Optional std deviation scaling (developed with Frank)
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function covarianceEllipse(x,P,color)
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function covarianceEllipse(x,P,color, k)
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% covarianceEllipse plots a Gaussian as an uncertainty ellipse
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% Based on Maybeck Vol 1, page 366
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% k=2.296 corresponds to 1 std, 68.26% of all probability
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% k=11.82 corresponds to 3 std, 99.74% of all probability
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%
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% covarianceEllipse(x,P,color)
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% covarianceEllipse(x,P,color,k)
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% it is assumed x and y are the first two components of state x
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% k is scaling for std deviations, defaults to 1 std
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[e,s] = eig(P(1:2,1:2));
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s1 = s(1,1);
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s2 = s(2,2);
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k = 2.296;
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if nargin<4, k = 2.296; end;
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[ex,ey] = ellipse( sqrt(s1*k)*e(:,1), sqrt(s2*k)*e(:,2), x(1:2) );
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line(ex,ey,'color',color);
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