GDOP is sometimes taken to mean the largest eigenvalue or trace of the covariance matrix. It's a metric for the badness of the estimate.

Often, GDOP is broken into components HDOP, VDOP, etc for the values corresponding to some earth-fixed coordinate frame. That starts to look more like statistics about the covariance matrix.

Here's a derivation: https://en.wikipedia.org/wiki/Dilution_of_precision_(navigat...

Here, it ends up being (usually) the sqrt(trace(covariance))