[en] A critical breakthrough in the understanding of Hall effect thrusters (HETs) has been the emergence of mapping techniques to fuse multiple time-varying plasma measurements from spatially distributed probes into a unified reconstruction describing the full spatiotemporal dynamics of the HET plasma. The most basic requirement for generating such a spatiotemporal reconstruction is a robust and accurate method to build a map between a single input and a single output signal. This work describes a new nonlinear phase space based mapping technique, the shadow manifold interpolation (SMI) technique, and assesses its performance versus traditional linear FFT-based mapping. Results demonstrate the superiority of the SMI reconstruction for short, noisy and aperiodic signals. Analysis in conjunction with the convergent cross mapping methodology (Sugihara et al 2012 Science 338 496–500) provides theoretical justification for the physical relevance of SMI application to a given signal reconstruction. (paper)