# Understanding a paper on Gaussian Processes

I am reading and trying to understand the paper "Gaussian Processes for Signal Strength-Based Location Estimation" by Ferris et al. (A copy of the paper may be accessed here). At the moment I am stuck with Section II A. All notation used below is consistent with the paper.

1. The authors introduce two covariance functions in equations 3 and 4. Can anyone explain the difference between these two functions? (i.e. why they are useful.)

2. In equations 5 and 6, the authors use $\textbf{k}_*$, which is "the $n\times1$ vector of covariances between $x_*$ and the training inputs $\textbf{X}$," I don't understand how to compute it though. Any insights? (Is it found from equation 4?)

I'm not very familiar with the theory of Gaussian Processes, and unfortunately don't have the luxury of time to spend understanding the theory. I would appreciate answers that focus on the "functional" aspects of the paper, as that is the reason I am reading it.

2. You compute it using Eq. 3 (or .4); it is the covariance of your point of estimation $x_*$ and the known/input put in $X$. So practically you compute Eq.3 iterating over all $x_i$ (something like $cov(y_p,y_*) = k(x_p,x_*)$ and you end up with a vector $k_*$.