Speed estimation by finite differences (4): comparison to Kalman filter

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 18:34

*Enlace a Spanish version

Summary:

This video concludes the case study of videos [fdest1EN], [fdest2EN] and [fdest3EN], where we discussed ‘naive’ finite difference velocity estimation, and optimal minimum variance estimation with two position measurements.

With infinitely many past measurements to estimate velocity, the Kalman filter emerges as the optimal estimator (recurrent, infinite memory). Theory is not the focus here, we simply use the dlqe and kalman commands to calculate the variance of the prediction error and check that, as expected, it is way smaller than all the options discussed in previous videos.

The final part of the video discusses that the assumption of constant variance measurement noise as the sampling period decreases is no longer valid as the sampling period approaches the time constants of the probe filters and analog-to-digital conversion electronics, so although the graphs seem to indicate that as the sampling period is reduced the Kalman filter converges to an estimate with ‘zero variance’ error, this cannot be physically true. For brevity, no theoretical detail is given on all this, referring the reader to other (pending) materials.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.