CN105095680B - Meet at random probabilistic rescue method and system are estimated based on differential - Google Patents
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Abstract
Meet at random probabilistic rescue method and system are estimated based on differential the invention discloses one kind, wherein method comprises the following steps：Step 1, the missing path L of the person of wandering away D institutes is determined, and determine that the person of wandering away D finally appears in the location point on the L of path；The location point of step 2, measurement searcher C on the L of path；Step 3, calculate the probability density function p that the searcher C and person of wandering away D is distributed in path Lc、pd, C is located at probability of the road through that can be met during one on L with D, and it is x to find the location point corresponding to differential collision probability maximumm；The person of wandering away D collision probability can be found on the L of path by calculating searcher C；Step 5, the location point corresponding with differential collision probability maximum according to calculating, and collision probability arrange searcher C to be searched and rescued on the L of path.
Description
Technical Field
The invention relates to the field of search and rescue, in particular to a search and rescue method and system based on differential measurement random encounter uncertainty.
Background
In recent years, people search and rescue cases have occurred. For example, people in outdoor activities are lost and search and rescue, and the old and children are lost and search. A typical case is the following: the lost person is known to be present last in the middle of the path L and to be free to move on the path L; how likely a seeker will encounter a lost person on path L? Is the seeker most likely to encounter a lost person at which point along the route L?
1. Mechanism of operation of the method before improvement
The traditional rescue process often puts a large amount of search and rescue resources into a certain area around the last appearance place of the lost person due to the instinct or humanitarian meaning of people, and lacks accurate search and rescue planning (lobrachys, etc., 2014). The possibility that the searcher can meet the lost person is predicted, and the search and rescue scheme planning and the most possible successful rescue are the prerequisite. Existing probabilistic temporal geography adopts probability values to quantitatively express the encounter probability, and provides a discrete method (Winter, YIN, 2011) for calculating the encounter probability. The method provides that: the condition that seeker C and lost person D meet is that both C and D are located in the same discrete unit in the discrete geographic space.
Setting: the length of the path L between the seeker C and the lost person D is L. C. The probability density function of D distributed on the path L is c and D. The calculation steps of the discrete method of the encounter probability are as follows:
step 1: the path L is evenly divided into n segments: l is a radical of an alcohol 1 、L 2 、…、L n (FIG. 1 (a)).
Step 2: note that C and D are located in any small segment L respectively i Probability value c of i 、d i The method comprises the following steps: c is more than or equal to 0 i ≤1,0≤d i Less than or equal to 1 (figure 1 (b)),
and 3, step 3: the movements of the two individuals may be considered independent until the seeker finds the lost person. Thus, the individuals C, D are located or meet at any unit L i Has a probability value of c i ×d i . Accordingly, the probability value of the entire path L is(FIG. 1 (c)).
For simplicity, c and d are uniformly distributed.
(1) When n =1, c and d are distributed in L 1 Probability value c of 1 ＝1，d 1 =1, corresponding encounter probability:
(2) When n =2, c and d are distributed in L 1 Probability value c of 1 ＝d 1 =0.5,c, d distributed in L 2 Probability value c of 2 ＝d 2 =0.5, corresponding encounter probability:
(3) When n =10, c and d are distributed in L i Probability value c of i ＝d i =0.1, corresponding encounter probability:
as can be seen from the above, when the number n of discrete units is continuously increased, the possibility that the searcher C meets the lost user D on the path L is continuously decreased, i.e. the probability of successful searching is inversely proportional to n; the conclusion is also applicable to the case where c and d are non-uniformly distributed, such as normal distribution, triangular distribution, etc.
2. Problems in improving the anterior approach
In summary, the discrete method depends on the scale of discrete units (Winter, YIN, 2011), and the encounter probability decreases as the number of discrete units increases; thus, the artifacts of scale or discrete cell number setting in the discrete approach tend to create a haphazard probability of meeting. However, the encounter probability as an objective rule has stability and is theoretically independent of the calculation method.
Disclosure of Invention
The present invention addresses the problem of probability that the seeker C can encounter the lost seeker D on the route L, and the discrete approach does not provide stable or unique encounter probabilities. A search and rescue method and system based on differential measure random encounter uncertainty are provided, which utilize continuous differentiation to calculate encounter probability with uniqueness according to non-uniform probability distribution of a searcher and a lost person on a path L.
The technical scheme adopted by the invention for solving the technical problem is as follows:
the search and rescue method based on the differential measure random encounter uncertainty comprises the following steps:
step 1, determining a lost path L of a lost person D, and determining a position point of the lost person D on the path L;
step 2, measuring the position point of the searcher C on the path L;
step 3, calculating the probability density function p of the distribution of the seeker C and the lost person D on the path L c 、p d And C is located at a position point x on the path L 0 Probability of time meeting D Other points x on the corresponding calculation path L 1 、x 2 、…、x k < i > 8230; obtaining the differential encounter probability { p (E) meet |x 0 ),p(E meet |x 1 ),…,p(E meet |x k ) 8230, finding the position point x corresponding to the maximum value of the differential encounter probability m ；
Step 4, when the searcher C is located at all points { x | x = x { (x |) } 0 ,x 1 ,…,x k 8230time, the probability p (E) of the search and rescue person C meeting the lost person D meet )：
Probability that seeker C can find lost person D on path L:
where md is the maximum distance that the seeker C can meet the lost person D, and the variable x represents the distance between the location of the seeker C and one of the endpoints O of the path L; the variable y represents the distance between the point of the lost person D and the endpoint O;
step 5, according to the calculated position point corresponding to the maximum value of the differential encounter probability and the encounter probability p (E) meet ) The searcher C is arranged to search and rescue on the path L.
In the search and rescue method of the invention, if the lost person D finally appears at the middle point of the path L and only freely moves on the path L, the probability density function p of the lost person D distributed on the path L can be reasonably assumed d The distribution is triangular; if the searcher C searches from the middle point of the path L, it can also reasonably assume the probability density function p of the path L where the searcher C is distributed c Is distributed in a triangle.
The invention also provides a search and rescue system based on differential measure random encounter uncertainty, which comprises:
the confirming module is used for determining a lost path L of the lost person D and determining a position point of the lost person D on the path L;
the data acquisition module is used for measuring the position point of the searcher C on the path L;
a probability density function calculation module for calculating the probability density function p of the seeker C and the lost person D distributed on the path L c 、p d And C is located at a position point x on the path L 0 Probability of time meeting D Other points x on the corresponding calculation path L 1 、x 2 、…、x k < 8230 >, obtaining { p (E) } meet |x 0 ),p(E meet |x 1 ),…,p(E meet |x k ) 8230, finding the position point corresponding to the maximum value of the differential encounter probability is x m ；
An encounter probability calculation module for calculating the probability that the searcher C is located at all points { x | x = x } 0 ,x 1 ,…,x k 8230time, the probability p (E) of the search and rescue person C meeting the lost person D meet )：
Then the probability that seeker C can find lost person D on route L is:
where md is the maximum distance that the seeker C can meet the lost person D, and the variable x represents the distance between the location of the seeker C and one of the endpoints O of the path L; the variable y represents the distance between the point of the lost person D and the endpoint O;
an analysis processing module for calculating the position point corresponding to the maximum value of the differential encounter probability and the encounter probability p (E) meet ) The searcher C is arranged to search and rescue on the path L.
In the search and rescue system, the probability density function calculation module is specifically configured to reasonably assume that the probability density functions p of the lost persons D distributed on the path L are generated when the lost persons D finally appear at the middle point of the path L and only move freely on the path L d The distribution is triangular; when the searcher C searches from the middle point of the path L, it is reasonable to assume the probability density function p of the path L where the searcher C is distributed c Is distributed in a triangle.
The invention has the following beneficial effects: the present invention utilizes the differentiation method of encounter probability, according to the maximum distance md that can be met and the probability density function p of searcher C and lost person D c 、p d The method can solve the problems that the probability that the C can find the D is the highest, and the like. The method for differentiating the encounter probability has the advantages that different from the discrete method, the encounter probability value calculated by the method has stability and uniqueness.
Drawings
The invention will be further described with reference to the following drawings and examples, in which:
FIG. 1: a discrete method graph of conventional encounter probability, wherein (a) the path is discretized; (b) the probability that an individual is located in a discrete unit; (c) encounter probability;
FIG. 2 is a schematic diagram: the seeker C can encounter the lost event D, wherein (a) variable definition; (b) encounter event examples;
FIG. 3: the inference method where the seeker C can meet the lost person D with the highest probability, wherein (a) the probability is differentiated; (b) the differential encounter probability of C being at a given point; (C) a sequence differential encounter probability that C is located at a sequence point;
FIG. 4 is a schematic view of: the invention relates to a reasoning method for the probability that a searcher C can meet a lost person D;
FIG. 5: the invention relates to a technical route map of an encounter probability differential method;
FIG. 6: in one embodiment of the invention, the spatial position of the maximum value of the encounter probability;
FIG. 7: in another embodiment of the present invention, the spatial locations where the probability maxima meet are located.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
1. The main technical scheme adopted by the invention
In a real-world environment, the encounter between two individuals is limited primarily by the spatial distance (e.g., the visible distance) between the two individuals. Here, the maximum distance at which two bodies can meet is denoted as md (meeting distance). Accordingly, the encounter semantics can be defined as: a meeting is considered to be possible if and only if the two individuals are not more than md apart. Thus, md determines the size of the encounter to some extent, thereby providing a theoretical basis for uniqueness of encounter probability.
The main technical solutions adopted by the present invention are described below.
1) Encounter events
Let one end point of the straight line segment L be O; seeker C is co-located on L with lost person D.
Setting: the variable x represents the distance between the location point of the searcher C and the endpoint O; the variable y represents the distance between the point of the lost person D and the end point O (fig. 2 a).
According to the meeting semantics, meeting event E meet = { event that the distance between the position x of the seeker C and the position y of the lost person D does not exceed md }, that is:
E meet = { (x, y) | | | y-x | ≦ md, x ∈ L, y ∈ L } (formula 1)
Or, E meet ＝{(x,y)|x-md≤y≤x+md，x∈L，y∈L}
Thus, if the lost person D is at the position y when the seeker C is at the position x 1 Satisfies formula 1, i.e. | y 1 X | ≦ md, then event E is encountered meet (ii) occurs; if the lost person D is at the position y 2 Cannot satisfy equation 1, i.e. | y 1 -x|>, md, meeting event E meet Which is unlikely to occur (fig. 2 b).
2) Where seeker C can find lost person D with maximum probability
Encounter probability p (E) meet ) Is the meeting event E meet The probability of occurrence. Let the probability density functions of the seeker C and the lost person D distributed on the path L be: p is a radical of c 、p d And the movements of C and D are independent of each other.
In general, the increment Δ x of the variable x is called the differential of x, denoted dx, i.e. dx = Δ x.
Seeker C located at point x 0 Probability p of (A) c (x 0 ) Differential probability p can be used c (x 0 ) dx represents. Wherein the differential probability p c (x 0 ) dx equal to the probability density function p of searcher C c Distribution at point x 0 Probability p of (A) c (x 0 ) The product of the differential line segment length dx (the area of the shaded portion in fig. 3 a). At Δ x → 0, there is p according to the differentiation principle c (x 0 )dx→p c (x 0 ) (ii) a Thus, the probability p is differentiated c (x 0 ) dx is indicative of the probability p c (x 0 )。
When seeker C is located at onePoint x 0 (x 0 E is equal to L), meeting event E is carried out according to formula (1) meet Occurrence of (D) means that the lost person D is located at the point x 0 Nearby, i.e. | y-x 0 I is less than or equal to md (the thick horizontal line in figure 3 b). The lost person D is located at point x 0 The probability of the vicinity being(area of shaded portion in FIG. 3 b), which represents the probability p of D d Distributed in the region { | y-x 0 And | is less than or equal to md, and y belongs to the probability value on L. Thus, C is located at a point x 0 Probability of time meeting D
(formula 2)
Wherein p is c (x 0 ) dx indicates that C is located at point x 0 The differential probability of (c). Similarly, we can obtain other differential encounter probabilities:
c is located at a point x 1 Probability of time meeting D
C is located at a point x 2 Probability of time meeting D
……
C is located at a point x k Probability of time meeting D
……
In conclusion, { p (E) meet |x 0 ),p(E meet |x 1 ),…,p(E meet |x k ) The maximum value of (8230) ("c)" in FIG. 3, x can be the position of the maximum value m . Thus, seeker C is at x m The lost person D can be found with the maximum probability.
3) Probability that seeker C can find lost person D on route L
When searcher C is located at all points { x | x = x } 0 ,x 1 ,…,x k \8230;) the probability that C can meet D:
thus, the probability that seeker C can find lost person D on route L:
(formula 3)
From the point of view of integration, p (E) meet ) Is p (E) meet | X) and the X-axis (fig. 4).
2. Technical route
In the above-mentioned encounter probability solution, the probability calculation for the seeker C to find the lost seeker D can be divided into three steps (fig. 5).
Step 1: obtaining search basic data including the length of the path L, the maximum distance md that can be met, and the probability density function p of the searcher C and the lost device D distributed on L c 、p d And the like.
Step 2: according to the formula (2), the differential encounter probability of each point of the searcher C on L is calculated, and the position of the searcher C can be analyzed to find the lost device D with the maximum probability.
And 3, step 3: the probability that the seeker C can find the lost person D on the route L is inferred according to the formula (3).
The differentiation method of encounter probability of the present invention is based on the maximum distance md that can be met and the probability density function p of the seeker C and the lost person D c 、p d And the questions of the probability that D can be found by C and the probability of where D can be found is the maximum can be answered. On one hand, the differential method of the encounter probability is different from a discrete method, the encounter probability calculated by the former method has stability and uniqueness, and the latter method has randomness and non-uniqueness; the other partyThe surface is also different from an integration method, when the probability density functions of C and D are in non-uniform distribution, the integration method of the encounter probability cannot calculate the integration of a complex function because the encounter events are taken as a whole, or the calculation complexity is high; the differential method of encounter probability can convert the integration problem of complex function into the integration problem of simple function on single encounter event because the encounter event is divided into a plurality of sub-events, thereby being helpful to simplify the calculation of integration and encounter probability. Therefore, when the probability density functions of C and D are nonlinear features, the calculation complexity can be reduced by adopting a differential method; when the probability density functions of C and D are uniformly distributed or linearly characterized, an integral method or an equivalent differential method may be employed.
The invention discloses a search and rescue system based on differential measure random encounter uncertainty, which is used for realizing the search and rescue method and comprises the following steps:
the confirming module is used for confirming the lost path L of the lost person D and confirming the position point of the lost person D on the path L;
the data acquisition module is used for measuring the position point of the searcher C on the path L;
a probability density function calculation module for calculating the probability density function p of the seeker C and the lost person D distributed on the path L c 、p d And C is located at a position point x on the path L 0 Probability of time meeting D Other points x on the corresponding calculation path L 1 、x 2 、…、x k < i > 8230am, obtaining { p (E) meet |x 0 ),p(E meet |x 1 ),…,p(E meet |x k ) 8230, finding the position point corresponding to the maximum value of the differential encounter probability is x m ；
An encounter probability calculation module for calculating the probability that the searcher C is located at all points { x | x = x } 0 ,x 1 ,…,x k 8230the probability of the search and rescue C meeting the lost D is p (E) meet )：
The probability that seeker C can find lost person D on route L is:
where md is the maximum distance that the seeker C can meet the lost person D, and the variable x represents the distance between the location of the seeker C and one of the endpoints O of the path L; the variable y represents the distance between the point of the lost person D and the endpoint O.
An analysis processing module for calculating the position point corresponding to the maximum value of the differential encounter probability and the encounter probability p (E) meet ) The searcher C is arranged to search and rescue on the path L.
Wherein, the probability density function calculation module is specifically configured to reasonably assume the probability density function p of the lost person D distributed on the path L when the lost person D finally appears at the middle point of the path L and only freely moves on the path L d The distribution is triangular; when the searcher C searches from the middle point of the path L, it is reasonable to assume the probability density function p of the path L where the searcher C is distributed c Is distributed in a triangle.
The following description will use specific embodiments to illustrate specific applications of the search and rescue method.
Setting: the length L =10 of the path L, the maximum distance md =2 that can be met, and the probability that the seeker C can randomly find the lost person D and where it is found is analyzed to be the greatest.
Example 1:
step 1: when only the lost person D is known to be present at the middle point of the line L and to move freely only on L, it is reasonable to assume that the probability density function p of D distributed on L d Are distributed triangularly, i.e.Furthermore, knowing that the searcher C moves randomly on L, it can reasonably assume the probability density function p of C distribution on L c In a uniform distribution, i.e. p c (x) =0.1, x and y represent the position points of C and D, respectively.
Step 2: according to equation (2), C is located at a point x k Probability of time meeting D At x k When =1,2,3,4,5,6,7,8,9
Thus, the probability that seeker C will see lost person D when x =5 is at point is the greatest (fig. 6).
And 3, step 3: due to p c 、p d Are all symmetric about the middle point of L, and thus haveThus, according to equation (3), there is
Wherein the content of the first and second substances,
in summary, the encounter probability p (E) meet )＝2×0.19467＝0.38933。
Example 2:
step 1: when only the lost person D is known to be present in the middle of the line L and to move freely only on L, it is reasonable to assume that the probability density function p of D is distributed on L d Are distributed triangularly, i.e.Also, know to searchThe probability density function p of C distributed in L can be reasonably assumed when C is found from the middle point of L c Are distributed triangularly, i.e.x and y represent the position points of C and D, respectively.
Step 2: according to equation (2), C is located at a point x k Probability of time meeting D At x k When the value of {1,2,3,4,5,6,7,8,9} is not less than the predetermined value
Thus, the probability that seeker C will encounter lost person D when x =5 is at the point is greatest (fig. 7).
And step 3: due to p c 、p d Are all symmetric about the middle point of L, and thus haveThus, according to the formula (3), there are
Wherein the content of the first and second substances,
in summary, the encounter probability p (E) meet )＝2×(0.0181333+0.0405333+0.1898667)＝0.49707。
As can be seen from the above example, the encounter probability based on the differential method has the following characteristics: (1) encounter probability p (E) meet ) Is completely defined by the meeting distance md andprobability density function p of the moving object itself c (x)、p d (y) decision, independent of variables in the algorithmic process, and thus stability and uniqueness; (2) different position points x of searcher C on path L k Probability p (E) of encountering a lost person D meet |x k ) Is x k Function of (4), presence of mode x m Or the position point x corresponding to the maximum probability value m I.e. C at point x k The probability of encountering D is greatest; (3) when the probability density function of the lost person D is not changed, the searcher C adopts different strategies of uniform distribution and triangular distribution, so that different search success rates appear, the former is 0.38933, the latter is 0.49707, and the latter is 21.68% higher than the former, so that the encounter probability is the premise and the basis of accurate planning and optimization of the search and rescue scheme.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
Claims (4)
1. A search and rescue method based on differential measure random encounter uncertainty is characterized by comprising the following steps:
step 1, determining a lost path L of a lost person D, and determining a position point of the lost person D on the path L;
step 2, measuring the position point of the searcher C on the path L;
step 3, calculating the probability density function p of the distribution of the seeker C and the lost person D on the path L c 、p d And C is located at a position point x on the path L 0 Probability of time meeting D Other points x on the corresponding calculation path L 1 、x 2 、…、x k < 8230 >, obtaining the differential encounter probability of { p (E) meet |x 0 ),p(E meet |x 1 ),…,p(E meet |x k ) 8230, finding the position point corresponding to the maximum value of the differential encounter probability is x m ；
Step 4, when the searcher C is located at all points { x | x = x { (X {) 0 ,x 1 ,…,x k 8230time, the probability p (E) that seeker C will meet lost person D meet )：
Probability that seeker C can find lost person D on path L:
where md is the maximum distance that the seeker C can meet the lost person D, and the variable x represents the distance between the location of the seeker C and one of the endpoints O of the path L; the variable y represents the distance between the point of the lost person D and the endpoint O;
step 5, according to the calculated position point corresponding to the maximum value of the differential encounter probability and the encounter probability p (E) meet ) The searcher C is arranged to search and rescue on the path L.
2. A method as claimed in claim 1, wherein if the lost person D finally appears at the middle point of the path L and moves freely only on the path L, it can be reasonably assumed that the probability density function p of the lost person D distributed on the path L d The distribution is triangular; if the searcher C searches from the middle point of the path L, it can also be reasonably assumed that the probability density function p of the path L is distributed by the searcher C c Is distributed in a triangle.
3. A search and rescue system based on differential measure random encounter uncertainty, the system comprising:
the confirming module is used for confirming the lost path L of the lost person D and confirming the position point of the lost person D on the path L;
the data acquisition module is used for measuring the position point of the searcher C on the path L;
a probability density function calculation module for calculating the probability density function p of the seeker C and the lost person D distributed on the path L c 、p d And C is located at a position point x on the path L 0 Probability of time meeting D Other points x on the corresponding calculation path L 1 、x 2 、…、x k < i > 8230am, obtaining { p (E) meet |x 0 ),p(E meet |x 1 ),…,p(E meet |x k ) 8230, finding the position point x corresponding to the maximum value of the differential encounter probability m ；
An encounter probability calculation module for calculating the probability that the searcher C is located at all points { x | x = x } 0 ,x 1 ,…,x k 8230time, the probability p (E) that seeker C will meet lost person D meet )：
Then the probability that seeker C can find lost person D on route L is:
where md is the maximum distance that the seeker C can meet the lost person D, and the variable x represents the distance between the location of the seeker C and one of the endpoints O of the path L; the variable y represents the distance between the point where the lost person D is located and the end point O;
an analysis processing module for calculating the position point corresponding to the maximum of the differential encounter probabilityAnd the probability of encounter p (E) meet ) The searcher C is arranged to search and rescue on the path L.
4. A search and rescue system based on differential measure random encounter uncertainty as claimed in claim 3, wherein the probability density function calculation module is specifically configured to reasonably assume the probability density function p of the lost person D distributed on the path L when the lost person D finally appears at the middle point of the path L and only freely moves on the path L d The distribution is triangular; when the searcher C searches from the middle point of the path L, it is reasonable to assume the probability density function p of the path L where the searcher C is distributed c Is distributed in a triangle.
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