在Matlab中用fsolve解决声音测距功能

Question

我正在尝试解决此链接中描述的声音范围问题：

http://en.wikipedia.org/wiki/Sound_ranging#cite_note-old-5

我有一个像这样的Matlab函数：

function [f]=equation1(x)
c = 330 ;%speed of sound meters per second 
% unknown variable : 
% r1 => x(1) 
% theta => x(2)

time2 = 0.455; % Microphone 1 to Microphone 2 time delay
time3 = 0.606; % Microphone 1 to Microphone 3 time delay
% gives : 
r2 = 150 %time2*c;
r3 = 200 %time3*c; 

r4 = 1267.9; % Distance from Microphone 2 to Microphone 3
r5 = 499.1; % Distance from Microphone 1 to Microphone 3

phi = 16.177; % Angle between Microphone 1 and Microphone 2 measured from Microphone 3

f(1)= -(x(1) + r2)^2 + (x(1)+r3)^2 +r4^2 -2*(x(1)+r3)*r4*cosd(x(2));
f(2)= - x(1)^2  + (x(1)+r3)^2  + r5^2 - 2*(x(1)+r3)*r5*cosd(x(2)-phi);
end

当我运行[x,feval]=fsolve(@equation1,[100 10])时，代码会返回结果x= 581.4332 -31.8492。但在示例中r1是1621米。我在这个程序中没有看到我的错误。

Answer 1

您交换了r4和r5的值，它应该是：

r4 = 499.1; % Distance from Microphone 2 to Microphone 3
r5 = 1267.9; % Distance from Microphone 1 to Microphone 3

此外，控制台返回的输出值为feval，而不是x。使用r4和r5的正确值，我会显示正确的答案：

[x,feval]=fsolve(@equation1,[100 10]);
disp(x);

输出

1.0e+03 *

1.6230    0.0764

正如所料。