Magnetic particle imaging (MPI) is a rapidly developing medical imaging modality that exploits the non-linear response of magnetic nanoparticles (MNPs). Color MPI widens the functionality of MPI, empowering it with the capability to distinguish different MNPs and/or MNP environments. The system function approach for color MPI relies on extensive calibrations that capture the differences in the harmonic responses of the MNPs. An alternative calibration-free x-space-based method called TAURUS estimates a map of the relaxation time constant, τ , by recovering the underlying mirror symmetry in the MPI signal. However, TAURUS requires a back and forth scanning of a given region, restricting its usage to slow trajectories with constant or piecewise constant focus fields (FFs). In this work, we propose a novel technique to increase the performance of TAURUS and enable τ map estimation for rapid and multi-dimensional trajectories. The proposed technique is based on correcting the distortions on mirror symmetry induced by time-varying FFs. We demonstrate via simulations and experiments in our in-house MPI scanner that the proposed method successfully estimates high-fidelity τ maps for rapid trajectories that provide orders of magnitude reduction in scanning time (over 300 fold for simulations and over 8 fold for experiments) while preserving the calibration-free property of TAURUS.