Iím hoping someone can give me a hand with this as I'm quite stuck and need to figure this out quickly.

I have a node that knows its current (x, y) position, its previous (x, y) position one second ago and will know its current speed.

I am trying to implement a scheme from a paper that tells me the following :

v(I,T): motion vector of node I at time T
p(I,T): position vector of node I at time T.

It gives the following relationship:
p(I,Tc) = p(I,Tr) + v(I,Tr).(Tc-Tr)where Tr is a past time, Tc is the current time.
Part of the algorithm says that a node can predict the position of another node at time Tc + Δt, where Δt is a small time like 1s, if it knows the nodes current position and motion vector. It says it replies on the accuracy of the motion vector and then says the following:

Let m denote the motion vector directly access from GPS. Mold and Mnew are the report motion vectors at the last time and this time respectively
Mnew = α . Mold + (1- α).m, 0<= α<=1.
α is 0.3 if a vehicle is in the area of a junction and 0.7 otherwise.
Now my questions are these. Am I correct in thinking a nodeís position vector is simply its (x,y) position at a certain time? I donít understand fully what information should actually be stored in the motion vector and still donít understand how given a nodeís (x,y) position and speed at time Tc, I can work out its position at time Tc + 1 given that it could have moved in any direction?

Many thanks in advance