CN110146092B - Double-body asteroid detection track optimization method based on navigation information evaluation - Google Patents

Double-body asteroid detection track optimization method based on navigation information evaluation Download PDF

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CN110146092B
CN110146092B CN201910529154.2A CN201910529154A CN110146092B CN 110146092 B CN110146092 B CN 110146092B CN 201910529154 A CN201910529154 A CN 201910529154A CN 110146092 B CN110146092 B CN 110146092B
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CN110146092A (en
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朱圣英
刘东宸
崔平远
徐瑞
田鹏
梁子璇
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/24—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for cosmonautical navigation

Abstract

The invention discloses a method for optimizing a double-body asteroid detection track based on navigation information evaluation, and belongs to the field of autonomous navigation. The implementation method of the invention comprises the following steps: when the position of the main star is known and the position of the auxiliary star is unknown, establishing a dynamic equation of the detector under an inertial coordinate system of the double-small planetary system; establishing a distance and angle measurement model between the sight line observation model of the main satellite and the auxiliary satellite and a distance and angle measurement model between the detectors according to a navigation system used by the detectors, establishing an observability matrix according to a state equation and an observation equation, and calculating an observability degree; and selecting a track optimization performance index, determining track constraint of double-body asteroid detection, optimizing the track by adopting an optimization algorithm, obtaining the optimal flight tracks of the two detectors according to the searched optimal initial positions and speeds of the two detectors, flying along the optimal tracks to enable the overall navigation performance of the two detectors to be optimal, and accurately estimating the positions of the satellites.

Description

Double-body asteroid detection track optimization method based on navigation information evaluation
Technical Field
The invention relates to a method for optimizing a double-body asteroid detection track based on navigation information evaluation, and belongs to the field of autonomous navigation.
Background
Asteroid exploration is a research hotspot in the field of current deep space exploration. Compared with a single asteroid, the double asteroid system has more complex dynamics, high detection difficulty and high requirement on a navigation system due to factors such as irregular gravitational field, spinning, double asteroid interaction and the like of the double asteroid system. The autonomous optical navigation is one of key technologies for realizing the detection of the double-body asteroid, and in order to realize the accurate detection of the double-body asteroid, an autonomous accurate navigation technology of a double-body asteroid detector needs to be researched, wherein how to design the track of the detector so as to meet the expected navigation performance requirement is a key technology for the navigation of the double-body asteroid, the autonomous positioning capability of the detector is directly influenced, whether the detection task can be successfully completed is determined, and therefore a track optimization method based on the navigation information evaluation is one of key problems concerned by current technologists.
In the developed catamaran asteroid navigation method,prior art [1](see, Vasil M, Torre F, Serra R, et al. angles-Only Navigation of a Formation in the knowledge of a Binary System [ C ]]2018 Space Flight Mechanics Meeting, kissemee, Florida,2018.), obtaining observation information only by using communication between the camera and the detector, and adopting traceless H∞The filtering method carries out state estimation and researches the navigation and position maintenance of the single/two detectors around the Lagrange point L4 of the double small planetary system. Because the navigation of the single/two detectors in the method is carried out under the condition that the positions of the master star and the slave star are known, the ephemeris of the master star and the slave star is not accurate in the actual process, the position of the slave star relative to the master star is also inaccurate, the navigation precision is also poor, and the position of the slave star relative to the master star needs to be estimated.
In the developed track optimization method based on navigation information evaluation, in the prior art [2] (European Wei, Zhanghong Bow, Zheng Wei, Arrax autonomous navigation system design and parameter optimization research [ J ]. deep space exploration academic newspaper, 2017,4(1):43-50.), the two detectors adopt a particle swarm optimization method to optimize the tracks of the two detectors in a Mars surrounding section based on observability degree, and adopt extended Kalman filtering to determine the positions and speeds of the detectors. However, in the method, the tracks of two detectors are optimized based on observability under the dynamic environment of a single celestial body, and the track optimization method is not suitable because the observation models are different due to different binary asteroid dynamic environments.
Disclosure of Invention
In order to solve the problem that the satellite calendars of the main satellite and the auxiliary satellites are inaccurate in the navigation process of the double-body asteroid, so that the positions of the auxiliary satellites relative to the main satellite are inaccurate and the navigation precision is influenced, the invention discloses a method for optimizing the detection track of the double-body asteroid based on navigation information evaluation, which aims to solve the technical problems that: the observability degree of the double-body asteroid detection navigation system is used as an evaluation standard, the track constraint of the double-body asteroid detection is combined, the optimization algorithm is adopted to optimize the detector track to obtain the optimal track, the position and speed estimation accuracy of the two detectors is optimal when the double-body asteroid detection navigation system flies along the optimal track, and the estimation accuracy of the satellite position is also optimal.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a double-body asteroid detection track optimization method based on navigation information evaluation.A dynamic equation of a detector is established under an inertial coordinate system of a double-body asteroid system when the position of a main star is known and the position of a secondary star is unknown; establishing a distance and angle measurement model between the sight line observation model of the main satellite and the auxiliary satellite and a distance and angle measurement model between the detectors according to a navigation system used by the detectors, establishing an observability matrix according to a state equation and an observation equation, and calculating an observability degree; and selecting a track optimization performance index, determining track constraint of double-body asteroid detection, optimizing the track by adopting an optimization algorithm, obtaining the optimal flight tracks of the two detectors according to the searched optimal initial positions and speeds of the two detectors, flying along the optimal tracks to enable the overall navigation performance of the two detectors to be optimal, and accurately estimating the positions of the satellites.
The invention discloses a double-body asteroid detection track optimization method based on navigation information evaluation, which comprises the following steps of:
step 1, establishing a dynamic equation of the detector under an inertial coordinate system of the double small planetary system.
The mass center of the double-asteroid system is selected as an origin to establish an inertial coordinate system of the double-asteroid system, the X axis is selected to point to the spring minute point, the Z axis is the angular velocity direction along which the double-asteroid rotates mutually, and the Y axis is perpendicular to the X axis and the Z axis to form a right-hand coordinate system. And a secondary star fixed connection coordinate system is established by taking a secondary star mass center as an origin, the x axis is along the direction of the minimum inertia axis of the secondary star, the z axis is along the direction of the self-rotation axis of the secondary star, and the y axis is vertical to the x axis and the z axis to form a right-hand coordinate system.
Definition of rA、rB、rSAnd rScRepresenting the positions of the main star, the auxiliary star, the sun and the detector in the inertial system of the two-star system respectively, and defining a position vector r of the detector relative to the main starASc＝rSc-rAPosition vector r of the detector relative to the slave starBSc＝rSc-rBPosition vector r of the detector relative to the sunSSc＝rSc-rSThen the detector is in the inertia seat of the double small planetary systemThe kinetic equation under the standard system is expressed as
Figure GDA0002643148070000021
In the kinetic equation, μAIs the gravitational constant of the dominant star, muBIs the gravitational constant from the star, muSIs the constant of the gravitational force of the sun,IRBis a transformation matrix from a satellite fixed connection coordinate system to a two-satellite system inertia coordinate system, has
Figure GDA0002643148070000022
ωBT represents time as the angular velocity of the rotation from the star about the Z axis.
In equation (1) of dynamics, U20,22Is the gravitational field of the slave star, there are
Figure GDA0002643148070000031
δrBSc＝[xB yB zB]TIs the relative position vector between the slave satellite and the detector in the slave satellite fixed connection coordinate system, and the spherical harmonic coefficient C20And C22Is equal to the minor axis a of the starB、bB、cBThe function of the correlation is then determined,
Figure GDA0002643148070000032
Figure GDA0002643148070000033
θBand
Figure GDA00026431480700000310
respectively a latitude and a longitude, respectively, of the user,
Figure GDA0002643148070000034
Figure GDA0002643148070000035
in the kinetic equation (1), aSRPAcceleration due to solar radiation pressure is provided by
Figure GDA0002643148070000036
A and mScRespectively the cross-sectional area and mass of the detector, CRIs the reflection coefficient, AU is 1 astronomical unit, pSIs a solar radiation pressure of 1 AU.
And 2, establishing an observation equation of the detector according to the optical navigation system.
In the double-body asteroid detection autonomous cooperative optical navigation, the detector obtains observation information through the navigation camera and inter-satellite measurement. Selecting the optical center of the camera as the origin to establish a fixed coordinate system, Z, of the navigation cameraCThe axis being the optical axis of the camera, perpendicular to the image plane, XCAxis, YCThe axes are parallel to the two sides of the image plane, respectively, to form a right-hand coordinate system. Selecting the detector mass center as an origin to establish a detector body fixed connection coordinate system ZbPrincipal axis of maximum inertia, X, of the edge detectorbAxis, YbThe axis points to the other two principal axes of inertia to form a right-hand coordinate system.
For the navigation camera observation information, the coordinate of the position of the centroid of the small celestial body in the navigation camera coordinate system is (X)C,YC,ZC)TThe corresponding image point pixel is (u, v)TThe focal length of the navigation camera is f. According to the principle of pinhole imaging, the relationship between two points is as follows
Figure GDA0002643148070000037
The unit pointing vector formula of the centroid of the asteroid in the camera coordinate system is
Figure GDA0002643148070000038
The sight information of the detector for observing the master satellite and the slave satellite is respectively
Figure GDA0002643148070000039
Wherein, VCAAs the information of the main star's sight line, VCBFor the secondary starsight information, the primary star centroid pixel is (u)A,vA)TFrom the star heart pixel is (u)B,vB)T。
For inter-satellite measurement, the detectors adopt laser ranging to obtain the relative distance between the two detectors, and adopt a visual navigation system to obtain the angle information between the two detectors. In the system of any one of the detectors, the relative position between the two detectors is rr＝(xr,yr,zr)TRelative distance is drThe azimuth of the line of sight is
Figure GDA0002643148070000041
Pitch angle psirThen d isr、
Figure GDA0002643148070000042
ψrAre respectively:
Figure GDA0002643148070000043
Figure GDA0002643148070000044
Figure GDA0002643148070000045
the inter-satellite measurement is composed of the relative distance, azimuth angle and pitch angle between the detectors, and the expression is as follows
Figure GDA0002643148070000046
And 3, constructing an observability matrix according to the state equation and the observation equation, and calculating the observability degree.
For double-body asteroid detection, the position speed and the position of the two detectors need to be estimated, the two detectors respectively carry out sight line observation on the main satellite and the auxiliary satellite and carry out inter-satellite measurement simultaneously, and then the state equation and the observation equation of the system are
Figure GDA0002643148070000047
Wherein r issc1And rsc2Respectively the position of two detectors, vsc1And vsc2Speed, V, of two detectors respectivelyCA1And VCA2Viewing information, V, of the main star for two detectors respectivelyCB1And VCB2The sight line information from the star is observed for two detectors respectively.
Solving the partial derivative by transposing the state quantity by the state equation and the observation equation to obtain a linearized system matrix F and an observation matrix H
Figure GDA0002643148070000048
Figure GDA0002643148070000051
The observability matrix of the system is represented as
O＝[HT FTHT L (F14)THT]T (15)
Using reciprocal of observability matrix condition number as observability measure of system
Figure GDA0002643148070000052
Where cond (O) is the condition number of matrix O.
And 4, selecting a track optimization performance index.
The integral performance index is adopted to reflect the integral performance of the navigation of the two detectors, and the representation form is as follows:
Figure GDA0002643148070000053
wherein, t0Is an initial time tfIs the termination time.
And 5, determining the track constraint of the double body asteroid detection.
For double body asteroid detection, two detectors cannot collide with the master and slave stars, i.e.
Figure GDA0002643148070000054
Wherein a isA、bAAnd cAMajor semi-major axis of the star, aB、bBAnd cBIs a minor axis of the star, rAIs the position of the main star under the inertial system of the double small planetary system rBThe position of the slave planet under the inertial system of the double small planet system.
The two line-of-sight vectors of the detector not being collinear, i.e.
Figure GDA0002643148070000055
Wherein r isASc1And rASc2Respectively, the position vectors, r, of the two detectors relative to the main starBSc1And rBSc2Respectively, the position vectors of the two detectors relative to the slave star.
The line-of-sight vectors of two detectors observing the same star cannot be collinear, i.e.
Figure GDA0002643148070000061
The two detectors use inter-satellite measurement for navigation in addition to the main satellite and the secondary satellite observed by the cameras, and the two detectors need to keep a certain distance, that is, the two detectors need to keep a certain distance
dr＞dmin (21)
Wherein d isrIs the relative distance between two detectors, dminIs the shortest distance between two detectors.
And 6, optimizing the track by adopting an optimization algorithm to obtain a catamaran asteroid detection optimized track based on navigation information evaluation, and flying along the optimal track to enable the position and speed estimation accuracy of the two detectors to be optimal as a whole and the estimation accuracy of the satellite position to be optimal.
The optimization problem of the detection track of the double-body asteroid based on the navigation information evaluation is to select the initial positions and the speeds of two detectors, the two detectors move in the initial state according to a kinetic equation to enable the performance index to be minimum, and simultaneously, constraint conditions are met, namely:
Figure GDA0002643148070000062
Figure GDA0002643148070000063
the track detected by the double-body asteroid is optimized by adopting an optimization algorithm to search the initial positions and the speeds of the two detectors so as to minimize the performance index, simultaneously satisfy the constraint condition, obtain the optimal flight tracks of the two detectors according to the optimal initial positions and the speeds of the two detectors, fly along the optimal tracks so as to optimize the overall navigation performance of the two detectors, and accurately estimate the positions of the asteroids.
Therefore, the optimization of the detection track of the double-body asteroid based on the navigation information evaluation is realized.
Has the advantages that:
the invention discloses a catamaran asteroid detection track optimization method based on navigation information evaluation, which is characterized in that an observability matrix is constructed according to a state equation and an observation equation of a system, the reciprocal of the condition number of the observability matrix is taken as the observability degree of the system, the observability degree is taken as a performance index and combined with the flight track constraint of a detector, the detector track is optimized, and the detector flies along the optimal track, so that the overall position and speed estimation precision of two detectors is optimal, and the estimation precision from the star position is also optimal. The invention has the advantages of good real-time performance and high navigation precision.
Drawings
FIG. 1 is a flow chart of a catamaran asteroid exploration trajectory optimization method based on navigation information evaluation;
FIG. 2 is a graph of the trajectories of two detectors in an example of the invention in different coordinate systems, wherein: fig. 2a) is the track of two detectors under the inertial system of the double small planetary system, and fig. 2b) is the track of two detectors under the fixed connection coordinate system of the main satellite.
FIG. 3 is a state error of the detector navigation along an optimal trajectory in an embodiment of the present invention, where FIG. 3a) is a detector 1 position error curve, 3b) a detector 1 velocity error curve, 3c) a detector 2 position error curve, 3d) a detector 2 velocity error curve, and 3e) an error curve estimated from the position of the star;
FIG. 4 is a Monte Carlo plot of the navigation error of a probe flying along an optimized trajectory and a random trajectory satisfying constraints in an embodiment of the present invention. Wherein fig. 4a) is the position error of the whole two detectors when flying along the optimized trajectory and the random trajectory, 4b) is the speed error of the whole two detectors when flying along the optimized trajectory and the random trajectory, and 4c) is the position error of the slave star when flying along the optimized trajectory and the random trajectory.
Detailed Description
To better illustrate the objects and advantages of the present invention, the following description is given with reference to the accompanying drawings and examples.
Example 1:
select Didymos for the target celestial object on the double-little planetary system 65803, and Table 1 lists the double-little rowsThe parameters of the star system 65803 dymos. The orbit of the double-body asteroid rotating around the center of the double-star system and the orbit of the double-star system rotating around the sun are in the same plane. The resolution of the navigation camera is 500 multiplied by 500 pixels, the field angle is 90 degrees, the focal length of the navigation camera is 20mm, and the measurement error of the camera is 4 multiplied by 10-3rad, inter-satellite range error of 0.1m, inter-satellite angular error of 1 × 10-3And (7) rad. The mass of the detector is constant at 500kg, and the maximum cross-sectional area is 20m2The reflection coefficient is assumed to be 1.
TABLE 1 parameters of the twinkle asteroid 65803 Didymos
Figure GDA0002643148070000071
Figure GDA0002643148070000081
The method for optimizing the detection track of the double-body asteroid based on the navigation information evaluation disclosed by the embodiment comprises the following specific implementation steps:
step 1, establishing a dynamic equation of the detector under an inertial coordinate system of the double small planetary system.
The mass center of the double-asteroid system is selected as an origin to establish an inertial coordinate system of the double-asteroid system, the X axis is selected to point to the spring minute point, the Z axis is the angular velocity direction along which the double-asteroid rotates mutually, and the Y axis is perpendicular to the X axis and the Z axis to form a right-hand coordinate system. And a secondary star fixed connection coordinate system is established by taking a secondary star mass center as an origin, the x axis is along the direction of the minimum inertia axis of the secondary star, the z axis is along the direction of the self-rotation axis of the secondary star, and the y axis is vertical to the x axis and the z axis to form a right-hand coordinate system.
Definition of rA、rB、rSAnd rScRepresenting the positions of the main star, the auxiliary star, the sun and the detector in the inertial system of the two-star system respectively, and defining a position vector r of the detector relative to the main starASc＝rSc-rAPosition vector r of the detector relative to the slave starBSc＝rSc-rBPosition vector r of the detector relative to the sunSSc＝rSc-rSThe dynamic equation of the detector under the inertial coordinate system of the double small planetary system is expressed as
Figure GDA0002643148070000082
In the kinetic equation, μAIs the gravitational constant of the dominant star, muBIs the gravitational constant from the star, muSIs the constant of the gravitational force of the sun,IRBis a transformation matrix from a satellite fixed connection coordinate system to a two-satellite system inertia coordinate system, has
Figure GDA0002643148070000083
ωBT represents time as the angular velocity of the rotation from the star about the Z axis.
In equation (1) of dynamics, U20,22Is the gravitational field of the slave star, there are
Figure GDA0002643148070000091
δrBSc＝[xB yB zB]TIs the relative position vector between the slave satellite and the detector in the slave satellite fixed connection coordinate system, and the spherical harmonic coefficient C20And C22Is equal to the minor axis a of the starB、bB、cBThe function of the correlation is then determined,
Figure GDA0002643148070000092
Figure GDA0002643148070000093
θBand
Figure GDA0002643148070000094
respectively a latitude and a longitude, respectively, of the user,
Figure GDA0002643148070000095
Figure GDA0002643148070000096
in the kinetic equation (1), aSRPAcceleration due to solar radiation pressure is provided by
Figure GDA0002643148070000097
A and mScRespectively the cross-sectional area and mass of the detector, CRIs the reflection coefficient, AU is 1 astronomical unit, pSIs a solar radiation pressure of 1 AU.
And 2, establishing an observation equation of the detector according to the optical navigation system.
In the double-body asteroid detection autonomous cooperative optical navigation, the detector obtains observation information through the navigation camera and inter-satellite measurement. Selecting the optical center of the camera as the origin to establish a fixed coordinate system, Z, of the navigation cameraCThe axis being the optical axis of the camera, perpendicular to the image plane, XCAxis, YCThe axes are parallel to the two sides of the image plane, respectively, to form a right-hand coordinate system. Selecting the detector mass center as an origin to establish a detector body fixed connection coordinate system ZbPrincipal axis of maximum inertia, X, of the edge detectorbAxis, YbThe axis points to the other two principal axes of inertia to form a right-hand coordinate system.
For the navigation camera observation information, the coordinate of the position of the centroid of the small celestial body in the navigation camera coordinate system is (X)C,YC,ZC)TThe corresponding image point pixel is (u, v)TThe focal length of the navigation camera is f. According to the principle of pinhole imaging, the relationship between two points is as follows
Figure GDA0002643148070000098
The unit pointing vector formula of the centroid of the asteroid in the camera coordinate system is
Figure GDA0002643148070000099
The sight information of the detector for observing the master satellite and the slave satellite is respectively
Figure GDA00026431480700000910
Wherein, VCAAs the information of the main star's sight line, VCBFor the secondary starsight information, the primary star centroid pixel is (u)A,vA)TFrom the star heart pixel is (u)B,vB)T. For inter-satellite measurement, the detectors adopt laser ranging to obtain the relative distance between the two detectors, and adopt a visual navigation system to obtain the angle information between the two detectors. In the system of any one of the detectors, the relative position between the two detectors is rr＝(xr,yr,zr)TRelative distance is drThe azimuth of the line of sight is
Figure GDA0002643148070000101
Pitch angle psirThen d isr、
Figure GDA0002643148070000102
ψrAre respectively expressed as
Figure GDA0002643148070000103
Figure GDA0002643148070000104
Figure GDA0002643148070000105
The inter-satellite measurement is composed of the relative distance, azimuth angle and pitch angle between the detectors, and the expression is as follows:
Figure GDA0002643148070000106
and 3, constructing an observability matrix according to the state equation and the observation equation, and calculating the observability degree.
For double-body asteroid detection, two detectors respectively observe the sight of a main star and a secondary star, simultaneously measure the distance between the planets, estimate the position speed and the position of the secondary star of the two detectors, and then the state equation and the observation equation of the system are
Figure GDA0002643148070000107
Wherein r issc1And rsc2Respectively two detector positions, vsc1And vsc2Respectively two detector speeds, VCA1And VCA2Viewing information, V, of the main star for two detectors respectivelyCB1And VCB2The sight line information from the star is observed for two detectors respectively. The transpose of the state quantity of the formula (12) is used for solving the partial derivative to obtain a linearized system matrix F and an observation matrix H
Figure GDA0002643148070000108
Figure GDA0002643148070000111
The observability matrix of the system can be represented as
O＝[HT FTHT L (F14)THT]T (15)
Using reciprocal of observability matrix condition number as observability measure of system
Figure GDA0002643148070000112
Where cond (O) is the condition number of matrix O. The formula can be expressed as
Figure GDA0002643148070000113
σmaxAnd σminRespectively representing the maximum and minimum singular values, λ, of the matrix Omax(OTO) is a matrix OTMaximum eigenvalue of O, λmin(OTO) is a matrix OTMinimum eigenvalue of O. The larger the condition number of the matrix, the closer the matrix is to the ill-conditioned state, and thus can be used to measure the observability of the system. As shown in the formula (17), if the condition number cond (O) is greater than or equal to 1, the value range of the observable degree D is greater than 0 and less than or equal to 1. If cond (O) approaches infinity, D approaches 0, and the system is not observable; if cond (o) is 1, the observability matrix is an orthogonal matrix at this time, the observability level D takes the maximum value of 1, and the larger the observability level is, the higher the estimation accuracy of the navigation system is.
And 4, selecting a track optimization performance index.
The integral performance index is adopted to embody the integral performance of the navigation of the two detectors, and the representation form is as follows
Figure GDA0002643148070000114
Wherein, t0Is an initial time tfIs the termination time.
And 5, determining the track constraint of the double body asteroid detection.
For double body asteroid detection, two detectors cannot collide with the master and slave stars, i.e.
Figure GDA0002643148070000121
Wherein a isA、bAAnd cAMajor semi-major axis of the star, aB、bBAnd cBIs a minor axis of the star, rAIs the position of the main star under the inertial system of the double small planetary system rBThe position of the slave planet under the inertial system of the double small planet system.
The two line-of-sight vectors of the detector not being collinear, i.e.
Figure GDA0002643148070000122
Wherein r isASc1And rASc2Respectively, the position vectors, r, of the two detectors relative to the main starBSc1And rBSc2Respectively, the position vectors of the two detectors relative to the slave star.
The line-of-sight vectors of two detectors observing the same star cannot be collinear, i.e.
Figure GDA0002643148070000123
The two detectors use inter-satellite measurement for navigation in addition to the main satellite and the secondary satellite observed by the cameras, and the two detectors need to keep a certain distance, that is, the two detectors need to keep a certain distance
dr＞dmin (22)
Wherein d isrIs the relative distance between two detectors, dminIs the shortest distance between two detectors.
And 6, optimizing the track by adopting an optimization algorithm to obtain a catamaran asteroid detection optimized track based on navigation information evaluation, and flying along the optimal track to enable the position and speed estimation accuracy of the two detectors to be optimal as a whole and the estimation accuracy of the satellite position to be optimal.
The optimization problem of the detection track of the double-body asteroid based on the navigation information evaluation is to select the initial positions and the speeds of two detectors, the two detectors move in the initial state according to a kinetic equation to enable the performance index to be minimum, and simultaneously satisfy constraint conditions, namely
Figure GDA0002643148070000124
Figure GDA0002643148070000131
The track detected by the double-body asteroid is optimized by adopting an optimization algorithm to search the initial positions and the speeds of the two detectors so as to minimize the performance index, simultaneously satisfy the constraint condition, obtain the optimal flight tracks of the two detectors according to the optimal initial positions and the speeds of the two detectors, fly along the optimal tracks so as to optimize the overall navigation performance of the two detectors, and accurately estimate the positions of the asteroids. In this embodiment, the optimization algorithm used is a genetic algorithm.
Therefore, the optimization of the detection track of the double-body asteroid based on the navigation information evaluation is realized. The flight trajectories of the two detectors are optimized by the method, and the initial states and the optimization results of the two detectors obtained by the genetic algorithm are shown in table 2.
TABLE 2 initial State and optimization results of the Detector
Figure GDA0002643148070000132
According to the optimization result, the two detectors are respectively positioned at the point L4 and the point L5 of the double-asteroid system. Selecting the center of mass of the main satellite as the origin to establish a fixed coordinate system of the main satellite, xaAxis in the direction of the main star's minimum inertia axis, zaThe axis being in the direction of the spin axis of the main star, yaAxis and xaAxis, zaThe axes are vertical to form a right-hand coordinate system, and the tracks of the two detectors under the inertial system of the double-small planetary system and the tracks of the two detectors under the fixed-connection coordinate system of the main satellite are shown in fig. 2.
For navigation of the two detectors, an unscented Kalman filter is adopted for filtering estimation, and the position speed and the position of the slave star of the two detectors are determined. The state equation and observation equation of the system are expressed as
Figure GDA0002643148070000141
Wherein r issc1And rsc2Respectively the position of two detectors, vsc1And vsc2Speed, V, of two detectors respectivelyCA1And VCA2Viewing information, V, of the main star for two detectors respectivelyCB1And VCB2The sight line information from the star is observed for two detectors respectively. The random variables u and v represent process noise and observation noise respectively, the u and v are uncorrelated zero mean Gaussian white noise sequences and are distributed according to u: N (0, Q) and v: N (0, R), Q is a process noise covariance matrix, and R is an observation error variance matrix.
For the unscented Kalman filter, first the covariance matrix needs to be combined
Figure GDA0002643148070000142
By comparing state quantities
Figure GDA0002643148070000143
The unscented transformation constructs a series of sigma points chii，i＝0,1,2,L,2l：
Figure GDA0002643148070000144
Wherein, the x matrix is composed of 2l +1 vectors, l is the dimension of the state vector, and the parameter lambda which controls the sigma point distribution is alpha2(l + κ) -l, where κ ═ 3-l, α ═ 0.001, and subscript i denotes the ith column of the matrix. And updating time of the sigma point by using a state equation, and calculating a weighted mean value and a covariance:
Figure GDA0002643148070000145
wherein
Figure GDA0002643148070000146
Is the weight used in calculating the weighted mean and covarianceThe formula is as follows:
Figure GDA0002643148070000147
where β is used to reduce higher order term errors, which can be determined from a priori knowledge of the state x distribution, β is 2 optimal for a gaussian distribution. And (3) carrying out measurement updating by using an observation equation and a sigma point, and calculating a weighted mean value and a covariance:
Figure GDA0002643148070000151
calculating the unscented Kalman filtering gain, updating the state vector and the covariance matrix, and realizing the unscented Kalman filtering estimation:
Figure GDA0002643148070000152
the estimation errors of the initial state of the detector are 20% of the actual initial state of the detector, and the simulation time is the same as the rotation period of the double-small planetary system and is about 11.92 hours. The navigation error of the two detectors flying along the optimized track under the condition that the position of the slave star is unknown relative to the master star is shown in fig. 3, and it can be seen from fig. 3 that under the condition that the position of the slave star is unknown, the final position precision of both the detector 1 and the detector 2 can reach 6m, the speed precision can reach 0.2m/s for the optimized navigation of the two detectors, and the position speed of the two detectors and the position of the slave star can be accurately determined under the condition that the position of the slave star relative to the master star is unknown.
And carrying out Monte Carlo analysis on the detector navigation based on the optimized track flight and the detector navigation based on the random track flight, and judging whether the navigation performance of the optimized track is optimal or not. Wherein the random trajectory flight satisfies the constraint of step 5, and 1000 times of simulation operation is performed. Because the simulation time and the step length of the detector flight are the same, the navigation precision is judged according to the magnitude of the integral of the absolute value of the navigation error. The integral quantity of the absolute value of the navigation error is large, so that the navigation precision is actually judged by the average value of the absolute value of the navigation error in the whole process, for the position error and the speed error of the two detectors, the sum of the average values of the absolute values of the errors of the two detectors in the whole process is adopted to measure the whole navigation performance, and then
Figure GDA0002643148070000161
Wherein e isrx1(t)、ery1(t)、erz1(t) three-axis position error of the detector 1 at the present time, evx1(t)、evy1(t)、evz1(t) three-axis velocity error of the detector 1 at the present moment, erx2(t)、ery2(t)、erz2(t) three-axis position error of the detector 2 at the present time, evx2(t)、evy2(t)、evz2(t) three-axis velocity error of the detector 2 at the current time, erbx(t)、erby(t)、erbzAnd (t) is the position error of the satellite from three axes at the current moment, the Monte Carlo graph of the navigation error is shown in FIG. 4, and as can be seen from FIG. 4, under the condition that the position of the satellite is unknown, the optimized track position, the speed error and the position error of the satellite are better than those of a random track.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. The method for optimizing the detection track of the double-body asteroid based on the navigation information evaluation is characterized by comprising the following steps of: comprises the following steps of preparing a mixture of a plurality of raw materials,
step 1, establishing a dynamic equation of a detector under an inertial coordinate system of a double-small planetary system;
step 2, establishing an observation equation of the detector according to the optical navigation system;
step 3, constructing an observability matrix according to the state equation and the observation equation, and calculating an observability degree;
step 4, selecting a track optimization performance index;
step 5, determining the track constraint of double-body asteroid detection;
step 6, optimizing the track by adopting an optimization algorithm to obtain a double-body asteroid detection optimized track based on navigation information evaluation, and flying along the optimal track to enable the position and speed estimation precision of the two detectors to be optimal as a whole and the estimation precision of the satellite position to be optimal;
the step 1 is realized by the method that,
selecting the mass center of the double-asteroid system as an origin to establish an inertial coordinate system of the double-asteroid system, selecting an X axis to point to a spring point, selecting a Z axis as an angular velocity direction along which the double-asteroid rotates mutually, and forming a right-hand coordinate system by the Y axis, the X axis and the Z axis which are perpendicular to each other; a secondary star mass center is selected as an origin to establish a secondary star fixed connection coordinate system, the x axis is along the direction of the minimum inertia axis of the secondary star, the z axis is along the direction of the self-rotation axis of the secondary star, and the y axis is perpendicular to the x axis and the z axis to form a right-hand coordinate system;
definition of rA、rB、rSAnd rScRepresenting the positions of the main star, the auxiliary star, the sun and the detector in the inertial system of the two-star system respectively, and defining a position vector r of the detector relative to the main starASc＝rSc-rAPosition vector r of the detector relative to the slave starBSc＝rSc-rBPosition vector r of the detector relative to the sunSSc＝rSc-rSThe dynamic equation of the detector under the inertial coordinate system of the double small planetary system is expressed as
Figure FDA0002785202970000011
In the kinetic equation, μAIs the gravitational constant of the dominant star, muBIs the gravitational constant from the star, muSIs the constant of the gravitational force of the sun,IRBis a transformation matrix from a satellite fixed connection coordinate system to a two-satellite system inertia coordinate system, has
Figure FDA0002785202970000012
ωBIs the angular velocity of the rotation from the star about the Z axis, t represents time;
in equation (1) of dynamics, U20,22Is the gravitational field of the slave star, there are
Figure FDA0002785202970000013
δrBSc＝[xB yB zB]TIs the relative position vector between the slave satellite and the detector in the slave satellite fixed connection coordinate system, and the spherical harmonic coefficient C20And C22Is equal to the minor axis a of the starB、bB、cBThe function of the correlation is then determined,
Figure FDA0002785202970000014
Figure FDA0002785202970000015
θBand
Figure FDA0002785202970000016
respectively a latitude and a longitude, respectively, of the user,
Figure FDA0002785202970000017
Figure FDA0002785202970000021
in the kinetic equation (1), aSRPAcceleration due to solar radiation pressure is provided by
Figure FDA0002785202970000022
A and mScRespectively the cross-sectional area and mass of the detector, CRIs the reflection coefficient, AU is 1 astronomical unit, pSSolar radiation pressure of 1 AU;
the step 2 is realized by the method that,
in the double-body asteroid detection autonomous collaborative optical navigation, a detector obtains observation information through the measurement between a navigation camera and the asteroid; selecting the optical center of the camera as the origin to establish a fixed coordinate system, Z, of the navigation cameraCThe axis being the optical axis of the camera, perpendicular to the image plane, XCAxis, YCThe axes are respectively parallel to two sides of the image plane to form a right-hand coordinate system; selecting the detector mass center as an origin to establish a detector body fixed connection coordinate system ZbPrincipal axis of maximum inertia, X, of the edge detectorbAxis, YbThe axis points to other two inertia main axes to form a right-hand coordinate system;
for the navigation camera observation information, the coordinate of the position of the centroid of the small celestial body in the navigation camera coordinate system is (X)C,YC,ZC)TThe corresponding image point pixel is (u, v)TThe focal length of the navigation camera is f; according to the principle of pinhole imaging, the relationship between two points is as follows
Figure FDA0002785202970000023
The unit pointing vector formula of the centroid of the asteroid in the camera coordinate system is
Figure FDA0002785202970000024
The sight information of the detector for observing the master satellite and the slave satellite is respectively
Figure FDA0002785202970000025
Wherein, VCAAs the information of the main star's sight line, VCBFor the secondary starsight information, the primary star centroid pixel is (u)A,vA)TFrom the star heart pixel is (u)B,vB)T；
For inter-satellite measurement, the detectors adopt laser ranging to obtain the relative distance between the two detectors, and adopt a visual navigation system to obtain the angle information between the two detectors; in the system of any one of the detectors, the relative position between the two detectors is rr＝(xr,yr,zr)TRelative distance is drThe azimuth of the line of sight is
Figure FDA0002785202970000026
Pitch angle psirThen d isr、
Figure FDA0002785202970000027
ψrAre respectively:
Figure FDA0002785202970000028
Figure FDA0002785202970000029
Figure FDA0002785202970000031
the inter-satellite measurement is composed of the relative distance, azimuth angle and pitch angle between the detectors, and the expression is as follows
Figure FDA0002785202970000032
The step 3 is realized by the method that,
for double-body asteroid detection, the position speed and the position of the two detectors need to be estimated, the two detectors respectively carry out sight line observation on the main satellite and the auxiliary satellite and carry out inter-satellite measurement simultaneously, and then the state equation and the observation equation of the system are
Figure FDA0002785202970000033
Wherein r issc1And rsc2Respectively the position of two detectors, vsc1And vsc2Speed, V, of two detectors respectivelyCA1And VCA2Viewing information, V, of the main star for two detectors respectivelyCB1And VCB2Observing the sight line information of the slave star for the two detectors respectively;
solving the partial derivative by transposing the state quantity by the state equation and the observation equation to obtain a linearized system matrix F and an observation matrix H
Figure FDA0002785202970000034
Figure FDA0002785202970000035
The observability matrix of the system is represented as
O＝[HT FTHT L (F14)THT]T (15)
Using reciprocal of observability matrix condition number as observability measure of system
Figure FDA0002785202970000041
Wherein cond (O) is the condition number of matrix O;
step 4, the method is realized by the following steps,
the integral performance index is adopted to reflect the integral performance of the navigation of the two detectors, and the representation form is as follows:
Figure FDA0002785202970000042
wherein, t0Is an initial time tfIs the termination time;
step 5 the method is realized by the following steps,
for double body asteroid detection, two detectors cannot collide with the master and slave stars, i.e.
Figure FDA0002785202970000043
Wherein a isA、bAAnd cAMajor semi-major axis of the star, aB、bBAnd cBIs a minor axis of the star, rAIs the position of the main star under the inertial system of the double small planetary system rBThe position of the slave planet under the inertial system of the double small planet system;
the two line-of-sight vectors of the detector not being collinear, i.e.
Figure FDA0002785202970000044
Wherein r isASc1And rASc2Respectively, the position vectors, r, of the two detectors relative to the main starBSc1And rBSc2The position vectors of the two detectors relative to the slave star respectively;
the line-of-sight vectors of two detectors observing the same star cannot be collinear, i.e.
Figure FDA0002785202970000045
The two detectors use inter-satellite measurement for navigation in addition to the main satellite and the secondary satellite observed by the cameras, and the two detectors need to keep a certain distance, that is, the two detectors need to keep a certain distance
dr＞dmin (21)
Wherein d isrIs the relative distance between two detectors, dminThe shortest distance between the two detectors;
step 6 is realized by the method that,
the optimization problem of the detection track of the double-body asteroid based on the navigation information evaluation is to select the initial positions and the speeds of two detectors, the two detectors move in the initial state according to a kinetic equation to enable the performance index to be minimum, and simultaneously, constraint conditions are met, namely:
Figure FDA0002785202970000051
Figure FDA0002785202970000052
optimizing the track detected by the double-body asteroid by adopting an optimization algorithm to search the initial positions and the speeds of the two detectors so as to minimize the performance index, simultaneously meeting the constraint condition, obtaining the optimal flight tracks of the two detectors according to the optimal initial positions and the speeds of the two detectors, flying along the optimal tracks so as to optimize the overall navigation performance of the two detectors, and accurately estimating the positions of the asteroids;
therefore, the optimization of the detection track of the double-body asteroid based on the navigation information evaluation is realized.
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