CN105095680A - Search-and-rescue method and system based on differential measure random meet uncertainty - Google Patents

Abstract

The invention discloses a search-and-rescue method and system based on differential measure random meet uncertainty. The method comprises the following steps: 1, determining a path L along which a lost person D gets lost, and determining a position point where the lost person D is located on the path L finally; 2, measuring a position point where a searcher C is located on the path L; 3, calculating probability density functions pc and pd that the searcher C and the lost person D are distributed on the path L and the probability that C can meet D when being located at a point of the path L, and finding a position point xm corresponding to the maximum value of the differential meet probability; calculating the meet probability that the searcher C can find the lost person D on the path L; 5, arranging the searcher C to conduct search and rescue on the path L according to the position point corresponding to the maximum value of the differential meet probability and the meet probability obtained through calculation.

Description

Meet at random probabilistic rescue method and system is estimated based on differential

Technical field

The present invention relates to search and rescue field, particularly relate to one and estimate based on differential meet at random probabilistic rescue method and system.

Background technology

In recent years, personnel's search and rescue case happen occasionally.Such as, the personnel's lost contact in outdoor activities and search and rescue, child old man wandering away and searching.A kind of typical case is such: the known person of wandering away finally appears at the centre position of path L and moves freely on the L of path; Does the possibility that one searcher runs into the person of wandering away on the L of path have much? is the possibility that searcher meets at which location point of path L the person of wandering away maximum?

1. the mechanism of method work before improving

Often for instinct or the humanitarianism of people, finally being there is the certain area of place periphery by traditional rescue operations in a large amount of search and rescue resource input, lacks and search and rescue planning (Liu Zhao, etc., 2014) accurately to the person of wandering away.Wherein, precognition searcher can meet the possibility of the person of wandering away, and is the prerequisite of searching and rescuing programme planning and success rescue most possibly.Existing probability times geography adopts probable value quantification to express possibility of meeting, and proposes a kind of discrete type method (Winter, YIN, 2011) calculating collision probability.The method specifies: the condition that searcher C and the person of wandering away D can meet is that C, D are arranged in same discrete unit in discrete type geographical space.

If: searcher C is l with the length of the path L at the person of wandering away D place.C, D probability density function be distributed on the L of path is c, d.The calculation procedure of the discrete type method of collision probability is as follows:

Step 1: path L is evenly divided into n segment: L ₁, L ₂..., L _n(Fig. 1 (a)).

Step 2: note C, D lay respectively at arbitrary segment L _iprobable value c _i, d _i, have: 0≤c _i≤ 1,0≤d _i≤ 1 (Fig. 1 (b)), ${\mathrm{\Σ}}_{i=1}^n{c}_i=1,{\mathrm{\Σ}}_{i=1}^n{d}_i=1,i=1,2,...,n.$

Step 3: before searcher finds the person of wandering away, the mobile visible of two individualities is independently.Like this, individual C, D are positioned at or meet in arbitrary unit L _iprobable value be c _i× d _i.Correspondingly, the probable value of meeting in whole path L is ${\mathrm{\Σ}}_{i=1}^n{c}_i\×d_i,i=1,2,...,n$ (Fig. 1 (c)).

For simplicity, make c, d for being uniformly distributed.

(1) as n=1, then c, d are distributed in L ₁probable value c ₁=1, d ₁=1, corresponding collision probability: ${\mathrm{\Σ}}_{i=1}^n{c}_i\×d_i={\mathrm{\Σ}}_{i=1}^1{c}_i\×d_i=c_1\×d_1=1.$

(2) as n=2, then c, d are distributed in L ₁probable value c ₁=d ₁=0.5, c, d are distributed in L ₂probable value c ₂=d ₂=0.5, corresponding collision probability: ${\mathrm{\Σ}}_{i=1}^n{c}_i\×d_i={\mathrm{\Σ}}_{i=1}^2{c}_i\×d_i=c_1\×d_1+c_2\×d_2=$ $\mathrm{0.5.}$

(3) as n=10, then c, d are distributed in L _iprobable value c _i=d _i=0.1, corresponding collision probability: ${\mathrm{\Σ}}_{i=1}^n{c}_i\×d_i={\mathrm{\Σ}}_{i=1}^{10}{c}_i\×d_i=10\×(0.1\×0.1)=\mathrm{0.1.}$

As from the foregoing, when the quantity n of discrete unit constantly increases, the possibility that searcher C meets the person of wandering away D on the L of path constantly reduces, i.e. probability and the n of success search are inversely proportional to; This conclusion is equally applicable to the situation that c, d are non-uniform Distribution, as normal distribution, Triangle-Profile etc.

2. method Problems existing before improving

To sum up, discrete type method depends on the yardstick (Winter, YIN, 2011) of discrete unit, and collision probability can reduce with the increase of discrete unit quantity; Like this, the artificial property that discrete type method mesoscale or discrete unit quantity are arranged certainly will cause the randomness of collision probability.But the collision probability as objective law has stability, have nothing to do with computing method in theory.

Summary of the invention

The present invention is directed to searcher C on the L of path and can meet the probability problem of the person of wandering away D, discrete type method can not provide the collision probability with stability or uniqueness.Propose a kind of non-homogeneous probability distribution be distributed according to searcher and the person of wandering away on the L of path, what utilize continuous differential to extrapolate the collision probability with uniqueness estimates based on differential meet at random probabilistic rescue method and system.

The technical solution adopted for the present invention to solve the technical problems is:

There is provided a kind of and estimate based on differential probabilistic rescue method that meets at random, comprise the following steps:

Step 1, determine the missing path L of the person of wandering away D, and determine that the person of wandering away D finally appears at the location point on the L of path;

Step 2, the location point of measurement searcher C on the L of path;

Step 3, calculating searcher C and the person of wandering away D are distributed in the probability density function p of path L _c, p _d, C is positioned at the location point x of road on L ₀the probability that Shi Nengyu D meets other x on corresponding calculating path L ₁, x ₂..., x _k... differential collision probability obtain { p (E _meet| x ₀), p (E _meet| x ₁) ..., p (E _meet| x _k) ..., find the location point corresponding to differential collision probability maximal value to be x _m;

Step 4, be positioned at whole point { x|x=x as searcher C ₀, x ₁..., x _k... time, search and rescue person C can with the collision probability p (E of the person of wandering away D _meet):

$\begin{array}{c}p\left(E_{meet}\right)=p\left(E_{meet}\right|x_0)+p\left(E_{meet}\right|x_1)+...+p\left(E_{meet}\right|x_k)+...\\ =p_c\left(x_0\right)dx\×\underset{\left|y-x_0\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+p_c\left(x_1\right)dx\×\underset{\left|y-x_1\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+...+p_c\left(x_k\right)dx\\ \×\underset{\left|y-x_k\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+...\\ =\underset{x\∈L}{\mathrm{\Σ}}{p}_c\left(x\right)dx\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy=\underset{x\∈L}{\∫}{p}_c\left(x\right)\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dydx\end{array}$

Then searcher C can find the probability of the person of wandering away D on the L of path:

wherein md is the ultimate range that searcher C can meet with the person of wandering away D, and variable x represents the distance between searcher C position point and an end points O of path L; Variable y represents the distance between the person of wandering away D position point and end points O;

Step 5, according to the location point corresponding with differential collision probability maximal value calculated, and collision probability p (E _meet) arrange searcher C to search and rescue on the L of path.

In rescue method of the present invention, if the person of wandering away D finally appears at the intermediate point of path L and only moves freely on the L of path, then can be distributed in the probability density function p of path L by the reasonable assumption person of wandering away D _ddistribution triangular in shape; If searcher C looks for from the intermediate point of path L, then also can be distributed in the probability density function p of path L by reasonable assumption searcher C _cdistribution triangular in shape.

The present invention also provides a kind of and estimates based on differential probabilistic search and rescue system that meets at random, and this system comprises:

Confirming module, for determining the missing path L of the person of wandering away D, and determining that the person of wandering away D finally appears at the location point on the L of path;

Data acquisition module, for the location point of searcher C on the L of path measured;

Probability density function computing module, is distributed in the probability density function p of path L for calculating searcher C and the person of wandering away D _c, p _d, C is positioned at the location point x of road on L ₀the probability that Shi Nengyu D meets other x on corresponding calculating path L ₁, x ₂..., x _k... differential collision probability, obtain { p (E _meet| x ₀), p (E _meet| x ₁) ..., p (E _meet| x _k) ..., find the location point corresponding to differential collision probability maximal value to be x _m;

Collision probability computing module, for calculating when searcher C is positioned at whole point { x|x=x ₀, x ₁..., x _k... time, search and rescue person C can with the collision probability p (E of the person of wandering away D _meet):

$\begin{array}{c}p\left(E_{meet}\right)=p\left(E_{meet}\right|x_0)+p\left(E_{meet}\right|x_1)+...+p\left(E_{meet}\right|x_k)+...\\ =p_c\left(x_0\right)dx\×\underset{\left|y-x_0\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+p_c\left(x_1\right)dx\×\underset{\left|y-x_1\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+...+p_c\left(x_k\right)dx\\ \×\underset{\left|y-x_k\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+...\\ =\underset{x\∈L}{\mathrm{\Σ}}{p}_c\left(x\right)dx\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy=\underset{x\∈L}{\∫}{p}_c\left(x\right)\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dydx\end{array}$

Then searcher C can find the probability of the person of wandering away D to be on the L of path:

wherein md is the ultimate range that searcher C can meet with the person of wandering away D, and variable x represents the distance between searcher C position point and an end points O of path L; Variable y represents the distance between the person of wandering away D position point and end points O;

Analysis and processing module, for the location point corresponding with differential collision probability maximal value according to calculating, and collision probability p (E _meet) arrange searcher C to search and rescue on the L of path.

In search and rescue system of the present invention, when described probability density function computing module is specifically for finally appearing at the intermediate point of path L at the person of wandering away D and only moving freely on the L of path, then the reasonable assumption person of wandering away D is distributed in the probability density function p of path L _ddistribution triangular in shape; When searcher C looks for from the intermediate point of path L, then also reasonable assumption searcher C is distributed in the probability density function p of path L _cdistribution triangular in shape.

The beneficial effect that the present invention produces is: the present invention utilizes the differential method of collision probability, according to the probability density function p of the ultimate range md that can meet and searcher C, the person of wandering away D _c, p _d, C can be solved and can find the problems such as the probability of D and the maximum probability that finds wherein.The differential method of collision probability of the present invention, is different from discrete type method, and the collision probability value that the present invention calculates has stability and uniqueness.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing:

Fig. 1: the discrete type method figure of traditional collision probability, the wherein discretize in (a) path; B () individuality is positioned at the probability of discrete unit; (c) collision probability;

Fig. 2: searcher C can meet the event of the person of wandering away D, wherein (a) variable-definition; B () is met Event Example;

Fig. 3: the searcher C inference method meeting the maximum probability of the person of wandering away D wherein, wherein (a) differential probability; B () C is positioned at the differential collision probability of set point; C () C is positioned at the sequential derivatives collision probability of sequence of points;

Fig. 4: in the present invention, searcher C can meet the inference method of the probability of the person of wandering away D;

Fig. 5: the Technology Roadmap of the collision probability differential method of the present invention;

Fig. 6: the locus at collision probability maximal value place in one embodiment of the invention;

Fig. 7: the locus at collision probability maximal value place in another embodiment of the present invention.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

1. the main technical schemes taked of the present invention

In actual environment, meeting between two individualities is main by space length (as visual range) restriction between the two.Here, by the ultimate range that two individualities can meet, be designated as md (meetingdistance).Accordingly, the semanteme that meets may be defined as: just think and can meet when the distance of and if only if two individualities is no more than md.Like this, md determines the yardstick met to a certain extent, thus provides theoretical foundation for the uniqueness of collision probability.

Introduce the main technical schemes that the present invention takes below.

1) to meet event

Order, an end points of straight-line segment L is O; Searcher C and the person of wandering away D are located on L.

If: variable x represents the distance between searcher C position point and end points O; (Fig. 2 a) for the distance that variable y represents between the person of wandering away D position point and end points O.

According to the semanteme that meets, meet event E _meet={ being no more than the event of md between the position x at searcher C place and the position y at the person of wandering away D place in distance }, 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}

Like this, when searcher C is positioned at location point x, if the position y at the person of wandering away D place ₁meet formula 1, namely | y ₁-x|≤md, then meet event E _meetoccur; If the position y at the person of wandering away D place ₂formula 1 can not be met, namely | y ₁-x|>md, then meet event E _meetcan not occur (Fig. 2 b).

2) searcher C can find the person of wandering away D with maximum probability wherein

Collision probability p (E _meet) be exactly the event E that meets _meetthe probability occurred.Order, the probability density function that searcher C and the person of wandering away D is distributed on the L of path is respectively: p _c, p _d, and the motion of C and D is separate.

Under normal circumstances, the increment Delta x of variable x is called as the differential of x, is denoted as dx, i.e. dx=Δ x.

Searcher C is positioned at an x ₀the Probability p at place _c(x ₀) differential Probability p can be adopted _c(x ₀) dx represents.Wherein, differential Probability p _c(x ₀) dx, equal the probability density function p of searcher C _cbe distributed in an x ₀the Probability p at place _c(x ₀) with the product (area of Fig. 3 a dash area) of differential line segment length dx.When Δ x → 0, there is p according to Differential Principle _c(x ₀) dx → p _c(x ₀); Like this, differential Probability p _c(x ₀) dx can represent Probability p _c(x ₀).

When searcher C is positioned at a some x ₀(x ₀∈ L) time, to meet event E according to formula (1) _meetmean that the person of wandering away D is positioned at an x ₀near, namely | y-x ₀|≤md (the thick horizontal line of Fig. 3 b).The person of wandering away D is positioned at an x ₀neighbouring probability is (area of Fig. 3 b dash area), it represents the Probability p of D _dbe distributed in region | y-x ₀| the probable value on≤md, y ∈ L}.Like this, C is positioned at a some x ₀the probability that Shi Nengyu D meets

$p\left(E_{meet}\right|x_0)=p_c\left(x_0\right)dx\×\underset{\left|y-x_0\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy$ (formula 2)

Wherein, p _c(x ₀) dx represents that C is positioned at an x ₀differential probability.Similarly, we can obtain other differential collision probabilitys:

C is positioned at a some x ₁the probability that Shi Nengyu D meets

C is positioned at a some x ₂the probability that Shi Nengyu D meets

……

C is positioned at a some x _kthe probability that Shi Nengyu D meets

……

To sum up, { p (E can be obtained _meet| x ₀), p (E _meet| x ₁) ..., p (E _meet| x _k) ... maximal value (as Suo Shi Fig. 3 (c)), the location point at this maximal value place can be set without loss of generality as x _m.Like this, searcher C is at x _mplace can find the person of wandering away D with maximum probability.

3) searcher C can find the probability of the person of wandering away D on the L of path

When searcher C is positioned at whole point { x|x=x ₀, x ₁..., x _k... time, the probability that C can meet with D:

$\begin{array}{c}p\left(E_{meet}\right)=p\left(E_{meet}\right|x_0)+p\left(E_{meet}\right|x_1)+...+p\left(E_{meet}\right|x_k)+...\\ =p_c\left(x_0\right)dx\×\underset{\left|y-x_0\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+p_c\left(x_1\right)dx\×\underset{\left|y-x_1\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+...+p_c\left(x_k\right)dx\\ \×\underset{\left|y-x_k\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+...\\ =\underset{x\∈L}{\mathrm{\Σ}}{p}_c\left(x\right)dx\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy=\underset{x\∈L}{\∫}{p}_c\left(x\right)\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dydx\end{array}$

Like this, searcher C can find the probability of the person of wandering away D on the L of path:

$p\left(E_{meet}\right)=\underset{x\∈L}{\∫}{p}_c\left(x\right)\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dydx$ (formula 3)

From the angle of integration, p (E _meet) be exactly p (E _meet| the area (Fig. 4) x) and between X-axis.

2. technology path

Above-mentioned collision probability technical scheme, searcher C finds the probability calculation of the person of wandering away D can be divided into three steps (Fig. 5).

Step 1: obtain and search master data, comprise the length of path L, the ultimate range md that can meet, and searcher C, the person of wandering away D are distributed in the probability density function p of L _c, p _ddeng.

Step 2: according to formula (2), calculates the differential collision probability that searcher C is positioned at each point on L, analyzes searcher C and can find the person of wandering away D with maximum probability wherein.

Step 3: according to formula (3), reasoning searcher C can find the probability of the person of wandering away D on the L of path.

The differential method of collision probability of the present invention, according to the probability density function p of the ultimate range md that can meet and searcher C, the person of wandering away D _c, p _d, the problem such as the probability that C can find D and the maximum probability found wherein can be answered.The differential method of collision probability, is different from discrete type method on the one hand, and the collision probability value that the former calculates has stability and uniqueness, and latter has randomness and nonuniqueness; On the other hand also be different from integral method, when the probability density function for C, D is non-uniform Distribution, the integral method of collision probability is due to integrally thus often can not the integration of calculation of complex function by the event of meeting, or the complexity calculated is large; The Integral Problem of complicated function, due to the event of meeting is divided into some subevents, thus can be converted to the Integral Problem of simple function in single event of meeting by the differential law of collision probability, thus contributes to the calculating simplifying integration and collision probability.Therefore, when the probability density function for C, D is nonlinear characteristic, adopt the differential method to reduce computation complexity; For C, D probability density function for be uniformly distributed or linearly feature time, the differential method of integral method or equivalence can be adopted.

Of the present inventionly estimate based on differential probabilistic search and rescue system that meets at random, for realizing above-mentioned rescue method, this system comprises:

Confirming module, for determining the missing path L of the person of wandering away D, and determining that the person of wandering away D finally appears at the location point on the L of path;

Data acquisition module, for the location point of searcher C on the L of path measured;

Probability density function computing module, is distributed in the probability density function p of path L for calculating searcher C and the person of wandering away D _c, p _d, C is positioned at the location point x of road on L ₀the probability that Shi Nengyu D meets other x on corresponding calculating path L ₁, x ₂..., x _k... differential collision probability, obtain { p (E _meet| x ₀), p (E _meet| x ₁) ..., p (E _meet| x _k) ..., find the location point corresponding to differential collision probability maximal value to be x _m;

Collision probability computing module, for calculating when searcher C is positioned at whole point { x|x=x ₀, x ₁..., x _k... time, search and rescue person C can with the collision probability p (E of the person of wandering away D _meet):

$\begin{array}{c}p\left(E_{meet}\right)=p\left(E_{meet}\right|x_0)+p\left(E_{meet}\right|x_1)+...+p\left(E_{meet}\right|x_k)+...\\ =p_c\left(x_0\right)dx\×\underset{\left|y-x_0\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+p_c\left(x_1\right)dx\×\underset{\left|y-x_1\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+...+p_c\left(x_k\right)dx\\ \×\underset{\left|y-x_k\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy+...\\ =\underset{x\∈L}{\mathrm{\Σ}}{p}_c\left(x\right)dx\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dy=\underset{x\∈L}{\∫}{p}_c\left(x\right)\·\underset{\left|y-x\right|\≤md,y\∈L}{\∫}{p}_d\left(y\right)dydx\end{array}$

Then searcher C can find the probability of the person of wandering away D to be on the L of path:

wherein md is the ultimate range that searcher C can meet with the person of wandering away D, and variable x represents the distance between searcher C position point and an end points O of path L; Variable y represents the distance between the person of wandering away D position point and end points O.

Analysis and processing module, for the location point corresponding with differential collision probability maximal value according to calculating, and collision probability p (E _meet) arrange searcher C to search and rescue on the L of path.

Wherein, when described probability density function computing module is specifically for finally appearing at the intermediate point of path L at the person of wandering away D and only moving freely on the L of path, then the reasonable assumption person of wandering away D is distributed in the probability density function p of path L _ddistribution triangular in shape; When searcher C looks for from the intermediate point of path L, then also reasonable assumption searcher C is distributed in the probability density function p of path L _cdistribution triangular in shape.

Below utilize specific embodiment so that the embody rule of above-mentioned rescue method to be described.

If: the length l=10 of path L, the ultimate range md=2 that can meet, analyze the maximum probability that searcher C can find the probability of the person of wandering away D at random and find wherein.

Example 1:

Step 1: when only knowing that the person of wandering away D finally appears at the intermediate point of circuit L and only moves freely on L, can be distributed in the probability density function p of L by reasonable assumption D _dfor Triangle-Profile, namely $p_d\left(y\right)=\left\{\begin{array}{cc}\frac{y}{25},& 0\&le;y\&le;5\\ \frac{10-y}{25},& 5<y\&le;10\end{array}\right..$ Again, know searcher C movement at random on L, the probability density function p of L can be distributed in by reasonable assumption C _cfor being uniformly distributed, i.e. p _cx ()=0.1, x, y represent the location point of C, D respectively.

Step 2: according to formula (2), C is positioned at a some x _kthe probability that Shi Nengyu D meets at x _k={ have during 1,2,3,4,5,6,7,8,9}

$p\left(E_{meet}\right|x_k=1)=p_c\left(x_k\right)dx\underset{0\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;{\&Integral;}_0^3\frac{y}{25}dy=\frac{4.5}{250}dx.$

$p\left(E_{meet}\right|x_k=2)=p_c\left(x_k\right)dx\underset{0\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;{\&Integral;}_0^4\frac{y}{25}dy=\frac{8}{250}dx.$

$p\left(E_{meet}\right|x_k=3)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;{\&Integral;}_1^5\frac{y}{25}dy=\frac{12}{250}dx.$

$p\left(E_{meet}\right|x_k=4)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;({\&Integral;}_2^5\frac{y}{25}dy+{\&Integral;}_5^6\frac{10-y}{25}dy)=\frac{15}{250}dx.$

$p\left(E_{meet}\right|x_k=5)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;({\&Integral;}_3^5\frac{y}{25}dy+{\&Integral;}_5^7\frac{10-y}{25}dy)=\frac{16}{250}dx.$

$p\left(E_{meet}\right|x_k=6)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;({\&Integral;}_4^5\frac{y}{25}dy+{\&Integral;}_5^8\frac{10-y}{25}dy)=\frac{15}{250}dx.$

$p\left(E_{meet}\right|x_k=7)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;{\&Integral;}_5^9\frac{10-y}{25}dy=\frac{12}{250}dx.$

$p\left(E_{meet}\right|x_k=8)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;{\&Integral;}_6^{10}\frac{10-y}{25}dy=\frac{8}{250}dx.$

$p\left(E_{meet}\right|x_k=9)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{10}\&times;{\&Integral;}_7^{10}\frac{10-y}{25}dy=\frac{4.5}{250}dx.$

Like this, the maximum probability (Fig. 6) of the person of wandering away D can be met when searcher C is positioned at some during x=5.

Step 3: due to p _c, p _dintermediate point all about L is symmetrical, therefore has $\underset{x\&Element;\&lsqb;0,5\&rsqb;}{\&Integral;}{p}_c\left(x\right)\underset{\left|y-x\right|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dydx=\underset{x\&Element;\&lsqb;5,10\&rsqb;}{\&Integral;}{p}_c\left(x\right)\&CenterDot;\underset{\left|y-x\right|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dydx;$ Like this, according to formula (3), have $p\left(E_{meet}\right)$ $=2\underset{x\&Element;\&lsqb;0,5\&rsqb;}{\&Integral;}{p}_c\left(x\right)\&CenterDot;\underset{\left|y-x\right|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dydx.$

Wherein,

To sum up, collision probability p (E _meet)=2 × 0.19467=0.38933.

Example 2:

Step 1: when only knowing that the person of wandering away D finally appears at the intermediate point of circuit L and only moves freely on L, can be distributed in the probability density function p of L by reasonable assumption D _dfor Triangle-Profile, namely $p_d\left(y\right)=\left\{\begin{array}{cc}\frac{y}{25},& 0\&le;y\&le;5\\ \frac{10-y}{25},& 5<y\&le;10\end{array}\right..$ Again, know that searcher C looks for from the intermediate point of L, also can be distributed in the probability density function p of L by reasonable assumption C _cfor Triangle-Profile, namely $p_c\left(x\right)=\left\{\begin{array}{cc}\frac{x}{25},& 0\&le;x\&le;5\\ \frac{10-x}{25},& 5<x\&le;10\end{array}\right.,$ X, y represent the location point of C, D respectively.

Step 2: according to formula (2), C is positioned at a some x _kthe probability that Shi Nengyu D meets at x _k={ have during 1,2,3,4,5,6,7,8,9}

$p\left(E_{meet}\right|x_k=1)=p_c\left(x_k\right)dx\underset{0\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{dx}{25}\&times;{\&Integral;}_0^3\frac{y}{25}dy=\frac{4.5}{625}dx.$

$p\left(E_{meet}\right|x_k=2)=p_c\left(x_k\right)dx\underset{0\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{2dx}{25}\&times;{\&Integral;}_0^4\frac{y}{25}dy=\frac{16}{625}dx.$

$p\left(E_{meet}\right|x_k=3)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{3dx}{25}\&times;{\&Integral;}_1^5\frac{y}{25}dy=\frac{36}{625}dx.$

$p\left(E_{meet}\right|x_k=4)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{4dx}{25}\&times;({\&Integral;}_2^5\frac{y}{25}dy+{\&Integral;}_5^6\frac{10-y}{25}dy)=\frac{60}{625}dx.$

$p\left(E_{meet}\right|x_k=5)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{5dx}{25}\&times;({\&Integral;}_3^5\frac{y}{25}dy+{\&Integral;}_5^7\frac{10-y}{25}dy)=\frac{80}{625}dx.$

$p\left(E_{meet}\right|x_k=6)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{10-6}{25}dx\&times;({\&Integral;}_4^5\frac{y}{25}dy+{\&Integral;}_5^8\frac{10-y}{25}dy)=\frac{60}{625}dx.$

$p\left(E_{meet}\right|x_k=7)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{10-7}{25}dx\&times;{\&Integral;}_5^9\frac{10-y}{25}dy=\frac{36}{625}dx.$

$p\left(E_{meet}\right|x_k=8)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{10-8}{25}dx\&times;{\&Integral;}_6^{10}\frac{10-y}{25}dy=\frac{16}{625}dx.$

$p\left(E_{meet}\right|x_k=9)=p_c\left(x_k\right)dx\underset{x_k-2\&le;y\&le;x_k+2}{\&Integral;}{p}_d\left(y\right)dy=\frac{10-9}{25}dx\&times;{\&Integral;}_7^{10}\frac{10-y}{25}dy=\frac{4.5}{625}dx.$

Like this, the maximum probability (Fig. 7) of the person of wandering away D can be met when searcher C is positioned at some during x=5.

Step 3: due to p _c, p _dintermediate point all about L is symmetrical, therefore has $\underset{x\&Element;\&lsqb;0,5\&rsqb;}{\&Integral;}{p}_c\left(x\right)\&CenterDot;\underset{\left|y-x\right|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dydx=\underset{x\&Element;\&lsqb;5,10\&rsqb;}{\&Integral;}{p}_c\left(x\right)\&CenterDot;\underset{\left|y-x\right|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dydx;$ Like this, according to formula (3), have $p\left(E_{meet}\right)$ $=2\underset{x\&Element;\&lsqb;0,5\&rsqb;}{\&Integral;}{p}_c\left(x\right)\&CenterDot;\&le;\underset{\left|y-x\right|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dydx.$

Wherein,

To sum up, collision probability p (E _meet)=2 × (0.0181333+0.0405333+0.1898667)=0.49707.

As known from the above examples, the collision probability based on differential method has following features: 1. collision probability p (E _meet) completely by the probability density function p of can meet distance md and mobile object itself _c(x), p _dy () determines, have nothing to do, thus have stability and uniqueness with the variable in algorithmic procedure; 2. the diverse location point x of searcher C on the L of path _kprobability p (the E of the person of wandering away D can be met _meet| x _k) be x _kfunction, there is mode x _mor the location point x that most probable value is corresponding _m, namely C is at an x _kthe maximum probability of D can be met; 3. when the probability density function of the person of wandering away D is constant, searcher C employing is uniformly distributed, the Different Strategies of Triangle-Profile, different success probability of search will be there is, the former is 0.38933, the latter is 0.49707, comparatively the former exceeds 21.68% to the latter, and therefore collision probability is the accurate planning of search and rescue scheme and the prerequisite of optimization and basis.

Should be understood that, for those of ordinary skills, can be improved according to the above description or convert, and all these improve and convert the protection domain that all should belong to claims of the present invention.

Claims (4)

1. estimate based on differential probabilistic rescue method that meets at random, it is characterized in that, comprise the following steps:

Step 1, determine the missing path L of the person of wandering away D, and determine that the person of wandering away D finally appears at the location point on the L of path;

Step 2, the location point of measurement searcher C on the L of path;

Step 3, calculating searcher C and the person of wandering away D are distributed in the probability density function p of path L _c, p _d, C is positioned at the location point x of road on L ₀the probability that Shi Nengyu D meets other x on corresponding calculating path L ₁, x ₂..., x _k... differential collision probability obtain { p (E _meet| x ₀), p (E _meet| x ₁) ..., p (E _meet| x _k) ..., find the location point corresponding to differential collision probability maximal value to be x _m;

Step 4, be positioned at whole point { x|x=x as searcher C ₀, x ₁..., x _k... time, search and rescue person C can with the collision probability p (E of the person of wandering away D _meet):

$\begin{array}{c}p\left(E_{meet}\right)=p\left(E_{meet}\right|x_0)+p\left(E_{meet}\right|x_1)+...+p\left(E_{meet}\right|x_k)+...\\ =p_c\left(x_0\right)dx\&times;\underset{|y-x_0|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dy+p_c\left(x_1\right)dx\&times;\underset{|y-x_1|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dy+...+p_c\left(x_k\right)dx\\ \&times;\underset{|y-x_k|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dy+...\\ =\underset{x\&Element;L}{\mathrm{\&Sigma;}}{p}_c\left(x\right)dx\&CenterDot;\underset{|y-x|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dy=\underset{x\&Element;L}{\&Integral;}{p}_c\left(x\right)\&CenterDot;\underset{|y-x|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dydx\end{array}$

Then searcher C can find the probability of the person of wandering away D on the L of path:

wherein md is the ultimate range that searcher C can meet with the person of wandering away D, and variable x represents the distance between searcher C position point and an end points O of path L; Variable y represents the distance between the person of wandering away D position point and end points O.

Step 5, according to the location point corresponding with differential collision probability maximal value calculated, and collision probability p (E _meet) arrange searcher C to search and rescue on the L of path.

2. rescue method according to claim 1, is characterized in that, if the person of wandering away D finally appears at the intermediate point of path L and only moves freely on the L of path, then can be distributed in the probability density function p of path L by the reasonable assumption person of wandering away D _ddistribution triangular in shape; If searcher C looks for from the intermediate point of path L, then also can be distributed in the probability density function p of path L by reasonable assumption searcher C _cdistribution triangular in shape.

3. estimate based on differential probabilistic search and rescue system that meets at random, it is characterized in that, this system comprises:

Confirming module, for determining the missing path L of the person of wandering away D, and determining that the person of wandering away D finally appears at the location point on the L of path;

Data acquisition module, for measuring the location point of searcher C on the L of path;

Probability density function computing module, is distributed in the probability density function p of path L for calculating searcher C and the person of wandering away D _c, p _d, C is positioned at the location point x of road on L ₀the probability that Shi Nengyu D meets other x on corresponding calculating path L ₁, x ₂..., x _k... differential collision probability, obtain { p (E _meet| x ₀), p (E _meet| x ₁) ..., p (E _meet| x _k) ..., find the location point corresponding to differential collision probability maximal value to be x _m;

Collision probability computing module, for calculating when searcher C is positioned at whole point { x|x=x ₀, x ₁..., x _k... time, search and rescue person C can with the collision probability p (E of the person of wandering away D _meet):

$\begin{array}{c}p\left(E_{meet}\right)=p\left(E_{meet}\right|x_0)+p\left(E_{meet}\right|x_1)+...+p\left(E_{meet}\right|x_k)+...\\ =p_c\left(x_0\right)dx\&times;\underset{|y-x_0|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dy+p_c\left(x_1\right)dx\&times;\underset{|y-x_1|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dy+...+p_c\left(x_k\right)dx\\ \&times;\underset{|y-x_k|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dy+...\\ =\underset{x\&Element;L}{\mathrm{\&Sigma;}}{p}_c\left(x\right)dx\&CenterDot;\underset{|y-x|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dy=\underset{x\&Element;L}{\&Integral;}{p}_c\left(x\right)\&CenterDot;\underset{|y-x|\&le;md,y\&Element;L}{\&Integral;}{p}_d\left(y\right)dydx\end{array}$

Then searcher C can find the probability of the person of wandering away D to be on the L of path:

wherein md is the ultimate range that searcher C can meet with the person of wandering away D, and variable x represents the distance between searcher C position point and an end points O of path L; Variable y represents the distance between the person of wandering away D position point and end points O.

Analysis and processing module, for the location point corresponding with differential collision probability maximal value according to calculating, and collision probability p (E _meet) arrange searcher C to search and rescue on the L of path.

4. search and rescue system according to claim 3, it is characterized in that, when described probability density function computing module is specifically for finally appearing at the intermediate point of path L at the person of wandering away D and only moving freely on the L of path, then the reasonable assumption person of wandering away D is distributed in the probability density function p of path L _ddistribution triangular in shape; When searcher C looks for from the intermediate point of path L, then also reasonable assumption searcher C is distributed in the probability density function p of path L _cdistribution triangular in shape.