CN108882198B - Mean value positioning method for unknown sensor nodes of wireless sensor network - Google Patents

Mean value positioning method for unknown sensor nodes of wireless sensor network Download PDF

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CN108882198B
CN108882198B CN201810884680.6A CN201810884680A CN108882198B CN 108882198 B CN108882198 B CN 108882198B CN 201810884680 A CN201810884680 A CN 201810884680A CN 108882198 B CN108882198 B CN 108882198B
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CN108882198A (en
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乔学工
段亚青
王华倩
周文祥
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Taiyuan University of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30—Services specially adapted for particular environments, situations or purposes
    • H04W4/38—Services specially adapted for particular environments, situations or purposes for collecting sensor information
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0278—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves involving statistical or probabilistic considerations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/80—Services using short range communication, e.g. near-field communication [NFC], radio-frequency identification [RFID] or low energy communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
    • H04W64/006—Locating users or terminals or network equipment for network management purposes, e.g. mobility management with additional information processing, e.g. for direction or speed determination
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention relates to a wireless sensor network positioning technology, in particular to a mean value positioning method for unknown sensor nodes of a wireless sensor network. The problems of low positioning accuracy and complex algorithm of the conventional positioning algorithm based on distance measurement are solved. The method of the invention firstly uses the signal intensity value received between the nodes to be converted into the distance value between the nodes, uses any 3 beacon nodes A, B, C around the unknown node to calculate the three possible coordinates of the unknown node through the common edge proportion theorem, and calculates the mean value as the coordinate of the unknown node to complete the coordinate positioning of the unknown node. The method improves the precision of the algorithm, reduces the complexity of the algorithm, reduces the energy consumption of the node, and prolongs the life cycle of the node.

Description

Mean value positioning method for unknown sensor nodes of wireless sensor network
Technical Field
The invention relates to a wireless sensor network positioning technology, in particular to a mean value positioning method of unknown sensor nodes of a wireless sensor network, which is mainly used for acquiring accurate position information of the unknown sensor nodes of the wireless sensor network.
Background
In recent years, the technology of the internet of things continuously obtains new achievements, and the wireless sensor network serving as one of the bottom important technologies of the internet of things has become a research hotspot when being applied to the fields of national defense and military, environmental monitoring, traffic management, medical treatment and health, manufacturing industry, disaster resistance and emergency rescue and the like. The accurate position information obtained through the positioning algorithm is an important content of the wireless sensor network.
The positioning algorithm is classified into a non-ranging-based positioning algorithm (e.g., DV-HOP algorithm) and a ranging-based positioning algorithm. The positioning accuracy of the ranging-based positioning algorithm is higher than that of the non-ranging-based positioning algorithm. Some algorithms related to the positioning algorithm based on the distance measurement include a trilateral positioning algorithm, a trilateral centroid positioning algorithm, a particle swarm positioning algorithm and the like. These existing algorithms either have low positioning accuracy (e.g., centroid location algorithms) or are too complex (e.g., particle swarm location algorithms) because they require a large number of iterative operations.
Disclosure of Invention
The invention solves the problems of low positioning accuracy and complex algorithm of the existing positioning algorithm based on distance measurement, and provides a mean positioning method for unknown sensor nodes of a wireless sensor network.
The invention is realized by adopting the following technical scheme: the mean value positioning method of the unknown sensor nodes of the wireless sensor network is realized by the following steps:
z1: the unknown node P receives signals of surrounding beacon nodes and converts the received signal strength value into a distance value between the unknown node and the beacon nodes; the conversion here uses the well-known log-constant wireless signal propagation model.
Z2: setting the number of beacon nodes of the unknown node P for receiving signals as m, wherein m is more than or equal to 3, and taking any 3 beacon nodes with non-collinear positions as a group, wherein k groups are shared;
z3: sequentially calculating the coordinates of the unknown node P from the first group of beacons to the kth group of beacons to obtain k coordinates which are respectively expressed as (x)P1,yP1)，……(xPk,yPk) (ii) a Selecting the u-th group of beacon nodes, setting the value of u to be 1 to k, setting the group of beacon nodes to be A, B, C, and calculating the u-th coordinate (x) of the unknown node PPu,yPu) Is one of the k coordinates; the 3 beacons A, B, C divide the entire plane into four regions:
region 1: a delta ABC region;
region 2: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area in the area of the angle BAC;
region 3: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area from the area of the angle ACB;
region 4: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area in the region of the angle ABC;
z4: coordinates A (x) of the u-th group of three beacons A, B, C are collectedA,yA)，B(xB,yB)，C(xC,yC) (ii) a MeterCalculating distance L between beacon node A and beacon node BAB(ii) a Calculating the distance L between the beacon node B and the beacon node CBC(ii) a Calculating the distance L between the beacon node A and the beacon node CAC(ii) a The distance between the unknown node P and the beacon node a obtained according to the step Z1 is denoted as LPAAnd the distance between the unknown node P and the beacon node B is recorded as LPB(ii) a Distance L between unknown node P and beacon node CPC；
Z5: judging the relative positions of the unknown node P, the beacon node A, the beacon node B and the beacon node C:
a) judging whether the unknown node P is on the straight line AB, the straight line BC and the straight line AC:
when L isAB＝LPA+LPBOr LAB＝|LPA-LPBI, the unknown node P is located on the straight line AB,
when L isAB＝LPA+LPBWhen the unknown node P is located between the line segments AB
LAB＝LPA-LPBWhen the unknown node P is positioned on the extension line of the line segment AB
LAB＝LPB-LPAWhen the unknown node P is located on the extension line of the line BA
When L isAC＝LPC+LPAOr LAC＝|LPC-LPAI, the unknown node P is located on the straight line AC,
when L isAC＝LPC+LPAWhen the unknown node P is located on the line segment AC
When L isAC＝LPC-LPAWhen the unknown node P is positioned on the extension line of the line segment CA
When L isAC＝LPA-LPCWhen the unknown node P is positioned on the line segment AC extension line
When L isBC＝LPC+LPBOr LBC＝|LPC-LPBI, the unknown node P is located on the straight line BC,
when L isBC＝LPC+LPBWhile the unknown node P is located on the segment BC
When L isBC＝LPC-LPBWhen the unknown node P is positioned on the extension line of the segment CB
When L isBC＝LPB-LPCWhen the unknown node P is located on the extension line of the segment BC
b) When the point P is not on the straight line AB, the straight line BC, or the straight line AC,
satisfies the formula SΔABC＝SΔPAB+SΔPAC+SΔPBCThe unknown node P is located in the delta ABC area, and the unknown node P is located in the area 1;
satisfies the formula SΔPAB+SΔPAC＝SΔABC+SΔPBCOr satisfies the formula SΔPBC＝SΔPAB+SΔABC+SΔPACThe unknown node P is positioned in a region except a delta ABC region in the < BAC region and a diagonal region thereof, and the unknown node P is positioned in a region 2;
satisfies the formula SΔPAC+SΔPBC＝SΔABC+SΔPABOr satisfies the formula SΔPAB＝SΔPAC+SΔABC+SΔPBCThe unknown node P is positioned in a region except a delta ABC region in a < ACB region and a diagonal region thereof, and the unknown node P is positioned in a region 3;
satisfies the formula SΔPBC+SΔPAB＝SΔABC+SΔPACOr satisfies the formula SΔPAC＝SΔPBC+SΔABC+SΔPABThe unknown node P is positioned in a region of the & lt ABC region except the residual region of the delta ABC region and the opposite vertex region, and the unknown node P is positioned in a region 4;
wherein S is the area of the corresponding triangle calculated by adopting a Helen formula, and three letters in the subscript of S are three vertexes of the triangle;
z6: u-th coordinate (x) of unknown node PPu,yPu) The calculation formula of (a) is as follows:
a) when point P is on line AB, line BC, line AC,
when L isAB＝LPA+LPBOr LAB＝|LPA-LPBWhen, the unknown node is P bitOn the straight line AB, the line a,
when L isAB＝LPA+LPBWhen the unknown node P is located between the line segments AB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000031
Figure BDA0001755123220000032
When L isAB＝LPA-LPBWhen the unknown node P is located on the extension line of the line segment AB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000033
Figure BDA0001755123220000034
When L isAB＝LPB-LPAWhen the unknown node P is located on the extension line of the line BA, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000035
Figure BDA0001755123220000036
When L isAC＝LPC+LPAOr LAC＝|LPC-LPAI, the unknown node P is located on the straight line AC,
when L isAC＝LPC+LPAWhen the unknown node P is located on the line segment AC, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000037
Figure BDA0001755123220000038
When L isAC＝LPC-LPAWhen the unknown node P is positioned on the extension line of the line segment CA, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000039
Figure BDA0001755123220000041
When L isAC＝LPA-LPCWhen the unknown node P is positioned on the extension line of the line segment AC, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000042
Figure BDA0001755123220000043
When L isBC＝LPC+LPBOr LBC＝|LPC-LPBI, the unknown node P is located on the straight line BC,
when L isBC＝LPC+LPBThen, the unknown node P is located on the segment BC, and the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000044
Figure BDA0001755123220000045
When L isBC＝LPC-LPBWhen the unknown node P is positioned on the extension line of the segment CB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000046
Figure BDA0001755123220000047
When L isBC＝LPB-LPCWhen the unknown node P is located on the extension line of the segment BC, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000048
Figure BDA0001755123220000049
b) When the point P is not on the straight line AB, the straight line BC, or the straight line AC,
let A ' be the intersection point of the straight line PA and the straight line BC, B ' be the intersection point of the straight line BP and the straight line AC, and C ' be the intersection point of the straight line PC and the straight line AB;
kBCa sign representing the slope of the straight line BC, wherein k is set when the slope of the straight line BC is equal to or greater than 0BCIf the slope of the straight line BC is less than 0, k is 1BC＝-1；kABA sign representing the slope of the straight line AB, and k is set when the slope of the straight line AB is 0 or moreABIf the slope of the straight line AB is less than 0, k is 1AB＝-1；kACThe sign of the slope of the line AC ifGreater than or equal to 0, then kACIf the slope of the straight line AC is less than 0, k is 1AC＝-1。
1) When the unknown node P is located in the region 1, it is available by the princess proportion theorem (at least in the publication with the title "three-line coordinates and triangle feature points", published by the harabine university of industry press, the author wuyuchen, and the publication date 2015, 04 months) in detail):
a' is crossed by a straight line PA and a straight line BC, and the following components are provided:
Figure BDA0001755123220000051
the coordinates of point a' are expressed as:
Figure BDA0001755123220000052
line PB intersects line AC at B' with:
Figure BDA0001755123220000053
the coordinates of point B' are expressed as:
Figure BDA0001755123220000054
line PC intersects line AB at C', with:
Figure BDA0001755123220000055
the coordinates of point C' are expressed as:
Figure BDA0001755123220000056
2) when the unknown node P is located in the area 2, the following can be obtained by using the common edge proportion theorem:
line PA intersects line BC at A' with:
Figure BDA0001755123220000057
the coordinates of point a' are expressed as:
Figure BDA0001755123220000058
line PB intersects line AC at B' with:
Figure BDA0001755123220000061
the coordinates of point B' are expressed as:
Figure BDA0001755123220000062
line PC intersects line AB at C', with:
Figure BDA0001755123220000063
the coordinates of point C' are expressed as:
Figure BDA0001755123220000064
3) when the unknown node P is located in the area 3, the following can be obtained by using the common edge proportion theorem:
line PA intersects line BC at A' with:
Figure BDA0001755123220000065
the coordinates of point a' are expressed as:
Figure BDA0001755123220000066
line PB intersects line AC at B' with:
Figure BDA0001755123220000067
the coordinates of point B' are expressed as:
Figure BDA0001755123220000068
line PC intersects line AB at C', with:
Figure BDA0001755123220000069
the coordinates of point C' are expressed as:
Figure BDA00017551232200000610
4) when the unknown node P is located in the area 4, the following can be obtained by using the common edge proportion theorem:
line PA intersects line BC at A' with:
Figure BDA0001755123220000071
the coordinates of point a' are expressed as:
Figure BDA0001755123220000072
line PB intersects line AC at B' with:
Figure BDA0001755123220000073
the coordinates of point B' are expressed as:
Figure BDA0001755123220000074
line PC intersects line AB with C', having:
Figure BDA0001755123220000075
the coordinates of point C' are expressed as:
Figure BDA0001755123220000076
let the intersection point of the straight line AA 'and the straight line BB' be (x)Pu1,yPu1) The intersection of line AA 'and line CC' is (x)Pu2,yPu2) The intersection of the straight line BB 'and the straight line CC' is (x)Pu3,yPu3)；
U-th coordinate (x) of unknown node PPu,yPu)：
Figure BDA0001755123220000077
Z7 coordinate value optimization
K coordinates (x) of unknown node P are obtainedP1,yP1)，……(xPk,yPk) The abscissa average value and the ordinate average value of (a) are used as coordinates of the optimized unknown node P.
The method of the invention firstly uses the signal intensity value received between the nodes to be converted into the distance value between the nodes, uses any 3 beacon nodes A, B, C around the unknown node to calculate the three possible coordinates of the unknown node through the common edge proportion theorem, and calculates the mean value as the coordinate of the unknown node to complete the coordinate positioning of the unknown node. The method improves the precision of the algorithm, reduces the complexity of the algorithm, reduces the energy consumption of the node, and prolongs the life cycle of the node.
Drawings
FIG. 1 is a schematic diagram of the method of the present invention.
Detailed Description
The mean value positioning method of the unknown sensor nodes of the wireless sensor network is realized by the following steps:
z1: the unknown node P receives signals of surrounding beacon nodes and converts the received signal strength value into a distance value between the unknown node and the beacon nodes; the conversion here uses the well-known log-constant wireless signal propagation model.
Z2: setting the number of beacon nodes of the unknown node P for receiving signals as m, wherein m is more than or equal to 3, and taking any 3 beacon nodes with non-collinear positions as a group, wherein k groups are shared;
z3: sequentially calculating the coordinates of the unknown node P from the first group of beacons to the kth group of beacons to obtain k coordinates which are respectively expressed as (x)P1,yP1)，……(xPk,yPk) (ii) a Selecting the u-th group of beacon nodes, setting the value of u to be 1 to k, setting the group of beacon nodes to be A, B, C, and calculating the u-th coordinate (x) of the unknown node PPu,yPu) Is one of the k coordinates; the 3 beacons A, B, C divide the entire plane into four regions:
region 1: a delta ABC region;
region 2: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area in the area of the angle BAC;
region 3: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area from the area of the angle ACB;
region 4: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area in the region of the angle ABC;
z4: coordinates A (x) of the u-th group of three beacons A, B, C are collectedA,yA)，B(xB,yB)，C(xC,yC) (ii) a Calculating the distance L between the beacon node A and the beacon node BAB(ii) a Calculating the distance L between the beacon node B and the beacon node CBC(ii) a Calculating the distance L between the beacon node A and the beacon node CAC(ii) a The unknown node P-to-node information obtained according to the step Z1The distance between the marking points A is marked as LPAAnd the distance between the unknown node P and the beacon node B is recorded as LPB(ii) a Distance L between unknown node P and beacon node CPC；
Z5: judging the relative positions of the unknown node P, the beacon node A, the beacon node B and the beacon node C:
a) judging whether the unknown node P is on the straight line AB, the straight line BC and the straight line AC:
when L isAB＝LPA+LPBOr LAB＝|LPA-LPBI, the unknown node P is located on the straight line AB,
when L isAB＝LPA+LPBWhen the unknown node P is located between the line segments AB
LAB＝LPA-LPBWhen the unknown node P is positioned on the extension line of the line segment AB
LAB＝LPB-LPAWhen the unknown node P is located on the extension line of the line BA
When L isAC＝LPC+LPAOr LAC＝|LPC-LPAI, the unknown node P is located on the straight line AC,
when L isAC＝LPC+LPAWhen the unknown node P is located on the line segment AC
When L isAC＝LPC-LPAWhen the unknown node P is positioned on the extension line of the line segment CA
When L isAC＝LPA-LPCWhen the unknown node P is positioned on the line segment AC extension line
When L isBC＝LPC+LPBOr LBC＝|LPC-LPBI, the unknown node P is located on the straight line BC,
when L isBC＝LPC+LPBWhile the unknown node P is located on the segment BC
When L isBC＝LPC-LPBWhen the unknown node P is positioned on the extension line of the segment CB
When L isBC＝LPB-LPCWhen the unknown node P is located on the line segmentOn BC extension line
b) When the point P is not on the straight line AB, the straight line BC, or the straight line AC,
satisfies the formula SΔABC＝SΔPAB+SΔPAC+SΔPBCThe unknown node P is located in the delta ABC area, and the unknown node P is located in the area 1;
satisfies the formula SΔPAB+SΔPAC＝SΔABC+SΔPBCOr satisfies the formula SΔPBC＝SΔPAB+SΔABC+SΔPACThe unknown node P is positioned in a region except a delta ABC region in the < BAC region and a diagonal region thereof, and the unknown node P is positioned in a region 2;
satisfies the formula SΔPAC+SΔPBC＝SΔABC+SΔPABOr satisfies the formula SΔPAB＝SΔPAC+SΔABC+SΔPBCThe unknown node P is positioned in a region except a delta ABC region in a < ACB region and a diagonal region thereof, and the unknown node P is positioned in a region 3;
satisfies the formula SΔPBC+SΔPAB＝SΔABC+SΔPACOr satisfies the formula SΔPAC＝SΔPBC+SΔABC+SΔPABThe unknown node P is positioned in a region of the & lt ABC region except the residual region of the delta ABC region and the opposite vertex region, and the unknown node P is positioned in a region 4;
wherein S is the area of the corresponding triangle calculated by adopting a Helen formula, and three letters in the subscript of S are three vertexes of the triangle;
z6: u-th coordinate (x) of unknown node PPu,yPu) The calculation formula of (a) is as follows:
a) when point P is on line AB, line BC, line AC,
when L isAB＝LPA+LPBOr LAB＝|LPA-LPBI, the unknown node P is located on the straight line AB,
when L isAB＝LPA+LPBWhen the unknown node P is located between the line segments AB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000091
Figure BDA0001755123220000092
When L isAB＝LPA-LPBWhen the unknown node P is located on the extension line of the line segment AB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000093
Figure BDA0001755123220000101
When L isAB＝LPB-LPAWhen the unknown node P is located on the extension line of the line BA, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000102
Figure BDA0001755123220000103
When L isAC＝LPC+LPAOr LAC＝|LPC-LPAI, the unknown node P is located on the straight line AC,
when L isAC＝LPC+LPAWhen the unknown node P is located on the line segment AC, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000104
Figure BDA0001755123220000105
When L isAC＝LPC-LPAWhen the unknown node P is positioned on the extension line of the line segment CA, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000106
Figure BDA0001755123220000107
When L isAC＝LPA-LPCWhen the unknown node P is positioned on the extension line of the line segment AC, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000108
Figure BDA0001755123220000109
When L isBC＝LPC+LPBOr LBC＝|LPC-LPBI, the unknown node P is located on the straight line BC,
when L isBC＝LPC+LPBThen, the unknown node P is located on the segment BC, and the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA00017551232200001010
Figure BDA0001755123220000111
When L isBC＝LPC-LPBWhen the unknown node P is positioned on the extension line of the segment CB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000112
Figure BDA0001755123220000113
When L isBC＝LPB-LPCWhen the unknown node P is located on the extension line of the segment BC, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure BDA0001755123220000114
Figure BDA0001755123220000115
b) When the point P is not on the straight line AB, the straight line BC, or the straight line AC,
let A ' be the intersection point of the straight line PA and the straight line BC, B ' be the intersection point of the straight line BP and the straight line AC, and C ' be the intersection point of the straight line PC and the straight line AB;
kBCa sign representing the slope of the straight line BC, wherein k is set when the slope of the straight line BC is equal to or greater than 0BCIf the slope of the straight line BC is less than 0, k is 1BC＝-1；kABA sign representing the slope of the straight line AB, and k is set when the slope of the straight line AB is 0 or moreABIf the slope of the straight line AB is less than 0, k is 1AB＝-1；kACA sign representing the slope of the straight line AC, wherein k is set when the slope of the straight line AC is equal to or greater than 0ACIf the slope of the straight line AC is less than 0, k is 1AC＝-1。
1) When the unknown node P is located in the region 1, it is available by the princess proportion theorem (at least in the publication with the title "three-line coordinates and triangle feature points", published by the harabine university of industry press, the author wuyuchen, and the publication date 2015, 04 months) in detail):
a' is crossed by a straight line PA and a straight line BC, and the following components are provided:
Figure BDA0001755123220000116
the coordinates of point a' are expressed as:
Figure BDA0001755123220000117
line PB intersects line AC at B' with:
Figure BDA0001755123220000121
the coordinates of point B' are expressed as:
Figure BDA0001755123220000122
line PC intersects line AB at C', with:
Figure BDA0001755123220000123
the coordinates of point C' are expressed as:
Figure BDA0001755123220000124
2) when the unknown node P is located in the area 2, the following can be obtained by using the common edge proportion theorem: line PA intersects line BC at A' with:
Figure BDA0001755123220000125
the coordinates of point a' are expressed as:
Figure BDA0001755123220000126
line PB intersects line AC at B' with:
Figure BDA0001755123220000127
the coordinates of point B' are expressed as:
Figure BDA0001755123220000128
line PC intersects line AB at C', with:
Figure BDA0001755123220000129
the coordinates of point C' are expressed as:
Figure BDA00017551232200001210
3) when the unknown node P is located in the area 3, the following can be obtained by using the common edge proportion theorem:
line PA intersects line BC at A' with:
Figure BDA0001755123220000131
the coordinates of point a' are expressed as:
Figure BDA0001755123220000132
line PB intersects line AC at B' with:
Figure BDA0001755123220000133
the coordinates of point B' are expressed as:
Figure BDA0001755123220000134
line PC intersects line AB at C', with:
Figure BDA0001755123220000135
the coordinates of point C' are expressed as:
Figure BDA0001755123220000136
4) when the unknown node P is located in the area 4, the following can be obtained by using the common edge proportion theorem:
line PA intersects line BC at A' with:
Figure BDA0001755123220000137
the coordinates of point a' are expressed as:
Figure BDA0001755123220000138
line PB intersects line AC at B' with:
Figure BDA0001755123220000139
the coordinates of point B' are expressed as:
Figure BDA0001755123220000141
line PC intersects line AB with C', having:
Figure BDA0001755123220000142
the coordinates of point C' are expressed as:
Figure BDA0001755123220000143
let the intersection point of the straight line AA 'and the straight line BB' be (x)Pu1,yPu1) The intersection of line AA 'and line CC' is (x)Pu2,yPu2) The intersection of the straight line BB 'and the straight line CC' is (x)Pu3,yPu3)；
U-th coordinate (x) of unknown node PPu,yPu)：
Figure BDA0001755123220000144
Z7 coordinate value optimization
K coordinates (x) of unknown node P are obtainedP1,yP1)，……(xPk,yPk) The abscissa average value and the ordinate average value of (a) are used as coordinates of the optimized unknown node P.

Claims (1)

1. A mean value positioning method for unknown sensor nodes of a wireless sensor network is characterized by comprising the following steps:
z1: the unknown node P receives signals of surrounding beacon nodes and converts the received signal strength value into a distance value between the unknown node and the beacon nodes; the conversion here uses the well-known log-constant wireless signal propagation model;
z2: setting the number of beacon nodes of the unknown node P for receiving signals as m, wherein m is more than or equal to 3, and taking any 3 beacon nodes with non-collinear positions as a group, wherein k groups are shared;
z3: sequentially calculating the coordinates of the unknown node P from the first group of beacon nodes to the kth group of beacon nodes to obtain k coordinates in total, and respectively representing the k coordinatesIs (x)P1,yP1)，……(xPk,yPk) (ii) a Selecting the u-th group of beacon nodes, setting the value of u to be 1 to k, setting the group of beacon nodes to be A, B, C, and calculating the u-th coordinate (x) of the unknown node PPu,yPu) Is one of the k coordinates; the 3 beacons A, B, C divide the entire plane into four regions:
region 1: a delta ABC region;
region 2: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area in the area of the angle BAC;
region 3: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area in the region of the angle ABC;
region 4: removing the residual area of the delta ABC area and the opposite angle area of the delta ABC area from the area of the angle ACB;
z4: coordinates A (x) of the u-th group of three beacons A, B, C are collectedA,yA)，B(xB,yB)，C(xC,yC) (ii) a Calculating the distance L between the beacon node A and the beacon node BAB(ii) a Calculating the distance L between the beacon node B and the beacon node CBC(ii) a Calculating the distance L between the beacon node A and the beacon node CAC(ii) a The distance between the unknown node P and the beacon node a obtained according to the step Z1 is denoted as LPAAnd the distance between the unknown node P and the beacon node B is recorded as LPB(ii) a Distance L between unknown node P and beacon node CPC；
Z5: judging the relative positions of the unknown node P, the beacon node A, the beacon node B and the beacon node C:
a) judging whether the unknown node P is on the straight line AB, the straight line BC and the straight line AC:
when L isAB＝LPA+LPBOr LAB＝|LPA-LPBI, the unknown node P is located on the straight line AB,
when L isAB＝LPA+LPBWhen the unknown node P is located between the line segments AB
LAB＝LPA-LPBWhen the unknown node P is positioned on the extension line of the line segment AB
LAB＝LPB-LPAWhen the unknown node P is located on the extension line of the line BA
When L isAC＝LPC+LPAOr LAC＝|LPC-LPAI, the unknown node P is located on the straight line AC,
when L isAC＝LPC+LPAWhen the unknown node P is located on the line segment CA
When L isAC＝LPC-LPAWhen the unknown node P is positioned on the extension line of the line segment CA
When L isAC＝LPA-LPCWhen the unknown node P is positioned on the line segment AC extension line
When L isBC＝LPC+LPBOr LBC＝|LPC-LPBI, the unknown node P is located on the straight line BC,
when L isBC＝LPC+LPBWhen the unknown node P is located on the line segment CB
When L isBC＝LPC-LPBWhen the unknown node P is positioned on the extension line of the segment CB
When L isBC＝LPB-LPCWhen the unknown node P is located on the extension line of the segment BC
b) When the point P is not on the straight line AB, the straight line BC, or the straight line AC,
satisfies the formula SΔABC＝SΔPAB+SΔPAC+SΔPBCThe unknown node P is located in the delta ABC area, and the unknown node P is located in the area 1;
satisfies the formula SΔPAB+SΔPAC＝SΔABC+SΔPBCOr satisfies the formula SΔPBC＝SΔPAB+SΔABC+SΔPACThe unknown node P is positioned in a region except a delta ABC region in the < BAC region and a diagonal region thereof, and the unknown node P is positioned in a region 2;
satisfies the formula SΔPBC+SΔPAB＝SΔABC+SΔPACOr satisfies the formula SΔPAC＝SΔPBC+SΔABC+SΔPABThe unknown node P is positioned in the region of < ABC except the residual region of delta ABC and the opposite angle region thereofIn the area, the unknown node P is in the area 3;
satisfies the formula SΔPAC+SΔPBC＝SΔABC+SΔPABOr satisfies the formula SΔPAB＝SΔPAC+SΔABC+SΔPBCThe unknown node P is positioned in a region of the < ACB region except the delta ABC region and the opposite vertex region thereof, and the unknown node P is positioned in a region 4;
wherein S is the area of the corresponding triangle calculated by adopting a Helen formula, and three letters in the subscript of S are three vertexes of the triangle;
z6: u-th coordinate (x) of unknown node PPu,yPu) The calculation formula of (a) is as follows:
a) when point P is on line AB, line BC, line AC,
when L isAB＝LPA+LPBOr LAB＝|LPA-LPBI, the unknown node P is located on the straight line AB,
when L isAB＝LPA+LPBWhen the unknown node P is located between the line segments AB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure FDA0002766656660000021
Figure FDA0002766656660000022
When L isAB＝LPA-LPBWhen the unknown node P is located on the extension line of the line segment AB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure FDA0002766656660000031
Figure FDA0002766656660000032
When L isAB＝LPB-LPAWhen the unknown node P is located on the extension line of the line BA, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure FDA0002766656660000033
Figure FDA0002766656660000034
When L isAC＝LPC+LPAOr LAC＝|LPC-LPAI, the unknown node P is located on the straight line AC,
when L isAC＝LPC+LPAThen, the unknown node P is located on the line segment CA, and the u-th coordinate (x) of the unknown node PPu,yPu)
Figure FDA0002766656660000035
Figure FDA0002766656660000036
When L isAC＝LPC-LPAWhen the unknown node P is positioned on the extension line of the line segment CA, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure FDA0002766656660000037
Figure FDA0002766656660000038
When L isAC＝LPA-LPCWhen the unknown node P is positioned on the extension line of the line segment AC, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure FDA0002766656660000039
Figure FDA00027666566600000310
When L isBC＝LPC+LPBOr LBC＝|LPC-LPBI, the unknown node P is located on the straight line BC,
when L isBC＝LPC+LPBWhen the unknown node P is located on the line segment CB, the u-th coordinate (x) of the unknown node P isPu,yPu)
Figure FDA0002766656660000041
Figure FDA0002766656660000042
When L isBC＝LPC-LPBWhen the unknown node P is positioned on the extension line of the segment CB, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure FDA0002766656660000043
Figure FDA0002766656660000044
When L isBC＝LPB-LPCWhen the unknown node P is located on the line segment BCOn the long line, the u-th coordinate (x) of the unknown node PPu,yPu)
Figure FDA0002766656660000045
Figure FDA0002766656660000046
b) When the point P is not on the straight line AB, the straight line BC, or the straight line AC,
let A ' be the intersection point of the straight line PA and the straight line BC, B ' be the intersection point of the straight line AC and the straight line BP, and C ' be the intersection point of the straight line AB and the straight line PC;
kBCa sign representing the slope of the straight line BC, wherein k is set when the slope of the straight line BC is equal to or greater than 0BCIf the slope of the straight line BC is less than 0, k is 1BC＝-1；kABA sign representing the slope of the straight line AB, and k is set when the slope of the straight line AB is 0 or moreABIf the slope of the straight line AB is less than 0, k is 1AB＝-1；kCAA sign representing the slope of the straight line CA, wherein k is the same as or greater than 0CAIf the slope of the straight line CA is less than 0, k is 1CA＝-1。
1) When the unknown node P is located in the area 1, the following can be obtained by using the common edge proportion theorem:
a' is crossed by a straight line PA and a straight line BC, and the following components are provided:
Figure FDA0002766656660000047
the coordinates of point a' are expressed as:
Figure FDA0002766656660000051
line PB intersects line AC at B' with:
Figure FDA0002766656660000052
the coordinates of point B' are expressed as:
Figure FDA0002766656660000053
line PC intersects line AB at C', with:
Figure FDA0002766656660000054
the coordinates of point C' are expressed as:
Figure FDA0002766656660000055
2) when the unknown node P is located in the area 2, the following can be obtained by using the common edge proportion theorem:
line PA intersects line BC at A' with:
Figure FDA0002766656660000056
the coordinates of point a' are expressed as:
Figure FDA0002766656660000057
line PB intersects line AC at B' with:
Figure FDA0002766656660000058
the coordinates of point B' are expressed as:
Figure FDA0002766656660000059
line PC intersects line AB at C', with:
Figure FDA0002766656660000061
the coordinates of point C' are expressed as:
Figure FDA0002766656660000062
3) when the unknown node P is located in the area 3, the following can be obtained by using the common edge proportion theorem:
line PA intersects line CB at A', with:
Figure FDA0002766656660000063
the coordinates of point a' are expressed as:
Figure FDA0002766656660000064
line PB intersects line CA at B' and has:
Figure FDA0002766656660000065
the coordinates of point B' are expressed as:
Figure FDA0002766656660000066
line PC intersects line AB at C', with:
Figure FDA0002766656660000067
the coordinates of point C' are expressed as:
Figure FDA0002766656660000068
4) when the unknown node P is located in the area 4, the following can be obtained by using the common edge proportion theorem:
line PA intersects line BC at A' with:
Figure FDA0002766656660000069
the coordinates of point a' are expressed as:
Figure FDA00027666566600000610
line PB intersects line CA at B' and has:
Figure FDA0002766656660000071
the coordinates of point B' are expressed as:
Figure FDA0002766656660000072
line PC intersects line AB with C', having:
Figure FDA0002766656660000073
the coordinates of point C' are expressed as:
Figure FDA0002766656660000074
let the intersection point of the straight line AA 'and the straight line BB' be (x)Pu1,yPu1) The intersection of line AA 'and line CC' is (x)Pu2,yPu2) The intersection of the straight line BB 'and the straight line CC' is (x)Pu3,yPu3)；
U-th coordinate (x) of unknown node PPu,yPu)：
Figure FDA0002766656660000075
Z7 coordinate value optimization
K coordinates (x) of unknown node P are obtainedP1,yP1)，……(xPk,yPk) The abscissa average value and the ordinate average value of (a) are used as coordinates of the optimized unknown node P.
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