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We can the transform the covarience matrix by using the 5x4 track representation derivative matrix A = d x_acd / d x_tkr:
  C_acd (5x5) = A C_tkr (4x4) A_T

Wiki MarkupIf we then use the track parameterization to calculate a \ [point of closest approach (POCA) or an intersection point (p), the covarience on that point can be found using 5x3 solution derivative matrix

  B = d p /  d A_acd
with the covarience given by:
  C_p (3x3) = B C_acd (5x5) B_T

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Errors on POCA between a track and a ray

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Call the ray (r,q) and the track (x,v), the POCA occurs at an arclength along the track    s = \track
   s = [b(r.(x-q) - v.(x-q)\] / \ [1-b*b\]
and an arclength along the ray:   t = \
  t = [r.(x-q) - b(v.(x-q))\] / \ [1-b*b\]
where b = v.r

Then the poca and vector of closest approach are:
  p = x + sv
  J = (x-q) + sv - tr

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 Errors on point where a track crosses a plane

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Given a plane defined by a point q and a rotation matrix R, the intersection occurs at:   s = \[
  s = [ (x-q).R_z \ ] / \ [ v. R_z \ ]

Then the intersection point in the global frame is:
  p = x + sv

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