Many signal processing algorithms for distributed sensors are capable of improving their performance if the positions of sensors are known. In this paper, we focus on estimators for inferring the relative geometry of distributed arrays and sources, i.e. the setup geometry up to a scaling factor. Firstly, we present the Maximum Likelihood estimator derived under the assumption that the Direction of Arrival measurements follow the von Mises-Fisher distribution. Secondly, using unified notation, we show the relations between the cost functions of a number of state-of-the-art relative geometry estimators. Thirdly, we derive a novel estimator that exploits the concept of rays between the arrays and source event positions. Finally, we show the evaluation results for the presented estimators in various conditions, which indicate that major improvements in the probability of convergence to the optimum solution over the existing approaches can be achieved by using the proposed ray-based estimator.
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