Robust Inference of Room Geometry from Acoustic Measurements Using the Hough Transform

The problem of localizing reflective boundaries in an acoustic environment from acoustic measurements is considered. Specifically, localization of multiple two-dimensional (2-D) line reflectors is achieved by estimation of the time of arrival (TOA) of reflected signals by analysis of acoustic impulse responses (AIRs). The estimated TOAs are used in conjunction with the source and receiver locations to find the loci of solutions whose common tangents correspond to the location of a reflector. The solution to the common tangent estimation is a nonlinear and non-convex problem that can yield local sub-optimal solutions using existing approaches. We therefore propose an analytic method, based on a closed-form estimator, that is guaranteed to converge to the global minimum in an error-free scenario. We further improve the robustness of the approach when errors are introduced in the estimated TOAs by using the Hough transform to find the optimal solution. The proposed approach is evaluated through Monte Carlo runs, using simulated rooms, that demonstrate the feasibility of the proposed approach.