# Math Help - Motion/Position Vector - Calculate a position at a future time

1. ## Motion/Position Vector - Calculate a position at a future time

Hi,

Im 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 relies 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 nodes position vector is simply its (x,y) position at a certain time? I dont understand fully what information I should actually store in the motion vector and still dont understand how given a nodes (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?

2. At base, this is just saying that "velocity = distance moved/time" so that distance moved= velocity*time and then you add the distance moved to the old position. Yes, a "node's" position is just it (x, y) coordinates and the velocity is the "vector" with $(v_x, v_y)$, the x and y components of velocity. The direction of motion is given by $v_x$ and $v_y$. Add the x and y components separately: $(x_{new}, y_{new})=(x_{old}+ v_xt, y_{old}+v_yt)$.

3. Thanks for the reply. What form does Vx and Vy take and how can I calculate it?

4. Well, you said "v(I, T): motion vector of node I at time T" in your first post. The components of that should be $v_x$ and $v_y$.

5. Yes this is what the paper said I need.

I'm trying to figure out what values I need to gather/presume to know and what form they need to take so that I can calculate the nodes future position. The values I currently have are the node's current (x,y) position, its past (x,y) position and its current speed.

Perhaps from that I can calculate a motion vector?