Speed estimation by finite differences (1): motivation and problem statement (stochastic processes)

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 19:55

*Enlace a Spanish version

Summary:

This video addresses the problem of estimating the velocity (i.e., the derivative) of a signal from position measurements separated by a known time interval.

It is actually the first of a 4-video case study. In this first video, we will simply address the problem, stating it, discussing the concepts of process noise (random acceleration), measurement noise, the discretization of said process noise, and the simulation to generate the signal that we will then derive approximately with ‘finite differences’ in forthcoming videos.

The concrete example process will be $1∕{(s+0.25)}^2$ subject to input white noise with unit power spectral density. The problem will be addressed in the ‘stochastic differential equation’ representation $\frac{dx}{dt}=Ax+Gw$, or formally $dx=Axdt+GdB$.

The technical detail of the speed estimation and its accuracy (or lack thereof) formally studied in statistical terms will be addressed in the video [fdest2EN], following this case study.

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