function pdf_pred = agd(pdf,system,params,u,eta,I)% AGD creates a grid for the point-mass filter using the anticipative%   approach.% Nonlinear Filtering Toolbox version 2.0-rc4% Copyright (c) 1995 - 2007 NFT developement Team,%              Department of Cybernetics,%              University of West Bohemia in PilsenQ  = var(system.pw);  % state noise covariace matrixnx = system.nx;nu = system.nu;nw = system.nw;f  = system.f;x  = system.x;if isa(pdf,'pmf') && (nargin > 4) %*** Grid design at the prediction step    % mean and covariance matrix    [C_eta,m_eta] = var(pdf,eta,I);    C_eta = C_eta + Q;    % Jordan decomposition    [T,D]  = eig(C_eta);    sqrtD  = sqrt(diag(D));    sqrtQT = sqrt(diag(T'*Q*T));else                              %*** Grid design at the initialization step    % mean and covariance matrix    m_eta = mean(pdf);    C_eta = var(pdf);    % Jordan decomposition    [T,D]  = eig(C_eta);    sqrtD  = sqrt(diag(D))';    sqrtQT = sqrt(diag(T'*Q*T))';    % Subsidiary grid for computation of max abs Jacobian    ngpts = 11*ones(1,nx);    mass  = 2*params.b * sqrtD./ngpts;    axgrid = cell(nx);    for l = 1:nx        axgrid{l} = mass(l) * ([1:ngpts(l)] - (ngpts(l)+1)/2);    end    eta = T*cartprod(axgrid) + repmat(m_eta,1,prod(ngpts));end% Maximum absolute value of Jacobian of the state functionif isempty(params.fixedNGPTS)    if islinear(f,x)  % Jacobian for linear system        if isa(system,'lga')            jacob = abs(det(system.F));        else            jacob = abs(det( nfdiff(f, [zeros(1,nu); zeros(nx,1); zeros(nw,1)], x) ));        end    else            % Jacobian for nonlinear system        jacob = 0;        if nargin < 4            u = zeros(1, nu);        end        zero_w = zeros(nw,1);        for i = 1:size(eta,2)            if system.nu>0                abs_detF = abs(det( nfdiff(f, [u; eta(:,i); zero_w], x) ));            else                abs_detF = abs(det( nfdiff(f, [eta(:,i); zero_w], x) ));            end            if abs_detF > jacob                jacob = abs_detF;            end        end    end    % Adaptive number of grid points    ngpts = max( 7, ceil( params.b/params.gamma*jacob^(1/nx) * sqrtD./sqrtQT  ) );else    % Fixed number of grid points    ngpts = params.fixedNGPTS;endmass  = 2*params.b * sqrtD./ngpts;pdf_pred = pmpdf(mass, ngpts, ones(1,prod(ngpts)), T, m_eta);  % Create the predictive pdf object (pdf values are identical for this moment)