PDF of distance between measured coordinates with normally distr. errors

by omg!
Tags: coordinates, distance, distr, errors, measured
omg! is offline
May15-10, 10:08 AM
P: 52
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


where r is the projected distance on the plane.

Thanks for all the help
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city

Register to reply

Related Discussions
Distance Matrix and coordinates General Math 0
Light speed measured from distance Special & General Relativity 1
Distance between 2 points in spherical coordinates Calculus 5
normal distr Calculus & Beyond Homework 3
Finding the coordinates and distance of this drawing Introductory Physics Homework 4