I’m trying to get a displacement from a velocity.
For a constant velocity, the formula is:

x_h = x_c + V*t

Where x_c is an initial value, V is the velocity magnitude and t a time vector.

I now have a velocity u that is as below. Theta is an azimuthal position, it is essentially related to time.

It starts from an undisturbed value (equal to V) then drops and recovers twice and at the end of the period (theta = 360 deg) it goes back to the undisturbed value.

To compute the displacement, I do:

x_h = x_c + cumtrapz(u,t)

Below the displacements for constant velocity (formula with no integration) and non-constant velocity are plotted:

The issue is that, as you can see, cumtrapz drifts more and more away from the undisturbed value as time goes by.
Consider that there’s also another period preceding theta = 0 deg, so x_h is not starting at the undisturbed value at theta=0 deg, although it should. This would only happen if there was no drift introduced by cumtrapz.

If I try to do:

x_h(t) = x_h(t-1) + u(t-1) dt(t-1)

I get basically the same.
I checked that x_h(t) - x_h(t-1) behaves as the above-plotted u, which is the case, so both the integration formulas are correct.

However, I get the above-mentioned drift issue.

Please note: u velocity is supposed to behave like that, its trend is not due to some sort of bias or noise in the data.

How can I fix this, preferably keeping x_h(t) - x_h(t-1) behaving as the u velocity?
Thanks for your help.