PDF of distance between measured coordinates with normally distr. errors

  1. hi,
    the problem i have is this:

    consider a line segment L of length d in R^3. the projection of the endpoints of L on a fixed plane can be determined with an error that is normally distributed, and the errors for the two endpoints needs not to be equal. Assuming that L is randomly oriented in R^3, what is the distribution of the projected distance?

    I have been thinking about this for quite a while, reading up on chi(-squared), rice, reighley distributions. the problem is that the coordinates are not independent, so that dX,dY in sqrt(dX^2+dY^2) are not independent, making these distributions unsuitable. The PDF of the projected distance neglecting contribution of errors is

    r/d*1/sqrt(d^2-r^2)

    where r is the projected distance on the plane.

    Thanks for all the help
     
  2. jcsd
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