jiangx
20d52e1953
git-svn-id: http://svn.eurecom.fr/openair4G/trunk@5910 818b1a75-f10b-46b9-bf7c-635c3b92a50f
50 lines
1.4 KiB
Matlab
50 lines
1.4 KiB
Matlab
%
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% PURPOSE : TLS solution for AX = B based on SVD
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% ARGUMENTS :
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%
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% A : observation of A
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% B : observation of B
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% OUTPUTS :
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%
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% X : TLS solution for X
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%
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%**********************************************************************************************
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% EURECOM - All rights reserved
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%
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% AUTHOR : Xiwen JIANG, Florian Kaltenberger
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%
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% DEVELOPMENT HISTORY :
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%
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% Date Name(s) Version Description
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% ----------- ------------- ------- ------------------------------------------------------
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% Apr-30-2014 X. JIANG 0.1 creation of code
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%
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% REFERENCES/NOTES/COMMENTS :
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%
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% - I. Markovsky and S. V. Huffel, “Overview of total least-squares methods,” Signal Processing, vol. 87, pp.
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% 2283–2302, 2007
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%
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%**********************************************************************************************
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function [X_est A_est B_est]= f_tls_svd(A,B)
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C = [A B];
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n = size(A,2);
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d = size(B,2);
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[U S V] = svd(C,0);
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V12 = V(1:n,n+1:end);
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V22 = V(n+1:end,n+1:end);
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S1 = S(1:n,1:n);
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Z12 = zeros(n,d);
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Z22 = zeros(d);
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Z21 = zeros(d,n);
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X_est = - V12/V22;
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C_est = U*[S1 Z12;Z21 Z22]*V';
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A_est = C_est(:,1:n);
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B_est = C_est(:,n+1:end);
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% delta_C = -U*diag([zeros(n,1);diag(S(n+1:end,n+1:end))])*V';
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% delta_C = [A_est-A B_est-B]; %same as the previous calculation
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% err = norm(delta_C,'fro')^2/norm(C,'fro')^2;:w
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end
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