I am writing an application that consumes GPS data - and I am trying to calculate direction traveled based on a change in distance to the destination and origin.
Assume that I have a straight path of travel like below:
A <----------------------------------------------------------------------------------> B
I have an object denoted by X that travels between these two points. I do not get directional information from the GPS, just coordinates. From this I can calculate the distance to each of the endpoints of the path of travel.
A <-----------X----------------------------------------------------------------------> B
At this point, the object has traveled a given distance from A to B (but we do not know that). We are a distance of 11 units from A, and 129 units from B.
A <------------------------X---------------------------------------------------------> B
Here we have traveled some more distance, and have a new coordinate point. I have a distance of 23 units to A, and 117 units to B.
What I want to do
What I would like to do, is to be able to take the distances [I will have a whole list of distances to each point as a function of time], and create some sort of equation that I can program in that will accept the points and return some number that correlates a change in the distance to point A versus a change in the distance to point B, that would give me a reasonable indicator that I am in fact traveling from point A to point B, and not the other way.
Is this something that can be done? I always got the change formulas mixed up, and given this is for an application I would like to make sure it is done the right way!
If it can be done, what would be the best way to approach it?
If you can remember your position in the previous step, say previously, you are at distance $x_{t-1}$ from $A$ and now you are at distance $x_t$ from $A$.
If you are in the right direction, then $x_t-x_{t-1}>0$.