Stability and generalized scattering models

Develop stability estimates for the moving point-scatterer inverse problem with respect to measurement errors and extend the time-domain point-interaction framework to multiple point scatterers or extended obstacles.

Background

The paper establishes well-posedness of the forward problem and unique trajectory recovery for a single moving point-like scatterer using four non-coplanar moving receivers. However, the theoretical treatment does not quantify how measurement errors affect the reconstructed trajectory, despite the numerical experiments examining noise sensitivity. The authors also restrict the model to one point-like scatterer and identify extensions to multiple point scatterers and extended obstacles as unresolved directions for future research.