CN106054127B - Wireless sensor network intelligently corrects distance-measuring and positioning method - Google Patents

Wireless sensor network intelligently corrects distance-measuring and positioning method Download PDF

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Publication number
CN106054127B
CN106054127B CN201610338877.0A CN201610338877A CN106054127B CN 106054127 B CN106054127 B CN 106054127B CN 201610338877 A CN201610338877 A CN 201610338877A CN 106054127 B CN106054127 B CN 106054127B
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mrow
beaconing nodes
msub
region
unknown node
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CN106054127A (en
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乔学工
曹建
王华倩
李瑞莲
武娟萍
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Taiyuan University of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S5/00Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02Position-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
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S11/00Systems for determining distance or velocity not using reflection or reradiation
    • G01S11/02Systems for determining distance or velocity not using reflection or reradiation using radio waves
    • G01S11/06Systems for determining distance or velocity not using reflection or reradiation using radio waves using intensity measurements
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S5/00Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02Position-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
    • G01S5/10Position of receiver fixed by co-ordinating a plurality of position lines defined by path-difference measurements, e.g. omega or decca systems

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The present invention relates to wireless sensor network location technologies, are specially that wireless sensor network intelligently corrects distance-measuring and positioning method.Solve the problems, such as that prior art positioning accuracy is low and algorithm is complicated.The method of the invention determines unknown node and the relative position of beaconing nodes first with area value, by establishing coefficientT A 、T B 、T C With the method for regional relation, the coordinate of direct solution unknown node P has simultaneously carried out coordinate value optimization;Secondly, user's group hunting algorithm of the present invention(SOA)Further optimization has been carried out to the coordinate value being obtained.It is compared by simulation analysis and with some other algorithms, the method for the invention improves the precision of algorithm, reduces the complexity of algorithm, reduces the energy expenditure of node, extends the life cycle of node.

Description

Wireless sensor network intelligently corrects distance-measuring and positioning method
Technical field
The present invention relates to wireless sensor network location technologies, are specially that wireless sensor network intelligently corrects ranging localization Method.It is mainly used in obtaining the accurate location information of sensor node in wireless sensor network.
Background technology
Technology of Internet of things constantly obtains new achievement in recent years, has applied to national defense and military, environmental monitoring, traffic pipe Reason, health care, manufacturing industry, the fields such as provide rescue and relief for disasters and emergencies, the wireless sensor network as one of Internet of Things bottom important technology Have become research hotspot.Wherein, it is that wireless sensor network is very heavy to obtain accurate location information by location algorithm The content wanted.
Intelligent algorithm obtains higher attention recently, for optimizing original algorithm, e.g., using immune genetic algorithm to base It optimizes in the trilateration of RSSI, DV-HOP algorithms is optimized using particle cluster algorithm, sought by continuous iteration It is excellent to improve positioning accuracy.These intelligent algorithms can be used to improve positioning accuracy, but need to carry out substantial amounts of iteration fortune It calculates." wireless sensor network distance measurement localization method " is combined by the present invention with crowd's searching algorithm so that only needs a small amount of change Positioning accuracy can be further improved for computing.
The content of the invention
The present invention solves the problems, such as that existing algorithmic technique positioning accuracy is low and related intelligent algorithm iterations is more, provides one Kind wireless sensor network intelligently corrects distance-measuring and positioning method.
The present invention adopts the following technical scheme that realization:Wireless sensor network intelligently corrects distance-measuring and positioning method, is It is realized by following steps:
Z1:Unknown node P receives the signal of surrounding beaconing nodes, and the signal strength values received are converted into unknown section The distance between point and beaconing nodes value;
Z2:It sets unknown node P and receives the anchor node number of signal as m, m≤3 are not conllinear with wantonly 3 positions Beaconing nodes for one group, k groups altogether;
Z3:From first group of beaconing nodes until kth group beaconing nodes calculate the coordinate of unknown node P successively, one there are To k coordinate, (x is expressed asp1,yp1) ... ... (xpk,ypk).Wherein u groups beaconing nodes are chosen, u values are 1 to k, will This group of beaconing nodes are set as A, B, C, calculate the coordinate (x of unknown node Ppu,ypu), as one of above-mentioned k coordinate.3 Entire plane is divided into seven regions by beaconing nodes A, B, C:
Region 1:The triangle interior region that 3 beaconing nodes A, B, C are formed;
Region 2:Straight line, beaconing nodes A and beacon beyond the A points for the ray BA that beaconing nodes B and beaconing nodes A is formed The region that straight line beyond the C points for the ray BC that line segment AC, the beaconing nodes B and beaconing nodes C that node C is formed are formed surrounds;
Region 3:Straight line, beaconing nodes A and beacon beyond the B points for the ray CB that beaconing nodes C and beaconing nodes B is formed The region that straight line beyond the A points for the ray CA that line segment AB, the beaconing nodes C and beaconing nodes A that node B is formed are formed surrounds;
Region 4:Straight line, beaconing nodes B and beacon beyond the B points for the ray AB that beaconing nodes A and beaconing nodes B is formed The region that straight line beyond the C points for the ray AC that line segment BC, the beaconing nodes A and beaconing nodes C that node C is formed are formed surrounds;
Region 5:Straight line, beaconing nodes A and beacon beyond the C points for the ray BC that beaconing nodes B and beaconing nodes C is formed The region that straight line beyond the C points for the ray AC that node C is formed surrounds;
Region 6:Straight line, beaconing nodes A and beacon beyond the B points for the ray CB that beaconing nodes C and beaconing nodes B is formed The region that straight line beyond the B points for the ray AB that node B is formed surrounds;
Region 7:Straight line, beaconing nodes C and beacon beyond the A points for the ray BA that beaconing nodes B and beaconing nodes A is formed The region that straight line beyond the A points for the ray CA that node A is formed surrounds;
Z4:Determine region residing for unknown node P:
Meet formula:SABC=SABP+SACP+SBCPUnknown node P is in region 1;
Meet formula:SABP+SBCP=SABC+SACPUnknown node P is in region 2;
Meet formula:SACP+SBCP=SABC+SABPUnknown node P is in region 3;
Meet formula:SACP+SABP=SABC+SBCPUnknown node P is in region 4;
Meet formula:SABP=SACP+SABC+SBCPUnknown node P is in region 5;
Meet formula:SACP=SABP+SABC+SBCPUnknown node P is in region 6;
Meet formula:SBCP=SACP+SABC+SABPUnknown node P is in region 7;
Wherein S is the area of the corresponding triangle calculated using Heron's formula, and three letters in S subscripts are triangle Three vertex;
Z5:U-th of coordinate (x of unknown node Ppu,ypu) calculation formula it is as follows:
xpu=TA·xa+TB·xb+TC·xc
ypu=TA·ya+TB·yb+TC·yc
Wherein, (xa,ya) be beaconing nodes A coordinate, (xb,yb) be beaconing nodes B coordinate, (xc,yc) it is beacon section The coordinate of point C;TA、TB、TCIt is related with P points region for coefficient of region.
When unknown node P is in region 1,
When unknown node P is in region 2,
When unknown node P is in region 3,
When unknown node P is in region 4,
When unknown node P is in region 5,
When unknown node P is in region 6,
When unknown node P is in region 7,
Z6:Using crowd's searching algorithm of improvement to obtained k coordinate (xp1,yp1) ... ... (xpk,ypk) optimize, The coordinate of unknown node P after being optimized.
Difference lies in fitness with conventionally known crowd's searching algorithm (SOA) for crowd's searching algorithm of the improvement Function is different, and the step-length in conventionally known crowd's searching algorithm (SOA) is reduced 50%;Crowd's search of the improvement The fitness function of algorithm is:
Coordinate (x in formulas,ys) represent k coordinate (xp1,yp1) ... ..., (xpk,ypk) in any one coordinate, coordinate (xi, yi) for any one coordinate in m beaconing nodes;diRepresent the distance value described in step Z1;In k obtained fitness letter In numerical value F, minimum value is selected.
Conventionally known crowd's searching algorithm (SOA) is at least in title《MATLAB optimization algorithm analyses of cases With application》, published by publishing house of Tsinghua University, author Yu Shengwei, the publication date has in detail on the publication in September, 2014 It is thin open.
The method of the invention determines unknown node and the relative position of beaconing nodes first with area value, is by establishing Number TA、TB、TCWith the method for regional relation, the coordinate of direct solution unknown node P has simultaneously carried out coordinate optimizing.Secondly, the present invention The coordinate value of unknown node P of the user's group hunting algorithm (SOA) to being obtained has carried out further optimization;Crowd, which searches for, to be calculated Method is a kind of heuristic random searching algorithm based on population.Localization method proposed by the present invention is improving the same of positioning accuracy When also reduce the iterations of algorithm.Present invention uses new fitness function, by Pearson came distance (mathematical statistics:Skin Er Xun distances subtract Pearson correlation coefficient equal to 1) as fitness function value F, fitness function value F is smaller, the seat of solution Scale value is closer to actual value.
It is compared by simulation analysis and with some other algorithms, the method for the invention improves the essence of algorithm Degree reduces the complexity of algorithm, reduces the energy expenditure of node, extends the life cycle of node.
Description of the drawings
Entire plane is divided into seven area schematics by Fig. 1 for step Z3 tri- beaconing nodes A, B, C.
Specific embodiment
Wireless sensor network intelligently corrects distance-measuring and positioning method, is realized by following steps:
Z1:Unknown node P receives the signal of surrounding beaconing nodes, and the signal strength values received are converted into unknown section The distance between point and beaconing nodes value;Here convert using well known logarithm-constant wireless signal propagation model.
Z2:It sets unknown node P and receives the anchor node number of signal as m, m≤3 are not conllinear with wantonly 3 positions Beaconing nodes for one group, k groups altogether;
Z3:From first group of beaconing nodes until kth group beaconing nodes calculate the coordinate of unknown node P successively, one there are To k coordinate, (x is expressed asp1,yp1) ... ... (xpk,ypk).Wherein u groups beaconing nodes are chosen, u values are 1 to k, will This group of beaconing nodes are set as A, B, C, calculate the coordinate (x of unknown node Ppu,ypu), as one of above-mentioned k coordinate.3 Entire plane is divided into seven regions by beaconing nodes A, B, C:
Region 1:The triangle interior region that 3 beaconing nodes A, B, C are formed;
Region 2:Straight line, beaconing nodes A and beacon beyond the A points for the ray BA that beaconing nodes B and beaconing nodes A is formed The region that straight line beyond the C points for the ray BC that line segment AC, the beaconing nodes B and beaconing nodes C that node C is formed are formed surrounds;
Region 3:Straight line, beaconing nodes A and beacon beyond the B points for the ray CB that beaconing nodes C and beaconing nodes B is formed The region that straight line beyond the A points for the ray CA that line segment AB, the beaconing nodes C and beaconing nodes A that node B is formed are formed surrounds;
Region 4:Straight line, beaconing nodes B and beacon beyond the B points for the ray AB that beaconing nodes A and beaconing nodes B is formed The region that straight line beyond the C points for the ray AC that line segment BC, the beaconing nodes A and beaconing nodes C that node C is formed are formed surrounds;
Region 5:Straight line, beaconing nodes A and beacon beyond the C points for the ray BC that beaconing nodes B and beaconing nodes C is formed The region that straight line beyond the C points for the ray AC that node C is formed surrounds;
Region 6:Straight line, beaconing nodes A and beacon beyond the B points for the ray CB that beaconing nodes C and beaconing nodes B is formed The region that straight line beyond the B points for the ray AB that node B is formed surrounds;
Region 7:Straight line, beaconing nodes C and beacon beyond the A points for the ray BA that beaconing nodes B and beaconing nodes A is formed The region that straight line beyond the A points for the ray CA that node A is formed surrounds;
Z4:Determine region residing for unknown node P:
Meet formula:SABC=SABP+SACP+SBCPUnknown node P is in region 1;
Meet formula:SABP+SBCP=SABC+SACPUnknown node P is in region 2;
Meet formula:SACP+SBCP=SABC+SABPUnknown node P is in region 3;
Meet formula:SACP+SABP=SABC+SBCPUnknown node P is in region 4;
Meet formula:SABP=SACP+SABC+SBCPUnknown node P is in region 5;
Meet formula:SACP=SABP+SABC+SBCPUnknown node P is in region 6;
Meet formula:SBCP=SACP+SABC+SABPUnknown node P is in region 7;
Wherein S is the area of the corresponding triangle calculated using Heron's formula, and three letters in S subscripts are triangle Three vertex;
The Heron's formula is common knowledge:
In formula:S is triangle area, and it is long that L1, L2, L3 represent three sides of a triangle.
Z5:U-th of coordinate (x of unknown node Ppu,ypu) calculation formula it is as follows:
xpu=TA·xa+TB·xb+TC·xc
ypu=TA·ya+TB·yb+TC·yc
Wherein, (xa,ya) be beaconing nodes A coordinate, (xb,yb) be beaconing nodes B coordinate, (xc,yc) it is beacon section The coordinate of point C;TA、TB、TCIt is related with P points region for coefficient of region.
When unknown node P is in region 1,
When unknown node P is in region 2,
When unknown node P is in region 3,
When unknown node P is in region 4,
When unknown node P is in region 5,
When unknown node P is in region 6,
When unknown node P is in region 7,
Z6:Using crowd's searching algorithm of improvement to obtained k coordinate (xp1,yp1) ... ... (xpk,ypk) optimize, The coordinate of unknown node P after being optimized;
Difference lies in fitness with conventionally known crowd's searching algorithm (SOA) for crowd's searching algorithm of the improvement Function is different, and the step-length in conventionally known crowd's searching algorithm (SOA) is reduced 50%;Crowd's search of the improvement The fitness function of algorithm is:
Coordinate (x in formulas,ys) represent k coordinate (xp1,yp1) ... ..., (xpk,ypk) in any one coordinate, coordinate (xi, yi) for any one coordinate in m beaconing nodes;diRepresent the distance value described in step Z1;In k obtained fitness letter In numerical value F, minimum value is selected.

Claims (1)

1. a kind of wireless sensor network intelligently corrects distance-measuring and positioning method, it is characterised in that is realized by following steps:
Z1:Unknown node P receive surrounding beaconing nodes signal, and by the signal strength values received be converted into unknown node and The distance between beaconing nodes value;
Z2:It sets unknown node P and receives the anchor node number of signal as m, m≤3, with the not conllinear letter in wantonly 3 positions It is one group to mark node, altogether k groups;
Z3:From first group of beaconing nodes until kth group beaconing nodes calculate the coordinate of unknown node P successively, one is obtained k Coordinate is expressed as (xp1,yp1) ... ... (xpk,ypk);Wherein u groups beaconing nodes are chosen, u values are 1 to k, by the group Beaconing nodes are set as A, B, C, calculate the coordinate (x of unknown node Ppu,ypu), as one of above-mentioned k coordinate;3 beacons Entire plane is divided into seven regions by node A, B, C:
Region 1:The triangle interior region that 3 beaconing nodes A, B, C are formed;
Region 2:Straight line, beaconing nodes A and beaconing nodes beyond the A points for the ray BA that beaconing nodes B and beaconing nodes A is formed The region that straight line beyond the C points for the ray BC that line segment AC, the beaconing nodes B and beaconing nodes C that C is formed are formed surrounds;
Region 3:Straight line, beaconing nodes A and beaconing nodes beyond the B points for the ray CB that beaconing nodes C and beaconing nodes B is formed The region that straight line beyond the A points for the ray CA that line segment AB, the beaconing nodes C and beaconing nodes A that B is formed are formed surrounds;
Region 4:Straight line, beaconing nodes B and beaconing nodes beyond the B points for the ray AB that beaconing nodes A and beaconing nodes B is formed The region that straight line beyond the C points for the ray AC that line segment BC, the beaconing nodes A and beaconing nodes C that C is formed are formed surrounds;
Region 5:Straight line, beaconing nodes A and beaconing nodes beyond the C points for the ray BC that beaconing nodes B and beaconing nodes C is formed The region that straight line beyond the C points for the ray AC that C is formed surrounds;
Region 6:Straight line, beaconing nodes A and beaconing nodes beyond the B points for the ray CB that beaconing nodes C and beaconing nodes B is formed The region that straight line beyond the B points for the ray AB that B is formed surrounds;
Region 7:Straight line, beaconing nodes C and beaconing nodes beyond the A points for the ray BA that beaconing nodes B and beaconing nodes A is formed The region that straight line beyond the A points for the ray CA that A is formed surrounds;
Z4:Determine region residing for unknown node P:
Meet formula:SABC=SABP+SACP+SBCPUnknown node P is in region 1;
Meet formula:SABP+SBCP=SABC+SACPUnknown node P is in region 2;
Meet formula:SACP+SBCP=SABC+SABPUnknown node P is in region 3;
Meet formula:SACP+SABP=SABC+SBCPUnknown node P is in region 4;
Meet formula:SABP=SACP+SABC+SBCPUnknown node P is in region 5;
Meet formula:SACP=SABP+SABC+SBCPUnknown node P is in region 6;
Meet formula:SBCP=SACP+SABC+SABPUnknown node P is in region 7;
Wherein S is the area of the corresponding triangle calculated using Heron's formula, and three letters in S subscripts are three of triangle Vertex;
Z5:U-th of coordinate (x of unknown node Ppu,ypu) calculation formula it is as follows:
xpu=TA·xa+TB·xb+TC·xc
ypu=TA·ya+TB·yb+TC·yc
Wherein, (xa,ya) be beaconing nodes A coordinate, (xb,yb) be beaconing nodes B coordinate, (xc,yc) for beaconing nodes C's Coordinate;TA、TB、TCIt is related with P points region for coefficient of region,
When unknown node P is in region 1,
When unknown node P is in region 2,
When unknown node P is in region 3,
When unknown node P is in region 4,
When unknown node P is in region 5,
When unknown node P is in region 6,
When unknown node P is in region 7,
Z6:Using crowd's searching algorithm of improvement to obtained k coordinate (xp1,yp1) ... ... (xpk,ypk) optimize, it obtains The coordinate of unknown node P after optimization;
Difference lies in fitness functions with conventionally known crowd's searching algorithm (SOA) for crowd's searching algorithm of the improvement Difference, and the step-length in conventionally known crowd's searching algorithm (SOA) is reduced 50%;Crowd's searching algorithm of the improvement Fitness function be:
<mrow> <mi>F</mi> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> <mi>m</mi> </mfrac> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>-</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>d</mi> <mi>i</mi> </msub> </mrow> <mi>m</mi> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msup> <mrow> <mo>(</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> <mi>m</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>&amp;times;</mo> <msqrt> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>-</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>d</mi> <mi>i</mi> </msub> </mrow> <mi>m</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow>
Coordinate (x in formulas,ys) represent k coordinate (xp1,yp1) ... ..., (xpk,ypk) in any one coordinate, coordinate (xi,yi) For any one coordinate in m beaconing nodes;diRepresent the distance value described in step Z1;In k obtained fitness function In value F, minimum value is selected.
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