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How is an acoustically diffuse field defined? To what extent are the equations of diffuse field theory valid? These are the questions addressed in this presentation. The answers are explained through more general theories, in turn explained with figures. The starting point is the idealization of diffuse sound field, from where the basic calculation tools used in architectural acoustics are derived. Then, we go through the physical-mathematical models of wave theory and ray theory assuming diffuse field simplifications and analyze the scope of diffuse field models. Wave models and ray models are presented in a simple format with visual support and reference to the underlying mathematical models. The criteria used to define a diffuse field in frequency domain as well as in temporal domain are analyzed. Finally, we present a review of several state of the art tools used to address the real cases when diffuse field cannot be assumed.

SUMMARY: This paper addresses the problem of a features selection criterion for a simultaneous localization and mapping (SLAM) algorithm implemented on a mobile robot. This SLAM algorithm is a sequential extended Kalman filter (EKF) implementation that extracts corners and lines from the environment. The selection procedure is made according to the convergence theorem of the EKF-based SLAM. Thus, only those features that contribute the most to the decreasing of the uncertainty ellipsoid volume of the SLAM system state will be chosen for the correction stage of the algorithm. The proposed features selection procedure restricts the number of features to be updated during the SLAM process, thus allowing real time implementations with non-reactive mobile robot navigation controllers. In addition, a Monte Carlo experiment is carried out in order to show the map reconstruction precision according to the Kullback–Leibler divergence curves. Consistency analysis of the proposed SLAM algorithm and experimental results in real environments are also shown in this work.