CN104572576A - Quick analysis method for analyzing collision during approaching of objects - Google Patents
Quick analysis method for analyzing collision during approaching of objects Download PDFInfo
- Publication number
- CN104572576A CN104572576A CN201310475114.7A CN201310475114A CN104572576A CN 104572576 A CN104572576 A CN 104572576A CN 201310475114 A CN201310475114 A CN 201310475114A CN 104572576 A CN104572576 A CN 104572576A
- Authority
- CN
- China
- Prior art keywords
- objects
- collision
- analyzing
- analysis method
- calculation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Landscapes
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention belongs to the technical field of collision analysis and application. The invention provides a quick analysis method for analyzing collision according to a relative motion relation when objects approach to one another. The quick analysis method is characterized by building an intersection coordinate system and a vector correlation equation based on an assumption according to quasi linear motion by using a relative vector relation in space motion of two objects, and quickly analyzing minimum approach distance and approach moment between two objects; the contradiction between calculation efficiency and accuracy in numerical calculation is avoided; the complexity and calculation quantity of the conventional analysis method are reduced; the relation between the calculation efficiency and the accuracy are well considered. The quick analysis method has a wide application prospect in nature and human activities of analyzing collision of the celestial objects, early warning collision of satellites, screening dangerous objects, analyzing hit rate of shooting and striking targets and analyzing collision of high-rate particles.
Description
Technical field
The invention belongs to crash analysis and applied technical field, relate to the contents such as object of which movement, spatial intersection, minimum approach distance, risk of collision distance, at collision of celestial body analysis, satellite anti-collision warning, dangerous objects screens, projectile strikes target natures such as hitting analysis, high-velocity particles collision and be with a wide range of applications in mankind's activity.According to relative motion relation during object proximity, the present invention proposes a kind of fast resolving algorithm of crash analysis.This algorithm utilizes the relative vector relation in disome spatial movement, according to (standard) linear movement hypothesis structure intersection coordinate system and vector correlation equation, fast resolving calculates minimum approach distance between disome and close to the moment, both avoid in numerical evaluation the contradiction calculated between efficiency and precision, also reduce complicacy and the operand of conventional analytic method.Therefore, the present invention has taken into account the relation of counting yield and precision well, and application benefit is good, have a extensive future.
Background technology
Collision is ubiquitous a kind of spontaneous phenomenon and human activity.At occurring in nature, from minimum microscopic particle to macroscopical galaxy (body), all there is the possibility of collision.Crash analysis is the original state according to two or more object, the one activity whether analytical calculation can collide each other, the important evidence that its analysis result is anti-collision warning, risk is disposed, gone after profits and advoided disadvantages
Carry out the crash analysis of moving object, namely calculate moving object close to time collision situation.This problem can be expressed as: judge two, space object, whether preset time interval [
t b,
t e] in, there is distance and be less than given risk distance
dissituation; If existed, calculate time and distance that two articles arrives closest approach.For this problem, usually there is numerical value and resolve two kinds of computing method
Method one: numerical computation method
First set up unified coordinate system, determine that two objects are at initial time
t bposition vector and velocity; Then according to the position vector in regular hour in each moment of step-length step by step calculation, velocity and relative distance therebetween, until
t emoment terminates; By comparing check one by one obtain preset time interval [
t b,
t e] minimum relative distance in (subscript B, E represent Begin and End respectively), with given risk distance
disrelatively, judge whether to there is risk of collision.When using the method to solve, the problem that material calculation brings must be considered.This is because only have the long-pending smaller of relative velocity as time step and two (at least should be less than given risk distance
dis) time, could not fail to report, obtain the approximate solution of minimum approach distance.Therefore, these calculating are very consuming time, especially when dimension of object is less, speed is very high.Even if carry out variable step optimization to algorithm, first calculate according to larger step-length, find out two objects time range relatively; In this time range, use small step progress row to calculate again, although accelerate calculation procedure so to a certain extent, but still have larger calculated amount.In addition, the approximate solution of problem can only be obtained with this numerical computation method, and inaccurate
Method two: Analytic Calculation Method
In order to avoid the step-length in numerical evaluation and precision problem, improve counting yield and quality, the method for analytical Calculation can be used.When analytical Calculation, often according to high-speed object (as relied on spacecraft and the space junk of inertia high-speed motion on Earth's orbit) close to time kinetic characteristic carry out linearization hypothesis, that is: due to whole be (the accurate Inertial Processing) that occur within very short several seconds close to process, the motion of two objects can be thought linear, and speed is all invariable.According to linear movement hypothesis, the people such as Chan give a kind of analytical algorithm for calculating minimum approach distance based on space projection and analysis geometry
[1].But this method comparison is complicated, solves and extremely bothers, the conversion of multiple geometric relationship be related to
The present invention is directed to the deficiency of above method, propose a kind of fast resolving algorithm based on linear movement hypothesis, simple and effective
Pertinent literature:
[1] Chan F K. Spacecraft collision probability [M]. The Aerospace Press, El Segundo, California, 2008: 30-37。
Summary of the invention
The present invention, first according to the motion state parameters of two objects, sets up the intersection coordinate system describing relative motion relation; Relative position when then utilizing two object of which movement and velocity relation, construct the vector correlation equation of time variations under linear motion conditions, minimum approach distance between analytical Calculation disome and close to the moment, thus the efficiency and precision that improve that crash analysis calculates
Technical scheme of the present invention is as follows:
(1) linearise movement hypothesis is carried out
According to high-speed object close to time kinetic characteristic, do linearise movement hypothesis, that is: due to whole be (quasistatic process) that occur within very short several seconds close to process, the motion of two objects is thought linear, and velocity is all invariable
(2) intersection coordinate system is constructed
In object (being designated as object D and object S) is close to process, defines intersection coordinate system (encounter coordinate system), is designated as
s e (
x,
y,
z): initial point O on object S,
yaxle is along relative velocity vector
(subscript
d,
srepresent object D and object S respectively) direction, object S place be called intersection plane with the plane of relative velocity vector normal,
xthe projected position (see figure 1) of axle directed towards object D in intersection plane.At intersection (collision) moment object D also in intersection plane, in intersection plane
xaxle just in time points to the position of now object D,
zaxle is obtained by the right-hand rule.Under linear motion conditions, for once close to event, be unique at this intersection coordinate system of given moment.In intersection moment (two objects are closest), the position of object D in intersection coordinate system be (
x e , 0,0), wherein
x e represent the minimum approach distance of two objects
After defining this coordinate system, on the one hand when calculating collision problem, the three-dimensional problem of two object space motions can be changed into two-dimensional problems and do not lose any information in the calculation, do like this and can simplify calculating to a great extent, thus increase substantially counting yield.On the other hand, owing to being the direction of relative velocity (remaining unchanged in close to process) to the direction of intersection plane projection, become factor when not existing in the calculation, so time term has been eliminated, when calculating collision situation, only need focus on the distance of intersection moment two objects
(3) minimum approach distance and moment is calculated
Suppose
t bin the moment, object D and object S enters access areas (relative distance is less, can do linearization approximate), and their positions in a certain inertial coordinates system known and velocity are respectively
with
, then Relative position vector and relative velocity vector (see figure 2) are respectively
(1)
In access areas, according to the hypothesis of linear movement, relative velocity vector remains unchanged, and can calculate through Δ
trelative position vector after time and relative velocity vector
(2)
Obviously, when
with
not during conllinear, and a plane can be formed, namely in intersection coordinate system
xyplane, vector
starting point on object S, terminal is edge on object D
yaxle moves, and easily knows, the distance between object D and object S according to vector geometric relationship
minimum sufficient and necessary condition is
, namely
(3)
(2) formula is substituted into (3) formula, obtains about the time
tlinear equation with one unknown, solve and obtain unique time Δ
t, namely
(4)
This formula is equally applicable to
with
the situation of conllinear.When
time, this formula has real solution, otherwise,
, show that object D is identical with the speed of object S, the relative position of the two is forever constant, there is not minimum approach distance.The intersection moment is tried to achieve by (4) formula
t e for
(5)
Again (4) formula is substituted into (2) formula, try to achieve the intersection moment
t e relative position vector
(6)
Direction is wherein just in time in intersection coordinate system
xthe opposite direction of axle, its size
r dse it is then minimum approach distance
x e
(4) risk of collision is calculated
The minimum approach distance that (6) formula of utilization is tried to achieve
x e , with given risk distance
disrelatively, whether there is risk of collision between judgment object D and object S.If
x e ≤
dis, then there is risk of collision; Otherwise, between object D and object S, there is not risk of collision
Calculation process of the present invention is specifically shown in Fig. 3
Advantage of the present invention:
(1) structure of intersection coordinate system significantly can simplify the calculating of moving object three-dimensional relationship, and three-dimensional problem is reduced to two-dimensional problems;
(2) utilize the unchangeability of relative velocity in disome object proximity process, recursion is close to the Relative position vector relation in process, and method is easy;
(3) vector geometric relationship when utilizing disome object nearest, set up about the time
tunitary one parsing equation, direct solution intersection moment and minimum approach distance, counting yield is high, and there is not the error of calculation;
(4) method of the present invention is applicable to analyze linear or almost linear object collision situation, and applicability is strong.
Accompanying drawing explanation
The structure of Fig. 1 intersection coordinate system
Length velocity relation in Fig. 2 intersection coordinate system
Fig. 3 calculation process of the present invention
Embodiment
Core of the present invention is the calculating to object proximity process centre-exchange-meeting moment and minimum approach distance.Illustrate the specific embodiment of the present invention below
Suppose
t bin=0 moment, the position of object D and object S in a certain inertial coordinates system and velocity are respectively
km,
km/s and
,
, then Relative position vector and relative velocity vector are respectively
In access areas, relative velocity vector remains unchanged, and
, between object D and object S, there is minimum approach distance.(4) formula of utilization solves and obtains unique time Δ
t
Try to achieve the intersection moment
t e for
Try to achieve the intersection moment again
t e relative position vector
Then
size 2km be minimum approach distance
x e .Finally, by 2km and given risk distance
disrelatively can draw risk of collision situation
Visible according to above implementation process, only need the simple Vector operation of 2 ~ 3 times when utilizing the present invention to calculate, computation process is very simple, and result does not exist error.Compare with utilizing the result of numerical computation method, as shown in the table.Visible, the counting yield of numerical computation method and precision are subject to the impact of interval and time step preset time, even if in interval preset time relatively more accurate (in scope very little near the intersection moment), the more rational situation of step-length, counting yield of the present invention and precision are also obviously better than numerical computation method.
Claims (2)
1. disome spatial movement intersection coordinate system building method.
2. based on motion vector equation close to parameter calculation method.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310475114.7A CN104572576A (en) | 2013-10-13 | 2013-10-13 | Quick analysis method for analyzing collision during approaching of objects |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310475114.7A CN104572576A (en) | 2013-10-13 | 2013-10-13 | Quick analysis method for analyzing collision during approaching of objects |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN104572576A true CN104572576A (en) | 2015-04-29 |
Family
ID=53088683
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201310475114.7A Pending CN104572576A (en) | 2013-10-13 | 2013-10-13 | Quick analysis method for analyzing collision during approaching of objects |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104572576A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109597061A (en) * | 2018-12-28 | 2019-04-09 | 北京润科通用技术有限公司 | A kind of target state method of discrimination and system |
| CN111477003A (en) * | 2020-04-13 | 2020-07-31 | 联陆智能交通科技(上海)有限公司 | Calculation method and system for acquiring time of collision with weak traffic and medium |
| CN114547860A (en) * | 2022-01-18 | 2022-05-27 | 宁波天巡科技有限公司 | Space target collision early warning method based on agile screening strategy |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103234538A (en) * | 2013-04-07 | 2013-08-07 | 北京理工大学 | Autonomous navigation method for planet in final approaching section |
-
2013
- 2013-10-13 CN CN201310475114.7A patent/CN104572576A/en active Pending
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103234538A (en) * | 2013-04-07 | 2013-08-07 | 北京理工大学 | Autonomous navigation method for planet in final approaching section |
Non-Patent Citations (3)
| Title |
|---|
| 吴波: "空间目标交会期间碰撞概率研究", 《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》 * |
| 白显宗: "空间目标碰撞预警中的碰撞概率问题研究", 《中国优秀硕士学位论文全文数据库工程科技II辑》 * |
| 白显宗等: "空间目标碰撞概率计算方法研究", 《宇航学报》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109597061A (en) * | 2018-12-28 | 2019-04-09 | 北京润科通用技术有限公司 | A kind of target state method of discrimination and system |
| CN111477003A (en) * | 2020-04-13 | 2020-07-31 | 联陆智能交通科技(上海)有限公司 | Calculation method and system for acquiring time of collision with weak traffic and medium |
| CN114547860A (en) * | 2022-01-18 | 2022-05-27 | 宁波天巡科技有限公司 | Space target collision early warning method based on agile screening strategy |
| CN114547860B (en) * | 2022-01-18 | 2022-09-27 | 宁波天巡科技有限公司 | Space target collision early warning method based on agile screening strategy |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| KR101402206B1 (en) | Multiple target tracking method with kinematics and feature information of targets | |
| Kim et al. | Particle filter for ballistic target tracking with glint noise | |
| CN104035083A (en) | Radar target tracking method based on measurement conversion | |
| CN105093198A (en) | Flight path fusion method for networking detection of distributed external radiation source radars | |
| CN104199022A (en) | Target modal estimation based near-space hypersonic velocity target tracking method | |
| Li et al. | Auxiliary truncated particle filtering with least-square method for bearings-only maneuvering target tracking | |
| CN102064783A (en) | Design method for probability hypothesis density particle filter and filter | |
| CN104572576A (en) | Quick analysis method for analyzing collision during approaching of objects | |
| CN107238835B (en) | Formation target point navigation anti-crossing association method | |
| CN105372653A (en) | High-efficiency turning maneuver target tracking method for shore-based air traffic control radar system | |
| Lian et al. | Joint spatial registration and multi-target tracking using an extended PM-CPHD filter | |
| Xiao et al. | A multiple model particle filter for maneuvering target tracking based on composite sampling | |
| CN102307041A (en) | Designing of current-statistical-model-based probability hypothesis density particle filter and filter | |
| Kreucher et al. | A comparison of tracking algorithms for supermaneuverable targets | |
| Tan et al. | Joint range ambiguity resolving and multiple maneuvering targets tracking in clutter via MMPHDF-DA | |
| CN113835061B (en) | Single-platform Doppler two-stage closed positioning method in presence of signal carrier frequency prior error | |
| Messaoudi et al. | Comparison of interactive multiple model particle filter and interactive multiple model unscented particle filter for tracking multiple manoeuvring targets in sensors array | |
| Yang et al. | Particle swarm optimization algorithm for passive multi-target tracking | |
| Li et al. | 3-D tracking of air targets using a single 2-D radar | |
| Park et al. | Detection and classification of a ballistic missile in ascent phase | |
| Liang-Qun et al. | Multiple model Rao-Blackwellized particle filter for manoeuvring target tracking | |
| Wang et al. | Turn rate estimation based on curve fitting in maneuvering target tracking | |
| Zhifeng et al. | A data fusion algorithm for multi-sensor dynamic system based on Interacting Multiple Model | |
| HE et al. | A Distance Azimuth Tracking Algorithm Based on Alpha-beta Filtering | |
| CN116224320B (en) | Radar target tracking method for processing Doppler measurement under polar coordinate system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20150429 |