三维数据集的最小二乘拟合

采用最小二乘法拟合:

t = (1:0.1:5)';

% model
px = [ 5 2 1 ];
x =  polyval(px,t);

py = [ -2 1 1 ];
y = polyval(py,t);

pz = [ 1 20 1 ];
z = polyval(pz,t);

%  plot model
figure
plot3(x,y,z)
hold all

% simulate measurement 
xMeasured = x+2*(rand(length(x),1)-0.5);
yMeasured = y+2*(rand(length(y),1)-0.5);
zMeasured = z+2*(rand(length(z),1)-0.5);

% plot simulated measurements
plot3(xMeasured, yMeasured, zMeasured,'or')
hold off
grid on

% least squares fit 
A = [t.^2, t, t./t];
pxEstimated = A\xMeasured;
pyEstimated = A\yMeasured;
pzEstimated = A\zMeasured;

顺便说一句:我认为你需要的是一个卡尔曼滤波器,而不是一个多项式拟合的相机路径。但我不确定matlab是否有内置的支持。

首先让我感谢stackoverflow.com,然后感谢zellus和nikie让我开始更多地思考这个问题。所以现在我得到了一个解决方案,它遵循zellus方法,正如nikie所指出的,我使用了参数't'。 我的最终代码如下所示,适合三维数据集:

t = linspace(1,343,343)';

 load cx.mat;
 load cy.mat;
 load cz.mat;

 plot3(cx, cy, cz,'r'),title('source Camera Path');
 hold all

 A = [t.^2, t, t./t];
 fx = A\cx;
 fy = A\cy;
 fz = A\cz;


 Xev = polyval(fx,t);
 Yev = polyval(fy,t);
 Zev = polyval(fz,t);

 plot3(Xev,Yev,Zev,'+b'),title('Fitting Line');

我期待着与乐于助人的人就StackOverflow进行更有趣的讨论。