CN103017772A - Optical and pulsar fusion type self-navigating method based on observability analysis - Google Patents

Abstract

The invention provides an optical and pulsar fusion type self-navigating method based on observability analysis. The optical and pulsar fusion type self-navigating method comprises the following steps of firstly, mounting an optical sensor and a pulsar sensor on a detector to respectively detect a gazing direction of a single asteroid and time that pulse reaches the detector; secondly, respectively establishing an observation equation of optical navigation and an observation equation of pulsar navigation, and combining the observation equations to be an observation equation of a fusion navigation system; and finally, selecting an asteroid capable of being detected and a pulsar as measurement navigational stars, and calculating a navigation position and a navigation speed by using standard Kalman filtering.

Description

A kind of optics and pulsar based on Observability Analysis merges autonomous navigation method

Technical field

The invention belongs to the satellite navigation field, relate to a kind of fusion optical guidance based on Observability Analysis and the method for pulsar navigation.

Background technology

Compare with airship with earth satellite, the flying distance of space flight spacecraft is far away, long operational time, intellectual is not stronger for environment, and it is higher in the requirement aspect real-time, precision and the reliability to navigation and control system.The restriction that traditional navigation and control method based on the ground observing and controlling net is subject to the aspects such as precision, transmission time, operating cost and Observable segmental arc more and more has been difficult to satisfy needs increasing and the survey of deep space task that distance is farther.Therefore, deep space Spacecraft Autonomous Navigation and control technology come into one's own gradually, also become the focus of research.

At present, the independent navigation mode of deep space probe main flow is based on the air navigation aid of Optical imaging measurement.The principle of work of optical guidance is that celestial body with near some the known ephemeris target celestial body or the orbit is as nautical star, then plan and process the celestial body optical imagery that observes, utilize known celestial body information, determine position and speed and the attitude information of detector

But, at present the autonomous deep-space airmanship based on Optical imaging measurement of main flow generally all is for survey of deep space detailed programs and the development of demand in specific tasks stage, independent toward each other, lack systematicness, existing autonomous navigation system also can't be realized deep space multitask section to the navigation needs of different astronomical observations, and therefore the requirement apart from the autonomous deep-space navigation also has a certain distance; In addition, this independent navigation mode of Optical imaging measurement of only utilizing also is difficult to satisfy survey of deep space to the requirement of high precision and high reliability, and the high deep space mission section of ask for something still adopts the integrated navigation mode of Ground Nuclear Magnetic Resonance Deep Space Network and Optical imaging measurement at present.

Preliminary checking has been passed through in autonomous deep-space navigation based on the X ray pulsar, its ultimate principle is similar to GPS, to utilize the measurement means such as very long baseline interference to determine the position of pulsar in solar system geocentric coordinate system and the standard time of arrival of X ray pulse, it was compared with the X-ray detector that carries the pulsar direction of visual lines and the actual time of arrival that record on the deep space probe, adopt suitable filtering algorithm, obtain the navigation informations such as Position, Velocity and Time of detector.Navigation based on the X ray pulsar can realize that equally attitude is definite, and its principle is similar to based on the attitude of optical camera to be determined.Obtain its coordinate in detector coordinates system by the imaging of paired pulses star, thereby can estimate line of sight with respect to the azimuth information of detector.Independent navigation based on pulsar information can obtain the complete higher navigation datas of precision such as position, attitude and time simultaneously, but it can't directly provide the high precision navigation information of relative target celestial body.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of method that merges navigation has been proposed, and to having carried out Observability Analysis based on single pulsar and single asteroid Information fusion navigation, the mark analytic solution of error covariance matrix have been provided, design best observation source geometric configuration, improved navigation accuracy.

Technical solution of the present invention is: a kind of optics and pulsar based on Observability Analysis merges autonomous navigation method, and step is as follows:

(1) at detector optical sensor and pulsar sensor are installed, are used for respectively measuring the time of single asteroidal direction of visual lines and pulse arrival detector;

(2) information that records according to optical sensor is set up the observation equation of optical guidance:

$\tilde{b}=\mathrm{Ar}+v,$

Wherein

The asteroid direction of visual lines vector that records for sensor; Be the projection of asteroid direction of visual lines vector under inertial system; R _a, R is respectively the position vector of asteroidal position vector and detector under the inertial system; A is the attitude matrix that inertia is tied to the sensor coordinate system; V is the measurement noise of optical sensor, and v satisfies Gaussian distribution;

(3) information that records according to the pulsar sensor is set up the observation equation of pulsar navigation:

$\tilde{z}=t_{\mathrm{sun}}-t_{\mathrm{SC}}=\frac{1}{c}\hat{n}\·R+v_t,$

T wherein _SunArrive the time of solar system barycenter for pulse; t _SCArrive the time of detector for the pulse of measuring;

The pulsar direction of visual lines vector that records for sensor; C is the light velocity; v _tFor the impulsive measurement noise, satisfy Gaussian distribution;

(4) observation equation that obtains merging navigation according to step (2) and step (3) is:

$\left[\begin{array}{c}\tilde{b}\\ \tilde{z}\end{array}\right]=\left[\begin{array}{c}\mathrm{Ar}\\ \frac{1}{c}\hat{n}\·R\end{array}\right]+\left[\begin{array}{c}v\\ v_t\end{array}\right];$

(5) choose respectively an asteroid that can detect and a pulsar as the measure and navigation star, measure and obtain asteroid direction of visual lines vector

And pulse arrives the time t of detector _SC, utilize the Kalman filtering of standard to carry out resolving of navigation position and speed.

Choose in the described step (5) as the asteroid of measure and navigation star and be parallel to each other with choosing as the pulsar of the measure and navigation star direction of visual lines to the pulsar sensor to the direction of visual lines of optical sensor.

The present invention's beneficial effect compared with prior art is: the inventive method has merged single optical guidance and single pulsar navigation system; The navigation accuracy of the navigational system after the fusion is improved, by original 10 ⁴The km magnitude is brought up in the 500km; This method can reasonably dispose the observation source also based on Observability Analysis, more effectively raises the performance that merges navigation, and navigation accuracy has been improved about 100km than the navigation accuracy of not carrying out Observability Analysis.

Description of drawings

Fig. 1 is the inventive method process flow diagram;

Fig. 2 be single optical guidance and pulsar navigation Performance Ratio;

Fig. 3 for the fusion navigational system Performance Ratio that do not carry out Observability Analysis and carry out Observability Analysis.

Embodiment

As shown in Figure 1, a kind of optics and pulsar based on Observability Analysis merges autonomous navigation method, and its step is as follows:

(1) at detector optical sensor and pulsar sensor are installed, are used for respectively measuring the time of single asteroidal direction of visual lines and pulse arrival detector;

(2) based on the optical navigation system of single asteroid direction of visual lines, set up the observation equation of optical guidance:

$\tilde{b}=\mathrm{Ar}+v,$

Wherein

The asteroid direction of visual lines vector that records for sensor;

Be the projection of asteroid direction of visual lines vector under inertial system; R _a, R is respectively the position vector of asteroidal position vector and detector; A is the attitude matrix that inertia is tied to the sensor coordinate system; V is the measurement noise of optical sensor, and v satisfies Gaussian distribution, and namely average is 0, and variance is σ ²

(3) based on the navigational system of pulsar direction of visual lines, set up the observation equation of pulsar navigation:

$\tilde{z}=t_{\mathrm{sun}}-t_{\mathrm{SC}}=\frac{1}{c}\hat{n}\·R+v_t,$

T wherein _SunArrive the time of solar system barycenter for pulse; t _SCArrive the time of aircraft for the pulse of measuring;

Direction vector for pulsar; C is the light velocity; v _tFor the impulsive measurement noise, satisfy Gaussian distribution, namely average is 0, variance is

(4) order Be observed quantity

With respect to the probability density function of the Gaussian distribution of state variable x, corresponding Fisher information matrix is:

$F=-E\left\{\frac{{\∂}^2}{\∂x\∂x^T}\ln f(y;x)\right\},$

Wherein E{} is the average operator;

The observation equation of the optical guidance that obtains according to step (2) can obtain

Average be Ar, variance is σ ²I; Obtain the probability density function of optical guidance according to the probability density function definition of Gaussian distribution:

$f_o(\tilde{b};R)=\frac{1}{{\left(2\mathrm{\π}\right)}^{1/2}{\left[\det \left({\mathrm{\σ}}^{2}I\right)\right]}^{1/2}}\exp \{-\frac{1}{2}[{\tilde{b}-\mathrm{Ar}]}^T{\left({\mathrm{\σ}}^{2}I\right)}^{-1}[\tilde{b}-\mathrm{Ar}]\},$

Det represents the determinant computing in the following formula, I representation unit battle array; Following formula is updated in the Fisher information matrix that step (3) obtains, obtains the information matrix of optical guidance

$F_o={-\mathrm{\σ}}^{-2}\frac{1}{{\left|R\right|}^2}{[r\×]}^2,$

Wherein " * " is the multiplication cross operator;

(5) according to the observation equation of the pulsar navigation that obtains in the step (3), can obtain

Average be

Variance is σ _t ²Obtain the probability density function of pulsar navigation according to the probability density function definition of Gaussian distribution:

$f_{\mathrm{ps}}(\tilde{y};R)=\frac{1}{{\left(2\mathrm{\π}\right)}^{1/2}{\mathrm{\σ}}_t}\exp \{-\frac{1}{2}{\mathrm{\σ}}_t^{-2}{(\tilde{y}-\frac{1}{c}\hat{n}\·R)}^2\}$

Following formula is updated in the Fisher information matrix that step (4) obtains, obtains the information matrix of pulsar navigation:

$F_{\mathrm{ps}}=p_t\hat{n}{\hat{n}}^T,$

Wherein, $p_t={2\mathrm{\σ}}_t^{-2}/c^2;$

The information matrix of the optical guidance that (6) obtains according to step (4) and the information matrix of the pulsar navigation that step (5) obtains calculate the information matrix based on single asteroid and single pulsar Information fusion navigational system:

$F=F_o+F_{\mathrm{ps}}$

$={-\mathrm{\σ}}^{-2}\frac{1}{{\left|R\right|}^2}{[r\×]}^2+p_t\hat{n}{\hat{n}}^T,$

The proper polynomial that merges the information matrix of navigational system is expressed as:

$\det ({\mathrm{\λI}}_3-F)=\det (\mathrm{\λI}+{\mathrm{\κ}}_1{[r\×]}^2-p_t\hat{n}{\hat{n}}^T)=0,$

Wherein: κ ₁=σ ^-2/ | R| ², λ is eigenwert;

(7) when The time, because [r *] ²=-I ₃+ rr ^TSo the information matrix that merges navigational system in the step (6) can be simplified to:

$F={\mathrm{\κ}}_1{I}_3-({\mathrm{\κ}}_1-p_t)p_t\hat{n}{\hat{n}}^T,$

Obviously, can find two vectors

So that

With

Form one group of orthogonal vector base; Utilize the character of orthogonal basis, i.e. equation

Obtain

Therefore under this situation, three eigenwerts that merge the information matrix of navigational system are respectively p _t, κ, κ, the characteristic of correspondence vector is

(8) when

The time, then have

Thereby the eigenwert of F is κ, and the characteristic of correspondence vector is λ-κ factorization from proper polynomial is out obtained:

${\mathrm{\λ}}^2-(\mathrm{\κ}+p_t)\mathrm{\λ}+{\mathrm{\κp}}_t{|r\·\hat{n}|}^2=0,$

Thereby can be in the hope of two other eigenwert:

${\mathrm{\λ}}_{\mathrm{2,3}}\left(F\right)=\frac{1}{2}((\mathrm{\κ}+p_t)\±\sqrt{{(\mathrm{\κ}+p_t)}^2-{4\mathrm{\κp}}_t{|r\·\hat{n}|}^2}),$

When

The time, λ is arranged ₂=κ+p _t, λ ₃=0, corresponding proper vector is

And r; When r with

Both during unequal also out of plumb, because three proper vector bases are mutually orthogonal, and one of them proper vector was

Therefore two other proper vector then must be

Linear combination with r; If two other proper vector is expressed as:

$v_{\mathrm{2,3}}=\hat{n}+c_{\mathrm{2,3}}r,$

Wherein: c _2,3Be undetermined coefficient; Following formula is updated to λ v=Fv to be obtained:

${\mathrm{\λ}}_{\mathrm{2,3}}(\hat{n}+c_{\mathrm{2,3}}r)=(\mathrm{\κ}+p_t+c_{\mathrm{2,3}}{p}_t{\hat{n}}^T\hat{n})\hat{n}-\mathrm{\κ}{\hat{n}}^T\mathrm{rr},$

Solve undetermined coefficient c according to following formula _2,3:

$c_{\mathrm{2,3}}=\frac{-(\mathrm{\κ}+p_t)\±\sqrt{{(\mathrm{\κ}+p_t)}^2-4\mathrm{\κ}{p}_t{(\hat{n}\·r)}^2}}{2p_t\hat{n}\·r}=-\frac{\mathrm{\κ}\hat{n}\·r}{{\mathrm{\λ}}_{\mathrm{2,3}}},$

(9) according to the Cramer-Rao inequality, the error covariance matrix P of estimator satisfies arbitrarily

$P=E\left\{(x-\hat{x}){(x-\hat{x})}^T\right\}\≥F^{-1},$

Wherein

Estimated value for state.

When estimator is the inclined to one side optimal estimation of nothing, P=F ^-1, so λ _i(P)=1/ λ _i(F), thus have

$\mathrm{Tr}\left(P\right)=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\λ}}_i\left(P\right)=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}1/{\mathrm{\λ}}_i\left(F\right),$

$=\frac{\mathrm{\κ}+p_t}{\mathrm{\κ}{p}_t{|\hat{n}\·r|}^2}$

In the following formula, Tr characterizes the computing of mark, λ _iBe i eigenwert; As can be seen from the above equation

Less with the angle of r, considerable degree is higher, and

The time, considerable degree is the highest; Therefore when nautical star being observed, should choose the direction of visual lines of the pulsar pulsar parallel with the asteroid direction of visual lines and asteroid as nautical star, to improve navigation accuracy.

(10) choose respectively an asteroid that can detect and a pulsar as the measure and navigation star, and according to the observation equation that step (2) and step (3) can obtain merging navigational system be:

$\left[\begin{array}{c}\tilde{b}\\ \tilde{z}\end{array}\right]=\left[\begin{array}{c}\mathrm{Ar}\\ \frac{1}{c}\hat{n}\·R\end{array}\right]+\left[\begin{array}{c}v\\ v_t\end{array}\right];$

(11) obtain asteroid direction of visual lines vector by measuring And pulse arrives the time t of detector _SC, obtain after the observed reading, utilize the Kalman filtering of standard to carry out resolving of navigation position and speed.

" Kalman filtering and integrated navigation principle " book of being write by Qin Yongyuan, a big vast battle-axe used in ancient China, Wang Shuhua that the recursion computation process of Kalman filtering algorithm can be published with reference to publishing house of Northwestern Polytechnical University 1998.

The navigation of fiery transfer orbit by emulation, illustrates the validity of the method for the invention as background take ground.Initial emulation is 00:00 on May 19th, 2018 constantly, and the initial position of track is [49436266.943696 ,-132599580.772721 ,-58475583.57835] ^TKm, initial velocity are that [29.41081 ,-10.854612 ,-5.431271] km/s. observation cycle is 2 days.

Consider four kinds of scenes, scene one is only observed an asteroid (asteroid is numbered 2063) at every turn, two fixing pulsar B0531+21 of observation of scene, scene three each asteroid of observation and pulsars, and the angle of both direction of visual lines is near 90 degree, scene four a same asteroid of observation and pulsars, and both direction of visual lines are near parallel.

Fig. 2 has provided the Cramer-Rao lower bound of scene one and scene two, as seen from the figure, is convergence based on the filtering of the navigational system of single asteroid sight line, and can't restrains based on the filtering of Sing plus star navigational system.This is because asteroidal direction of visual lines can provide the status information of both direction, and pulse arrival time only can provide the status information of a direction.It can also be seen that from Fig. 2 that in addition the navigation error of two scenes is all very large, site error is all 10 ⁴About the km magnitude.

Fig. 3 has provided the Cramer-Rao lower bound of scene three and scene four, as seen from the figure, the Navigation of two scenes is all restrained, and navigation performance is better than the navigation performance of scene one and scene two, stable after the magnitude of site error drop in the 500km scope.In addition, the navigation performance of scene four is better than the navigation performance of scene three.This is that and both direction of visual lines near vertical of three kinds of scenes are so the considerable degree of scene four will be higher than scene three because the asteroid direction of visual lines in the scene four and pulsar direction of visual lines are to be close to parallelly.

Simulation result shows that single asteroid or pulsar based on ornamental that the present invention proposes merge the performance that air navigation aid can effectively improve navigational system.Main technical content of the present invention can be applicable to the autonomous navigation system design of deep space probe.

The present invention not detailed description is technology as well known to those skilled in the art.

Claims (2)

1. optics and the pulsar based on Observability Analysis merges autonomous navigation method, it is characterized in that step is as follows:

(1) at detector optical sensor and pulsar sensor are installed, are used for respectively measuring the time of single asteroidal direction of visual lines and pulse arrival detector;

(2) information that records according to optical sensor is set up the observation equation of optical guidance:

$\tilde{b}=\mathrm{Ar}+v,$

Wherein

The asteroid direction of visual lines vector that records for sensor;

Be the projection of asteroid direction of visual lines vector under inertial system; R _a, R is respectively the position vector of asteroidal position vector and detector under the inertial system; A is the attitude matrix that inertia is tied to the sensor coordinate system; V is the measurement noise of optical sensor, and v satisfies Gaussian distribution;

(3) information that records according to the pulsar sensor is set up the observation equation of pulsar navigation;

$\tilde{z}=t_{\mathrm{sun}}-t_{\mathrm{SC}}=\frac{1}{c}\hat{n}\·R+v_t,$

T wherein _SunArrive the time of solar system barycenter for pulse; t _SCArrive the time of detector for the pulse of measuring; The pulsar direction of visual lines vector that records for sensor; C is the light velocity; v _iFor the impulsive measurement noise, satisfy Gaussian distribution;

(4) observation equation that obtains merging navigation according to step (2) and step (3) is:

$\left[\begin{array}{c}\tilde{b}\\ \tilde{z}\end{array}\right]=\left[\begin{array}{c}\mathrm{Ar}\\ \frac{1}{c}\hat{n}\·R\end{array}\right]+\left[\begin{array}{c}v\\ v_t\end{array}\right];$

(5) choose respectively an asteroid that can detect and a pulsar as the measure and navigation star, measure and obtain asteroid direction of visual lines vector

And pulse arrives the time t of detector _SC, utilize the Kalman filtering of standard to carry out resolving of navigation position and speed.

2. a kind of optics and pulsar based on Observability Analysis according to claim 1 merges autonomous navigation method, it is characterized in that: choose in the described step (5) as the asteroid of measure and navigation star to the direction of visual lines of optical sensor and choose as the pulsar of the measure and navigation star direction of visual lines to the pulsar sensor and be parallel to each other.

Images