In Global Navigation Satellite Systems (GNSS), ionospheric scintillation is one of the more challenging propagation scenarios, particularly affecting high-precision receivers based on carrier phase measurements. In this contribution, we propose a new digital carrier synchronization state-space formulation for the mitigation of strong scintillation. It takes into account multi-frequency GNSS observations, allowing tracking of both line-of-sight phase variations and complex gain scintillation components, that is, scintillation amplitude and phase. The joint carrier tracking and scintillation mitigation problem is solved using a multi-frequency nonlinear Kalman filter-based solution. The performance improvement of the new approach is shown using realistic synthetic data, and compared to state-of-the-art PLL and KF-based architectures.