%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ DV-Hop算法 ~~~~~~~~~~~~~~~~~~~~~~~~
% Length-----------正方形区域的边长,单位:m
% NodeAmount-------网络节点的个数
% BeaconAmount-----锚节点数
% UNAmount---------未知节点数
% Sxy--------------用于存储节点的序号,横坐标,纵坐标的矩阵
% Beacon-----------锚节点坐标矩阵;
% Unknown----------未知节点坐标矩阵;
% Distance---------未知节点到锚节点距离矩阵;
% h----------------节点间初始跳数矩阵
% X----------------节点估计坐标初始矩阵,X=[x,y]'
% R----------------节点的通信距离,单位:m
clear,close all;
Length=100;
NodeAmount=100;
BeaconAmount=10;
UNAmount=NodeAmount-BeaconAmount;
R=50;
D=zeros(BeaconAmount,NodeAmount);%未知节点到锚节点距离初始矩阵;BeaconAmount行NodeAmount列
h=zeros(NodeAmount,NodeAmount);%初始跳数为0;BeaconAmount行NodeAmount列
X=zeros(2,UNAmount);%节点估计坐标初始矩阵
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~在正方形区域内产生均匀分布的随机拓扑~~~~~~~~~~~~~~~~~~~~
Sxy=Length*rand(2,NodeAmount);
Beacon=[Sxy(1,1:BeaconAmount);Sxy(2,1:BeaconAmount)];%锚节点坐标
Unknown=[Sxy(1,(BeaconAmount+1):NodeAmount);Sxy(2,(BeaconAmount+1):NodeAmount)];%未知节点坐标
plot(Sxy(1,1:BeaconAmount),Sxy(2,1:BeaconAmount),'r*',Sxy(1,(BeaconAmount+1):NodeAmount),Sxy(2,(BeaconAmount+1):NodeAmount),'k.')%画出节点分布图
xlim([0,Length]);%x轴的范围
ylim([0,Length]);%y轴的范围
title('* 红色为锚节点 .黑色为未知节点')
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~初始化节点间距离、跳数矩阵~~~~~~~~~~~~~~~~~~~~~~
for i=1:NodeAmount
for j=1:NodeAmount
Dall(i,j)=((Sxy(1,i)-Sxy(1,j))^2+(Sxy(2,i)-Sxy(2,j))^2)^0.5;%所有节点间相互距离
if (Dall(i,j)<=R)&(Dall(i,j)>0)
h(i,j)=1;%初始跳数矩阵
elseif i==j
h(i,j)=0;
else h(i,j)=inf;
end
end
end
%~~~~~~~~~~~~~~~~~~~~~~~~~最短路径算法计算节点间跳数~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
for k=1:NodeAmount
for i=1:NodeAmount
for j=1:NodeAmount
if h(i,k)+h(k,j)<h(i,j) %找出节点间最小的路数,min(h(i,j),h(i,k)+h(k,j))
h(i,j)=h(i,k)+h(k,j);
end
end
end
end
h
%~~~~~~~~~~~~~~~~~~~~~~~~~求每个锚节点的校正值~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
h1=h(1:BeaconAmount,1:BeaconAmount); %所有锚节点间跳数矩阵
D1=Dall(1:BeaconAmount,1:BeaconAmount); %所有锚节点间距离矩阵
for i=1:BeaconAmount
dhop(i,1)=sum(D1(i,:))/sum(h1(i,:)); %每个锚节点的平均每跳距离
end
D2=Dall(1:BeaconAmount,(BeaconAmount+1):NodeAmount);%所有未知节点到锚节点的距离,BeaconAmount行UNAmount列
for i=1:BeaconAmount
for j=1:UNAmount
if min(D2(:,j))==D2(i,j)
Dhop(1,j)=D2(i,j); %未知节点从最近的锚获得校正值
end
end
end
Dhop
%~~~~~~~~~~~~~~~~~~~~~~~~~~~用跳数估计距离~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
hop1=h(1:BeaconAmount,(BeaconAmount+1):NodeAmount)%未知节点到锚节点跳数,BeaconAmount行UNAmount列
for i=1:UNAmount
hop=Dhop(1,i);%hop为从最近锚节点获得的校正值
Distance(:,i)=hop*hop1(:,i);%%Beacon行Unknown列;
end
% %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~最小二乘法求未知点坐标~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
d=Distance;
for i=1:2
for j=1:(BeaconAmount-1)
a(i,j)=Beacon(i,j)-Beacon(i,BeaconAmount);
end
end
A=-2*(a');
for m=1:UNAmount
for i=1:(BeaconAmount-1)
B(i,1)=d(i,m)^2-d(BeaconAmount,m)^2-Beacon(1,i)^2+Beacon(1,BeaconAmount)^2-Beacon(2,i)^2+Beacon(2,BeaconAmount)^2;
end
X1=inv(A'*A)*A'*B;
X(1,m)=X1(1,1);
X(2,m)=X1(2,1);
end
Unknown
X
for i=1:UNAmount
error(1,i)=(((X(1,i)-Unknown(1,i))^2+(X(2,i)-Unknown(2,i))^2)^0.5); %每个未知节点的误差
end
figure;plot(error,'-+')
title('每个未知节点的误差')
accuracy=error/R
figure;plot(accuracy,'-o')
title('每个未知节点相对于通信半径的误差值')
ave_error=sum(error)/UNAmount %所有未知节点的平均误差
ave_accuracy=ave_error/R %所有未知节点相对于通信半径的平均误差值