A novel algorithm developed within muon radiography to localize objects or cavities hidden inside large material volumes was recently proposed by some of the authors (Bonechi et al. 2015 J. Instrum. 10 , P02003 ( doi:10.1088/1748-0221/10/02/P02003 )). The algorithm, based on muon back projection, helps to estimate the three-dimensional position and the transverse extension of detected objects without the need for measurements from different points of view, which would be required to make a triangulation. This algorithm can now be tested owing to the availability of real data collected both in laboratory tests and from real-world measurements. The methodology and some test results are presented in this paper. This article is part of the Theo Murphy meeting issue ‘Cosmic-ray muography’.