I have a dataset of trajectories. These trajectories are represented in 3D space (x,y,z). All trajectories of this dataset are similar in their shape, but they are not exactly the same, I mean, there is some variation along the points. The trajectories are nonlinear.
What I need is a kind of regression (polynomial?) on the data to fit the curve along the 3D points, at the end I need a smoothed trajectory, say a generalized one (result of curve fitting/regression).
I just find curve fitting for 2D data (x,y). Can anyone give hints of how to solve it? I heard about local polynomial regression on manifolds, but I dont know how it works, seems to be complex.
thank you in advance