CN104765373B - Relative motion state acquiring method on a kind of star - Google Patents
Relative motion state acquiring method on a kind of star Download PDFInfo
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- CN104765373B CN104765373B CN201510051446.1A CN201510051446A CN104765373B CN 104765373 B CN104765373 B CN 104765373B CN 201510051446 A CN201510051446 A CN 201510051446A CN 104765373 B CN104765373 B CN 104765373B
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Abstract
The invention discloses relative motion state acquiring method on a kind of star, its analytic solutions is drawn according to C W equations first, unknown quantity is used as using the amount that C W equation analytic solutions are unrelated with the time, it regard the higher relative position of relative measurement sensor measurement accuracy as measurement amount, unknown quantity unrelated with the time is solved by the method fitting of least square fitting, the relative motion state high accuracy for obtaining representing the actual relative motion situation of two stars forecasts solution (referred to as fitting C W solutions) for a long time.The benefit of this method is that fitting C W solution forecast results are constrained by the higher actual measurement amount of precision, reflect the actual relative motion state of two stars, overcome the limitation of C W equation analytic solutions, and forecast precision is higher, solve the problems, such as relative measurement sensor interval it is unavailable in the case of long-time relative motion state forecast on high-precision Relative Navigation and star, with stronger engineering practice.
Description
Technical field
The present invention relates in spacecraft formation flight, spacecrafts rendezvous to high-precision Relative Navigation technology on task culminant star
Field.
Background technology
The size and Orientation of major control relative velocity in formation flight relative orbit control, therefore the essence of relative velocity
Spend and vital effect is played to the formation effect of formation flight, especially in small yardstick precise formation flight space control task
Among.In practice for the detection of some noncooperative targets, the relative velocity precision of Relative Navigation sensor output is poor, or even has
Can not directly it obtain a bit, and relative positional accuracy is higher, and may have intermittent unavailable, it is impossible to export Relative Navigation letter
Breath；In addition, for the accompanying flying pattern of motor platform, to formulate optimal Relative motion control strategy, it is necessary to long-time Exact Forecast
The relative motion state of two stars, determines to reach the error boundary moment, formulates control strategy, therefore relative measurement sensor with accurate
Long-time relative motion state forecast problem needs urgent solve on high-precision Relative Navigation and star in the case of intermittently unavailable.
Current common practice is that relative velocity is filtered by Kalman filter, obtains the relative of degree of precision
Speed initial information, solves C-W non trivial solutions analysis solution coefficient, so as to utilize parsing under navigation data interruption using single event point
Solution carries out relative motion state forecast.Use Kalman filtering and single event point C-W non trivial solutions analyse solution carry out forecast exist with
Lower shortcoming：One is that can not accurately describe the relative motion of two stars in steric configuration；Two be not account for C-W non trivial solutions analysis solution to miss
Difference, because analytic solutions do not account for the constraint length Time Forecast low precisions such as space perturbation, Guidance and control is carried out using forecast result
When rule is calculated, Guidance Law error is big, and formation control error is big；Three be computationally intensive, it is necessary to carried out on star it is more sampling can just obtain
Desired result is obtained, if navigation data is interrupted, filter result is poor, or even gives formation flight to control bringing on a disaster property consequence.
The content of the invention
Present invention solves the technical problem that being：The deficiencies in the prior art are overcome to be obtained there is provided relative motion state on a kind of star
Method is taken, acquisition and the long-time relative motion state of the intermittent unavailable lower high-precision relative status amount of navigation sensor is realized
Forecast, solve relative measurement sensor interval it is unavailable in the case of long-time relative motion shape on high-precision Relative Navigation and star
State forecasting problem.
The technical scheme is that：A kind of relative motion state acquiring method on star, step is as follows：
1) target satellite orbital coordinate system is set up
Target satellite orbital coordinate system is defined as (O-XoYoZo)：The origin of coordinates is located at target satellite barycenter, and Z axis is in target
The earth's core is pointed to by target satellite barycenter in satellite orbit plane；Y-axis vertical track plane, points to orbit plane and bears normal, with rail
Road angular momentum vectorIn the opposite direction；X-axis constitutes right-handed helix with Y, Z axis, points to satellite and flies to direction；
The relative status of two stars are expressed under target satellite orbital coordinate system, two star relative positions, velocity is defined
It is expressed as in target satellite orbital coordinate system
2) C-W equation analytic solutions are solved in satellite orbit coordinate system
Two star dynamics of relative motion equations are described with C-W equations, then C-W equations are in target satellite orbital coordinate system：
Wherein ω is target satellite orbit angular velocity, ax、ay、azThe controling power applied for each axle,For relative position
Vector is put in first derivative of the target satellite orbital coordinate system component to the time,Defended for Relative position vector in target
Second dervative of the star orbital coordinate system component to the time；
When target satellite does not make maneuvering flight, i.e. ax=ay=az=0, it is known that t0Relative position (the x of the star of moment two0, y0, z0)
And relative velocityOrder k
=y0, then C-W equations parsing inducing diaphoresis be shown as
Wherein τ=t-t0, (xt, yt, zt) represent the star of t two relative position,Represent t two
The relative velocity of star；
3) least square fitting measurement equation is set up
By coefficient ε0, σ, c, d, h, k is as quantity of state, the relative position that will be obtained from relative navigation sensor
As measurement amount, then tiThe measurement equation of moment C-W fitting relative motion forecast is expressed as
pi=ΨiX； (4)
If there is l tiThe relative position measurement amount at moment, then the measurement equation of total C-W fittings relative motion forecast can
To be expressed as
P=Φ X； (5)
4) fitting C-W solution coefficients are solved
According to least square method for solving, then the solution of equation (5) is
X=(ΦTΦ)-1ΦTP； (6)
5) fitting C-W solutions are solved
Accurately solved by (6) formula after X, being then fitted C-W solutions is
6) according to current time t, then τ=t-t0, bring τ and target satellite orbit angular velocity ω into formula (7), obtain t
The relative motion state of the star of moment two；Described target satellite orbit angular velocity ω is in formation flight by ground orbit determination or autonomous
Definitely navigation is provided.
Compared with the prior art, the invention has the advantages that：
Analysed and solved according to C-W non trivial solutions, it is known that initial relative movement state pointWhen with to correspondence
Carve t0, the relative motion state of t can be forecastThis forecasting procedure is only initial with selection
Dotted state is relevant.Initial point chooses Main Basiss relative measurement sensor measurement result on star, and wherein relative velocity error is larger.
The forecast of C-W equations analytic solutions is carried out because analytic solutions are more sensitive to relative velocity initial value, therefore based on an original state point
Precision is poor.
The proposition of the invention utilizes the higher relative position pair for being separated by several case points in a period of time of precision
C-W non trivial solutions analysis solution coefficient is fitted, and analytic solutions is have modified, so as to obtain accurately describing two star actual motion shapes
The forecast for a long time of the high accuracy of state solves (referred to as fitting C-W solutions), calculates simplicity, that is, obtains the relative velocity letter of degree of precision
Breath, but can it is high-precision progress long-time relative motion state forecast, meet navigation sensor data it is unavailable under formation
Flight navigation demand data.
Brief description of the drawings
Fig. 1 is target satellite orbital coordinate system schematic diagram；
Fig. 2 be orbit altitude be 650km, two astrologies away from 90km, in two orbital periods C-W analytic solutions and fitting C-W side
Method relative position prediction error simulation result；
Fig. 3 is the inventive method flow chart.
Embodiment
Below by motor platform to target satellite carry out formation flight exemplified by, the present invention will be described, specifically include as
Lower step：
1) target satellite orbital coordinate system is set up
As shown in figure 1, target satellite orbital coordinate system is defined as (O-XoYoZo)：The origin of coordinates is located at target satellite barycenter,
Z axis points to the earth's core in target satellite orbit plane by target satellite barycenter；Y-axis vertical track plane, points to orbit plane and bears
Normal, with orbital angular momentum vectorIn the opposite direction；X-axis constitutes right-handed helix with Y, Z axis, points to satellite and flies to direction.
The relative status of two stars are expressed under target satellite orbital coordinate system by the present invention, define two star relative positions, speed
Degree vector is expressed as in target satellite orbital coordinate system
2) C-W equation analytic solutions are solved in satellite orbit coordinate system
Two star dynamics of relative motion equations are described for C-W equations, are in target satellite orbital coordinate system：
Wherein ω is target satellite orbit angular velocity, ax、ay、azThe controling power applied for each axle,For relative position
Vector is put in second dervative of the target satellite orbital coordinate system component to the time.
When target satellite does not make maneuvering flight, ax=ay=az=0, now equation (1) analytic solutions be：
Wherein (x0, y0, z0) represent t0The relative position of the star of moment two,Represent its relative velocity, τ=
t-t0, (xt, yt, zt) represent the star of t two relative position,For the relative velocity of the star of t two.
Order K=y0, then C-W solution of equations
Analysis solution (2)-(3) formula can be expressed as
Formula (4)-(5) show only it is to be understood that t0The relative motion state (relative position and speed) at moment can be solved
ε0, σ, c, d, h, k, so as to solve the relative motion state of t using analytic solutions.This forecasting procedure is only first with selection
Initial point state is relevant.
But the condition that C-W equations are set up is：Target track is nearly circle；Space perturbation is not examined；Two astrologies are adjusted the distance to be near
Distance.Therefore in formation flight task using C-W equations analytic solutions carry out long-time relative motion state forecast will with compared with
Big error.In addition, the general direct measurement relative position of relative measuring device, its precision is higher, and relative velocity precision is poor, adopts
When carrying out relative motion state forecast with C-W equations analytic solutions, due to simply employing t0Moment relative motion state carries out pre-
Report, and velocity accuracy is not high, therefore accumulative situation occurs in long-time prediction error.
3) least square fitting measurement equation is set up
Influence forecast precision immediate cause, which is can be seen that, from C-W equation analytic solutions is coefficient ε0, σ, c, d, h, k standard
True property, under real space environment, how accurately to solve analytic solutions coefficient turns into key.By coefficient ε0, σ, c, d, h, k is used as shape
State amount, using the higher relative position of measurement accuracy as measurement amount, then tiThe measurement side of moment C-W fitting relative motion forecast
Journey can be expressed as
pi=ΨiX (6)
If any l tiThe relative position measurement amount at moment, then the measurement equation of total C-W fittings relative motion forecast can
To be expressed as
P=Φ X (7)
4) fitting C-W solution coefficients are solved
According to least square method for solving, then the solution of equation (7) is
X=(ΦTΦ)-1ΦTP (8)
5) fitting C-W solutions are solved
Accurately solved by (8) formula after X, being then fitted C-W solutions is
6) utilize and be fitted C-W solution forecast relative motion states
Known current time t, then τ=t-t0, by τ and target satellite orbit angular velocity ω (by ground in formation flight
Orbit determination or autonomous definitely navigation are provided) bring formula (9) into, (9) formula of utilization just can forecast the relative motion shape of the star of t two
State.
Fig. 2 give orbit altitude for 650km, two astrologies away from 90km, in two orbital periods C-W analytic solutions and fitting C-
W method relative position prediction error simulation results, as can be seen from the figure within two orbital periods 11760s second, are fitted C-W
Method relative position prediction error is much smaller than C-W analytic solutions, and it is higher to carry out relative position forecast precision using fitting C-W methods.
By this patent, the relative velocity amount of degree of precision has been tried to achieve using the higher relative position measurement information of relative accuracy,
High to relative velocity measurement accuracy requirement during formation flight is met, two star actual motion states of accurate description have been obtained
C-W non trivial solutions analysis solution, high-precision relative motion state forecast for a long time can be carried out, C-W equation general analyticals are compensate for
The shortcoming of forecast precision difference is solved, can be applied directly among China's formation flight and spacecrafts rendezvous task Relative motion control,
Have a extensive future.
Unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.
Claims (1)
1. relative motion state acquiring method on a kind of star, it is characterised in that comprise the following steps：
1) target satellite orbital coordinate system is set up
Target satellite orbital coordinate system is defined as (O-XoYoZo)：The origin of coordinates is located at target satellite barycenter, and Z axis is in target satellite
The earth's core is pointed to by target satellite barycenter in orbit plane；Y-axis vertical track plane, points to orbit plane and bears normal, dynamic with track
Measure moment vectorIn the opposite direction；X-axis constitutes right-handed helix with Y, Z axis, points to satellite and flies to direction；
The relative status of two stars are expressed under target satellite orbital coordinate system, two star relative positions, velocity are defined in mesh
Mark satellite orbit coordinate system is expressed as
2) C-W equation analytic solutions are solved in satellite orbit coordinate system
Two star dynamics of relative motion equations are described with C-W equations, then C-W equations are in target satellite orbital coordinate system：
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4) fitting C-W solution coefficients are solved
According to least square method for solving, then the solution of equation (5) is
X=(ΦTΦ)-1ΦTP； (6)
5) fitting C-W solutions are solved
Accurately solved by (6) formula after X, being then fitted C-W solutions is
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6) according to current time t, then τ=t-t0, bring τ and target satellite orbit angular velocity ω into formula (7), obtain t two
The relative motion state of star；Described target satellite orbit angular velocity ω is definitely led in formation flight by ground orbit determination or independently
Boat is provided.
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| CN106767768A (en) * | 2016-12-06 | 2017-05-31 | 东南大学 | A kind of autonomous navigation method of Double Satellite |
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| CN108519109B (en) * | 2018-04-20 | 2020-04-10 | 北京空间飞行器总体设计部 | Method for determining installation parameters of space non-cooperative target relative navigation on-orbit demonstration |
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