function?A?=?DEKF（yp）
%Dual?Extended?Klman?Filter?（DEKF）?for?MVAR?parameter?estimation
%
%?Arguments:
%?A:?Estimated?time-varying?parameters?A?=?[A1?A2?...?Ar]
%?y:?（CH?x?LEN）?data?matrix
%?p:?Model?order
%?
%?
%?References:
%?[1]?E.?A.?Wan?and?A.?T.?Nelson?揘eural?dual?extended?Kalman?filtering:?applications?in?speech?
%?enhancement?and?monaural?blind?signal?separation?in?Neural?Networks?for?Signal?Processing?
%?of?the?1997?IEEE?Workshop?1997?pp.?466-475.
%?
%?[2]?E.?A.?Wan?and?A.?T.?Nelson?“Dual?Extended?Kalman?Filter?Methods“?Kalman?Filtering?and?
%?Neural?Networks?pp.?123-173:?John?Wiley?&?Sons?Inc.?2002.
%?
%?[3]?S.?Haykin?Kalman?Filtering?and?Neural?Networks?p.^pp.?304:?John?Wiley?and?Sons?2001.
%?
%?
%?See?also:?‘Linear?Kalman?Filter‘?MATLAB?implementation?written?by?Amir?Omidvarnia?available?at:
%?http://www.mathworks.com/matlabcentral/fileexchange/29127-linear-kalman-filter
%?
%?Written?by:?Amir?Omidvarnia

%%?
CH?=?size（y1）;????????????????????????????%?Number?of?states?（here?CH?=?N）
LEN?=?size（y2）;???????????????????????????%?Number?of?the?multivariate?observations

%%?Initial?parameters?for?Dual?Extended?Kalman?Filter
%%%%%?（EKF?1）
xh?=?zeros（CH*pLEN）;??????????????????????%?（EKF?1）?Initial?a-posteriori?states?（Mp?x?1）
Px?=?.1*eye（CH*p）;?????????????????????????%?（EKF?1）?Initial?a-posteriori?state?covariance?matrix
R?=?eye（CH）;
B?=?zeros（CH*pCH）;????????????????????????%?（EKF?1）?Relationship?between?states?and?the?process?noise?（?x（k）?=?F[x（k-1）]?+?B*v（k）?）
B（1:CH:）?=?eye（CH）;???????????????????????%?（EKF?1）?B?=?[I?0?...?0]‘

%%%%%?EKF?2
Pa?=?eye（CH*CH*p）;?????????????????????????%?（EKF?2）?Initial?a-posteriori?parameters?covariance?matrix
Ah?=?zeros（CH*pCH*pLEN）;?????????????????%?（EKF?2）?Initial?a-posteriori?parameters?estimates?（matrix?form?of?‘ah‘?plus?identity?matrices）
Ah（1:CH1:CH*pp）?=?.1*randn（CHCH*p）;?????%?（EKF?2）?Initial?a-posteriori?parameters?estimates?（matrix?form?of?‘ah‘?plus?identity?matrices）
for?r?=?2?:?p
????Ah（（r-1）*CH+1:r*CH（r-2）*CH+1:（r-1）*CH?p）?=?eye（CH）;
end

for?r?=?1?:?p
????xh（（r-1）*CH+1:r*CHp+1）?=?y（:p-r+1）;
end

%%%%%?Mutual?variables?between?EKF?1?and?DEKF?2
Q?=?10*eye（CH）;????????????????????????????%?（EKF?12）?Initial?process?noise?covariance?matrix
C?=?B‘;????????????????????????????????????%?（EKF?12）?Measurement?matrix?（identity?matrix?C?=?B‘）

%%?DEKF?starts?....
for?i?=?p+1?:?LEN
????????
????[J_x?J_A]?=?MVAR_JacCSD（Ah（::i-1）xh（:i-1）p）;??%?xh（k）?=?F（A（k-1）?*?xh（k-1））?=?Ah（k-1）?*?xh（k-1）
????Ah_?=?Ah（::i-1）;?????????????????????????????????%?Ah_（k）?=?Ah（k-1）

????%%?EKF?1?--->?States?estimation????
????%----------?Time?Update?（EKF1）?----------
????Rv?=?B?*?Q?*?B‘;??????????????????????????%?According?to?Haykin‘s?book
????xh_?=?Ah_?*?xh（:i-1）;????????????????????%?xh_（k）?=?A_h（k-1）?*?xh（k-1）
????Px_?=?J_x?*?Px?*?J_x‘?+?Rv;???????????????%?Px_（k）?=?A_h（k-1）?*?Px（k-1）?*?A_h（k-1）‘?+?B?*?Q?*?B‘
????
?

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2011-11-21?19:18??DEKF_Mathworks\
?????文件????????4675??2011-11-21?16:30??DEKF_Mathworks\DEKF.m
?????文件????????2055??2011-11-21?16:05??DEKF_Mathworks\MVAR_JacCSD.m
?????文件????????1949??2011-11-21?16:42??DEKF_Mathworks\TVMVAR_Estimation_script.m
?????文件????????1536??2011-11-21?04:32??license.txt