Converting Match to Probability and Spatial Evidence

Define the constant       H*   =   Hi

The probability of M if the correct displacement D were k:
P( M | D=k )   =   Gk H* / Hk

Bayes' theorem and H* cancellations convert this to

P( D=k | M )     =

Gk / Hk P(D=k)   Gi / Hi P(D=i)

where P(D=i) is the prior probability that the correct D is i.

A given prior and noise assumption derives a probability curve, which is convolved with a stereoscopic range uncertainty model to make an evidence ray backbone, which is swept to make a 2D cross-section, itself swept again to add a 3D cone of evidence to a gid map:



  ->     ->     ->   3D Map