function [xPts, wPts, nPts] = scaledSymmetricSigmaPoints(x,P,alpha,beta,kappa)% This function returns the scaled symmetric sigma point distribution.%%  [xPts, wPts, nPts] = scaledSymmetricSigmaPoints(x,P,alpha,beta,kappa)  %% Inputs:%	 x	      mean%	 P	      covariance%        alpha        scaling parameter 1%        beta         extra weight on zero'th point%	 kappa	      scaling parameter 2 (usually set to default 0)%% Outputs:%        xPts	 The sigma points%        wPts	 The weights on the points%	 nPts	 The number of points%%%% (C) 2000      Rudolph van der Merwe  % (C) 1998-2000 S. J. Julier.% Number of sigma points and scaling termsn    = size(x(:),1);nPts = 2*n+1;            % we're using the symmetric SUT% Recalculate kappa according to scaling parameterskappa = alpha^2*(n+kappa)-n;% Allocate spacewPts=zeros(1,nPts);xPts=zeros(n,nPts);% Calculate matrix square root of weighted covariance matrixPsqrtm=(chol((n+kappa)*P))';  % Array of the sigma pointsxPts=[zeros(size(P,1),1) -Psqrtm Psqrtm];% Add mean back inxPts = xPts + repmat(x,1,nPts);  % Array of the weights for each sigma pointwPts=[kappa 0.5*ones(1,nPts-1) 0]/(n+kappa);% Now calculate the zero'th covariance term weightwPts(nPts+1) = wPts(1) + (1-alpha^2) + beta;