CN103927289B - A kind of method for determining low rail target satellite preliminary orbit according to space-based satellite Angle Measured Data - Google Patents
A kind of method for determining low rail target satellite preliminary orbit according to space-based satellite Angle Measured Data Download PDFInfo
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Abstract
The invention discloses a kind of method for determining low rail target satellite preliminary orbit according to space-based satellite Angle Measured Data, Angle Measured Data of the method using the low rail target satellite of high-speed motion relative to low rail observation satellite obtains the relative observation star unit vector of target satelliteConditional equation.The ρ that finds range is obtained on the premise of to conditional equation addition of constraints0Conditional equationWithUsing one fixed step size of selection, to the ρ in constraint equation0And the semi-major axis a of target satellite0Plus the method for certain weight, obtain initial value of the iterative solution as next step iteration：PositionSpeedAnd then iterate to calculate until convergence obtains low rail target satellite preliminary orbit, false solution thus is shielded from, true solution is obtained, determine position and the speed of target satellite.The present invention is by way of to solving target addition of constraints condition, solve the problems, such as the high speed dynamic and the false solution caused by the missing of observed quantity due to the relative observation star of target satellite, calculation procedure is converged near true solution, make orbit determination result close to theoretical optimum solution C.R lower bounds.
Description
Technical field
The present invention relates to the satellite initial orbit technical field in artificial satellite precise orbit determination, and in particular to surveyed according to observation star
The method that the low rail target satellite Angle Measured Data for obtaining determines its preliminary orbit.
Background technology
Determine low rail target satellite track according to space-based satellite Angle Measured Data, be initially considered that and ground based observa tion station Angle Measured Data
Initial orbit is determined without what difference, and the sky is only moved in observation station from ground.In fact both has very big difference, ground
Base survey station is only with earth rotation, and the observation satellite then high-speed cruising on low rail track, the Laws of Mechanics and low rail mesh of its motion
Mark satellite is extremely similar to.When initial orbit is calculated to the Angle Measured Data of low rail target satellite according to observation star, due to being seen without distance
Measurement, will appear from double solution, and true solution is target satellite track, and false solution is observation satellite own orbit.
If indiscriminately imitating the initial orbit computing method of ground based observa tion, to the rail target high of more than semi-major axis 20000km, can restrain
To near true solution, this is that, because rail satellite motion speed high is slower, and the characteristics of motion of observation star has a larger difference, but for
Low rail target satellite, due to the extreme similitude of sport dynamics rule, and the relative observation star of target satellite high speed dynamic and
Apart from observed quantity missing, if do not determine the initial orbit equation of motion to traditional Angle Measured Data improved, can cause calculation procedure certainly
Dynamic to converge near false solution, this will have a strong impact on orbit determination accuracy.
The content of the invention
Determine that low orbit satellite target track technology can be converged near false solution automatically for existing space-based, have a strong impact on orbit determination
The problem of precision, initial orbit is determined it is an object of the invention to provide a kind of according to the relative observation star Angle Measured Data of low rail target satellite
Method, the method shields the false solution that traditional foundation Space-based Angle Measured Data determines the initial orbit equation of motion, makes program towards the side of true solution
To convergence, and reach orbit determination accuracy higher.
In order to achieve the above object, the present invention is adopted the following technical scheme that：
A kind of method for determining low rail target satellite preliminary orbit according to space-based satellite Angle Measured Data, the method is using weighting
Angle Measured Data determines the equation of motion of low orbit satellite preliminary orbit, and causes calculation procedure to all targets using the equation of motion
Converge to true solution.
In the preferred scheme of this programme, methods described is seen first with the low rail target satellite of high-speed motion relative to low rail
The Angle Measured Data of satellite is surveyed, the relative observation star unit vector of target satellite is obtainedConditional equation；
Then, the ρ that finds range is obtained on the premise of to conditional equation addition of constraints0The conditional equation of addition of constraints
With
Finally, using one fixed step size of selection, to the ρ in constraint equation0And the semi-major axis a of target satellite0Plus certain weight
Method, obtains initial value of the iterative solution as next step iteration：PositionSpeedAnd then iterate to calculate until convergence obtains low
Rail target satellite preliminary orbit, and false solution thus is shielded from, true solution is obtained, determine position and the speed of target satellite.
Further, concrete implementation step is as follows：
Step 1,
The unit vector method of initial orbit is determined according to ground, the unit vector of the relative observation star of target is obtained
In formulaUnit vector for target satellite relative to observation star, ρkDistance for target satellite relative to observation star, observation
Amount (αk,δk) beRight ascension declination under inertial coodinate system；
Step 2,
Introduce two withOrthogonal unit vector
Unit vectorBy observed quantity right ascension declination (αk,δk) calculate, thus to each observed quantity (αk,δk) under generation
State two conditional equations of addition of constraints：
Wherein weight
σ is the middle error obtained in iterative process in formula；
Step 3,
Increase to ρ0Constraints；
Primary iteration is only to range finding ρ0Addition of constraints is solvedTo ρ0Addition of constraints conditional equation is：
Weighting 1/wr,(wr=100 meters)
Its solution as following iterative calculation initial value
During second iteration, it is changed to solveReduction
Now to each observed quantity (αk,δk) form following two conditional equations：
(1/ ρ of weightingk *σ)
In formulaByCalculate, andByCalculate；
Step 4,
FoundationAgain to range finding ρ0Addition of constraints condition, obtains the ρ that finds range0The conditional equation of addition of constraints：
ρ0Initial value be calculated by circular orbit, conditional equation is added and states the solution of constraints as next step iteration
Initial value
Step 5,
In the iterative calculation later stage to semi-major axis a0A constraints is added, it is necessary to suitably weight, to match ρ0, to carry
Orbit determination accuracy high.
Solved for low rail target satellite using the present invention, due to similar, the relative observation of target of sport dynamics rule
The high speed dynamic of star and apart from observed quantity missing so that calculation procedure converges to the mathematics singular problem near false solution automatically,
The beneficial effect of the true and false for judging solution is achieved, and effectively raises surely first rail precision.
Brief description of the drawings
The present invention is further illustrated below in conjunction with the drawings and specific embodiments.
Fig. 1 is the geometrical relationship figure of target satellite and observation star；
Fig. 2 is calculation flow chart of the invention；
Fig. 3 is to determine initial orbit result apart from the low rail target for observing star 1000km or so；
Fig. 4 is to determine initial orbit result apart from the low rail target for observing star 1600km or so；
Fig. 5 is to determine initial orbit result apart from the low rail target for observing star 2000km or so.
Specific embodiment
In order that technological means, creation characteristic, reached purpose and effect that the present invention is realized are easy to understand, tie below
Conjunction is specifically illustrating, and the present invention is expanded on further.
The present invention obtains the unit of the relative observation star of target satellite using the unit vector method for determining one of the current techique of initial orbit
VectorThe equation of (subscript k is the sequence number of sampled point), wherein unit vectorNon trivial solution has two conditional equations of addition of constraints：
Thus, shield false solution and obtain true solution, determine position and the speed of target satellite.Its concrete implementation process is as follows：
Referring to Fig. 1, its geometrical relationship figure for showing target satellite and observation star.As seen from the figure,
Formula 1
ρ k are the distance of target and survey station in formula.
Determine one of current techique of initial orbit unit vector method according to ground by calculation procedure, obtain the relative observation star of target
Unit vector(such as formula 2), (α in following formulak,δk) it is observed quantity, characterizeRight ascension declination under the inertial coodinate system in direction.
Formula 2
According to the kinetic model of two-body problem, tkMomentWith t0MomentThere is following relation
Formula 3
In formula, fk,gkIt is t0,tk,Function.
Can be obtained by above-mentioned derivation：
Formula 4
In order to eliminate unknown quantity ρk, formation condition equation, introduce two withOrthogonal unit vectorAs reference
Vector：
Formula 5
The two vectors are by observed quantity right ascension declination (αk,δk) calculate, use respectivelyPoint multiplier 4 both sides, eliminate
.So, to each observed quantity (αk,δk), following two conditional equations will be produced：
(1/ ρ of weightingkσ) formula 6
σ is the middle error obtained in iterative process in above formula.
Initial orbit of determining in the present invention refers to determining initial orbit according to the observation Angle Measured Data that measures of star that target is that semi-major axis is
The low rail target satellite of below 9000km.When the orbit altitude of low rail target satellite is similar with observation astrology, occur in that i.e.
Make to increased to interstellar distance ρ0The still not convergent situation of the constraints of (subscript 0 represents initial value).Thus, in unit vector
In method, while increasing to ρ0With a0Two constraintss, will have good convergence to low rail target satellite.Its process is as follows：
Primary iteration is only to ρ0Addition of constraints, solvesTo ρ0The conditional equation of addition of constraints is：
Weighting 1/wρ,(wρ=100 meters) formula 7
Its solution as following iterative calculation initial value
During second iteration, it is changed to solveReductionThat is reference vector method.
Formula 8
Use respectivelyDot product(formula is the reduction of formula 4, that is, after correcting
WithWithSubtract each other the value for obtaining, the symbol with * is each calculating iterative value in formula, is known quantity) both sides, now
To each observed quantity (αk,δk) form following two conditional equations：
(1/ ρ of weightingk *σ) formula 9
In formulaByCalculate, andByCalculate.
FoundationAnd the geometrical relationship shown in Fig. 1, then to range finding ρ0Addition of constraints condition, by under formation
State conditional equation：
Weighting 1/wρ,(wρ=100 meters) formula 10
ρ0Initial value be calculated by circular orbit, conditional equation is added and states the solution of constraints as next step iteration
Initial value
The circular orbit Preliminary orbit determination algorithm for referring here to, refers to assume that target track is circular orbit, i.e. rk=r0=a, this is one
The algorithm scanned for a.Merely with first point of (t of observation segmental arc1,α1,δ1) and last point (tN,αN,δN) or equivalenceBy
Both sides square：
Make r now1=a, can solve：
Similarly
I.e. as known a can solve ρ1,ρN, thenMean angular velocity can be calculated：
On the other hand, by n2a3=μ, can calculate a n' again, if the value of semi-major axis a is correct, it should have
Semi-major axis a being scanned for, that is, finds an a, made | n*-n'| after trying to achieve semi-major axis a, is just obtained up to minimum
WithBy
Can solveSo as to obtain initial orbit.F in above formula1,g1,fN,gNIt is satellitosis t0,t1,tN,Letter
Number.
Since the 4th iteration (i.e. iteration later stage), to semi-major axis a0Adding a constraints (needs appropriate adding
Power, to match ρ0), it forms following conditional equations：
Weighting 1/wa,(wa=100 meters) formula 11
In formula：
Formula 12
The two formulas right-hand member all substitutes into iterative valuea0 *Calculate, a0 *Calculated by following formula：
Formula 13
By to ρ in such scheme0With a0Increase by two constraintss so that low rail target satellite there will be convergence well
Property.Three kinds of methods of addition of constraints are introduced in detail below：
(1) the 1st kind of method
To the ρ at moment epoch (it needs to be determined that moment of initial orbit)0With a0While addition of constraints, wherein to ρ0With a0Weight all
Take 100 meters of inverse.
To moment epoch semi-major axis a0Scan for, an a0One ρ of correspondence0, to a0Searching sector be defined as 9000km
To 6600km.Three layers of search will be divided, ground floor is searched for centered on 7800km, upper and lower 1200km, and step-size in search is 5km, second
Centered on the Best Point that layer last layer is searched for, upper and lower 5km spatial domains, step-length is 0.5km, is eventually found Best Point a0With it is corresponding
ρ0As constraints.
(2) the 2nd kinds of methods
To the ρ at moment epoch0With a0While addition of constraints, wherein to ρ0The inverse for being weighted to 100 meters, and to a0Weight
It is taken as the inverse of 15km.
(3) the 3rd kinds of methods
Only to moment epoch ρ0Addition of constraints, to the inverse that its weight is 100 meters.
Latter two method is to a0Search starting point be all taken as first method to a0Search solution, hunting zone is upper and lower
75km.Divide two-layer search, ground floor step-size in search is 3km, and second layer step-size in search is 0.3km.
Referring to Fig. 2, it show the flow chart calculated based on above-mentioned three kinds of addition of constraints methods.By scheming, whole flow process
It is as follows：
1) the 1st kind of method is calculated first, to the ρ at moment epoch (it needs to be determined that moment of initial orbit)0With a0While addition of constraints,
Wherein to ρ0With a0Weight all take 100 meters of inverse, detailed process is not as described above, repeat herein.
2) in the case of true solution can not be converged to a small number of targets, the 3rd kind of method is calculated, is taken only to ρ0Addition of constraints, it is right
Its weight is taken as 100 meters of inverse.To a0Search starting point take the 1st kind of method to a0Search solution, hunting zone is upper and lower
75km, a then point two-layer is searched for, and ground floor step-size in search is 3km, and second layer step-size in search is 0.3km, judges whether convergence, if
Convergence, then calculate and terminate, with its solution as initial orbit；If do not restrained, step 3 is transferred to).
3) when the 3rd kind of method does not restrain, the 2nd kind of method is calculated, using ρ0With a0While addition of constraints, wherein to ρ0Plus
The inverse for 100 meters is weighed, and to a0Weight be taken as the inverse of 15km, judge whether convergence.If convergence, calculating terminates,
With its solution as initial orbit；If do not restrained, step 4 is transferred to.
4) if latter two method does not restrain, and the 1st kind of method observation is small with the middle error of the difference (o-c) of calculated value
In 50 σ, then calculate and terminate, with the 1st kind of solution of method as initial orbit；
5) if latter two method does not restrain, and the 1st kind of method observation is big with the middle error of the difference (o-c) of calculated value
In 50 σ, then initial orbit is calculated with circular orbit algorithm.Circular orbit method assumes that satellite motion angular speed is identical, and the condition of convergence is | n*-n'|
≤ ε, specific method is as described above.
6) finally judge it is true and false obtain true solution, calculating terminates.
For initial orbit computing problem, if observed quantity right ascension, declination αk,δkFor average be 0, variance for σ ' normal distribution with
Machine amount, C.R lower bounds are：
Formula 14
The parameter θ of initial orbit computing is six-vector, be can be taken asAlso can be taken as orbital tracking.Original state θ, time
Under the premise of t is known, (θ, t) (θ, can t) ask function alpha, using correct poor θ and t, you can calculate the C.R of initial orbit with δ
Lower bound.Because initial orbit computing is nonlinear model, it is impossible to reach C.R lower bounds this optimum precisions, can only be close to optimum precision.
From the expression formula of C.R lower bounds, it is made up of two parts product, and a part is observation error, and a part is fixed
Initial orbit normal equation coefficient matrix it is inverse.Therefore, judge whether a certain method is optimum precision algorithm, there should be two criterions：
(1) just rail precision and observation error into directrix sexual intercourse；
(2) just rail precision close to C.R lower bounds.
Initial orbit computing for the condition of throwing the reins to can be seen that by C.R Lower Bound Formulas, its Affecting Factors of Accuracy is as follows：
(1) observation error σ '：σ ' is smaller, i.e., angle measurement accuracy is higher, and just rail precision is higher；
(2) sample frequency f：Sample frequency f is higher, i.e., the sampled data points N in same time is more, and just rail precision is got over
It is high；
(3) observation arc-segment time span T：Observation time is more long, i.e., the sampled data points N under identical sample frequency is more,
First rail precision is higher.
As Fig. 3, Fig. 4, Fig. 5 are respectively the low rail target of distance observation star 1000km or so, 1600km or so, 2000km or so
Satellite determines initial orbit result figure.The observation star orbit altitude that emulation is based on is 660km, 6 during southbound node place:30 sun synchronization
Track, optical axis is oriented to orbital plane normal direction negative direction, and simulation observation data are target empty in inertia relative to the vector of observation star
Between in Angle Measured Data.Example provided below gives further appreciating that for the present invention program.
Embodiment 1
The orbital tracking of satellite is as follows：
A=7203.709km
I=80 °
Ω=130.14 °
E=0.00187
λ=M+ ω=272.59 °
ρ0=1526.9km
ρmin=635.4km
19 rads of angle measurement accuracy, data 479 seconds, 240 points, every 2 seconds points, initial orbit precision simulation result and and C.R
The relation of lower bound is shown in Fig. 3.
Embodiment 2
Target satellite orbital tracking is as follows：
A=7311.066km
I=70 °
Ω=143.93 °
E=0.0016
λ=M+ ω=272.95 °
ρ0=1840.2km
ρmin=1187.3km
19 rads of angle measurement accuracy, data 258 seconds, 129 points, every 2 seconds points, initial orbit precision simulation result and and C.R
The relation of lower bound is shown in Fig. 4.
Embodiment 3
The orbital tracking of satellite is as follows：
A=7405.907km
I=70 °
Ω=146.75 °
E=0.00133
λ=M+ ω=275.11 °
ρ0=2241.6km
ρmin=1523.4km
19 rads of angle measurement accuracy, data 281 seconds, 141 points, every 2 seconds points, initial orbit precision simulation result and and C.R
The relation of lower bound is shown in Fig. 5.
From simulation result, can be converged in calculation procedure result near true solution by the scheme provided by the present invention,
And with theoretical optimum solution C.R lower bounds difference less, fully prove the correct feasibility of the method.
General principle of the invention, principal character and advantages of the present invention has been shown and described above.The technology of the industry
Personnel it should be appreciated that the present invention is not limited to the above embodiments, simply explanation described in above-described embodiment and specification this
The principle of invention, without departing from the spirit and scope of the present invention, various changes and modifications of the present invention are possible, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appending claims and its
Equivalent thereof.
Claims (1)
1. a kind of method that foundation space-based satellite Angle Measured Data determines low rail target satellite preliminary orbit, it is characterised in that described
Method determines the equation of motion of low orbit satellite preliminary orbit using Space-based Angle Measured Data, and causes to calculate journey using the equation of motion
Ordered pair all low rail moving targets converge to true solution when solving preliminary orbit；Methods described is first with the low rail target of high-speed motion
Satellite obtains the relative observation star unit vector of target satellite relative to the Angle Measured Data of low rail observation satelliteConditional equation；
Then, the ρ that finds range is obtained on the premise of to conditional equation addition of constraints0The conditional equation of addition of constraintsWith
Finally, using one fixed step size of selection, to the ρ in constraint equation0And the semi-major axis a of target satellite0Plus the side of certain weight
Method, obtains initial value of the iterative solution as next step iteration：PositionSpeedAnd then iterate to calculate until convergence obtains low rail
Target satellite preliminary orbit, thus is shielded from false solution, obtains true solution, determines position and the speed of target satellite；
Concrete implementation step is as follows：
Step 1,
The unit vector method of initial orbit is determined according to ground, the unit vector of the relative observation star of target is obtained
In formulaUnit vector for target satellite relative to observation star, ρkDistance for a certain moment target satellite relative to observation star,
Observed quantity (αk,δk) beRight ascension declination under inertial coodinate system；
Step 2,
Introduce two withOrthogonal unit vector
Unit vectorBy observed quantity right ascension declination (αk,δk) calculate, thus to each observed quantity (αk,δk) produce following two
The conditional equation of individual addition of constraints：
Wherein weight 1/ ρk *σ
σ is the middle error obtained in iterative process in formula；
Step 3,
Increase to ρ0Constraints；
Primary iteration is only to range finding ρ0Addition of constraints is solvedTo ρ0Addition of constraints conditional equation is：
Weighting 1/wr,(wr=100 meters)
Its solution as following iterative calculation initial value
During second iteration, it is changed to solveReduction
Now to each observed quantity (αk,δk) form following two conditional equations：
In formulaByCalculate, andByCalculate；
Step 4,
FoundationAgain to range finding ρ0Addition of constraints condition, obtains the ρ that finds range0The conditional equation of addition of constraints：
ρ0Initial value be calculated by circular orbit, using conditional equation plus stating the solution of constraints as the initial value of next step iteration
Step 5,
In the iterative calculation later stage to semi-major axis a0A constraints is added, it is necessary to suitably weight, to match ρ0, it is fixed to improve
Rail precision.
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| CN104794268B (en) * | 2015-04-09 | 2017-12-26 | 中国科学院国家天文台 | A kind of method of utilization space Density Distribution generation space object track |
| CN105466477B (en) * | 2015-12-07 | 2018-05-18 | 中国科学院光电研究院 | A kind of Space borne detection simulation system and method towards Satellite Targets and stars |
| CN105973232B (en) * | 2016-07-19 | 2018-10-16 | 上海航天控制技术研究所 | Constellation of Low Earth Orbit Satellites autonomous navigation method and its system |
| CN106446446B (en) * | 2016-10-14 | 2020-02-18 | 上海微小卫星工程中心 | High-precision autonomous entry and exit method on satellite |
| CN108536990B (en) * | 2018-04-26 | 2022-07-12 | 上海微小卫星工程中心 | Method for calculating change of revisit satellite load incident angle along with orbit drift amount |
| CN110017832B (en) * | 2019-03-19 | 2020-10-16 | 华中科技大学 | Short arc initial orbit determination method based on Gauss solution group optimization |
| CN111428365B (en) * | 2020-03-24 | 2021-12-28 | 中国人民解放军32035部队 | Method for distinguishing GEO target by using astronomical measurement data |
| CN115096319B (en) * | 2022-08-24 | 2022-11-18 | 航天宏图信息技术股份有限公司 | Method and device for determining initial orbit of satellite in star chain based on optical angle measurement data |
| CN115143955B (en) * | 2022-09-06 | 2022-11-25 | 中国人民解放军32035部队 | Method for determining initial orbit of geosynchronous orbit with spacecraft based on astronomical angle measurement data |
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