Minimum volume ellipsoid scaled to contain a tangent sphere, with application to integrity monitoring

An ellipsoid bound is introduced and proven to be a tight and conservative approximation of a sphere to which it is tangent. The bounding ellipsoid is constructed with a fixed shape that can be scaled arbitrarily (so, for example, the ellipsoid shape matches the contours of a given probability density function). The ellipsoid bound is proven conservative in that the bound always contains the sphere to which it is tangent. The ellipsoid bound is proven tight in that its volume is the minimum guaranteeing conservative bounding. Applications for the ellipsoid bound include analysis of vector integrity monitors with nominally chi-square distributions.