  This paper unifies the theory of consistent-set maximization for robust
outlier detection in a simultaneous localization and mapping framework. We
first describe the notion of pairwise consistency before discussing how a
consistency graph can be formed by evaluating pairs of measurements for
consistency. Finding the largest set of consistent measurements is transformed
into an instance of the maximum clique problem and can be solved relatively
quickly using existing maximum-clique solvers. We then generalize our algorithm
to check consistency on a group-$k$ basis by using a generalized notion of
consistency and using generalized graphs. We also present modified maximum
clique algorithms that function on generalized graphs to find the set of
measurements that is internally group-$k$ consistent. We address the
exponential nature of group-$k$ consistency and present methods that can
substantially decrease the number of necessary checks performed when evaluating
consistency. We extend our prior work to multi-agent systems in both simulation
and hardware and provide a comparison with other state-of-the-art methods.
