculate.To the calculating of this three, sets forth analytical expression and algorithm, all can reach the precision being better than 1ns in theory.For binary pulsar, navigation measurement model must calculate the delay that pulsar orbital motion causes.Pulsar orbital motion postpones to comprise geometric delay, companion star's gravitation postpones, time coordinate conversion and the aberration that causes relative to double star barycenter transverse velocity due to pulsar postpone.The calculating that binary pulsar orbital motion postpones is based on single order post newton method orbital motion.

On the pulsar independent navigation measurement model basis building universality, give the observation equation of pulsar navigation.Pulsar navigation observation equation is relevant with pulsar pulse TOA measuring method.Consider aircraft relative to pulsar motion to the impact building high s/n ratio pulse profile, we utilize the position vector adopted value of pulsar navigation measurement model and observation moment aircraft, each x-ray photon TOA that X-ray detector measurement is obtained, convert the photo emissions moment of pulsar to, thus pulsar position (not being solar system barycenter), build high s/n ratio integrated pulse profile.Again by comparing with the full sized pules profile of pulsar position, obtain the pulsar impulse ejection moment observed.In this case, observations of pulsar equation describes, the relation between the same impulse ejection moment that impulse ejection moment of pulsar rotation model prediction and observing on board the aircraft obtains.The difference of the two is the error of position of aircraft vector adopted value and the function of aircraft clock clock correction.

Below for the navigation of the earth satellite of apply pulse star, the construction method of pulsar navigation measurement model is described:

1. build pulsar navigation measurement model

(1) geometric delay of signal

Signal Geometrical propagation postpones mainly accurate Calculation and observes moment pulsar relative to the position vector of spacecraft, and for reaching 1ns precision, computing formula must comprise single order item and the second order term of pulsar spatial movement speed.Suppose that in solar system center-of-mass system, pulsar (or binary pulsar barycenter) unit vector is at ephemeris (comprising pulsar Spin parameters and uranometry parameter) with reference to epoch relative solar system centroid distance is R ₀, spatial movement speed is (can be analyzed to proper motion in right ascension, proper motion in declination and radial velocity component), observation moment satellite relative solar system barycenter vector is observation moment and ephemeris are Δ t with reference to difference epoch, and the light velocity is c, are ignoring signal propagation R ₀in constant range delay situation, the geometric delay of pulsar pulse signal can calculate with following formula.

${\mathrm{\Δ}}_g=\frac{1}{c}[(\hat{n}\·\stackrel{\→}{V})\mathrm{\Δt}-(\hat{n}\·\stackrel{\→}{r})]+\frac{1}{2c{R}_0}[r^2-{(\hat{n}\·\stackrel{\→}{r})}^2]-\frac{1}{c{R}_0}[\stackrel{\→}{V}\·\stackrel{\→}{r}-(\hat{n}\·\stackrel{\→}{V})(\hat{n}\·\stackrel{\→}{r})]\mathrm{\Δt}+\frac{1}{2c{R}_0}[V^2-{(\hat{n}\·\stackrel{\→}{V})}^2]{\left(\mathrm{\Δt}\right)}^2---\left(1\right)$

Formula (1) is also the precise calculation that solar system Roemer postpones, and includes speed doppler delay, even if for the larger pulsar of movement velocity, formula (1) can reach the computational accuracy of 1ns.Formula (1) have ignored and above item, for pulsar navigation application, ignore the error of item much smaller than 1ns.

(2) physical delay of signal

Signal physical delay refers to that solar system Shapiro postpones, and the expression formula only comprising single order item is as follows:

${\mathrm{\Δ}}_{\mathrm{Sh}1}=-\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{{2\mathrm{GM}}_k}{c^3}\ln \left|\frac{\hat{n}\·{\stackrel{\→}{r}}_k+r_k}{2R_0}\right|=\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{2{\mathrm{GM}}_k}{c^3}\ln \left(2R_0\right)-\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{{2\mathrm{GM}}_k}{c^3}\ln |\hat{n}\·{\stackrel{\→}{r}}_k+r_k|$

On the right of above formula, Section 1 is constant term, is ignored, and consider the second order term (only calculating sun impact) that Shapiro postpones, the actual Shapiro Delay computing formula adopted is

${\mathrm{\Δ}}_{\mathrm{Sh}}=-\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{{2\mathrm{GM}}_k}{c^3}\ln |\hat{n}\·{\stackrel{\→}{r}}_k+r_k|+\frac{4G^2{m}_{\mathrm{\Θ}}^2}{c^5{r}_{\mathrm{\Θ}}\tan \mathrm{\ψ}\sin \mathrm{\ψ}}---\left(2\right)$

In formula (2), PB _sSbe the main celestial body number of the solar system, G is Newtonian gravitational constant, M _ka kth celestial body in solar system quality, the vector of the relative kth of a satellite celestial body in solar system, r _kbe mould.M _Θsolar mass, r _Θbe satellite to sun distance, ψ is the subtended angle of the sun and pulsar relative satellite.Formula (2) is consistent with the correlation formula of the radio timing model determining pulsar ephemeris.

(3) reference frame conversion

The fundamental reference system of pulsar navigation is solar system barycenter inertial reference system, and for the purpose of convenience of calculation, pulsar navigation theoretical model needs the conversion carrying out reference frame to calculate.In reference frame conversion calculates, relativity transformer effect of space length is less than 1ns, can ignore.The most complicated is the calculating that between different reference frame, time coordinate is changed, and corrects also referred to as Einstein.Suppose that earth satellite clock is synchronous with terrestrial time TT, need calculating observation moment TT to geocentric coordinate time (TCG) conversion, TCG to solar system barycentric coordinate time (TCB) conversion and TCB to the transfer problem of binary pulsar barycentric coordinate time.TT and TCG closes

TCG-TT＝L _G(t _TCG-t ₀) (3)

Wherein t ₀corresponding JD=2443144.5003725, t _tCGthe TCG moment, w ₀being terrestrial gravitation gesture and the rotation gesture sum at Geoid place, is known quantity.TCG and TCB closes

$\mathrm{TCB}-\mathrm{TCG}=\frac{1}{c^2}{\stackrel{\→}{r}}_S\·{\stackrel{\→}{v}}_E+{\∫}_{t_0}^{t_{\mathrm{TCB}}}[\frac{1}{c^2}(U_E+\frac{v_E^2}{2})+\mathrm{\Δ}{L}_C^{\left(\mathrm{PN}\right)}+\mathrm{\Δ}{L}_C^{\left(A\right)}]{\mathrm{dt}}_{\mathrm{TCB}}---\left(4\right)$

In formula (4) the position vector of observation moment satellite relative to the earth's core, be the earth's core relative to solar system velocity vector of enter of mass, provided by position of the earth ephemeris, t _tCBbe the TCB moment, celestial body in solar system is in the gravitational potential at the earth's core place m _jthe quality of extratellurian J the celestial body in solar system of removing (not containing asteroid), r _eJit is the distance that the earth arrives this celestial body.In integrand be the impact of relativity higher order term, the impact of relativity higher order term can be analyzed to linear term and periodic term, and its periodic term is negligible. represent all asteroid impacts of the solar system, asteroid impact can be analyzed to linear term and periodic term equally, and its periodic term is very little, can ignore completely.Usually with utilize U.S. JPL celestial body in solar system ephemeris to analyze and research separately to determine, their value is respectively with formula (4) integration item must utilize JPL DE ephemeris to adopt numerical integrating to calculate, integration starting point t ₀corresponding to JD=2443144.5003725.Numerical integration computational accuracy reaches 0.1ns.The result of calculation of numerical integration is referred to as ephemeris between terrestrial time, and between terrestrial time, ephemeris forms the basis of TCG to TCB conversion, can directly utilize ephemeris between terrestrial time computed in advance to carry out interpolation when practical application.It should be noted that, containing U in integrand _eand v _ethe integral result of item can be decomposed into linear term and periodic term two parts, makes its linear term coefficient be Δ L _c, according to the analysis result of DE405, have Δ L _c=1.48082685594 × 10 ^-8.Order here, L _caccurately determine it is necessary, because L _b=L _c+ L _g(vide infra) is as the linear coefficient of linear transformation between TDB and TCB.At L _cafter determining, some authors define ephemeris between terrestrial time and only include periodic term part, in this case, when time coordinate conversion calculates, utilize the interpolation results of time ephemeris must add all linear components and correct, be i.e. L _c(t _tCB-t ₀) value.At present, the Tempo2 software systems of radio timing observation, adopt ephemeris between the terrestrial time that calculates based on DE405 ephemeris.Upgrade the high-precision JPL ephemeris of version if adopted, likely obtain ephemeris between more high-precision terrestrial time.Obviously, terrestrial time TT is transformed into the calculating of barycentric coordinate time TCB, should be above-mentioned formula (3) and formula (4) sum.For keep high precision, TT be transformed into TCG and TCG be transformed into TCB calculate must adopt iterative algorithm.TCB is transformed into for TCG, the time variable on formula (4) the right is TCB instead of TCG yardstick, the known TCG moment should be first adopted to calculate TCB, using the TCB that calculates first as time variable, again new TCB is calculated by formula (4) again, to obtain high-precision conversion result of calculation.In general, only need iteration once just passable.

According to International Astronomical association (IAU) resolution in 2006, barycentric dynamical time (TDB) TDB and barycentric coordinate time TCB has following relation,

TDB＝TCB-L _B×(JD _TCB-T ₀)×86400+TDB ₀ (5)

In formula (5), T ₀=2443144.5003725JD,

L _B＝L _C+L _G＝1.550519768×10 ^-8，

TDB ₀＝-6.55×10 ^-5s。

The TDB of such definition can think the time variable of JPL DE405.Needing to be utilized by known TCB formula (5) to convert TDB to, the coordinate figure exported by DE405 when reading DE405, needing to be multiplied by K again ^-1, to be transformed into SI units system.Here, scale factor K=1+L _b.When time coordinate conversion calculates employing redaction JPL ephemeris, ephemeris, L between the terrestrial time of its correspondence _cand TDB ₀the possibility of result Deng constant and DE405 has little difference, based on redaction JPL ephemeris terrestrial time between the analysis and research work of ephemeris and dependent constant thereof be necessary.

Suppose that the relative velocity of solar system barycenter and binary pulsar barycenter is barycentric coordinate time TCB be transformed into double star barycentric coordinate time (for pulse list star, be then TCB be transformed into pulsar former time), need to consider special relativity time dilation, have

${\mathrm{\Δ}}_{\mathrm{ES}}=\frac{V^2}{2c^2}(t_{\mathrm{BB}}-t_{\mathrm{pos}})---\left(6\right)$

T in formula (6) _bBthat the pulsar pulse represented with double star barycentric coordinate time arrives the double star barycenter moment (pulse arrives the solar system barycenter moment and is transformed into same pulse and arrives the double star barycenter moment, during calculating, usually neglects pulsar distance R ₀corresponding light time).T _posthat pulsar ephemeris is with reference to epoch.Owing to calculating Δ _eStime, we do not know t _bB, only know that pulse arrives the TCB moment of double star barycenter, therefore formula (6) needs to adopt iterative algorithm.First calculate Δ with the TCB moment of pulse arrival double star barycenter _eS, the TCB moment then pulse being arrived double star barycenter adds the Δ that first time calculates _eSas t _bB, then recalculate Δ _eS.General iteration is once just much of that.

Make Δ t _crepresent that time coordinate conversion is corrected, Δ t _cequal above-mentioned formula (3), (4) and (6) sum.

(4) binary pulsar orbital motion postpones

In general, binary pulsar timing model parameter provides the Keplerian orbit parameter of binary pulsar: projection semi-major axis of orbit, orbital period, excentricity, periastron time and periastron argument, on different accuracy, also provide relativity parameter of double star orbital motion simultaneously, as: the advance of periastron, orbital period derivative, pulsar and companion star's quality etc.Based on general relativity, application kepler parameters and double star mass parameter can also derive other relevant parameters.Utilize these parameters, we can calculate double star orbital motion easily and postpone Δ t _ob, Δ t _obcomprise: Roemer postpones, Einstein postpones, Shapiro postpones and aberration postpones.Document " Tempo2:Timing model and precision " summarizes binary pulsar orbital motion achievement in research, describe binary pulsar timing model and the precision thereof of the employing of Tempo2 software systems, give computing formula and the algorithm of all kinds double star orbital motion delay, Δ t can be directly applied to _obcalculating.

(5) the pulsar independent navigation measurement model of universality

The clock correction supposing satellite clock is δ t, and be arranged on X-ray detector on satellite within certain integral time, observing the pulsar pulse obtained arrive the satellite moment (TOA) is t _obs, the impulse ejection moment of pulsar rotation model prediction is expressed as t _p, pass is therebetween

t _p-t _obs＝-Δ _g-Δ _Sh+Δt _C-Δt _ob+δt (7)

Formula (1) and (2) are substituted into formula (7), Wo Menyou

$\begin{array}{c}{t}_p-t_{\mathrm{obs}}=\mathrm{\Δ}{t}_C-\frac{1}{c}[(\hat{n}\·\stackrel{\→}{V})\mathrm{\Δt}-(\hat{n}\·\stackrel{\→}{r})]-\frac{1}{2c{R}_0}[r^2-{(\hat{n}\·\stackrel{\→}{r})}^2]+\frac{1}{c{R}_0}[\stackrel{\→}{V}\·\stackrel{\→}{r}-(\hat{n}\·\stackrel{\→}{V})(\hat{n}\·\stackrel{\→}{r})]\mathrm{\Δt}\\ -\frac{1}{2c{R}_0}[V^2-{(\hat{n}\·\stackrel{\→}{V})}^2]{\left(\mathrm{\Δt}\right)}^2+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{{2\mathrm{GM}}_k}{c^3}\ln |\hat{n}\·{\stackrel{\→}{r}}_k+r_k|-\frac{4G^2{m}_{\mathrm{\Θ}}^2}{c^5{r}_{\mathrm{\Θ}}\tan \mathrm{\ψ}\sin \mathrm{\ψ}}-\mathrm{\Δ}{t}_{\mathrm{ob}}+\mathrm{\δt}\\ \end{array}---\left(8\right)$

In formula (8), the meaning of each symbol is the same, Δ t _cthat time coordinate conversion is corrected, Δ t _obthat double star track postpones.

In actual navigation application, the apparent position vector of satellite known, be error, then

$\stackrel{\→}{r}=\widetilde{\stackrel{\→}{r}}+\mathrm{\δ}\stackrel{\→}{r}---\left(9\right)$

Formula (9) is substituted into formula (8), and by nonlinear terms linearization, obtains

$\begin{array}{c}{t}_p-t_{\mathrm{obs}}=\mathrm{\Δ}\widetilde{t_C}-\frac{1}{c}[(\hat{n}\·\stackrel{\→}{V})\mathrm{\Δt}-(\hat{n}\·\widetilde{\stackrel{\→}{r}})]-\frac{1}{2c{R}_0}[{\tilde{r}}^2-{(\hat{n}\·\widetilde{\stackrel{\→}{r}})}^2]+\frac{1}{c{R}_0}[\stackrel{\→}{V}\·\widetilde{\stackrel{\→}{r}}-(\hat{n}\·\stackrel{\→}{V})(\hat{n}\·\widetilde{\stackrel{\→}{r}})]\mathrm{\Δt}\\ -\frac{1}{2c{R}_0}[V^2-{(\hat{n}\·\stackrel{\→}{V})}^2]{\left(\mathrm{\Δt}\right)}^2+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{{2\mathrm{GM}}_k}{c^3}\ln |\hat{n}\·\widetilde{\stackrel{\→}{r_k}}+\widetilde{r_k}|-\frac{4G^2{m}_{\mathrm{\Θ}}^2}{c^5\widetilde{r_{\mathrm{\Θ}}}\tan \widetilde{\mathrm{\ψ}}\sin \widetilde{\mathrm{\ψ}}}-\mathrm{\Δ}\widetilde{t_{\mathrm{ob}}}\\ +\frac{1}{c}[\hat{n}-\frac{1}{R_0}\widetilde{\stackrel{\→}{r}}+\frac{1}{R_0}(\hat{n}\·\widetilde{\stackrel{\→}{r}})\hat{n}+\frac{1}{R_0}\stackrel{\→}{V}\mathrm{\Δt}-\frac{1}{R_0}(\hat{n}\·\stackrel{\→}{V}\mathrm{\Δt})\hat{n}+\frac{1}{c}{\stackrel{\→}{v}}_E+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}(\frac{{2\mathrm{GM}}_k}{c^2}\·\frac{\hat{n}+\frac{\widetilde{\stackrel{\→}{r_k}}}{\widetilde{r_k}}}{\hat{n}\·\widetilde{\stackrel{\→}{r_k}}+\widetilde{r_k}}){]}^T\mathrm{\δ}\stackrel{\→}{r}+\mathrm{\δt}\end{array}---\left(10\right)$

In formula (10), each symbol with " ~ " represent satellite apparent position vector or by Proximity Vector the physical quantity calculated. formula (3), (4) and (6) sum, utilize observation when the moment, satellite clock was former and satellite position adopted value calculates. be that binary pulsar orbital motion postpones, calculated by double star barycentric coordinate time, double star orbit parameter and satellite position adopted value. unknown quantity to be asked with δ t.If navigation pulsar is single star, about the physical quantity of double star is omitted in formula (1).Formula (10) is the pulsar navigation measurement model of universality.

2. build pulsar independent navigation observation equation

Pulse TOA to be compared with full sized pules profile by observation integrated pulse profile and determines.Each x-ray photon TOA in the X-ray detector observational record lower integral time, if build integrated pulse profile by photon TOA at satellite position, due to the motion of satellite relative pulse star, can make integrated pulse profile fog.For improving signal to noise ratio (S/N ratio), we utilize the removing of formula (10) the right other all known terms sum with beyond δ t item, is transformed into pulsar x-ray photon x time by each x-ray photon TOA, builds integrated pulse profile in pulsar position, by comparing with full sized pules profile, obtains the impulse ejection moment t observed _pobs.So have

$\begin{array}{c}{t}_p-t_{\mathrm{pobs}}=\\ \frac{1}{c}{[\hat{n}-\frac{1}{R_0}\widetilde{\stackrel{\→}{r}}+\frac{1}{R_0}(\hat{n}\·\widetilde{\stackrel{\→}{r}})\hat{n}+\frac{1}{R_0}\stackrel{\→}{V}\mathrm{\Δt}-\frac{1}{R_0}(\hat{n}\·\stackrel{\→}{V}\mathrm{\Δt})\hat{n}+\frac{1}{c}{\stackrel{\→}{v}}_E+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}(\frac{{2\mathrm{GM}}_k}{c^2}\·\frac{\hat{n}+\frac{\widetilde{\stackrel{\→}{r_k}}}{\widetilde{r_k}}}{\hat{n}\·\widetilde{\stackrel{\→}{r_k}}+\widetilde{r_k}})]}^T\mathrm{\δ}\stackrel{\→}{r}+\mathrm{\δt}\end{array}---\left(11\right)$

Formula (11) is the observation equation of pulsar navigation.

Pulsar independent navigation measurement model and observation equation build for earth satellite navigation, in principle, are also applicable to the independent navigation application of deep space exploration aircraft.Such as, the artificial satellite around Mars of apply pulse star navigates, and just time coordinate conversion calculating is different from earth satellite.Need to be transformed into Mars barycentric coordinate time around during Martian satellite former, and then be transformed into solar system barycentric coordinate time (TCB).Mars barycentric coordinate time is transformed into TCB and calculates, and needs to utilize JPL DE series celestial body in solar system ephemeris, adopts numerical integrating method, precalculates and obtain Mars time ephemeris.The construction method of Mars time ephemeris, be quite analogous to geocentric coordinate time (TCG) be transformed into TCB adopt terrestrial time between ephemeris (see " reference frame conversion " trifle).

Claims (1)

1. a pulsar independent navigation measurement model construction method for universality, is characterized in that comprising the steps:

(1) geometric delay of pulsar pulse signal is calculated

${\mathrm{\Δ}}_g=\frac{1}{c}[(\hat{n},\stackrel{\→}{V})\mathrm{\Δt}-(\hat{n}\·\stackrel{\→}{r})]+\frac{1}{2c{R}_0}[r^2-{(\hat{n}\·\stackrel{\→}{r})}^2]-\frac{1}{c{R}_0}[\stackrel{\→}{V}\·\stackrel{\→}{r}-(\hat{n}\·\stackrel{\→}{V})(\hat{n}\·\stackrel{\→}{r})]\mathrm{\Δt}+\frac{1}{2c{R}_0}[V^2-{(\hat{n}\·\stackrel{\→}{V})}^2]{\left(\mathrm{\Δt}\right)}^2$

Wherein, at ephemeris with reference in epoch, solar system center-of-mass system, pulsar unit vector is relative solar system centroid distance is R ₀, spatial movement speed is observation moment satellite relative solar system barycenter vector is observation moment and ephemeris are Δ t with reference to difference epoch, and the light velocity is c;

(2) physical delay of signal is calculated

${\mathrm{\Δ}}_{\mathrm{Sh}}=-\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{2{\mathrm{GM}}_k}{c^3}\ln |\hat{n}\·{\stackrel{\→}{r}}_k+r_k|+\frac{4G^2{m}_{\mathrm{\Θ}}^2}{c^5{r}_{\mathrm{\Θ}}\tan \mathrm{\ψ}\sin \mathrm{\ψ}}$

Wherein, PB _sSbe the main celestial body number of the solar system, G is Newtonian gravitational constant, M _ka kth celestial body in solar system quality, the vector of the relative kth of a satellite celestial body in solar system, r _kbe mould, m _Θsolar mass, r _Θbe satellite to sun distance, ψ is the subtended angle of the sun and pulsar relative satellite;

(3) computing time, coordinate conversion corrected Δ t _c

${\mathrm{\Δt}}_C=L_G(t_{\mathrm{TCG}}-t_0)+\frac{1}{c^2}{\stackrel{\→}{r}}_S\·{\stackrel{\→}{v}}_E+{\∫}_{t_0}^{t_{\mathrm{TCB}}}[\frac{1}{c^2}(U_E+\frac{v_E^2}{2})+{\mathrm{\ΔL}}_C^{\left(\mathrm{PN}\right)}+{\mathrm{\ΔL}}_C^{\left(A\right)}]{\mathrm{dt}}_{\mathrm{TCB}}+\frac{V^2}{2c^2}(t_{\mathrm{BB}}-t_{\mathrm{pos}})$

Wherein t ₀corresponding JD=2443144.5003725, t _tCGthe TCG moment, w ₀terrestrial gravitation gesture and the rotation gesture sum at Geoid place, the position vector of observation moment satellite relative to the earth's core, be the earth's core relative to solar system velocity vector of enter of mass, t _tCBbe the TCB moment, celestial body in solar system is in the gravitational potential at the earth's core place m _jthe quality removing extratellurian J celestial body in solar system, r _eJthe distance that the earth arrives this celestial body, the impact of relativity higher order term, represent all asteroid impacts of the solar system, t _bBarrive the double star barycenter moment, t with the pulsar pulse that double star barycentric coordinate time represents _posthat pulsar ephemeris is with reference to epoch;

(4) calculate double star orbital motion and postpone Δ t _ob, Δ t _obcomprise Roemer delay, Einstein postpones, Shapiro postpones and aberration postpones;

(5) the pulsar independent navigation measurement model of universality

The clock correction supposing satellite clock is δ t, and it is t that the X-ray detector be arranged on satellite observes the pulsar pulse obtained arrive the satellite moment within integral time _obs, the impulse ejection moment of pulsar rotation model prediction is expressed as t _p, closing therebetween is t _p-t _obs=-Δ _g-Δ _sh+ Δ t _c-Δ t _ob+ δ t, obtains the pulsar navigation measurement model of universality:

$\begin{array}{c}{t}_p-t_{\mathrm{obs}}=\mathrm{\Δ}{\tilde{t}}_C-\frac{1}{c}[(\hat{n}\·\stackrel{\→}{V})\mathrm{\Δt}-(\hat{n}\·\stackrel{\widetilde{\→}}{r})-\frac{1}{2c{R}_0}[{\tilde{r}}^2-{(\hat{n},\stackrel{\widetilde{\→}}{r})}^2]+\frac{1}{c{R}_0}[\stackrel{\→}{V}\·\stackrel{\widetilde{\→}}{r}-(\hat{n}\·\stackrel{\→}{V})(\hat{n},\stackrel{\widetilde{\→}}{r})]\mathrm{\Δt}\\ -\frac{1}{2c{R}_0}[V^2-{(\hat{n}\·\stackrel{\→}{V})}^2]{\left(\mathrm{\Δt}\right)}^2+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}\frac{2{\mathrm{GM}}_k}{c^3}\ln |\hat{n}\·{\stackrel{\stackrel{\‾}{\→}}{r}}_k+{\tilde{r}}_k|-\frac{4G^2{m}_{\mathrm{\Θ}}^2}{c^5{\tilde{r}}_{\mathrm{\Θ}}\tan \widetilde{\mathrm{\ψ}}\sin \widetilde{\mathrm{\ψ}}}-\mathrm{\Δ}{\tilde{t}}_{\mathrm{ob}}\\ +\frac{1}{c}{[\hat{n}-\frac{1}{R_0}\stackrel{\widetilde{\→}}{r}+\frac{1}{R_0}(\hat{n}\·\stackrel{\widetilde{\→}}{r})\hat{n}+\frac{1}{R_0}\stackrel{\→}{V}\mathrm{\Δt}-\frac{1}{R_0}(\hat{n}\·\stackrel{\→}{V}\mathrm{\Δt})\hat{n}+\frac{1}{c}{\stackrel{\→}{v}}_E+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}(\frac{2{\mathrm{GM}}_k}{c^2}\·\frac{\hat{n}+\frac{{\stackrel{\widetilde{\→}}{r}}_k}{{\tilde{r}}_k}}{\hat{n}+{\stackrel{\widetilde{\→}}{r}}_k+{\tilde{r}}_k})]}^T\mathrm{\δ}\stackrel{\→}{r}+\mathrm{\δt}\end{array};$

(6) pulsar independent navigation observation equation is built

$\begin{array}{c}{t}_p-t_{\mathrm{pobs}}=\\ \frac{1}{c}{[\hat{n}-\frac{1}{R_0}\stackrel{\widetilde{\→}}{r}+\frac{1}{R_0}(\hat{n}\·\stackrel{\widetilde{\→}}{r})\hat{n}+\frac{1}{R_0}\stackrel{\→}{V}\mathrm{\Δt}-\frac{1}{R_0}(\hat{n}\·\stackrel{\→}{V}\mathrm{\Δt})\hat{n}+\frac{1}{c}{\stackrel{\→}{v}}_E+\underset{k=1}{\overset{{\mathrm{PB}}_{\mathrm{SS}}}{\mathrm{\Σ}}}(\frac{2{\mathrm{GM}}_k}{c^2}\·\frac{\hat{n}+\frac{{\stackrel{\widetilde{\→}}{r}}_k}{{\tilde{r}}_k}}{\hat{n}\·{\stackrel{\widetilde{\→}}{r}}_k+{\tilde{r}}_k})]}^T\mathrm{\δ}\stackrel{\→}{r}+\mathrm{\δt}\end{array}.$