CN105203101A - Deep space explorer acquisition phase celestial navigation method based on target object ephemeris correction - Google Patents

Abstract

The invention relates to a deep space explorer acquisition phase celestial navigation method based on target object ephemeris correction. According to the method, firstly, a Martian explorer state model, a startlight angle navigation sub system measuring model and an X-ray pulsar navigation sub system measuring model are built; then, the startlight angle and the X-ray pulsar quantity measurements are respectively obtained; filtering estimation is performed to obtain the position and the speed of a detector in a heliocentric inertia coordinate system and a target object center inertia coordinate system; on the basis, a state model and a measuring model of target object ephemeris error are built; the quantity measurement about the target object ephemeris error is obtained through estimation state vectors of the startlight angle navigation sub system and the X-ray pulsar navigation sub system; a Kalman filtering method is used for estimating the target object ephemeris error; the target object ephemeris error is fed back into a navigation system model; the position of a target object in the navigation model is corrected. The deep space explorer acquisition phase celestial navigation method belongs to the technical field of aerospace navigation, can be used for estimating the object ephemeris error and correcting the model error of the navigation system on line, and is applicable to the explorer acquisition phase.

Description

The deep space probe section of the catching astronomical navigation method of a kind of based target celestial body ephemeris correction

Technical field

The present invention relates to when deep space probe is in the section of catching, in particular to the deep space probe section of the catching astronomical navigation method of a kind of based target celestial body ephemeris correction, concrete, it is the astronomical navigation method of based target celestial image and X pulsar signal revise goal celestial body ephemeris error, is a kind of air navigation aid being highly suitable for the deep space probe section of catching.

Background technology

Survey of deep space technology, as the key character of a national overall national strength and scientific technological advance level and mark, has caused the very big concern of countries in the world.Prelude has been pulled open in the fight of new round survey of deep space.At the beginning of 21 century, sight is focused to the deep space universe beyond the distance earth 380,000 kilometers by each spacefaring nation one after another.Main space flight group is proposed following survey of deep space plan in the interior world for the U.S., European Space Agency, Russia, Japan and India, will carry out manned or based on the unmanned probing of robot to each major planet and satellite thereof.Along with China's carrier rocket and the development of other survey of deep space technology and the raising of economic strength, China has possessed the ability of the even farther planets of the solar system of detection Mars.

Deep space probe flight course mainly comprise earth escape, day heart transfer, target acquistion, around, land, make an inspection tour the process such as detection.Wherein the section of catching refers to the overall process to igniting braking from deep space probe target approach affects ball, and the deep space probe flying speed being in this stage is fast, and flight segmental arc is short, and control accuracy requires high, and chance is unique.The injection point distance objective planetary surface very near (perigee) of deep space probe retarding braking, captured is a material time node of whole survey of deep space task, the Relative Navigation precision of acquisition phase relative target celestial body and having a direct impact subsequent probe task relative to the absolute navigation accuracy of the sun or the earth.But deep space probe is fast at the section of catching headway, space ionization environment is unknown, atmospheric environment is complicated, these factors all have a great impact the orbit injection accuracy of deep space probe, also govern after deep space probe is caught be diversion, the navigation accuracy in the stage such as landing, when orbit injection accuracy can not touch the mark require time, even cannot complete scientific exploration task, cause the failure of whole task.

Target celestial body almanac data is one of principal element affecting the deep space probe section of catching navigation performance.Target celestial body almanac data is the class celestial body database describing the features such as target celestial body position, speed, by long-term astronomical sight matching.If a period of time does not have astronomical sight information to revise, target celestial body almanac data error can recursion in time and increasing.The current ephemeris error of solar system inner planet (except the earth) is about 200m ~ 100km.

Traditional survey of deep space navigate mode is mainly ground based radio navigation, and as the Deep Space Network of the U.S., but China cannot carry out round-the-clock deep space radio navigation due to reasons such as regions, and radio navigation exists high latency, easily the shortcoming such as to be disturbed.Celestial navigation is a kind of spaceborne full autonomous navigation system, based on celestial navigation system measurement target celestial body and the background fixed star image information thereof of starlight angular distance, thus from image, obtains the navigation information relative to target celestial body (as Mars).Based on the astronomical navigation method of starlight angular distance owing to being subject to the impact of precision of star sensor this factor limited, its relative target coelonavigation precision of information obtained is limited, and being subject to the impact of target celestial body ephemeris error, the relative solar navigation precision obtained by the method is low.Estimated position and the velocity information of the relative and sun of detector by the mistiming obtaining the pulse of X pulsar and arrive the sun and arrive detector based on the celestial navigation system of X pulsar information.X pulsar can obtain high-precision measurement information, but long based on the celestial navigation system measurement update cycle of X pulsar, is difficult to realize real-time navigation.Therefore the feature of this two amounts measurement information how is utilized, to the estimation of the ephemeris error of target celestial body and revise to detector kinetic model and based on the measurement model of starlight angular distance, reducing the impact of target celestial body ephemeris error, is one of key issue of the survey of deep space section section of catching high precision navigation.

Chinese patent CN201510197935.8 discloses a kind of section of catching deep space probe celestial self-navigation method based on ephemeris correction, first this air navigation aid sets up target celestial body ephemeris error state model and measurement model, and obtains ephemeris error measurement amount according to prediction and the alternate position spike of actual celestial image; Secondly using ephemeris error state model and dynamics of orbits model simultaneous as celestial navigation system state model, and using ephemeris error measurement model and the starlight angular distance measurement model measurement model as celestial navigation system, adopt Unscented kalman filter method, estimate detector position, speed and target celestial body ephemeris error, and estimated ephemeris error is fed back in state model, revise goal celestial body almanac data, obtain after autonomous calibration ephemeris error relative to target celestial body and relative to day the heart detector position and speed.The present invention and Chinese patent CN201510197935.8 belong to aerospace navigation technical field equally, can On-line Estimation celestial body ephemeris error, revise the model error of navigational system, are applicable to the detector section of catching.The X pulsar of the navigation sources that X pulsar navigation uses for naturally existing, not by the interference of extraneous factor, belongs to completely autonomous air navigation aid.The navigation information that rational and efficient use starlight angular distance of the present invention and X pulsar provide, for the deep space probe section of catching provides another high-precision full independent combined navigation method.

Summary of the invention

The technical problem to be solved in the present invention is: overcome the impact of ephemeris error on celestial navigation precision, make up existing method to be difficult to eliminate target celestial body ephemeris error and to affect that this is not enough to detector's status model and measurement model, the navigation information that rational and efficient use starlight angular distance and X pulsar provide, for the deep space probe section of catching provides a kind of high-precision Combinated navigation method.

The technical solution adopted for the present invention to solve the technical problems is: the deep space probe section of the catching astronomical navigation method of a kind of based target celestial body ephemeris correction, to set up in day heart inertial coordinates system and in target celestial body centered inertial coordinate system based on the deep space probe state model of the sun and the eight major planets of the solar system gravitation, set up the measurement model based on starlight angular distance and X-ray pulsar, target celestial body is obtained and angle information measurement amount between satellite and fixed star by optical guidance sensor, X-ray pulsar both sides amount is obtained by X ray receiving trap, and use Unscented kalman filter method to obtain position and the speed parameter of deep space probe relative target celestial body and the sun, state model and the measurement model of target celestial body ephemeris error is set up, when there being X-ray pulsar measurement amount, by the estimated value of starlight angular distance/X-ray pulsar integrated navigation system estimating target celestial body ephemeris error based on above-mentioned estimated result, within the filtering cycle only having starlight angular distance information, utilize and estimate that the target celestial body ephemeris error obtained is revised state model and both sides model, thus obtain the higher detector position of precision, velocity estimation value.

Specifically comprise the following steps:

1. set up based on the sun and the eight major planets of the solar system Attractive Orbit dynamic (dynamical) deep space probe navigational system state model

A. deep space probe is set up in the inertial coordinates system centered by target celestial body based on the sun and dynamic (dynamical) first state model of the eight major planets of the solar system Attractive Orbit;

${\stackrel{\·}{X}}^{\′}\left(t\right)=f_1(X^{\′}\left(t\right),t)+w^{\′}\left(t\right)---\left(1\right)$

In formula, X ' (t)=[x ', y ', z ', v ' _x, v ' _y, v ' _z] ^tfor state vector, f ₁(X ' (t), t) is mission nonlinear continuous state transfer function, w ' (t)=[w ' _x, w ' _y, w ' _z] ^tfor state model error.

B. in day heart inertial coordinates system, deep space probe is set up based on the sun and dynamic (dynamical) second state model of the eight major planets of the solar system Attractive Orbit;

$\stackrel{\·}{X}\left(t\right)=f_2(X\left(t\right),t)+w\left(t\right)---\left(2\right)$

In formula, X (t)=[x, y, z, v _x, v _y, v _z] ^tfor state vector, f ₂(X (t) t) is mission nonlinear continuous state transfer function, w (t)=[w _x, w _y, w _z] ^tfor state model error.

2. set up starlight angular distance and X-ray pulsar measurement model respectively

(1) starlight angular distance navigational system measurement model

The angle information θ of target celestial body and two satellites and three background fixed stars _1i, θ _2iand θ _3i(i=1,2,3) expression formula is:

$\left\{\begin{array}{c}{\mathrm{\θ}}_{1i}=\arccos (-{\stackrel{\→}{l}}_{p1}^I\·{\stackrel{\→}{s}}_{1i}^I)\\ {\mathrm{\θ}}_{2i}=\arccos (-{\stackrel{\→}{l}}_{p2}^I\·{\stackrel{\→}{s}}_{2i}^I)\\ {\mathrm{\θ}}_{3i}=\arccos (-{\stackrel{\→}{l}}_{p3}^I\·{\stackrel{\→}{s}}_{3i}^I)\end{array}\right.---\left(3\right)$

In formula, for in inertial coordinates system target celestial body to the unit vector of detector, for the unit vector of i-th fixed star in target celestial body image in inertial coordinates system; for in inertial coordinates system first satellite of target celestial body to the unit vector of detector, for the unit vector of i fixed star in target celestial body first satellite image in inertial coordinates system; for in inertial coordinates system the satellite of second target celestial body to the unit vector of detector, for the unit vector of i fixed star in target celestial body second satellite image in inertial coordinates system.

If starlight angular distance navigation subsystem measurement amount Z ₁=[θ ₁₁, θ ₁₂, θ ₁₃, θ ₂₁, θ ₂₂, θ ₂₃, θ ₃₁, θ ₃₂, θ ₃₃] ^t, starlight angular distance navigation subsystem measurement noise $v_1={[v_{{\mathrm{\θ}}_{11}},v_{{\mathrm{\θ}}_{12}},v_{{\mathrm{\θ}}_{13}},v_{{\mathrm{\θ}}_{21}},v_{{\mathrm{\θ}}_{22}},v_{{\mathrm{\θ}}_{23}},v_{{\mathrm{\θ}}_{31}},v_{{\mathrm{\θ}}_{32}},v_{{\mathrm{\θ}}_{33}}]}^T,$ be respectively and measure θ ₁₁, θ ₁₂, θ ₁₃, θ ₂₁, θ ₂₂, θ ₂₃, θ ₃₁, θ ₃₂, θ ₃₃observational error, because each variable is all the variable relevant with time t, then the expression formula can setting up starlight angular distance navigation subsystem measurement model according to formula (3) is:

Z ₁(t)＝h ₁[X(t)，t]+v ₁(t)(4)

In formula, h ₁[X ' (t), t] is the non-linear continuous measurement function of starlight angular distance navigation subsystem.

(2) X-ray pulsar navigation subsystem measurement model

The time that the X-ray pulse that X-ray pulsar is launched arrives solar system barycenter is obtained by astronomical sight database, the time that X-ray pulse arrives detector is obtained by the photon counter on detector, arrives the mistiming of solar system barycenter and arrival detector as measurement information according to X-ray pulse.As shown in Figure 3, pulse arrives solar system barycenter and arrives mistiming of detector and to be multiplied with light velocity c and to be the projection of detector position vector on pulsar direction vector.The mistiming arriving solar system barycenter and detector according to many pulsar pulses can obtain the position of detector under sun geocentric coordinate system.X-ray pulsar measurement model can be described below:

Δt _i＝(n _ix·x+n _iy·y+n _iz·z)/c(5)

In formula, Δ t _ibe the measurement information (pulsar pulse arrives the mistiming of solar system barycenter and detector) of i-th X pulsar, i=1,2,3, (n _ix, n _iy, n _iz) be the direction vector of X-ray pulsar in day heart inertial coordinates system, (x, y, z) is the position of detector under heliocentric coordinates.

If X-ray pulsar navigation subsystem measurement amount Z ₂=[Δ t ₁, Δ t ₂, Δ t ₃] ^t, X-ray pulsar navigation subsystem measurement noise Δ t ₁, Δ t ₂, Δ t ₃be respectively the mistiming that detector X-ray pulsar that detector measurement obtains arrives solar system barycenter and detector, be respectively and measure Δ t ₁, Δ t ₂, Δ t ₃observational error, because each variable is all the variable relevant with time t, then the expression formula can setting up X-ray pulsar navigation subsystem measurement model according to formula (5) is:

Z ₂(t)＝h ₂[X(t)，t]+v ₂(t)(6)

In formula, h ₂[X (t), t] is the non-linear continuous measurement function of X-ray pulsar navigation subsystem.

3. the state model in pair step 1 and step 2 and measurement model carry out discretize

X′(k)＝F ₁(X′(k-1)，k-1)+W′(k-1)(7)

X(k)＝F ₂(X(k-1)，k-1)+W(k-1)(8)

Z′(k)＝H ₁(X′(k)，k)+V ₁(k)(9)

Z(k)＝H ₂(X(k)，k)+V ₂(k)(10)

In formula, k=1,2 ..., F ₁(X ' (k-1), k-1) and F ₂(X (k-1), k-1) is respectively f ₁(X ' (t), t) and f ₂(X (t), from kth-1 moment to the nonlinear state transfer function in kth moment after t) discrete, H ₁(X ' (k), k) and H ₂(X (k) k) is respectively h ₁(X ' (t), t) and h ₂(X (t), t) the non-linear measurement function in discrete rear kth moment, W ' (k), W (k), V ₁(k), V ₂k () is respectively w ' (t), w (t), v ₁(t) and v ₂the equivalent noise in (t) discrete rear kth moment, and W ' (k) and V ₁(k), W (k) and V ₂k () is uncorrelated mutually.

4. the acquisition of measuring of starlight angular distance and X-ray pulsar amount of navigation and process

(1) acquisition of starlight angular distance navigational system measurement amount and process

Obtained the image of target celestial body by star sensor, utilize image processing techniques, determine that the pixel of celestial body barycenter is as line coordinates; Through being tied to two-dimensional imaging plane coordinate system from pixel as line coordinates, being tied to three times of sensor surving coordinate system conversions from two-dimensional imaging planimetric coordinates, determine celestial body and the unit vector of background fixed star in sensor coordinate system thereof; Finally calculate the starlight angular distance between celestial body unit vector and background fixed star unit vector.

(2) acquisition of X-ray pulsar navigation subsystem measurement amount and process

The time that the X-ray pulse that X-ray pulsar is launched arrives solar system barycenter is obtained by astronomical sight database, the time that X-ray pulse arrives detector is obtained by the photon counter on detector, arrives the mistiming of solar system barycenter and arrival detector as measurement information according to X-ray pulse.

5. pair starlight angular distance navigational system carries out Unscented Kalman filtering

According to the measurement amount that the first state model, starlight angular distance navigation subsystem measurement model, star sensor obtain, carry out celestial navigation subsystem Unscented Kalman filtering, obtain the estimated state vector representing deep space probe position and speed in target celestial body inertial coordinates system with estimation mean squared error matrix

6. pair X-ray pulsar navigation subsystem carries out Unscented Kalman filtering

According to the measurement amount that the second state model, X-ray pulsar navigation subsystem measurement model, X ray receiving trap obtain, carry out X ray navigation subsystem Unscented Kalman filtering, obtain the estimated state vector representing deep space probe position and speed in day heart inertial coordinates system with estimation mean squared error matrix P _k.

7. determine whether to need to carry out target celestial body ephemeris corrections

When there being X pulsar measurement amount, carrying out fused filtering and target celestial body ephemeris error estimated and revises, perform step 8; When not having new X pulsar measurement amount to produce, utilize single starlight angular distance to revise target celestial body ephemeris error as measurement amount and upper one ephemeris error revising phase estimate, perform step 9 pair target celestial body ephemeris error and carry out modeling, estimate and feedback compensation.

8. the ephemeris error of pair target celestial body is estimated and is revised

A. target celestial body ephemeris error state model is set up

Its error characteristics in the section of catching are thought of as constant error, and in day heart inertial coordinates system, set up target celestial body ephemeris error state model is:

$\stackrel{\·}{X}\mathrm{err}=0---\left(11\right)$

In formula, $\stackrel{\·}{X}\mathrm{err}=\left[\begin{array}{ccc}{\stackrel{\·}{x}}_{\mathrm{err}}& {\stackrel{\·}{y}}_{\mathrm{err}}& {\stackrel{\·}{z}}_{\mathrm{err}}\end{array}\right],$ for the differential of three shaft position errors of target celestial body ephemeris in day heart inertial coordinates system, can be abbreviated as after discretize:

X _err(k)＝F _err(X _err(k-1)，k-1)+W _err(k-1)(12)

In formula, state transition function F _err(X _err(k-1), k-1)=Φ _{err, k, k-1}x _{err, k-1}, Φ _{err, k, k-1}for kth-1 moment is to the state-transition matrix in kth moment, X _errk () is kth moment target celestial body ephemeris error state vector, and X _err(k)=X _{err, k}, W _err(k-1) be kth-1 moment target celestial body ephemeris error state model error.

B. target celestial body ephemeris error measurement model is set up

The measurement model of target celestial body ephemeris error can be expressed as:

Z _err＝H ₃(X _err(k)，k)+V ₃(13)

In formula, H ₃(X _errk (), k) is the measurement function in k moment, V ₃for target celestial body ephemeris error measurement noise.

C. target celestial body ephemeris error measurement amount is obtained

Target celestial body ephemeris error measurement amount Z _errcan be expressed as:

$Z_{\mathrm{err}}=X_{\mathrm{xray}}^s-X_{\mathrm{opt}}^m-X_{\mathrm{Mars}}^s---\left(14\right)$

In formula, the position relative to the sun obtained for X-ray pulsar navigation subsystem and speed, the position relative to target celestial body obtained for starlight angular distance navigation subsystem and speed, for target celestial body is relative to the position of the sun and speed, obtain from celestial body almanac data storehouse.

D. Kalman Filter Estimation is carried out to target celestial body ephemeris error

The target celestial body ephemeris error state model set up according to steps A and step B and measurement model, and the target celestial body ephemeris error measurement amount that step C obtains, utilize kalman filter method, target celestial body ephemeris error is estimated, obtain target celestial body ephemeris error estimated state vector and estimate mean squared error matrix, specific as follows:

The one-step prediction of target celestial body ephemeris error state vector:

$X_{\mathrm{err},k/k-1}={\mathrm{\Φ}}_{\mathrm{err},k,k-1}{\hat{X}}_{\mathrm{err},k-1}---\left(15\right)$

In formula, for k-1 moment Mars ephemeris error one-step prediction state vector.

The estimation mean squared error matrix one-step prediction of target celestial body ephemeris error state vector:

P _err，k/k-1＝Φ _{err，k，k-1}P _err，k-1Φ _{err，k，k-1} ^T+Q _err，k(16)

In formula, P _{err, k-1}for the estimation mean squared error matrix of k-1 moment target celestial body ephemeris error state vector, Q _{err, k}for k moment target celestial body ephemeris error state model error covariance matrix.

Kalman filtering gain

K _err，k＝P _err，k/k-1H _err，k ^T(H _err，kP _err，k/k-1H _err，k ^T+R _err，k) ^-1(17)

In formula, H _{err, k}for k moment target celestial body ephemeris error measurement matrix, H _{err, k}x _{err, k}=H ₃(X _err, k), R _{err, k}for k moment target celestial body ephemeris error measurement model error covariance matrix.

Target celestial body ephemeris error estimated state vector

${\hat{X}}_{\mathrm{err},k}=X_{\mathrm{err},k/k-1}+K_{\mathrm{err},k}(Z_{\mathrm{err},k}-H_{\mathrm{err},k}{X}_{\mathrm{err},k/k-1})---\left(18\right)$

In formula, Z _{err, k}for k moment target celestial body ephemeris error measurement amount.

Target celestial body ephemeris error estimates mean squared error matrix,

P _err，k＝(I-K _err，kH _err，k)P _err，k/k-1(19)

In formula, I is unit battle array.

E. feedback compensation is carried out to target celestial body ephemeris error

By the target celestial body ephemeris error obtained in step D mean squared error matrix P is estimated with target celestial body ephemeris error _{err, k}in the first state model feeding back to deep space probe and the second state model, and redefine the model error covariance matrix of the first state model and the second state model, finally the model error covariance matrix after correction is inputed in starlight angular distance navigation subsystem Unscented Kalman filtering and X-ray pulsar navigation subsystem Unscented Kalman filtering, revise the navigation results of subsequent time.

9. information fusion

Utilize the ephemeris error that ephemeris update the system obtains, the navigation information of X-ray pulsar navigational system is converted in the inertial coordinates system centered by target celestial body, merge with the navigation information of starlight angular distance navigational system.The cycle of X ray sensor amount to obtain measurement information is longer, when detector navigational system does not have X-ray pulsar measurement amount, be used alone starlight angular distance and Unscented Kalman filtering is carried out to navigational system, use the target celestial body ephemeris error estimated value in a cycle to revise the state model of starlight angular distance navigational system and measurement model, X-ray pulsar navigation subsystem only utilizes the second state model to carry out time renewal; When detector obtains X-ray pulsar measurement amount, Unscented Kalman filtering is carried out to two navigation subsystem simultaneously;

Be engraved in during final output kth and in the inertial coordinates system centered by target celestial body, represent that the estimated state vector sum of detector position and speed estimates mean squared error matrix, and go through according to revised target line star, by in this results conversion Summer Solstice or the Winter Solstice heart inertial coordinates system, export in day heart inertial coordinates system, represent that the estimated state vector sum of detector position and speed estimates mean squared error matrix, these navigation informations are returned respectively in starlight angular distance navigation subsystem and X-ray pulsar navigation subsystem, for the position in k+1 moment, the estimation of speed navigation information, k=1, 2, ...,

Principle of the present invention is: first select dynamics of orbits model based on the sun and the eight major planets of the solar system gravitation as System State Model, according to the different characteristics that starlight angular distance and X-ray pulsar are measured, be based upon two state models in inertial coordinates system centered by target celestial body and day heart inertial coordinates system respectively, afterwards according to the principle of work of star sensor and X ray receiving trap, obtain and the star sensor processed and the measurement amount measured by X-ray pulse receiving apparatus, then, the measurement model of starlight angular distance navigation subsystem and X-ray pulsar navigation subsystem is set up, after this, because the state model of detector and measurement model all present nonlinear characteristic, and system noise is non-Gaussian noise, therefore adopts Unscented kalman filter method, estimates the detector navigation information of two subsystems, secondly, because the navigation of starlight angular distance can measure high-precision relative target coelonavigation information, and X pulsar navigation can be measured high-precision relative to solar navigation information, the geometric relationship of combining target celestial body, detector, the sun, can determine the ephemeris of target celestial body, compared with original target celestial body ephemeris, can obtain target celestial body ephemeris error measurement amount, in order to obtain target celestial body ephemeris error more accurately, short in conjunction with the section of the catching duration, target celestial body ephemeris error changes little feature in the section of catching, set up state model and the measurement model of the section of catching target celestial body ephemeris error, and be all the feature of linear model according to target celestial body ephemeris error state model and measurement model, adopt kalman filter method, estimating target celestial body ephemeris error, and estimated target celestial body ephemeris error is fed back in the first state model and the second state model, revise goal celestial body almanac data, improve the model accuracy of state model, finally by information fusion method, effectively utilize the metrical information of starlight angular distance navigation subsystem and X-ray pulsar navigation subsystem, improve relative to target celestial body and the estimated accuracy of detector navigation information relative to the day heart.

The present invention's advantage is compared with prior art: utilize the target celestial body ephemeris error estimated by ephemeris corrections process, achieve on the one hand and the high precision of target celestial body ephemeris error is estimated, obtain the detector high precision navigation information of relative target celestial body and relative day heart simultaneously, have modified the state model of navigational system on the other hand, reduce the impact of target celestial body ephemeris error on state model precision, further increase the navigation accuracy of deep space probe.

Accompanying drawing explanation

Fig. 1 is the deep space probe section of the catching astronomical navigation method process flow diagram that the present invention is based on the correction of target celestial body ephemeris.

Fig. 2 is the imaging schematic diagram of starlight angular distance navigation subsystem of the present invention star sensor used.

Fig. 3 is that pulse arrives solar system barycenter and arrives mistiming of detector and to be multiplied with light velocity c and to be the schematic diagram of the projection of detector position vector on pulsar direction vector.

Embodiment

The present invention is further illustrated below in conjunction with accompanying drawing and specific embodiment.

As shown in Figure 1, target celestial body involved in preceding solution can be the interplanetary celestial bodies such as Mars, Venus, Jupiter, Saturn, below using Mars as embodiment, specific embodiment of the invention process is described:

1. set up deep space probe based on the sun and the dynamic (dynamical) state model of the eight major planets of the solar system Attractive Orbit

First initialized location, speed, if X=is [xyzv _xv _yv _z] ^tfor the state vector in day heart inertial coordinates system, be respectively position and the speed of detector three axles in day heart inertial coordinates system, X '=[x ' y ' z ' v _x' v _y' v _z'] ^tfor the state vector in fiery heart inertial coordinates system, x ', y ', z ', v ' _x, v ' _y, v ' _zbe respectively position and the speed of detector three axles in fiery heart inertial coordinates system, above-mentioned variable is all the function relevant with t, and according to the Track desigh of detector, position and the speed initial value of choosing detector are X (0) and X ' (0); Secondly initialization Mars ephemeris error initial value is X _err(0)=[x _erry _errz _errv _xerrv _yerrv _zerr] ^t, x _err, y _err, z _err, v _xerr, v _yerr, v _zerrbe respectively site error and velocity error that heliocentric coordinates moderate heat star goes through three axles.

A. in fiery heart inertial coordinates system, deep space probe is set up based on the sun and dynamic (dynamical) first state model of the eight major planets of the solar system Attractive Orbit, i.e. the state model of starlight angular distance navigation subsystem;

Consider that the sun and the sun such as Mars, the earth and the eight major planets of the solar system are to the graviational interaction of detector, choose fiery heart inertial coordinates system, can obtain deep space probe first state model in fiery heart inertial coordinates system, namely the state model of starlight angular distance navigation subsystem is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}^{\′}={v_x}^{\′}\\ {\stackrel{\·}{y}}^{\′}={v_y}^{\′}\\ {\stackrel{\·}{z}}^{\′}={v_z}^{\′}\\ {{\stackrel{\·}{v}}_x}^{\′}={-\mathrm{\μ}}_m\frac{x^{\′}}{r_{\mathrm{pm}}^{\′3}}{-\mathrm{\μ}}_s[\frac{x^{\′}-x_s^{\′}}{r_{\mathrm{ps}}^{\′3}}+\frac{x_s^{\′}}{r_{\mathrm{ms}}^{\′3}}]-\underset{i_c}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{i_c}[\frac{x^{\′}-x_{i_c}^{\′}}{r_{{\mathrm{pi}}_c}^{\′3}}+\frac{x_{i_c}^{\′}}{r_{{\mathrm{mi}}_c}^3}]+w_x^{\′}\\ {{\stackrel{\·}{v}}_y}^{\′}={-\mathrm{\μ}}_m\frac{y^{\′}}{r_{\mathrm{pm}}^{\′3}}{-\mathrm{\μ}}_s[\frac{y^{\′}-y_s^{\′}}{r_{\mathrm{ps}}^{\′3}}+\frac{y_s^{\′}}{r_{\mathrm{ms}}^{\′3}}]-\underset{i_c}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{i_c}[\frac{y^{\′}-y_{i_c}^{\′}}{r_{{\mathrm{pi}}_c}^{\′3}}+\frac{y_{i_c}^{\′}}{r_{{\mathrm{mi}}_c}^3}]+w_y^{}\′\\ {{\stackrel{\·}{v}}_z}^{\′}={-\mathrm{\μ}}_m\frac{z^{\′}}{r_{\mathrm{pm}}^{\′3}}{-\mathrm{\μ}}_s[\frac{z^{\′}-z_s^{\′}}{r_{\mathrm{ps}}^{\′3}}+\frac{z_s^{\′}}{r_{\mathrm{ms}}^{\′3}}]-\underset{i_c}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{i_c}[\frac{z^{\′}-z_{i_c}^{\′}}{r_{{\mathrm{pi}}_c}^{\′3}}+\frac{z_{i_c}^{\′}}{r_{{\mathrm{mi}}_c}^3}]+w_z^{}\′\end{array}\right.---\left(1\right)$

In formula, x ', y ', z ' is detector three shaft positions in fiery heart inertial coordinates system, v ' _x, v ' _y, v ' _zfor detector three axle speed in fiery heart inertial coordinates system, for the differential of detector three shaft positions in fiery heart inertial coordinates system, for the differential of detector three axle speed in fiery heart inertial coordinates system, μ _s, μ _mwith be respectively the sun, Mars and i-th _cthe gravitational constant of planet; R ' _psfor day the heart to the distance of detector; R ' _pmfor Mars is to the distance of detector; R ' _msfor day the heart to the distance of the fiery heart; be i-th _cplanet is to the distance of detector; R ' _mibe i-th _cplanet barycenter is to the distance of the fiery heart; (x ' _s, y ' _s, z ' _s), be respectively the sun, i-th _cthe three shaft position coordinates of planet in fiery heart inertial coordinates system, can be obtained by planet ephemerides according to the time, w _x', w _y', w _z' be respectively the state model error of detector three axle in the first state model; i _cto represent in the sun and the eight major planets of the solar system i-th from the inside to the outside _cplanet, i _c=1,2,3..., N (i _c≠ 4), N=8, due to i _c=4 represent the 4th planet (Mars), are not therefore included in summation expression formula.

Each variable in formula (1) is all the variable relevant with time t, can be abbreviated as:

${\stackrel{\·}{X}}^{\′}=f_1(X^{\′}\left(t\right),t)+w^{\′}\left(t\right)---\left(2\right)$

In formula, be the state vector of the first state model, for the differential of X ' (t), f ₁(X ' (t), t) is the mission nonlinear continuous state transfer function of the first state model, w ' (t)=[w ' _x, w ' _y, w ' _z] ^tit is the state model error of the first state model.

B. in day heart inertial coordinates system, deep space probe is set up based on the sun and dynamic (dynamical) second state model of the eight major planets of the solar system Attractive Orbit, i.e. the state model of X-ray pulsar navigation subsystem;

Consider that the sun and the sun such as Mars, the earth and the eight major planets of the solar system are to the graviational interaction of detector, choose a day heart inertial coordinates system, can obtain the second state model that deep space probe expands into component form in day heart inertial coordinates system, namely the state model of X-ray pulsar navigation subsystem is:

$\left\{\begin{array}{c}\stackrel{\·}{x}=v_x\\ \stackrel{\·}{y}=v_y\\ \stackrel{\·}{z}=v_z\\ {\stackrel{\·}{v}}_x={-\mathrm{\μ}}_s\frac{x}{r_{\mathrm{ps}}^3}-\underset{i_c}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{i_c}[\frac{x-x_{i_c}}{r_{{\mathrm{pi}}_c}^3}+\frac{x_{i_c}}{r_{{\mathrm{si}}_c}^3}]+w_x\\ {\stackrel{\·}{v}}_y={-\mathrm{\μ}}_s\frac{y}{r_{\mathrm{ps}}^3}-\underset{i_c}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{i_c}[\frac{x-x_{i_c}}{r_{{\mathrm{pi}}_c}^3}+\frac{x_{i_c}}{r_{{\mathrm{si}}_c}^3}]+w_y^{}\\ {\stackrel{\·}{v}}_z={-\mathrm{\μ}}_s\frac{z}{r_{\mathrm{ps}}^3}-\underset{i_c}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{i_c}[\frac{x-x_{i_c}}{r_{{\mathrm{pi}}_c}^3}+\frac{x_{i_c}}{r_{{\mathrm{si}}_c}^3}]+w_z^{}\end{array}\right.---\left(3\right)$

In formula, x, y, z be detector in day heart inertial coordinates system three shaft positions, v _x, v _y, v _zfor detector three axle speed in day heart inertial coordinates system, for the differential of detector three shaft positions in day heart inertial coordinates system, for the differential of detector three axle speed in day heart inertial coordinates system, μ _sfor solar gravitation constant, be i-th _cthe gravitational constant of individual planet; r _psfor day the heart to the distance of detector; be i-th _cindividual planet is to the distance of detector; be i-th _cindividual planet barycenter is to the distance of the day heart; be respectively i-th _cthe coordinate of individual planet in day heart inertial coordinates system, can be obtained by planet ephemerides according to the time, w _x, w _y, w _zbe respectively the state model error of detector three axle in the second state model;

Each variable in formula (3) is all the variable relevant with time t, can be abbreviated as:

$\stackrel{\·}{X}\left(t\right)=f_2(X\left(t\right),t)+w\left(t\right)---\left(4\right)$

In formula, be the state vector of the second state model, for the differential of X (t), f ₂(X (t) t) is the second state model mission nonlinear continuous state transfer function, w (t)=[w _x, w _y, w _z] ^tit is the state model error of the second state model.

2. set up starlight angular distance navigation subsystem and X-ray pulsar navigation subsystem measurement model respectively

(1) starlight angular distance navigation subsystem measurement model

Angle information θ between Mars and i-th background fixed star _misize be identical in different coordinates, therefore its expression formula is:

${\mathrm{\θ}}_{\mathrm{mi}}=\arccos (-{\stackrel{\→}{l}}_{\mathrm{pm}}^S\·{\stackrel{\→}{s}}_{1i}^S)=\arccos (-{\stackrel{\→}{l}}_{\mathrm{pm}}^I\·{\stackrel{\→}{s}}_{1i}^I)---\left(5\right)$

In formula, for in Mars sensor surving coordinate system from Mars to the unit vector of detector, for in inertial coordinates system, Mars, to the unit vector of detector, can be expressed as:

${\stackrel{\→}{l}}_{\mathrm{pm}}^I=\frac{1}{\sqrt{x^{{\′}^2}+y^{{\′}^2}+z^{{\′}^2}}}\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\\ z^{\′}\end{array}\right]---\left(6\right)$

In formula, (x ', y ', z ') be detector three shaft position coordinates in fiery heart inertial coordinates system, for the unit vector of i-th background fixed star in Mars sensor surving coordinate system in Mars image, for the unit vector of i-th background fixed star starlight in inertial coordinates system, i=1,2,3, directly can be obtained by fixed star almanac data storehouse,

In like manner can obtain phobos and angle information θ between Deimos and its i-th background fixed star _piand θ _diexpression formula be:

${\mathrm{\θ}}_{\mathrm{pi}}=\arccos (-{\stackrel{\→}{l}}_{\mathrm{pp}}^I\·{\stackrel{\→}{s}}_{2i}^I)---\left(7\right)$

${\mathrm{\θ}}_{\mathrm{di}}=\arccos (-{\stackrel{\→}{l}}_{\mathrm{pd}}^I\·{\stackrel{\→}{s}}_{3i}^I)---\left(8\right)$

If starlight angular distance navigation subsystem measurement amount Z ₁=[θ _m1, θ _m2, θ _m3, θ _p1, θ _p2, θ _p3, θ _d1, θ _d2, θ _d3] ^t, starlight angular distance navigation subsystem measurement noise $v_1={[v_{{\mathrm{\θ}}_{m1}},v_{{\mathrm{\θ}}_{m2}},v_{{\mathrm{\θ}}_{m3}},v_{{\mathrm{\θ}}_{p1}},v_{{\mathrm{\θ}}_{p2}},v_{{\mathrm{\θ}}_{p3}},v_{{\mathrm{\θ}}_{d1}},v_{{\mathrm{\θ}}_{d2}},v_{{\mathrm{\θ}}_{d3}}]}^T,$ be respectively and measure θ _m1, θ _m2, θ _m3, θ _p1, θ _p2, θ _p3, θ _d1, θ _d2, θ _d3observational error, because each variable is all the variable relevant with time t, then the expression formula can setting up starlight angular distance navigation subsystem measurement model according to formula (6) ~ formula (8) is:

Z ₁(t)＝h ₁[X′(t)，t]+v ₁(t)(9)

In formula, h ₁[X ' (t), t] is the non-linear continuous measurement function of starlight angular distance navigation subsystem.

(2) X-ray pulsar navigation subsystem measurement model

The time that the X-ray pulse that X-ray pulsar is launched arrives solar system barycenter is obtained by astronomical sight database, the time that X-ray pulse arrives detector is obtained by the photon counter on detector, arrives the mistiming of solar system barycenter and arrival detector as measurement information according to X-ray pulse.As shown in Figure 3, pulse arrives solar system barycenter and arrives mistiming of detector and to be multiplied with light velocity c and to be the projection of detector position vector on pulsar direction vector.The mistiming arriving solar system barycenter and detector according to many pulsar pulses can obtain the position of detector under sun geocentric coordinate system.X-ray pulsar measurement model can be described below:

Δt _i＝(n _ix·x+n _iy·y+n _iz·z)/c(10)

In formula, Δ t _ibe the measurement information (pulsar pulse arrives the mistiming of solar system barycenter and detector) of i-th X pulsar, i=1,2,3, (n _ix, n _iy, n _iz) be the direction vector of X-ray pulsar in day heart inertial coordinates system, (x, y, z) is the position of detector under heliocentric coordinates.

If X-ray pulsar navigation subsystem measurement amount Z ₂=[Δ t ₁, Δ t ₂, Δ t ₃] ^t, X-ray pulsar navigation subsystem measurement noise Δ t ₁, Δ t ₂, Δ t ₃be respectively the mistiming that detector X-ray pulsar that detector measurement obtains arrives solar system barycenter and detector, be respectively and measure Δ t ₁, Δ t ₂, Δ t ₃observational error, because each variable is all the variable relevant with time t, then the expression formula can setting up X-ray pulsar navigation subsystem measurement model according to formula (10) is:

Z ₂(t)＝h ₂[X(t)，t]+v ₂(t)(11)

In formula, h ₂[X (t), t] is the non-linear continuous measurement function of X-ray pulsar navigation subsystem.

3. the state model in pair step 1 and step 2 and measurement model carry out discretize

X′(k)＝F ₁(X′(k-1)，k-1)+W′(k-1)(12)

X(k)＝F ₂(X(k-1)，k-1)+W(k-1)(13)

Z′(k)＝H ₁(X′(k)，k)+V ₁(k)(14)

Z(k)＝H ₂(X(k)，k)+V ₂(k)(15)

In formula, k=1,2 ..., F ₁(X ' (k-1), k-1) and F ₂(X (k-1), k-1) is respectively f ₁(X ' (t), t) and f ₂(X (t), from kth-1 moment to the nonlinear state transfer function in kth moment after t) discrete, H ₁(X ' (k), k) and H ₂(X (k) k) is respectively h ₁(X ' (t), t) and h ₂(X (t), t) the non-linear measurement function in discrete rear kth moment, W ' (k), W (k), V ₁(k), V ₂k () is respectively w ' (t), w (t), v ₁(t) and v ₂the equivalent noise in (t) discrete rear kth moment, and W ' (k) and V ₁(k), W (k) and V ₂k () is uncorrelated mutually.

4. the acquisition of starlight angular distance and X-ray pulsar measurement amount and process

(1) acquisition of starlight angular distance navigation subsystem measurement amount and process

Fig. 2 gives the imaging schematic diagram of starlight angular distance navigation subsystem Mars sensor used, and phobos sensor, Deimos sensor imaging process are similar with it.Mars sensor forms, at sensor surving coordinate system O ' X primarily of optical lens and two-dimensional imaging face battle array _cy _cz _cthe middle direction vector along Mars to detector mars sunlight reflection directive Mars sensor, now, the coordinate of Mars in Mars sensor surving coordinate system is (x _c, y _c, z _c); The optical lens of Mars sensor will be imaged in the battle array of two-dimensional imaging face with focal distance f after the light refraction of Mars, the image brightness signal impinged upon on each image-generating unit stores by two-dimensional imaging face battle array.According to the image-forming principle of sensor, the processing procedure of starlight angular distance navigation subsystem measurement amount is as follows:

A. the process of celestial image

Because the image of Mars in the battle array of two-dimensional imaging face is not a point, but a circle, by image processing techniques determination Mars images such as barycenter identifications at two-dimensional imaging plane coordinate system OX _2dy _2dbarycenter (x _2d, y _2d), this center can with pixel as line coordinates system O _p1x _p1y _p1in pixel represent as line (p, l).

B. center-of-mass coordinate is converted to the conversion of two-dimensional imaging plane coordinate system as line coordinates system from pixel

According to pixel as the relation between line coordinates system and two-dimensional imaging plane coordinate system, Mars center-of-mass coordinate is converted to two-dimensional imaging plane coordinate system from pixel as line coordinates system:

$\left[\begin{array}{c}{x}_{2d}\\ y_{2d}\end{array}\right]=K^{-1}(\left[\begin{array}{c}p\\ l\end{array}\right]-\left[\begin{array}{c}{p}_0\\ l_0\end{array}\right])---\left(16\right)$

In formula, (x _2d, y _2d) for Mars is at two-dimensional imaging plane OX _2dy _2din coordinate, p and l be respectively Mars the pixel of Mars sensor two-dimensional imaging plane and picture line, $K=\left[\begin{array}{cc}{K}_x& K_{\mathrm{yx}}\\ K_{\mathrm{xy}}& K_y\end{array}\right]$ For being transferred to the sensor transition matrix of pixel by millimeter, p ₀and l ₀be respectively Mars sensor center at pixel as line coordinates system OX _p1y _p1in pixel and picture line.

C. center-of-mass coordinate is converted to the conversion of sensor surving coordinate system from two-dimensional imaging plane coordinate system

According to lens imaging principle, Mars center-of-mass coordinate is converted to sensor surving coordinate system from two-dimensional imaging plane coordinate system:

${\stackrel{\→}{l}}_{\mathrm{pm}}^S=\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\end{array}\right]=\frac{1}{\sqrt{x_{2d}^2+y_{2d}^2+f^2}}\left[\begin{array}{c}{x}_{2d}\\ y_{2d}\\ -f\end{array}\right]---\left(17\right)$

In formula, f is the focal length of Mars sensor, for in Mars sensor surving coordinate system from Mars to the unit vector of detector.

In like manner can obtain the unit vector of i-th background fixed star in Mars sensor surving coordinate system in Mars image i=1,2,3.

D. starlight angular distance is calculated

According to Mars in Mars sensor surving coordinate system to the unit vector of detector with the unit vector of i-th background fixed star in Mars image calculate the starlight angular distance θ between two vectors _mi:

${\mathrm{\θ}}_{\mathrm{mi}}=\arccos [(-{\stackrel{\→}{l}}_{\mathrm{pm}}^S)\·{\stackrel{\→}{s}}_{1i}^S]---\left(18\right)$

In like manner can obtain phobos and its background fixed star, starlight angular distance θ between Deimos and its background fixed star _pi, θ _di.

(2) acquisition of X-ray pulsar navigation subsystem measurement amount and process

Choose the measurement amount of mistiming as X-ray pulsar navigation subsystem that X-ray pulse arrives solar system barycenter and detector.

What the photon counter that detector loads obtained is the real time that X-ray pulse arrives detector, calculating pulse arrives solar system barycenter to be needed unified to same standard with the mistiming arriving detector, due to the various factors in space, pulsar signal needs the impact considering factors in time transfer process, and concrete transfer equation is:

${\tilde{t}}_{\mathrm{SSB}}=t_{\mathrm{sc}}+{\mathrm{\δt}}_1+{\mathrm{\δt}}_2+{\mathrm{\δt}}_3+{\mathrm{\δt}}_4---\left(19\right)$

In formula, for pulse arrives the time of solar system barycenter, t _scfor pulse arrives the time of detector, δ t ₁for the time delay caused due to geometric relationship, δ t ₂that the Shapiro that planets of the solar system celestial body produces postpones effect, δ t ₂with δ t ₂that the light path that solar gravitation field is caused bends and gravitation delay.Can find out except the geometric delay shown in Fig. 3 by formula, pulse arrival time is subject to the impact of celestial body in solar system and solar gravitation, so the measurement amount of X-ray pulsar can be expressed as:

${\mathrm{\δt}}_1={\tilde{t}}_{\mathrm{SSB}}-t_{\mathrm{sc}}-{\mathrm{\δt}}_2-{\mathrm{\δt}}_3-{\mathrm{\δt}}_4---\left(20\right)$

5. pair starlight angular distance navigation subsystem carries out Unscented Kalman filtering

According to the first state model formula (12), starlight angular distance navigation subsystem measurement model formula (14), the measurement amount formula (18) that obtained by star sensor, carry out starlight angular distance navigation subsystem Unscented Kalman filtering.Concrete steps are as follows:

A. initialization

${\hat{x}}_0^{\′}=E\left[x_0^{\′}\right],P_0^{\′}=E\left[(x_0^{\′}-{\hat{x}}_0^{\′}){(x_0^{\′}-{\hat{x}}_0^{\′})}^T\right]---\left(21\right)$

In formula, be three shaft positions and the velocity estimation value of the 0th moment (initial time) detector in fiery heart inertial coordinates system, x ' ₀be three shaft positions and the speed actual value of the 0th moment (initial time) detector in fiery heart inertial coordinates system, P ' ₀for the initial mean squared error matrix of state vector.

B. calculating sampling point

In starlight angular distance navigation subsystem kth-1 moment state vector near choose a series of sample point, average and the mean squared error matrix of these sample points are respectively with P ' _k-1.If state vector is 6 × 1 dimensions, so sample point χ ' of 13 starlight angular distance navigation subsystem _{0, k}..., χ ' _{12, k}and weights W ₀' ... W ' ₁₂as follows respectively:

$\begin{array}{c}{\mathrm{\χ}}_{0,k-1}^{\′}={\hat{x}}_{k-1}^{\′},{W_0}^{\′}=-1\\ {\mathrm{\χ}}_{j,k-1}^{\′}={\hat{x}}_{k-1}^{\′}+\sqrt{3}{\left(\sqrt{P_{k-1}^{\′}}\right)}_j,{W_j}^{\′}=1/6\\ {\mathrm{\χ}}_{j+6,k-1}^{\′}={\hat{x}}_{k-1}^{\′}-\sqrt{3}{\left(\sqrt{P_{k-1}^{\′}}\right)}_j,W_{j+6}^{\′}=1/6\end{array}---\left(22\right)$

In formula, as P ' _k-1=A ' ^ta ' time, get the jth row of A ', as P ' _k-1=A ' A ' ^ttime, get the jth row of A ', obtain kth-1 instance sample point χ ' _k-1uniform expression be:

C. the time upgrades

The one-step prediction χ ' of starlight angular distance navigation subsystem state vector _k|k-1for:

χ′ _k|k-1＝F ₁(χ′ _k-1，k-1)(24)

Result after the one-step prediction weighting of all sampled point state vectors of starlight angular distance navigation subsystem for:

${\hat{x}}_k^{\′-}=\underset{j=0}{\overset{12}{\mathrm{\Σ}}}{W}_j^{\′}{{\mathrm{\χ}}^{\′}}_{j,k|k-1}---\left(25\right)$

In formula, W _j' be the weights of a jth sampled point;

The estimation mean squared error matrix one-step prediction of starlight angular distance navigation subsystem state vector for:

$P_k^{\′-}=\underset{j-0}{\overset{12}{\mathrm{\Σ}}}{W}_j^{\′}[{\mathrm{\χ}}_{j,k|k-1}^{\′}-{\hat{x}}_k^{\′-}]{[{\mathrm{\χ}}_{j,k|k-1}^{\′}-{\hat{x}}_k^{\′-}]}^T+Q_k^{\′}---\left(26\right)$

In formula, Q ' _kfor the state model error covariance matrix of k moment starlight angular distance navigation subsystem;

The measurement estimate vector Z ' that starlight angular distance navigation subsystem sampled point is corresponding _k|k-1

Z′ _k|k-1＝H ₁(χ′ _k|k-1，k)(27)

The all sampled points of starlight angular distance navigation subsystem measure estimates weighing vector

${\hat{z}}_k^{\′-}=\underset{j=0}{\overset{12}{\mathrm{\Σ}}}{W}_j^{\′}{Z}_{j,k|k-1}^{\′}---\left(28\right)$

D. renewal is measured

Starlight angular distance navigation subsystem measures mean squared error matrix for:

$P_{{\hat{Z}}_k{\hat{Z}}_k}^{\′}=\underset{j=0}{\overset{12}{\mathrm{\Σ}}}{W}_j^{\′}[Z_{j,k|k-1}^{\′}-{\hat{z}}_k^{\′-}]{\left[Z_{j,k|k-1}^{\′}{\hat{z}}_k^{\′-}\right]}^T+R_k^{\′}---\left(29\right)$

In formula, R ' _kfor the measurement noise covariance matrix of k moment starlight angular distance navigation subsystem;

Starlight angular distance navigation subsystem state vector measurement amount mean squared error matrix

$P_{{\hat{x}}_k{\hat{Z}}_k}^{\′}=\underset{j=0}{\overset{12}{\mathrm{\Σ}}}{W}_j^{\′}[{\mathrm{\χ}}_{j,k|k-1}^{\′}-{\hat{x}}_k^{\′-}]{\left[Z_{j,k|k-1}^{\′}{\hat{z}}_k^{\′-}\right]}^T---\left(30\right)$

Starlight angular distance navigation subsystem filter gain K ' _kfor:

$K_k^{\′}=P_{{\hat{x}}_k{\hat{Z}}_k}^{\′}{P}_{{\hat{Z}}_k{\hat{Z}}_k}^{\′-1}---\left(31\right)$

The estimated state vector of starlight angular distance navigation subsystem with estimation mean squared error matrix P _k' be:

${\hat{x}}_k^{\′}={\hat{x}}_k^{\′-}+K_k^{\′}(Z_k^{\′}-{\hat{z}}_k^{\′-})---\left(32\right)$

$P_k^{\′}=P_k^{\′-}-K_k^{\′}{P}_{{\hat{Z}}_k{\hat{Z}}_k}^{\′}{K}_k^{\′T}---\left(33\right)$

6. pair X-ray pulsar navigation subsystem carries out Unscented Kalman filtering

According to the second state model formula (13), X-ray pulsar navigation subsystem measurement model formula (15), the measurement amount formula (19) obtained by X reception of impulse device and formula (20), carry out X-ray pulsar navigation subsystem Unscented Kalman filtering.Concrete steps are as follows:

A. initialization

${\hat{x}}_0=E\left[x_0\right],P_0=E\left[(x_0-{\hat{x}}_0){(x_0-{\hat{x}}_0)}^T\right]---\left(34\right)$

In formula, three shaft positions of the detector that is the 0th moment (initial time) X-ray pulsar navigation subsystem in day heart inertial coordinates system and velocity estimation value, x ₀three shaft positions of the detector that is the 0th moment (initial time) detector in day heart inertial coordinates system and speed actual value, P ₀for the initial mean squared error matrix of X-ray pulsar navigation subsystem state vector.

B. calculating sampling point

In X-ray pulsar navigation subsystem kth-1 moment state vector near choose a series of sample point, average and the mean squared error matrix of these sample points are respectively and P _k-1.If state vector is 6 × 1 dimensions, so sample point χ of 13 X-ray pulsar navigation subsystem _{0, k}..., χ _{12, k}and weights W ₀w ₁₂as follows respectively:

$\begin{array}{c}{\mathrm{\χ}}_{0,k-1}={\hat{x}}_{k-1},W_0=-1\\ {\mathrm{\χ}}_{j,k-1}={\hat{x}}_{k-1}+\sqrt{3}{\left(\sqrt{P_{k-1}}\right)}_j,W_j=1/6\\ {\mathrm{\χ}}_{j+6,k-1}={\hat{x}}_{k-1}-\sqrt{3}{\left(\sqrt{P_{k-1}}\right)}_j,W_{j+6}=1/6\end{array}---\left(35\right)$

In formula, work as P _k-1=A ^tduring A, get the jth row of A, work as P _k-1=AA ^ttime, get the jth row of A, obtain kth-1 instance sample point χ _k-1uniform expression be:

C. the time upgrades

The one-step prediction χ of X-ray pulsar navigation subsystem state vector _k|k-1for:

χ _k|k-1＝F ₂(χ _k-1，k-1)(37)

Result after the one-step prediction weighting of all sampled point state vectors of X-ray pulsar navigation subsystem for:

${\hat{x}}_k^{-}=\underset{j-0}{\overset{12}{\mathrm{\Σ}}}{W}_j{\mathrm{\χ}}_{j,k|k-1}---\left(38\right)$

In formula, W _jfor the weights of a jth sampled point;

The estimation mean squared error matrix one-step prediction of X-ray pulsar navigation subsystem state vector for:

$P_k^{-}=\underset{j=0}{\overset{12}{\mathrm{\Σ}}}{W}_j[{\mathrm{\χ}}_{j,k|k-1}-{\hat{x}}_k^{-}]{[{\mathrm{\χ}}_{j,k|k-1}-{\hat{x}}_k^{-}]}^T+Q_k---\left(29\right)$

In formula, Q _kfor the state model error covariance matrix of k moment X-ray pulsar navigation subsystem;

The measurement estimate vector Z that X-ray pulsar navigation subsystem sampled point is corresponding _k|k-1:

Z _k|k-1＝H ₂(χ _k|k-1，k)(40)

The all sampled points of X-ray pulsar navigation subsystem measure estimates weighing vector

${\hat{z}}_k^{-}=\underset{j=0}{\overset{12}{\mathrm{\Σ}}}{W}_j{Z}_{j,k|k-1}---\left(41\right)$

D. renewal is measured

X-ray pulsar navigation subsystem measures mean squared error matrix for:

$P_{{\hat{Z}}_k{\hat{Z}}_k}=\underset{j-0}{\overset{12}{\mathrm{\Σ}}}{W}_j[Z_{j,k|k-1}-{\hat{z}}_k^{-}]{[Z_{j,k|k-1}-{\hat{z}}_k^{-}]}^T+R_k---\left(42\right)$

In formula, R _kfor X-ray pulsar navigation subsystem measurement noise covariance matrix;

X-ray pulsar navigation subsystem state vector measurement amount mean squared error matrix for:

$P_{{\hat{x}}_k{\hat{Z}}_k}=\underset{j=0}{\overset{12}{\mathrm{\Σ}}}{W}_j[{\mathrm{\χ}}_{j,k|k-1}-{\hat{x}}_k^{-}]{\left[Z_{j,k|k-1}{\hat{z}}_k^{-}\right]}^T---\left(43\right)$

X-ray pulsar navigation subsystem filter gain K _kfor:

$K_k=P_{{\hat{x}}_k{\hat{Z}}_k}{P}_{{\hat{Z}}_k{\hat{Z}}_k}^{-1}---\left(44\right)$

X-ray pulsar navigation subsystem estimated state vector with estimation mean squared error matrix P _kfor:

${\hat{x}}_k={\hat{x}}_k^{-}+K_k(Z_k-{\hat{z}}_k^{-})---\left(45\right)$

$P_k=P_k^{-}-K_k{P}_{{\hat{Z}}_k{\hat{Z}}_k}{K}_k^T---\left(46\right)$

7. determine whether to need to carry out Mars ephemeris corrections

When there being X pulsar measurement amount, carrying out fused filtering and target celestial body ephemeris error estimated and revises, perform step 8; When not having new X pulsar measurement amount to produce, utilize single starlight angular distance to revise target celestial body ephemeris error as measurement amount and upper one ephemeris error revising phase estimate, perform step 9 pair target celestial body ephemeris error and carry out modeling, estimate and feedback compensation;

8. pair Mars ephemeris error carries out modeling, estimates and feedback compensation

X-ray pulsar is navigated, the position and speed information of mistiming to detector mainly utilizing pulse to arrive solar system barycenter and arrival detector is estimated, this navigate mode directly can measure the navigation information relative to the sun, utilizes starlight angular distance to navigate the navigation information can directly measured relative to target celestial body (as Mars).There is error (200m ~ 100km) in the ephemeris due to target celestial body, and X pulsar navigation method can obtain the high precision navigation information of the relative sun, and the relative target coelonavigation precision of information therefore obtained by the method is low; Although utilize starlight angular distance to navigate can obtain the information of relative target coelonavigation comparatively accurately, the high-precision navigation information of the relative sun cannot be obtained by the method.Therefore need to estimate target celestial body ephemeris error, and the navigation error that feedback compensation is caused by target celestial body ephemeris error.

The position relative to Mars that starlight angular distance navigation subsystem obtains and speed are the position relative to the sun that starlight angular distance navigation subsystem obtains and speed are ( for Mars is relative to the position of the sun and speed, can obtain from celestial body almanac data storehouse); The position relative to the sun that X-ray pulsar navigation subsystem obtains and speed are the position relative to Mars that X-ray pulsar navigation subsystem obtains and speed are this shows, single navigational system can be subject to the impact of Mars ephemeris error, cannot meet the demand of the relative sun of detector and the navigation of Mars high precision simultaneously.Therefore the result of starlight angular distance navigation subsystem Unscented Kalman filtering and the result of X-ray pulsar navigation subsystem Unscented Kalman filtering can be utilized to estimate Mars ephemeris error, and concrete steps are as follows:

A. Mars ephemeris error state model is set up

Consider the section of catching duration short (about 40 days) this feature, the change of Mars ephemeris error is less, and the ephemeris error characteristic of Mars in the section of catching is thought of as constant error, sets up Mars ephemeris error state model and be in day heart inertial coordinates system:

$\stackrel{\·}{X}\mathrm{err}=0---\left(47\right)$

In formula, $\stackrel{\·}{X}\mathrm{err}=\left[\begin{array}{ccc}{\stackrel{\·}{x}}_{\mathrm{err}}& {\stackrel{\·}{y}}_{\mathrm{err}}& {\stackrel{\·}{z}}_{\mathrm{err}}\end{array}\right],$ for the differential of the three shaft position errors that day heart inertial coordinates system moderate heat star is gone through, be abbreviated as after discretize:

X _err(k)＝F _err(X _err(k-1)，k-1)+W _err(k-1)(48)

In formula, state transition function F _err(X _err(k-1), k-1)=Φ _{err, k, k-1}x _{err, k-1}, Φ _{err, k, k-1}for kth-1 moment is to the state-transition matrix in kth moment, X _errk () is kth moment Mars ephemeris error state vector, and X _err(k)=X _{err, k}, W _err(k-1) be kth-1 moment Mars error state model error.

B. Mars ephemeris error measurement model is set up

Therefore the measurement model of Mars ephemeris error can be expressed as:

Z _err＝H ₃(X _err(k)，k)+V ₃(49)

In formula, H ₃(X _errk (), k) is the measurement function in k moment, V ₃for Mars ephemeris error measurement noise.

C. Mars ephemeris error measurement amount is obtained

Mars ephemeris error measurement amount Z _errcan be expressed as:

$Z_{\mathrm{err}}=X_{\mathrm{xray}}^s-X_{\mathrm{opt}}^m-X_{\mathrm{Mars}}^s---\left(50\right)$

In formula, the position relative to the sun obtained for X-ray pulsar navigation subsystem and speed, the position relative to Mars obtained for starlight angular distance navigation subsystem and speed, for Mars is relative to the position of the sun and speed, obtain from celestial body almanac data storehouse.

D. Kalman Filter Estimation is carried out to Mars ephemeris error

Mars ephemeris error state model formula (48) set up according to steps A and step B and measurement model formula (49), and Mars ephemeris error measurement amount formula (50) that step C obtains, utilize kalman filter method, Mars ephemeris error is estimated, obtain Mars ephemeris error estimated state vector and estimate mean squared error matrix, specific as follows:

The one-step prediction of Mars ephemeris error state vector:

$X_{\mathrm{err},k/k-1}={\mathrm{\Φ}}_{\mathrm{err},k,k-1}{\hat{X}}_{\mathrm{err},k-1}---\left(51\right)$

In formula, for k-1 moment Mars ephemeris error one-step prediction state vector.

The estimation mean squared error matrix one-step prediction of Mars ephemeris error state vector:

P _err，k/k-1＝Φ _{err，k，k-1}P _err，k-1Φ _{err，k，k-1} ^T+Q _err，k(52)

In formula, P _{err, k-1}for the estimation mean squared error matrix of k-1 moment Mars ephemeris error state vector, Q _{err, k}for k moment Mars ephemeris error state model error mean square error battle array.

Kalman filtering gain:

K _err，k＝P _err，k/k-1H _err，k ^T(H _err，kP _err，k/k-1H _err，kT+R _err，k) ^-1(53)

In formula, H _{err, k}for k moment Mars ephemeris error measurement matrix, H _{err, k}x _{err, k}=H ₃(X _err, k), R _{err, k}for k moment Mars ephemeris error measurement model error covariance matrix.

Mars ephemeris error estimated state vector:

${\hat{X}}_{\mathrm{err},k}=X_{\mathrm{err},k/k-1}+K_{\mathrm{err},k}(Z_{\mathrm{err},k}-H_{\mathrm{err},k}{X}_{\mathrm{err},k/k-1})---\left(54\right)$

In formula, Z _{err, k}for k moment Mars ephemeris error measurement amount.

Mars ephemeris error estimates mean squared error matrix:

P _err，k＝(I-K _err，kH _err，k)P _err，k/k-1(55)

In formula, I is unit battle array.

E. feedback compensation is carried out to Mars ephemeris error

By the Mars ephemeris error obtained in step D mean squared error matrix P is estimated with Mars ephemeris _{err, k}in the first state model feeding back to deep space probe and the second state model, and redefine the model error covariance matrix Q ' of the first state model and the second state model _kand Q _k, finally by the model error covariance matrix Q ' after correction _kand Q _kinput in starlight angular distance navigation subsystem Unscented Kalman filtering and X-ray pulsar navigation subsystem Unscented Kalman filtering, revise the navigation results of subsequent time.

9. information fusion

Because X pulse receiver acquisition X pulsar amount is longer for measuring period, when sensor does not have new X pulse to measure generation, the amount of navigation that X-ray pulsar navigation subsystem does not input is measured, now Unscented Kalman filtering is carried out to starlight angular distance navigation subsystem, comprise time renewal and measure steps such as upgrading (the step C of the 5th step and step D), X pulsar navigation subsystem only carries out time renewal (the step C of the 6th step); When the X pulse receiver on detector produces new, X-ray pulsar navigation subsystem has input quantity to measure, and carries out Unscented Kalman filtering to two subsystems simultaneously, all carries out time renewal and measure upgrading.

Two the partial estimation state vectors obtained in filtering $X_{i_w}\left(k\right)(i_w=1,2)\left(X_1\right(k)={\hat{x}}_k^{\′},$ $X_2\left(k\right)={\hat{x}}_k-X_{mars,k}^m-{\hat{X}}_{err,k}),$ Estimate mean squared error matrix for two $P_{i_w}\left(k\right)\left(P_1\right(k)=P_k^{\′},P_2(k)=P_k),$ Merge by following formula, the estimated state vector sum overall situation obtaining the overall situation estimates that mean squared error matrix is respectively:

${\hat{X}}_g\left(k\right)=P_g\left(k\right)[{P_1}^{-1}\left(k\right)X_1\left(k\right)+{P_2}^{-1}\left(k\right)X_2\left(k\right)]---\left(56\right)$

$P_g\left(k\right)={[{P_1}^{-1}\left(k\right)+{P_2}^{-1}\left(k\right)]}^{-1}---\left(57\right)$

Overall estimated result is fed back to two navigation subsystem, the estimated result as k moment two navigation subsystem:

${\hat{X}}_1\left(k\right)={\hat{X}}_g\left(k\right)---\left(58\right)$

${\hat{X}}_2^s\left(k\right)={\hat{X}}_g\left(k\right)+X_{\mathrm{mars},k}^m+{\hat{X}}_{\mathrm{err},k}---\left(59\right)$

$Q_{i_w}^{-1}\left(k\right)={\mathrm{\β}}_{i_w}{Q}_g^{-1}\left(k\right)---\left(60\right)$

$P_{i_w}^{-1}\left(k\right)={\mathrm{\β}}_{i_w}{P}_g^{-1}\left(k\right)---\left(61\right)$

${\mathrm{\β}}_1+{\mathrm{\β}}_2=1(0\≤{\mathrm{\β}}_{i_w}\≤1,i_w=\mathrm{1,2})---\left(62\right)$

In formula, for the information distribution factor.

The cardinal rule of information distribution selecting predictors is directly proportional to Local Navigation filtering accuracy under the prerequisite meeting information conservation formula, in order to make navigational system have stronger adaptive ability and fault-tolerant ability, use the algorithm based on the dynamic assignment information factor estimating mean squared error matrix norm.

Order

${\mathrm{\β}}_{i_w}\left(k\right)=\frac{{\left({\left|\right|P_{i_w}(k-1)\left|\right|}_F\right)}^{-1}}{\underset{i_w=1}{\overset{2}{\mathrm{\Σ}}}{\left({\left|\right|P_{i_w}(k-1)\left|\right|}_F\right)}^{-1}}---\left(63\right)$

In formula, || || _ffor Frobenius norm, namely for Arbitrary Matrix A,

The most at last formula (58) and formula (59) obtain kth time to be engraved in fiery heart inertial coordinates system and estimated state vector in day heart inertial coordinates system with estimation mean squared error matrix P ₁(k), P ₂k () exports, estimated state vector to be illustrated respectively in fiery heart inertial coordinates system and the position of detector, velocity information in day heart inertial coordinates system, the estimation mean squared error matrix P of output ₁(k), P ₂k () illustrates the performance that filtering is estimated, and returned respectively by these navigation informations in starlight angular distance navigation subsystem and X-ray pulsar navigation subsystem, for position, the speed navigation information in k+1 moment, and k=1,2 ....

The content be not described in detail in instructions of the present invention belongs to the known prior art of professional and technical personnel in the field.

Claims (1)

1. the deep space probe section of the catching astronomical navigation method of based target celestial body ephemeris correction, it is characterized in that: first set up the state model of detector and the measurement model based on starlight angular distance/X-ray pulsar, utilize celestial navigation system to obtain measurement amount based on starlight angular distance and X-ray pulsar, by Unscented Kalman Filter Estimation obtain detector day heart inertial coordinates system and target celestial body centered inertial coordinate system in position and velocity estimation value; On this basis, set up state model and the amount side form type of target celestial body ephemeris error, obtain the measurement amount about ephemeris error, the estimated value obtaining target celestial body ephemeris error is estimated by filtering, and target celestial body ephemeris error is fed back in Navigation System Model, system model is revised, obtain correct after ephemeris error relative to day the heart detector position and speed; Specifically comprise the following steps:

Step 1., set up detector's status equation based on the sun and the main planet of the solar system;

A., in the inertial coordinates system centered by target celestial body, deep space probe is set up based on the sun and dynamic (dynamical) first state model of the eight major planets of the solar system Attractive Orbit;

B., in day heart inertial coordinates system, deep space probe is set up based on the sun and dynamic (dynamical) second state model of the eight major planets of the solar system Attractive Orbit;

Step 2., set up measurement model based on starlight angular distance and X pulsar;

A. the starlight angular distance measurement model with ephemeris error is set up;

B. the measurement model based on X pulsar is set up;

Step 3., to step 1. with step 2. in state model and measurement model carry out discretize;

Step 4., the acquisition of starlight angular distance and X-ray pulsar measurement amount and process;

5., based on starlight angular distance step is estimated detector's status;

According to the starlight angular distance that the first state model in target celestial body centre coordinate system, starlight angular distance measurement model and star sensor obtain, carry out Unscented filtering, estimate to obtain the position and speed state vector of detector under the inertial coordinates system centered by target celestial body and estimation mean squared error matrix P ' _k;

6., based on X pulsar step is estimated detector's status;

According to the second state model under day heart inertial coordinates system, based on the measurement model of X pulsar and measurement amount, carry out Unscented filtering and estimate to obtain the position and speed state vector of detector under day heart inertial coordinates system and estimate mean squared error matrix P _k;

Step 7., determine whether to need to carry out target celestial body ephemeris corrections;

When there being X pulsar measurement amount, carrying out fused filtering and target celestial body ephemeris error estimated and revises, perform step 8.; When not having new X pulsar measurement amount to produce, utilizing single starlight angular distance to revise target celestial body ephemeris error as measurement amount and upper one ephemeris error revising phase estimate, performing step 9.;

Step 8., target celestial body ephemeris error estimated and revises;

A. target celestial body ephemeris error state model is set up;

In day heart inertial coordinates system, set up target celestial body ephemeris error state model is:

$\stackrel{\·}{X}err=0$

In formula, for the differential of three shaft position errors of target celestial body ephemeris in day heart inertial coordinates system, after discretize be:

X _err(k)＝F _err(X _err(k-1),k-1)+W _err(k-1)

In formula, state transition function F _err(X _err(k-1), k-1)=Φ _{err, k, k-1}x _{err, k-1}, wherein Φ _{err, k, k-1}for kth-1 moment is to the state-transition matrix in kth moment, X _errk () is kth moment target celestial body ephemeris error state vector, and X _err(k)=X _{err, k}, W _err(k-1) be kth-1 moment target celestial body ephemeris error state model error, k=1,2 ...;

B. target celestial body ephemeris error measurement model is set up;

The measurement model setting up target celestial body ephemeris error is:

Z _err＝H ₃(X _err(k),k)+V ₃

In formula, H ₃(X _errk (), k) is the measurement function in k moment, V ₃for target celestial body ephemeris error measurement noise;

C. target celestial body ephemeris error measurement amount is obtained;

Measurement amount using starlight angular distance as ephemeris error;

D. Kalman Filter Estimation is carried out to target celestial body ephemeris error;

Target celestial body ephemeris error measurement amount according to the state model of target celestial body ephemeris error, measurement model and acquisition utilizes kalman filter method, target celestial body ephemeris error is estimated, obtains target celestial body ephemeris error estimated state vector and estimate mean squared error matrix;

E. feedback compensation is carried out to target celestial body ephemeris error;

By the target celestial body ephemeris error estimated state obtained in step D vector and estimate in the one the second state models that mean squared error matrix feeds back to deep space probe and measurement model, and redefine the model error covariance matrix of the one the second state models and measurement model, finally the state model after correction target celestial body ephemeris, measurement model and model error covariance matrix are inputed in navigational system Unscented Kalman filtering, revise the navigation results of subsequent time;

Step utilizes 9., separately starlight angular distance to carry out filtering as measurement amount;

When there is no X pulsar measurement amount, be used alone starlight angular distance as measurement amount, and used the target celestial body ephemeris error estimated value in a upper cycle to revise target celestial body position in model, the position of detector and speed state are estimated;

Be engraved in during final output kth and in the inertial coordinates system centered by target celestial body, represent that the estimated state vector sum of detector position and speed estimates mean squared error matrix, and go through according to revised target line star, by in this results conversion Summer Solstice or the Winter Solstice heart inertial coordinates system, export in day heart inertial coordinates system, represent that the estimated state vector sum of detector position and speed estimates mean squared error matrix, these navigation informations are returned respectively in starlight angular distance navigation subsystem and X-ray pulsar navigation subsystem, for the position in k+1 moment, the estimation of speed navigation information, k=1,2 ....