Optimal Estimation of Dynamic Systems, 2nd Edition

706 Optimal Estimation of Dynamic Systems

% Get Eigenvectors

u1=[ r (1 ,2); lam1−r (1 ,1) ] / den1; u2=[ r (1 ,2);lam2−r (1 ,1)]/ den2;

u=[u1 u2];

% Get Correlated Noise

v=(u∗ v

uncorr ’) ’; v(: ,1)=v(: ,1)+mean x(1);

v(:,2)=v(: ,2)+mean

x(2);

% Determine x and y Values

x3=sqrt(lam1)∗ 3; x

pos=[0:x3/50:x3] ’;

y

pos=3∗(lam2∗(1−x pos.ˆ2/x3ˆ2)).ˆ(0.5);

x=[x

pos; flipud(x pos);−x pos;−flipud (x pos )] ’;

y=[y

pos;−flipud (y pos);−y pos; flipud(y pos )] ’;

% Get Bounds Through Rotation

x

bound=x∗cos ( theta)+y∗ sin(theta)+mean x(1);

y

bound=−x∗ sin(theta)+y∗cos(theta)+mean x(2);

% Plot Results

plot(x

bound ,y bound ,v (: ,1) ,v (: ,2) , ’ . ’ )

References

[1] Bryson, A.E. ...