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Make multivariate kalman filter and smoother robust to badly scaled covariance matrix of observables. 

This avoids shifting to univariate filter in most cases.
time-shift
Marco Ratto 2015-10-13 17:15:01 +02:00
parent d3eca9338b
commit 05fc096569
5 changed files with 19 additions and 15 deletions
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11
matlab/kalman/likelihood/kalman_filter.m
View File

@ -169,7 +169,8 @@ while notsteady && t<=last
v = Y(:,t)-a(Z);
F = P(Z,Z) + H;
end
if rcond(F) < kalman_tol
sig=sqrt(diag(F));
if any(diag(F)<kalman_tol) || rcond(F./(sig*sig')) < kalman_tol
if ~all(abs(F(:))<kalman_tol)
return
else
@ -178,9 +179,9 @@ while notsteady && t<=last
end
else
F_singular = 0;
dF = det(F);
iF = inv(F);
likk(s) = log(dF)+transpose(v)*iF*v;
log_dF = log(det(F./(sig*sig')))+2*sum(log(sig));
iF = inv(F./(sig*sig'))./(sig*sig');
likk(s) = log_dF+transpose(v)*iF*v;
if Zflag
K = P*Z'*iF;
Ptmp = T*(P-K*Z*P)*transpose(T)+QQ;
@ -245,7 +246,7 @@ if t <= last
Hess = Hess + tmp{3};
end
else
[tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag);
[tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,log_dF,Z,pp,Zflag);
end
end

2
matlab/kalman/likelihood/kalman_filter_fast.m
View File

@ -221,7 +221,7 @@ if t <= last
Hess = Hess + tmp{3};
end
else
[tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag);
[tmp, likk(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,log(dF),Z,pp,Zflag);
end
end

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

@ -1,4 +1,4 @@
function [LIK, likk, a] = kalman_filter_ss(Y,start,last,a,T,K,iF,dF,Z,pp,Zflag,analytic_derivation,Da,DT,DYss,D2a,D2T,D2Yss)
function [LIK, likk, a] = kalman_filter_ss(Y,start,last,a,T,K,iF,log_dF,Z,pp,Zflag,analytic_derivation,Da,DT,DYss,D2a,D2T,D2Yss)
% Computes the likelihood of a stationnary state space model (steady state kalman filter).
%@info:
@ -130,7 +130,7 @@ while t <= last
end
% Adding constant determinant of F (prediction error covariance matrix)
likk = likk + log(dF);
likk = likk + log_dF;
% Add log-likelihhod constants and divide by two
likk = .5*(likk + pp*log(2*pi));

11
matlab/kalman/likelihood/missing_observations_kalman_filter.m
View File

@ -102,7 +102,8 @@ while notsteady & t<=last
v = Y(d_index,t) - a(z);
F = P(z,z) + H(d_index,d_index);
end
if rcond(F) < kalman_tol
sig=sqrt(diag(F));
if any(diag(F)<kalman_tol) || rcond(F./(sig*sig')) < kalman_tol
if ~all(abs(F(:))<kalman_tol)
return
else
@ -111,9 +112,9 @@ while notsteady & t<=last
end
else
F_singular = 0;
dF = det(F);
iF = inv(F);
lik(s) = log(dF) + transpose(v)*iF*v + length(d_index)*log(2*pi);
log_dF = log(det(F./(sig*sig')))+2*sum(log(sig));
iF = inv(F./(sig*sig'))./(sig*sig');
lik(s) = log_dF + transpose(v)*iF*v + length(d_index)*log(2*pi);
if Zflag
K = P*z'*iF;
P = T*(P-K*z*P)*transpose(T)+QQ;
@ -140,7 +141,7 @@ lik(1:s) = .5*lik(1:s);
% Call steady state Kalman filter if needed.
if t<=last
[tmp, lik(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,dF,Z,pp,Zflag);
[tmp, lik(s+1:end)] = kalman_filter_ss(Y,t,last,a,T,K,iF,log_dF,Z,pp,Zflag);
end
% Compute minus the log-likelihood.

6
matlab/missing_DiffuseKalmanSmootherH1_Z.m
View File

@ -168,11 +168,13 @@ while notsteady && t<smpl
ZZ = Z(di,:);
v(di,t) = Y(di,t) - ZZ*a(:,t);
F = ZZ*P(:,:,t)*ZZ' + H(di,di);
if rcond(F) < kalman_tol
sig=sqrt(diag(F));
if any(diag(F)<kalman_tol) || rcond(F./(sig*sig')) < kalman_tol
alphahat = Inf;
return
end
iF(di,di,t) = inv(F);
iF(di,di,t) = inv(F./(sig*sig'))./(sig*sig');
PZI = P(:,:,t)*ZZ'*iF(di,di,t);
atilde(:,t) = a(:,t) + PZI*v(di,t);
K(:,di,t) = T*PZI;