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Correct description of Kstar

time-shift
Johannes Pfeifer 2016-10-28 11:40:35 +02:00
parent e2e16339a8
commit 57d600301b
2 changed files with 5 additions and 5 deletions
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6
matlab/kalman/likelihood/kalman_filter_d.m
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@ -87,7 +87,7 @@ while rank(Pinf,diffuse_kalman_tol) && (t<=last)
else
iFstar = inv(Fstar);
dFstar = det(Fstar);
Kstar = Pstar*Z'*iFstar; %(5.15) of DK (2012) with Kstar=K^(0)*T^{-1}
Kstar = Pstar*Z'*iFstar; %(5.15) of DK (2012) with Kstar=T^{-1}*K^(0)
dlik(s)= log(dFstar) + v'*iFstar*v; %set w_t to bottom case in bottom equation page 172, DK (2012)
Pinf = T*Pinf*transpose(T); % (5.16) DK (2012)
Pstar = T*(Pstar-Pstar*Z'*Kstar')*T'+QQ; % (5.17) DK (2012)
@ -96,7 +96,7 @@ while rank(Pinf,diffuse_kalman_tol) && (t<=last)
end
else %F_{\infty,t} positive definite
%To compare to DK (2012), this block makes use of the following transformation
%Kstar=K^{(1)}*T^{-1}=M_{*}*F^{(1)}+M_{\infty}*F^{(2)}
%Kstar=T^{-1}*K^{(1)}=M_{*}*F^{(1)}+M_{\infty}*F^{(2)}
% =P_{*}*Z'*F^{(1)}+P_{\infty}*Z'*((-1)*(F_{\infty}^{-1})*F_{*}*(F_{\infty}^{-1}))
% =[P_{*}*Z'-Kinf*F_{*})]*F^{(1)}
%Make use of L^{0}'=(T-K^{(0)}*Z)'=(T-T*M_{\infty}*F^{(1)}*Z)'
@ -106,7 +106,7 @@ while rank(Pinf,diffuse_kalman_tol) && (t<=last)
% =T*[(P_{\infty}*(-K^{(1)*Z}))+P_{*}*(I-Z'*Kinf')*T'+RQR]
dlik(s)= log(det(Finf)); %set w_t to top case in bottom equation page 172, DK (2012)
iFinf = inv(Finf);
Kinf = Pinf*Z'*iFinf; %define Kinf=K_0*T^{-1} with M_{\infty}=Pinf*Z'
Kinf = Pinf*Z'*iFinf; %define Kinf=T^{-1}*K_0 with M_{\infty}=Pinf*Z'
Fstar = Z*Pstar*Z' + H; %(5.7) DK(2012)
Kstar = (Pstar*Z'-Kinf*Fstar)*iFinf; %(5.12) DK(2012)
Pstar = T*(Pstar-Pstar*Z'*Kinf'-Pinf*Z'*Kstar')*T'+QQ; %(5.14) DK(2012)

4
matlab/kalman/likelihood/missing_observations_kalman_filter_d.m
View File

@ -106,10 +106,10 @@ while rank(Pinf,diffuse_kalman_tol) && (t<=last)
else
iFstar = inv(Fstar);
dFstar = det(Fstar);
Kstar = Pstar*ZZ'*iFstar; %(5.15) of DK (2012) with Kstar=K^(0)*T^{-1}
Kstar = Pstar*ZZ'*iFstar; %(5.15) of DK (2012) with Kstar=T^{-1}*K^(0)
dlik(s) = log(dFstar) + v'*iFstar*v + length(d_index)*log(2*pi); %set w_t to bottom case in bottom equation page 172, DK (2012)
Pinf = T*Pinf*transpose(T); % (5.16) DK (2012)
Pstar = T*(Pstar-Pstar*ZZ'*Kstar')*T'+QQ; % (5.17) DK (2012)
Pstar = T*(Pstar-Pstar*ZZ'*Kstar')*T'+QQ; % (5.17) DK (2012) with L_0 plugged in
a = T*(a+Kstar*v); % (5.13) DK (2012)
end
end