function [x,q] = bootstrap(actualx,y,R,Q,initVar,numSamples);% PURPOSE : This m file performs the bootstrap algorithm (a.k.a. SIR,%           particle filter, etc.) for the model specified in the%           file sirdemo1.m. % INPUTS  : - actualx = The true hidden state. %           - y = The observation.%           - R = The measurement noise variance parameter.%           - Q = The process noise variance parameter.%           - initVar = The initial variance of the state estimate.%           - numSamples = The number of samples.% OUTPUTS : - x = The estimated state samples.%           - q = The normalised importance ratios.% AUTHOR  : Nando de Freitas - Thanks for the acknowledgement :-)% DATE    : 08-09-98if nargin < 6, error('Not enough input arguments.'); end[rows,cols] = size(y);      % rows = Max number of time steps.S = numSamples;             % Number of samples;Nstd = 2;                   % No of standard deviations for error bars;x=zeros(S,rows);xu=zeros(S,rows);q=zeros(S,rows);% SAMPLE FROM THE PRIOR:% =====================x(:,1) = sqrt(initVar)*randn(S,1);mean(x(:,1));cov(x(:,1));figure(1)clf;subplot(221)plot(actualx)ylabel('State x','fontsize',15);xlabel('Time','fontsize',15);% UPDATE AND PREDICTION STAGES:% ============================for t=1:rows-1,     figure(1)    subplot(222)  plot(y)  ylabel('Output y','fontsize',15);  xlabel('Time','fontsize',15);  hold on  plot(t*ones(1,49),[-19:1:29],'r');  hold off  subplot(223)  hold on  plot(t,mean(x(1:S,t,1)),'ro',t,actualx(t,1),'go');  hold on  errorbar(t,mean(x(1:S,t,1)),Nstd*std(x(1:S,t,1)),Nstd*std(x(1:S,t,1)),'k')  legend('Posterior mean estimate','True value');  ylabel('Sequential state estimate','fontsize',15)  xlabel('Time','fontsize',15)  xu(:,t) = predictstates(x(:,t),t,Q);  q(:,t+1) = importanceweights(xu(:,t),y(t+1,1),R);  x(:,t+1) = updatestates(xu(:,t),q(:,t+1));end;