[Python] How to interpolate position using velocity and position samples

I have a dynamic dataset of length n, which is greater than or equal to one. The dataset contains m-dimensional position and velocity values for discrete time.

import numpy as np

times = np.array([t1, t2, ..., tn])
positions = np.array([[p11, p12, ..., p1m],
[p21, p22, ..., p2m],
... ,
[pn1, pn2, ..., pnm]])
velocities = np.array([[v11, v12, ..., v1m],
[v21, v22, ..., v2m],
... ,
[vn1, vn2, ..., vnm]])


I would like to calculate the position and velocity value for any time, including if the value is outside of the range of the dataset. I can achieve a simple linear interpolation for the velocity using,

interp_vel = [np.interp(t, times, v) for v in velocities.T]


Instead of applying the same method to find the position, I would like to utilize the velocity samples in my calculation.

Continue reading...