Mulawa - 4 
matrix 2p P shows that it contains a large axis pointing in the direction ß of the line IL 
The uncertainty of the point P along the direction ß of the line IL is immaterial. What is 
important is the uncertainty perpendicular to the direction ß of the line IL. The 
covariance matrix Z PP can be collapsed along the direction ß of the line IL to an 
covariance matrix Zpp with a rank equal to two by using the orthogonal projection 
matrix: 
function of the arc length parameter s. Analysis of the projected covariance matrix 2pp 
produces an ellipse of constant probability in the plane at the point P that is perpendicular 
to the line IL . The arc length parameter s is allowed to move along its entire interval and 
sweeps out a probability surface for the line IL . An example a probability surface 
generated by this method is given below. The size of the probability surface has been 
greatly enlarged for graphical reasons. 
An interesting note is that the presented projection method to collapse the error ellipsoids 
along the direction of the tangent of the linear features can be applied to other linear 
E = I - ßß T 
( 8 ) 
and following the error propagation: 
V 17V 17 T 
Zpp = EZppE 
(9) 
= + ¿E^cßE + sESß^E + s E2ßßE 
It is important to note that Zpp is still an Si 3 object. Note that 2pp is a quadratic