Magnetic particle imaging (MPI) is a tracer-based medical imaging modality that enables quantification and spatial mapping of magnetic nanoparticle (MNP) distribution. The magnetization response of MNPs depends on experimental conditions such as drive field (DF) settings and medium viscosity, as well as on magnetic parameters of MNPs such as magnetic core diameter, hydrodynamic diameter, and magnetic anisotropy constant. A comprehensive understanding of the magnetization response of MNPs can facilitate the optimization of DF and MNP type for a given MPI application, without the need for extensive experimentation. In this work, we propose a calibration-free iterative algorithm using model-based dictionaries for MNP signal prediction at untested settings. Dictionaries were constructed with the MNP signals simulated using the coupled Brown-Néel rotation model. Based on the available measurements, the proposed algorithm jointly estimates the dictionary weights and the transfer functions due to non-model-based dynamics. These dynamics include the system response of the measurement setup as well as magnetization dynamics not accounted for by the employed coupled Brown-Néel rotation model. The algorithm was first validated on synthetic signals at SNR levels of 1 and 10, and then tested on an in-house MPS setup across six viscosity levels (0.89-15.33 mPa.s) and DF frequencies of 0.25-2 kHz using two commercial MNPs. Validation on synthetic signals showed accurate weight and transfer function estimation even at SNR 1. MPS experiments demonstrated successful prediction of MNP signals at untested viscosities, with NRMSE below 1.51% and 3.5% for the two tested MNPs across all DF settings. Predicted signals captured viscosity dependent trends, and NWD values remained low (<0.10 and <0.07 for the two tested MNPs), confirming robust weight estimation.