Speed estimation by finite differences (2): prediction error variance, statistical analysis

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 21:51

*Enlace a Spanish version

Summary:

This video continues the case study from the video [fdest1EN], going into technical detail on how to determine the prediction error and its variance when estimating velocity using the finite difference of two positions.

First, it calculates the covariance between states (position, velocity) at an instant $t=0$, say $x(0)$, and at the instant $t=T_s$, $x(T_s)$, where $T_s$ is the sampling period (the time separation between samples).

With this covariance matrix, a principal component analysis (covariance eigenvalues and eigenvectors) is performed and it is verified that, indeed, there is an ‘almost deterministic’ equation (very small variance) that relates velocities and position increments, specifically $(pos(T_s)-pos(0))∕T_s\approx (vel(0)+vel(T_s))∕2$.

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