# Estimating the bycycle model using point sets from consucutive frames

I have two sets of points from two consecutive frames (restored from a video). The data represent points on the surface of a single-vehicle moving between frames. Points are in 3D and are assumed not to change in the $$y$$ axis (flat world) between frames. In each frame, we assume all points are of a single plain (The vehicle plane). The points are indexed and we can recognize the same point in different frames.

How do I apply the bicycle model in this case? It needs a steering input variable which I do not have, as well as a velocity input variable.

Since I can calculate $$dx$$ and $$dz$$ between consecutive frames, I think I can get $$v$$ somehow using:

$$v = \sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dz}{dt}\right)^2},$$

however, I do not have the frame rate $$dt$$, so I can only get the direction of $$v$$. Also, I don't know the size of the target Vachel, only some points, nor the direction of movement. How do I account for these? I need to take one of the points as a reference?

my final goal is to get a vector $$(dx, dy, dz, d\theta)$$ with $$dy$$ obviously $$0$$, representing the motion between frames.

Also, and this an intuition, Is it wrong to calculate $$d\theta$$ simply as the angle between the planes? My intuition tells me it is not that easy, however, I cannot think of a reason it is not correct.