I have an observer located at position E (I do not know this position). I have multiple targets located at a positions T1,T2,T3 (or however many is needed). Observer looks at targets through a plane located some distance away and given by a point on this plane H (I do not know this point) and a normal N (I do know normal and it is parallel to YZ plane). On this plane targets are marked and locations of these markers are known M1, M2, M3 (corresponding to T1, T2, T3). The marker coordinates are given as scaled YZ points relative to H. I can find the 3d position of the markers: $\displaystyle TintersectionX = (MX * S) + H$ (X can be 1,2,3). S is not known to me. I do know that that TintersectionX belongs to a line between E and TX. I also know that TintersectionX belongs to the plane $\displaystyle TintersectionX.dot(N) = H.dot(N)$. Given that I know TX and MX I would like to find out what S, H, E are. What would be the best way approach this task?

In general this has two parts. Setting up the actual system of equations and then solving it. I would assume that there should be software that can find the solution automatically. Any ideas?

Thank you,