Carrier synchronization in standard, mass-market GNSS receivers typically utilizes well understood locked-loop architectures. The performance obtained with such architectures is sufficient for benign propagation scenarios, but typically deliver poor performance under harsh propagation conditions. Code and carrier tracking, as well as joint code/carrier synchronization, can be formulated as an estimation problem which can be solved using Bayesian filtering methods. It has been shown in the GNSS literature that KF-based synchronization solutions can be used to overcome the performance limitations of standard approaches, offering implicitly adaptive filter bandwidth, and opening up the possibility of using nonlinear models to avoid certain limitations associated with the use of code, phase or frequency discriminators. In this contribution, we will leverage powerful nonlinear tracking algorithms, including cubature, unscented, and sigma point Kalman filters in order to produce realizations of carrier and joint code-carrier tracking blocks which promise to be more effective and adaptable in challenging GNSS environments when compared to traditional architectures.