2009-12-11 12:49:02 +01:00
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function [LIK,lik] = monte_carlo_SIS_particle_filter(reduced_form_model,Y,start,number_of_particles)
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% hparam,y,nbchocetat,nbchocmesure,smol_prec,nb_part,g,m,choix
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% Evaluates the likelihood of a nonlinear model with a particle filter without systematic resampling.
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%
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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_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
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% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
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% reduced_form_model.state.dr [structure] output of resol.m.
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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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% start [integer] scalar, likelihood evaluation starts at 'start'.
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% mf [integer] pp*1 vector of indices.
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% number_of_particles [integer] scalar.
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%
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% OUTPUTS
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% LIK [double] scalar, likelihood
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% lik [double] vector, density of observations in each period.
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%
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% REFERENCES
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%
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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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% Copyright (C) 2009 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 <http://www.gnu.org/licenses/>.
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global M_ bayestopt_
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persistent init_flag
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persistent restrict_variables_idx observed_variables_idx state_variables_idx mf0 mf1
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persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
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% Set defaults.
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if (nargin<4) || (nargin==4 && isempty(number_of_particles))
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2009-12-11 18:12:49 +01:00
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number_of_particles = 10 ;
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2009-12-11 12:49:02 +01:00
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end
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if nargin==2 || isempty(start)
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start = 1;
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end
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dr = reduced_form_model.state.dr;% Decision rules and transition equations.
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Q = reduced_form_model.state.Q;% Covariance matrix of the structural innovations.
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H = reduced_form_model.measurement.H;% Covariance matrix of the measurement errors.
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% Set persistent variables.
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if isempty(init_flag)
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mf0 = bayestopt_.mf0;
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mf1 = bayestopt_.mf1;
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restrict_variables_idx = bayestopt_.restrict_var_list;
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observed_variables_idx = restrict_variables_idx(mf1);
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state_variables_idx = restrict_variables_idx(mf0);
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sample_size = size(Y,2);
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number_of_state_variables = length(mf0);
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number_of_observed_variables = length(mf1);
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number_of_structural_innovations = length(Q);
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init_flag = 1;
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end
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% Set local state space model (second order approximation).
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ghx = dr.ghx(restrict_variables_idx,:);
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ghu = dr.ghu(restrict_variables_idx,:);
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half_ghxx = .5*dr.ghxx(restrict_variables_idx,:);
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half_ghuu = .5*dr.ghuu(restrict_variables_idx,:);
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ghxu = dr.ghxu(restrict_variables_idx,:);
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steadystate = dr.ys(dr.order_var(restrict_variables_idx));
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constant = steadystate + .5*dr.ghs2(restrict_variables_idx);
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state_variables_steady_state = dr.ys(dr.order_var(state_variables_idx));
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StateVectorMean = state_variables_steady_state;
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StateVectorVariance = lyapunov_symm(ghx(mf0,:),ghu(mf0,:)*Q*ghu(mf0,:)',1e-12,1e-12);
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StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
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state_variance_rank = size(StateVectorVarianceSquareRoot,2);
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%state_idx = 1:state_variance_rank;
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%innovation_idx = 1+state_variance_rank:state_variance_rank+number_of_structural_innovations;
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Q_lower_triangular_cholesky = chol(Q)';
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% Set seed for randn().
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seed = [ 362436069 ; 521288629 ];
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randn('state',seed);
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const_lik = log(2*pi)*number_of_observed_variables;
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lik = NaN(sample_size,1);
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nb_obs_resamp = 0 ;
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w = ones(number_of_particles,1) ;
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2009-12-11 12:49:02 +01:00
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for t=1:sample_size
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PredictedState = zeros(number_of_particles,number_of_state_variables);
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PredictionError = zeros(number_of_particles,number_of_observed_variables);
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%PredictedStateMean = zeros(number_of_state_variables,1);
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PredictedObservedMean = zeros(number_of_observed_variables,1);
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%PredictedStateVariance = zeros(number_of_state_variables,number_of_state_variables);
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PredictedObservedVariance = zeros(number_of_observed_variables,number_of_observed_variables);
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%PredictedStateAndObservedCovariance = zeros(number_of_state_variables,number_of_observed_variables);
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for i=1:number_of_particles
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if t==1
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StateVector = StateVectorMean + StateVectorVarianceSquareRoot*randn(state_variance_rank,1);
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else
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StateVector = StateUpdated(i,:)' ;
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end
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yhat = StateVector-state_variables_steady_state;
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epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,1);
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tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,half_ghxx,half_ghuu,ghxu);
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% stockage des particules et des erreurs de pr<70>visions
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PredictedState(i,:) = tmp(mf0)' ;
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PredictionError(i,:) = (Y(:,t) - tmp(mf1))' ;
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% calcul des moyennes et des matrices de variances covariances
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%PredictedStateMean_old = PredictedStateMean;
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PredictedObservedMean_old = PredictedObservedMean;
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%PredictedStateMean = PredictedStateMean + (tmp(mf0)-PredictedStateMean)/i;
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PredictedObservedMean = PredictedObservedMean + (tmp(mf1)-PredictedObservedMean)/i;
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%psm = PredictedStateMean*PredictedStateMean';
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pom = PredictedObservedMean*PredictedObservedMean';
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%pcm = PredictedStateMean*PredictedObservedMean';
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%PredictedStateVariance = PredictedStateVariance ...
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% + ( (tmp(mf0)*tmp(mf0)'-psm-PredictedStateVariance)+(i-1)*(PredictedStateMean_old*PredictedStateMean_old'-psm) )/i;
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PredictedObservedVariance = PredictedObservedVariance ...
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+ ( (tmp(mf1)*tmp(mf1)'-pom-PredictedObservedVariance)+(i-1)*(PredictedObservedMean_old*PredictedObservedMean_old'-pom) )/i;
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%PredictedStateAndObservedCovariance = PredictedStateAndObservedCovariance ...
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% + ( (tmp(mf0)*tmp(mf1)'-pcm-PredictedStateAndObservedCovariance)+(i-1)*(PredictedStateMean_old*PredictedObservedMean_old'-pcm) )/i;
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end
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PredictedObservedVariance = PredictedObservedVariance + H;
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iPredictedObservedVariance = inv(PredictedObservedVariance);
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lnw = -0.5*(const_lik + log(det(PredictedObservedVariance)) + sum((PredictionError*iPredictedObservedVariance).*PredictionError,2)) ;
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%bidouille num<75>rique Schorfheide
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dfac = max(lnw);
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wtilde = w.*exp(lnw - dfac) ;
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% vraisemblance de l'observation
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lik(t) = log(mean(wtilde)) + dfac ;
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%clear (PredictionError) ;
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%clear (lnw) ;
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% calcul des poids
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w = wtilde/sum(wtilde) ;
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%clear (wtilde) ;
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%update
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Neff = 1/sum(w.*w) ;
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if Neff>number_of_particles %no resampling
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StateUpdated = PredictedState ;
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%clear (PredictedState) ;
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w = number_of_particles*w ;
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else %resampling
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nb_obs_resamp = nb_obs_resamp+1 ;
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%kill the smallest particles before resampling :! facultatif ?
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%to_kill = [w PredictedState] ;
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%to_kill = delif(to_kill,w<(1/number_of_particules)*1E-12);%%
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%[n,m] = size(to_kill) ;
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%w = to_kill(:,1) ;
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%PredictedState = to_kill(:,2:m) ;
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%clear (to_kill) ;
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%if number_of_particles neq n
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% 'Elimination de '; number_of_particles - n ; ' particules <20> l''observation ';t ;
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%end
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%fin de kill
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%remise <20> l'<27>chelle des poids sur les particules restantes
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%w = cumsum( w/sum(w) );
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%R<><52>chantillonage syst<73>matique
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%rnduvec = ( (1:number_of_particles)-1+rand )/number_of_particles ;
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%selind = (number_of_particles - sum( w > rnduvec ) + 1)'; % probl<62>me de m<>moire car w .> rnduvec' tr<74>s grande !
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%clear (rnduvec) ;
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%StateUpdated = PredictedState(selind,:) ;
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%clear (selind) ;
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% initialize
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selind = zeros(number_of_particles,1);
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% construct CDF
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c = cumsum(w);
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% draw a starting point
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rnduvec = ( (1:number_of_particles)-1+rand)/number_of_particles ;
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% start at the bottom of the CDF
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j=1;
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for i=1:number_of_particles
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% move along the CDF
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while (rnduvec(i)>c(j))
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j=j+1;
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end
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% assign index
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selind(i) = j;
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end
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StateUpdated = PredictedState(selind,:);
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w = ones(number_of_particles,1) ;
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end
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end
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LIK = -sum(lik(start:end));
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