[seanhunter]

BTW the author mentions Mahalanobis distance[1]. This is a good one to know about but it isn't useful in this application. As I understand it (having used it a bit and even implemented the algorithm a couple of times) Mahalanobis distance multiplies by the inverse of the covariance matrix. What that does is essentially undo covariance if the dimensions of your space are not equivalent. So if moving in one dimension is highly correlated with moving in another dimension, Mahalanobis distance corrects for that effect.

[1] https://en.wikipedia.org/wiki/Mahalanobis_distance

[setopt]

Another formulation of this which I like is that the Mahalanoubis distance measures “how many standard deviations apart” two state vectors are.

Note that since the covariance matrix has variance on the diagonal, it corrects not only for correlations but also normalizes each dimension using their standard deviation.