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.