Expected time of arrival with uncertainty

[username27]

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

 

[Dale]

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

 

[username27]

Thanks DaleSpam. I will take a look and come back.