function [StateMuPrior, StateSqrtPPrior, StateWeightsPrior, StateMuPost, StateSqrtPPost, StateWeightsPost] =...
    gaussian_mixture_filter_bank(ReducedForm, obs, StateMu, StateSqrtP, StateWeights, ...
                                 StructuralShocksMu, StructuralShocksSqrtP, StructuralShocksWeights, ...
                                 ObservationShocksWeights, H, H_lower_triangular_cholesky, normfactO, ...
                                 ParticleOptions, options_, M_)

% Computes the proposal with a Gaussian approximation for importance
% sampling. This proposal is a gaussian distribution calculated à la Kalman
%
% INPUTS:
% - ReducedForm                    [struct]        MATLAB's structure describing the reduced form model.
% - obs                            [double]        pp*1 vector of (detrended) data, where pp is the maximum number of observed variables
% - StateMu                        [double]        mean of the states
% - StateSqrtP                     [double]        square root of the state covariance matrix
% - StateWeights                   [double]        weights of the state particles
% - StructuralShocksMu             [double]        mean of the structural shocks
% - StructuralShocksSqrtP	       [double]        square root of covariance matrix of the structural shocks
% - StructuralShocksWeights	       [double]        weights of structural shocks
% - ObservationShocksWeights       [double]        weights of measurement errors
% - H                              [double]        Measurement error covariance
% - H_lower_triangular_cholesky    [double]        Cholesky of measurement error covariance
% - normfactO                      [double]        normalizing constant in likelihood
% - ParticleOptions                [struct]        filter options
% - options_                       [struct]        describing the options
% - M_                             [struct]        describing the model
%
% OUTPUTS:
% - StateMuPrior                   [double]        prior mean of the states
% - StateSqrtPPrior                [double]        square root of prior covariance of the states
% - StateWeightsPrior              [double]        prior weight of the states
% - StateMuPost                    [double]        posterior mean of the states
% - StateSqrtPPost                 [double]        square root of posterior covariance of the states
% - StateWeightsPost               [double]        posterior weight of the states

% Copyright © 2009-2026 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare.  If not, see <https://www.gnu.org/licenses/>.

mf0 = ReducedForm.mf0;
mf1 = ReducedForm.mf1;
number_of_state_variables = length(mf0);
number_of_observed_variables = length(mf1);
number_of_structural_innovations = length(ReducedForm.Q);

numb = number_of_state_variables+number_of_structural_innovations;

if ParticleOptions.proposal_approximation.cubature
    [nodes3, weights3] = spherical_radial_sigma_points(numb);
    weights_c3 = weights3;
elseif ParticleOptions.proposal_approximation.unscented
    [nodes3, weights3, weights_c3] = unscented_sigma_points(numb, ParticleOptions.unscented);
else
    if ParticleOptions.proposal_approximation.montecarlo
        error('The montecarlo approximation for the proposal is not implemented.')
    else
        error('This approximation for the proposal is unknown.')
    end
end

epsilon = bsxfun(@plus, StructuralShocksSqrtP*nodes3(:,number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations)', StructuralShocksMu);
StateVectors = bsxfun(@plus, StateSqrtP*nodes3(:,1:number_of_state_variables)', StateMu);
tmp=iterate_law_of_motion(StateVectors,epsilon,ReducedForm,M_,options_,ReducedForm.use_k_order_solver,false);

PredictedStateMean = tmp(mf0,:)*weights3;
PredictedObservedMean = tmp(mf1,:)*weights3;

if ParticleOptions.proposal_approximation.cubature
    PredictedStateMean = sum(PredictedStateMean, 2);
    PredictedObservedMean = sum(PredictedObservedMean, 2);
    dState = (bsxfun(@minus, tmp(mf0,:), PredictedStateMean)').*sqrt(weights3);
    dObserved = (bsxfun(@minus, tmp(mf1,:), PredictedObservedMean)').*sqrt(weights3);
    PredictedStateVariance = dState'*dState;
    big_mat = [dObserved,  dState ; H_lower_triangular_cholesky, zeros(number_of_observed_variables, number_of_state_variables)];
    [~, mat] = qr2(big_mat, 0);
    mat = mat';
    PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables, 1:number_of_observed_variables);
    CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables), 1:number_of_observed_variables);
    StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables), number_of_observed_variables+(1:number_of_state_variables));
    iPredictedObservedVarianceSquareRoot = inv(PredictedObservedVarianceSquareRoot);
    iPredictedObservedVariance = iPredictedObservedVarianceSquareRoot'*iPredictedObservedVarianceSquareRoot;
    sqrdet = 1/sqrt(det(iPredictedObservedVariance));
    PredictionError = obs - PredictedObservedMean;
    StateVectorMean = PredictedStateMean + CovarianceObservedStateSquareRoot*iPredictedObservedVarianceSquareRoot*PredictionError;
else
    dState = bsxfun(@minus, tmp(mf0,:), PredictedStateMean);
    dObserved = bsxfun(@minus, tmp(mf1,:), PredictedObservedMean);
    PredictedStateVariance = dState*diag(weights_c3)*dState';
    PredictedObservedVariance = dObserved*diag(weights_c3)*dObserved' + H;
    PredictedStateAndObservedCovariance = dState*diag(weights_c3)*dObserved';
    sqrdet = sqrt(det(PredictedObservedVariance));
    iPredictedObservedVariance = inv(PredictedObservedVariance);
    PredictionError = obs - PredictedObservedMean;
    KalmanFilterGain = PredictedStateAndObservedCovariance*iPredictedObservedVariance;
    StateVectorMean = PredictedStateMean + KalmanFilterGain*PredictionError;
    StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
    StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
    StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
end

data_lik_GM_g = exp(-0.5*PredictionError'*iPredictedObservedVariance*PredictionError)/abs(normfactO*sqrdet) + 1e-99;
StateMuPrior = PredictedStateMean;
StateSqrtPPrior = reduced_rank_cholesky(PredictedStateVariance)';
StateWeightsPrior = StateWeights*StructuralShocksWeights;
StateMuPost = StateVectorMean;
StateSqrtPPost = StateVectorVarianceSquareRoot;
StateWeightsPost = StateWeightsPrior*ObservationShocksWeights*data_lik_GM_g;
