matlab中实现最小二乘拟合函数曲线

ID:216631 · 发表于 2017-7-2 20:34

通过矩阵计算的方式实现用最小二乘法拟合高次函数曲线

matlab源程序如下:

clc;
clear;
close all;
%% 取样并代入曲线
x_all = 0:0.01:1.81;
[y_truth_all,y_all]=unknown_model1(x_all);
N = length(x_all);
%用前半段取样点训练并显示理想值
x = x_all(1:N/2);
y = y_all(1:N/2);
y_truth = y_truth_all(1:N/2);
plot(x,y_truth,'g-x','LineWidth',1.5);
hold on;
plot(x,y,'m-x','LineWidth',1.5);
legend('model truth','observation');
title('training');
%% 二阶曲线拟合
X = [x.^2;x;ones(1,length(x))]';
Y = y';
lambda1 = (X'*X)\X'*Y;
% evaluate the esimated model
ye1 = X*lambda1;
hold on;
plot(x,ye1,'c-o','LineWidth',1.5);
legend('model truth','observation', 'order-2 poly fitting');
%% 四阶曲线拟合
X = [x.^4;x.^3;x.^2;x;ones(1,length(x))]';
Y = y';
lambda2 = (X'*X)\X'*Y;
% evaluate the esimated model
ye2 = X*lambda2;
hold on;
plot(x,ye2,'r-o','LineWidth',1.5);
legend('model truth','observation', 'order-2 poly fitting','order-4 poly fitting');
%% 八阶曲线拟合
X = [x.^8;x.^7;x.^6;x.^5;x.^4;x.^3;x.^2;x;ones(1,length(x))]';
Y = y';
lambda3 = (X'*X)\X'*Y
% evaluate the esimated model
ye3 = X*lambda3;
a=ye3'-y;
a1=20*log10(a);
hold on;
plot(x,ye3,'b-o','LineWidth',1.5);
xlabel('Fs');
ylabel('幅频值');
legend('model truth','observation', 'order-2 poly fitting','order-4 poly fitting','order-8 poly fitting');
%拟合的1/sinc曲线与理想曲线的误差范围
figure;
plot(x,-20*log10(y./abs(a)));
xlabel('Fs');
ylabel('1/sinc拟合误差(dB)');
title('1/sinc拟合误差');
%% 补偿后的误差
b=ye3'.*sinc(x);
figure;
subplot(2,1,1);
plot(x,sinc(x),x,b);
xlabel('Fs');
ylabel('幅频');
title('补偿后对比');
subplot(2,1,2);
plot(x,-20*log10(1./(1-b)));
xlabel('Fs');
ylabel('补偿后的误差(dB)');
title('补偿后的误差');
%% show future trends
%X = [x_all;ones(1,length(x_all))]';
%ye1 = X*lambda1;
%X = [x_all.^3;x_all.^2;x_all;ones(1,length(x_all))]';
%ye2 = X*lambda2;
%X = [x_all.^5;x_all.^4;x_all.^3;x_all.^2;x_all;ones(1,length(x_all))]';
%ye3 = X*lambda3;
%figure;
%plot(x_all,y_truth_all,'g-x',x_all,y_all,'m-x',x_all,ye1,'c-o',x_all,ye2,'r-o',x_all,ye3,'b-o','LineWidth',1.5);
%legend('model truth','observation', 'order-1 poly fitting','order-3 poly fitting', 'order-5 poly fitting');
%title('testing');
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