A Graph-Theoretic Approach to Constrained Floor Plan Estimation From Radar Measurements

This paper proposes an approach to deducing the floor plan of a building using only a set of noisy room dimension measurements that have been obtained indirectly through radar probes. It is not assumed that the set of measurements is complete. The key feature of this approach is a method of relating, via a graph-theoretical construction, a given floor plan topology to a model that depends linearly on a minimal set of parameters. Given a list of floor-plan topologies and a system of realizability constraints, it is possible to formulate this problem as a constrained least-squares optimization problem. An algorithm for generating all floor plan topologies with a specified number of rooms is presented, as well as an algorithm for deciding if two floor plan representations are isomorphic. The techniques in this paper are intended to serve as an exploration into the theoretical performance bounds on the floor plan estimation problem.