Methods for filtering position signal

Question

I'm working on a location detection algorithm. This is my outcome - postion:

Here's first derivative after time - velocity:

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My goal is to apply some filtration to the signal for smoothing the waveforms. I'm searching for a method of filtration that can work in real-time applications.

I need to smooth the waveforms because of the next step which is synthesis of the PID algorithm. These "peaks" in velocity are too big. I tried simple Kalman Filter but it doesn't give the expected results.

First trajectories x(t) will be linear, next I would like to study some non-linear trajectories of x(t). Algorithm for filtration should work for both cases.

I am looking for ideas, what filtering algorithms can I apply? I heard about EKF, and average based methods (moving average etc.).

Thank You all in advance for Your help. I'm new here :)