The weighted average position of a point cloud can sometimes be more useful than the ordinary average position, especially if there are outliers in the data. The maths behind it is relatively simple:

w ... weight
sum(d) ... sum of distances between the weighted point and all other points
p(w) ... weighted average position

w = 1 / sum(d)

p(w) = (p1*w1 + p2*w2 + ... + pn*wn) / (w1 + w2 + ... + wn)

You’ll only need a function that calculates all distances like in QGIS – fTools – Distance Matrix.

If you know any GIS implementing this function, please post them.