With limited knowledge of mathematics, I am not sure what tags to use for this question.
I have a path on a 2D surface called $(p1)$. A path consists of a set of ordered $(x,y)$ coordinates. By ordered I mean the first line segment in a path would be $(x1,y1) to (x2,y2)$, the second line segment would be $(x2,y2) to (x3,y3)$ and so on. So these ordered points create a shape and direction of travel similar to what you would see on top-down Google Maps view.
I need to match this path $(p1)$ against some other arbitrary paths to determine which one is the closest to the original path $(p1)$ in terms of shape and direction of travel. The number of line segments making up each path could be arbitrary by the way so there needs to be a way of handling tolerance.
Not sure what this is called but I have explored some LQE techniques such as the Kalman Filter in vain. What I am looking for is analysing a static set of ordered points against another rather than progressive prediction.
I am not sure what constructs can represent similarity between paths. Any guidance would be highly appreciated.