30 lines
880 B
Mathematica
30 lines
880 B
Mathematica
|
function [sig2_error] = getErrorCovariance(W, Y_tau, nbDOF)
|
||
|
|
|
||
|
|
% Authors: Quentin Leboutet, Julien Roux, Alexandre Janot and Gordon Cheng
|
||
|
|
%
|
||
|
|
% Gives the error covariance from the observation matrix following the
|
||
|
|
% approach of Gautier and Poignet (2001). This is used for weighted least
|
||
|
|
% squares computation.
|
||
|
|
|
||
|
|
sig2_error = zeros(nbDOF,1);
|
||
|
|
|
||
|
|
for i=1:nbDOF
|
||
|
|
[~,Ri] = qr(W(i:nbDOF:end,:),0);
|
||
|
|
Diag_Ri = abs(diag(Ri));
|
||
|
|
Diag_Ri_red = find(Diag_Ri >= 1.0);
|
||
|
|
|
||
|
|
% Keep relevant columns:
|
||
|
|
W_reduced_i = W(i:nbDOF:end,Diag_Ri_red);
|
||
|
|
[neq,np] = size(W_reduced_i);
|
||
|
|
|
||
|
|
% Calculate OLS solution:
|
||
|
|
Beta_LS = W_reduced_i\Y_tau(i:nbDOF:end);
|
||
|
|
|
||
|
|
% Compute error covariance:
|
||
|
|
Residual = Y_tau(i:nbDOF:end) - W_reduced_i*Beta_LS;
|
||
|
|
normRes = norm(Residual);
|
||
|
|
|
||
|
|
sig2_error(i) = normRes^2/(neq-np); % Compute the resulting error covariance estimate
|
||
|
|
end
|
||
|
|
|
||
|
|
end
|