  Cooperative localization is a promising solution to improve the accuracy and
overcome the shortcomings of GNSS. Cooperation is often achieved by measuring
the distance between users. To optimally integrate a distance measurement
between two users into a navigation filter, the correlation between the errors
of their estimates must be known. Unfortunately, in large scale networks the
agents cannot compute these correlations and must use consistent filters. A
consistent filter provides an upper bound on the covariance of the error of the
estimator taking into account all the possible correlations. In this paper, a
consistent linear filter for integrating a distance measurement is derived
using Split Covariance Intersection. Its analysis shows that a distance
measurement between two agents can only benefit one of them, i.e., only one of
the two can use the distance measurement to improve its estimator. Furthermore,
in some cases, none can. A necessary condition for an agent to benefit from the
measurement is given for a general class of objective functions. When the
objective function is the trace or the determinant, necessary and sufficient
conditions are given.
