SpaceTimeCovMatEst

SpaceTimeCovMatEst(X); 

  Rhat = SpaceTimeCovMatEst(X,MaxLag) estimates the space-time covariance 
  matrix over the lag range (-MagLag ... +MaxLag) based on L snapshots of 
  M-array data. The estimate Rhat is unbias and has a variance as described 
  in [1].

  Input parameters
     X           MxL  data matrix
     MaxLag      described desired lag range of Rhat
 
  Output parameter
     Rhat        estimated space-time covariance matrix

  Reference:

  [1] C. Delaosa, J. Pestana, and S. Weiss: "..." ICASSP'19.

0001 function Rhat = SpaceTimeCovMatEst(X,MaxLag);
0002 %SpaceTimeCovMatEst(X);
0003 %
0004 %  Rhat = SpaceTimeCovMatEst(X,MaxLag) estimates the space-time covariance
0005 %  matrix over the lag range (-MagLag ... +MaxLag) based on L snapshots of
0006 %  M-array data. The estimate Rhat is unbias and has a variance as described
0007 %  in [1].
0008 %
0009 %  Input parameters
0010 %     X           MxL  data matrix
0011 %     MaxLag      described desired lag range of Rhat
0012 %
0013 %  Output parameter
0014 %     Rhat        estimated space-time covariance matrix
0015 %
0016 %  Reference:
0017 %
0018 %  [1] C. Delaosa, J. Pestana, and S. Weiss: "..." ICASSP'19.
0019 
0020 % S. Weiss, UoS, 14/10/18
0021 
0022 %------------------------------------------------------------------------------
0023 %  parameters
0024 %------------------------------------------------------------------------------
0025 [M,L] = size(X);
0026 Rhat = zeros(M,M,2*MaxLag+1);
0027 
0028 %------------------------------------------------------------------------------
0029 %  evaluation
0030 %------------------------------------------------------------------------------
0031 Rhat(:,:,MaxLag+1) = X*X'/L; 
0032 for tau = 1:MaxLag,
0033   Rhat(:,:,MaxLag+1+tau) = X(:,1+tau:L)*X(:,1:L-tau)'./(L-tau);
0034   Rhat(:,:,MaxLag+1-tau) = Rhat(:,:,MaxLag+1+tau)';
0035 end;
0036