50 lines
1.4 KiB
Matlab
Executable File
50 lines
1.4 KiB
Matlab
Executable File
%
|
||
% PURPOSE : TLS solution for AX = B based on SVD
|
||
%
|
||
% ARGUMENTS :
|
||
%
|
||
% A : observation of A
|
||
% B : observation of B
|
||
%
|
||
% OUTPUTS :
|
||
%
|
||
% X : TLS solution for X
|
||
%
|
||
%**********************************************************************************************
|
||
% EURECOM - All rights reserved
|
||
%
|
||
% AUTHOR : Xiwen JIANG, Florian Kaltenberger
|
||
%
|
||
% DEVELOPMENT HISTORY :
|
||
%
|
||
% Date Name(s) Version Description
|
||
% ----------- ------------- ------- ------------------------------------------------------
|
||
% Apr-30-2014 X. JIANG 0.1 creation of code
|
||
%
|
||
% REFERENCES/NOTES/COMMENTS :
|
||
%
|
||
% - I. Markovsky and S. V. Huffel, “Overview of total least-squares methods,” Signal Processing, vol. 87, pp.
|
||
% 2283–2302, 2007
|
||
%
|
||
%**********************************************************************************************
|
||
|
||
function [X_est A_est B_est]= f_tls_svd(A,B)
|
||
C = [A B];
|
||
n = size(A,2);
|
||
d = size(B,2);
|
||
[U S V] = svd(C,0);
|
||
V12 = V(1:n,n+1:end);
|
||
V22 = V(n+1:end,n+1:end);
|
||
S1 = S(1:n,1:n);
|
||
Z12 = zeros(n,d);
|
||
Z22 = zeros(d);
|
||
Z21 = zeros(d,n);
|
||
X_est = - V12/V22;
|
||
C_est = U*[S1 Z12;Z21 Z22]*V';
|
||
A_est = C_est(:,1:n);
|
||
B_est = C_est(:,n+1:end);
|
||
% delta_C = -U*diag([zeros(n,1);diag(S(n+1:end,n+1:end))])*V';
|
||
% delta_C = [A_est-A B_est-B]; %same as the previous calculation
|
||
% err = norm(delta_C,'fro')^2/norm(C,'fro')^2;:w
|
||
end
|