  Achieving resolution in the sub-Rayleigh regime (superresolution) is one of
the rapidly developing topics in quantum optics and metrology. Recently, it was
shown that perfect measurement based on spatial mode demultiplexing (SPADE) in
Hermite-Gauss modes allows one to reach the quantum limit of precision for
estimation of separation between two weak incoherent stationary sources. Since
then, different imperfections such as misalignment or crosstalk between modes
have been studied to check how this result translates into more realistic
experimental setups. In this paper, we consider another deviation from the
perfect setup by discarding the assumption about the stationarity of the
sources. This is relevant for example for astrophysical applications where
planets necessarily orbit around the star. We analyze two examples of dynamics:
rotations and oscillations, showing the robustness of the SPADE-based
measurement against them. The analysis is based on Fisher information, which
allows one to obtain the precision limit through Cram\'er-Rao bound.
Furthermore, we formulate a measurement algorithm that allows for the reduction
of one parameter for estimation (system orientation angle) in the stationary
sources scenario, maintaining the measurement precision despite the lack of
knowledge about this parameter.
