Uncertainty Decrease with Varying Prior

The following images show the decrease in uncertainty, relative to our prior information, by integrating one pixel only. The brighter a pixel, the more information it provides on the state variables that are less known. The images below show the decrease in the trace of the state covariance matrix starting with different amounts of prior information, as characterized by P.

The example shows the information gain for a pan-tilt-roll movement of the camera. In the first image, the standard deviation on tilt is 1 degree, while pan and roll are known absolutely. In the second image, pan is the uncertain quantity, etc...

 

tilt unknown

 

pan unknown

 

roll unknown

 

pan, tilt and roll unknown

 

pan and tilt unknown

 

tilt and roll unknown

 

pan and roll unknown

 

Copyright 1999 Frank Dellaert and Bob Collins. All rights reserved.