show_2D_cov_rot.m

clear all; close all; clc

x = randn(2,3);
PN = cov(x'); % covariance in the navigation frame

error_ellipse(PN,'style','b');
axis equal; 
hold on; 
grid on;

stdx = sqrt(PN(1,1));
stdy = sqrt(PN(2,2));
%rho = PN(1,2) / (stdx*stdy)

[E,D] = eig(PN);
alpha_x = atan2(E(2,2),E(1,2))
alpha_y = atan2(E(2,1),E(1,1))

Cx = rot2z(-alpha_x);
Cy = rot2z(-alpha_y);

PPx = Cx*PN*Cx';
PPy = Cy*PN*Cy';

error_ellipse(PPx,'style','g')
error_ellipse(PPy,'style','r')

legend('original','rotated x','rotated y')