CN102607564A - Small satellite autonomous navigation system based on starlight/ geomagnetism integrated information and navigation method thereof - Google Patents

Abstract

The invention provides a small satellite autonomous navigation system based on starlight/ geomagnetism integrated information and a navigation method thereof and belongs to the technical field of integrated navigation. The autonomous navigation system comprises a star sensor measuring system, an earth magnetic field measuring system, an orbit determination system and an attitude determination system. The navigation method comprises the following steps of: the establishment of a navigation system state equation, the measurement equation establishment of the navigation system and integrated navigation system information fusion based on UKF(unscented kalman filter). According to the method, a large view filed star sensor is utilized to simultaneously observe starlight vector information of multiple navigational stars, thereby making up the defect caused by overlarge measurement noise of a magnetometer and obtaining high navigation accuracy; based on track and attitude information contained in the measured values of a magnetometer and the star sensor and in comprehensive consideration of influences of various factors, a measurement equation of the system is established, the adaptability and the stability of a filter to measurement noise are improved; therefore, the method is suitable for navigation of a low earth rail small satellite adopting a cheap small autonomous navigation system.

Description

A kind of moonlet autonomous navigation system and air navigation aid thereof based on starlight/earth magnetism combined information

Technical field

The present invention relates to a kind of moonlet independent navigation conceptual design system and air navigation aid thereof, belong to the integrated navigation technical field based on starlight/earth magnetism combined information.

Background technology

Autonomous navigation of satellite is meant satellite under the condition that does not rely on land station, only relies on measuring equipment on the satellite to confirm position, speed and the attitude of satellite in real time, accomplishes desired function of aerial mission or operation at rail.Current satellite mainly relies on land station to follow the tracks of and orbit determination; But because number of satellite is more in the moonlet networking; Networking positions to exist and measures the short and more difficulty of measurement target of segmental arc to satellite to utilize uphole equipment; And along with the continuous increase of middle low orbit moonlet, the conventional floor measuring and controlling equipment is difficult to satisfy the practical application needs.Moonlet realizes that independent navigation helps to improve the viability of satellite self on the one hand; On the other hand, can also reduce the cost of ground observing and controlling system greatly.In view of limitation that relies on land station's satellite navigation and autonomous navigation of satellite technology remarkable advantages, independent navigation has become an important topic in the design of satellites.

Consider the characteristics of moonlet, need to adopt the navigational system that volume is little, in light weight, low-cost, reliability is high to realize confirming of its track and attitude.Three axis magnetometer has that independence is strong, volume is little, in light weight, cost is low, dependable performance, do not have advantages such as region restriction, and the navigation information of all-weather, real-time continuous can be provided.Since people such as Pasiaki proposed to utilize magnetometer to carry out autonomous navigation of satellite, current many spacecrafts all selected for use magnetometer to be used for confirming of attitude and control.But, because the error of terrestrial magnetic field model and magnetometer survey is bigger, use the earth-magnetic navigation system accuracy of magnetometer lower merely at present, therefore, need utilize other independent navigation means to remedy the deficiency of earth-magnetic navigation.

Celestial navigation is to utilize heavenly body sensor aircraft to be carried out a kind of method of independent navigation; It has good concealment, orientation accuracy high, do not receive the interference of manual work and natural electromagnetic field, outside advantage such as radiated electromagnetic wave not, successfully be applied in the autonomous navigation system of various spacecrafts at present.Star sensor is as current application heavenly body sensor the most widely, and it is the important component part of celestial navigation system, and it has characteristics such as volume is little, precision is high, low in energy consumption; Be one of desirable small-sized independent navigation equipment; The appearance of novel big visual field star sensor makes the starlight Vector Message that obtains three and three above nautical stars simultaneously become possibility, under the prerequisite of outside reference information; Can realize high-precision independent navigation, and not accumulation in time of measuring error.

The navigation data that present earth-magnetic navigation system (GNS) can provide is more comprehensive; The positional information of carrier not only can be provided, and the attitude information of carrier can be provided, and the data output rating is high; But the precision of earth-magnetic navigation is lower, can not satisfy spacecraft precise navigation performance requirement; Celestial navigation (CNS) and earth-magnetic navigation belong to the environment sensitive navigational system together, though the celestial navigation data transfer rate is low, its error does not increase in time.Therefore, adopt the performance requirement that can satisfy the moonlet independent navigation based on the navigation scheme (CNS/GNS) of starlight/earth magnetism combined information.

Summary of the invention

To the problem that exists in the prior art; The present invention proposes a kind of moonlet autonomous navigation system and air navigation aid thereof based on starlight/earth magnetism combined information; Solved the lower and excessive problem of earth-magnetic navigation error that causes of magnetometer survey precision; Analyze earth-magnetic navigation and based on the characteristics and the limitation of the celestial navigation of star sensor, the starlight Vector Message that makes full use of many nautical stars that big visual field star sensor provides obtains earth geomagnetic field information on every side with three axis magnetometer, has realized the mutual supplement with each other's advantages of the two; And carry out information fusion through the UKF filtering method, when improving precision, also improved reliability.

The present invention proposes a kind of moonlet autonomous navigation system based on starlight/earth magnetism combined information, comprises that star sensor measuring system, geomagnetic field measuring system, track confirm system and attitude and heading reference system;

The star sensor measuring system comprises big visual field star sensor, data acquisition unit, star atlas recognition unit, navigation ephemeris and starlight vector acquiring unit; Big visual field star sensor offers data acquisition unit and starlight vector acquiring unit with the starlight Vector Message that measures; Data acquisition unit carries out the data pre-service to the starlight Vector Message that comes arrogant visual field star sensor, and pretreatment information is sent to star atlas recognition unit; Star atlas recognition unit is carried out the star chart coupling according to the reference information that provides from the pretreatment information of data acquisition unit and navigation ephemeris, obtain the starlight vector under inertial coordinates system component and it is offered starlight vector acquiring unit; Starlight vector acquiring unit records starlight vector and starlight vector with big visual field star sensor and offers track at the component under the inertial coordinates system and confirm system and attitude and heading reference system;

The geomagnetic field measuring system comprises three axis magnetometer, international terrestrial magnetic field model and earth magnetism vector error acquiring unit; Three axis magnetometer is through measuring the terrestrial magnetic field of earth surface and terrestrial space; Obtain the component of local geomagnetic fieldvector in the satellite body coordinate system, the measured value of geomagnetic fieldvector; International terrestrial magnetic field model provides the estimated value of geomagnetic fieldvector; Earth magnetism vector error acquiring unit utilizes the measured value of the geomagnetic fieldvector that three axis magnetometer records and estimated value that international terrestrial magnetic field model obtains to calculate the geomagnetic fieldvector error of the two, and it is offered track confirms system and attitude and heading reference system;

Track confirms that system comprises satellite orbit kinetic model unit, β angle acquiring unit, UKF wave filter A unit and satellite-orbit information acquiring unit; Track confirms that foundation is used for the state equation that track is confirmed according to the dynamics of orbits model unit in system, and this state equation is sent to UKF wave filter A unit; The measured value of the geomagnetic fieldvector that the acquiring unit utilization of β angle obtains and starlight Vector Message calculate the angle between the two, and it is offered UKF wave filter A unit as observed quantity; UKF wave filter A unit is according to the observed quantity that obtains and be used for the state equation that track is confirmed, carries out information fusion, estimates and proofreaies and correct the orbit parameter error of satellite in real time, and the orbit parameter that obtains is offered the satellite-orbit information acquiring unit; The satellite-orbit information acquiring unit offers satellite with the orbit parameter that obtains, and accomplishes the track of satellite and confirms;

Attitude and heading reference system comprises attitude of satellite kinetic model unit, UKF wave filter B unit, attitude prediction unit, attitude error estimation unit and attitude of satellite information acquisition unit, and attitude and heading reference system is set up according to the attitude dynamics model unit and is used for the state equation that attitude is confirmed; The state equation that UKF wave filter B unit is definite with being used for attitude according to the metrical information that obtains carries out information fusion; The attitude prediction unit carries out pre-estimation according to the attitude information that the attitude dynamics model unit obtains to the attitude of satellite, obtains attitude prediction information; The attitude error estimation unit is according to the attitude error of estimating satellite from the information of UKF wave filter B unit; Attitude prediction unit and attitude error estimation unit are realized attitude correction through information interchange, and the attitude information after the attitude prediction unit will be proofreaied and correct offers attitude of satellite information acquisition unit; Attitude of satellite information acquisition unit offers satellite with the attitude information that obtains, and realizes that the attitude of satellite is confirmed.

The present invention proposes a kind of autonomous navigation method based on starlight/earth magnetism combined information, specifically may further comprise the steps:

Step 1: the foundation of navigational system state equation

The state variable

of definition navigational system does

$\stackrel{\‾}{X}={[\mathrm{\δx},\mathrm{\δy},\mathrm{\δz},\mathrm{\δ}{v}_x,\mathrm{\δ}{v}_y,\mathrm{\δ}{v}_z,\mathrm{\Δ}\stackrel{\‾}{w},\mathrm{\Δ}\stackrel{\‾}{q}]}^T---\left(1\right)$

In the formula, δ x, δ y, δ z, δ v _x, δ v _y, δ v _zRepresenting the position and the component of velocity error in inertial coordinates system of satellite respectively, is the quantity of state that track is confirmed system;

Be the angular velocity error of satellite body coordinate system with respect to inertial space;

Be error quaternion vector part,

With

Quantity of state for attitude and heading reference system;

Choose equator, the earth's core epoch inertial coordinates system, consider earth centroid gravitation and J ₂The influence of the non-spherical perturbation of item is a white Gaussian noise with other perturbation factors equivalence, and the dynamics of orbits model that satellite orbit kinetic model unit provides does

$\left\{\begin{array}{c}\frac{\mathrm{dx}}{\mathrm{dt}}=v_x+{\mathrm{\ω}}_x\\ \frac{\mathrm{dy}}{\mathrm{dt}}=v_y+{\mathrm{\ω}}_y\\ \frac{\mathrm{dz}}{\mathrm{dt}}=v_z+{\mathrm{\ω}}_z\\ \frac{{\mathrm{dv}}_x}{\mathrm{dt}}=-\mathrm{\μ}\frac{x}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-1.5)]+{\mathrm{\ω}}_{\mathrm{vx}}\\ \frac{{\mathrm{dv}}_y}{\mathrm{dt}}=-\mathrm{\μ}\frac{y}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-1.5)]+{\mathrm{\ω}}_{\mathrm{vy}}\\ \frac{{\mathrm{dv}}_x}{\mathrm{dt}}=-\mathrm{\μ}\frac{z}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-4.5)]+{\mathrm{\ω}}_{\mathrm{vz}}\end{array}\right.---\left(2\right)$

Wherein, x, y, z represent the position in the satellite inertial coordinates system respectively; v _x, v _y, v _zRepresent the speed in the satellite inertial coordinates system respectively;

Be the distance of satellite to the earth's core; R _eBe earth radius; μ is a geocentric gravitational constant; J ₂Be the humorous gravitation perturbation coefficient of the non-spherical second order band of the earth; ω _x, ω _y, ω _zBe respectively the alliance information noise; ω _Vx, ω _Vy, ω _VzBe respectively the system speed information noise;

Define the state of the satellite's orbit is

Equation (2) reduces to

where, t represents time; is the track status and the function of time t;

as the system noise;

The position and the velocity error variable

of definition navigational system do

${\stackrel{\‾}{x}}_o={\widehat{\stackrel{\‾}{X}}}_o-{\stackrel{\‾}{X}}_o{[\mathrm{\δx},\mathrm{\δy},\mathrm{\δz},\mathrm{\δ}{v}_x,\mathrm{\δ}{v}_y,\mathrm{\δ}{v}_z]}^T---\left(3\right)$

Wherein, is the estimated value of

;

Then system track confirms that the state equation of part is expressed as

${\stackrel{\·}{\stackrel{\‾}{x}}}_o=f_o[{\stackrel{\‾}{X}}_o,t]\·{\stackrel{\‾}{x}}_o+{\stackrel{\‾}{\mathrm{\ω}}}_o---\left(4\right)$

Wherein,

is the differential of

;

is corresponding system noise;

Adopt the Quaternion Representation attitude of satellite, then the attitude dynamics model that provides of Satellite Attitude Movement model unit does

$\left\{\begin{array}{c}\stackrel{\·}{\stackrel{\‾}{w}}={\stackrel{\‾}{I}}^{-1}[{\stackrel{\‾}{T}}_c+{\stackrel{\‾}{T}}_d-\stackrel{\‾}{w}\×(\stackrel{\‾}{I}\·\stackrel{\‾}{w})\\ \stackrel{\·}{q}=\frac{1}{2}q\⊗{\stackrel{\‾}{w}}_{\mathrm{ob}}\\ {\stackrel{\‾}{w}}_{\mathrm{ob}}=\stackrel{\‾}{w}-C_o^b\left(q\right){\stackrel{\‾}{w}}_{\mathrm{io}}\end{array}\right.---\left(5\right)$

Wherein,

Control moment for satellite; Disturbance torque for satellite;

Three moment of inertia for satellite;

Be the angular velocity vector of satellite body coordinate system with respect to orbital coordinate system;

Be satellite orbit angular velocity vector, w _oBe the satellite orbit angular speed;

Be the absolute angle speed of satellite with respect to inertial space; Q is the attitude quaternion of satellite;

Be respectively Differential with q;

Be the attitude matrix under the Quaternion Representation;

According to the hypercomplex number compositional rule, and formula (5) carried out linearization, the state equation that obtains attitude and heading reference system does

$\left\{\begin{array}{c}\mathrm{\Δ}\stackrel{\·}{\stackrel{\‾}{w}}={\stackrel{\‾}{I}}^{-1}[\mathrm{\Δ}{\stackrel{\‾}{T}}_c+\mathrm{\Δ}{\stackrel{\‾}{T}}_d-\mathrm{\Δ}\stackrel{\‾}{w}\×(\stackrel{\‾}{I}\·\widehat{\stackrel{\‾}{w}})-\widehat{\stackrel{\‾}{w}}\×(\stackrel{\‾}{I}\·\mathrm{\Δ}\stackrel{\‾}{w})+2\mathrm{\Δ}\stackrel{\‾}{w}\×(\stackrel{\‾}{I}\·\mathrm{\Δ}\stackrel{\‾}{w})\\ \mathrm{\Δ}\stackrel{\·}{\stackrel{\‾}{q}}=-[\widehat{\stackrel{\‾}{w}}\×]\·\mathrm{\Δ}\stackrel{\‾}{q}+\frac{1}{2}\mathrm{\Δ}\stackrel{\‾}{w}\end{array}\right.---\left(6\right)$

Wherein,

expression satellite is with respect to the absolute angle speed of inertial space, and

is its estimated value;

is the error of satellite control moment; is the error of satellite interference moment;

is three moment of inertia of satellite;

is the angular velocity error of satellite body coordinate system with respect to inertial space; Its differential is

is error quaternion vector part, and its differential is

The track that provides respectively according to formula (4) and (6) is confirmed the state equation of system and attitude and heading reference system, obtains the state equation of navigational system;

Step 2: the measurement equation of navigational system is set up

Choose the geomagnetic fieldvector measured value that starlight Vector Message that big visual field star sensor records, earth magnetism vector error value that earth magnetism vector error acquiring unit obtains and three axis magnetometer record and the angle of starlight Vector Message respectively and measure, set up measurement equation as systematic perspective;

A, set up based on the measurement equation of starlight Vector Message

The starlight vector acquiring unit of star sensor measuring system is exported the starlight Vector Message of many nautical stars simultaneously, and attitude and heading reference system is used to the starlight Vector Message L from two navigation fixed stars of starlight vector acquiring unit _M1, L _M2Carrying out the attitude of satellite confirms; The starlight Vector Message L that big visual field star sensor records _mCan be expressed as

$L_m=C_o^b\left(q\right)C_i^o{L}_i+{\mathrm{\υ}}_L---\left(7\right)$

In the formula, L _iBe the component of starlight vector in inertial system, utilize star atlas recognition unit and navigation ephemeris to obtain; υ _LBe the star sensor measuring error;

Be the attitude matrix under the Quaternion Representation; Be tied to the transition matrix of orbital coordinate system for inertia; Q representes the attitude quaternion of satellite; In conjunction with

Formula (7) is expressed as

$L_m={\left[C_o^b\left(\mathrm{\Δq}\right)\right]}^T{C}_o^b\left(\hat{q}\right)C_i^o{L}_i+{\mathrm{\υ}}_L$

(8)

$=(I_{3\×3}+2[\mathrm{\Δ}\stackrel{\‾}{q}\×\left]\right)C_o^b\left(\hat{q}\right)C_i^o{L}_i+{\mathrm{\υ}}_L={\hat{L}}_b+2[{\hat{L}}_b\×]\mathrm{\Δ}\stackrel{\‾}{q}+{\mathrm{\υ}}_L$

In the formula, Be the estimated value of starlight vector in body coordinate system;

For estimating the attitude matrix under the attitude quaternion;

Be the attitude matrix under the error quaternion; I _{3 * 3}The representation unit matrix; Vector part for error quaternion;

Obtain measurement equation Z based on the starlight vector ₁For

$Z_1=\left[\begin{array}{c}{\hat{L}}_{b1}+2[{\hat{L}}_{b1}\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+{\mathrm{\&upsi;}}_{L1}\\ {\hat{L}}_{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000142142780000011.png"\; state="\{\{state\}\}">b</figure-callout>}2}+2[{\hat{L}}_{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000142142780000011.png"\; state="\{\{state\}\}">b</figure-callout>}2}\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+{\mathrm{\&upsi;}}_{L2}\end{array}\right]---\left(9\right)$

Wherein,

The estimated value of starlight vector in body coordinate system for nautical star 1; υ _L1Measuring error for the starlight vector of nautical star 1;

The estimated value of starlight vector in body coordinate system for nautical star 2; υ _L2Measuring error for the starlight vector of nautical star 2;

B, set up based on the measurement equation of earth magnetism vector error

The component B of the terrestrial magnetic field of three axis magnetometer output under satellite body system _mCan be expressed as

$B_m=C_i^b{C}_n^i{B}_n+{\mathrm{\&upsi;}}_{B1}---\left(10\right)$

Wherein, B _nBe the actual value of geomagnetic fieldvector in geographic coordinate system; Be respectively geography and be tied to the transition matrix of inertial system, the transition matrix that inertia is tied to body series; υ _B1Geomagnetic fieldvector measuring error for three axis magnetometer;

The component

of the estimated value of geomagnetic fieldvector in body series does

${\hat{B}}_b={\hat{C}}_i^b{\hat{C}}_e^i{\hat{B}}_n+{\mathrm{\&upsi;}}_{B2}---\left(11\right)$

Wherein, Be B _nEstimated value, try to achieve according to international geomagnetic reference field (IGRF) model; Be respectively

With

Estimated value; υ _B2Be the terrestrial magnetic field model error;

Then the observed quantity Δ B of earth magnetism vector error acquiring unit acquisition does

$\mathrm{\&Delta;B}={\hat{B}}_b-B_m={\hat{C}}_i^b{\hat{C}}_n^i{\hat{B}}_n-C_i^b{C}_n^i{B}_n+{\mathrm{\&upsi;}}_{B2}-{\mathrm{\&upsi;}}_{B1}---\left(12\right)$

Definition $\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)={\hat{C}}_i^b{\hat{C}}_n^i{\hat{B}}_n-C_i^b{C}_n^i{B}_n,$ υ _B=υ _B2-υ _B1, then formula (12) is reduced to

$\mathrm{\&Delta;B}=\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)+{\mathrm{\&upsi;}}_B---\left(13\right)$

According to the rule of differentiating, first of formula (13) right-hand member is expressed as

$\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)=C_i^b\mathrm{\&Delta;}\left(C_n^i{B}_n\right)+\mathrm{\&Delta;}{C}_i^b\left(C_n^i{B}_n\right)---\left(14\right)$

The component B of base area magnetic vector in geographic coordinate system _nDefinition, set up

With the orbit error state Relational expression

H _oExpression formula do

$H_o[{\stackrel{\&OverBar;}{X}}_o,t]=C_i^b\&CenterDot;\frac{\&PartialD;\left[C_n^i(\mathrm{\&theta;},\mathrm{\&lambda;})B_n(r,\mathrm{\&theta;},\mathrm{\&lambda;})\right]}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}---\left(15\right)$

Wherein,

$\frac{\&PartialD;\left[C_n^i(\mathrm{\&theta;},\mathrm{\&lambda;})B_n(r,\mathrm{\&theta;},\mathrm{\&lambda;})\right]}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}$

$=(\frac{\&PartialD;C_n^i}{\&PartialD;\mathrm{\&theta;}}{B}_n+C_n^i\frac{\&PartialD;B_n}{\&PartialD;\mathrm{\&theta;}})\frac{\&PartialD;\mathrm{\&theta;}}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+(\frac{\&PartialD;C_n^i}{\&PartialD;\mathrm{\&lambda;}}{B}_n+C_n^i\frac{\&PartialD;B_n}{\&PartialD;\mathrm{\&lambda;}})\frac{\&PartialD;\mathrm{\&lambda;}}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+C_n^i(\frac{\&PartialD;B_n}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+C_n^i\frac{\&PartialD;B_n}{\&PartialD;r}\frac{\&PartialD;r}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o})$

Second of formula (14) right-hand member is rewritten as

$\mathrm{\&Delta;}{C}_i^b\left(C_n^i{B}_n\right)=\mathrm{\&Delta;}{C}_i^b{B}_i---\left(16\right)$

Wherein, B _iBe the real component of geomagnetic fieldvector in inertial system;

Be that attitude error by satellite causes that its expression formula does

$\mathrm{\&Delta;}{C}_i^b={\hat{C}}_i^b-C_i^b---\left(17\right)$

According to attitude quaternion is in a small amount, can obtain

$\mathrm{\&Delta;}{C}_i^b={\hat{C}}_i^b-C_i^b=(I_{3\&times;3}-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;\left]\right)C_i^b-C_i^b=-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;]C_i^b---\left(18\right)$

Wherein, I _{3 * 3}The representation unit matrix;

Vector part for error quaternion;

(16 obtain to bring formula (18) into formula

$\mathrm{\&Delta;}{C}_i^b{B}_i=(-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;\left]C_i^b\right)B_i=-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;]B_b=2[B_b\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}---\left(19\right)$

Wherein, B _bBe the real component of geomagnetic fieldvector in the body coordinate system;

According to formula (13)～(19), formula (12) is expressed as

$\mathrm{\&Delta;B}=2[B_b\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+H_o{\stackrel{\&OverBar;}{x}}_o+{\mathrm{\&upsi;}}_B---\left(20\right)$

Because B _bBe unknown quantity, adopt the measured value B of three axis magnetometer _mReplace; The observation equation Z of navigational system then ₂For

${\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="HDA0000142142780000011.png"\; state="\{\{state\}\}">Z</figure-callout>}}_2=2[B_m\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+H_o{\stackrel{\&OverBar;}{x}}_o+{\mathrm{\&upsi;}}_B---\left(21\right)$

Wherein, H _oExpression orbit error state

The measurement matrix; υ _BBe corresponding measurement noise;

C, set up based on the measurement equation of starlight vector and earth magnetism vector angle

β angle acquiring unit is chosen the earth magnetism vector B that magnetometer records _mThe starlight vector L that measures with star sensor _M3Between angle as observed quantity, corresponding measurement equation Z ₃For

$Z_3=\mathrm{\&beta;}=\arccos \left(\frac{L_{m3}^T{B}_m}{\left|\right|B_m\left|\right|}\right)+{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}---\left(22\right)$

Wherein, || B _m|| be B _mMould; υ _βThe measuring error of angle;

Obtain the measurement equation of navigational system according to formula (9), (21) and (22);

Step 3: based on the integrated navigation system information fusion of UKF

UKF wave filter A unit by using dynamics of orbits model unit is set up the state equation that track is confirmed system; The angle β that will obtain from the earth magnetism vector error Δ B and the β angle acquiring unit of earth magnetism vector error acquiring unit is as observed quantity; Orbit error state to satellite under the framework of UKF filtering is estimated in real time; And send it to the satellite-orbit information acquiring unit, and the orbit parameter of satellite is proofreaied and correct, realize that track is definite;

UKF wave filter B unit by using attitude dynamics model unit is set up the state equation of attitude and heading reference system, will be from the earth magnetism vector error Δ B of earth magnetism vector error acquiring unit and the starlight Vector Message L of starlight vector acquiring unit _M1And L _M2As observed quantity, the attitude error state to satellite under the framework of UKF filtering is estimated, and it is offered the attitude error estimation unit; The attitude prediction unit by using is carried out attitude prediction from the information of attitude dynamics model unit; And carry out attitude correction with the attitude error estimation unit through message exchange; Be input in the attitude information acquiring unit proofreading and correct the back attitude information, thereby the attitude of accomplishing satellite is confirmed.

The invention has the advantages that:

(1) the present invention proposes a kind of moonlet autonomous navigation system and air navigation aid thereof based on starlight/earth magnetism combined information; Utilize big visual field star sensor to observe the starlight Vector Message of many nautical stars simultaneously; Remedy because of the excessive defective that causes of magnetometer survey noise, thereby obtain higher navigation accuracy;

(2) the present invention proposes a kind of moonlet autonomous navigation system and air navigation aid thereof based on starlight/earth magnetism combined information; Make full use of the track and the attitude information that comprise in the measured value of magnetometer and star sensor; The measurement equation of system is set up in the influence of taking all factors into consideration various factors, has improved wave filter to measuring the adaptive faculty and the stability of noise;

(3) the present invention proposes a kind of moonlet autonomous navigation system and air navigation aid thereof based on starlight/earth magnetism combined information; Track and attitude dynamics model according to satellite; Derivation has also been set up and can have been accomplished track and the definite system state equation of attitude simultaneously, and carries out information fusion through the UKF algorithm and accomplish confirming of track and attitude;

(4) the present invention proposes a kind of moonlet autonomous navigation system and air navigation aid thereof based on starlight/earth magnetism combined information; Have simple in structure, characteristics such as volume is little, system reliability height; Can satisfy low rail moonlet independent navigation requirement; For the low rail moonlet that adopts the small inexpensive autonomous navigation system, be a kind of very promising autonomous navigation of satellite method.

Description of drawings

A kind of moonlet autonomous navigation system structural representation that Fig. 1 proposes for the present invention based on starlight/earth magnetism combined information;

Fig. 2 is the graph of a relation between terrestrial magnetic field spheric coordinate system among the present invention and each magnetic element;

Among the figure:

The 1-star sensor measuring system 2-geomagnetic field measuring 3-of system track is confirmed the 4-of system attitude and heading reference system

The big visual field of 101-star sensor 201-three axis magnetometer 301-dynamics of orbits 401-attitude dynamics mould

Model unit type unit

302-β angle, the international terrestrial magnetic field of 102-data acquisition unit 202-obtains single 402-UKF wave filter B

(IGRF) model element unit

103-star atlas recognition unit 203-earth magnetism vector error 303-UKF wave filter 403-attitude prediction unit

Acquiring unit A unit

304-satellite orbit letter 404-attitude error is estimated

The 104-ephemeris that navigates

Breath acquiring unit unit

105-starlight vector acquiring unit 405-attitude of satellite information

Acquiring unit

Embodiment

To combine accompanying drawing that the present invention is done further detailed description below.

The present invention proposes a kind of moonlet autonomous navigation system and air navigation aid thereof based on starlight/earth magnetism combined information, and is as shown in Figure 1, and this design of Autonomous Navigation System is divided into track and confirms to confirm two parts with attitude.Dynamics of orbits model and attitude dynamics modelling system state equation according to satellite; Starlight vector (the L that records with star sensor _M1, L _M2And L _M3), the ground magnetic vector (B that records of starlight vector and magnetometer _m) between angle (β), the measured value (B of magnetic vector _m) and estimated value

Poor (Δ B) measure as systematic perspective; Utilize the UKF filtering algorithm to estimate the track and the attitude parameter of satellite, realize the independent navigation of moonlet.

A kind of moonlet autonomous navigation system based on starlight/earth magnetism combined information that the present invention proposes comprises that star sensor measuring system 1, geomagnetic field measuring system 2, track confirm system 3 and attitude and heading reference system 4.

Star sensor measuring system 1 mainly comprises big visual field star sensor 101, data acquisition unit 102, star atlas recognition unit 103, navigation ephemeris 104 and starlight vector acquiring unit 105.Big visual field star sensor 101 can obtain the starlight Vector Message of navigation fixed star more than three in synchronization observation, and the starlight Vector Message that measures is offered data acquisition unit 102 and starlight vector acquiring unit 105; 102 pairs of data acquisition units come the starlight Vector Message of arrogant visual field star sensor 101 to carry out the data pre-service, and pretreatment information is sent to star atlas recognition unit 103; Star atlas recognition unit 103 is carried out the star chart coupling according to the pretreatment information from data acquisition unit 102 with the reference information that navigation ephemeris 104 provides, obtain the starlight vector under inertial coordinates system component and it is offered starlight vector acquiring unit 105; Starlight vector acquiring unit 105 records starlight vector and starlight vector with big visual field star sensor 101 and offers track at the component under the inertial coordinates system and confirm system 3 and attitude and heading reference system 4.

Geomagnetic field measuring system 2 mainly comprises three axis magnetometer 201, international terrestrial magnetic field (IGRF) model 202 and earth magnetism vector error acquiring unit 203.Track confirm with the attitude deterministic process in, three axis magnetometer 201 obtains the component of local geomagnetic fieldvector in the satellite body coordinate system, i.e. the measured value of geomagnetic fieldvector through measuring the terrestrial magnetic field of earth surface and terrestrial space; International terrestrial magnetic field (IGRF) model 202 can provide the estimated value of geomagnetic fieldvector; Earth magnetism vector error acquiring unit 203 utilizes the measured value of the geomagnetic fieldvector that three axis magnetometer 201 records and estimated value that international terrestrial magnetic field (IGRF) model 202 obtains to calculate the geomagnetic fieldvector error of the two, and it is offered track confirms system 3 and attitude and heading reference system 4.

Track confirms that system 3 comprises satellite orbit kinetic model unit 301, β angle acquiring unit 302, UKF wave filter A unit 303 and satellite-orbit information acquiring unit 304.In the track deterministic process, track confirms that 301 foundation are used for the state equation that track is confirmed according to the dynamics of orbits model unit in system 3, and this state equation is sent to UKF wave filter A unit 303; β angle acquiring unit 302 utilizes the measured value of the geomagnetic fieldvector that obtains and starlight Vector Message to calculate the angle between the two, and it is offered UKF wave filter A unit 303 as observed quantity; UKF wave filter A unit 303 is according to the observed quantity that obtains and be used for the state equation that track is confirmed, carries out information fusion, estimates and proofreaies and correct the orbit parameter error of satellite in real time, and the orbit parameter that obtains is offered satellite-orbit information acquiring unit 304; Satellite-orbit information acquiring unit 304 offers satellite with the orbit parameter that obtains, and accomplishes the track of satellite and confirms.

Attitude and heading reference system 4 mainly comprises attitude of satellite kinetic model unit 401, UKF wave filter B unit 402, attitude prediction unit 403, attitude error estimation unit 404 and attitude of satellite information acquisition unit 405.In the attitude deterministic process, attitude and heading reference system 4 is set up according to attitude dynamics model unit 401 and is used for the state equation that attitude is confirmed; The state equation that UKF wave filter B unit 402 is definite with being used for attitude according to the metrical information that obtains carries out information fusion; Attitude prediction unit 403 carries out pre-estimation according to the attitude information that attitude dynamics model unit 401 obtains to the attitude of satellite, obtains attitude prediction information; Attitude error estimation unit 404 is according to the attitude error of estimating satellite from the information of UKF wave filter B unit 402; Attitude prediction unit 403 is realized attitude correction with attitude error estimation unit 404 through information interchange, and the attitude information after attitude prediction unit 403 will be proofreaied and correct offers attitude of satellite information acquisition unit 405; Attitude of satellite information acquisition unit 405 offers satellite with the attitude information that obtains, and realizes that the attitude of satellite is confirmed.

The present invention proposes a kind of autonomous navigation method based on starlight/earth magnetism combined information, specifically may further comprise the steps:

Step 1: the foundation of navigational system state equation

The state variable

of definition navigational system does

$\stackrel{\&OverBar;}{X}={[\mathrm{\&delta;x},\mathrm{\&delta;y},\mathrm{\&delta;z},\mathrm{\&delta;}{v}_x,\mathrm{\&delta;}{v}_y,\mathrm{\&delta;}{v}_z,\mathrm{\&Delta;}\stackrel{\&OverBar;}{w},\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}]}^T---\left(1\right)$

In the formula, δ x, δ y, δ z, δ v _x, δ v _y, δ v _zRepresenting the position and the component of velocity error in inertial coordinates system of satellite respectively, is the quantity of state that track is confirmed system 3;

Be the angular velocity error of satellite body coordinate system with respect to inertial space;

Be error quaternion vector part, With

Quantity of state for attitude and heading reference system 4.

Choose (J2000.0) equator, the earth's core inertial coordinates system epoch, mainly consider earth centroid gravitation and J ₂The influence of the non-spherical perturbation of item (refers to other perturbation factors except earth centroid gravitation and J ₂Perturbation beyond the non-spherical perturbation) equivalence is a white Gaussian noise, and then the dynamics of orbits model that provides of satellite orbit kinetic model unit 301 does

$\left\{\begin{array}{c}\frac{\mathrm{dx}}{\mathrm{dt}}=v_x+{\mathrm{\&omega;}}_x\\ \frac{\mathrm{dy}}{\mathrm{dt}}=v_y+{\mathrm{\&omega;}}_y\\ \frac{\mathrm{dz}}{\mathrm{dt}}=v_z+{\mathrm{\&omega;}}_z\\ \frac{{\mathrm{dv}}_x}{\mathrm{dt}}=-\mathrm{\&mu;}\frac{x}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-1.5)]+{\mathrm{\&omega;}}_{\mathrm{vx}}\\ \frac{{\mathrm{dv}}_y}{\mathrm{dt}}=-\mathrm{\&mu;}\frac{y}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-1.5)]+{\mathrm{\&omega;}}_{\mathrm{vy}}\\ \frac{{\mathrm{dv}}_x}{\mathrm{dt}}=-\mathrm{\&mu;}\frac{z}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-4.5)]+{\mathrm{\&omega;}}_{\mathrm{vz}}\end{array}\right.---\left(2\right)$

In the formula, x, y, z represent the position in the satellite inertial coordinates system respectively; v _x, v _y, v _zRepresent the speed in the satellite inertial coordinates system respectively;

Be the distance of satellite to the earth's core; R _eBe earth radius; μ is a geocentric gravitational constant; J ₂Be the humorous gravitation perturbation coefficient of the non-spherical second order band of the earth; ω _x, ω _y, ω _zBe respectively the alliance information noise; ω _Vx, ω _Vy, ω _VzBe respectively the system speed information noise.

Define the state of the satellite's orbit is

Equation (2) can be abbreviated as where, t represents time;

is the track status

and the function of time t;

as the system noise.

The position and the velocity error variable

of definition navigational system do

${\stackrel{\&OverBar;}{x}}_o={\widehat{\stackrel{\&OverBar;}{X}}}_o-{\stackrel{\&OverBar;}{X}}_o{[\mathrm{\&delta;x},\mathrm{\&delta;y},\mathrm{\&delta;z},\mathrm{\&delta;}{v}_x,\mathrm{\&delta;}{v}_y,\mathrm{\&delta;}{v}_z]}^T---\left(3\right)$

In the formula,

is the estimated value of

.

Then system track confirms that the state equation of part 3 can be expressed as

${\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{x}}}_o=f_o[{\stackrel{\&OverBar;}{X}}_o,t]\&CenterDot;{\stackrel{\&OverBar;}{x}}_o+{\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_o---\left(4\right)$

In the formula,

is the differential of

;

is corresponding system noise.

Adopt the Quaternion Representation attitude of satellite, then the attitude dynamics model that provides of Satellite Attitude Movement model unit 401 does

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{w}}={\stackrel{\&OverBar;}{I}}^{-1}[{\stackrel{\&OverBar;}{T}}_c+{\stackrel{\&OverBar;}{T}}_d-\stackrel{\&OverBar;}{w}\&times;(\stackrel{\&OverBar;}{I}\&CenterDot;\stackrel{\&OverBar;}{w})\\ \stackrel{\&CenterDot;}{q}=\frac{1}{2}q\&CircleTimes;{\stackrel{\&OverBar;}{w}}_{\mathrm{ob}}\\ {\stackrel{\&OverBar;}{w}}_{\mathrm{ob}}=\stackrel{\&OverBar;}{w}-C_o^b\left(q\right){\stackrel{\&OverBar;}{w}}_{\mathrm{io}}\end{array}\right.---\left(5\right)$

In the formula, Control moment for satellite;

Disturbance torque for satellite;

Three moment of inertia for satellite; Be the angular velocity vector of satellite body coordinate system with respect to orbital coordinate system;

Be satellite orbit angular velocity vector, w _oBe the satellite orbit angular speed;

Be the absolute angle speed of satellite with respect to inertial space; Q is the attitude quaternion of satellite;

Be respectively Differential with q;

Be the attitude matrix under the Quaternion Representation.

According to the hypercomplex number compositional rule, and expression formula (5) is carried out the state equation that linearization can obtain attitude and heading reference system 4 do

$\left\{\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{w}}={\stackrel{\&OverBar;}{I}}^{-1}[\mathrm{\&Delta;}{\stackrel{\&OverBar;}{T}}_c+\mathrm{\&Delta;}{\stackrel{\&OverBar;}{T}}_d-\mathrm{\&Delta;}\stackrel{\&OverBar;}{w}\&times;(\stackrel{\&OverBar;}{I}\&CenterDot;\widehat{\stackrel{\&OverBar;}{w}})-\widehat{\stackrel{\&OverBar;}{w}}\&times;(\stackrel{\&OverBar;}{I}\&CenterDot;\mathrm{\&Delta;}\stackrel{\&OverBar;}{w})+2\mathrm{\&Delta;}\stackrel{\&OverBar;}{w}\&times;(\stackrel{\&OverBar;}{I}\&CenterDot;\mathrm{\&Delta;}\stackrel{\&OverBar;}{w})\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{q}}=-[\widehat{\stackrel{\&OverBar;}{w}}\&times;]\&CenterDot;\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+\frac{1}{2}\mathrm{\&Delta;}\stackrel{\&OverBar;}{w}\end{array}\right.---\left(6\right)$

Wherein, expression satellite is with respect to the absolute angle speed of inertial space, and

is its estimated value;

is the error of satellite control moment;

is the error of satellite interference moment; is three moment of inertia of satellite;

is the angular velocity error of satellite body coordinate system with respect to inertial space; Its differential is is error quaternion vector part, and its differential is

Can know that by following formula error quaternion nature depression of order is a hypercomplex number vector part, thereby avoid because the singularity problem that the constraint of hypercomplex number orthogonality is caused.The independent navigation of satellite is divided into design and is divided into track and confirms to confirm two parts with attitude, and the track that provides respectively according to formula (4) and (6) is confirmed the state equation of system and attitude and heading reference system, can obtain the state equation of navigational system.

Step 2: the measurement equation of navigational system is set up

Choose the geomagnetic fieldvector measured value that starlight Vector Message that big visual field star sensor 101 records, earth magnetism vector error value that earth magnetism vector error acquiring unit 203 obtains and three axis magnetometer 201 record and the angle of starlight Vector Message respectively and measure, set up measurement equation as systematic perspective.

A, set up based on the measurement equation of starlight Vector Message

Can know that according to Fig. 1 the starlight vector acquiring unit 105 of star sensor measuring system 1 can be exported the starlight Vector Message of many nautical stars simultaneously.Attitude and heading reference system 4 is used to the starlight Vector Message (L from two navigation fixed stars (nautical star 1 and nautical star 2) of starlight vector acquiring unit 105 _M1, L _M2) attitude of carrying out satellite confirms.The starlight Vector Message L that big visual field star sensor 101 records _mCan be expressed as

$L_m=C_o^b\left(q\right)C_i^o{L}_i+{\mathrm{\&upsi;}}_L---\left(7\right)$

In the formula, L _iBe the component of starlight vector in inertial system, star atlas recognition unit 103 capable of using is obtained with navigation ephemeris 104; υ _LBe the star sensor measuring error;

Be the attitude matrix under the Quaternion Representation;

Be tied to the transition matrix of orbital coordinate system for inertia; Q representes the attitude quaternion of satellite; In conjunction with

Formula (7) can be expressed as

$L_m={\left[C_o^b\left(\mathrm{\&Delta;q}\right)\right]}^T{C}_o^b\left(\hat{q}\right)C_i^o{L}_i+{\mathrm{\&upsi;}}_L$

(8)

$=(I_{3\&times;3}+2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;\left]\right)C_o^b\left(\hat{q}\right)C_i^o{L}_i+{\mathrm{\&upsi;}}_L={\hat{L}}_b+2[{\hat{L}}_b\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+{\mathrm{\&upsi;}}_L$

In the formula,

Be the estimated value of starlight vector in body coordinate system;

For estimating the attitude matrix under the attitude quaternion; Be the attitude matrix under the error quaternion; I _{3 * 3}The representation unit matrix;

Vector part for error quaternion.

Obtain measurement equation Z based on the starlight vector ₁For

$Z_1=\left[\begin{array}{c}{\hat{L}}_{b1}+2[{\hat{L}}_{b1}\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+{\mathrm{\&upsi;}}_{L1}\\ {\hat{L}}_{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000142142780000011.png"\; state="\{\{state\}\}">b</figure-callout>}2}+2[{\hat{L}}_{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000142142780000011.png"\; state="\{\{state\}\}">b</figure-callout>}2}\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+{\mathrm{\&upsi;}}_{L2}\end{array}\right]---\left(9\right)$

Wherein,

The estimated value of starlight vector in body coordinate system for nautical star 1; υ _L1Measuring error for the starlight vector of nautical star 1;

The estimated value of starlight vector in body coordinate system for nautical star 2; υ _L2Measuring error for the starlight vector of nautical star 2.

B, set up based on the measurement equation of earth magnetism vector error

The component B of the terrestrial magnetic field of three axis magnetometer 201 outputs under satellite body system _mCan be expressed as

$B_m=C_i^b{C}_n^i{B}_n+{\mathrm{\&upsi;}}_{B1}---\left(10\right)$

In the formula, B _nBe the actual value of geomagnetic fieldvector in geographic coordinate system;

Be respectively geography and be tied to the transition matrix of inertial system, the transition matrix that inertia is tied to body series; υ _B1Geomagnetic fieldvector measuring error for three axis magnetometer 201.

The component

of the estimated value of geomagnetic fieldvector in body series does

${\hat{B}}_b={\hat{C}}_i^b{\hat{C}}_e^i{\hat{B}}_n+{\mathrm{\&upsi;}}_{B2}---\left(11\right)$

Wherein,

Be B _nEstimated value, can try to achieve according to international geomagnetic reference field (IGRF) model 202;

Be respectively

With

Estimated value; υ _B2Be the terrestrial magnetic field model error.

Then the observed quantity Δ B of earth magnetism vector error acquiring unit 203 acquisitions does

$\mathrm{\&Delta;B}={\hat{B}}_b-B_m={\hat{C}}_i^b{\hat{C}}_n^i{\hat{B}}_n-C_i^b{C}_n^i{B}_n+{\mathrm{\&upsi;}}_{B2}-{\mathrm{\&upsi;}}_{B1}---\left(12\right)$

Definition $\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)={\hat{C}}_i^b{\hat{C}}_n^i{\hat{B}}_n-C_i^b{C}_n^i{B}_n,$ υ _B=υ _B2-υ _B1, then formula (12) can be reduced to

$\mathrm{\&Delta;B}=\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)+{\mathrm{\&upsi;}}_B---\left(13\right)$

According to the rule of differentiating, first of formula (13) right-hand member can be expressed as

$\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)=C_i^b\mathrm{\&Delta;}\left(C_n^i{B}_n\right)+\mathrm{\&Delta;}{C}_i^b\left(C_n^i{B}_n\right)---\left(14\right)$

Fig. 2 has provided the graph of a relation between terrestrial magnetic field spheric coordinate system and each magnetic element.Among the figure, O _iX _iY _iZ _iExpression Earth central inertial system; O _eX _eY _eZ _eThe expression terrestrial coordinate system; G is the Greenwich right ascension of meridian; B _r, B _θ, B _λBe the component of geomagnetic fieldvector on three axles of terrestrial magnetic field spheric coordinate system; R is the distance of satellite apart from the earth's core, and λ is a geographic longitude, and θ is a geocentric colatitude; ONET representes local geographic coordinate system, and O is the barycenter of satellite, and ON points to geographic north, and OE points to geographical east, and OT is perpendicular to the ONE plane and point to the earth's core.B _nBe the component of geomagnetic fieldvector in geographic coordinate system, B _HBe B _nComponent in the ONE plane is called horizontal component; X is B _HComponent on the ON axle is called north component; Y is B _HComponent on the OE axle is called east component; Z is B _nComponent on the OT axle is called vertical intensity or vertical component; D is B _HDepart from the angle of geographic north, be called magnetic declination, eastwards partially for just; I is B _nAnd the angle between the surface level ONE is called magnetic dip, dips down to just.

The component B of geomagnetic fieldvector in geographic coordinate system that provides according to Fig. 2 _nDefinition can know that geography is tied to the transition matrix of inertial system

B _nRelevant with the positional information (the earth's core of satellite is apart from r, geographic longitude λ and geocentric colatitude θ) of satellite, promptly first of equality (14) right-hand member mainly caused by the orbit parameter error.Therefore, can set up

With the orbit error state

Relational expression

H _oExpression formula do

$H_o[{\stackrel{\&OverBar;}{X}}_o,t]=C_i^b\&CenterDot;\frac{\&PartialD;\left[C_n^i(\mathrm{\&theta;},\mathrm{\&lambda;})B_n(r,\mathrm{\&theta;},\mathrm{\&lambda;})\right]}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}---\left(15\right)$

Wherein,

$\frac{\&PartialD;\left[C_n^i(\mathrm{\&theta;},\mathrm{\&lambda;})B_n(r,\mathrm{\&theta;},\mathrm{\&lambda;})\right]}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}$

$=(\frac{\&PartialD;C_n^i}{\&PartialD;\mathrm{\&theta;}}{B}_n+C_n^i\frac{\&PartialD;B_n}{\&PartialD;\mathrm{\&theta;}})\frac{\&PartialD;\mathrm{\&theta;}}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+(\frac{\&PartialD;C_n^i}{\&PartialD;\mathrm{\&lambda;}}{B}_n+C_n^i\frac{\&PartialD;B_n}{\&PartialD;\mathrm{\&lambda;}})\frac{\&PartialD;\mathrm{\&lambda;}}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+C_n^i(\frac{\&PartialD;B_n}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+C_n^i\frac{\&PartialD;B_n}{\&PartialD;r}\frac{\&PartialD;r}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o})$

Second attitude measurement matrix with satellite of formula (14) right-hand member is relevant, and it can be rewritten as

$\mathrm{\&Delta;}{C}_i^b\left(C_n^i{B}_n\right)=\mathrm{\&Delta;}{C}_i^b{B}_i---\left(16\right)$

Wherein, B _iBe the real component of geomagnetic fieldvector in inertial system;

Mainly be that attitude error by satellite causes that its expression formula does

$\mathrm{\&Delta;}{C}_i^b={\hat{C}}_i^b-C_i^b---\left(17\right)$

According to attitude quaternion is in a small amount, can obtain

$\mathrm{\&Delta;}{C}_i^b={\hat{C}}_i^b-C_i^b=(I_{3\&times;3}-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;\left]\right)C_i^b-C_i^b=-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;]C_i^b---\left(18\right)$

Wherein, I _{3 * 3}The representation unit matrix;

Vector part for error quaternion.

Bring formula (18) into formula (16), can get

$\mathrm{\&Delta;}{C}_i^b{B}_i=(-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;\left]C_i^b\right)B_i=-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;]B_b=2[B_b\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}---\left(19\right)$

Wherein, B _bBe the real component of geomagnetic fieldvector in the body coordinate system.

According to formula (13)～(19), formula (12) can be expressed as

$\mathrm{\&Delta;B}=2[B_b\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+H_o{\stackrel{\&OverBar;}{x}}_o+{\mathrm{\&upsi;}}_B---\left(20\right)$

Because B _bBe unknown quantity, in real process, can adopt the measured value B of three axis magnetometer 201 _mReplace.The observation equation Z of navigational system then ₂For

${\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="HDA0000142142780000011.png"\; state="\{\{state\}\}">Z</figure-callout>}}_2=2[B_m\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+H_o{\stackrel{\&OverBar;}{x}}_o+{\mathrm{\&upsi;}}_B---\left(21\right)$

Wherein, H _oExpression orbit error state

The measurement matrix; υ _BBe corresponding measurement noise.

C, set up based on the measurement equation of starlight vector and earth magnetism vector angle

β angle acquiring unit 302 is chosen the earth magnetism vector B that magnetometer 201 records _mThe starlight vector L that measures with star sensor 101 _M3Between angle as observed quantity, corresponding measurement equation Z ₃For

$Z_3=\mathrm{\&beta;}=\arccos \left(\frac{L_{m3}^T{B}_m}{\left|\right|B_m\left|\right|}\right)+{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}---\left(22\right)$

Wherein, || B _m|| be B _mMould; υ _βThe measuring error of angle.

According to formula (9), (21) and (22), can obtain the measurement equation of navigational system.

Step 3: based on the integrated navigation system information fusion of UKF

In autonomous navigation system based on starlight/earth magnetism combined information; Three axis magnetometer 201 is all relevant with the track and the attitude information of satellite with the metrical information of big visual field star sensor 101, so navigational system can utilize the UKF filtering algorithm to realize that simultaneously the track of satellite is confirmed and attitude is confirmed.

UKF wave filter A unit 303 utilizes dynamics of orbits model unit 301 to set up the state equation that track is confirmed system; The angle β that will obtain from the earth magnetism vector error Δ B and the β angle acquiring unit 302 of earth magnetism vector error acquiring unit 203 is as observed quantity; Orbit error state to satellite under the framework of UKF filtering is estimated in real time; And send it to satellite-orbit information acquiring unit 304, and the orbit parameter of satellite is proofreaied and correct, realize that track is definite.

UKF wave filter B unit 402 utilizes attitude dynamics model unit 401 to set up the state equation of attitude and heading reference system, will be from the earth magnetism vector error Δ B of earth magnetism vector error acquiring unit 203 and the starlight Vector Message (L of starlight vector acquiring unit 105 _M1, L _M2) as observed quantity, the attitude error state to satellite under the framework of UKF filtering is estimated, and it is offered attitude error estimation unit 404; Attitude prediction unit 403 is used to carry out attitude prediction from the information of attitude dynamics model unit 401; And carry out attitude correction with attitude error estimation unit 404 through message exchange; Be input in the attitude information acquiring unit 405 proofreading and correct the back attitude information, thereby the attitude of accomplishing satellite is confirmed.

Claims (3)

1. moonlet autonomous navigation system based on starlight/earth magnetism combined information is characterized in that: comprise that star sensor measuring system, geomagnetic field measuring system, track confirm system and attitude and heading reference system;

The star sensor measuring system comprises big visual field star sensor, data acquisition unit, star atlas recognition unit, navigation ephemeris and starlight vector acquiring unit; Big visual field star sensor offers data acquisition unit and starlight vector acquiring unit with the starlight Vector Message that measures; Data acquisition unit carries out the data pre-service to the starlight Vector Message that comes arrogant visual field star sensor, and pretreatment information is sent to star atlas recognition unit; Star atlas recognition unit is carried out the star chart coupling according to the reference information that provides from the pretreatment information of data acquisition unit and navigation ephemeris, obtain the starlight vector under inertial coordinates system component and it is offered starlight vector acquiring unit; Starlight vector acquiring unit records starlight vector and starlight vector with big visual field star sensor and offers track at the component under the inertial coordinates system and confirm system and attitude and heading reference system;

The geomagnetic field measuring system comprises three axis magnetometer, international terrestrial magnetic field model and earth magnetism vector error acquiring unit; Three axis magnetometer is through measuring the terrestrial magnetic field of earth surface and terrestrial space; Obtain the component of local geomagnetic fieldvector in the satellite body coordinate system, the measured value of geomagnetic fieldvector; International terrestrial magnetic field model provides the estimated value of geomagnetic fieldvector; Earth magnetism vector error acquiring unit utilizes the measured value of the geomagnetic fieldvector that three axis magnetometer records and estimated value that international terrestrial magnetic field model obtains to calculate the geomagnetic fieldvector error of the two, and it is offered track confirms system and attitude and heading reference system;

Track confirms that system comprises satellite orbit kinetic model unit, β angle acquiring unit, UKF wave filter A unit and satellite-orbit information acquiring unit; Track confirms that foundation is used for the state equation that track is confirmed according to the dynamics of orbits model unit in system, and this state equation is sent to UKF wave filter A unit; The measured value of the geomagnetic fieldvector that the acquiring unit utilization of β angle obtains and starlight Vector Message calculate the angle between the two, and it is offered UKF wave filter A unit as observed quantity; UKF wave filter A unit is according to the observed quantity that obtains and be used for the state equation that track is confirmed, carries out information fusion, estimates and proofreaies and correct the orbit parameter error of satellite in real time, and the orbit parameter that obtains is offered the satellite-orbit information acquiring unit; The satellite-orbit information acquiring unit offers satellite with the orbit parameter that obtains, and accomplishes the track of satellite and confirms;

Attitude and heading reference system comprises attitude of satellite kinetic model unit, UKF wave filter B unit, attitude prediction unit, attitude error estimation unit and attitude of satellite information acquisition unit, and attitude and heading reference system is set up according to the attitude dynamics model unit and is used for the state equation that attitude is confirmed; The state equation that UKF wave filter B unit is definite with being used for attitude according to the metrical information that obtains carries out information fusion; The attitude prediction unit carries out pre-estimation according to the attitude information that the attitude dynamics model unit obtains to the attitude of satellite, obtains attitude prediction information; The attitude error estimation unit is according to the attitude error of estimating satellite from the information of UKF wave filter B unit; Attitude prediction unit and attitude error estimation unit are realized attitude correction through information interchange, and the attitude information after the attitude prediction unit will be proofreaied and correct offers attitude of satellite information acquisition unit; Attitude of satellite information acquisition unit offers satellite with the attitude information that obtains, and realizes that the attitude of satellite is confirmed.

2. autonomous navigation method based on starlight/earth magnetism combined information is characterized in that: specifically may further comprise the steps:

Step 1: the foundation of navigational system state equation

The state variable

of definition navigational system does

$\stackrel{\&OverBar;}{X}={[\mathrm{\&delta;x},\mathrm{\&delta;y},\mathrm{\&delta;z},\mathrm{\&delta;}{v}_x,\mathrm{\&delta;}{v}_y,\mathrm{\&delta;}{v}_z,\mathrm{\&Delta;}\stackrel{\&OverBar;}{w},\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}]}^T---\left(1\right)$

In the formula, δ x, δ y, δ z, δ v _x, δ v _y, δ v _zRepresenting the position and the component of velocity error in inertial coordinates system of satellite respectively, is the quantity of state that track is confirmed system;

Be the angular velocity error of satellite body coordinate system with respect to inertial space;

Be error quaternion vector part,

With

Quantity of state for attitude and heading reference system;

Choose equator, the earth's core epoch inertial coordinates system, consider earth centroid gravitation and J ₂The influence of the non-spherical perturbation of item is a white Gaussian noise with other perturbation factors equivalence, and the dynamics of orbits model that satellite orbit kinetic model unit provides does

$\left\{\begin{array}{c}\frac{\mathrm{dx}}{\mathrm{dt}}=v_x+{\mathrm{\&omega;}}_x\\ \frac{\mathrm{dy}}{\mathrm{dt}}=v_y+{\mathrm{\&omega;}}_y\\ \frac{\mathrm{dz}}{\mathrm{dt}}=v_z+{\mathrm{\&omega;}}_z\\ \frac{{\mathrm{dv}}_x}{\mathrm{dt}}=-\mathrm{\&mu;}\frac{x}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-1.5)]+{\mathrm{\&omega;}}_{\mathrm{vx}}\\ \frac{{\mathrm{dv}}_y}{\mathrm{dt}}=-\mathrm{\&mu;}\frac{y}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-1.5)]+{\mathrm{\&omega;}}_{\mathrm{vy}}\\ \frac{{\mathrm{dv}}_x}{\mathrm{dt}}=-\mathrm{\&mu;}\frac{z}{r^3}[1-J_2{\left(\frac{R_e}{r}\right)}^2(7.5\frac{z^2}{r^2}-4.5)]+{\mathrm{\&omega;}}_{\mathrm{vz}}\end{array}\right.---\left(2\right)$

Wherein, x, y, z represent the position in the satellite inertial coordinates system respectively; v _x, v _y, v _zRepresent the speed in the satellite inertial coordinates system respectively;

Be the distance of satellite to the earth's core; R _eBe earth radius; μ is a geocentric gravitational constant; J ₂Be the humorous gravitation perturbation coefficient of the non-spherical second order band of the earth; ω _x, ω _y, ω _zBe respectively the alliance information noise; ω _Vx, ω _Vy, ω _VzBe respectively the system speed information noise;

Define the state of the satellite's orbit is

Equation (2) reduces to

where, t represents time;

is the track status

and the function of time t;

is the system noise;

The position and the velocity error variable

of definition navigational system do

${\stackrel{\&OverBar;}{x}}_o={\widehat{\stackrel{\&OverBar;}{X}}}_o-{\stackrel{\&OverBar;}{X}}_o{[\mathrm{\&delta;x},\mathrm{\&delta;y},\mathrm{\&delta;z},\mathrm{\&delta;}{v}_x,\mathrm{\&delta;}{v}_y,\mathrm{\&delta;}{v}_z]}^T---\left(3\right)$

Wherein, is the estimated value of

;

Then system track confirms that the state equation of part is expressed as

${\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{x}}}_o=f_o[{\stackrel{\&OverBar;}{X}}_o,t]\&CenterDot;{\stackrel{\&OverBar;}{x}}_o+{\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_o---\left(4\right)$

Wherein,

is the differential of ;

is corresponding system noise;

Adopt the Quaternion Representation attitude of satellite, then the attitude dynamics model that provides of Satellite Attitude Movement model unit does

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{w}}={\stackrel{\&OverBar;}{I}}^{-1}[{\stackrel{\&OverBar;}{T}}_c+{\stackrel{\&OverBar;}{T}}_d-\stackrel{\&OverBar;}{w}\&times;(\stackrel{\&OverBar;}{I}\&CenterDot;\stackrel{\&OverBar;}{w})\\ \stackrel{\&CenterDot;}{q}=\frac{1}{2}q\&CircleTimes;{\stackrel{\&OverBar;}{w}}_{\mathrm{ob}}\\ {\stackrel{\&OverBar;}{w}}_{\mathrm{ob}}=\stackrel{\&OverBar;}{w}-C_o^b\left(q\right){\stackrel{\&OverBar;}{w}}_{\mathrm{io}}\end{array}\right.---\left(5\right)$

Wherein,

Control moment for satellite; Disturbance torque for satellite;

Three moment of inertia for satellite;

Be the angular velocity vector of satellite body coordinate system with respect to orbital coordinate system;

Be satellite orbit angular velocity vector, w _oBe the satellite orbit angular speed;

Be the absolute angle speed of satellite with respect to inertial space; Q is the attitude quaternion of satellite;

Be respectively

Differential with q;

Be the attitude matrix under the Quaternion Representation;

According to the hypercomplex number compositional rule, and formula (5) carried out linearization, the state equation that obtains attitude and heading reference system does

$\left\{\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{w}}={\stackrel{\&OverBar;}{I}}^{-1}[\mathrm{\&Delta;}{\stackrel{\&OverBar;}{T}}_c+\mathrm{\&Delta;}{\stackrel{\&OverBar;}{T}}_d-\mathrm{\&Delta;}\stackrel{\&OverBar;}{w}\&times;(\stackrel{\&OverBar;}{I}\&CenterDot;\widehat{\stackrel{\&OverBar;}{w}})-\widehat{\stackrel{\&OverBar;}{w}}\&times;(\stackrel{\&OverBar;}{I}\&CenterDot;\mathrm{\&Delta;}\stackrel{\&OverBar;}{w})+2\mathrm{\&Delta;}\stackrel{\&OverBar;}{w}\&times;(\stackrel{\&OverBar;}{I}\&CenterDot;\mathrm{\&Delta;}\stackrel{\&OverBar;}{w})\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{q}}=-[\widehat{\stackrel{\&OverBar;}{w}}\&times;]\&CenterDot;\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+\frac{1}{2}\mathrm{\&Delta;}\stackrel{\&OverBar;}{w}\end{array}\right.---\left(6\right)$

Wherein,

expression satellite is with respect to the absolute angle speed of inertial space, and

is its estimated value;

is the error of satellite control moment;

is the error of satellite interference moment; is three moment of inertia of satellite;

is the angular velocity error of satellite body coordinate system with respect to inertial space; Its differential is is error quaternion vector part, and its differential is

The track that provides respectively according to formula (4) and (6) is confirmed the state equation of system and attitude and heading reference system, obtains the state equation of navigational system;

Step 2: the measurement equation of navigational system is set up

Choose the geomagnetic fieldvector measured value that starlight Vector Message that big visual field star sensor records, earth magnetism vector error value that earth magnetism vector error acquiring unit obtains and three axis magnetometer record and the angle of starlight Vector Message respectively and measure, set up measurement equation as systematic perspective;

A, set up based on the measurement equation of starlight Vector Message

The starlight vector acquiring unit of star sensor measuring system is exported the starlight Vector Message of many nautical stars simultaneously, and attitude and heading reference system is used to the starlight Vector Message L from two navigation fixed stars of starlight vector acquiring unit _M1, L _M2Carrying out the attitude of satellite confirms; The starlight Vector Message L that big visual field star sensor records _mCan be expressed as

$L_m=C_o^b\left(q\right)C_i^o{L}_i+{\mathrm{\&upsi;}}_L---\left(7\right)$

In the formula, L _iBe the component of starlight vector in inertial system, utilize star atlas recognition unit and navigation ephemeris to obtain; υ _LBe the star sensor measuring error;

Be the attitude matrix under the Quaternion Representation;

Be tied to the transition matrix of orbital coordinate system for inertia; Q representes the attitude quaternion of satellite; In conjunction with

Formula (7) is expressed as

$L_m={\left[C_o^b\left(\mathrm{\&Delta;q}\right)\right]}^T{C}_o^b\left(\hat{q}\right)C_i^o{L}_i+{\mathrm{\&upsi;}}_L$

(8)

$=(I_{3\&times;3}+2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;\left]\right)C_o^b\left(\hat{q}\right)C_i^o{L}_i+{\mathrm{\&upsi;}}_L={\hat{L}}_b+2[{\hat{L}}_b\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+{\mathrm{\&upsi;}}_L$

In the formula,

Be the estimated value of starlight vector in body coordinate system; For estimating the attitude matrix under the attitude quaternion;

Be the attitude matrix under the error quaternion; I _{3 * 3}The representation unit matrix;

Vector part for error quaternion;

Obtain measurement equation Z based on the starlight vector ₁For

$Z_1=\left[\begin{array}{c}{\hat{L}}_{b1}+2[{\hat{L}}_{b1}\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+{\mathrm{\&upsi;}}_{L1}\\ {\hat{L}}_{b2}+2[{\hat{L}}_{b2}\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+{\mathrm{\&upsi;}}_{L2}\end{array}\right]---\left(9\right)$

Wherein,

The estimated value of starlight vector in body coordinate system for nautical star 1; υ _L1Measuring error for the starlight vector of nautical star 1; The estimated value of starlight vector in body coordinate system for nautical star 2; υ _L2Measuring error for the starlight vector of nautical star 2;

B, set up based on the measurement equation of earth magnetism vector error

The component B of the terrestrial magnetic field of three axis magnetometer output under satellite body system _mCan be expressed as

$B_m=C_i^b{C}_n^i{B}_n+{\mathrm{\&upsi;}}_{B1}---\left(10\right)$

Wherein, B _nBe the actual value of geomagnetic fieldvector in geographic coordinate system;

Be respectively geography and be tied to the transition matrix of inertial system, the transition matrix that inertia is tied to body series; υ _B1Geomagnetic fieldvector measuring error for three axis magnetometer;

The component

of the estimated value of geomagnetic fieldvector in body series does

${\hat{B}}_b={\hat{C}}_i^b{\hat{C}}_e^i{\hat{B}}_n+{\mathrm{\&upsi;}}_{B2}---\left(11\right)$

Wherein,

Be B _nEstimated value, try to achieve according to international geomagnetic reference field (IGRF) model;

Be respectively

With

Estimated value; υ _B2Be the terrestrial magnetic field model error;

Then the observed quantity Δ B of earth magnetism vector error acquiring unit acquisition does

$\mathrm{\&Delta;B}={\hat{B}}_b-B_m={\hat{C}}_i^b{\hat{C}}_n^i{\hat{B}}_n-C_i^b{C}_n^i{B}_n+{\mathrm{\&upsi;}}_{B2}-{\mathrm{\&upsi;}}_{B1}---\left(12\right)$

Definition $\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)={\hat{C}}_i^b{\hat{C}}_n^i{\hat{B}}_n-C_i^b{C}_n^i{B}_n,$ υ _B=υ _B2-υ _B1, then formula (12) is reduced to

$\mathrm{\&Delta;B}=\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)+{\mathrm{\&upsi;}}_B---\left(13\right)$

According to the rule of differentiating, first of formula (13) right-hand member is expressed as

$\mathrm{\&Delta;}\left(C_i^b{C}_n^i{B}_n\right)=C_i^b\mathrm{\&Delta;}\left(C_n^i{B}_n\right)+\mathrm{\&Delta;}{C}_i^b\left(C_n^i{B}_n\right)---\left(14\right)$

The component B of base area magnetic vector in geographic coordinate system _nDefinition, set up With the orbit error state

Relational expression H _oExpression formula do

$H_o[{\stackrel{\&OverBar;}{X}}_o,t]=C_i^b\&CenterDot;\frac{\&PartialD;\left[C_n^i(\mathrm{\&theta;},\mathrm{\&lambda;})B_n(r,\mathrm{\&theta;},\mathrm{\&lambda;})\right]}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}---\left(15\right)$

Wherein,

$\frac{\&PartialD;\left[C_n^i(\mathrm{\&theta;},\mathrm{\&lambda;})B_n(r,\mathrm{\&theta;},\mathrm{\&lambda;})\right]}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}$

$=(\frac{\&PartialD;C_n^i}{\&PartialD;\mathrm{\&theta;}}{B}_n+C_n^i\frac{\&PartialD;B_n}{\&PartialD;\mathrm{\&theta;}})\frac{\&PartialD;\mathrm{\&theta;}}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+(\frac{\&PartialD;C_n^i}{\&PartialD;\mathrm{\&lambda;}}{B}_n+C_n^i\frac{\&PartialD;B_n}{\&PartialD;\mathrm{\&lambda;}})\frac{\&PartialD;\mathrm{\&lambda;}}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+C_n^i(\frac{\&PartialD;B_n}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o}+C_n^i\frac{\&PartialD;B_n}{\&PartialD;r}\frac{\&PartialD;r}{\&PartialD;{\stackrel{\&OverBar;}{X}}_o})$

Second of formula (14) right-hand member is rewritten as

$\mathrm{\&Delta;}{C}_i^b\left(C_n^i{B}_n\right)=\mathrm{\&Delta;}{C}_i^b{B}_i---\left(16\right)$

Wherein, B _iBe the real component of geomagnetic fieldvector in inertial system;

Be that attitude error by satellite causes that its expression formula does

$\mathrm{\&Delta;}{C}_i^b={\hat{C}}_i^b-C_i^b---\left(17\right)$

According to attitude quaternion is in a small amount, can obtain

$\mathrm{\&Delta;}{C}_i^b={\hat{C}}_i^b-C_i^b=(I_{3\&times;3}-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;\left]\right)C_i^b-C_i^b=-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;]C_i^b---\left(18\right)$

Wherein, I _{3 * 3}The representation unit matrix;

Vector part for error quaternion;

(16 obtain to bring formula (18) into formula

$\mathrm{\&Delta;}{C}_i^b{B}_i=(-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;\left]C_i^b\right)B_i=-2[\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}\&times;]B_b=2[B_b\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}---\left(19\right)$

Wherein, B _bBe the real component of geomagnetic fieldvector in the body coordinate system;

According to formula (13)～(19), formula (12) is expressed as

$\mathrm{\&Delta;B}=2[B_b\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+H_o{\stackrel{\&OverBar;}{x}}_o+{\mathrm{\&upsi;}}_B---\left(20\right)$

Because B _bBe unknown quantity, adopt the measured value B of three axis magnetometer _mReplace; The observation equation Z of navigational system then ₂For

$Z_2=2[B_m\&times;]\mathrm{\&Delta;}\stackrel{\&OverBar;}{q}+H_o{\stackrel{\&OverBar;}{x}}_o+{\mathrm{\&upsi;}}_B---\left(21\right)$

Wherein, H _oExpression orbit error state

The measurement matrix; υ _BBe corresponding measurement noise;

C, set up based on the measurement equation of starlight vector and earth magnetism vector angle

β angle acquiring unit is chosen the earth magnetism vector B that magnetometer records _mThe starlight vector L that measures with star sensor _M3Between angle as observed quantity, corresponding measurement equation Z ₃For

$Z_3=\mathrm{\&beta;}=\arccos \left(\frac{L_{m3}^T{B}_m}{\left|\right|B_m\left|\right|}\right)+{\mathrm{\&upsi;}}_{\mathrm{\&beta;}}---\left(22\right)$

Wherein, || B _m|| be B _mMould; υ _βThe measuring error of angle;

Obtain the measurement equation of navigational system according to formula (9), (21) and (22);

Step 3: based on the integrated navigation system information fusion of UKF

UKF wave filter A unit by using dynamics of orbits model unit is set up the state equation that track is confirmed system; The angle β that will obtain from the earth magnetism vector error Δ B and the β angle acquiring unit of earth magnetism vector error acquiring unit is as observed quantity; Orbit error state to satellite under the framework of UKF filtering is estimated in real time; And send it to the satellite-orbit information acquiring unit, and the orbit parameter of satellite is proofreaied and correct, realize that track is definite;

UKF wave filter B unit by using attitude dynamics model unit is set up the state equation of attitude and heading reference system, will be from the earth magnetism vector error Δ B of earth magnetism vector error acquiring unit and the starlight Vector Message L of starlight vector acquiring unit _M1And L _M2As observed quantity, the attitude error state to satellite under the framework of UKF filtering is estimated, and it is offered the attitude error estimation unit; The attitude prediction unit by using is carried out attitude prediction from the information of attitude dynamics model unit; And carry out attitude correction with the attitude error estimation unit through message exchange; Be input in the attitude information acquiring unit proofreading and correct the back attitude information, thereby the attitude of accomplishing satellite is confirmed.

3. a kind of autonomous navigation method based on starlight/earth magnetism combined information according to claim 2 is characterized in that: other perturbation factors is except earth centroid gravitation and the perturbation the non-spherical perturbation of J2 item in the described step 1.

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