Accurate vehicle localization is considered to be a key element in future automated driving systems. A network of multiple sensors is employed to deliver information for this localization process. Loosely coupled integration of global navigation satellite systems (GNSS) and inertial navigation systems (INS) data is a common sensor-fusion method for such positioning. One of the problems of this approach, is that exact knowledge of the process- and measurement noise covariance matrices is often not available. The GNSS measurement noise uncertainties, in particular, are highly dynamic and, depending on the specific environment, might follow a non-Gaussian distribution. Since particle filter are known to be superior in non-Gaussian environments, a hybrid filtering variant is proposed: adaptive particle-aided cubature Kalman filtering. This algorithm compromises between a particle filter with kernel density estimation algorithm in periods of non-Gaussian GNSS noise, and a standard cubature Kalman filter in case of Gaussian GNSS noise. The results of GNSS/INS-based localization simulations indicate that the proposed adaptive particle-aided cubature Kalman filter outperforms traditional filtering methods in terms of minimal localization errors.