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I have a set of data for a car position, velocity and acceleration.

% my data

time
car_x
car_velocity
car_acc

The problem is that these arrays have error and I need to fix the error of them. The requirements is that

  • There are unreasonable error bumps on my car position according to the photo. These bumps cause unnecessary jags on acceleration. An idea is to use a low-pass filter on car position however, low-pass filter deforms my signal when a real sudden change happens.

  • At the same time, when we calculate the double derivation of the position it should not be very far from the original car_acc signal.

How to implement such filtering?

Note:

  • currently due to errors, the double integral of acceleration diverges from the position in an unstable way (two times integration of a small error diverges over time).

  • I tried many corrections on car position and made it nice. However the double derivation of it had very high frequency oscillation with high amplitude.

Signal correction

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  • $\begingroup$ Are the same errors in all three measurements? Or were they taken independently of one another as compared to estimating the velocity and acceleration from the measured position? $\endgroup$ – AnonSubmitter85 Jun 3 '15 at 19:54
  • $\begingroup$ @AnonSubmitter85 There are independent errors on each measurements $\endgroup$ – Nofoos Jun 4 '15 at 0:48
  • $\begingroup$ Have you tried splines? What about Kalman filtering? $\endgroup$ – AnonSubmitter85 Jun 4 '15 at 17:27

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