Measurement, optimal filtering (2/3): discrete-time vs continuous-time Kalman filters, example (Matlab)

Antonio Sala, UPV

Difficulty: ***** ,       Relevance: ,      Duration: 23:16

Summary:

This video is a continuation of the [medex1EN] case study on the measurement and digital conversion process + discrete filtering whose ideas in abstract were discussed in the video [medabsEN].

After summarizing the previous video, here a discrete-time Kalman filter is calculated with the Matlab command kalman and the variance of the position and velocity estimates obtained is compared with that of the continuous-time Kalman filter. For low sampling periods, the discrete and continuous time results are identical, which was the main goal of the case study.

The final part of the video discusses the accuracy of the ‘simplest’ use of the measurement which would be to plainly ‘believe’ that the average over $T_s$ time units is the measured signal. If the sampling period is small, it is very sensitive to measurement noise, if the sampling period is large then it is sensitive to changes in position and velocity during the averaging interval (‘blurred’ photo if the photographed subject moves). Therefore, there is an optimal averaging (acquisition) time in this case; this is not the case for discrete Kalman filters: the smaller the sampling period, the closer one is to the continuous-time result.

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