50 lines
1.7 KiB
Matlab
50 lines
1.7 KiB
Matlab
function [K,iF,P] = steady_state_kalman_gain(T,R,Q,H,mf)
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% Given the invariant state space representation of a model, this
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% function computes the gain matrix and the covariance matrix of the
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% state vector at the steady state of the kalman filter.
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%
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% INPUTS
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% T [double] m*m transition matrix of the state vector.
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% R [double] m*q matrix (q is the number of structural innovations).
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% Q [double] q*q covariance matrix of the structural innovations.
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% H [double] p*p covariance matrix of the measurement error.
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% mf [integer] p*1 vector, indices for the observed variables
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%
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% OUTPUTS
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% K [double] kalman gain matrix.
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% P [double] covariance matrix of the state vector.
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%
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% SPECIAL REQUIREMENTS
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% Needs a solver for Riccati equations (dare.m)
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% Copyright © 2004-2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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m = length(T);
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p = length(mf);
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Z = build_selection_matrix(mf,m,p);
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if isempty(H)
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H = zeros(p,p);
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end
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QQ = R*Q*transpose(R);
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P = dare(T,transpose(Z),QQ,H);
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iF = inv(Z*P*transpose(Z)+H);
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K = T*P*transpose(Z)*iF; |