On the resolvability of normally distributed vector parameter estimates

This paper presents a metric useful in analyzing the resolution of multidimensional (vector) parameter estimators that produce normal estimates. This metric is based on the distance between ellipsoidal confidence regions about each of the parameters. When the ellipsoids are disjoint the parameters are deemed resolvable. This paper presents a method for finding the noise level at which all of the ellipsoids are disjoint, but at least two are tangent. This is deemed the resolution threshold noise level. The underlying mathematical result treats the problem of finding a dilation (noise level) at which two coupled quadratic equations have a unique solution.