factorize some codes across options and modify the definition of mixtures.
parent
ffd62a5923
commit
2858470942
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@ -3,28 +3,24 @@ function [LIK,lik] = gaussian_filter(ReducedForm, Y, start, ParticleOptions, Thr
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% predictive (prior) and filtered (posterior) densities for state variables
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% predictive (prior) and filtered (posterior) densities for state variables
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% by gaussian distributions.
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% by gaussian distributions.
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% Gaussian approximation is done by:
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% Gaussian approximation is done by:
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% - a Kronrod-Paterson gaussian quadrature with a limited number of nodes.
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% - a spherical-radial cubature (ref: Arasaratnam & Haykin, 2009).
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% Multidimensional quadrature is obtained by the Smolyak operator (ref: Winschel & Kratzig, 2010).
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% - a scaled unscented transform cubature (ref: Julier & Uhlmann 1995)
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% - a spherical-radial cubature (ref: Arasaratnam & Haykin, 2008,2009).
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% - a scaled unscented transform cubature (ref: )
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% - Monte-Carlo draws from a multivariate gaussian distribution.
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% - Monte-Carlo draws from a multivariate gaussian distribution.
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% First and second moments of prior and posterior state densities are computed
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% First and second moments of prior and posterior state densities are computed
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% from the resulting nodes/particles and allows to generate new distributions at the
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% from the resulting nodes/particles and allows to generate new distributions at the
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% following observation.
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% following observation.
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% => The use of nodes is much faster than Monte-Carlo Gaussian particle and standard particles
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% Pros: The use of nodes is much faster than Monte-Carlo Gaussian particle and standard particles
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% filters since it treats a lesser number of particles and there is no need
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% filters since it treats a lesser number of particles. Furthermore, in all cases, there is no need
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% of resampling.
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% of resampling.
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% However, estimations may reveal biaised if the model is truly non-gaussian
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% Cons: estimations may be biaised if the model is truly non-gaussian
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% since predictive and filtered densities are unimodal.
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% since predictive and filtered densities are unimodal.
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%
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%
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% INPUTS
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% INPUTS
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% reduced_form_model [structure] Matlab's structure describing the reduced form model.
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% Reduced_Form [structure] Matlab's structure describing the reduced form model.
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% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
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% Y [double] matrix of original observed variables.
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% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
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% start [double] structural parameters.
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% reduced_form_model.state.dr [structure] output of resol.m.
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% ParticleOptions [structure] Matlab's structure describing options concerning particle filtering.
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% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
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% ThreadsOptions [structure] Matlab's structure.
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% start [integer] scalar, likelihood evaluation starts at 'start'.
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% smolyak_accuracy [integer] scalar.
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%
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%
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% OUTPUTS
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% OUTPUTS
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% LIK [double] scalar, likelihood
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% LIK [double] scalar, likelihood
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@ -34,7 +30,7 @@ function [LIK,lik] = gaussian_filter(ReducedForm, Y, start, ParticleOptions, Thr
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%
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%
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% NOTES
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% NOTES
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% Copyright (C) 2009-2013 Dynare Team
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% Copyright (C) 2009-2015 Dynare Team
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%
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%
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% This file is part of Dynare.
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% This file is part of Dynare.
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%
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%
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@ -110,12 +106,7 @@ const_lik = (2*pi)^(number_of_observed_variables/2) ;
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lik = NaN(sample_size,1);
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lik = NaN(sample_size,1);
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LIK = NaN;
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LIK = NaN;
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SampleWeights = 1/number_of_particles ;
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ks = 0 ;
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%Estimate = zeros(number_of_state_variables,sample_size) ;
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%V_Estimate = zeros(number_of_state_variables,number_of_state_variables,sample_size) ;
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for t=1:sample_size
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for t=1:sample_size
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% build the proposal
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[PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = ...
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[PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = ...
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gaussian_filter_bank(ReducedForm,Y(:,t),StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,ParticleOptions,ThreadsOptions) ;
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gaussian_filter_bank(ReducedForm,Y(:,t),StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,ParticleOptions,ThreadsOptions) ;
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if ParticleOptions.distribution_approximation.cubature || ParticleOptions.distribution_approximation.unscented
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if ParticleOptions.distribution_approximation.cubature || ParticleOptions.distribution_approximation.unscented
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@ -126,40 +117,21 @@ for t=1:sample_size
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PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
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PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
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weights2,weights_c2,ReducedForm,ThreadsOptions) ;
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weights2,weights_c2,ReducedForm,ThreadsOptions) ;
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SampleWeights = weights2.*IncrementalWeights ;
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SampleWeights = weights2.*IncrementalWeights ;
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SumSampleWeights = sum(SampleWeights) ;
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else
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lik(t) = log(SumSampleWeights) ;
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SampleWeights = SampleWeights./SumSampleWeights ;
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StateVectorMean = StateParticles*SampleWeights ;
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temp = bsxfun(@minus,StateParticles,StateVectorMean) ;
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StateVectorVarianceSquareRoot = reduced_rank_cholesky( bsxfun(@times,SampleWeights',temp)*temp' )';
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else % Monte-Carlo draws
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StateParticles = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean) ;
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StateParticles = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean) ;
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IncrementalWeights = ...
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IncrementalWeights = ...
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gaussian_densities(Y(:,t),StateVectorMean,...
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gaussian_densities(Y(:,t),StateVectorMean,...
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StateVectorVarianceSquareRoot,PredictedStateMean,...
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StateVectorVarianceSquareRoot,PredictedStateMean,...
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PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
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PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
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1/number_of_particles,1/number_of_particles,ReducedForm,ThreadsOptions) ;
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1/number_of_particles,1/number_of_particles,ReducedForm,ThreadsOptions) ;
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%SampleWeights = SampleWeights.*IncrementalWeights ;
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SampleWeights = IncrementalWeights/number_of_particles ;
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SampleWeights = IncrementalWeights/number_of_particles ;
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SumSampleWeights = sum(SampleWeights) ;
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%VarSampleWeights = IncrementalWeights-SumSampleWeights ;
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%VarSampleWeights = VarSampleWeights*VarSampleWeights'/(number_of_particles-1) ;
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lik(t) = log(SumSampleWeights) ; %+ .5*VarSampleWeights/(number_of_particles*(SumSampleWeights*SumSampleWeights)) ;
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SampleWeights = SampleWeights./SumSampleWeights ;
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% Neff = neff(SampleWeights) ;
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% if (Neff<0.5*sample_size && ParticleOptions.resampling.status.generic) || ParticleOptions.resampling.status.systematic
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% ks = ks + 1 ;
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% StateParticles = resample(StateParticles',SampleWeights,ParticleOptions)' ;
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% StateVectorMean = mean(StateParticles,2) ;
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% StateVectorVarianceSquareRoot = reduced_rank_cholesky( (StateParticles*StateParticles')/(number_of_particles-1) - StateVectorMean*(StateVectorMean') )';
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% SampleWeights = 1/number_of_particles ;
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% elseif ParticleOptions.resampling.status.none
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StateVectorMean = StateParticles*SampleWeights ;
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temp = bsxfun(@minus,StateParticles,StateVectorMean) ;
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StateVectorVarianceSquareRoot = reduced_rank_cholesky( bsxfun(@times,SampleWeights',temp)*temp' )';
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%disp(StateVectorVarianceSquareRoot)
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% end
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end
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end
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SumSampleWeights = sum(SampleWeights) ;
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lik(t) = log(SumSampleWeights) ;
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SampleWeights = SampleWeights./SumSampleWeights ;
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StateVectorMean = StateParticles*SampleWeights ;
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temp = bsxfun(@minus,StateParticles,StateVectorMean) ;
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StateVectorVarianceSquareRoot = reduced_rank_cholesky( bsxfun(@times,SampleWeights',temp)*temp' )';
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end
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end
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LIK = -sum(lik(start:end));
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LIK = -sum(lik(start:end));
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@ -52,8 +52,7 @@ function [LIK,lik] = gaussian_mixture_filter(ReducedForm,Y,start,ParticleOptions
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% You should have received a copy of the GNU General Public License
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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 <http://www.gnu.org/licenses/>.
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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persistent init_flag mf0 mf1
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persistent init_flag mf0 mf1 Gprime Gsecond
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persistent nodes weights weights_c I J G number_of_particles
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persistent nodes weights weights_c I J G number_of_particles
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persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
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persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
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@ -71,16 +70,10 @@ if isempty(init_flag)
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number_of_observed_variables = length(mf1);
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number_of_observed_variables = length(mf1);
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number_of_structural_innovations = length(ReducedForm.Q);
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number_of_structural_innovations = length(ReducedForm.Q);
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G = ParticleOptions.mixture_state_variables; % number of GM components in state
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G = ParticleOptions.mixture_state_variables; % number of GM components in state
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I = 1 ; %ParticleOptions.mixture_structural_shocks ; % number of GM components in structural noise
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J = 1 ; %ParticleOptions.mixture_measurement_shocks ; % number of GM components in observation noise
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Gprime = G*I ;
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Gsecond = G*I*J ;
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number_of_particles = ParticleOptions.number_of_particles;
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number_of_particles = ParticleOptions.number_of_particles;
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init_flag = 1;
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init_flag = 1;
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end
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end
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SampleWeights = ones(Gsecond,1)/Gsecond ;
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% compute gaussian quadrature nodes and weights on states and shocks
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% compute gaussian quadrature nodes and weights on states and shocks
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if isempty(nodes)
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if isempty(nodes)
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if ParticleOptions.distribution_approximation.cubature
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if ParticleOptions.distribution_approximation.cubature
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@ -111,29 +104,54 @@ else
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end
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end
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Q_lower_triangular_cholesky = reduced_rank_cholesky(Q)';
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Q_lower_triangular_cholesky = reduced_rank_cholesky(Q)';
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% Initialize all matrices
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% Initialize mixtures
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StateWeights = ones(1,G)/G ;
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StateWeights = ones(1,G)/G ;
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StateMu = ReducedForm.StateVectorMean*ones(1,G) ;
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StateMu = ReducedForm.StateVectorMean ;
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StateSqrtP = zeros(number_of_state_variables,number_of_state_variables,G) ;
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StateSqrtP = zeros(number_of_state_variables,number_of_state_variables,G) ;
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temp = reduced_rank_cholesky(ReducedForm.StateVectorVariance)' ;
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temp = reduced_rank_cholesky(ReducedForm.StateVectorVariance)' ;
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StateMu = bsxfun(@plus,StateMu,bsxfun(@times,diag(temp),(-(G-1)/2:1:(G-1)/2))/10) ;
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for g=1:G
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for g=1:G
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StateSqrtP(:,:,g) = temp ;
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StateSqrtP(:,:,g) = temp ;
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end
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end
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StructuralShocksWeights = ones(1,I)/I ;
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if ParticleOptions.proposal_approximation.cubature
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StructuralShocksMu = zeros(number_of_structural_innovations,I) ;
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[StructuralShocksMu,StructuralShocksWeights] = spherical_radial_sigma_points(number_of_structural_innovations);
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StructuralShocksWeights = ones(size(StructuralShocksMu,1),1)*StructuralShocksWeights ;
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elseif ParticleOptions.proposal_approximation.unscented
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[StructuralShocksMu,StructuralShocksWeights,raf] = unscented_sigma_points(number_of_structural_innovations,ParticleOptions);
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else
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if ~ParticleOptions.distribution_approximation.montecarlo
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error('Estimation: This approximation for the proposal is not implemented or unknown!')
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end
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end
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I = size(StructuralShocksWeights,1) ;
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StructuralShocksMu = Q_lower_triangular_cholesky*(StructuralShocksMu') ;
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StructuralShocksSqrtP = zeros(number_of_structural_innovations,number_of_structural_innovations,I) ;
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StructuralShocksSqrtP = zeros(number_of_structural_innovations,number_of_structural_innovations,I) ;
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for i=1:I
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for i=1:I
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StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky ;
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StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky ;
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end
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end
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ObservationShocksWeights = ones(1,J)/J ;
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if ParticleOptions.proposal_approximation.cubature
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ObservationShocksMu = zeros(number_of_observed_variables,J) ;
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[ObservationShocksMu,ObservationShocksWeights] = spherical_radial_sigma_points(number_of_observed_variables);
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ObservationShocksWeights = ones(size(ObservationShocksMu,1),1)*ObservationShocksWeights;
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elseif ParticleOptions.proposal_approximation.unscented
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[ObservationShocksMu,ObservationShocksWeights,raf] = unscented_sigma_points(number_of_observed_variables,ParticleOptions);
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else
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if ~ParticleOptions.distribution_approximation.montecarlo
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error('Estimation: This approximation for the proposal is not implemented or unknown!')
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end
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end
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J = size(ObservationShocksWeights,1) ;
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ObservationShocksMu = H_lower_triangular_cholesky*(ObservationShocksMu') ;
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ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
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ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
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for j=1:J
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for j=1:J
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ObservationShocksSqrtP(:,:,j) = H_lower_triangular_cholesky ;
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ObservationShocksSqrtP(:,:,j) = H_lower_triangular_cholesky ;
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end
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end
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Gprime = G*I ;
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Gsecond = G*I*J ;
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SampleWeights = ones(Gsecond,1)/Gsecond ;
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StateWeightsPrior = zeros(1,Gprime) ;
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StateWeightsPrior = zeros(1,Gprime) ;
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StateMuPrior = zeros(number_of_state_variables,Gprime) ;
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StateMuPrior = zeros(number_of_state_variables,Gprime) ;
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StateSqrtPPrior = zeros(number_of_state_variables,number_of_state_variables,Gprime) ;
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StateSqrtPPrior = zeros(number_of_state_variables,number_of_state_variables,Gprime) ;
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StateMuPost = zeros(number_of_state_variables,Gsecond) ;
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StateMuPost = zeros(number_of_state_variables,Gsecond) ;
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StateSqrtPPost = zeros(number_of_state_variables,number_of_state_variables,Gsecond) ;
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StateSqrtPPost = zeros(number_of_state_variables,number_of_state_variables,Gsecond) ;
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%estimate = zeros(sample_size,number_of_state_variables,3) ;
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const_lik = (2*pi)^(.5*number_of_observed_variables) ;
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const_lik = (2*pi)^(.5*number_of_observed_variables) ;
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ks = 0 ;
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lik = NaN(sample_size,1);
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lik = NaN(sample_size,1);
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LIK = NaN;
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LIK = NaN;
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for t=1:sample_size
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for t=1:sample_size
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for i=1:I
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for i=1:I
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for j=1:J
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for j=1:J
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for g=1:G ;
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for g=1:G ;
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a = g + (j-1)*G ;
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gprime = g + (i-1)*G ;
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b = a + (i-1)*Gprime ;
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gsecond = gprime + (j-1)*Gprime ;
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[StateMuPrior(:,a),StateSqrtPPrior(:,:,a),StateWeightsPrior(1,a),...
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[StateMuPrior(:,gprime),StateSqrtPPrior(:,:,gprime),StateWeightsPrior(1,gprime),...
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StateMuPost(:,b),StateSqrtPPost(:,:,b),StateWeightsPost(1,b)] =...
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StateMuPost(:,gsecond),StateSqrtPPost(:,:,gsecond),StateWeightsPost(1,gsecond)] =...
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gaussian_mixture_filter_bank(ReducedForm,Y(:,t),StateMu(:,g),StateSqrtP(:,:,g),StateWeights(1,g),...
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gaussian_mixture_filter_bank(ReducedForm,Y(:,t),StateMu(:,g),StateSqrtP(:,:,g),StateWeights(g),...
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StructuralShocksMu(:,i),StructuralShocksSqrtP(:,:,i),StructuralShocksWeights(1,i),...
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StructuralShocksMu(:,i),StructuralShocksSqrtP(:,:,i),StructuralShocksWeights(i),...
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ObservationShocksMu(:,j),ObservationShocksSqrtP(:,:,j),ObservationShocksWeights(1,j),...
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ObservationShocksMu(:,j),ObservationShocksSqrtP(:,:,j),ObservationShocksWeights(j),...
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H,H_lower_triangular_cholesky,const_lik,ParticleOptions,ThreadsOptions) ;
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H,H_lower_triangular_cholesky,const_lik,ParticleOptions,ThreadsOptions) ;
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end
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end
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end
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end
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StateParticles,H,const_lik,1/number_of_particles,...
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StateParticles,H,const_lik,1/number_of_particles,...
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1/number_of_particles,ReducedForm,ThreadsOptions) ;
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1/number_of_particles,ReducedForm,ThreadsOptions) ;
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% calculate importance weights of particles
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% calculate importance weights of particles
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% SampleWeights = SampleWeights.*IncrementalWeights ;
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SampleWeights = IncrementalWeights/number_of_particles ;
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SampleWeights = IncrementalWeights/number_of_particles ;
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SumSampleWeights = sum(SampleWeights,1) ;
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SumSampleWeights = sum(SampleWeights,1) ;
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SampleWeights = SampleWeights./SumSampleWeights ;
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SampleWeights = SampleWeights./SumSampleWeights ;
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lik(t) = log(SumSampleWeights) ;
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lik(t) = log(SumSampleWeights) ;
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% First possible state point estimates
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%estimate(t,:,1) = SampleWeights*StateParticles' ;
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% Resampling if needed of required
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% Neff = neff(SampleWeights) ;
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% if (ParticleOptions.resampling.status.generic && Neff<.5*sample_size) || ParticleOptions.resampling.status.systematic
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% ks = ks + 1 ;
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% StateParticles = resample(StateParticles',SampleWeights,ParticleOptions)' ;
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% StateVectorMean = mean(StateParticles,2) ;
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% StateVectorVarianceSquareRoot = reduced_rank_cholesky( (StateParticles*StateParticles')/number_of_particles - StateVectorMean*(StateVectorMean') )';
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% SampleWeights = 1/number_of_particles ;
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% elseif ParticleOptions.resampling.status.none
|
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||||||
% StateVectorMean = StateParticles*sampleWeights ;
|
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||||||
% temp = sqrt(SampleWeights').*StateParticles ;
|
|
||||||
% StateVectorVarianceSquareRoot = reduced_rank_cholesky( temp*temp' - StateVectorMean*(StateVectorMean') )';
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|
||||||
% end
|
|
||||||
% Use the information from particles to update the gaussian mixture on state variables
|
|
||||||
[StateMu,StateSqrtP,StateWeights] = fit_gaussian_mixture(StateParticles,StateMu,StateSqrtP,StateWeights,0.001,10,1) ;
|
[StateMu,StateSqrtP,StateWeights] = fit_gaussian_mixture(StateParticles,StateMu,StateSqrtP,StateWeights,0.001,10,1) ;
|
||||||
%estimate(t,:,3) = StateWeights*StateMu' ;
|
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
|
|
||||||
|
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Loading…
Reference in New Issue