CN110044362A - The quick calculation method of relative distance minimum between a kind of extraterrestrial target - Google Patents
The quick calculation method of relative distance minimum between a kind of extraterrestrial target Download PDFInfo
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- CN110044362A CN110044362A CN201910357088.5A CN201910357088A CN110044362A CN 110044362 A CN110044362 A CN 110044362A CN 201910357088 A CN201910357088 A CN 201910357088A CN 110044362 A CN110044362 A CN 110044362A
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- G—PHYSICS
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- 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
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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
- G01C21/24—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for cosmonautical navigation
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Abstract
The invention discloses a kind of quick calculation methods of relative distance minimum between extraterrestrial target, height is required in order to solve local minimum computational accuracy between two extraterrestrial targets, traditional directly interpolation computing method the problem of time-consuming, compared with prior art, the present invention is directed to the characteristics of spacecraft and extraterrestrial target running track, propose a kind of quick calculation method of all local minimums of relative distance between two extraterrestrial targets combined based on numerical method with analytic method, local minimum computational accuracy requires height between efficiently solving two extraterrestrial targets, traditional directly interpolation computing method the problem of time-consuming.
Description
Technical field
The present invention relates between field of aerospace measurement and control more particularly to a kind of extraterrestrial target relative distance minimum it is fast
Fast calculation method.
Background technique
Being constantly progressive and develop with space technology, mankind's solar-system operation continues to increase, and space debris is in continuing play
Strong increased trend.According to statistics, space junk of the diameter less than 1 centimetre has several ten million at present, and diameter is at 1 centimetre to 10 lis
Space junk between rice has ten tens of thousands of, and the space junk greater than 10 centimetres is now more than 20000, so far, ground
Face can observe and area meets or exceeds extraterrestrial target sum about more than 16000 of sub- square decimeter.On 2 11st, 2009,
What " iridium 33 " number business telecommunication spacecraft of iridium spacecraft LLC company, U.S. transmitting in 1997 and Russia launched for 1993
" universe 2251 " number military communication spacecraft bumps against in space, this is that complete in-orbit spacecraft bumps against thing for the first time in human history
Part has caused attention of each spacefaring nation to space collision accident, confirmed, and the detectable fragment that this time collision generates is more than
1200.The average stroke speed of space junk and spacecraft is 10 kilometers per second, is equal to that mass times the speed square according to kinetic energy
Formula scales, the kinetic energy that the impact from space debris spacecrafts of 10 gram weights generates is equivalent on highway car with speed per hour
The kinetic energy that 100 kilometers of speed impacts generate, it is envisaged that its consequence will be it is catastrophic, space junk more than Centimeter Level can
Spacecraft is caused thoroughly to damage.
In order to ensure the in-orbit safe operation of spacecraft, for the extraterrestrial target that can be tracked at present, using observation data
Orbit prediction is carried out to it, predicts whether they have the possibility to collide between spacecraft, by adjusting space flight in due course
For device track to ensure that it is not collided, this has become one of external space technology developed country spacecraft safety guarantee " often
Rule movement ".
Most important work is exactly to calculate two extraterrestrial targets at one section in prediction of collision analysis between spacecraft and extraterrestrial target
All local minimums of relative distance in time.Since the relative velocity between two extraterrestrial targets is generally measured at 10 kilometers per second
Grade, in order to make the computational accuracy of relative distance minimum reach a meter magnitude, then should just calculate milli at the time of minimum corresponds to
Below second grade.According to traditional calculation method, if Millisecond or less need to be calculated, it is necessary to the orbital data of quantity space target
It is interpolated into Millisecond or less.In-orbit extraterrestrial target sum about more than 1.6 ten thousand at present, if so many target is all one by one according to biography
System be directly interpolated into Millisecond calculate, calculation amount is big to be difficult to imagine, though computer nowadays high speed development epoch all
It is less likely to obtain result in a short time.
In view of the foregoing, the present invention is directed to the characteristics of spacecraft and extraterrestrial target running track, proposes one kind and is based on
The quick calculation method of all local minimums of relative distance between two extraterrestrial targets that numerical method is combined with analytic method.
Summary of the invention
The object of the invention is that providing relative distance minimum between a kind of extraterrestrial target to solve the above-mentioned problems
Quick calculation method.
The present invention through the following technical solutions to achieve the above objectives:
The present invention includes the following steps:
Step 1: [t at a given time period0,t1] in, it is known that two spaces target is one point in J2000 inertial coodinate system
Clock any position be respectively [x1i y1i z1i], [x2i y2i z2i], wherein i=1,2 ... n, n are (t1-t0) × 1440 it is whole
Number part；According to the location components of above-mentioned two target, then the relative distance of two targets can be calculatedWherein i=1,2 ... n；Meet condition d for alli< di-1And di<
di+1, the relative distance of i=2,2 ... n-1 is denoted as T at the time of correspondencek, m are shared, i.e. k=1,2 ... m；
Step 2: in each period [Tk- 1 minute, Tk+ 1 minute] in, according to [x known in step 11i y1i z1i]
[x2i y2i z2i], respectively take [Tk- 3 minutes, Tk+ 4 minutes] corresponding 8 position datas, using Lagrange's interpolation by two
Target position data interpolation is the data for being spaced 0.5 second, is denoted asWithWherein k=1,
2 ... m, j=1,2 ... 240；
Step 3: it is obtained according to step 2WithCalculate relative distance valueRemember Dkj(j=1,2 ... 240) at the time of minimum value corresponds in
For Tka, wherein k=1,2 ... m；
Step 4: based on the D in step 3kj(j=1,2 ... 240), take [Tka- 1.5 seconds, Tka+ 2.0 seconds] in corresponding 8
A relative distance value, is denoted as [Dka1,Dka2,Dka3,Dka4,Dka5,Dka6,Dka7,Dka8], [T is denoted as at the time of correspondingka1,Tka2,
Tka3,Tka4,Tka5,Tka6,Tka7,Tka8], a 7 rank multinomial D can be obtained according to Lagrange's interpolation formulak(T), as follows
It is shown:
Wherein
Step 5: to 7 rank multinomial D in step 4k(T), wherein k=1,2 ... m ask it first derivative that can obtain
To a 6 rank multinomial D'k(T), as follows:
Wherein
6 rank multinomial D' is solved using dichotomyk(T) in section [Tka- 1.5 seconds, Tka+ 2.0 seconds] in unique zero point,
Setting convergence threshold is Δ t=1 × 10-4Second, T at the time of relative distance local minimum corresponds to can be obtainedkmin, wherein k=
1,2 ... m shares m；
Step 6: according to the T being calculated in step 5kmin, [the x in conjunction with known in step 11i y1i z1i] and [x2i
y2i z2i], respectively take [Tkmin- 3 minutes, Tkmin+ 4 minutes] corresponding 8 position datas, it can then be obtained using Lagrange's interpolation
To TkminCorresponding position data [the x of two target of moment1kmin y1kmin z1kmin] and [x2kmin y2kmin z2kmin], and then can obtain
To relative distance minimumWherein k=1,
2 ... m share m.
The beneficial effects of the present invention are:
The present invention is a kind of quick calculation method of relative distance minimum between extraterrestrial target, compared with prior art, this
The characteristics of invention is for spacecraft and extraterrestrial target running track, proposes a kind of two combined based on numerical method with analytic method
The quick calculation method of all local minimums of relative distance, efficiently solves local minimum between two extraterrestrial targets between extraterrestrial target
It is worth the problem of computational accuracy requires high, tradition directly interpolation computing method time-consuming.
Specific embodiment
The invention will be further described below:
The present invention includes the following steps:
Step 1: [t at a given time period0,t1] in, it is known that two spaces target is one point in J2000 inertial coodinate system
Clock any position be respectively [x1i y1i z1i], [x2i y2i z2i], wherein i=1,2 ... n, n are (t1-t0) × 1440 it is whole
Number part；According to the location components of above-mentioned two target, then the relative distance of two targets can be calculatedWherein i=1,2 ... n；Meet condition d for alli< di-1And di<
di+1, the relative distance of i=2,2 ... n-1 is denoted as T at the time of correspondencek, m are shared, i.e. k=1,2 ... m；
Step 2: in each period [Tk- 1 minute, Tk+ 1 minute] in, according to [x known in step 11i y1i z1i]
[x2i y2i z2i], respectively take [Tk- 3 minutes, Tk+ 4 minutes] corresponding 8 position datas, using Lagrange's interpolation by two
Target position data interpolation is the data for being spaced 0.5 second, is denoted asWithWherein k=1,
2 ... m, j=1,2 ... 240；
Step 3: it is obtained according to step 2WithCalculate relative distance valueRemember Dkj(j=1,2 ... 240) at the time of minimum value corresponds in
For Tka, wherein k=1,2 ... m；
Step 4: based on the D in step 3kj(j=1,2 ... 240), take [Tka- 1.5 seconds, Tka+ 2.0 seconds] in corresponding 8
A relative distance value, is denoted as [Dka1,Dka2,Dka3,Dka4,Dka5,Dka6,Dka7,Dka8], [T is denoted as at the time of correspondingka1,Tka2,
Tka3,Tka4,Tka5,Tka6,Tka7,Tka8], a 7 rank multinomial D can be obtained according to Lagrange's interpolation formulak(T), as follows
It is shown:
Wherein
Step 5: to 7 rank multinomial D in step 4k(T), wherein k=1,2 ... m ask it first derivative that can obtain
To a 6 rank multinomial D'k(T), as follows:
Wherein
6 rank multinomial D' is solved using dichotomyk(T) in section [Tka- 1.5 seconds, Tka+ 2.0 seconds] in unique zero point,
Setting convergence threshold is Δ t=1 × 10-4Second, T at the time of relative distance local minimum corresponds to can be obtainedkmin, wherein k=
1,2 ... m shares m；
Step 6: according to the T being calculated in step 5kmin, [the x in conjunction with known in step 11i y1i z1i] and [x2i
y2i z2i], respectively take [Tkmin- 3 minutes, Tkmin+ 4 minutes] corresponding 8 position datas, it can then be obtained using Lagrange's interpolation
To TkminCorresponding position data [the x of two target of moment1kmin y1kmin z1kmin] and [x2kmin y2kmin z2kmin], and then can obtain
To relative distance minimumWherein k=1,
2 ... m share m.
In the TLE data for 16912 extraterrestrial targets announced from the November in 2018 of the U.S. on the 5th, a target is arbitrarily selected
The calculating of relative distance local minimum is carried out as between major heading, with remaining 16911 extraterrestrial targets.The major heading of selection
NORAD number is 40059, and selecting the period calculated is 5 days 8 November in 2018 when 8 days 8 November in 2018, due to a piece
Width is limited, and the thresholding of local minimum output is fixed tentatively as 10 kms, the allocation of computer of selection are as follows: Inter i3-6300CPU@
3.7GHz, 4.0G memory, Windows732 bit manipulation system, with this condition, calculated result is shown in Table 1, and completes to calculate institute
Need time be 1 point 34 seconds
Relative distance local minimum calculated result between 1 target 40059 of table and other targets
As it can be seen from table 1 relative distance minimum quick calculation method between use space target, for a major heading
Minimum calculates at a distance between more than 16000 extraterrestrial targets, it is only necessary to which 1 point can be completed calculating in 3 days for 34 seconds, and computational accuracy reaches
To more than Millisecond.This explanation, can meet time requirement and required precision using the calculated result of this method simultaneously.
Basic principles and main features and advantages of the present invention of the invention have been shown and described above.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the above embodiments and description only describe this
The principle of invention, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its
Equivalent thereof.
Claims (1)
1. the quick calculation method of relative distance minimum between a kind of extraterrestrial target, characterized by the following steps:
Step 1: [t at a given time period0,t1] in, it is known that two spaces target is one minute one in J2000 inertial coodinate system
The position of point is respectively [x1i y1i z1i], [x2i y2i z2i], wherein i=1,2 ... n, n are (t1-t0The integer portion of) × 1440
Point；According to the location components of above-mentioned two target, then the relative distance of two targets can be calculatedWherein i=1,2 ... n；Meet condition d for alli< di-1And di<
di+1, the relative distance of i=2,2 ... n-1 is denoted as T at the time of correspondencek, m are shared, i.e. k=1,2 ... m；
Step 2: in each period [Tk- 1 minute, Tk+ 1 minute] in, according to [x known in step 11i y1i z1i] and
[x2i y2i z2i], respectively take [Tk- 3 minutes, Tk+ 4 minutes] corresponding 8 position datas, using Lagrange's interpolation by two mesh
Cursor position data interpolating is the data for being spaced 0.5 second, is denoted asWithWherein k=1,
2 ... m, j=1,2 ... 240；
Step 3: it is obtained according to step 2WithCalculate relative distance valueRemember Dkj(j=1,2 ... 240) be at the time of minimum value corresponds in
Tka, wherein k=1,2 ... m；
Step 4: based on the D in step 3kj(j=1,2 ... 240), take [Tka- 1.5 seconds, Tka+ 2.0 seconds] in corresponding 8 phases
It adjusts the distance value, is denoted as [Dka1,Dka2,Dka3,Dka4,Dka5,Dka6,Dka7,Dka8], [T is denoted as at the time of correspondingka1,Tka2,Tka3,
Tka4,Tka5,Tka6,Tka7,Tka8], a 7 rank multinomial D can be obtained according to Lagrange's interpolation formulak(T), as follows:
Wherein
Step 5: to 7 rank multinomial D in step 4k(T), wherein k=1,2 ... m ask first derivative to can be obtained one it
A 6 rank multinomial D'k(T), as follows:
Wherein
6 rank multinomial D' is solved using dichotomyk(T) in section [Tka- 1.5 seconds, Tka+ 2.0 seconds] in unique zero point, setting
Convergence threshold is Δ t=1 × 10-4Second, T at the time of relative distance local minimum corresponds to can be obtainedkmin, wherein k=1,
2 ... m share m；
Step 6: according to the T being calculated in step 5kmin, [the x in conjunction with known in step 11i y1i z1i] and [x2i y2i
z2i], respectively take [Tkmin- 3 minutes, Tkmin+ 4 minutes] corresponding 8 position datas, it then can be obtained using Lagrange's interpolation
TkminCorresponding position data [the x of two target of moment1kmin y1kmin z1kmin] and [x2kmin y2kmin z2kmin], and then can be obtained
Relative distance minimumWherein k=1,
2 ... m share m.
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| CN112906246B (en) * | 2021-03-23 | 2022-09-27 | 中国人民解放军63768部队 | Calculation method for assessment of intersection between space target and carrier rocket before launching |
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