CN103217161B - A kind of pulsar navigation position and velocity joint method of estimation - Google Patents

Abstract

A kind of pulsar navigation position and velocity joint method of estimation, belong to Spacecraft Autonomous Navigation field.First observation interval is divided into multiple sub-interval by the method.Then, in the sub-interval of each observation, by pulsar radiation period superimposed pulse signal to obtain the sub-profile of pulse accumulation, adopt the sub-profile of accurate maximum Likelihood process pulse accumulation to obtain the pulse arrival time at every sub-interval.Finally, according to these pulse arrival times, the least square estimation method is utilized to estimate position and the speed of spacecraft.Location of the present invention and constant speed precision very high, close to the U.S. labor lower bound of carat, and calculated amount is very little.Therefore, the present invention has important practical significance to the 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 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 carries out survey of deep space activity one after another, and accurate navigator fix is prerequisite and the basis of all survey of deep space activities.At present, spacecraft navigation system mainly comprises following several: land station's navigational system, GPS (Global Position System, GPS), gravity navigation system, earth-magnetic navigation system and celestial navigation system (CelestialNavigation System, CNS) etc.But these technology are all not suitable for survey of deep space, and subject matter is as follows: land station's navigational system, GPS, gravity navigation system and earth-magnetic navigation system can only provide navigation information for the spacecraft of the aircraft of earth surface and terrestrial space; CNS installs optical sensitive device on spacecraft, realizes location by the relative position measuring fixed star and nearly celestial body, and its positioning precision affects by the distance between spacecraft and nearly celestial body, cannot meet the requirement of interplanetary mission hi-Fix.

X-ray pulsar navigation is a kind of emerging Spacecraft Autonomous Navigation mode, can provide the navigation informations such as long-time, high-precision location and constant speed in whole space for spacecraft.X-ray pulsar is a kind of magnetic neutron star of high speed rotation, can continuous external stable radiation, foreseeable, unique X ray signal.Spaceborne X-ray detector receives the pulse signal of a period of time (5 ~ 10 minutes), to accumulate and process the time t that can obtain and arrive spacecraft to it by the recurrence interval _sC.And this pulse arrives solar system barycenter (solar system barycenter, SSB) time t _bthen obtain by pulse timing model prediction.Time delay t _b-t _sCit is then the basic observation of pulsar navigation system.Can obtain multiple observed quantity from many pulsar direction of visual lines, recycling Navigation Filter can estimate Space Vehicle position.

The acquisition of pulse arrival time need by long-time (5 ~ 10 minutes) pile-up pulse star radiation signal.But because spacecraft is motion, and cannot obtain long-time, high-precision velocity information, the pulse signal that X-ray detector receives will inevitably be subject to the impact of Doppler effect, and this effect cannot effectively be eliminated.In pulse signal accumulation, if accumulate by the pulsar radiation signal natural period, pulse accumulation profile there will be " passivation ", and positioning precision also can significantly decline, and pulsar navigation system even can be caused time serious normally to work.In upper " On pulse phase estimation and tracking of variable celestial X-ray sources (impulse phase about variable celestial X-ray source is estimated and the follows the tracks of) " literary composition announced of Institute of Navigation 63rd Annual Meeting (the 63rd annual meeting of navigation association), Golshan, according to the distortion of pulse profile, utilizes maximum Likelihood to determine position and speed.The precision of the method is close to the U.S. labor lower bound of carat.But because this technology obtains velocity estimation value by the maximal value of gridding method search likelihood function, the calculating of each net point all relates to whole impulse radiation signal raw data.Under prior art conditions, detector resolution is at musec order, and accumulated time is 5 ~ 10 minutes, then original data volume is 10 ⁸~ 10 ⁹magnitude, very huge.This causes calculated amount, and (only the calculating of a net point just comprises 10 very greatly ⁸~ 10 ⁹magnitude additive operation and 10 ⁸~ 10 ⁹magnitude multiplying), so this algorithm cannot requirement of real time.At periodical " Science China:Physics, Mechanics & Astronomy (Chinese science: physics mechanics uranology) " the 6th phase in 2011 " Modeling and Doppler measurement of X-ray pulsar (X-ray pulsar modeling and Doppler measurement) " literary composition in, pulsar signal is decomposed into multiple Gaussian function, propose the concept of pulse accumulation profile entropy, with the error between full sized pules profile and accumulation profile for objective function, by adjustment time delay and Doppler speed, make objective function minimum, thus obtain the velocity estimation value of degree of precision.These two kinds of methods also need the raw data repeatedly calculating impulse radiation signal, and calculated amount is very large.

Summary of the invention

The present invention is directed to existing pulsar navigation location and constant speed method calculated amount this defect large, provide one pulsar navigation position and velocity joint method of estimation fast, to realize calculating in real time in-orbit.

Technical scheme of the present invention is a kind of pulsar navigation position and velocity joint method of estimation, comprises the following steps:

Step 1, total observation interval (t ₀, t _f) be divided into the individual equal sub-interval of observation of m, (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 the sub-interval of each observation, by pulsar cycle superimposed pulse signal, obtains the sub-profile of pulse accumulation, then utilizes accurate maximum Likelihood to estimate impulse phase estimated value according to gained impulse phase estimated value conversion obtains pulse arrival time t _i;

Step 3, with Least Square in Processing step 2 gained pulse arrival time t _i, obtain Space Vehicle position and speed.

And, in step 2, describedly utilize accurate maximum Likelihood to estimate impulse phase estimated value as shown in the formula,

Wherein, function h () is normalization full sized pules profile, be i-th observation sub-interval pile-up pulse profile, θ and represent phase place.

And, in step 2, by gained impulse phase estimated value conversion obtains pulse arrival time t _iimplementation be, by impulse phase estimated value as the impulse phase at i-th sub-interval of observation following formula is adopted to change,

Wherein, n _ithe pulse number of cycles between spacecraft and solar system barycenter, it is solar system barycenter the phase place that moment is corresponding, P ₀for the recurrence interval.

And, in step 3, obtain the estimated value of Space Vehicle position and speed by following formula

$\hat{r}=\frac{c\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{t}_i}{m}-\frac{\stackrel{\⩓}{v}\·T_{\mathrm{obs}}}{2}$

$\hat{v}=\frac{6\·T_{\mathrm{obs}}^{-1}\·c\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}(2i-m-1)t_i}{m^2-1}$

Wherein, c is the light velocity.

The present invention's advantage is compared with prior art:

(1) the present invention carrys out estimating Doppler speed according to the distortion of pulse accumulation profile, but utilizes the change of pulse arrival time to carry out estimating speed.Therefore, calculate without the need to relating to a large amount of impulse radiation photon, calculated amount greatly reduces.

(2) estimated accuracy provided by the invention is close to the U.S. labor lower bound of carat, location and constant speed precision high.

Accompanying drawing explanation

Fig. 1 is embodiments of the invention process flow diagrams.

Embodiment

Technical solution of the present invention is described in detail below in conjunction with drawings and Examples.The technical program can adopt the automatic operational scheme of computer software technology.

Embodiment is using Crab pulsar as navigation pulsar, and see Fig. 1, the flow process of embodiment comprises the following steps:

Step 1: embodiment utilizes X-ray detector to collect pulsar x-ray photon, by the observation interval segmentation in such a way that the pulsed photonic sequence pair that detector obtains is answered.Total observation interval (t ₀, t _f) be divided into the individual equal sub-interval (t of observation of m ₀+ (i-1) T _obs/ m, t ₀+ iT _obs/ m), i=1,2 ... m, wherein, t ₀for observation initial time, t _ffor the observation end time, observation time is T _obs=t _ft ₀.T is set in embodiment ₀=0s, t _f=300s, m=30.

The value of m need meet wherein, c is the light velocity, and v is spacecraft speed, and δ is pulse signal resolution, and its value equals X-ray detector temporal resolution.δ=1ms, v=10km/s in embodiment.

Step 2: in the sub-interval of each observation, by pulsar radiation period superimposed pulse signal, obtains the sub-profile of pulse accumulation, then utilizes quick accurate maximum Likelihood to estimate impulse phase, by the impulse phase estimated value obtained be converted into pulse arrival time t _i.As shown in fig. 1, there is the sub-profile 1 of accumulation, accumulate sub-profile 2 ... accumulate sub-profile m, process respectively.

Because accurate maximum Likelihood of the prior art only estimates impulse phase, its calculated amount is only relevant with profile length, instead of pulse signal photon numbers, so calculated amount is less.Can see 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 transacting), 2013,93 (1): 326-331. the present invention utilize accurate maximum Likelihood to improve arithmetic speed.

The present invention utilizes accurate maximum Likelihood to estimate phase place as shown in Equation 1:

Wherein, function h () is normalization full sized pules profile, it is the pulse accumulation profile at i-th sub-interval of observation.As in Fig. 1, the 1st, 2 ... the pulse accumulation profile at m the sub-interval of observation is designated as the sub-profile 1,2 of accumulation respectively ... m.θ and represent phase place, be variable, wherein θ is integration variable, for independent variable.During concrete enforcement, full sized pules profile observes acquisition for a long time by land station, and then normalization makes profile integration be 1, can obtain normalization full sized pules profile.EPN database (The EuropeanPulsar Network Data Archive, Europe observations of pulsar grid database) disclose full sized pules profile and the correlation parameter of pulsar, China technician obtains full sized pules profile by this database.

Due to the motion of spacecraft, i-th sub-interval (t of observation of acquisition ₀+ (i-1) T _obs/ m, t ₀+ iT _obs/ m) the corresponding initial time of phase value be not t ₀.Below, the present invention investigates i-th initial time observing the phase value at sub-interval corresponding of acquisition.The present invention supposes that the recurrence interval is P ₀, the speed of spacecraft on pulsar direction of visual lines is v, and first impulse phase at i-th sub-interval of observation is wherein, therefore, a kth impulse phase at i-th sub-interval of observation is

${\mathrm{\θ}}_k^i={\mathrm{\θ}}_{k-1}^i+\frac{2\mathrm{\π}\·v}{c}={\mathrm{\θ}}_0^i+\frac{2\mathrm{\π}\·v\·k}{c}---\left(2\right)$

Wherein, c is the light velocity.

The present invention supposes there be K pulse in a sub-interval of observation, and the span of k is 0,1 ... K-1.When adopting nearly Likelihood estimation, the impulse phase at i-th sub-interval of observation of acquisition for average, can calculate by formula 3:

This impulse phase equals the phase place of (K-1)/2 pulse, the phase value at i-th the sub-interval of observation namely obtained corresponding to the intermediate time at i-th sub-interval of observation,

By the impulse phase at i-th sub-interval of observation be converted into pulse arrival time t _i, as shown in Equation 4:

Wherein, n _ithe pulse number of cycles between spacecraft and solar system barycenter, at solar system barycenter the impulse phase that moment is corresponding.P ₀for the recurrence interval.

In embodiment, estimate that such as formula utilizing nearly maximum Likelihood shown in (1) phase place obtains impulse phase estimated value then such as formula the impulse phase estimated value will obtained (4) Suo Shi as the impulse phase at i-th sub-interval of observation be converted into pulse arrival time t _i.In the present embodiment, the recurrence interval P of Crab pulsar ₀for 0.0334s.

Step 3: with Least Square in Processing step 2 gained pulse arrival time t _i, Space Vehicle position and speed can be obtained.

According to step 2, the present invention obtains a series of data pair, i=1,2 ... m. with pulse arrival time t _ibetween relation as follows:

$c\·t_i=\hat{r}+\hat{v}\·(i-\frac{1}{2})\frac{T_{\mathrm{obs}}}{m}---\left(5\right)$

Wherein, with for spacecraft is at t ₀the position in moment and speed, c is the light velocity.

Therefore, position and velocity estimation value as follows:

$\hat{r}=\frac{c\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{t}_i}{m}-\hat{v}\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}(i-\frac{1}{2})\frac{T_{\mathrm{obs}}}{m}}{m}=\frac{c\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{t}_i}{m}-\frac{\hat{v}\·T_{\mathrm{obs}}}{2}---\left(6\right)$

$\hat{v}=\frac{m\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[(i-\frac{1}{2})\·\frac{T_{\mathrm{obs}}}{m}\·t_i\·c]-\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[(i-\frac{1}{2})\·\frac{T_{\mathrm{obs}}}{m}]\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[t_i\·c]}{m\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{[(i-\frac{1}{2})\·\frac{T_{\mathrm{obs}}}{m}]}^2-{\left\{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\right[(i-\frac{1}{2})\·\frac{T_{\mathrm{obs}}}{m}\left]\right\}}^2}=\frac{6\·T_{\mathrm{obs}}^{-1}\·c\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}(2i-m-1)t_i}{m^2-1}---\left(7\right)$

Specific embodiment described herein is only to the explanation for example of the present invention's spirit.Those skilled in the art can make various amendment or supplement or adopt similar mode to substitute to described specific embodiment, but can't depart from spirit of the present invention or surmount the scope that appended claims defines.

Claims (3)

1. pulsar navigation position and a velocity joint method of estimation, is characterized in that: comprise the following steps,

Step 1, total observation interval (t ₀, t _f) be divided into the individual equal sub-interval of observation of m, (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;

The value of m need meet wherein, c is the light velocity, and v is spacecraft speed, and δ is pulse signal resolution, and its value equals X-ray detector temporal resolution;

Step 2, in the sub-interval of each observation, by pulsar cycle superimposed pulse signal, obtains the sub-profile of pulse accumulation, then utilizes accurate maximum Likelihood to estimate impulse phase estimated value according to gained impulse phase estimated value conversion obtains pulse arrival time t _i;

Step 3, with Least Square in Processing step 2 gained pulse arrival time t _i, obtain Space Vehicle position and speed; Comprise the estimated value simultaneously obtaining Space Vehicle position and speed by following formula

$\hat{r}=\frac{c\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{t}_i}{m}-\frac{\hat{v}\·T_{\mathrm{obs}}}{2}$

$\hat{v}=\frac{6\·T_{\mathrm{obs}}^{-1}\·c\·\underset{i=1}{\overset{m}{\mathrm{\Σ}}}(2i-m-1)t_i}{m^2-1}$

Wherein, c is the light velocity.

2. pulsar navigation position and velocity joint method of estimation according to claim 1, is characterized in that: in step 2, describedly utilizes accurate maximum Likelihood to estimate impulse phase estimated value as shown in the formula,

Wherein, function h () is normalization full sized pules profile, be i-th observation sub-interval pile-up pulse profile, θ and represent phase place.

3. pulsar navigation position and velocity joint method of estimation according to claim 2, is characterized in that: in step 2, by gained impulse phase estimated value conversion obtains pulse arrival time t _iimplementation be, by impulse phase estimated value as the impulse phase at i-th sub-interval of observation following formula is adopted to change,

Wherein, n _ithe pulse number of cycles between spacecraft and solar system barycenter, it is solar system barycenter the phase place that moment is corresponding, P ₀for the recurrence interval.