CN103017772B - 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 based on Observability Analysis and pulsar fusion autonomous navigation method

Technical field

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

Background technology

Compare with airship with earth satellite, the flying distance of space flight spacecraft be far away, the non-intellectual of long operational time, environment is comparatively strong, its to navigation and the requirement of control system in real-time, precision and reliability higher.Traditional navigation and vehicle controL method based on ground observing and controlling net is subject to the restriction of the aspects such as precision, transmission time, operating cost and Observable segmental arc, has more and more been difficult to meet increasing and apart from the needs of farther survey of deep space task.Therefore, deep-space spacecraft independent 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 the air navigation aid based on Optical imaging measurement.The principle of work of optical guidance is using the celestial body of the known ephemeris of some near target celestial body or orbit as nautical star, then plan and process the celestial body optical imagery observed, utilize known celestial body information, determine the position of detector and speed and attitude information

But, the Deep-space TT&C network technology based on Optical imaging measurement of current main flow is all generally 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 cannot realize the navigation needs of deep space multitask section to different astronomical observation, and therefore the requirement of distance Deep-space TT&C network also has a certain distance; In addition, this independent navigation mode of Optical imaging measurement that only utilizes also is difficult to meet the requirement of survey of deep space to high precision and high reliability, and the deep space mission section that current ask for something is high still adopts the integrated navigation mode of Ground Nuclear Magnetic Resonance Deep Space Network and Optical imaging measurement.

Deep-space TT&C network based on X-ray pulsar have passed preliminary checking, its ultimate principle is similar to GPS, utilize the position of measurement means determination pulsar in solar system geocentric coordinate system and the standard time of arrival of X-ray pulse such as very long baseline interference, the pulsar direction of visual lines that itself and the X-ray detector that deep space probe carries record was compared with the actual time of arrival, adopt suitable filtering algorithm, obtain the navigation informations such as the Position, Velocity and Time of detector.Navigation based on X-ray pulsar can realize attitude equally and determine, the attitude that its principle is similar to based on optical camera is determined.Obtain its coordinate in detector coordinates system by the imaging of paired pulses star, thus the azimuth information of line of sight relative to detector can be estimated.Independent navigation based on pulsar information can obtain the higher navigation data of the complete precision such as position, attitude and time simultaneously, but it directly cannot 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, propose a kind of method merging navigation, and Observability Analysis has been carried out to the fusion navigation based on single pulsar and single asteroid information, give the mark analytic solution of error covariance matrix, devise best observation source geometric configuration, improve navigation accuracy.

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

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

(2) information recorded according to optical sensor sets up the observation equation of optical guidance:

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

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

(3) information recorded according to pulsar sensor sets up the observation equation of pulsar navigation:

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

Wherein t _sunfor pulse arrives the time of solar system barycenter; t _sCfor the pulse of measuring arrives the time of detector; for the pulsar direction of visual lines vector that sensor records; C is the light velocity; v _tfor impulsive measurement noise, meet Gaussian distribution;

(4) according to step (2) and step (3) obtain merge navigation observation equation be:

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

(5) choose an asteroid that can detect and a pulsar respectively as 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.

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

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

Accompanying drawing explanation

Fig. 1 is the inventive method process flow diagram;

Fig. 2 is single optical guidance and pulsar navigation Performance comparision;

Fig. 3 is the fusion navigational system Performance comparision not carrying out Observability Analysis He carry out Observability Analysis.

Embodiment

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

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

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

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

Wherein for the asteroid direction of visual lines vector that sensor records; for 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 sensor coordinate system; V is the measurement noises of optical sensor, and v meets Gaussian distribution, and namely average is 0, and variance is σ ²;

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

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

Wherein t _sunfor pulse arrives the time of solar system barycenter; t _sCfor the pulse of measuring arrives the time of aircraft; for the direction vector of pulsar; C is the light velocity; v _tfor impulsive measurement noise, meet Gaussian distribution, namely average is 0, and variance is

(4) make for observed quantity relative 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 mean operator;

According to the observation equation of the optical guidance that step (2) obtains, can obtain average be Ar, variance is σ ²i; The probability density function of optical guidance is obtained according to the probability density function definition of Gaussian distribution:

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

In above formula, det represents determinant computing, I representation unit battle array; Above 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 multiplication cross operator;

(5) according to the observation equation of the pulsar navigation obtained in step (3), can obtain average be variance is σ _t ²; The probability density function of pulsar navigation is obtained according to the probability density function definition of Gaussian distribution:

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

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

(6) information matrix of the pulsar navigation that the information matrix of the optical guidance obtained according to step (4) and step (5) obtain, calculates the information matrix of the fusion navigational system based on single asteroid and single pulsar information:

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

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

The proper polynomial merging 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 time, due to [r ×] ²=-I ₃+ rr ^t, so the information matrix merging navigational system in 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, two vectors can be found make with form one group of orthogonal vector base; Utilize the character of orthogonal basis, i.e. equation obtain therefore, under this situation, three eigenwerts merging the information matrix of navigational system are respectively p _t, κ, κ, characteristic of correspondence vector is

(8) when time, then have thus F eigenwert is κ, characteristic of correspondence vector is λ-κ factorization from proper polynomial out, is obtained:

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

Thus can 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 time, there is λ 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 is therefore two other proper vector then necessarily with the linear combination of r; If two other proper vector is expressed as:

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

Wherein: c _2,3for undetermined coefficient; Above formula is updated to λ v=Fv to obtain:

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

Undetermined coefficient c is solved according to above 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 Cramer-Rao inequality, the error covariance matrix P of any estimator meets

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

Wherein for the estimated value of state.

When estimator is without inclined optimal estimation time, P=F ^-1, therefore λ _i(P)=1/ λ _i, thus have (F)

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

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

In above formula, Tr characterizes the computing of mark, λ _ibe i-th eigenwert; As can be seen from the above equation less with the angle of r, considerable degree is higher, and time, considerable degree is the highest; When therefore nautical star being observed, the direction of visual lines of the pulsar pulsar parallel with asteroid direction of visual lines and asteroid should be chosen as nautical star, to improve navigation accuracy.

(10) choose an asteroid that can detect and a pulsar respectively as 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) asteroid direction of visual lines vector is obtained by measuring and pulse arrives the time t of detector _sC, obtain after observed reading, utilize the Kalman filtering of standard to carry out resolving of navigation position and speed.

The recurrence calculation process of Kalman filtering algorithm can with reference to " Kalman filtering and integrated navigation principle " book write by Qin Yongyuan, a big vast battle-axe used in ancient China, Wang Shuhua of publishing house of Northwestern Polytechnical University 1998 publication.

With the navigation of ground fire transfer orbit for background, by emulation, the validity of the method for the invention is described.The initial emulation moment is 00:00 on May 19th, 2018, and the initial position of track is [-49436266.943696 ,-132599580.772721 ,-58475583.57835] ^tkm, initial velocity is [29.41081 ,-10.854612 ,-5.431271] km/s. observation cycle is 2 days.

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

Fig. 2 gives the Cramer-Rao lower bound of scene one and scene two, and as seen from the figure, the filtering based on the navigational system of single asteroid sight line is convergence, and cannot restrain 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 in a direction.It can also be seen that from Fig. 2 in addition, the navigation error of two scenes is all very large, and site error is all 10 ⁴km magnitude.

Fig. 3 gives the Cramer-Rao lower bound of scene three and scene four, as seen from the figure, the Navigation of two scenes is all convergence, and navigation performance is better than the navigation performance of scene one and scene two, and after stable, the magnitude of site error drops within the scope of 500km.In addition, the navigation performance of scene four is better than the navigation performance of scene three.This is because asteroid direction of visual lines in scene four and pulsar direction of visual lines are almost parallel, and both direction of visual lines near vertical of scene three kinds, therefore the considerable degree of scene four is higher than scene three.

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

The non-detailed description of the present invention is known to the skilled person technology.

Claims (1)

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

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

(2) information recorded according to optical sensor sets up the observation equation of optical guidance:

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

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

(3) information recorded according to pulsar sensor sets up the observation equation of pulsar navigation:

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

Wherein t _sunfor pulse arrives the time of solar system barycenter; t _sCfor the pulse of measuring arrives the time of detector; for the pulsar direction of visual lines vector that sensor records; C is the light velocity; v _tfor impulsive measurement noise, meet Gaussian distribution;

(4) according to step (2) and step (3) obtain merge navigation observation equation be:

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

(5) choose an asteroid that can detect and a pulsar respectively as 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;

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