Measured moments of multidimensional angular distributions are useful as an intermediate step in partial-wave amplitude analysis (PWA) because they they have a well-known quadratic relation to the partial wave amplitudes on the one hand, and on the other hand they are simple model-independent representations of the experimental data, at least in the limit of full experimental acceptance. However, introducing a realistic model for the acceptance can break the simplicity of how the moments are extracted from the measured data. Standard practice is to use a joint multi-parameter fit to experimental data and simulated Monte Carlo events that generally involves a selection of the moments included in the fit to match those required for a favored model interpretation. This approach hampers the clean separation between analysis of experimental data and their interpretation in terms of amplitudes. A new approach to this problem is proposed for extraction of large basis sets of acceptance-corrected moments from experimental data using only linear algebra, enabling a clean separation between analysis and interpretation of experimental data without the use of fits. Extraction of trial-model PWA amplitudes from measured angular distributions is demonstrated using mock experimental data from a simulation of the GlueX experiment, without the use of multi-parameter fits at any stage.
