## Expected time of arrival with uncertainty

Hi,
This is actually related to my research work. Let say a location (x1,y1) is given with uncertainty in location is given by co-variance matrix P1. A vehicle is moving towards (x1,y1) from a location (x2,y2) with velocity (x2dot, y2dot). The uncertainty of the vehicle location is given by co-variance matrix P2 and uncertainty of the vehicle velocity is given by co-variance matrix P3. How can I calculate the expected time of arrival for the vehicle for this scenario?

The uncertainty is given by Gaussian distribution. For e.g., location based covariance will be in the following form P = [ σ(xx) σ(xy); σ(yx) σ(yy)]

I am pretty sure, there are no closed answers for this. What I want is what kind of research papers or books I have to read to get the idea for this problem? I could not able to find anything for the above problem until now.

Thanks

 PhysOrg.com physics news on PhysOrg.com >> Promising doped zirconia>> New X-ray method shows how frog embryos could help thwart disease>> Bringing life into focus
 Mentor Hi username27, welcome to PF! As long as you can express the ETA as some function f(x1,y1,x2,y2,x2dot,y2dot) then you can use the standard propagation of errors technique: http://mathworld.wolfram.com/ErrorPropagation.html
 Thanks DaleSpam. I will take a look and come back.

 Tags eta, gaussian distribtion