%三边测量的定位算法 %dA,dB,dC 为 A,B,C 到未知节点(假定坐标[x,y]未知)的模拟测量距离 function [P] = Triangle(A,B,C,dA,dB,dC) %A,B,C 为三个选定的信标节点,节点坐标已知(为便于防真及验证,代码中采用的等边三 角形) %A = [0,0]; %B = [25,25*sqrt(3)]; %C = [50,0]; %定义未知坐标 x,y 为符号变量 syms x y; %距离方程,以信标节点为圆心,信标节点到未知节点的测量距离为半径作三个圆 f1 = (A(1)-x)^2+(A(2)-y)^2-dA^2; f2 = (B(1)-x)^2+(B(2)-y)^2-dB^2; f3 = (C(1)-x)^2+(C(2)-y)^2-dC^2; %任两个方程联立,求任两圆交点 s1 = solve(f1,f2); %求 A,B 两圆的交点 s2 = solve(f2,f3); %求 B,C 两圆的交点 s3 = solve(f1,f3); %求 A,C 两圆的交点 %将结果(符号变量)转换为双精度数值 x1 = double(s1.x); y1 = double(s1.y); x2 = double(s2.x); y2 = double(s2.y); x3 = double(s3.x); y3 = double(s3.y); %选择内侧的三个交点 %两圆相交于两点,距第三个圆心近的为选定交点 Pab,Pbc,Pac d1(1) = sqrt(((C(1)-x1(1))^2+(C(2)-y1(1))^2)); d1(2) = sqrt(((C(1)-x1(2))^2+(C(2)-y1(2))^2)); if d1(1) <= d1(2) else Pab(1) = x1(1); Pab(2) = y1(1); Pab(1) = x1(2); Pab(2) = y1(2); end d2(1) = sqrt(((A(1)-x2(1))^2+(A(2)-y2(1))^2)); d2(2) = sqrt(((A(1)-x2(2))^2+(A(2)-y2(2))^2)); if d2(1) <= d2(2) 

else Pbc(1) = x2(1); Pbc(2) = y2(1); Pbc(1) = x2(2); Pbc(2) = y2(2); end d3(1) = sqrt(((B(1)-x3(1))^2+(B(2)-y3(1))^2)); d3(2) = sqrt(((B(1)-x3(2))^2+(B(2)-y3(2))^2)); if d3(1) <= d3(2) else Pac(1) = x3(1); Pac(2) = y3(1); Pac(1) = x3(2); Pac(2) = y3(2); end %Pab %Pbc %Pac %求三个圆内侧三个交点 Pab,Pbc,Pac 的质心,即为未知节点 P,完成定位 P(1) = (Pab(1)+Pbc(1)+Pac(1))/3; P(2) = (Pab(2)+Pbc(2)+Pac(2))/3;