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

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

    Hi,

    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 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 nodeís position vector is simply its (x,y) position at a certain time? I donít understand fully what information I should actually store 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
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  2. #2
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    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).
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  3. #3
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    Thanks for the reply. What form does Vx and Vy take and how can I calculate it?
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  4. #4
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    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.
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  5. #5
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    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?
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